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The Columbia University Libraries reserve the right to refuse to accept a copying order if, in its judgement, fulfillment of the order would involve violation of the copyright law. Author: Wellington, Arthur Mellen Title: The economic theory of the location of railways Place: New York Date: 1888 Q}LniZ6-5 COLUMBIA UNIVERSITY LIBRARIES PRESERVATION DIVISION BIBLIOGRAPHIC MICROFORM TARGET MASTER NEGATIVE * ORIGINAL MATERIAL AS FILMED - EXISTING BIBLIOGRAPHIC RECORD BUSINESS 530 .65 W461 Wellington, Arthur Mellen, 1847-1895. The economic theory of the location of railways; an analysis of the conditions controlling the laying out of railways to effect the most judicious expenditure of capital, by Arthur Mellen Wellington ..3i Rev. and enl. ed. New York, J. Wilev & sons: ,otc., etc.,^fW.1888* XX, 980 p. Incl. lllus., tables, fold. maps, diagrs. (part fold.) 21i« 1. Railroads— Location. 2. Ilallroads— Economics of construction. Library of Congress Copy 2. Copyright 1887: 11001 TF190.W4ri7 3—19320 i40hl, -625.11 RESTRICTIONS ON USE: TECHNICAL MICROFORM DATA FILM SIZE: 35rn m REDUCTION RATIO: \V\ IMAGE PLACEMENT: lA (n^ IB IIB DATE FILMED: C"H'^^ INITIALS: 1Cjl& TRACKING # : M5f40i:ifiA FILMED BY PRESERVATION RESOURCES. BETHLEHEM. PA. BIBLIOGRAPHIC IRREGULARITIES MAIN ENTRY: Wellington. Arthur Meilen The economic theory of the location of. ■ ■ Bibliographic Irregularities in the Original Document: List all volumes and pages affected; include name of institution if filming borrowed text. ,Page(s) missing/not available: Volume(s) missing/not available:. X ^Illegible and/or damaged page(s) : ^water damage Page(s) or volume(s) misnumbered:. Bound out of sequence: Page(s) or volume(s) filmed from copy borrowed from:. Other: TRACKINGS: MSH01 388 3 3 O >> fiD CD ?3.o 3 I T3 ^ 1° ^c en ox ^-< o 3 3 > o m (DO OQ 0J_, ^ o o X < N M ^; > ^3W > ^-> ^x^^ ^^^y^ .^? > o 3 3 o o 3 3 N3 r^^i^EPisuisi? nw bo a- s g cn 1.0 mm 1.5 mm 2.0 mm ABCDEFGHtJKLMNOPQRSTUVWXYZ abcdefghiiklmnopqrjtuvwiyz 1234567890 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyzl234567890 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 ABCDEFGHIJKLMNOPQRSTUVWXYZ ^ ^ abcdefghijklmnopqrstuvwxyz 2.5 mm 1234567890 r.<^ ^ V ^ #p V wo ^ k^ ^O fp ¥cr -?•, ■/!•. 4^^''^^. /^..*5^. ♦J V V ><<^ ^,^>. ^ tcr iP^ r^ fcP ?CP ¥^ ^Sr m H o Tj m "D X TJ ^ m o m A» ^-'^^. '/^^^^. li IS Si §1 is fo ^P H-* r>o cn o E 3 CT O :^ M (/) OOM O ^. D530.G5 W44I THE LIBRARIES School of Business THE Economic Theory OK THE Location of Railways. IN PREPARATION By thb Samb Author la one thio rolumc of ordinary pocket-book form and size THE FIELD WORK OF RAILWAY LOCATION AND Laying Out of Works ACCORDING TO THB MOST RECENT AND APPROVED PRACTICE ON AMERICAN RAILWAYS. In this volume will be included various formula and methods never heretofore published for the expeditious and correct con- duct of the mechanical work of location. It is hoped to give everything which is essential and noihinfr which is unessential to a thorough understanding of the principles and methods of instrumental field-work, when conducted to insure final excel- lence in the simplest way and with due subordination to eco- nomic considerations. The tables, while strictly limited to the requirements of good practice, will be an especial feature, modelled typographically on the best German models. THE ECONOMIC THEORY OF THE Location of Railways AN ANALYSIS OF THE CONDITIONS CONTROLLING THE LAYING OUT OF RAILWAYS TO EFFECT THE MOST JUDICIOUS EXPENDI- TURE OF CAPITAL BY ARTHUR MELLEN WELLINGTON M. Am. Soc. C.E. I^TE PRINCIPAL ASSISTANT ENGINEER FOR LOCATION AND SURVEVS MEXICAN NATIONAL RAIL- WAV, ASSISTANT GENERAL MANAGER IN CHARGE OF LOCATION MEXICAN CEN- TRAL RAILWAY AND CHIEF ENGINEER OF THE AMERICAN LINE FROM VERA CRUZ TO THB CITY OF MEXICO •For K i. clear that in whatever it is our duty to act. those matters also it is our duty to study." •*•'*• I \ \ ••/* '*S • -*^R- Thomas Arnoli> • * •• , «•,♦•••••' • .• •• , ,*•♦• •••«« • »• ••• ••••• • •••••• » • • :••:•••*'.:•:••.• THIRD revised; ^'pipiEjiltA^Gfij^ ClilTION ''* • • t • , • • •• * • * • « •• • • NEW YORK / 'ii John Wiley & Sons 15 AsTOR Place London Engineering News Tribune Building )N WAL (fsL^A.Q^*^.^^''*-*^ J)5'30,66 y Ti '\\ Copyright, 1887, 0v A. M. WELLINGTON. • • • . • « • ' • « « • * ! • » • i « . • • ( * « t « « • Electrotypera, New York. r* Ci TO THE GREAT MEN OF A FORMER GENERATION, WHO ORIGINATED THE AMERICAN RAILWAY SYSTEM, THIS ATTEMPT TO IM- PROVE UPON THEIR PRACTICE IS ADMIRINGLY INSCRIBED, IN TOKEN OF RESPECT FOR THEIR FAR-SIGHTED SAGACITY AND STILL UNEQUALLED SKILL. PREFACE. Only in a very figurative sense can this book be said to be a " revised edition" of the little volume under the same title which the writer pub- lished ten years ago. The substance of the old book remains unchanged, so far as it went, but every page and sentence has been rewritten, except the dedication. The most important change in the nature of an addition is the much greater attention given to traffic and revenue questions, which are particularly likely to be underrated or forgotten. The mechan- ics of curve resistance have been discussed, it is hoped, more adequately than heretofore, and on a more solid basis of experimental fact, with some important practical questions which depend thereon. The theory of the -effect of variations in velocity on the motion of trains is an entirely new addition, supplying one of the most important omissions of the former ■edition and of other engineering text-books. The theory of various de- tails of the locomotive, which did not seem to have been elsewhere ade- •quately discussed for the purposes of this volume, has been given, it is hoped, more fully and correctly than heretofore. Parts IV. and V. are entirely new. On the other hand, the new edition has been abbreviated by omitting the discussions, some thirty in all, where reasons why the writer felt com- pelled to differ from some previously published conclusions or estimates were given in deta.:!. This seemed necessary ten years ago, but at present it appeared as if the space might be better used. The number of engravings has been increased from half a dozen to 313, the number of pages from 216 to 950, and the number of tables from 44 to 204. All of the tables, with a few exceptions noted in connection with each, are original computations of the writer or compilations from original sources of information. As practically all the work of prepar- ing them, and of rewriting the text, has been done outside of those hours which are ordinarily and more rationally regarded as working hours, a long delay in republication has been unavoidable ; but if there be truth Vlll PREFACE, enough in the old antithesis of "easy writing" and "curst hard reading to hold good when twisted wrong end to. there should be some com- pensation in store for any reader who may have chanced to be annoyed ^^ In^rdeTto adapt the volume to the more convenient use of all classes of readers, three sizes of type have been used : Long Primer type is used for those parts of the volume which were deemed most likely to be such as every interested reader would wish to read, including those who desire only to ascertain the more important conclusions, free from technicali> ties. Bourgeois type is used for discussions which relate more to the details of the subject than to principles, and hence may be passed over by those who are not engineers, or who are ready to take the reasons for what ,s Printed in larger type for granted. Nevertheless, much of the matter E is printfd in' his smaller type, as for instance the long chapter on- The locomotive engine and the whole of Part V.. is among the most im- portant in the book for the professional engmeer. BREV1E1 type is used for minor notes and comments which it seemed essen- dal or dcsimbk to give, as of much possible importance to those w.shmg to look t:i^:::Z^orso;.. ,.n^cu^.r branch thereof, with still greater care, but which might otherwise be passed over. The mathematical form of discussion has been intentionally avoided first because the boolc has been written for practical men as well as for rre«r.c^^^^^^^^^^^^ ^rta^fixtd premises, mathematical methods furnish i-aluable w.ng* for flyingover tntermediate obstructions ; but whenever the ch.ef d,ffi- lu ty o" a problem lies in the multiplicity and ^f -»"^; "'/"^ P^^™; cuiLy v^i F r#»rnncilinff them with each other, there is the writer will not attempt. ,.orr^rt To fullv set forth in any one volume these premises for the correct Uyilg ou"^f railways, which'' ^'^^^^^^^^Z:^'^:^ their construction, operation, and finances, ana vary m cac PREFACE. IX l>e impossible. The purpose in view has been merely to give between the covers of one book whatever was necessary for some approach to a correct solution of every probable problem, which could not be found in other publications. This necessarily led to a large book, since this work still remains the only one on its subject in the language. Sev- eral of a somewhat similar nature have appeared in French and German since the first edition of this work was published, but from difference of •operating conditions, and their profuse use of mathematics, the resem- blance is not close. The word "ton" in this volume means 2000 lbs., unless otherwise ex- plicitly stated. . The term " velocity-head " has been borrowed from hydraulics to •designate a somewhat different thing, which heretofore has had no name at all. The " velocity- head " of hydraulics and of this volume are closely related but not identical, and should not be confused. Grades have been designated for the most part by their rate per cent and not by their rate per mile, in accordance with an increasing custom which may well become universal, as the more rational. The approxi- mate rate per* mile is given at once by multiplying the per cent by 50 (52.8). Owing to the great number of tables, and the probability that others might be added in future editions, it was impossible to even attempt to refer in the text to all those which contained a given class of information. To insure doing this reference must be had to the Index, which it has been endeavored to make very complete. Most of the computations of percentages, costs per mile, and the like. in this volume, were made with a slide-rule— an instrument too little known and used by engineers. Hence many errors of i or 2 in the third digit, or of one or two tenths of one per cent, probably exist, but. it is hoped, few of a more serious nature. The admirable computing instrument of Mr. Edwin Thacher. which would have insured greater accuracy with but little more trouble, was secured by the writer too late to be of much service. The author will be at all times pleased to receive corrections of typo-* graphical or other errors, or supposed errors, extensions of any of the tables, or other similar matter. A.M. W. Tribune Building, New York. May, 1887. mmm M-^-tpr- PREFACE TO THE FIRST EDITION. The investigation of which this volume is the fruit had its origin in the preparation of a few notes for an anticipated location, and has since gradually expanded into a single magazine article, a short series of papers, and at last into a volume. Even the latter has been expanded far beyond the writer's original intention by the close and, it is to be feared, tedious attention to detail which he found continually more needful ; and it is kept within its present dimensions only by excluding considerable matter and superficially considering or neglecting altogether a number of subjects which the writer deems of real importance for the correct conduct of location. In the improbable event that the sale of this volume should justify a thorough revision at some future day, he hopes to produce one more in keeping with the professional interest and importance of the subject, by rectifying the faults of omission and com- mission which he clearly perceives. The writer does not intend to imply, however, that he has fallen into unacknowledged errors of fact or theory. All known errors have been frankly corrected as soon as discovered. For such others as may prob- ably exist the writer can only hope that they will be regarded with that leniency which an exploration of a neglected field of labor may fairly ask. For such the present volume is, with all its imperfections. A recognition of the value of previous discussions of the same subjects would be a more welcome duty; but the writer deems it but simple justice to himself and his readers to declare frankly that, so far as his knowledge extends and he is competent to judge, all of the few existing discussions of the various leading topics of this volume are so superficial or so imperfect in method as to have little or no value as a guide for location. Some of them express correct views, and some of them will sometimes give correct results ; but none of them are trustworthy, and several of those which are given under distinguished names are incredi- bly defective. The various problems of location, in fact, have been dis- ill .'^V\ I XII PREFACE TO THE FIRST EDITION. cussed or neglected by technical writers with an airy lightness wh.ch would convince a,, unskilful reader that they were either too simple or too unimportant, or too well understood, for any careful analysis. And vet there is no field of professional labor in which a limited amount of modest incompetency, at $150 per month, can set so many picks and shovels and locomotives at work to no purpose whatever. As a natural consequence of this general negligence, all our railways are uneconomically located, most of them in respect to their genera! route and system of gradients, and all of them in respect to the minor details of alignment, and in many cases these errors are shockingly evident ... In the care taken in this respect we are not advancing beyond, but rather falling below, the standard set up forty years ago when the art of designing railways started out in this ^°""i;;y «'''> ="^^ brilliant promise. The works of Latrobe and Jervis and Thomson and Whistler show a truly remarkable ability, considering their early day. and bear the clearest marks of original and self-reliant thought : but the ereat men of that earlier day have no successors; for we have done nothing but copy them ill ever since, and a copyist is not a successor. We copy their errors, but we do not copy that admirable habit of per- sonal investigation and far-sighted intellectual courage which created precedents, and has made the work of their hands-in despite of many faults— the high-water mark of American locating skill. / .4- ^onalS^ CONTENTS. Introduction, PAGE I PART I. ECONOMIC PREMISES. ^^'1. The Inception of Railway Projects and Conditions governing it '^ II. The Modern Railway Corporation 28 III The Nature and Causes connected with Location which modify the Volume of Railway Revenue, . 48 IV. The Probable Volume of Traffic and Law of Growth therein '^ V. Operating Expenses ^^ [Maintenance of Way. 118; Fuel, 132; Repairs of Engines, 139; Repairs of Cars, 160; Train-wages, etc., 168; Summary, 180] PART II. THE MINOR. DETAILS OF ALIGNMENT VI. The Nature and Relative Importance of the Minor Details of Alignment '^5 VII. Distance • • • ^95 [Effect on Operating Expenses, 198; Effect on Receipts, 211; Law as to Connections, 219; Moral Effect of Short Line, 239.] VIII. Curvature ; * '^^'^ [Danger of Accident. 245: Statistics of Curvature, 259; Diffi- culty in Making Time, 26S; Effect on Smooth Riding of Cars, 275 ; fr,:nT-r--'mt m m xiv CONTENTS. PAG* CHAP. Moral Effect to deter Travel, 276; Effect to obstruct the use of Heavy Engines, 278; Mechanics of Curve Resistance, 281; Rail-sections, 307; Effect on Operating Expenses, 313; Long Tangents, 324.] IX. Rise and Fall 327 [Classes of. 330; Laws of Accelerated and Retarded Motion, 331; Virtual Profiles, 346; Safe Limits of Undulations of Grades, 356; Limits of Classes. 366; Effect on Operating Expenses, 375; Estimating Amount of, 384; Vertical Curves, 385.] PART III. LIMITING GRADIENTS AND CURVATURE. X. The Relative Importance of Gradients 39? XL The Locomotive Engine 399" [Tables of Standard Dimensions, 407; Running-Gear, 421; Tractive Power, 434; The Locomotive Boiler, 449; The Cylin- der Power, 457; Theoretical Gain by Expansion, 467; Causes of Loss of Efficiency, 470.J XII. Rolling-Stock 485 XIII. Train Resistance 49^ [Freight-Train Resistance, 496; Starting Resistances, 511; Effect of Size of Wheel and Axle, 513; Velocity Resistances, 517; Train Resistance Table, 524; Engine Friction, 530.] XIV. The Effect of Grades on Train-Load 53^ [Table of Capacity of all Engines on all Grades, 544; Percent- age of Change in Net Load from a Change in any Grade, 554 ] XV. The Effect of Train-Load on Operating Expenses, 560 [Cost of Increasing Weight of Engines, 560; Cost of Increas- ing Number of Engines, 568; Proportion of Traffic affected by Rate of Ruling Grade. 576; Effect of a Difference in Ruling Grade, on the Cost of Distance, Curvature, and Rise and Fall, 581.] ' XVI. Assistant Engines, • • 5^5 [Power of Assistant Engines, 591; Duty of Assistant Engines, 598; Cost of Assistant Engines, 601; Comparison of Pusher Grades with Uniform Gradients, 604.] XVII. The Balance of Grades for Unequal Traffic, . . 608: XVIII. Limiting Curvature and Compensation therefor, . 620 CONTENTS. XV PAGE CHAP. r XIX. The Limit of Maximum Curvature, o35 [The Inherent Costliness of Sharp Curvature, 638; The Limiting Effect of Curvature, 645.] XX. The Choice of Gradients, and Devices for Re- ducing Them, "59 [How to Project Low Grades. 660; How to Project Pusher Grades;— Easy Gradients, 666; Heavy Gradients, 669; Expe- dients for reducing the Rate and Cost of High Grades, 675; Great Inclines of the World, 699.] PART IV. LARGER ECONOMIC PROBLEMS. XXI. Trunk Lines and Branch Lines, ^ - 707 [Law of Geometric Increment of Traffic, 708; Trunk Lines, Non-Competitive, 718; Competitive Trunk Lines, 723; Branch Lines, 73I-] XXII. Light Rails and Light Railways, 737 [Rails, 737; Expedient Economies, 748; Rails and Track Labor, 758.] XXIII. The Economy of Construction 762 [Least harmful Economies, 764; Most harmful Economies, 768; Cross-ties, 775; Storms and Structures, 781.] XXIV. The Improvement of Old Lines, 78s [Usual Defects, 787; Constructing Virtual Profile, 798; Remedying Defects, 799.] XXV. Grade Crossings and Interlocking 809 • XXVI. Terminals, ^^^ PART V. THE CONDUCT OF LOCATION, XXVII. The Art of Reconnaissance 831 XXVIII. Ocular Illusions 843 XXIX. When to make Surveys 856 XXX. The Field-work of Surveys 860 XXXI. Topography: its Uses and Abuse, 874 ' XXXII. Mapping and Projecting Location 886 XXXIII. The Estimation of Quantities, 895 iliii XVI CONTENTS. -CHAP. APPENDICES. PAGB A. Experiments on the Resistances of Rolling-Stock, . . 909 B. Experiments with New Apparatus on Journal Friction AT Low Velocities, 9»3 C. The American Line from Vera Cruz to the City of Mexico via Jalapa. with Notes on the Best Methods OF surmounting High Elevations by Rail 925 [The usual List of Tables is omitted, as too voluminous. The tables and engravings are separately indexed at the back of the book.] 9! INDEX TO THE MORE IMPORTANT RULES, TABLES, FORMULA, AND FINAL CONCLUSIONS. WHICH MAY BE NEEDED FOR IMMEDIATE APPLICATION. <• It may be ^marked that it was no part of the purpose of thisvolume to fumi h a collection of mere rules, professing to require only an ab.Uty to rd tor their successful application. Rules can seldom be sa^eyappUed wTthou. a clear understanding of the principles on wh.ch ^ey rest_ _J. B. Henck, Preface to Field-Book. r This MX has purposely b»n ,nade and kept as brief as possible It HAS no CROsfREFERENCES NOR DOO«LE REFERENCES. For anything not found, see Gen- Z^nZuZ the subjoined references are repeated, and for the n,ost part .n SMALL capitals.] Assistant Engines- Advantages Balance of grades for Cost of service vs. Uniform grades Projecting . • Branch Lines- Rules for laying out Cable Railways Choice between close lines Construction- Order of expedient economies Worst errors in Curvature- Compensation for PAGE 593 602- 604 , 666 733-6 . 686 . 583 . 764 . 76S . 632 xviu INDEX TO CONCLUSIONS FOR IMMEDIATE APPLICATION XIX % i: ii if Curvature- Effect on accidents " expenses " use of heavy engines " making time " smooth riding of cars Maximum limit of Moral effect of Curve Resistance- Conclusions as to * • Dead Weight- Passenger, why tends to increase Distance— Effect on competitive receipts •• non-competitive receipts •• expenses Increasing, to secure more traflBc Law as to connections . • Moral effect of short line Freight-Train Speed . Grade-Crossings- And interlocking . . • Crades- ^ ,, Balance of, for unequal traffic, table Effect on passenger traffic '* train-load, law as to General law for choosing How to reduce in easy country Pusher grades, pros and cons Relative importance of gradients Train-load on all grades, table Trains affected by grades Value of reducing grades Crowth of Traffic- Geometric law as to Proper allowance for Inclined Planes Light Railways- Proper direction for economy Location— A priori basis for General law for good for example PACK . 258 . 321 . 281 . 274 . 275 . 653 . 277 . 304 . 567 . 228 234-6 . 209 . 238 . 219 . 240 . 371 . 811 . 185 . 580 554-6 , 660 . 665 . 669 . 396 . 546 . 576 . 572 . 715 80-86 . 686 . 761 . 18 . 660 and Rise and Locomotives- Adhesive traction limits . Dimensions, etc. . Train-load on all grades . Long Tangents- Value of . . • Mapping Surveys Minor Details-(Distance, Curvature Comparative importance Narrow Gauge Old Lines- Best manner of improving Usual defects to be corrected Operating Expenses- Percentages . . Rails- Proper form of . • ** weight of • Reconnaissance- Choice of lines to survey Fundamental rule for Revenue— Per head of population . Rise and Fall- Effect on operating expenses Estimating amount of Limits of classes . Safe limits for In grade-lines, to what extent admissible Superelevation- Proper rule for . • • • Surveys- Choice of lines to run . • • Switchbacks— For thin traffic and great inclines Termini- Location of . • • • Topography- . , (Physical geography). Harmonizing Ime wiin (Mapping), Its uses and abuse . Towns- Loss from not going to . Fall.) PAGE • 437 407-10 . 544 . 324 . 888 . 186 . 751 . 808 . 788 . 179 . 308 747. 761 . 857 . 835 . 104 . 381 . 384 . 374 363-8 . 368 . 301 . 860 . 950 . 67 . 655 . 880 . 63-4 XX INDEX TO CONCLUSIONS. Traffic- How to estimate the probable volume o Train-mile— Cost by items . , , Train Resistance- Freight, amount . Passenger, amount Trunk Lines- Competitive, conditions of success Non-competitive, rule for laying out Valley Lines— And inundations . . , Merits of, for railway lines Valleys- Descending into . • • Vertical Curves- Laying out . • • Length of . . • , Virtual Profile- Nature and use of . • PACE 86, 95-102 . 179 . 502 . 518 . 731 . 720 . 783 . 850- . 682 . 387 . 36s 346, 351. 354 { \ f i /i' -S' llOWh^^ ^^^ THE ECONOMIC THEORY OF THE LOCATION OF RAILWAYS. INTRODUCTION. As the correct solution of any problem depends primarily on a true understanding of what the problem really is, and wherein lies its difficulty, we may profitably pause upon the threshold of our subject to consider first, in a more general way its real nature; the causes which impede sound practice ; the condi- tions on which success or failure depends ; the directions in which error is most to be feared. Thus we shall more fully at- tain that great prerequisite for success in any work-a clear mental perspective, saving us from confusing the obvious with the important, and the obscure and remote with the un.m- portant. It would be well if engineering were less generally thought of, and even defined, as the art of constructing. In a certain im- portant sense it is rather the art of not constructing ; or, to de- fine it rudelv but not'inaptly, it is the art of doing that well with one dollar, which any bungler can do with two after a fashion. , ^ • • There are, indeed, certain great triumphs of engineering genius-the locomotive, the truss bridge, the steel rail-which so rude a definition does not cover, for the bungler cannot attempt them at all ; but such are rather invention than engineering proper. There is also in some branches of engineering, as w mrRODUCTION. INTRODUCTION, bridge-building, a certain other sic^e to 'it, not covered by such a definition, which consists in doing that safely, at some cost or other, which the bungler is likely to try to do and fail. He therefore, in such branches, who is simply able to design a struc- ture which will not fall down, may doubtless in some measure be called an engineer, although certainly not one of a very high tvpe. But to such engineering as is needed for laying out railways, at least, the definition given is literally applicable, for the eco- nomic problem is all there is to it. The ill-designed bridge breaks down ; the ill-designed dam gives way ; the ill-designed boiler explodes; the badly built tunnel caves in, and the bungler's bungling'is betrayed. But a little practice and a little study of field geometry will enable any one of ordinary intelligence, without any engineering knowledge whatever in the larger sense, to lay out a railway from almost anywhere to anywhere, which will carry the locomotive with perfect safety, and perhaps show no obtrusive defects under what is too often the only test- inspection after construction from the rear end of a palace-car. Thus, for such work, the healthful checks which reveal the bungler's errors to the world and to himself do not exist. Na- lure, unhappily, has provided no way for the locomotive— like Mr. Jingle's intelligent pointer— to refuse to pass over an ill- designed railway as it refuses to pass over an ill-designed bridge. Therefore, since there is no natural line between safety and danger to mark even so rude a distinction as that between the utterly bad and the barely tolerable, in the kind of engineering work we are to study, one may fairly say that the locating en- gineer has but the one end before him to justify his existence as such— to get the most value for a dollar which nature permits ; and but one failure to fear— that he will not do so. Except as his work necessarily involves the preliminary design of construc- tive details, he has no lives to save or imperil ; and the young en- gineer cannot too early nor too forcibly iiave it impressed upon his mind that it takes no skill worth speaking of to do such work after a fashion, unless in the comparatively few localities (rare in- m u '}>}. common-sense for the investors and their servants, but it is sound political economy for the community as a whole. It does not mean nor imply cheap and shabby construction. It simply means an avoidance of waste, either in saving money or spending it. It simply means a recognition of the fact that every dollar and every day's work which goes into the ground and does not bring something out of it, makes not only the indi- vidual but the whole community the poorer. The welfare of all mankind, as well as of investors in the enterprises which employ engineers, depends upon the skill with which the investment in its constructive or manufacturing enterprises (destruction of existing capital) is kept small, and the productive or earning power (creation of new capital) is made large. The difference between the two is the so-called "profit" (net addition to exist- ing capital), which goes indeed into the control of those who created it by perceiving the (supposed) opportunity or necessity and using their own means at their own risk to supply it ; but it is not, therefore, for the true interest of any person or class to make it less by increasing the investment, for otherwise there is a waste which, as it benefits no one, indirectly injures all. Not €ven the laborer who uses up a portion of the wasted capital is really the gainer; for if, on the one hand, the capital spent (i.e., destroyed) for construction or plant be needlessly large, although the poor man gains, for the time being, wages which he would tiot otherwise receive from that particular enterprise, yet it is as if he were paid wages to turn a crank which ground no grist — his time and his work go for naught. If he spend half his time in this way he must, in the long-run, do two days' work for the wages of one — a condition which is nearer to existing in railway -enterprises than is always realized or admitted. Comparison of the condition of laborers in countries and ages where human labor is economized (reduced to a minimum for each separate service) and where it is not, fully establishes this important economic truth, as to which many false notions prevail. 13. On the other hand, if the proper margin of profit has been reduced by reckless and costly economies, no one gains "^^V- — — ^<> 20 CHAP. L— INCEPTION OF RAILWAY PROJECTS. even the semblance of benefit, while both the projectors and the patrons of the enterprise are heavy losers— the projectors in money, the patrons in convenient service. These two vital truths, therefore, which directly result from what has preceded, should never be forgotten : that because a line will have or is expected to have a prosperous future— because,, perhaps, it is to be built by the State for great reasons of state,, or for any other reason will have plenty of money in the treasury,, there is therefore no justification in that fact alone for making it a costly road as well. On the other hand, no road is so poor that it can afford to economize when certain additional expenditure will be clearly very profitable. If it is clearly understood, or believed for good- reason, that a given additional investment will certainly pay lo or 15 or 25 or 50 per cent, as the case may be, it may almost be said that the poorest company can find ways and means for obtaining the capital, if the facts be properly and clearly pre- sented. 14. The temptation to err by neglecting these axiomatic laws— which is alwavs present with every one in laying out a railway— becomes especially difficult to guard against under two. circumstances of frequent occunence : First, when a line of light traffic is to be carried through an- inherently difficult country, so that the cost of construction must in any case be large. The tendency to look on a slight per- centage of increase in cost as a trifling matter, although it may,, nevertheless, involve an expenditure out of all proportion to the real advantage secured, is very strong, very difficult to avoids rarely or never avoided altogether. Per contra : 15. Secondly, when a line of comparatively heavy traffic is to. be carried through a region offering small natural difficulties, a dangerous tendency arises of an opposite character;— a tendency to unduly exaggerate the importance of a large percentage, and- yet small aggregate of increased cost. This tendency is especi- " ally probable and dangerous when means for construction are limited, or when the margin of profit on the enterprise as a CHAP. I.— INCEPTION OF RAILWAY whole is liable to be small : a fact which should not be per- mitted to exercise any influence whatever, except through its reflex effect on the rate of interest on capital. The most usual and most unfortunate form which an error of this kind can take is the adoption of unduly high gradients to effect a really trifling economy. The railways of the Western United States, as al- ready noted, have suffered greatly from this cause. The most experienced and cautious man cannot free himself wholly from these too grave errors ; the inexperienced engineer or projector should therefore be continually on his guard against xhem. 16. It has seemed essential thus to lay down certain prelimi- nary generalities as to what should be the attitude of mind of a locating engineer, because he is often unconsciously and im- properly guided in his actions by the mere bald feeling (whether justified or not does not matter) that his company is very rich or very poor, and that he can spend or must save accordingly. Supposing him to enter upon the work, therefore, with that most important of all preliminaries, a correct appreciation of the proper basis for decisions, the problem for which he is prop- erly responsible, when selecting a route for a railway whose construction has been determined on, may be again subdivided thus : Firsts and by very much the most important, is the selection of the general route between the two established termini, or, as very often happens, the selection of one or both termini as well. Secondly comes the adaptation of the line in detail to the topographical conditions which exist along the route selected. 17, The question of general route is commonly settled by the RECONNAISSANCE, whicli for this reason must be classed as by far the most important duty of the engineer in charge, and the one for which it is most essential that he should qualify himself properly, which he can only do by learning to estimate and give •due relative weight to all those circumstances which have or may have a bearing upon the future of the property, as well as CHAP. L^INCEPTJON OF RAILWAY PROJECTS. CHAP. I.— INCEPTION OF RAILWAY PROJECTS. 23 D 22 "^Z^TuI'physical possibilities of the route in question Oth^l se- fhe I qualLd merely in the latter respect-h.s ?.lTer is a double one: that he will give undue weight to :XeVneting questions -^X^:" r^^l:: u^rd -.ir f :: ':r'::r^^^'p^^^^ -^y -r. .. ^"-.reror-I re:^;r;hrb\:arst;e here .... .the ,L selection of the entire route between term.n., or r'ircafe: :f ttHermini -.se.v. js -lyjeft enu^ 1^^ t^rrthl ral"Va:;r:rerro! tr Caching „.. •mponance to some, at the expense of other, governing con- "'r'T°heart of correctlv discerning in advance by merely ocu^l; ex mination, assisted only by maps and a few portable instruments, the physical P--''>''''-/f ^'^j^f ^ most ad- • . A r.,' r^r^<^\h\e railway route, and of making tne moi>t ear_CAar^f__Xr^ sight, which in his eyes are "the ^ ^ -^ ^ ^ Company's," and not the Com- es pany's creditors', and a small Operatinf€xpeiisei I M. 0) N ^ '^. ^ ? CM S o» SjOOOfOOO :; o) ^ ^ .T — ^^ AJ ;:: 00 F,o.,._D,.o..MSHow,»o™. F.-Kc«.R^- part o{ which will suffiee for all 'SlZr'.^rJ.lZ %'Z«^,r^t'^^l possible requirements of h.s de- partment, the impulse ta spend ,roney freely may well become too great for average humaa Tture to resist ; l that the enormous sums of bonded money handled during construction will create an atmosphere of wealth leadtg to a r^ash improvidence, which has been the ch.ef cause of the Mnkruptcy of many lines. As the engmeer has the first « whack" at the Company's funds, and at a time when the judg- mint of the coolest men is most likely to be toss.ng about on The dancing waves of a "boom" at its very height h.s dagger .s particulari; great ; and he especially should reah«e that th« RULE with new American railways is, and must continue to be,, that a very moderate percentage of difference in either the first cost, or the operating expenses, or (above all) the revenue, means to the original projectors, whom alone he serves or knows, all the difference between success and failure. m up tOE Spi rj2.53 ni.Si /Q74 1875 76 77 78 79 /8B0 81 82 83 54 /88S 86- Fig. 3.— Diagram showing the Financial and Traffic Record of the Chicago & North* WESTERN Railway, 1874-1886. [Figures in squares, or points surrounded by squares, g:ive the receipts per ton-mile and passenger-mile ; the lower figures being those per ton-mile.] In Figs. I. 2, and 3 is shown graphically how very small is the margin of profit which makes the difference between solvency and insolvency even in the 36 CHAP. II.-THE MODERN RAILWAY CORP ORATION. ~~ ■ Tu... iin,« have not been chosen as specially mark»d tional revenue. 30 In fact, the situation is somewhat worse than if the Com- panv merely began business with a heavily mortgaged prop- Lu owned In fee. The theory that the Company - the own- in fact, as it is in form, of t'>VutcrvS.":.ti n i:!:;^ rrbuTutorrcreS rUtrasTth .. re. facts w..ici. prevail in the United States, and for the most P^" 'h-;^ ^'^^^^'^ world to consider that the mortgage mterest uself bu.kls and Zlt'Z real property, as a man might build a '-- or aco.-y to rent to others, induced thereto by the allegations of the man Iging Co-pany that in that case they can and will earn and pay SorT large rental on the property from the profits of the business which they propose to carry on with the property and ^"a! Tto'lhe truer manner of looking at the facts, both be- ; 0,e ' motVaKe" is ordinarily far in excess of the mort- Tg . valu^o t'h?;roperty as property, closely "PP-imat ng gagmg va >- , ^„^ because the property Use'lflsl but ab ottdy worthless except for the one particular bus in ss Wch it was built to carry on, so that the loan or mo,.- ^Se involves the ^^^^^^ r,^T:::v^::^:^- 1 r And as the full cost of all the fixed property .s then riwav'sfpfactalyfadvanced, and frequently the cost of all, or most of the portable plant (rolling stock) in addition, the nom.- Tl mortgag'interest is so large that it really amounts pract,- CHAP, II,— THE MODERN RAILWAY CORPORATION. 37 cally to an ownership interest in the real property ; and all that the mortgage interest does not own is the immaterial franchise, which necessarily goes with the property wlien and if they as- sume control of it. This is the additional security which makes the nominal mortgage interest a real one, except that usually, the operating company are obliged either to invest some money themselves in plant to borrow the rest of it, or to throw in an interest in the business (stock) in order to persuade outsiders to build the plant. Very frequently, — in fact — usually, individuals in the operating company (stockholders) also lend money (buy bonds) for the erection of the plant. 32. The instances where the original projectors, even of lines which liave ultimately proved well justified and highly success- ful, have been ruined by depleting their means too rapidly with unwarranted or deferable expenditures, and have been compelled to yield their control of the property, almost on the eve of its success, have been very numerous. A single instance, selected almost at random, of the startling vicissitudes to which such properties are subjected, and of the dangers of the most merito- rious enterprises from the long periods of depression through which they usually have to pass soon after their construction, and from the scanty means of the original projectors, may be in- structive. 33. Within a few years after its construction, what has since become the St. Paul, Minneapolis & Manitoba Railway, then the St. Paul & Pa- cific, was a very striking example of such reckless management of rail- way investments. Its construction began in the flush times of 1872-3. Working then 318 miles, it earned only $630,000 gross and $166,000 net, the latter being at the rate of only $523 per mile of road. Its debt (exclusive of stock) was then over $50,000 per mile, and, no interest being paid on any part of it, a receiver was appointed. In 1873-4 and 1874-5 ^^e net earnings were still less. In 1876-7, an extension of 104 miles into the Red River Valley hav- ing been completed, the net earnings were nearly doubled, and became $749 per mile. By 1878, although the bonds of the Company had become almost 38 CHAP. II.-THEMODERN^SAJI^i^^ .onhless, t>,e receiver succeeded in ^^^l^:Z:^^:7Z boundary, in time to save a large land g^"'' f""* '^';;^^;, projectors, property began to dawn ;-five V-s too la e fo^^^^^^^^^ A new company was then "^^-''^^.'^'P^",,, Love specified, and sale, and found itse f tl.e P°=^;^X° V^^,^,; g "gt^o-less than $.3,000 '« ■""," "TTentrst\hr atd r nt b^n to b; of immed.ate value, per m>le. Then fi/^'^'^.J^^^-Canada Pacific was building beyond U. rr;:;:rrrrdTprope% Which had been almost worthless. ^" x^bLrrtiru^i r^rZ-and its progress is shown in Table 4. Table 4. FINANCIAL HISTORY OP THE St. PaUL. MINNEAPOLIS & MANITOBA Railway. CHAP. II.— THE MODERN RAILWAY CORPORATION. 39 Rvthe end of .883 the road was earning net more than any road - H nf n^ica-'O ex-ept two (the Rock Island and Ch.cago & =.ld"th^';::m°.rs;t^i. -i.- THe r a. sur^^^^^^^^^^ ast - ^n: t:^ 'ZTS r^t ^m llX t!^ l the company the ;::ses"rn':!f "he trafhcof one of the most fertile valleys on the Con- *'"^^u .hh tide set in Immigration and the price of wheat fell off. years, which alone can be given in this volume, the record was as shown in the last two lines of Table 4, the contrast between which and the last year of the flush period is notable. In the last year, in spite of the falling off in prosperity, which had in it no element of immediate disaster, bonds to the amount of 50 per cent of the stock were " sold " to stockholders for 10 cents on the dollar, which was, of course, equivalent to a dividend of some 45 per cent, more if the future of the property did not belie its promise. From the point of view of the public interest there was no danger of this. Its future was magnificent and assured. As respects the individual owners, great as had been their profits to date from securing control of this for- merly bankrupt property, this was and is far less certain. 34. The instructive feature of the example is that even now (1885), failing anyone of these following conditions, ruin or serious loss of all recent investors in the stock of property would be near at hand : 1. The fixed charges are only $1358 per mile, whereas double that iigure or even more would be more usual. At the latter figure a com- bination of many causes might bring the net earnings below it. 2. The rapid fall of rates, which otherwise would have extinguished the surplus, was met by important improvements of the main-line grades, and by the introduction of more powerful locomotives, as well as by the natural economies resulting from heavier trafliic, so effectually, that in the last year but one of the table 24 per cent more freight was moved with- out any increase of engine mileage. 3. The revulsion occurred at a time when the general depression of business was not marked, when the Company was not embarrassed by excessive obligations for new construction, and when the falling ofl[ in trafllic and revenue was in no respect panic-like. Otherwise, even as sound a property as this had proved itself to be, had it entered upon considerable expenditure for new construction or improvement, based on a standard conforming to the present large earning power of the prop- erty as a whole instead of the probable earning power of the additions, separately considered, might well have found itself again a bankrupt. 35, That such contingencies and fluctuations are not excep- tional, is indicated by the aggregates of railway foreclosures, shown in Table 5, which in 1885 rose to the aggregate of 2880 miles with $139,658,000 in bonds ($48,500 per mile) and $120,- 090,000 in stock ($41,700 per mile) or $268,213,000 in all ($93,136 per mile) the bonds alone probably representing, as is so com- 40 CHAP. II.— THE MODERN RAILWAY CORPORATION. Table 5. Railway Foreclosures. Year. Miles. Capital Stock. I = XOQO. Funded Debt. I = 1000. Floatinjr Debt. X — 1000. Total. X = IO(X>. 1881 2,617 668 1,190 714 2,8So $51,273 20.751 24,588 12.894 120,090 $76,645 23-999 38.19S 13.061 139.658 ($10,000?) 10.074 2.4S2 423 8,465 $137,923 1882 54.824. 1883 65.268 1884 26.378 1885 268.213 Total, 5 yrs.. . 8,069 $229,601 $291,561 $31,444 $552,606 Per mile, average $28,455 $36,135 $3,897 $68,487 Per mile. i88^ $41,697 $48,499 $2,940 $93.13^ The above is compiled from " Poor's Manual," 1886. It is unquestionably full of errors, but no authentic or complete figures exist. The general fact that the bonds and stocks of bankrupt lines run a good deal higher than those for solvent lines is clear, as the most serious errors are probably in the earlier years. The Commercial and Financial Chronicle, in its October, 1884, Investors' Supple- ment presented a valuable table showing the railway companies now in default on pay- ment of interest on bonds. Only railways in the United States are included, Mexican and Canadian lines being omitted, and only the particular issues of bonds are taken on which default is made, although the mileage given includes all operated by the defaulting: companies. The table includes all companies defaulting during the period covered, which had not resumed payment in full, and which had not been foreclosed and reorganized. The totals are summed up in the following table, in which comparison is made with the defaults of 1873-76: Total defaults, October, 1884.. Entire railroad system of U. S. Per cent of defaults to total. . . Jan. I, 1884. Total defaults, 1S73-1876 Entire railroad system Jan. I, Per cent of defaults to total. . . 1876. Increase in mileage and bonds during five years pre- ceding Jan. I. 1884 Increase in mileage and bonds during five years pre ceding Jan. i, 1876 Mileage. 15.986 121.592 1314 Amount of Bonds. $315,283,000 3.455,040.283 9.12 74,096 39.818 21.232 $783,967,665 2,175,000.000 36.04 $1,157,249,467 *636,96o,o(X> * Estimated at $30,000 per mile. CHAP. II.— THE MODERN RAILWAY CORPORATION. 4 1 The whole number of companies in default in 1884 was only 42, against 197 in the former period. In the former period of defaults, about 20 companies out of the total 197 that were embarrassed were old railroads that were well established and once had a pay- ing business. In the later period, out of 42 companies named in the table, none can be fairly said to have had a well-established and paying business on the basis of their present lines and existing liabilities, unless such companies as Erie, Wabash, and Reading be classed in that category. On British railways, which are subject to far fewer vicissitudes than those of the United States, the average dividend of ^\ per cent is divided approximately as follows, — United States statistics from the census of 1889 being added for comparison : United States. British. 18.8 1 16. 1 per cent pays • no dividends. i.o " " under i per cent 10.2 4.9 " •• " 2 9.2 32 '« ii . " 3 3-1 7-3 " " . " 4 2.5 23 4 " '♦ . " 5 5.7 21.7 " ♦' " 6 6.5 20.0 " " " 7 <^-5 1.0 " " •' 8 7-4 0.4 " •♦ . " 9 3-4 0.4 " •' " 10 3.9 0.6 " ♦♦ about 15 WhMe exact figures on which to base a judgment are not available, it is not probable that more than one fourth of the exi.sting mileage of the United States has escaped fore- closure proceedings or default on bonds necessitating a receivership. Many roads which are now among the strongest properties have been through such difficulties several times in their earlier history; while, on the other hand, many others, like the Denver & Rio Grande, Philadelphia & Reading, and other strong properties whose future seemed assured, have been overtaken by disasters resulting in great part from the intoxication of long-continued success. So that the properties are few indeed — and those mainly the ones which build no new lines — of which it can be predicted with any certainty that they may not become insolvent in the next period of serious depression. Table 6. Estimate of Futitre Railway Construction in the United States. [Prepared by Edward Atkinson, of Massachusetts, for various groups of States as described on next paee.l Group of States. Mileape still needed from Jan. I. i88i. 19 years. Mileape built from Jrtn. i, 1881, t"-. Jan., 1885. 4 years. Per cent total estimate buik in 4 years. Mileape still needed before yv.D. 1900. 15 years. Class I Class II 36.236 27.199 34-472 9 6^2 9.8S8 8 597 5 282 8351 2.893 5.857 24 I9i 24 30 59 27639 21.917 26,121 6759 4031 Class III Class IV Class V Totals "7,447 30.980 26.3 86,467 42 CHAP. II.— THE MODERN RAILWAY CORPORATION, monly the case, somewhat more than the actual total expendi- ture to create the entire property. This amounts to nearly three per cent of the mileage, and over four per cent of the capitalized cost of the entire railway system of the country, and that too in a year which was in no respect a particularly bad one finan- cialiy, as will be seen from Table 5, which gives similar figures for several vears back. 36. The'fact, illustrated by the history just given of a road in the far West, that the intoxication of realized success will lead even prosperous companies to assume dangerous and reck- . less liabilities, becomes especially important in view of the fact that in the future a large portion of the new mileage will be constructed by such lines. A carefully studied forecast of the probable mileage to be constructed, by Mr. Edward Atkinson, made in 1881, and confirmed as a moderate and cautious esti- mate which will almost certainly be exceeded by experience up to 1885, brings out this fact clearly, in addition to having &n in- terest of its own, and is given in Table 6. Description of Groups, Table 6. ClaS I "retchinK down the Atlantic coast to Florida, estimated to have by .900 ^ "" cf^'^lil' tl^ \f^.SX 'the far West and South, with one mile fer .6 sg. "' cU' iv"inclute tie 5 States of Maine. Nevada, Colorado, Oregoi, and California, ^%^::. ^Hiik^ot^l^^'^y'^l^l^^loL Territories, with .« miU per 6, sg. "^^otal united States mileage whe^est^^e -^P-Pf^'^^^^'^'J^^^Sjirio^ .^.^5 ;2?; X? .18^ 'r5,76?miref ^^ainsfan-^verage of 7,745 miles per year for the prev«>us 4 yelrs. The Estimate is almost certain to be largely exceeded. Table 7. PRorRESS AND Extent of the Railway System of the World. Progress AND^ i=.xi ^^^^ j,„,h^„., .. oiconary of Statistics."] Miles Open. Cost (mi llions, $). 1840 I80O 1860 1870 1880 1850 1800 1870 1880 United Stairs... United Kingdom Continent Canada, etc 2.818 838 1,074 9,021 6,621 8,311 538 30,635 10,433 21,815 4.228 52,914 15.537 49,320 12.339 93,349 17,945 86.818 31,804 292 1,166 652 34 2.144 1,094 1,685 1.730 243 2,332 2,572 4,320 860 S.070 3.640 8.690 2,010 Total . 4-73° 24,49^ 67.111 130.110 229.916 4.752 10,084 19,410 CHAP. II.— THE MODERN RAILWAY CORPORATION. 43 Table 8, Railways of the World, January i, 1884. [From Prof. A. T. Hadley's " Railroad Transportation, its History and its Laws."] Miles. America. Europe. . Asia . . . . Africa. . . Australia 140,000 114,000 11,600 3.400 6,500 275,500 Capital Invested. $8,400,000,000 16,110.000.000 775,000,000 240.000,000 325.000,000 $25,850,000,000 Per Mile. $60,000 115.000 66,000 70,000 50,000 $72,200 Germany Great Britain and Ireland France Russia Austria and Hungary Italy Spain Sweden Belgium British India . United States Length, Jan. I, 1884. 22,300 18,600 18,500 15.700 12,800 5.900 5.100 4,000 2,600 10.500 120,000 Per cent Increase in 5 years. 8 5 18 7 12 13 16 14 6 20 43 Miles of Road to 100 sq. miles. 10.6 15-2 9- o. 5- 5- 2. 2. 23.2 0.7 3-4 .0 ,8 •3 ,1 ,6 3 Miles of Road to 10,000 inhab. 4 5 4 I 3 2 3 8 4 o 22 9 3 9 9 4 o o 7 8 4 5 Cost per mile. Dollars. 105.000 204.000 128 000 80,000 105,000 92,000 78,000 30.000 132.000 66,000 61,000 Equipment per 100 miles. Pass. Moved (Millions). Tons Moved Locom. Pass. cars. Freight. (Millions). Germany 1882 1882 1881 1881 1882 1882 1880 1881 1881 1883 18S3 51 76 46 40 30 29 26 16 72 24 22 95 232 105 50 62 88 77 36 139 65 21 I.oSi 2,298 1,207 775 716 510 468 401 1,840 436 663 224 655 180 33 47 34 15 7 57 65 313 198 Great Britain 291 France 93 Russia 14 Austria 70 Italv II Spain 9 Sweden ... 5 Belgium British India 37 19 United States 400 Comparison with Table 10 and others will show that there is considerable uncertainty in these figures. It should be remembered that American rolling-stock is much heavier and larger than foreign, and that the average distance over which each passenger or ton is moved is far greater. 44 CHAP. II.— THE MODERN RAILWAY CORPORATION, Table 9. Progress of American Railway Construction by Groups of States» AND OF Foreign Railway Construction. 1850 1855 1860 1865 1870 1875 1880 1885 ^iT N#*Av Rnc^land Stales 2,508! 2,807 395 1,620 4'5 1,256 20 3,469 4.849 624 3-294 X.523 4.>73 394 40 8 3,660 5.841 865 5.1" 3.726 8,684 2,380 345 23 3.834 7.594 945 5.228 3,901 9,646 3,201 503 233 4.494 9.709 1,282 6,094 5.»35 I3,»77 9,506 1.5S3 1.934 5.638 12,639 i,8i6 7.047 6.240 18,879 14.903 3,966 2,968 5-977 13.865 2,005 7,803 7,008 21,964 23,259 6,582 5.886 6,310 New York, N«w Jersey, Penna.. Delaware, Maryland, W. Virginia Virginia, N. Ca., S. Ca.,Ga., Fla. Alabama, Miss., La., Tenn., Ky.. Ohio, Michigan, Indiana, Illinois. Wisconsin, Minnesota, Dakota, Iowa, Nebraska, Kan., Mo Indian Ter., Arkansas, Texas,Col- orado, Wyoming, Montana Pacific States and Territories i6,97J^ 2,366 11,127 9.675 27,101 31,527 13-734- 9-954 Total United States 9,021 18,374 30,635 35.085 52.914 74,096 93.349 f_ 1 . 128,967 t „.v.:#>k The above was compiled trom me taoies in various issuer ^^ » -v.. ^ are full of numerical errors. These have been corrected as far as possible. Foreign Countries. 1840 1845 1850 1855 1860 1865 Great Britain Franre 838 271 340 2,536 551 1.429 6,621 1.879 3.747 38 8.335 3.459 5.138 1,218 10.433 5.900 7,212 2,173 13,289 8,477 9,105 2,231 frermanv Canada. T„TA, Mil FAfiE OF RAILWAY CONSTRUCTED AND IN OPF.RATION IN THE UNITED. STATE^ FOR EACH YEAR FROM THE BEGINNING OF RAILWAY CONSTRUCTION. isao 1840 1850 1860. 1870 1880 23 3,818 9,021 30.635 52.914 93.349 95 3.535 10,982 31,286 60,293 103,145 2 229 4.026 12,908 32,120 66,171 114.713 8 380 4.185 15.360 33.170 70.268 121,454 4 633 6 1,098 6 m 4 8 9 1.273 1.497 1.913 2,302- 4.377 4.633 4.930 5- 598 5.996 7.36s 16.720I 18,374 22,016 24.503 26,968 28.789 33.908 35.085 36,801 39.250 42,229 46,844 72,385 74,096 76,808 79,088 81,717 86,46j I 5.3791128,967! ANNUAL INCREASE. 134 151 253 465 175 224 416 389 49 > 159 192 256 297 668 398 1,369 1,926 2,452 1,360 i.6S4 3.642 2,687 2,465 1.821 834 1.050 738 1,177 1,716 2,449' 2,979 4,615 5.878 4.097 2,117 1,711 2,712 2,280 2,629 4,74^ 11,568 6,741 3-825 3.588 CHAP. II.— THE MODERN RAILWAY CORPORATION. 45 Table 10. Mileage, Cost, etc., of European Railways, with Total Cost of Construction and Average Cost per Mile. [Rearranged and recomputed from the Revue Generate des Chemins de Per, 1886.] Country. United Kingdom. Belgium France •Germany Austro- Hungary. Switzerland. Spain Portugal Russia Italy Holland Sweden ... . Denmark.. .. Norway Germany in detail — Prussia Bavaria Sa.x 3ny Wurtemburg , Baden Alsace-Lorraine Other German States .. Total Germany Minor European Countries — Bosnia and Hertzegovina Bulgaria Finland Greece Luxemburg Rou mania Turkey Miles. 1883-5. x8,864 1.885 16,578 21,785 12,603 X.795 4.550 927 14,226 5-871 1.406 3.975 926 970 Cost. Millions. 106,361 12,636 2,833 1.434 968 818 3.096 21,785 Kilos. 370 222 X,l8l 22 366 1,503 i.'73 4.837 $3,895.10 334-45 2,232.20 2,248.40 1,279.80 184 88 442 . 26 90. II 1,382.30 554 50 12734 59-34" 37.00 3351 Ay. Cost Per Mile. $12,901.19 1,309 40 268.39 149 35 110.95 99.70 310.61 2,248.40 (some 3.000 $206,490 177.420 134,640 103,210 101,550 103,000 97,200 97.200 97,168 94,448 90,918 41.563 39.961 34,548 $121,300 103,620 94.7-28 104.150 113.140 121,880 100,328 103,210 miles). Sq. Miles per Mile Ry. Eng... Scot.. Ire.. .. Aus... Hung. 4-4 10.3 13.0 ~5 4-2 XI I 9-4 14.7 24.0 18.8 9.2 38 37 130 18 9 41 13 127 Per Cent Increase, One Year. 32.9 X0.2 9-4 4-4 8.4 7.0 8.4 9-4 87.0 179 o 196 o xSoo.o 4 4 53 9 XII. 5 2.03 1.29 2.01 1. 91 2.13 2.05 2.07 2.98 3.12 3 04 3.66 330 4.98 5 72 4.86 3.21 I. 13 1.80 1.97 307 a. 13 X.76 2.36 2.24 1.95 1.96 a. 07 5- 14 2. 147 00 0.97 5- 7 •14 55 •92 •73 54 * There is an error in this sum, which should be about $100,000,000 greater — 150.66. The last three columns are taken (converting metric into English units) from the Statisque des Chemins de Fer de V Europe, 1882. Vienna, 1885. According to other, and perhaps more authentic figures, the railways of Great Britain have cost $205,842 per mile of road ; the Belgian State Railways, $123,986; for the French railways, $124,642; for the German State Railways, $105,204; the German private roads, $71,877 ; the Austro-Hungarian roads, $104,420. The cheapest system of Europe is the State Railways of Finland, $30,102; the other Russian railways stand at $82,244, against $63,250 per mile for the railways of the United States. The whole cost of the railways of the world has been more than $24,000,000,000, which. 46 CHAP. II,— THE MODERN RAILWAY CORPORATION-. however, is only about $24 per inhabitant. In this country the expenditure has been about $133 per inhabitant; in Great Britain, $107; in Germany, $47; in France, $57; in Austria-Hungary, $33; in Italy, $19; in Belgium, $41; in Sweden, $25; in Spain, $29; in Russia, $14 ; in Canada, $89. In France and Germany railways pay about 5 per cent on the capital invested, as an average ; in Great Britain, 4 to 4Mi; in all Europe and in the United States, about 4 per cent. Table 11. Extreme Fluctuations in Price of the Stocks of Various Companies OF Great Natural Strength. The lowest points in times of depression (distinguished by an 1) and the highest price in times of activity (distinguished by an h) are alone noted, except that in the last column is given the price in November, 1886. The list has been selected almost at random, regardless of their actual financial status, to include the more prominent companies which, from the nature of their traffic or other strategic advantages, might naturally be expected to be (as for the most part they are) least subject to erratic fluctuations of value. Company. New York Central Erie Pennsylvania Baltimore & Ohio Central of New Jersey. . Boston & Albany Lake Shore M ichiuan Central Canada So Piitsburp & Ft. Wayne. . . Chicago & Alton Ch., Burlinjrton & Q Ch., Milw. &St. P Ch. & N. Western Ch.. Rocklsl. &P 111. Central • • ■ Atchison.Topeka & St. F Denver & Rio Grande.. . Central Pacific Union Pacific Louisville & Nashv New York, N. H. & Hartf No. Pacific 1878. 1to3?^ '% 1879. 1880. 1881. I75 IrM 1 129 155% 158}^ I38 I85 166^ 1 32 I98' 172% 16.^ 1 153M 11155% 196" ih204 i8i%hi525^ I16 16i^hii3>4 1 63 h 102^)^ 1 79 b 190 hi74 1152% hi4oV4 lt2IO ll TI2 h<75Vlf 1»«3594 hi3oV6 h 90 h 142 hi56 hi82H ll izgj'^ hi36 h ioo9^ I168 b54% The above extremes are in many cases brought about temporarily only by the machi- nations of speculators. In many cases permanent changes in the nature of the company have also had great influence. On the other hand, these fluctuations of stock are far less than the fluctuations in the productiveness for the time being of the properties represented bv them for the price of a stock-neglecting the mere momentary fluctuations of a few points forced for the sake of a - turn"-is, at the most, merely this : It is the speculators ^timate of what permanent investors feel for the time being to be the permanent aver- AGE value of the stock. For there are always large holders who keep in mind the average value of the property during good times and bad times alike, and who will buy or sell in quantities large enough to immediately affect the price if THEY THINK it is falhng below the present worth of its future chances, all uncertainties included. CHAP. II.— THE MODERN RAILWAY CORPORATION. 47 Table 12. Rolling Stock Per Mile in the United States and British Colonies. Name of Railway. New England States, 1883 Middle States, 1883... Southern States, 1883 Western States, 1883 Pacific States, 1883 Canadian Pacific, 1885 Intercolonial of Can., Halifax to Quebec, 1884 Indian, 5 feet 6 inches gauge India, metre gauge, 18S4 Ceylon Government, 1883 Mauritius Government, 1884 Queensland Government, 1882 New South Wales Government, 1881 Victorian Government, 1882 South Australia Government. 1881 New Zealand Government, 1883 The Cape Government, 1882 Average of totals Per 100 Miles of Railway Of>en. Loco- motives. 28.76 41.93 13-32 16.23 9-63 10.9 19.2 27.2 20.4 31.8 40.9 7-9^ 23-4 16.8 13. 6^ 15-0 23-4 Passenger Cars. 19.86 48.31 45.34 12.06 13.74 12.06 10. 1 28.4 66.5 69.2 95.6 131. 8 II. 6 53.2 33.6 22.1 42.7 41.2 23.89 Freight Cars. 635.9 1714.5 283.2 4834 191. 8 276.2' 513.3* 512.2 369.7 296.1 500.53 112. 8 487.1 291.6 344.9 ■453.2 374.8 590-5 ' Only partially open for traffic. » Opened about 1876. • Freight traffic heavy during crop season. * Report states, *' We have been extremely short of engines all through the year." ' Report states that more locomotives are required. Condensed from a paper on "The Laying-out, Construction, and Equipment of Rail- ways in Newly-Developed Countries," by James Robert Mosse, M. Inst. C.E., in Trans- actions Inst. C.E., 1886. See also Table 8. f CHAP, III.— CAUSES MODIFYING VOLUME OF REVENUE. 49 CHAPTER III. THE NATURE AND CAUSES CONNECTED WITH LOCATION WHICH MODIFY THE VOLUME OF RAILWAY REVENUE. 37 With the invention of the railway began a new industry —the MANUFACTURE OF TRANSPORTATION. Transportation, in- deed existed before its invention, just as cotton cloth existed before the invention of modern machinery, but it was in eacli case mainly produced on a small scale by each consumer for his^own use and his immediate neiglibors'. With the invention o the railway first began the manufacture of transportation for sale on a large scale and by modern processes. 38 A railway corporation such as has been just considered —the' typical modern corporation-exists for this purpose. It finds itself, on completion of its works, in possession of a certain piece of improved real estate, of certain buildings and fixed machinerv (the track), and of certain tools and machines (the rolling-stock) for the manufacture of its commodities, together with certain establishments (the locomotives and car-shops) for the maintenance and repair of its machine-tools, which the extent of its business requires. In many instances it has not a dollar s worth of ownership interest in all this costly plant, excepting a portion of the minor machinery, but simply controls it at, in ef- fect a fixed rental (interest and other fixed charges). All that it really owns is, commonly, a portion of the business or franchise ; and this latter has likewise been hypothecated, or pledged, in the mortgage bonds as security for the payment of its rent charges As this business has, from the nature of railway busi- ness, assurance of always amounting to a certain minimum at least this franchise alone has a value as security which no ordi- nary business would have, and in a rapidly growing country its existence enables all or nearly all of the actual cost of the entire premises and plant to be borrowed, or rented, from others. On the premises so rented, the corporation carries on, for its own benefit, the business of manufacturing and selling transpor- tation, so to speak, at wholesale and retail, in lots to suit the purchasers. Since it owns the business only, and has, as a cor- porate body, no interest or ownership in the property itself, it will be clear, and should be fully realized, that all its interests are limited to the narrow debatable ground which lies between doing the best possible and doing the worst possible with the property in hand, which is in all ordinary cases simply lent to them for an annual consideration. 39. Now, continuing the parallel, which will perhaps help to enforce the truths required, and referring only to sales of trans- portation, or revenue : if a manufacturing company in such cir- cumstances should, in planning its works, so plan them as to cut itself off from disposing of certain lines of goods which it manu- factures, or should place its retailing establishments (stations) at inconvenient points, it is clear that it would have seriously hand- icapped itself, even if, perchance, justifiably. This a railway company does when, by failing to run close to any accessible towns, it is prevented from furnishing them with transportation, or is so far away that sales are inconvenient. If it strives to shorten its line it is, for certain parts of its traffic, trying to sell \^s>s yards of its goods, at a certain price /^rj^n/, in order to save the cost of its manufacture ; .forgetting that by the same act it also loses the selling price and hence the profit on them. If, on the contrary, it builds an over-long, or crooked, or otherwise objectionable line, it is in effect fitting itself to produce only an inferior article, which will command a lower price. 40. The force of this parallel is still further and greatly strengthened if we remember that, with much that is similar, there is, in one respect, a momentous and broad distinction between the seller of transportation and the seller of most other commodities. The production or partial production of trans- portation is, from the necessity of the business, considerably in 4 50 CHAP. III.-CAUSES MODIFYI^NG VOLUME^ OF R EVENUE. :a rthereto. Every time, for example, a P^-nger tram s^a. u out there is "manufactured," so to speak, several hund.ed pas senee tls If they be not sold, they cannot be stored away on hfshe fo the nex't day's trade, like the remnants of a lot o d v-goods. They are simply wasted and thrown away I -s wUh the railway much as if tradesmen were conu,elled to cut a Tew piece of each kind of goods each day and then throw away the part remaining unsold each night. We should probably under such circumstances observe a conspicuously greater zea ^ven than now exists for regulating and increasing sales so a Tsell the whole of every piece of goods ; whatever pnce the remnants might bring being so much clear gam. remnant mg g^ ^^^^ ^^^^^^ ^^^ ^^^^^^ ^^ ^ tant degree the conditions here suggested exist w.th respect to every part aid kind of railway traffic. We see, therefore, how vtal and peculiar is the interest of railways in neglect.ng no !on ideration which bv ever so little affects its revenue. It .s on si Jht differences of traffic and revenue that the corporation 'Tran^lig: before, that no probable effect upon tramc and Oraniing. ^^cur from the decisions reached in re^-^irai'tc^tro^Toui: be neglected it will be obvious, a already hinted, that such effects are possible from any one of the following ""^« = ^^ „, LINE-Even slight variations 42. I. THE LENGTH u revenue, as well as the ratio thereto. ^ .u^rpfore varying in almost every case, up to a ««-"P;;:^",i,f: a .'e net revenue frequently, will t.e gross revenueta. ad ^^^^ ^^ ^^^ ^^^^^^^^ ^ Bi;Tf':htrotsVbe carried too far, the traffic will be overbur- CHAP. III.— CAUSES MODIFYING VOLUME OF REVENUE. 5 I dened, discouraged, and decreased. The questions thus raised will be separately discussed in Chapter VII., on Distance. It is one of extreme importance. Such effects on revenue may also occur from — 2. The comparative weight allowed to securing way TRAFFIC, the quantity which may be expected, and the sacrifices which may or must be made to reach certain additional traffic points. Also, 3. Allied to the latter, is the question of how near to run TO CITIES, TOWNS, AND OTHER SOURCES OF TRAFFIC, which are already upon the line, and how much the traffic and revenue will be thereby affected. 4. Still other similar questions arise in connection with BRANCH LINES *. whether to build a branch at all, or take the main line through the given point ; whether, if a branch be de- cided on, the connection should be made at this or that point, there being often much choice, and the decision governed by commercial considerations to an unusual extent, or at least by very different laws from those which might govern the laying out of longer lines, owing to the shortness and isolation of most branches. 5. All of these questions together arise on a grand scale in the laying out of great systems of railway at once or in the connection of a number of isolated lines into a single system, as liappens with increasing frequency in modern times. In a certain sense, indeed, every line, even nominally inde- pendent, and no matter how short, is a part not only of one but perhaps of several great systems of roads. On this account, and because of the great importance of the questions which arise in connection with the laying out of branch lines and systems, a separate chapter (XXI.) is devoted hereafter to — not a general discussion, for that is impossible — but to the presentation of certain suggestions intended to illustrate the laws which govern their solution. Much of the chapter referred to has likewise a direct bearing on the remainder of this chapter. 43" It is unfortunate that the very great and often decisive $2 CHAP. III.-CAUSES MODIFYING VOLUME OF REVENUE. effect which differences of location may have upon the revenue of railways is not susceptible of more exact analysis, for it is very often, in properly conducted work, a consideration of such importance as to sink differences of engineering details into insignificance. The most that can be done is to lay down with all possible care the general principles which govern this effect, with the caution that the very difficulty of determining exactly what weight should be given to it creates too great a tendency to neglect it altogetlier. 44. The traffic of railways is often spoken and thought of as for the most part a monopoly. In a certain sense, of a cer- tain small part of its traffic, this is true, as already noted, to the extent that there is a certain fraction of the traffic of all railways which no folly can destroy or throw away. But in a larger sense^ the traffic of any and all railways is only to a very limited ex- tent a monopoly of such nature that to secure it the Company has nothing more to do than to put up its buildings, and station a man at the receipt of customs. The selling of transportion is governed to a very large extent, whether there be nominal' com- petition or not, by the same laws which govern the selling o£ any other commodity; and these laws require that the railway company, like any one else with something to sell, shall consult the convenience, and even sometimes the unreasonable whims, of the buyer, if it would sell its goods to him. 45. For only a small proportion of the traffic of any railway- is in the strict sense of the term necessary traffic, which must come to it anyway, under all circumstances. The amount of such traffic is measured, when a railway system is first coming into existence, by the stage-coach travel as respects passenger business, and by the carting on the common roads as respects freight business. Under the stimulus which the bare existence- of a'ny kind of railway facilities gives to the development of any country, the volume of this strictly necessary travel is no doubt increased many-fold. Nevertheless no railway is so prosperous, and so favorably situated that it would not, in literal truths Starve to death on it. The traffic would be so very greatly de- CHAP. I IL— CAUSES MODIFYING VOLUME OF RE VENUE ^ 53 creased that on most lines it would not be possible to run the trains at all. Neglecting altogether the traffic which, as respects any one company, is not necessary, because it has a choice of routes, and one line has to fight for it with others, a very large proportion of the business of the railway system as a whole is made up, as respects passenger business, not only of pleasure travel pure and simple, but of travel which is more or less a mat- ter of whim or of fancied or partial necessity; and even as respects freight business, of freight which will not be shipped except un- der reasonably favorable circumstances, especially by any one route, or shipped only at a lower rate : so that the rates must be solely fixed, not by the cost of the service, but by the price it will bear without discouraging traffic. 46. It will be evident therefore that, since we have already seen the vital importance to railways of making the largest possible sales of their wares, and since a large part of their sales are of such nature that they may be easily discouraged and prevented, any failure to facilitate traffic to the utmost is a se- rious matter. The question of encouraging or discpuraging traffic by the facilities offered will depend in the main, no doubt, upon the manner of operating the road after it has opened; yet in one respect at least (postponing for the present, as noted, the ■discussion of the first, fourth, and fifth considerations above) it is possible in the beginning to seriously and J>er ma fienf/y aflect the future traffic of the line : viz., by going on the principle, which has often been followed in the practice, that " if the rail- way DOES NOT GO TO THE TRAFFIC, THE TRAFFIC WILL COME TO THE RAILWAY." This argument is sometimes gravely advanced in support of the plea that it is of no particular importance whether the line pass through a town or a mile or two off from it, because in either case the line will get " all the business there is." From the very fact that there is a grain of truth in this plea lending a certain support to that cheapest of all ways of saving money, — and perhaps saving a little distance and curvature at the same time, — keeping the line off all land which is worth any considerable price, it is important that it 54 CHAP. III.— CAUSES MODIFYING VOLUME OF REVENUE. should be fully realized why it is a dangerous and fallacious argument. 47. It is particularly easy to see that the argument is both dangerous and fallacious when there is, or is liable to be, com- petition for the traffic, or any part of it, as may be said to be always the case, at least potentially, in the United States. In that case, the only safe rule is, that any considerable difference in haul to the station or in any other convenience to the public will al- most wholly destroy the possibility of profit from the traffic to be competed for, even if a portion be secured. For it might be proved by many instances that it requires but a very slight dif- ference in the convenience of access to practically destroy all equality of competition. Except for the very numerous in- stances of entire neglect of this danger it would hardly seem necessary to speak of the matter at all ; for it is evident that, as respects freight traffic, rates must in the long-run be made equal, not simply from station to station, hwX. from the door of the consignor to the door of the consignee : in other words, all additional cost for cartage or switching service, and something more as compensation for the trouble (usually a very considerable addi- tion), must be borne by the railway before it is in a position to compete at all. As respects passenger traffic, to a certain class ot long-trip travel such minor differences are of less importance, but there is a considerable fraction even of long-trip travel on which they have a recognized and important influence ; and de- vices of all kinds— free omnibuses, more or less open concessions on rates, etc., etc.— are required to counteract what may have been a mere oversight, or bit of indifferent negligence, in the original laying out of the line. 48. Let us imagine an instance which has frequently hap- pened already, and still more frequently will happen : A num- ber of good-sized towns, ten to fifty miles apart, served by two competing lines ; one of them coming appreciably nearer to the average centre of population than the other. It is abun- dantly established by experience that in such a case the favored line can by a moderate amount of effort— which may be counted CHAP. III.— CAUSES MODIFYING VOLUME OF REVENUE. 55 on with some certainty — not simply cripple, but almost destroy, its rival's local traffic. For " to him that hath shall be given," with short-haul traffic especially. If one line start with any ad- vantage, that very fact will tend to increase it. It will have a better reputation. It can offer better facilities. The tendency of the traffic of all kinds will be to concentrate itself upon it — just as water always seeks the level point, however little lower it may be. Even when a railway can, or thinks it can, count on permanent immunity from competition, it should naturally fol- low from what has preceded that it is still exceedingly dangerous to put the public to permanent inconvenience and expense under the false idea that " it will cost the Company nothing." Under the best of circumstances there will always be some loss; and the slighest addition to receipts, which might have been secured but is not, would have gone almost in gross to swell the surplus. The slight additional trouble and expense to shippers of all freight, and the horse-car and cab fares of passengers, must be paid for sooner or later, in one form or another, by the corpora- tion, if in no other form than in a decrease of traffic. _ It is not true that nothing which will still leave rates at so much a mile, without immediately affecting them at this or that non-competi- tive point, is of importance to the Company or has effect upon its revenue. 49. The universal law of trade ultimately obtains with sales of transportation as of everything else. The selling price, the amount sold, and the profit realized on all articles of bargain and sale is ultimately regulated by the quality of the article and the price the consumer is willing and able to pay, and this again is greatly affected even by trifling differences of convenience. We may see this illustrated every day by the difference in price of the same article at fashionable and unfashionable stores ; and even when there is but one point at which a certain desired ar- ticle can be bought, it is a truth universally admitted among business men that minute differences in the price or the quality of the article, or in convenience of access to the place of sale, do have a material influence on the volume of sales, especially if 56 CHAP, III.— CAUSES MODIFYING VOLUME OF REVENUE, CHAP. III.— CAUSES MODIFYING VOLUME OF REVENUE. 5/ such articles as are to be sold in great numbers to the general public. That precisely the same argument applies to railways can be denied only by asserting that the patronage of a railway is strictly a matter of necessity — a pure monopoly, except as competed for by another railway ; but this, even if it were true of the greater portion of traffic, would certainly not be true at all of the remaining fraction, and it is ordinarily this remaining fraction which alone makes the business of operating the prop- erty worth carrying on by the company controlling it : for let us suppose that by systematic negligence at several points in the original laying out of a line a corporation should succeed in af- fecting its gross yearly revenue so much as one per cent. It would represent certainly five to ten per cent, and very possibly one hundred per cent, of the value of the franchise owned by the corporation, which is usually all they do own, and sometimes a good deal more. 60. If it should seem improbable that any possible error of this kind could so affect revenue, it must be admitted that it is difficult and in fact impossible to produce statistical proof, nor would such proof, even if produced for one locality, be applicable elsewhere; but a striking example, among many, of the natural effect of such reckless neglect may be found at the town of Springfield, Ohio. A dispute about a trifling sum (about $50,000) of town aid to the Atlantic & Great Western Railway, now the New York, Pennsylvania & Ohio Railroad, caused the manager of the road to run the line two or three miles from the town — and this with a slight increase, if anything, in the dis- tance, curvature, and cost. This town has since become, as even then was probable, one of the best shipping points in the State; and, purely in consequence of its inconvenient location, the Atlantic & Great Western secures only an inconsiderable frac- tion of this traffic, both freight and passenger. Its annual loss of net revenue is, beyond all question, considerably larger than the whole sum originally in dispute; and the disadvantage was so serious that, very recently, arrangements to run into the town over another line were made at heavy cost, while still leaving the line at an immense disadvantage. 51. In this occurrence there is nothing exceptional, even in degree. There is hardly a town of any importance in the United States in which some one of the lines running to it has not done precisely the same thing ; so that it is known of all men to be at grave disadvantage in respect to some portion of its natural traffic, whether long-haul and short-haul, and whether passenger and freight. That natural and not unreason- able trait of human nature embodied in the homely proverb, *' Give a dog a bad name and hang him," then comes in to inten- sify this disadvantage. This in turn begets a poverty of means, which begets a poverty of service, which still further increases, and justifies on rational grounds, what may have been in the beginning a rather unreasonable popular prejudice; and the end, in all probability, is a receivership. It will be found, on looking over a list of roads which have failed in this way, that, almost without exception, they are those which merely skirt the edges of the towns which they nominally reach. 62. The effect on short-haul traffic of negligence of this kind is, as already hinted, far more serious proportionally than in the case of longer haul — not only because it is far more likely to drive the traffic to other lines, when such exist, but be- cause it is far more likely to have the still further effect of de- stroying a portion of the potential traffic completely. The longer the journey or the haul, evidently, the less effect will any trifling inconveniences have, and the proportional as well as ab- solute loss will naturally be less at small towns than large ones— especially than at very large ones where there is a regular and established suburban traffic. Nevertheless no town is so small that the short-haul local traffic is not materially affected by tri- fling difference of convenience of access. Differences which originate in the subsequent management of the operating de- partment, better cars, time, meals, train employees, surer con- nections, etc., may have, it has been admitted, relatively much more effect than a mere difference in convenience of access to the station ; but the latter, unlike the former, cannot be cor- rected at any time, and in trips of ten to twenty or fifty or even 58 CHAP. I I I. -^CAUSES MODIFYING VOLUME OF REVENUE, one hundred miles, the mere fact that the station is (or is not) convenient for taking and leaving the train is alone enough to- have a powerful influence upon the number of such trips, es- pecially in bad weather, but to an important extent in all weather, with the weaker three quarters of the population at least. 53. In very much less degree even the volume of non-com- petitive FREIGHT SHIPMENTS is similarly affected; besides the fact that it must be assumed, for reasons already stated, that the rates, in the long-run and in some direct or indirect form, will certainly be affected likewise. Sooner or later, in one form or another, the railway will be compelled to make concessions equivalent to paying for the cost and annoyance of cartage on much of its traffic, and lose altogether more than enough to pay for carting the whole of it. There is no clearer moral than this to be drawn from recent railway history. 54. It is also unmistakably evident from recent history that it is impossible to maintain more than a reasonable ratio of dispro- portion in rates between competitive and non-competitive rates, and between rates on one class of freight and another, even for those classes of freight which do not seem to be affected by any immediate cause tending to have this effect. A clear indication of the existence of this law may be found in Tables 93-5. It is now too well known and generally admitted to require more pre- cise evidence. 55. There is one peculiar phase of the question of running by A TOWN TO SAVE DISTANCE which may be more appropriately con- sidered in this connection, as illustrating what has preceded, than in the chapter on Distance. Let us suppose, to take definite figures, that we have run by a town of ten thousand inhabitants in order to save a deviation of five miles from an air line, involving a loss of a mile or two of distance. As we have already seen in part, and shall more fully see (Chap. VII.), the railway's revenue account suffers heavy loss due to the decreased mileage on most of its local and through business, competitive and non-competitive. Per contra, its ex- CHAP. III.— CAUSES MODIFYING VOLUME OF REVENUE. 59 pense account is decreased indeed, but in very much less ratio. The probabilities are very strong that there will be a net loss to the revenue. This might well be borne if it meant, as in ordi- nary cases, simply *a reduction of the transportation tax upon the traveller or shipper of freight, but how stands it with the latter? They save, indeed (in the case of local traffic only, buf not in the case of through traffic), the two or three cents per mile which the railway loses, owing to its shorter line ; but they lose the entire direct cost of cartage or switching charges on their freight and carriage, express or horse-car fares for their own conveyance, besides suffering an annoyance and inconveni- ence in both cases which they will surely estimate at a good round sum: In money, when by the existence of competition they are able to throw the whole of both of these losses on the rail- way which seeks their patronage from a distance ; in refusal of patronage, except under great concessions or the compulsion of necessity, when through absence of competition they cannot otherwise shift the burden from their own shoulders. Thus, under any possible conditions, in such a case there is a triple loss: The tax on the public is greater, the receipts of the railway are less per passenger or ton, and the number of pas- sengers or tons is decreased. 56. The net losses might be estimated something in thisway^ assuming the town, say, to be in Ohio : Loss TO THE Railway. Loss of traffic per head, by being 5 miles instead of i from centre of population (say 40 per cent : Table 13), on a natural revenue per head of $10, or $100,000 from the town $40,000 Loss of revenue, due to one-mile haul on $60,000 of traffic — say three per cent • 1,800 $41,800 Per contra : saving of expense on same, at 40 per cent on the total ex- penses, or 26f (40 X I) per cent on the total revenue 11,148^ Net loss to railway $30>652 6o CHAP. in.—CAUSES MODIFYING VOLUME OF REVENUE. Loss TO THE Individual Patrons. Expenses of reaching the railway from a point 5 miles off, at 50 cents per passenger or ton, probably about $25,000 Less saving by reduced payments to the railway, as above 1,800 Net loss to the public $23,200 Destroyed business, which the public would have been glad to enjoy and pay for, as shown by experience, and which hence would have been worth its cost to them — say one third of the 40 per cent (as above) of $100,000, the rest going to some other line 13,300 Net loss special to the public, per year $36. 500 Net loss special to the railway, per year 30.652 Aggregate loss to the community, per year $67,152 Which means from the point of view of political economy, and as a plain statement of a fact which would appear in the census statistics, that the capital of the country and the world is less than it otherwise would be by the capital sum of which $67,152 represents the interest, or (at six per cent) $1,119,200 ; the whole of which is clear loss, by which no one is benefited. 57. A few hackmen and expressmen are, indeed, diverted from working elsewhere, where they would be true producers, into earning a support by performing what might have been a needless service. It is plain that by tliis diversion they are, individually, neither benefited nor injured, so that they simply •do not enter into the question at all, even from the point of view of political economy. We are not, however, studying political •economy, but the art of directing private investment in railway property so as to be profitable, not primarily to the general public, but to the projectors. Making'all allowances for possible errors in the precise fig- ures used above, it represents an immense loss to all parties from running railways by towns without going to them, so far as the traffic of that town alone is concerned, separately considered. There is, however, this further disadvantage to be remembered : if we lengthen the line to reach a town we necessitate that the CHAP. III.— CAUSES MODIFYING VOLUME OF REVENUE. 6\ .. — ■ • ' ~ ' '~' whole traffic shall be hauled over this extra distance in order to accommodate the traffic of one town. 68. This raises the general question of the value of distance, for which see Chapter VII. It need only be premised here, what has been in fact already said, that although, as a mere question of political economy, the cost of this extra haul is certainly a net loss, conferring no added value on the service rendered, yet to the revenues of the railway only, considered as a private enter- prise for profit, this is by n*o means the case, since there is always a credit as well as a debit side to the extra haul. It is not uncommon to hear engineers speak and act, indeed, as if the extra haul were a mere burden on the traffic : which would be true enough if railways were charitable institutions built by moneyed philanthropists with the sole purpose of serving the public, and which is always true with respect to that consider- able fraction of traffic on which neither the amount nor the dis- tribution of the gross rate is modified by the distance. But, as matters actually stand, it may be rudely stated here that, as the actual cost of such trifling -extra haul is very little, the net effect of such deviation for such a purpose is very apt to have a favor- able effect, if any (sometimes a decidedly favorable effect), upon the net revenue derived from the entire traffic, independent of that from the particular point for the sake of which the devia- tion was made, as well as upon the public interest. For one most important reason why this should be so, see Chapter XXI. 59. It is true that, in so far as the burden upon the general traffic may be increased, there is a tendency to compel the cor- poration to reduce rates on all traffic to the point which it will bear, instead of making non-competitive rates strictly according to distance ; and in urging that a railway will " get something for nothing" out of extra haul, the previous claim (par. 46 et seq:) may seem to be contradicted, that even slight burdens on traffic are dangerous ; but it is evidently a very different matter for a railway to take measures which make its own charges on all traffic a trifle higher to relieve a part of it from other and 62 CHAP. III.— CAUSES MODIFYING VOLUME OF REVENUE. heavier burdens, and to take a course which throws a heavy burden on its own traffic and on its patrons as well, by provid- ing facilities for a lot of outside parties — teamsters, hackmen, and horse-car lines — to extract a percentage forever of the total payments which the traffic has to bear. 60, Admitting, therefore, that differences of location may have a material effect on the revenue, it becomes important to remember that, as we have already seen, as small a difference as one per cent in gross revenue will 'ordinarily represent from three to six per cent in net revenue, and from six to twelve or fifteen percent difference in profits to the company proper, after their rental or interest charges have been met, even in the most prosperous companies, and from that up to many hundred per cent in those less favored. Remembering also that errors in the original laying out of the line, unlike errors in subsequent man- agement, are mainly irremediable, — a kind of fixed charge for folly forever, — it will be seen how large is the interest of the company who employ and pay the engineer in avoiding all errors of the kind, and how particularly important it is that no possible difference should be regarded as trifling because it will consti- tute a trifling part of the total receipts or expenses. It is only a small fraction of that total which " the company" has even the hope of retaining to itself. When the cream of their traffic, the profit traffic, is lost to them, all is lost ; and although it is often true that the busi- ness sagacity, or lack of it, with which the enterprise as a whole has been planned will overcome all that the engineer can do to make or mar it, so that the enterprise will succeed or fail in spite of him, yet it is always true that a heavy percentage of the surplus or deficit which alone concerns the company proper — enough, for instance, to make all the difference between a great success and a small success, or a great failure and a small fatlure — is strictly dependent upon the engineer and upon those, by whatever name they may be called, who decide with him, or for him, the semi-engineering and semi-commercial questions which we have here considered. CHAP. III.— CAUSES MODIFYING VOLUME OF REVENUE. 63 61. Therefore, with an end so important before us, any guide is better than none, in order that we may reduce the unavoida- ble uncertainty to its lowest terms ; and under these circum- stances a rule which the writer has formulated as a sort of gen- eral average to estimate exceptions from is this : As A MINIMUM : At the smallest and most inert non-competitive points the annual loss of revenue from placing the station at a distance Jrom town may be taken as equivalent to 10 per cent of the revenue tiat- urally originating from such a to7vn, with the station in afty given loca- tion, for each additional mile that the station is moved off from the xentre of the town. As A MAXIMUM : At centres of considerable manufacturing or com- mercial activity, exposed to considerable actual or potential competition, a fair and moderate estimate of the probable loss of revenue from re- moving the station to a distance will be 25 per cent of the revenue naturally originating at such a toivn, for each additional mile tliat the station is moved off from the centre of the town ; and this is frequently liable, in cases of very sharp competition, to amount to as much as ^o per cent of the natural revenue, including all the indirect effects of such disadvantages. The first of these estimates the writer has considered to be applicable to such towns as the average of interior Mexico. It is below any class of towns in the United States or Canada, ex- cepting the strictly rural regions consuming and producing little freight shipped by rail. The last is a fair average (varying how- ever within wide extremes) of all the busier towns and cities of the United States. 62. The causes of variations are : 1. Manufacturing and especially mining towns are usually heavy shippers. 2. Towns which are the seats of special industries often make payments to railways out of all proportion to their apparent size and activity. 3. The number of competing lines will greatly affect the pro- portion tributary to any one lin,e. And many other like causes. Nothing definite can be pre- 64 CHAP. IIL— CAUSES MODIFYING VOLUME OF REVENUE, dieted about any one town from any figures in this chapter, but for the average town they are believed to be fair. They are the result of much comparison of earnings by dif- ferent lines at large and small towns made by the writer at dif- ferent times, with an effort to estimate the true cause of their disadvantages ; but to attempt to defend them in detail, except as the volume as a whole may do so, would occupy too much space. Table 13. Estimated Effect on Revenue of Removing Stations from the Centre OF Population of Towns. CHAP. I I I. -CAUSES MODIFYING VOLUME OF REVENUE. 6$ Distance. Minimum. lo per cent per mile. Ordinary Maximum. as per cent per mile. K.VTRRMR MaYIMITM Miles. Difference. Per cent. Per cent. Difference. Per cent. Per cent. O I 2 3 4 5 6 7 8 9 lO lO.O 9.0 8.1 7.3 6.6 5-9 5.3 4.8 4.3 3.8 100. 90.0 81.0 72.9 65.6 59.0 53.1 47.8 430 38.7 34-9 25.0 18.75 14.06 10.55 7.91 5-94 4.45 3-34 2.50 1.87 100. 75.0 56.25 42.2 31.65 23.74 17.80 13.35 10.01 7.50 5.62 Very materially greater under certaia circumstances, especially with sharp* competition, so that a difference of two or three miles often means the loss of nearly the whole traffic. Av. revenue per head per year. j. $2.00 to $3.00 $8.00 to $15.00 Column I. — Average distance of station from centre of population. Columns 2 and 4.— Loss per cent of total natural revenue for each additional mile of distance. Columns 3 and 5.— Remaining per cent of natural revenue left to the company. The effect of this rule is presented numerically in Table 13^ the percentages being in geometrical ratio to each other, so that any number in the column, divided by the first or second or third number above it, gives always the same quotient. Under this table, the percentage of loss for each additional mile the station is moved away is the same under all circum- stances, although the absolute loss is much less as the distance increases. «• . 63. The above rule, it should be repeated, is not offered as in any way precise, or perhaps even safe. Such an estimate must always remain, for the most part, a question of judgment. That is tlie author's judgment. He claims no more solid basis for it than that in many single instances there has been an actual difference in the receipts of competing lines at the same point, or in the receipts of the same line at points at different distances from it, but otherwise very similarly situated, which closely cor- respond with the figures given. 64. As example of the working of the above rule, to run two miles off, instead of one, from the centre of a town of 10,000 people would involve as a minimum a loss of 9 per cent of the natural revenue from such a town, or froq? $1800 to $2700 per vear. If the town were an active business place this might easily be several times this amount, and if competition were a factor of the problem it would be very certain to be. If it were a question of running into a town instead of a mile away, the loss would also be liable to be very much greater than the Uble above indicates, since the stimulating effect of better transportation might change the whole character of the town, besides the natural effect of a given difference of distance. The question would be affected likewise by the character of the ter- mini, etc., etc. 65. As an instance from actual practice, two important Mexi- can towns, of a population of about 100,000 and 60,000 respec- tively, and about forty miles apart, with considerable natural traffic between them, were left distant respectively two and a half miles and four and a half miles from the nearest point of the projected line. It was a question whether to bring the rail- way nearer to the town, in which case both stations would be half a mile from the centre of population : If we might assume the above minimum to be correct, the certain loss on all the traffic contributed to the railway by these ^ CHAP. III.— CAUSES MODIFYING VOLUME OF REVENUE, towns, and not simply on ihe traffic between them, would be an. nually — $200,000 X o 19 = $38,000 120,000 X 0.344 = 41,280 Total ($217 per day) $79,280 For Mexican towns, in their present condition of imperfect material development, this is possibly large enough ; but for American towns of equal size and importance it would almost certainly be far too low. If it were to be considered as solely affecting the passenger traffic, and of such traffic only that exist- ing between the two towns, it would amount to the loss of sixty- five to seventy round trips per day, and this in the United States, between two active business points at that distance from each other, would be far from an exaggerated estimate. It would in such a case, however, be extremely erroneous to consider only the traffic between the two points. All the traffic originating or terminating at each point is more or less affected, the importance of the effect decreasing with the length of tiie haul. The freight traffic will also be materially affected, in some slight degree in volume, and a large proportion of it in average rates, for reasons already pointed out, the chief of which is that the railway sooner or later pays for the cartage. 66. Yet all these arguments, like almost everything else con- nected with the laws of trade, require to be applied with great caution, and are subject to many exceptions, such as these which follow : Towns will in many cases move to the railway, if the railway does not come to the town, with ultimate benefit to all parties concerned. This is especially common and probable in the United States, but it is more or less true everywhere. In pro- portion as the population and traffic may be expected to increase, the importance of accommodating the line to that which already exists becomes less and less. Even in a region tolerably well settled, but heretofore unde- veloped by railways, or imperfectly developed, a bold neglect of CHAP. III.— CAUSES MODIFYING VOLUME OF REVENUE. 67 existing centres, especially those of minor importance, will be exceedingly apt to bring them sooner or later to the railway in- stead of losing the railway their traffic; and this will be in some cases, where other lines are not likely to compete, the more apt to follow the more completely such points are left out in the cold. Especially when, by taking a central line between two subor- dinate centres of this kind, about as much will be gained from the one as lost from the other, the ultimate effect will probably be to build up a new town between both, affording new traffic, while still retaining a good proportion of that which remains at each of the old centres, and could have been fully secured from one of them only by wholly neglecting the other; thus sub- stantially increasing the aggregate traffic of the line. This amounts to saying that in seeking* to pass through the centre of the population, as in determining the centre of gravity, we cannot always consider one body alone, but must consider several as constituting one composite entity. 67. So, too, it is easily possible, in laying out branch lines or the parts or links of extended systems, to be so over-anxious to secure some trifling advantages of local traffic as to seriously burden and cripple other and much more important interests, or perhaps lay the line open in the future to destructive competi- tion. These various possibilities — con as well SiS pro — are very fre- quently the most important of those which fix or should fix the location of a line. Especially in easy country it may almost be said to be the rule that these will be important enough to over- rule engineering disadvantages of considerable moment, the ex- tent of which latter, therefore, it will often be waste of time to consider; and even in the most difficult country it will usually require marked and decided engineering disadvantages to justly overbalance any considerable advantages as respects probable traffic and revenue. 68. The question of the location of termini, and its effect upon traffic, is really closely allied to, and in fact a part of the 68 CHAP. III.— CAUSES MODIFYING VOLUME OF REVENUE,. CHAP. III.—CAUSES MODIFYING VOLUME OF REVENUE. 69 geneial question of how near to bring the line to towns, which we have just been discussing. Nevertheless, from the fact that the terminal towns are usually by far the most important on the line and likewise the most costly points to approach closely, sound business judgment is violated more frequently and more danger- ously at such points than at points along the line. Had it not so often happened that lines which have expended mil- lions for the construction of long lines to a certain place have tiien begrudged or failed to raise the necessary additional per- centage to carry their line into it, contenting themselves with; hanging on to the skirts of the town somewhere, where they caa be reached by horse-cars or hacks and drays, it would seem in- credible that business corporations could so frequently commit an act of folly which can fairly be paralleled with that ©f binild- ing a long bridge and erecting every span but one — assuming,, on account of some difficulty with foundations, or what not,, that a ferry would be good enough for that, because it would be "such a little one." The lines which do or have pursued this course will be found to be those which figure most prominently in the list of bankrupt corporations ; and the evidence of that fact is so patent to any one who will take a list of such and study it over, that it is needless to add more to what has been already said than to note the great sums which successful properties spend in reaching the heart of great cities to remedy former errors. 69. In England hundreds of millions have been expended for this purpose, and tens of millions at the smaller towns alone. In America we are far more backward than the best interest of the properties requires : but many such works have been recently carried through, one example of which is the new entrance of the Pennsylvania Railroad into the city of Philadelphia ; while at New York, Boston, St. Louis, and other cities similar improve- ments have been made or are being projected on a lavish scale. Certainly it has never been questioned that the Philadelphia ter- minus was an expedient investment, and we may be sure that it was not undertaken with any other view by the management of the company. It was executed almost wholly for the local con- venience of Philadelphia, and consisted in carrying in the com- pany's tracks on an elevated structure to a point very near to the centre of the city. It was, moreover, an expenditure to which the company was not driven by competition, except as to a small part of their traffic, for they had good facilities for both freight and passengers ; facilities as conveniently accessible as they well could be by horse-cars — that ever-ready excuse for neglecting to bring railway-stations into the centre of population. Some in- crease of space was indeed desirable, but it might have been se- cured much more cheaply in other ways, had the company deemed it expedient. The Philadelphia improvement cost about $4,590,000, of -which about half was for land only ; or about $5 per head of the population concerned, the interest on which at five per cent is about $225,000 per annum, or twenty-five cents for each man, woman, and child of the population — a sum which should be largely increased, perhaps doubled, for the indirect loss on in- vestments already made, and from operating expenses for haul- ing the whole traffic into and out of the new station, to which the system of roads centring there had not been originally adapted. It is to be presumed, of course, that the value of this improve- ment to the corporation is expected to be considerably more than this. Nor does such expectation seem unreasonable ; for, independent of all necessity for competition, experience at other points proves that it would be a paying investment, from its direct and indirect effect to encourage new traffic. In the company's report for 1881 it was stated — "The cost of this work is already having a marked effect on the develop- ment of local traffic ; and it is believed that, in addition to its great value to through and competitive business, it will in a few years, by its promotion of suburban trains reaching the park and other portions of the city, and its stimulus to the traffic before referred to, fully realize all that was contemplated at the lime of its original construction." At the time of this report there were some two hundred pas- senger trains into and out of Broad Street Station daily. There are now about fifty per cent more. 5 70 CAr<4/>. III.— CAUSES MODIFYING VOLUME OF REVENUE, 70. At New York a costly improvement was carried through at the joint expense of the city and the New Yoriv Central and Hudson River Railroad, costing some $8,000,000, in order to per- manently insure the running of fast trains to the Grand Central Station at Forty-second Street, which will probably hereafter be the heart of the population patronizing the railway, although for the present it is rather far up-town. The then existing passen- ger station at Twenty-eighth Street was abandoned, in part on account of the difficulties and expense involved in securing room at that point for the immense traffic to be handled, and in carry- ing the line to it, but in part because the point selected was deemed to be so near the future centre of the city. An addi- tional passenger station (mainly for suburban trains) is still maintained on the west side, at Thirty-second Street, as are also freight stations farther down-town on both the east and west side, to and from which cars are hauled by horses. 71. At St. Louis, a union depot for all the railways centring there was built in connection with the great St. Louis Bridge, the whole costing some $7,000,000; while there is hardly a city of any importance where smaller improvements of the kind are not projected by some one of the lines reaching it, at a largely increased cost over what would have been originally nec- essary; — without considering in this statement the heavy losses of traffic through the dubious early years of the company's his- tory which have enforced such improvements. On the other hand, there is no instance on record where adequate terminal facilities once acquired have been abandoned for others more distant and less valuable, because the market value of the prop- ertv was greater than its productive value in the hands of the company. 72. To apply the same ratio of expenditure as is incurred at the larger cities to smaller places might not in many cases be safe for these reasons : First, The average receipts per head of population increase very much faster than the population. (See Chap. XXI., and the various tables giving revenue per head of population.) CHAP. III.— CAUSES MODIFYING VOLUME OF REVENUE, 7 1 Secondly, At very large cities like New York, Philadelphia, Chicago, and Boston, the distinctly suburban traffic, making daily trips at commutation rates, is a large element, which espe- cially requires the best attainable terminal facilities and the largest possible saving of time. Table 14 gives some idea — in part, it must be confessed, a deceptive and imperfect one — as to how large a part these various works constitute of the total cost of railways of the first class, and how small an element is the mere construction to sub-grade between stations. See also Chapter XXVI., on ••Terminals." Table 14. Proportion and Amount of the Various Items of Cost of Road and Equipment. New York Central & Hudson River Railroad, 1885, 953 miles ; amount of track, 2.85 times length of line ; and in less detail for Pennsylvania Railroad, 1257 miles. New York Central & Hudson River. Pennsylvania. Items. Per Mile. Per Cent. Itkms. Per Mile. Per Cent. Grading and masonry Bridge Superstructure $22,000 31030 32,500 15.400 15.740 6,630 1.617 15,830 3,160 293 18.9 3.6 37.9 13.3- 13.6 5-7 1-4 13-6 3.7 •3 Construction Equipment Real estate and telegraph . . Total $30,400 19.300 10,130 50.7 323 Sutions, etc 17.0 $59,830 TfV) C% Land and land-damages.... Locomotives Stock $75,300 53,500 Passenger cars Freight cars Bonds • ■ • • Engineering Floating Equipment The Pennsylvania owns enormous amounts of the securities of controlled roads, repre- sented by its securities. Its policy has been Total $116,300 100. Stock Bonds 93,800 59iOoo • • • • • • • • to defray expenses out of earnings rather than increase canital acroiint The small proportion which the bare cost of laying down the track bears to the total investment, on lines of importance, is clear from the above. Thirdly. At almost all points in the United States the proba- bilities of future growth must be remembered., which will some- times, as at New York, bring a point which is, for the time being, 72 CHAP. III.— CAUSES MODIFYING VOLUME OF REVENUE. CHAP. III.— CAUSES MODIFYING VOLUME OF REVENUE. 73 i considerably outside of the centre of population into the very heart of it. Nevertheless, no town is so small that the considerations advanced are not more or less applicable to it, and the usual law of development, when topographical impediments do not forbid it, is that the town spreads equally in all directions, its centre of gravity remaining unchanged, as in the case of London, and measurably of Chicago, Philadelphia, and other cities ; in which case the disadvantages of having a terminus at a distance from that centre do not decrease with time, but increase in direct ratio to the population. 73. Although the impossible task of definite technical analysis of the revenue considerations here discussed has been passed by, it is hoped that enough has been said to impress upon the minds of engineers and projectors that they are entitled to great, if somewhat indeterminate, weight, and that it is unsafe for any engineer to enter upon the work of laying out a railway with no more thought: of its financial future than a vague idea that the passenger revenue is obtained by selling tickets, and the freight revenue is measured by the sum of the war-bills, and that neither is any concern of his ; his duty being simply to get the shortest, che^ipest, and straightest line, — the phrase has almost hardened into a formula, — and that when he has gotten it he has done his whole duty. It may be that he has, but it does not follow ; and the chances are good that he will have not only completely failed to do it, but will have involved the projectors in certain ruin ; because, although the amount by which the revenue can be mod- ified by differences of location, or even by differences in the sub- sequent management, is, as a rule, only a small percentage of the aggregate revenue, yet it is this small percentage alone in which the original projectors have a property interest ; that por- tion of the revenue which goes to pay fixed charges and operat- ing expenses being in no sense theirs. The strength of the argument for neglecting no effort to reach all possible sources of traffic is greatly strengthened by the considerations which it seemed more appropriate to discuss in Chapter XXL, but which have a very direct bearing on the sub- ject-matter of this chapter. 74. That the effect of comparatively slight causes to influence revenue has not been exaggerated, may perhaps be proved, as effectually as in any way, by a trivial incident which the writer knows to be authentic : A certain railway, for competitive reasons, determined that some marked improvement in its eating stations must be made to meet the competition of dining-cars on a rival line. The pro- prietor of one of these establishments, therefore, was instructed to make certain decided improvements in the appointments of his table, and in the character and quality of the viands provided, at the expense of the company, and to send in his bills from time to time for this additional expenditure. The bills not com- ing in, although the desired betterments had been (with some reluctance) made, and with results very gratifying to the com- pany, the proprietor was again requested to send in his bills ; when it appeared, on inquiry as to each item in succession for which he had been specifically instructed to increase his expen- diture at the expense of the company, that the proprietor was *' satisfied that it paid him," or that it was "no more than he ouirht to do," or that he was *' well enough contented as it was" — in short, that he had no bills to present. Such an incident, the details of which were precisely as stated, must be admitted to be an extraordinary instance of the power of conscience in a class who are not often given credit for having any, but it is also a proof that great direct advantages to the proprietor, as well as indirect advantages to the company, must have resulted. To fully appreciate its bearing upon those semi-technical questions which depend more or less on the peculiarities of human nature, two additional facts must be remembered. On the one hand — 1. A large fraction of the passengers have but slight reason to choose between one or another railway before beginning their journey ; while, on the other hand, 2. The journey once entered on, they have no choice what- <*/> 1 74 CHAP. III.— CAUSES MODIFYING VOLUME OF REVENUE. ever as to where to take their meals, but to take such meals as are set before them at the appointed stopping-places, or go hungry. The railway restaurant business is pre-eminently non- competitive. If, therefore, a trifling improvement in meals, which had never been really bad, could so materially affect the non-competitive business of a railway restaurant, what is the probable effect of the same and other slight causes on the traffic— especially on the receipts from that considerable class who travel a great deal by rail, but hardly make a really necessary trip more than two or three times in a lifetime ? With this attempt to solve by a parable an essentially inde- terminate problem, we pass to those branches of our subject which are often of less real importance, but which admit of more definite and technical treatment, and which, perhaps for that reason, are, not unnaturally, too often the only ones considered by members of a definite and technical profession. CHAPTER IV. THE PROBABLE VOLUME OF TRAFFIC, AND LAW OF GROWTH THEREIN. 75, It having been once determined that a railway is to be built at all between any two points, with the consequent /r/'w^- facie corollary that, excepting when and as reasons to the con- trary appear, it is to be the cheapest line over which trains can be run with due safety and speed, tlie probable nature and volume of the future traffic becomes the vital question ; for both the revenue and the operating expenses will vary in close ratio therewith, and only to increase the one or diminish the other are we justified in expending more money than proper security in handling trains requires. The more the traffic of a railway the larger the pecuniary saving from a given betterment in the rate and distribution of gradients, curvature, or distance — and the more, consequently, tiie justifiable expenditure to effect it ; the criterion beincj : Will a certain betterment, which is not an essential for the safe passage of trains, save the company more per year in operating expenses (or add more to the revenue, in the limited class of problems in which that question comes in) than it will add to fixed charges by the capital expended to effect it? If it will, the expenditure and betterment should be made ; if it will not, it should not be made. 76. To determine the probable volume of traffic with exactness is of course impossible ; nor is it, fortunately, particularly im- portant to do so, if we make a reasonably close approximation ; for the reason elsewhere discussed, that, with a judiciously located hne, the saving by adopting a poorer line than one naturally adapted to the topography is ordmarily not so great that any 76 CHAP. IV.—PROBABLE VOLUME OF TRAFFIC. CHAP. IV.— PROBABLE VOLUME OF TRAFFIC. 77 probable deficiency in the estimate of traffic would permit of it; while, on the other hand, the cost of defying the natural topo- graphical conditions is ordinarily too great for any probable excess in the estimate of traffic to permit of it wrongly. In other words, the danger lies in having no criterion, or in a false per- spective as to the relative importance of various ends, or in purely arbitrary decisions based on no investigation whatever, rather than in a certain percentage of error in our criterion. All that we need to do, therefore,— all that will have any important bearing on our action, as experience will soon teach, — is to bring reasonably near to each other the maximum and minimum probabilities, — "the limits of error in either direc- tion, somewhere within which lies the truth and anywhere out- side of which lies a certainty of error." This there is ordinarily no difficulty in doing. 77. In a rude way it can be done at once by any one at all familiar with railroad work. We know at once whether a line is more likely to have a light local traffic or a trunk-line traffic. It is but a step further to determine with very approximate exact- ness that a line will have somewhat more traffic than this or that or the other line near it, or similarly situated in other regions, and less traffic than as many others ; from which the establish- ment of a mean for the immediate traffic and its future growth is, with some knowledge of railroad business, a simple matter. 78. The greatest difficulty in making such estimates is ordi- narily the fact tiiat to make them it is essential to estimate and allow for the probable future growth of traffic, since it is rarely the case that a railway, especially in the United States, is built simply and only to accommodate the traffic*' in sight," as min- ers say. On the contrary, it has been and will continue to be frequently the case that the railway is relied upon not only to accommodate but to create a great part or the whole of the traffic for which it is built. Even when the population of the region traversed cannot, as it can in most parts of the United States, be expected to rapidly increase, experience has shown that if the surrounding territory has heretofore been but scantily provided with railway facilities, (i) the traffic of the first few vears will be but a small proportion of what would nominally be expected from a similar population elsewhere, and (2) that it Table 14i. Earnings Per Head of Population and Per Mile of the Railways of THE State of Iowa. Miles of Road. Population. Gross Earnings. Year. Total. In- crease. Actual or Estimated. 1 = 1000. Per Mile of Road. Totals. Per Mile Road. Per Head Popula- tion. 1862 626 653 727 ■ • • • 27 74 778. 830. 882. 1,243 1,271 1.212 $1,109,346 $1,772 $1.42 i86^ 1-570,546 2,405 1.89 1864 2.553,699 3-512 2.89 1865 847 I30 934- 1. 103 3,871.783 i 4,572 4 14 1866 1,060 1,328 1,448 2.081 213 168 220 533 t 986. + 1,038. t 1,040. t 1,142. 930 838 734 550 4.118.006 5,867,501 8.024.931 10.409.950 3.884 4,778 5-541 5.002 4.12 1867 5.65 1868 1869 7-36 9.12 1870... . 2,683 602 * 1.194.320 445 11,932,352 4.447 10.00 1871 3,160 3^643 3.728 3.765 477 483 85 37 t 1,231.600 + 1,270.100 + 1.309.800 + 1.350.700 389 349 352 359 1872 i9.i-s i°73 1874 1875 3.S50 85 * 1.393.000 362 1876 3.939 4.134 4.157 4-396 89 195 23 239 t 1,436 500 t 1,481.400 + 1,527.700 t 1.575.400 365 360 368 359 5-903 5-587 ^077 1878 (24.550,000) (24.500.000) 16.08 i879--.. 15 54 1880 4.977 58X • 1,624.615 327 (27.250,000) 5-491 16.80 i88i 5i426 6,337 7.01s 7.249 449 911 678 234 t 1,675.400 t 1,727.7-0 t 1,781.700 t 1.837.400 309 272 258 253 28,452,181 32,023.966 34,433,355 35,735,272 5-084 5.607 5,386 5,481 16.98 1882 18.54 1881 19-35 i88a 19.46 ♦ Actual. t Estimated. The tendency of earnings to increase about as the square of the population tied together by convenient means of transportation, discussed in detail in Chapter XXL, is very con- spicuous in this and the following table. may be expected for the first few years to have an abnormally rapid growth. Table 14^ shows this clearly. Even in a com- paratively densely populated State like Massachusetts, or in a country like England, which are neither growing rapidly in population nor ill provided with existing facilities, experience has shown (Tables 15 and 16) that the rate of growth is rapid enough (from 5 to 8 per cent per annum, as an average) to '-^'m- 78 CHAP. IV.—PROBABLE VOLUME OF TRAFFIC, CHAP. JV.— PROBABLE VOLUME OF TRAFFIC. 79 Table 15. Earnings per Head of Population and Per Mile of Road of the Railways of Massachusetts. Miles of Road. Population. Gross Earnings. Year. Totol. Per cent, in Mass. Actual and Estimated. I 1000. Per Mile Koad. Total (Thousands). Per Mile Road. Per Head Popula- tion. "845 463 97 837- 1.885 $2,8q5 $6,350 S3 -35 46 632 715 787 945 96 95 94 93 882. 909. 937- 965. 1.542 1,336 1,265 i.oq6 3.642 4.965 5.406 5742 5.850 6,950 6.890 6.080 4.23 A1 ....••••>. 5.19 ^8 5.43 49 5-54 1850 1.092 92 994 514 992 6.420 5.890 5.770 5.990 6,870 7.300 5.94 ri 1,142 1,150 T.164 i.«94 9« 90 89 88 1,016. 1,038. 1.060. 1,083. 978 1,003 1,013 1.024 6.600 6,886 7.977 8.696 5 91 3* <; 95 D' 6.70 33 54 •• 7.04 1855 1,281 87 1. 107. 972 9.077 7.090 7. II c6 1.325 1.351 1,380 1.380 86 85 84 83 1.130. 1,155- 1.180. 1.205. 960 972 973 993 9,750 9-094 8,597 9,771 7.370 7.360 6,230 7,080 7.42 5" 6.69 0/ eg 6.12 3" • • * 59 6.7s i860 1.37' 82 1.231 066 1.033 1.063 1,080 1,042 1,070 9.936 7.260 6.63 61 1,366 1,386 1,475 1.486 81 81 83 83 1,252. 1,273. 1,295- 1.317 8.669 9-655 11,711 14.981 6.340 6.960 7.920 10.100 5.63 63 6.09 61 7.21 "j 64 9 78 1865 1.500 83 1,340. 1.108 17-459 11.660 11.04 66 . • • 67 1.550 1,612 1,749 1.979 84 84 85 85 1,362. 1.385. 1,409. 1.433- 1.088 1.076 1.023 930 19.242 19.444 20,788 22,495 12.430 12,100 11.920 11.380 12 16 12.17 68 12.60 69 13-35 1870 1.475 1.457 351 988 13.220 13 40 .71 ........... 2,098 2.194 2.365 2,418 1,601 1,658 1.735 1.783 1.487. 1,517- 1,548. 1.580. 930 914 962 887 27.186 30,879 34.930 34.000 12.950 14.080 14.800 14.070 l?-94 72 14-30 73 74 15-38 15.88 1875 2.4S9 1. 817 1,612. 895 31.495 12.820 14-35 76 2,479 2,496 2,492 2,626 1.837 1.855 1,850 1.862 1.645. 1.678. 1.713 1-747- 896 903 927 941 29,856 28.932 38,003 29.153 12.070 11.620 11,250 11,100 i3-4ti 77 12.77 78 12.15 79 11.80 1880 2.667 1.893 1.783.085 945 33,662 12.640 •3.38 81 82 2-755 2.778 2.783 2.852 1.928 1.949 1.953 1,974 1.820. 1.859. 1.897. 1,937- 944 955 974 982 35.936 39.094 41,636 41.457 13.070 14.100 15.010 14,560 13-85 14.78 81 IS 40 84 14.86 The actual mileage in the State limits is not given previously to 1870, and an assumed percentage has been used to determine the population and earnings per mile of road. From 1870 to 1884 the earnings per head are computed by assuming that the average earnings jjer mile of road were no greater inside than outside the State limits, which is certainly incorrect, and on an average will probably make the earnings per head fen io Jl/teen per cent too small. From 1861 to 1870 inclusive the total earnings within constitute an element which might be legitimately considered in laying out a new line. The table embodying this English ex- perience is very instructive, as indicating a minimum of growth under settled conditions which no large section of this country is likely to fall below for many decades. In all but the rarest instances, it would be absurd to claim that no allowance should be made for future growth of traffic, and often it should be a very large one. Nevertheless, while, theoretically, large allowances for this future traffic are almost Table 16. Growth of English Railways and Railway Traffic % Miles. Capital. No. of Passengers- Millions. Ybar. Double or more. Single. Total. Total. I $1,000,000. Per Mile. I = $1000. 1855 6,153 6,690 7,711 8,338 8,898 9,803 10,239 2,182 3.743 6,143 7.038 7,760 8,130 8,625 8,335 10.433 13,854 15,376 16,658 17,933 18,864 1446. 1692. 2213. 2574- 3061. 3537. 3892. 1734 164.0 166.6 165-7 183.8 197.2 206.1 118.6 I860 1634 1865 251.9 1870 336.5 1875 507.0 1880 1884 603.9 695.0 Receipts. Per Cent Oper- ating Expenses. Per Cent. Net Ybar. Total. Millions. Per Mile of Road. Per Train Mile. Per Cent from— Receipts to Pass. Freight. Capiul. 1855 $ 104.6 134-8 174.4 3I0.8 386.3 306.0 328.8 % 12,530 12,930 13.120 13,570 17,200 17,040 17,440 cts. 140.6 131-5 125.0 124.4 136.5 127.2 131.3 49-7 47.1 46.3 42.8 43.0 41-S 43.6 50.3 50.9 53-8 53-5 54.3 54-6 53.4 47 48 48 54 51 53 • • • • I860 1865 4 19 4.11 1870 4-41 1875 4-45 1880 1884 438 4.16 Compiled from the Board of Trade returns. the State were given separately. Previously to 1861, the total earnings divided by the population of the State was multiplied by the assumed per cent of mileage within the State limits for the earnings per head. The compilation for the years preceding 1871 was abstracted from an old volume of the Railway Times. See also Tables 21 to 26, 83, and various others for indications as to growth of traffic. '^^ 80 CHAP. IV,-^PROBABLE VOLUME OF TRAFFIC, CHAP. IV.— PROBABLE VOLUME OF TRAFFIC, 81 always justifiable, it is for practical reasons so exceedingly dan- gerous as to amount to absolute folly for an average American, corporation, even of the more prosperous kind, to look ahead for more than from three to— at most— ten years for the " rapidljr increasing traffic" which is to justify an increase of present expenditure over what the prospects of the present and the im- mediate future will justify. 79. Let us see why this is so. The theory of the subject is simple: In Table 18 is given the present value or present justi- fiable expenditure to save $1 (or one unit of any other value)- 'at the end of any given period at any given rate of interest; that is to say, the sum which, if placed at compound interest now, will produce $1 at the end of the specified period. This fact given, it logically follows, that if the value of a given betterment for a'given immediate traffic be $1, the present value of the same betterment for an equal traffic which is to exist only in the future will be that sum which at compound interest will produce $1 when the assumed traffic comes to exist. If, for example, we expect the traffic to double in ten years, we may spend for a betterment worth $1 to the present traffic, $1 + the sum which will produce $1 at the end of ten years, which latter is at 7 per cent (Table 18) 50.8 cents; so that under these conditions (which would apply to most new American lines) we should be war- ■ ranted in spending 50.8 per cent more money to effect givea betterments than we would for the traffic "in sight." Table 17. Value of $i placed at Compound Interest for a Term of Years. With Interest at— Years. 3 i 3H per cent, per cent. 3H percent. 4 per cent. 5 per cent. 6 per cent. 8 per cent. 10 per cent. X 9 3 4 1 \ X.06 1.09 X.X3 1.16 X.19 x.as X.27 1 30 1.06 1.10 X.14 1. 18 X.32 X.96 J -30 1-34 I 03 1.07 I.IZ X.IS X.19 X.23 x.a7 1.32 1.36 X.04 X.08 Z.12 X.17 1.23 1.27 1.39 1-37 1.42 x.05 I.IO X.16 x.aa 1.28 1-34 X.41 1.48 1-55 x.06 1. 12 1.19 i.a6 1-34 1.42 x.50 1-59 1.69 x.08 1. 17 x.26 x.36 x-47 x.59 1.71 1.85 2.00 X.IO 1.21 ».33 X.46 x.6x »-77 1.9s 2. 14 2.36 10 1 1.34 i 1-38 i.4t 1.48 1.63 I 79 2.16 a. 59 Table 17. — Continued. Value of $i placed at Compound Interest for a Term of Years. With Interest at — Years. 3 percent. 3^ per cent. per cent. 4 percent. 5 per cent. 6 per cent. 8 per cent. 10 per cent 10 1-34 1.38 1. 41 1.48 1.63 1.79 2.16 2 59 II 12 «3 X4 X5 16 17 18 19 1 38 1-43 1-47 »-5» 1.56 1.60 X.65 1.70 »-75 1-43 1.48 »-53 1.58 1.6^ 1.68 1-74 1.80 f.86 1.46 1. 51 1.56 1.62 1.68 1.73 1.79 1.86 1.92 1-54 1.60 1.67 1-73 1.80 1.87 X.95 2.03 2.11 1. 71 1.80 1.89 1.98 2.08 3.18 2.29 2.41 2-53 1.89 2.01 2-'3 2.26 2.40 2-54 2.69 2.85 3 03 2-33 2.52 2.72 2.94 3-17 3-43 3-70 4.00 4-31 2.85 3-«4 3-45 3-7^ 4-»7 4.60. 5-05 5-55 6. 11 20 1. 81 »-93 1. 99 2. 19 2.65 3-21 4.66 6.72 21 22 83 94 25 36 37 28 2q 1.86 1.93 1.97 3.03 3.09 3.16 3.32 2.39 2.36 1.99 3.06 2.13 3. 30 2.37 2-35 2-43 2.51 2.59 3.68 2.06 3.13 3.21 2.28 2.36 2.45 2-53 2.62 2.71 2.28 2.37 2.46 2.56 3.67 2.77 2.88 3.00 3" 324 2.79 2-93 3.07 323 3-39 3-56 3-73 392 4.12 3.40 3.60 3.82 4-05 4.29 4-55 4.82 5-" 5-42 503 5-44 5.87 6.34 6.85 7-39 7-99 8.62 931 7-39 8-13 8.04 9.83 10. 8i 11.90 13.08 14-39 15 83 30 2-43 2.81 4 32 5-74 10.06 17.41 3« 3a 33 34 II 37 38 39 a. 50 3.58 3.65 3.73 2. 81 2.90 3.99 3-07 3X7 3.77 3.86 3.96 3.06 3.16 3.27 3-37 348 3.60 2.91 301 3" 3-22 3-33 3-45 3-57 3 70 3.83 3-37 365 3-79 3 95 4.10 4.27 4-44 4.62 4-54 476 5.00 525 5-52 5-79 6.08 6-39 6.70 6.09 6.45 6.84 7.25 7.68 8.15 8.63 9-15 9.70 10.86 11.74 12.67 13-69 14.78 15.96 17.24 18.62 20.11 21.72 19-15 21.06 23.17 25-45 28 03. 30.83 33-91 37 • ^0 41.02 40 3.26 372 3 96 4.80 7.04 TO. 28 45-12 4» 44 46 48 3.67 3.90 4»3 3-97 4-23 4.83 424 4-54 487 5-2' 5-'9 5-62 6.07 6.57 7.76 8.56 9-43 10.40 11.56 12.98 14 59 16.39 25-33 29-54 34-46 40.19 54-59 66.04 79.90 96.67 60 4.38 5 »5 5.58 7. II 11.47 18.42 20 70 23.25 26.13 29.36 46 88 117.0 5a 54 ^\ 58 4.65 4-93 523 5-55 5-So 587 6.27 6.70 5 98 6.41 6.87 7-35 7.69 8.31 8.99 9-73 12.64 1394 15-37 16.94 54.68 63.78 74-39 86 77 i4»S 171.2 207.1 250-5 60 589 7 IS 7.88 10.52 18.68 32 -99 101 .2 30?-! 6a «4 66 68 6.25 6.63 7 03 7.46 7.64 8 15 8.71 930 8.44 9.04 9.68 10.37 11.38 12.31 13-31 14.40 «5-57 20.59 22.70 25-03 27 60 37.06 41.65 46.79 52.58 118.0 137-7 160.6 187-3 366.7 443-6 536- r 649-4 TO 7.Q2 9-93 11.11 .30.43 3883 40-56 63.25 80.73 5Q-o8 218.5 785 6 2 85 QO 9.18 10.64 12-34 M-30 It. 69 1378 16.23 »9 »3 13.20 15.68 18.62 22.11 18.95 23-05 28.04 3412 79.06 105.80 141.58 189-47 321.0 471.6 693.0 1018.1 1265. 2036. 3278. 5277- 100 19 22 26 55 31.19 50.50 131 50 339-30 2197-9 13677- Formula: 5" = (i + r)«, in which r amount of $1 at compound interest. z= rate of interest, n = number of years, and S = 82 CHAP. IV. -PROBABLE VOLUME OF TRAFFIC, Table 18. Present Justifiable Expenditure to se- cure A RETURN OF |l AT THE EnD OF ANY Number of Years. With Interest at — Table 19. Saving per Annum which WILL IN THE Aggregate AMOUNT TO |I at THE End of a Term of Years. With Interest at— 5 I e per per cent. cent. CHAP, IV.— PROBABLE VOLUME OF TRAFFIC, 83 Table 18. — Continued. Present Justifiable Expenditure to se- cure A Return of $i at the End of ANY Number of Years. Table 19. — Continued. Saving per Annum which WILL IN THE Aggregate amount to $I AT THE End of a Term of Years. With Interest at — Years. With Interest at — Years. 3 per cent. 4 per cent. 5 per cent. 6 per cent. 7 per cent. 8 per cent. 10 per cent. .009 3 per cent. 4 per cent. 5 per cent. 6 per cent. 60 .228 141 087 .054 •034 .021 50 .009 .006 .005 .004 .004 .cx)3 .003 .003 52 58 •215 .203 130 120 lit 103 079 072 065 059 .048 .043 .038 .034 .030 .026 .023 .020 .018 .016 .013 .012 .007 .006 .005 .004 52 54 56 58 .008 .008 .007 .006 .006 .005 .005 .004 .003 .003 .002 .002 60 ! .170 095 053 .030 .027 .024 .021 .019 017 .010 .003 60 .006 .004 .003 .002 63 64 66 68 .160 •'5» .142 •134 088 o8r 075 069 049 044 040 036 .015 •o»3 .011 .010 .008 .007 .006 • 005 .c»3 .002 .00a .002 62 64 66 68 .006 .005 .005 .005 .004 • 003 .003 .003 .002 .002 .002 .CX32 .002 .001 .001 .001 70 . 126 064 033 , .017 .009 .004 .001 70 .004 .003 .002 .C»I 75 80 85 90 .109 .094 .081 .070 053 043 036 029 026 020 016 012 .013 .009 .007 .005 .006 .004 .003 .002 .003 .002 .001 .001 .oot .000 .cwo .000 75 80 85 90 .004 .003 .003 .002 .002 .002 .001 .001 .001 .001 .CXJI .001 .001 .001 .000 .000 100 .052 020 008 .003 .001 .000 .000 100 .002 .001 .000 .000 Table 20. Showing the Justifiable Present Expenditure to save $i per Annum FOR various Terms of Years at various Rates per Cent for Capital. Term Justifiable Present Expenditure with Interest at — OF Ybaks. 3 per cent. 4 per cent. 5 per cent. 6 per cent. 7 per cent. 8 per cent. 9 per cent. 10 per cent. I 2 3 $o-97 1.91 2.83 $0.96 1.89 2.78 $0.95 1.86 3.72 $0.94 1.83 2.67 $0.93 1. 81 2.62 $0.93 2.58 $0 93 1.76 2.53 $0.91 1-74 2.49 4 1 3.72 4.58 542 363 4-45 • 524 3-55 3-47 4.21 4.92 3-39 4.10 4-77 3-31 3-99 4.62 3 24 389 4-49 3-17 3-79 4.36 \ 9 6.33 7.03 7-79 6.00 6.73 7-44 .S.79 6.46 7. II 6.21 6.80 5-39 5-97 6 52 5-21 5-75 6.25 5-03 5-53 6.00 4.87 5. 34 5.76 10 8.53 8. II 7.72 7 36 7.02 6.71 6.42 6.14 II 13 »3 925 9-95 10.64 8.76 9-39 9.99 8.31 8.86 9-39 7.89 8.38 8 85 7-50 7-94 8.36 7-14 7-54 7.90 6.81 7.16 7-49 6.50 6.81 7.10 16 XI. 30 "•94 13.56 10.56 II. 13 11.65 9.90 10. 38 10.84 930 9.71 10. II 8.75 9. II 9-45 8.24 8.56 8.8s 7-79 8.06 8.31 7-37 7.61 7.8J »7 18 «9 13.17 »3-75 «4-32 13.17 13.66 1313 11.27 11.69 12.09 10.48 10.83 11.16 9.76 10.06 10.34 9.12 9-37 9.60 8.54 8.76 8.95 8.0a 8. 30 8.37 20 14.88 ^3-59 12.46 11.47 10.59 9 82 9.13 8.51 84 CHAP. IV.-^PROBABLE VOLUME OF TRAFFIC. Term OF Years. 20 31 aa "3 26 27 38 29 30 31 32 33 34 35 36 38 39 40 41 42 43 44 45 46 47 48 49 60 55 60 65 _7^ 76 3 per cent. 80 85 90 95_ 100 Perpetuity 14 88 15 42 15-94 16.44 16.94 17.41 17.88 18.33 18.76 19.19 19.60 20.00 ao.39 20 77 21.13 21.49 21.83 22.17 22.49 22.08 23.12 23.41 23.70 23.98 24 -25 24-52 24.78 25-03 25.27 25-50 25-73 26.77 27.68 28.45 29.12 29.70 30.20 30-63 31-00 31^32 33-33 Table iq,— Continued. Justifiable Present Expenditure with Interest at— 4 per cent. 31-60 13-59 1403 14-45 14.86 15-25 15.62 15 98 16.33 i6.66 16.98 17.29 17 59 17.87 18.15 18.41 18.67 18.91 19.14 19-37 19-58 19.79 19.99 20.19 20.37 20.55 20.72 20.89 21.04 21.20 21.34 21.48 92.11 22 .62 23-05 23.40 23.68 5 per cent. 23.92 24.11 24.27 24.40 24.5 1 25.00 13.46 12.82 13.16 13-49 13.80 14.09 14-38 14.64 14.90 15-M '5-37 15-59 1580 16.00 16.19 i6-37 16.55 16.71 16.87 17.02 17.16 17.29 17.42 17-55 17.66 17-77 17.88 17.98 18 08 18.17 18.26 18.63 18.93 19.16 19-34 19 49 6 per cent. 19.60 19.68 19-75 19.81 ^9-85 20.00 11.47 II 76 12.04 12.30 12.5s 12.78 13.00 13.21 13.41 13-59 1377 13-93 14.08 14.23 14-37 14 50 14 62 14-74 1485 14-95 1505 1514 15-23 I5.3« 15-38 1546 15-52 15-59 15-65 15-71 15-76 15-99 16.16 16.29 16.39 16 46 16.51 16.55 16.58 16.60 16.62 7 per cent. 8 per cent. 16.67 10.59 10.84 11.06 11.27 11.47 11.65 11.83 11.99 12. 14 12.28 12.41 12-53 12.65 12-75 12.85 12.95 13-04 13.12 13.19 13.26 »3-33 13-39 13-45 13-51 1356 13-61 1365 13.69 13-73 13-77 13.80 13-94 14.04 14.10 14.16 14.20 14.22 14-24 14-25 14.26 14.27 14.29 9.82 10.02 10.20 10.37 10.53 10.67 10.81 10 94 11.05 11.16 9 per cent. 11.26 11-35 II 43 11.51 "•59 11.65 11.72 11.78 11.83 11.18 11.93 11.97 12.01 13.04 12.08 12.11 12.14 12 16 12.19 12.21 12.23 12.32 12.38 12.42 12.44 13.46 12.47 12.48 12.49 12.49 12.49 12.50 9-13 ID per cent. 8.51 9-29 9-44 9.58 9.71 9.82 9-93 10.03 10.12 10.20 10.27 8.65 8.77 8.88 8.99 9.08 9.16 9-24 9-31 9-37 943 10.34 10.41 10.46 10.52 10.57 10.61 10.65 10.69 10.7? 48 53 57 .61 ,64 .68 10.76 10.79 10. 8r 10.84 10.86 10.88 10.90 10.92 10 93 10.95 9.71 9-73 9.76 io.96_ 11.01 11.05 11.07 IJ.08 09 10 10 11 .11 .11 9-78 9.80 9.83 9.83 9.85 9.86 9.88 9.89 9.90 9. 91 9-92 II. IX 9-95 9-97 9.98 _9:99. 9-99 10.00 10.00 10.00 10.00 10.00 xo.oo This table gives simply the capital sum which will— (I) Return $i per annum in interest during the given term ; and, (2 Return an additional sum in interest each year which, placed at compound interest at the same rate, will extinguish the principal at the end of the given term. At 10 per cent for capital it is worth spending but twice as much to ensure a saving of $, p^r anrum for ever as to ensure it for 7 years only. At the much higher rates whid. people often wish to be assured of before spending money in new enterprises it is worth practically nothing to save money more than 6 or 8 years ahead. CHAP. IV.— PROBABLE VOLUME OF TRAFFIC. 85 80. All this is undeniably correct in theory, except, indeed, that it understates the case ; for we might enter into further mathematical subtleties, and prove that if the ratio of growth of traffic is greater than the rate of interest on capital, the present justifiable expenditure to provide for such increase of traffic is infinite. But this, while an excellent exercise for the student, we shall not attempt to do ; confining ourselves instead to the more profitable work of pointing out the reasons why, with any •ordinary corporation, all such speculations are wholly delusive, •so that even the indications of Table 18 are of value only as fixing a maximum which should never be exceeded. 81. The first and most vital reason is that, while it may be taken as a practical certainty that the traffic of any ordinary Tailvvay not only will grow, but that it will grow at an average rate of something like 5 to 8 per cent per annum east of the Alleghenies, and 7 to 10 or 15 or even 20 per cent per year west of there, yet that the rate of this growth of traffic is excessively variable and uncertain— liable to cease altogether at any time for many years, and at periods when it is particularly inconvenient to put interest on discounted expectancies. For this cause alone it is in general inexpedient to look forward more than at most five years for traffic to justify an increase of immediate expenditure; and when, as is of course more likely to be the case, a new project is floating upon the top of a " boom" or upward wave in the tide of business, it is unsafe to look ahead more than two or three years. It is at such times especially to be remembered that the wave may begin to flow backward at any time, and that even if it do not, the line is built with borrowed capital, and that it is difficult for the average financier to borrow large sums on future expectancies; nor can he in any case borrow $2000 per mile as cheaply as $1000 per mile. Borrowed, however, the money must be if the first supply gives out, or the whole investment of the original company will probably be lost ; and the instances are rare in which any large proportion of the entire capital has been positively secured before the surveys are substantially complete and construction in progress. 86 CHAP, IV.— PROBABLE VOLUME OF TRAFFIC. CHAP. IV.— PROBABLE VOLUME OF TRAFFIC. 87 82. A sequence of events which has been again and again repeated is that the company shall enter upon the work with vague visions of boundless prosperity, and look with certainty to securing " all the money they need;" shall encourage their engineer in a costly style of construction which, with the natural preference of an engineer for massive, durable, and stately works, he is all too ready to adopt ; and finally, often within a ridicu- lously short time of the period of their brightest hopes, be left stranded by the ebb-tide of speculation, a complete and helpless financial wreck. 83. Finally, there is another and still stronger reason why the growth of traffic should not be counted on for many years ahead in designing the works. It is usually a simple matter to so design large parts of the line, including most of the more expen- sive works, that their construction may be postponed until a more convenient season— a possibility so important that it is separately discussed hereafter (Chap. XXIII.). By so doing we at least make sure of keeping the capital account at a minimum and of (usually) retaining the line in the hands of the original company; while, when all causes are considered, the loss from postponing the execution of all more costly work which can be postponed will not be very great, even if one's brightest dreams are realized — which will rarely be the case. 84. We may conclude, therefore, that although a railway corporation which has in truth as well as in imagination un- limited means ; which is able to look ahead with certainty for a long period of years ; which is able without doubt to tide over long periods of depression without danger to its stability, and which has no anxiety to realize present profit, or even avoid present losses, on investments which will be ultimately profit- able ;— although such a corporation may legitimately make a large increase in its investments for the sake of a traffic which is still in the distant future, yet that no ordinary corporation can afford to look ahead more than two to five years for the traffic to pay interests on increased investments, and that even in that case they take much risk in doing so. Traffic should therefore. in ail cases, be rather under- than over-estimated, to the end that in no case extravagant expenditures shall be made for a costly perfection of alignment which the traffic will not justify : bearing in mind that an under-estimate of admissible expenditure is simply a failure to invest a small (or it may be, large) additional sum of money which would have earned good interest, but which may be invested later at nearly if not quite as good advantage ; whereas an over-liberal investment of additional sums on which interest cannot be earned greatly endangers, in the trying years which usually come soon after the line is opened, the permanency of the whole investment. In the one case, our economy only tndangers a minor loss, if the enterprise as a whole turns out well ; and if it does not, may save it from ruin. In the other case, our extravagance only gives us a fair investment for a little more money if all goes well, and if it does not, may be the ounce of additional load which breaks the back of the enterprise. Our only grave dan- ger, therefore, is of error in one direction only ; which makes it the easier to make an estimate of traffic sufficiently exact for all important purposes — that is to say, one which will be certainly not too large. 85. Tables 21 to 27 give various statistics of the growth of American railway traffic, such as are likely to be useful for checking in a rude way the estimated growth of traffic on any line. The most accurate and satisfactory method for estimating both traffic and expenses in any given case, however, is com- parison with the experience of neighboring roads of the same general character, because it is much easier to count on a line doing so much better or worse than another line, than to esti- mate the absolute traffic independently. Tables 23 to 27 inclusive, for the groups of States, cover a period extending from one period of business activity to another, with a severe depression be- tween. Table 28, for the whole United States, covers two preceding and four following years likewise, and by comparison with this table the general course of traffic and earnings for the same additional years can be determined with approximate accuracy. All these tables were computed from the statistics of Poor's Manual. 88 oo CO CO oo z O H O (d > pa tn U H on . Q CM H C>y^/>. jv.— PROBABLE VOLUME OF TRAFFIC. z Cd fa O tf) < (d •fa O x/i H en *« H 00 00 H R >*• M 8 8 8 8 8 8 8 so NO »r lo N 00 VP c« in •* m >o »o vo 00 ■>•■ T iri 0> UI "• 0> lO 00 t^r»r^''>t» r'2> WW " 00 00 M 00 M tn 00 '^ r^ r^ 00 m '0 ro vO 00 r* f. vO vO NO VO VO N H C4 O •* o 00 w 00 \n 00 ■♦ M N •♦ M IT) •* vO N H M M lO 00 M lA fl 00 NO o iri rfl r^ •* o t^ ro NO t^ fi •» N »o . • • • • • • M • • • ;j K M <^ f, "0 ^^ * \o»>.no'c5>o>*' «o VO (4 8t^ •* O * 00 ♦ ^ ^ S ,>. -ir, VO in O « f^ "O f^ 00 w ro « 8 1 N vO 00 ON I NO VO On ^ lO ON VO ON r» « »- ^ "1 cS ^ « « o» en On s r« 00 w ro - o 2 8- N O S 00. >n op ^ On NO «0 vO NO r^ O ►< On M 00 o- Z 2 (/3 2 b 04 c "St c 8i C -o *J to ^ c ?? *> «/) « •- o d = d °' rt CO oo oo 00 W3 Z o »^ O U C/) >« PQ en . w 5i V5 8t C z D Cd CI K (d H .J fa n O < rn h >• < Cd K H fa O . IV.—PROBABLE VOLUME OF TRAFFIC. 89 00 00 H Z u S a. D C td S ^ I Ul I > as a: u o: - O^ ^ u < z Sll en ^^ S£wii CC a. ^ M 00 m r^ 00 W t>. VO CO ro w •* VO « n "T VO u>2 r«. wi NO t^ r« On m VO e* Ul w M «n c u ti c 5d NO rri CI 00 »>. NO w rv t^ 00 c-i 1^ •>*■ t^ M NO 00 CO w s M u cQ «1 w Ul 00 * 00 N w 00 On ■♦ Ul Ul M Ul ■^ 0> 00 10 eT in w CO ■ en £l3.S he CO Ul 00 M CO f CI On VO O ■«; O; M VO cT tC Ul C.2 « a VO f< vO O' 00 00 00 !;nS NO VO ►« en O o o o 11 Ul O Q O Ul W NO II M CO 00 4» Ul t«. NO CO M M W 4.8 , o ro N ON -°- v8 00 Ul IT) Ul « C/l O O o Ul Ul 00 •♦ •* NO VO u o (/3 On m CO CO ■♦ ■<«- 00 CO M CO (0 C o ca CO O M CO Ul NO 00 VO M •-> NO HI VO CO ►>■ VO CO 00 o o c be c Cd « s it "^ - « "- 6 ^ ^ S n • rt etf (/i Zt U< Pi NO CO NO CO N >♦• VO t^ CO CO '#■ N m 8 CO N ON ^ ON Ul c« 1^ >«• r^ M CO NO Ci •«■ t». W W 0> t^ M ■«••<• fO Ul CO ei Ul no' NO •♦•♦VOOO 000 •* OnCOO^m O OncOi- in o^ On o_^ 00 M 00 00 cT vcT CO i-T M 8n PI C* 00 O O NO ■<»- Ul On Ul Ul Ul >♦• NO M r>. Q p* CO ■♦ NO On ro ON in •* Ul VO v8 Ul PI NO CO On l-i VO H M 1^ 8 NO PI •♦ t^ m PI ■♦ 00 CO NO On Ul Ul « On 00 PI M M »^ m M VO o U Ul CO PI t^ M- NO Ul M Kl M M 06 6 on6 uit^O\o t^vo r^m"ivo t>»t-> 00 ►" Ul CO ■•♦■ ■>«-'»■ >n O PI PI no" t^ 00 « f> PI PI p^ »-« 00 NO cr- NO 00 Ul NO On 00 PI Ul PI M t^ PI M Ul On O C< t^ On vO K O rv Ul NO 00 Ul ■♦ ■♦ 00 M 00 c« O PI M 00 Ul w CI w « »n PI VO 00 C c •3 O *j c C/5 ? o IS ^ w o o O rt ! 90 C/M/'. IV.— PROBABLE VOLUME OF TRAFFIC. CHAP. IV.— PROBABLE VOLUME OF TRAFFIC. The groups of States are those of Poor's Manual, which see for the years 1882 and 1886 for details. The population used for the first part of the Table (1881) was that of the Census of 1880, which was about three per cent too small. . ^ .. r By a different estimate, the number of inhabitants, of acres m gram and cotton, of bushels of grain and bales of cotton produced, per mile of railway, have been as follows for the last seven years, in all cases taking the mileage and population at the close of the year and the crops, etc., of the previous summer : Popu- lation. Acres. Bushels of Grain. Bales of Cotton. 1879 1880 581 545 509 473 466 458 461 1,565 1,466 1.359 1,236 1,204 1,216 1,216 31,600 28,932 19,804 23.405 21,563 23,690 23,241 67-73 70-53 52.65 60.18 47.00 45-44 1881 1882 1883.... 1884 1885 50.41 Table 22. Statistics of Revenue Per Head of Population and Per Mile FOR Each State Separately— 1881. [These statistics are based upon the same figures as those given for groups of States onlr in the first part of Table 21. The division of the miles of road operated between the dif^ ferent States is not exact, so that the figures can be regarded as approximations only.] Per Mile Railway. Maine New Hampshire. Vermont Massachusetts. . . Rhode Island... Connecticut Square Miles. 32.0 10.3 12.2 3-47 8.55 5- II New England. New York New Jersey Pennsylvania Delaware Maryland and D. C. . . . W. Virginia Popula- tion. II. O Middle States. 7.67 5.00 6.81 9-75 9.60 100.5 8.60 593 387 397 793 1,810 670 650 Per Cent. Sidings. 19.0 17.6 15.4 63.0 46.5 35.0 Per Cent. Operating Expenses. 848 679 633 677 485 271 775 37-4 75-3 79.6 64.6 69.0 64.0 80 71 61 64 70.0 Gross Revenue. Per Mile Railway. Per Head Populat'n. $4- 130 5.200 4.690 10.200 9.200 9.650 $6.54 10.90 12.40 16.50 5-90 16.00 52.2 193 67-3 61.0 63.9 61.5 70 60.7 83-4 8.420 62.9 13.000 6.850 15.800 2.880 5-490 3.670 14.000 13-10 15.90 28.10 23.70 4.08 12.30 13-60 18.50 91 Table 22. — Continued. Per Mile Railway. Per Cent. Sidings. Per Cent. Operating Expenses. Gross Revenue. Square Miles. Popula- tion. Per Mile Railway. Per Head Populat'n, Virginia 15.3 31-4 25.2 22.1 70.7 22.0 100.3 26.0 24.0 13-4 602 228 738 586 344 551 2,470 594 811 569 13.0 6.4 7-1 7.7 5-0 8.6 5-4 II. I 22.0 13. 1 65.6 66.5 68.0 60.7 62.8 69.9 65.9 71.0 67.7 55-8 5-590 2-590 3-250 3.740 3.210 4.150 3-320 8.080 4.500 5-590 7.00 2.70 4.04 6.14 1. 61 N. Carolina S. Carolina Georgia '. Florida Alabama 6-43 1.03 10.40 4.36 5.90 Mississippi Louisiana Tennessee Kentucky Southern States 25.7 681 10.9 65.0 4-550 5.20 Ohio 5.08 13.9 5.65 5.20 10.2 21.0 14.3 24.2 202 400 331 288 249 199 478 718 29.6 29.6 27.0 27.0 10.6 7.0 II. 4 9.9 62.8 68.2 76.5 54-7 59-7 61.4 54-0 64.0 8.790 5-850 5-750 7.560 3 -930 4 -370 7.000 3-570 20.50 12.40 17.30 29-05 14.70 15.90 13.60 3.92 Michigan Indiana Illinois Wisconsin Minnesota. Missouri Iowa N. W. Central States. 9.90 351 21.3 60.9 6.520 17.60 Nebraska 226 303 254 283 95 1,200 309 17.0 53-7 1. 160 Wvomincr Dakota Kansas 7-5 5.9 5-9 3-9 62.8 61. 1 58.5 68.0 5-170 6.530 3.960 4.480 Colorado 46.90 Arkansas Texas FarW. andS. W.... 61.9 310 7-1 60.2 6.420 16.10 New Mexico 230 104 148 140 301 230 Arizona Utah 13-7 49-3 53.8 49-5 56-4 Nevada California 8.620 Oregon Pacific States 181. 261 9.6 49.9 (7.500) 23.15 United States 29.0 481 25.1 61.9 7.690 14.50 '■( 92 CHAP. IV.— PROBABLE VOLUME OF TRAFFIC. CHAP. IV.— PROBABLE VOLUME OF TRAFFIC. 93 Table 23. Main Results op Operation of the Railways of the New England States, i 873-1881. Yka«. Popula- tion. 1 = 1,000,000. Miles Railway Operated. Revenue. X — $1,000,000. Divi- dends. Revenue per head. Rev. per Mile. Pass. Fght. Total Net. Pass. Fpht. Total 1= 1,000 3873 74 3-644 3.696 5.303 5.617 22.36 22.11 29 -3J 27-95 51-68 50.06 15-06 16.71 9.00 8.51 6-15 6.00 8.03 7-55 14.18 1355 9-73 8.91 1875 3748 5.732 21.78 26.55 25.24 24-52 23.29 23.81 48.33 15-32 8-79 5.80 7.10 12.90 8. 41 X876 77 78 79 3.801 3-853 3905 3-958 5.783 6,036 5.760 6,156 20.52 20.07 »7-97 17.52 45-76 44-59 41.26 41-33 »5-38 »3 74 13-69 15-59 7.61 6.98 7-57 7.24 5-44 5-21 4.60 4-45 6.67 6.36 6.00 6.02 T2.II 11.57 10.60 10.47 7.90 7.38 7.18 671 1880 4.010 6,071 19.32 29 44 48.76 17.19 8.00 1 4.82 7-37 12.19 8.00 1881 4.063 6,261 20.17 32-71 52.88 15-92 11.14 4.98 8.0s 13-03 8.43 Tabi"?: 25. Main Results of Operation of the Railways of the Southern States,, (South of Potomac and Ohio), 1873-1881. Yhar. Popula- tion. 1,000,000. Miles Railway Operated. Revenue. 1 ~ $1,000,000. Divi- dends. Revenue per head. Rev. per Mile. Pass. Fght. Total Net. Pass. Fght. Total 1— 1,000 1873 74 11.022 II. 196 13,908 »3.505 15-30 14.13 38-39 38 13 53-70 52.26 18.13 17.27 0.90 1.07 1-38 1.26 3-49 3-41 4-87 4.67 4-44 3-86 3-86 J875 H.370 13.522 13-86 36-53 r.40 50.74 39.81 42.80 43 92 16.74 1.50 1.22 3-22 3-73 1876 77 78 79 "•544 11.718 11. 892 12 066 13.948 11,272 12,498 13.389 11.88 9-95 11.22 11.32 38.87 29.86 31-58 32.60 17.12 12.66 14-38 14.67 1.86 2.74 2.81 2-13 1.03 0.84 0-99 0.94 3-37 2.54 2.66 2.70 4.40 3-38 365 3-64 3-64 3-53 3-43 3.28 1880 13.241 13.548 10.45 37.87 48-32 18.12 3-53 0.86 3-IO 3 96 3.56 1881 xa.415 14,002 17.11 46.63 63.74 22.24 3-59 1.38 3-76 5-14 4.72 Table 24. Main Results of Operation of the Railways of the Middle States, with Maryland and West Virginia, 1873-1881. Year. Popula- tion. 1 = 1,000,000. Miles Railway Operated. Revenue. 1 = $1,000,000. Divi- dends. Revenue per head. Rev. 3\?ile. Pass. Fght. Total Net. Pass. Fght. Total I —1,000 1873 74 10.915 11. 123 12,441 12,874 42.36 41.70 151.7 144.8 194.1 186.5 693 90.2 36.5 37-6 3.88 3.26 13.90 13.00 17.78 16.26 15.6 14.5 1875 "-331 i3.»73 40-77 «34-9 175-7 65 6 39-4 3.60 11.84 '5 44 133 1876 77 78 79 11.540 11.749 11.95S 12.167 13.647 13,607 14,600 14.941 47-48 39.26 35-95 43 20 130.1 116.7 119.5 127.1 177.6 «55-9 155-5 170.3 69-4 61.0 61.6 70.4 33-7 24-9 31.1 23-9 3-58 4.10 3-34 3-00 3-55 3-63 12.91 11.30 9.90 10.00 10.45 16-49 15-40 13 24 13.00 14.00 14-5 13-3 II. 4 10.6 11.3 1880.. .. 12.376 14,882 44-97 I1540 U;a.s 199.0 83-9 38.5 12.40 16.03 13-3 1881 12.585 16,213 49-92 228.4 84.9 33-3 3-97 14.30 18.17 14.1 Table 26. Main Results of Operation of the Railways of the Western and- Southwestern States (all North of Ohio and West of the Missis- sippi AND East of the Rocky Mountains), 1873-1881. Year. Popula- tion. I = 1,000,000. Miles Railway Operated. Revenue. 1 = $1,000,000. Divi- dends. Revenue per head. Rev. per Mile. Pass. Fght. Total Net. Pass. Fght. Total 1= 1.000 1873 74 16.025 16.589 32,973 35.639 51.62 56-78 160. 1 158.1 211.7 214.9 72.5 75-5 75-6 19.06 16.61 3-23 3-42 10.00 9-53 13.23 12.9s 6.43 6.02 1875 17.154 36,058 54-99 151.2 206.2 19.23 3-21 8.80 12.01 5-73 1876 77 78 79 17.718 18.282 18.847 19411 36.753 39.136 41,605 44,104 43 36 44-44 49.00 54-45 142-9 148.8 160.9 177.9 189.2 193-2 209.9 232-4 63-9 66.1 78.0 99.0 17.39 14.56 19.34 23.56 2.45 2-43 2.60 2.80 8.07 8.13 8.53 9.16 10.52 10.56 11.13 11. 96 5-95 4-95 5-05 5-27 1880 19.976 45.911 1 64.10 226.5 290.6 125.2 33.12 3-21 11.30 14-51 6-34 1881 20.540 53.224 71.40273.0 344.4 134-8 40.85 3.48 13.3c 16.78 6.49 94 CHAP. IV.— PROBABLE VOLUME OF TRAFFIC. CHAP. IV.— PROBABLE VOLUME OF TRAFFIC. 95 ,••1) Table 27. Main Results of Operation of the Railways of the Pacific States. 1S73-1881. YSAK. Popula- tion. I = 1,000,000. Miles Railway Operated. Revenue. X r= $1,000,000. Divi- dends. Revenue per head. Rev. per Mile. Pass. Fght. Total Net. Pass.l Fght. Total 14-43 14.12 1_ l.OOO 1873 74 1. 124 1.185 1,612 1,639 (5.9) 6.27 (10.3) TO. 48 (16.2) 16.77 (9-3) 985 (2.6) 3.26 5.26 5-99 9.17 8.83 10.2 10.2 1875 1.346 1,790 6.70 15-74 16.37 16.56 17 -35 18.08 19.92 22.44 12.23 5-43 5-39 12.60 17-99 12.5 1876 77 78 79 1-307 1.368 X.429 I.4QO 1,867 3,109 3,617 3-663 7.64 7.89 8.53 8.86 34.01 24 65 26.88 26.44 11. 75 11.32 12.97 9 97 4.53 458 (6.0) 1.63 3-99 S-85 5.76 5-97 5-93 12.50 12.10 12.07 12.17 18.35 17.86 18.04 18.10 12.9 7-9 7.4 7.24 1880 I.55I 3,813 8.82 28.74 10.79 5.68 12.77 16.40 18.45 7.53 1881 I.6I2 5,418 10. II 26.43] 36.54 18.64 7-79 6.28 23.68 6.75 Table 28. Main Results of Operation of the Railways of the Entire United States, 1871-1885. Ybak. Popula- tion. 1,000,000. Miles Railway Operated. Revenue. X = $1,000,000. Divi- dends. Revenue per head. Rev. per Mile. Pass. Fght. Total Net. 141.7 165.8 183.8 189.6 Pass. Fght. Total I— 1,000 1871 72 73 74 39.585 40.640 41.72a 42.834 44,614 57,323 66,237 69,273 108.9 132.3 1374 141.0 294.4 340.9 389.0 379-5 403.3 465 -2 526.4 520.5 56.5 64.4 67.1 67.0 2.76 3-24 330 3.30 7-44 8.40 9-30 8.85 10.20 11.64 13 60 12.15 9.04 8.10 7.93 7-53 1875 43.976 71,759 139 -» 364-0 503-1 185-5 74-3 3.16 8-27 11.43 7.03 1876 77 78 79 45-»47 46.350 47.585 48.853 73,508 74,112 78,960 82,223 136.1 125.2 124.6 142.3 147.7 361.1 347-7 365-5 386.7 497-3 472 -9 490.1 529.0 186.5 171.1 187.6 219.9 68.0 58.6 53.6 61.7 3.01 2.71 a.6x 3.93 8.00 7.50 7.62 7.92 11.01 10.31 10.33 10.84 6.77 6.39 6.3Z 6.43 1880 50.155 84,225 467.7 615-4 255.2 77- » 2.93 9.32 13.35 7-31 1881 8a 83 84 51.491 52.863 54.271 5S.7»7 94,486 95.752 106,938 "3,173 173-4 188. 1 206.8 206.8 200.9 5520 485.8 544-5 502-9 725 -3 728.0 807.1 763 -3 276.7 264.8 391.6 366.5 93-3 97.3 101.6 93. • 77-7 3-37 3-56 3.80 3.71 10.73 9.30 10.03 9.06 14.09 13.80 14.83 13-70 13-38 7-67 7.60 7-54 6.76 1885 57.202 123,110 5197 765-3 266.5 3-50 9.09 6.33 86. Experience has shown that the probable number of TRAINS PER DAY is at once the most convenient and the most exact basis for arriving at estimates of probable future traffic, and especially expenses. It is the most convenient, because it can be more easily and more correctly anticipated than any other item of future business, — as tonnage, for example, — and also be- cause we use the same unit for all our traffic, both freight and passenger ; and it is the most exact, because it is by very much the most uniform, measure of operating expenses, the cost of a train-mile being very nearly the same whether the trains are run full or empty, or long or short, and not being materially differ- 'Cnt for freight or passenger service, although usually less, by -one third to one fourth, for the latter, as we shall see hereafter. Assuming, therefore, this basis for estimates, it may be al- ways anticipated that there will be one passenger train per day each way, and that, unless the traffic be exceedingly limited, this train will be exclusively for passengers. Mixed trains, so called, .are in but little and decreasing favor with railway managers, al- though it is not always possible to avoid them. When used at .all, they are usually nothing more than freight trains under an- other name — accommodations for a few passengers being added chiefly as a convenience to special classes of travel, in the hope that such additional convenience may have, as it usually does, a favorable influence on the volume of travel. With freight traffic •of course no such motives intervene to modify the number of trains, so that mixed trains are always freight trains carrying a few passengers, and never, in regular service, passenger trains carrying freight. 87. Therefore, under the most unfavorable circumstances there are pretty sure to be two regular trains per day, one pas- senger and one freight or " mixed" train, over lines of any length. Less than this is certainly never contemplated on lines built as private business enterprises, unless on very short branches built as feeders. 88. The point at which it becomes reasonable to anticipate Tunning two regular passenger trains daily is more difficult to de- termine. 96 CJ/AP, IV,-PROBABLE VOLUME OF TRAFFIC, CHAP, IV.— PROBABLE VOLUME OF TRAFFIC. 97 m m I In the Northeastern third of the United States, as may be seen by examining any railway guide only a very small propor- tion of the minor branch lines run only one passenger tram a dav and but a very few of the lines run as few as two passenger trains a day. In the North Central United States, including both slopes of Mississippi Valley, two passenger trains per day may be said to be the rule, exceeded only in the more populous regions and on the important trunk lines; but only a small pro- ponion of the lines run as few as one train a day. In the Southern and extreme Western States the mileage may be said to be about equally divided between one train per day and two, only a few leading lines or sections of lines running more than two trains per day. In England and on the Continent the aver> age number of passenger trains per day is much greater than m the United States, except in the extreme Northeast : but this distinction is constantly growing less with the rapid increase of population and wealth in the United States. Tables 29 to 7S give many statistics of the average number of trains per day oa single roads, and in groups of States. 89. There are immense local fluctuations in every State and Territory, but as a rule, when the conditions are at all favorable for the development of passenger travel, a minimum of two- trains per day may be looked for with some confidence. This is especially probable because, in order to encourage and develop- traffic, it becomes expedient to put on two trains a day long be- fore a single train becomes so crowded as to actually compel it. The greater facilities so offered are almost certain to add a con- siderable percentage to the aggregate travel and revenue ; and as the actual additional cost of the extra train is, on the contrary, but a small percentage of the average cost per train-mile, such a train is almost always put on long before the mere statistics of tickets sold begin to indicate that it is a necessity. It is impos- sible, in fact, until the volume of travel becomes large and the number of passenger trains at least two or three per day, to make anv attempt to regulate the number of trains so as to have them run full, without serious injury to net revenue. 90. Beyond three or four trains per day there is much less necessity, as a rule, to add trains to accommodate and develop travel until the seating capacity itself becomes too small ; this being one of the many cases in which '* tiie destruction of the poor is their poverty." Nevertheless the results of experience with even the heaviest traffic is that it does not pay to scrimp train facilities. Certain trains carry enormous loads and bring up the average materially, but a multitude of trains carrying much lighter loads'are run with the heaviest traffic, at frequent intervals, bring about the close correspondence in average train- load on roads of widely different character, shown in Table 29. Table 29. Average Freight and Passenger Train-Load, Haul, Train Service, etc., FOR THE United States and Groups of States, 1885. Freight Traffic. Passenger Traffic. Aver- age Train- Load. Aver- age Haul. Miles. No. Trains per day. Miles per Engine. I — 1000 Ton- Miles per Car. I = 1000 Aver- Train- Load. Aver- age Haul. No. Trains per Day. A. New England B. Middle 102 179 139 93>^ 125 118 148 "5 60 145 108 103 132 159 162 3-74 7.42 4-44 2-43 2.31 2.17 2.13 I 81 19.8 21.3 26.3 19.8 21.0 20.6 17.9 14.4 424 53-9 72.8 60.9 61.3 58.1 69.6 51.8 59 44^ 2,m 32 43 36 47M 69>^ 16 i8l^ 37% 39H 48 49 60 31H 4 52 4.64. C No. Central. .... ...... 2.3T D. So Atlantic 1.52- E. Gulf and Miss. V. ... F. So. Western 1.64 1.36 G. No. Western H. Pacifc 1. 21 1.35 Total U. S., 1885... 1884... 1883... 1882... M3 »34 126 129 112 112 no 109 3-8t 4 OS 448 S.32 21.6 22.1 22.8 2i.3 57-4 56.0 56.6 53-8 43H 42^ 46% 45^ 26 26H 27^ 26 2.36 2.51 2.41 2 37 U. S. Census, 1880.. 129 III 3-91 22.4 • • • • 4i« 21 2.16 Excepting the figures for 1880 from the U. S. Census, the above is computed from the statistics of Poor's Manual. In this, as in all other tables in this volume, the railroad year is taken at 365 days, owing to the regrettable fact that the distinction between Sun- day and week days is fast disappearing. The " number of trains" always means each way. 7 CHAP. JV, .^PROBABLE VOLUME OF TRAFFIC. o en 2 — c *> A ^'S % $ CO « O « N et c« C4 H M NO CO «;\^7.'"''",^ffiei to be estimated on the basis fie the obtaining of full loads .s '^f'^'^%^^^^^,,\, Lrly Table 33. Growth of Average FRE.oHT-TKAm Load or Various Roads, 1873 TO 1885. N [ew York Trunk Lines. Year. N.Y. Cent. N.Y., L. Erie &w. Penna. B.& Alb. 129 Ill 122 75 1073 74 139 166 • ■ ■ • • • • 81 75 »34 128 82 -ft 180 166 186 191 219 138 145 146 i8s 132 137 154 170 87 7" 77 78 79 88 93 94 80 311 184 97 jIt 218 319 300 196 304 ai8 228 311 213 184 189 189 205 209 102 0- 104 9~ J03 "3 84 106 85 227 109 Minor Trunk Lines. Del., Lack. &W. Can. So. Mich. Cent. Pitts., Ft. W. &C. P..C. & St. L. 79 83 83 78 93 77 88 89 «35 96 T55 190 147 158 167 J95 90 80 99 99 208 275 301 97 96 116 120 I2S 186 173 184 198 132 132 131 '39 89 «3 98^ 116 129 140 t56 166 155 16s 160 161 107 303 138 i8s CHAP. IV.-PROBABLE VOLUME OF TRAFFIC, lOI pacity. Nevertheless, even on such lines, fluctuations and irreg- ularities of traffic are always so great, that it is no infrequent spectacle to see trains running light in the direction of heaviest traffic ; and the difficulty of fully filling up trains, of course, be- comes much greater as the tonnage is less, or, as already stated, when it is nearly equal in each direction. There is also always one train per day, the way-freight, which averages little more than one half an ordinary train-load, owing to the irregular service. Table 33. — Continued, Pennsylvania Railroad, by Half decades. s tram. 94f It should be mentioned also that, in attempting to draw conclusions as to probable traffic from statistics as to "miles run by freight trains" on neighboring roads, such statistics must be accepted with the greatest caution. An unfortunate custom exists of comparing locomotive expenses on the basis of the engine-mile instead of the car-mile, and as a consequence a habit has arisen among master mechanics and other officers of exaggerating the switching mileage (which is heavy enough at best) in every possible manner, by heavy allowances for switching at stations, and for running to and from the round-house. Instances might be given in which the excess of this nominal mileage over that actually run between termini amounted to nearly one fifth, independent of the usual and regular switching allowance of so many miles per hour to switching engines proper, which is separately given. This fact is im- portant to remember not only in estimating the volume of traffic, but also in estimating locomotive expenses ; for most roads make more or less allowance for mileage outside of the regular revenue distance, and it is always more or less deceptive, consequently, to use such data uncorrected for estimates of cost per revenue train-mile. Whenever there is a marked discrepancy in the cost per train-mile on similar roads this cause may with some confidence be regarded as the true explanation. Some reasonable approach to a correct estimate of the probable traffic can thus be made, by a little effort, from published statistics of various roads and towns, unless in a region which is entirely new to the rail- ways, or for other exceptional causes. The following statistics will also be of assistance: 95. The average payment to railroads of each man, woman, and child in the United States now averages about $13.50, of which about $3.50 is for passenger transportation and $10 for freight. Table 34 and several others (see Index) give further statistics for various groups of States, but the fluctuations from such averages are of necessity great. Points which are centres of manufacturing and transportation interests will have a many times greater traffic than this to dispose of ; while, on the other hand, there are few local stations which will fall very far below it, the great excess of the few points being compensated by the great multitude of small deficiencies. I04 CHAP, JV.— PROBABLE VOLUME OF TRAFFIC. CHAP. IV.^PROBABLE VOLUME OF TRAFFIC. 105 •4- »« f^ t«^ 00 w 0^ 00 00 oo CO « N f« «'» 0* to . . . • " CO 00 r* t^ f^ 00 d i^ • • • • • OS M N to i^ Tt CO »n t^ ►^ GO 3 k. W ^ • • • • to to «n xr% to t<^ c< w to W CO < u 33 (/} « - > • • • • • • • • • • • • • • • to NO >-* • • a. ■ 12 <'«. Z in • • • • • • • • • 5 d^ CO M .5 1 1 • • • • • • M GO r^ f^ f^ wn M I-" *^ to • • • • • • • • 0» 00 w M W « W N C« t-4 vd 1.^ 73 S >• •< H S H K P< 1 _ c '5^ •«^" 00 • • • • • • to »« 00 "* 'T r^ to CO vO ^ M »n M to to a PS •< ^c/j • CO • • • • • • 00 l-l O^ CO CO CO ON l-l ON • to . 1 1 ii • • • • • • a* 00 I-* Q "^ CO ON f ^ M 00 e< e • • • • • • • ■ to tn M M M M M 0* N M M M M -* ^ ** CA M 1 1 _ 4» tx3 vi. • • • • • • u^ "^ to to CO >o T • • 5 J3 U Z eo • • • • • • 00 t^ 1^ r^ »0 nO r^ CO - 1 Table 34. ABITANT BY S W CO 8 000 to to •-■ ■ • * en to to • M M M C4 (O t^ ON ON CO ei ci w w 00 • to CO 3 1 — 2> < K K H v> H A U X > < 1 = C/l • • • • • • ■ • 00 c^ to N N ... I-I >-l M to "^ o^ ^ CO On On CO « d d CO ON d CO CO M a — 3 Z 1— 1 A Z • • • • • • • • • • • . • • • • • • • • CO CO CO ON • CO .2 _ s M • CO • • • • • • • • c* ^ N to . . • \rt \rt yr% M to in vO f"^ to 00 00 r^ On 0^ nO »n in m tn »ft 00 • CO • u '5) — Si *f^* CO • • • • to N •-< »n CO M Tf "* nO CO w • • • * * • CO a e M •A H < 04 ^"c/j CO • • • • tn to to «n PI C» C« N to c< CO <4 ■a • • • • 00 CO N CO "^ Q »« to M to ^'^ *0 C^ in s • • • • • CO CO CO CO CO •«t to t*- Tt M Q Tj- N nO • • ■ i to to to tr > 3 — 8 • • • • • • • • • I? 8 « 1? ) ^ * r ^ oc * r > ON d « ro oo •- oc w •- » 1 ) > « Table 34. — Continued, Foreign Countries. 1876 .. . . 1880-1. . 1880 ... 1880 . . . . 1881.. .. 1876-80.. Great Britain and Ireland France *VUSll 1a •••••••••••••••••••••i ^ tcHjT ■■•••••••••• ••••• «•• • ••• Mexico (one railway only).. .. So'n U. S. (E. of Miss. Riv.). N. and W. U. S Total U. S. Miles. 16,658 15^227 7,086 5,4»8 293 11,892 66,714 78,606 Pass. 5.19 1.78 0.5S 0.06 0-93 3-35 2.84 Total of all earnings, $9.20). " " " 5.66). it u t( M it it it tt ( " 5.28). «.33)- 0-53)- 3.80). 12,98). 10.91). Fr'ght 4. ox 3-50 0.68 0.47 287 9.63 8.07 From the above statistics we may conclude that the average revenue to railways from each inhabitant of the different sections — bearing in mind that much of the trunk-line freight traffic credited to the Middle States is in reality a part of New England and Western payments — is (average of 1880-85) about as follows : New England States Middle States Pass. $5 00 3-50 3-00 550 Freight. $8. 00 zi.oo 11.50 14.00 Toul. $13.00 14 50 »4-5o 19 50 Ranging from $6.50 to $16.50 4.08 to 28.XO Western and Southwestern States Pacific States Average of all Northern and W'n States. 3-50 1. 00 11.00 3 50 14.50 4.50 Southern States (E. of Miss. River) Average of the entire U. S 3-00 9 00 12.00 The fluctuations from year to year hardly exceed 10 to 15 per cent more or less of these averages. There is, however, a gradual yearly growth in the payments per inhabi- tant amounting to an average of perhaps one per cent per annum, due largely to causes considered in Chapter XXL The fluctuations in the average payments of different localities are no doubt ex- treme, as may be seen from the statistics in other tables. The State of Florida pays but $1.60 per annum to its railways. The larger Eastern cities, probably $30 per head at least. There are doubtless considerable sections of each of the States in the above groups where the payments may be as low as half or as high as double the average for the whole group of States. The trunk-line export traffic constitutes only an insignificant fraction of the total revenue of United States railways, lai^e as it is absolutely. CHAPTER V. OPERATING EXPENSES. 96. We may gain a profitable insight into the general nature of the causes which modify operating expenses and espec.a ly of the effect thereon of differences of alignment by first consid- ering them in a very general way, neglecting all detail We have previously (Chap. III.) compared the railway to a great manufacturing establishment-manufacturing transporta- fion Its operating expenses, to carry out the analogy, should be only anothe'r name^for the total cost of P^o!'".<^'-S ^^f'^^^J^^'^l^Z which it sells ; but as a matter of fact this is not the case. The Tnt res^r " r ntal " charge on its real estate, and on most of it machTnery and plant-the heaviest single item by far >« the real "oDerS" or manufacturing expenses-is never included m wh'at aTc'alled the operating expenses, but constitutes the nx.. rHARGE for interest on bonds (see Figs, i, 2, 3). Counting in the 'fixed charges" as part of the " operating" or manufacturing expenseihe latlr neve'r amount to much less than 80 per cent and from that to considerably over 100 per cent, for ong periods of time The average for the whole United States is somewha iLToo oer cent leaving but little more than 10 per cent profit ^n the goods sold t^ be listributed to the managing companies^ vZ Lorable circumstances this profit is as much as ^^^^or 20 per cent ; very rarely more. Tables 35 ana 30 g ;Hf»a nf the law in this matter. 97 Is these fixed charges increase in somewhat faster rat,o than thecost of construction, and are the same per y--JJ^^f^^[ the business be large or small or none at all, the great impor tance of (t) diminishing the expenditure for construction as much CI/AP. v.— OPERATING EXPENSES. 107 Table 35. Stock and Bonds Per Mile of Road by Sections of the United States. 1880. Groups of States. Miles. Stock and Bonds Per Milk. I = $1,000. Revenue per Mile. I — $1,000. Stock. Bonds. Other D't. Total. New £ne:Iand 5.910 14.942 12,978 46,102 4.461 31.6 47.5 15.8 24.8 33-2 21.5 49-3 19.2 22.7 35.8 2.75 2.87 1.37 1.48 2.58 55.85 99.67 36.37 48.98 71.58 8.00 13.30 356 6.34 7-53 Middle Southern Western Pacific United States Canada 84.393 28.4 27.3 1.86 57.76 7.31 1885. New England. Middle Southern Western Pacific United States. 1884. 1883. 18S2. 6,412 18,595 20,584 74.854 7.284 127,729 31.8 57.3 20.2 25.2 340 21.9 53.6 24.6 25.6 28.5 30 9 30.1 30.8 30.7 29 5 293 28.7 28.3 2.46 4.87 1.20 56.16 115.77 46.00 1.49 2.20 52.29 64.70 2.03 2.0 61.43 61.4 1.9 1.9 61.4 60.9 8.87 11-53 3.66 5-25 4-55 6.22 6.76 7-54 7.60 1885. $55,100 The nominal cost of road and equipment for the whole United States was for these years : 1882. 1883. 1884. $52,790 $55,500 $55,300 The Canadian railways averag;e but $ri,ooo of bonds per mile, and $58,230 of stock and bonds together. Excluding the Grand Trunk, which, with 26 per cent of the mileage, has 45 per cent of the capital, there are only $28,000 per mile of both stock and bonds. More than one fourth of the total capital (145 millions out of 558, for 9,575 miles, in 1884) was contributed from governmental sources. Earnings are correspondingly small, being for 1884 : Canada Southern, ) ^^950 miles \ $^0'6o° P^^ mile. Grand Trunk, ) ' t 6,290 " " 316 remaining lines, 6,625 " 2,010 '* it 9,575 miles, 3,491 per mile. io8 CHAP, v.— OPERATING EXPENSES. CHAP, r.— OPERATING EXPENSES, 109 Table 36. Distribution of Gross Revenue, in Per Cent of Total Receipts. 1880. Groups or Statks. New England. Middle Southern Western Pacific Per Cent of Receipts Devoted to— Op'g Exp. Total U. S. 68.1 62.4 63.5 53.9 50.2 Net Rev. 58.3 31-9 37-6 36.5 46.1 49.8 41.7 Interest. 11.25 19-33 16.84 16.98 2305 Dividends. 17.58 16.83 14.24 7-43 11.72 14 50 12.55 1885. New England Middle Southern Western Pacific United States for each Year from 1879 to 1885. 1879- 1880. 1881. 1882. 1883 1884. 1885. 58.8 58.3 61. 1 63.6 63.8 65.2 65.1 41.2 41.7 38.9 36.4 36.2 34.8 34.9 21.18 17.58 18.32 20.02 21.00 22.90 24.52 11.72 12.55 13.30 13.23 12.38 12.09 10.05 as true economy permits, and (2) increasing the traffic (sales) so that this burden may constitute a less percentage of the entire business, is evident. Omitting them, the operating expenses PROPER (corresponding to the expenses of simply running and maintaining a factory which has once been thoroughly equipped and of selling the manufactured products) amount usually to about two thirds, or 67 per cent, of the receipts, varying however enormously (from but little over 50 to more than 90 per cent) with different roads. Table 37 and others give an idea of the general tendency for a long period of years. As the ratio of expenses to receipts may be made less either by the receipts being larger or the expenses being smaller, the fact that the ratio is low or high is no real test of economy in operation, nor of the value of the property. Wherever, from absence of competition, the rates are very high, — as formerly on the Pacific railways, Panama Railroad, and many lines in Europe, — this ratio will be small, even in the face of heavy ex- penses. Wherever all or nearly all railways have been very costly, as largely throughout Europe, it will also be small, since the fixed charges will constitute a larger proportion of the tax on earnings, and rates will naturally adjust themselves to pay (i) all operating expenses, (2) all rental or fixed charges, and (3) a fair profit to the managing company. Wherever several lines are so situated that their business is largely competitive, and must be handled at the same gross price, but one or more of them has better grades, or a shorter line, or more traffic, or other special advantages, one line will permanently show a lower percentage of expense than the others, which will have no meaning as an indication of real excellence of management. This latter law is strikingly illustrated by the trunk-line percentages in Table 37, the cause for the differences in which is explained in a following note and in Chap. XXI. 98. The operating expenses proper are very irregularly affected by the amount of business or by the character of the alignment. A very large proportion of them are, like the rental or fixed charges, independent of both : such as the salary of the president and other officers ; maintenance of works and plant against the deterioration which comes with time, irrespective of work done ; salaries of local freight and passenger agents, a large proportion of whom must be employed anyway, whether considerable sales are made or not. This immense class of the expenses amounts, as we shall see, to nearly one half of the no CHAP. V.—OPERA TING EXPENSES. CHAP, v.— OPERATING EXPENSES. Ill Table 37, Percentage of Operating Expenses to Revenue. 1849-50 1851-55 1856-60. 1861-65. 1866-70, 1871-75 1876-80 1876 54.6 1879 54-3 I8S0 68.0 1880 61.5 1880 51.0 United Kingdom. Prussia ' Italy Spain India Xul„crH,t fi^ris „ „ rtc, indicate the numlDer of years for »hich the average is givel. th^^iTh- ;: The'group of States are those of Poor's Manua, for the years ""'TrlTtke atov. MU ^, may cncluJ, that no mark«. tendency exists to increase or dimmish the ratio of receipts to operating expenses, both of »hich-as may be seen from other tables— have a tendency to tall rapidly and about equally. "rZluaUcns .finZiual lims in respect to this ratio are often extreme, as may be ll\T.L^^^ the frunk lines, and rarely affords any trustworthy indtcat.on of efiicenq^ oJ Tan^ement the cause almost always lying deeper, and being incapable of essential mo^ificaTorb" kny skill of management without change of external cond.t^ns. Thus the PennsvTvlnia Railroad, having the shortest haul (and consequently the h.ghest .ece,p« per mt) on traffic betw'een almost all points in the West and the Atlantic coas ,wll foreve maintain, under equal skill in management, a ratio of receipts to expenses from lO to .5 ~r clnt higher ttan the Erie. The New York Central would compare sull more un- Crably in this respect except that the enormous volume of its local traffic favorab y modifies its average, which will on this account, under existing conditions, be always more Z^bL tha:.;'e Erie. The low ratio of the Baltimore & Ohio as respects the Pe n- sylvania, is due almost exclusively to the greater relative volume of its coal traffic, which fe alway; carried in full trains at low cost. The same effect is still more strikingly visible rnlrWegWng the history of the PhiladelphU «= Reading Railroad. See Index, and operating expenses proper — the other half only varying more or less closely with the details of the line and grades, and very much less than half with slight changes in volume of traffic. 99. Therefore, it may be said in a general way that ten per cent added to revenue is as good as fifteen per cent taken off operating expenses ; and this again means thirty per cent taken off that portion of the operating expenses wliich varies with Ime and grades. To gain or lose ten per cent in revenue by slight differences in the route selected is very easy. To reduce the whole operating expenses fifteen per cent by differences in alignment which do not increase the cost of construction, is not so easy. Let us illustrate, by examples free from detail, the very important moral conveyed in these facts. We will assume the case of a fairly prosperous line of the second grade, whose in- come and outgo we shall find may be distributed in something like the following manner : Per Cent. Per Mile. Gross revenue loo.o $7,000 Operating expenses, unaffected by either alignment or volume of traffic (50 p. c. of operating expenses), . 33.3 $2,333 Ditto, increasing directly with considerable changes in alignment or volume of traffic, but not with trifling changes (40 p. c.) 26.7 1,867 Ditto, increasing directly with the less important changes in alignment or traffic (10 p. c.) 6.7 467 Total of nominal operating expenses 66.7 $4,667 Add to the latter the rental or interest charge (6 p. c. on $30,000 per mile, assumed cash cost of road and plant), 25.7 1,800 Total of true operating expenses, or cash cost of producing the transportation sold, 92.4 $6,467 Surplus available for dividends being the business profit resulting from operation, 7.6 $533 Let us now see the effect of increasing or decreasing the gross revenue ten per cent, as it is frequently possible to do (one Chapter XXI., pars. 973-4- |.' 112 CI/AP. V,— OPERATING EXPEN SES. might perhaps more fairly say, rarely difficult to do) by probably differences of alignment alone. We have, if it has been mcreased: Per Mile. Per Cent Increase. Gross revenue (increased lo per cent) ^^'^^ ^^ Operating expenses (lo p. c. only increased lo p. c), ^ ^ or $47 per mile increase . ^,7^^ ^^ Fixed charges (assumed unchanged), ...... j — Total charges against revenue, ^'5^3 ^^^^ Surplus available, The surplus available for dividends is more than doubled. On the other hand, if there has been ten per cent loss of traffic, we have— PerMile. Per cent. Decrease. . . $6,300 lo.o- Gross revenue, Operating expenses (lo p. c. of lo p. c. only decreased ^^^^ '° P- "=) \ . . 1,800 0.0 Fixed charges, 6 420 "■ Total charges against revenue * The expenses are a little over the receipts, and the road is on the way to a receivership, if it has been opened, as U is very apt to be, in one of the years in which an ebb in the business tide fs beginning, and there is no apparent growth (often a decrease) in traffic for several years. ,00. Again: Let us suppose that, by an improvement of or m- iury t.^ th! line and grades, we increase or decrease the average rIL load 30 per cent-often not difficult to effect. Our account, Ifwe htve improved the grades, will then stand as follows: Per Mile. Per Cent. %n 000 0.0 ^;:::trnr:x;enses-(3; p. c.- oi 5; p. c: sivea. or \,-^i 3.967 ;5.o Fixed charges (as above), _[ . 5.767 Surplus available for dividends, V^33 CHAP, v.— OPERATING EXPENSES. 113 Or, we have benefited the line greatly indeed, and yet but little more than if we had added lo per cent to revenue. On the other hand, reversing this process, we find, as before, that the road is on the way to a receivership. 101. Let us suppose, by an unnecessarily extravagant scale of expenditure, for purposes which do not really add much in dol- lars and cents to economy of operation, we have increased the capital account or rental charge 33 per cent, in a way which does not decrease operating expenses more than 2 per cent, nor add anything to revenue — a not uncommon case, since the use of 6° instead of 10° maximum curves will alone suffice to do it, in some cases. We have then Per Mile. Increased the rental charge 33 p. c, or $622 Decreased operating expenses 5 p. c, or .... 93 Net increase, $529 Or within $4 of wiping out the surplus over expenses and fixed charges. If we have, in addition, adopted a line which, instead of being better, is really more expensive to operate than another line which would have cost no more — or if, pos- sibly, we have adopted a line which, in addition to being more expensive, involves a certain sacrifice of revenue, a receiver- ship is practically assured. Both of these are very probable contingencies, but if we have escaped them, we have barely saved ourselves. The profit from the enterprise is destroyed. 102. A great change has taken place within the past ten or fifteen years, and indeed is still in progress, in the operat- ing expenses of railways, as a result of the introduction of cer- tain modern improvements, and notably the steel rail. At so recent a period as the publication of the first edition of this treatise (1877) these improvements had hardly begun to tell at all upon the statistics which were available for its preparation ; but they have already (1885) modified them profoundly, and where the process will end it is impossible to foresee with 8 CHAP, v.— OPERA TING EXPENSES. CHAP, v.— OPERATING EXPENSES. I h 114 :^^^^^:^^^Z^:^^^^^^^ the change will be very much more ^;^oi than even vet appears upon the surface. : ■-• •-"..ir.::;-.:::?; r. its: "/ir^s se V ce Mogul or Consolidation locomotives are rap.dly super- seivice. Mogui o ^^^^^^ supersede it. ;r;-r Mr-:" .=.t: - - -— ■ •- »■ client pro>p=c.. «' "'■'J "", ,„nt „„ h.. .1.0 been ind. The capacitv 01 orainar) ircigut 104. 1 he capa ^^^^^ ^^^ ^^^^^^ ^^^^^ cars have been b>"l • J^^ ^"^^^^^ . Car-Builders' Association so far that a committee of the Mastei v.- creosouHj, ui x. or.H Qprondlv the substitution of first- o«,'.ii hilt increasme use); and, seconuiy, m^. r^ba^-a'sUor wh^t iJs --ofore done du^^or t at piir^^^^^^^ "^"^ rre'r-taf^e^r; r.!a7 tt^m^f :o£t factor of to 34. a"tl othe.s) has ^^^ P ^^^ , ;„ ^^^^^^^ ^f producing ^"' ^"JotTmruCctur 'commodity consumed by railways. ^-aerTl^pos -"ble ^o.P-. with any ^^^^^^^^^^^^^^^ - ;^e. Rates of 8, 9, lo. x3i '5, ^^nd 44 cents. 115 Table 38. Receipts, Expenses, and Profits per Ton-Mile. Trunk Lines. Minor Trunk Lines. Year. Penn'a. N. Y. C. Erie. P., Ft. W. &C. B. & Alb. L. S. & M. S. Rec. Exp. Pr. Rec. Exp. Pr. Rec. 1.95 Exp. 1.03 Pr. •92 Rec. Exp. 1 Pr. Rec. Exp. Pr. Rec. Exp Pr, 1852 4.64 . . . . , , 53 3 7« 2.50 1.28 1 .22 , , , , . , • • , , • • 54 327 |2 28 •99 2 95 i.3» 1-64 2.58 1.41 1. 17 , . , , , , * . ^ , » , 55 2.84 I1.68 305 il.98 1.163.27 1.34 1.93 1.0713. iiji. 32 1-79 1.043.05 1.54 1.51 2.42 2.36 2.48 ^•I5 1.22 1. 17 1.27 1.14 '•3« •• •• •• Aver.iffc. ,. 1 . . 1856 2.70 ..69 .. 57 2.38 1.52 .86,3.19;!. 70 1.49 2.46 .90 1.56 2.27 I •.57 .70 , , , . , , 58 2 19 1-35 .8412.6311.37 1.26 2.32 •65 I 67 11.90 1.32 •.58 , , • • . , , . 59 2.02 1. 18 .842 16 1.28, .88 i.6i ^•-4 .28 1.651.18 •47 , , , ^ , , , , eo '•95 I1.17 .782.061.34' .72 1. 81 1. 00 81 1.67I1.18 •49 . .. Averaire.. 2.25 1.38 1-93 1 .9» . 87)2. 62 1.45 I. 17 I.02 I 98 1-341 .64 2.14 1-77 I.OI •93 I -13 .84 X.87 ;i.7i 1. 31 .98 •56 •73 •• .. 1 .. • • 1861 .. . . 62 2.05 (i 09 .962 23 I 36! .87 1.89 •95 .94 1.90 .98 .92 . • • • . • 63 2.20 1.16 1. 0412. 44 '•5» ^93 2.og .96 I.I3;2.0lll.20 .81 , , , , , , , , 64 2.46 11.R7 .592.76 1.96 .80 2.34 1.46 .88 2 381I.50 .88 , , , , . . , , , , 65 .. .. 2.66 2.28 .38 3 45 2.54' -91 2.76 1.98 .78 2-4411 79 65 Averatje.. 2.26 I 460.80J2.57 1.74I .61 2.17 2.43 1.26 1.66 .91 •77 2 09 1.29 2.0211.50 .80 •52 • • • . • .. 1 .. 1866. ... 2.28 1.82 .46 3 09 2 16 ■v> , , , ^ 67 209 |iS4' •5S 275 1-95 .81 2 04 I 47 •57 I 95|i^44 .51 • • 68 1.91 I1.25 .66 2 74 I 80 •94 1.81 '•34 •47 1.70JI.15 •55 2.81 • . • • 69 1.72 ii.20, .52 2 39 1.40 •99 154 1. 17 .37 1.62 I. II •51 2.43 • , • • , , 70 1.55 I. 00 .55 1.88 ^•I5 •73 l^33 •97 •36 1.45 ^86 •59 2.19 • . 1.50 •93 •57 Average.. I. 91 1.36 .5s 2.57 1.69 I.OI .88 .62 I 83 1.44 ^•3' I.OI •51 •43 1.75 I 21 1.43 .78 •54 •65 2.48 2.09 • . 1-39 .. a87i t.39 1 87 .52 1.63 .9i| .48 72 1.416 .886; 530 1.59 i.ij .46 '•53 .98 •55 1.40 .81 •59 2.02 1-37 .92 •45 73 I 416 .857 .559, 1-57 1.02 •55 1.46 .96 •50 1.40 •95 •45 1.96 1.59 •37 1-34 •95 •-39 74 I.2S5 .719 536 1.46 .98 .48 1. 31 .91 .40 1.26 •74 •52 1.82 I 39 •43 1. 18 •77 .41 75 1.058 .616 .442 1.27 1.70 .90 I.OI •37 •49 1. 21 1 19 .96 .25 •96 .431 III 1.32 .69 •79 •42 •53 I 53 1.88 I 10 1.48 •43 .40 I.OI 1.26 •74 .86 •27 Average.. i..^o7 •790 •517! .40 1876 .892 .582 .310 1.05 • 71 •.34 1. 10 .8q .21 •93 .61 •.30 1.28 1.03 •25 .82 •.S6 .26 77 .980 5.52 .428 I. 01 .70 •3' ■95 •75 .20 I.OI .67 •34 1. 21 1.03 .18 .86 •57 •29 78 .918 •483 -435 •93 .60 ••33 •97 .67 •.30 .88 •50 •38 ^•I3 •99 .14 •73 •47 .26 79 •796 .427 369 .80 •55 •25 .7« •56 .22 •76 •44 •32 1. 10 •78 •32 •64 .40 •24 80 .. .. .880 .470 .406 .88 •54 •34 M •53 •.30 .qi •51 .40 1. 21 1.02 .19 •75 •H3 •,32 Avcrajie.. .873 •503 390 •93 .62 3» •93 .68 ■25 .90 •55 •35 1. 19 •97 .22 .76 •49 ■ 27 x88i 82 84 •799 •437 -362 •78 •56 .22 .81 •53 28 •75 •43 •32 1.04 .96 .08 .62 .42 .20 .817 •473 344 •74 .60 •14 •75 •53 .22 •75 •47 .28 1.07 .98 .09 •63 .41 .22 .819 •477 342 .91 .68 •23 •99 •53 •25 •79 •55 •24 1. 19 1.09 1. 10 •73 •45 .28 .740 .441 .299 •83 .62 .21 •7^ •52 .20 .67 •49 .18 1.09 1.07 .02 .65 •43 .22 85 .627 .391 .236 .68 •54 •T4 .66 •48 .18 •.S8 •44 • 14 •94 .81 •^3 •55 .40 15 Average., .760 •444 ^'fi, .79' •^o .19 •75 •52 •23 •71 .48 .23 I 06 .98 .28 •64 •42 .22 For the whole United States the earnings per ton per mile were : 1880 1881 1882 1883 1884 1885 1.29 1.236 I 236 1. 124 ^•057 The receipts p>er ton per mile in the various sections of the United States, according to the Census of 1880, were : Group. Receipts Average haul— miles Tons per tram I. New Eng. II. N. Y., D.CInd. in. Va.. Ky., Miss. IV. Ill, Mo., Minn. v.* La., Ark., Ind. T. VI. Far W. and So. 1.83 55-7 90.6 1.02 106. 1 163.6 2.15 103.7 55-5 1.36 1533 122.8 12.57* 34^6 61.3 2 57 166.9 955 U.S. X.29 III. 129. ii6 CHAP, v.— OPERATING EXPENSES. Table 39. AVERAGE COST PER TRAm-M.LE OF THE FOUR TRUNK L.NES AND ENCUSH Railways. Year. N. Y. Cent. Cents per Train. Erie. Revenue. Mile. Penna. Revenue. Mile. B. &0. Cents per Engine. per K Mile. 1873. 74- 1875 76. 77- 73. 79 126.2 127.3 132-5 116. 6 122.0 95-5 89.6 71. 1 67.7 II9-3 80.1 114. 6 104.0 loi .0 95-5 114. 2 102.1 99-5 95-6 76.2 74-3 73-6 72.0 63 9 1880. 81. 82. 83. 84. 107 -3 1885 112. 5 118. 3 123.2 108.5 101.8 92.6 105.2 108.0 100.5 95-7 83.8 60.9 57.3 54-5 52.2 67.1 91.2 81. 1 88.2 85.7 84.4 78. 1 71.6 715 69.4 66.3 69.0 'liTIi^e Shore & Michigan Southern statistics, Tables 30, 3., and others fo^ lowing. , ^ ... ., ^„ T,-_ heen on the whole, a decline in The above suffices ^<'^f^^^^:^ZX\^^J:T^o.o^y V^r to„.n,i,e show» expenses per train-mTle, yet the aam part ° ' train-load shown in Table 33. and 'nte average earning per ->-iie<,r British raih»aysha^e^^^^^^^ since ,8,4, having been $..36 in 1874. $..^ '" ""^i^if .^"usVks great, so that the in working expenses has been almost as ««" "■ ^"„^„ "t. wSn L^ afd 6,.36 cents pe, Srr Tro- r^: r^::^ S^r rs„T"i™t - ^penses hav. bee. in cen» per train-mile : 1879. 1880. 126 24 125 -^a 66 00 64.74 1877. , 130 50 69 38 Profit 6*" Receipts Cost.... 1881. 123.48 64 56 1882. 123.80 64.94 1883. iai.76 64 -34 1884. 119.13 63.18 60.34 60 68 58.92 58.86 57 43 5S-9# .>, more uniform than would be shown in this country, even in .,r^tr.::::^"^r::^^^ ^.« ^ - - «^-ion me^penses o. CHAP, v.— OPERATING EXPENSES. 117 .the British railways has been in the cost of maintenance of road. This has fallen from 15.70 cents per train-mile in 1874 to 12.76 in 1879 and 11.64 cents in 1884. Per mile 0} road expenses ranjjed, for the five years from 1874 to 1878 inclusive, from $1,865 to $2,020 for maintenance of road, and averaged $1,965. Then they fell off suddenly to $1,690, and have never been so low since, ranging thence to $1,800 in 1883 and $1,750 in 1884, and averaging $1,751 from 1879 to 1884. The total expenses per mile of road have ranged from $9,665 in 1875 and $9,625 in 1883 to $8,775 in 1S79, and the gross earnings averaged $17,690 for the five years from 1874 to 1878, reaching the maximum, $18,255, in 1885. will probably be greater than those of the last ten, and all that we can be sure of is that the cost per ton-mile (not probably per train-mile) will continue to fall rapidly, although it hardly seems possible that it can fall quite so rapidly as in the last ten years. Table 38 and others will show the recent changes in the cost per ton-mile, and Table 39 the changes in the cost per train-mile. 106. Nevertheless, it fortunately happens that those items of expenditure with which we are more immediately concerned those which are affected by the location of the line — mav be anticipated with reasonable certainty from known facts and tendencies, although it is not expedient to rely too much on existing statistics of the iminediate past of railways in respect to some items, as notably steel rails; since it would tend to the dangerous error of overestimating the probable expenses. 107. The operating expenses of railways divide, naturalh% for the purpose which we have immediately in view, and in the main for all purposes, into the three great classes below : 1. Maintenance and Renewal of Way and Works, in- cluding all permanent structures and buildings, except engine and car-shops. This has until recently averaged very uniformly 25 per cent of the total expenses on all American railways. It is now •decreasing both relatively and absolutely, but far less rapidly than might be expected, because of both temporary and per- manent causes below mentioned. 2. Train Expenses, including all expenses of every nature and kind connected with the running, handling, maintenance and renewal of motive-power and rolling-stock, but not includ- Il8 CHAP, v.— OPERATING EXPENSES -RAILS. ing any station or terminal expenses, except switching. These expenses have heretofore averaged very close to 4^ per cent of the total operating expenses, and cost from 30 to 50 cents per train-mile. They have decreased considerably per train- Lie for the same class of engines, but the introduction of heavier engines will have a tendency to keep them more nearly constant. Relatively to the other operating expenses they are crowing continually more important. , Station, Terminal, and General Expenses and Taxes. With these we are very little concerned. Most of them vary more or less (for the most part, less) with the tonnage or volume of business; but all of them are independent of, or in- appreciably affected by, any of the details of hues and grades, and therefore, for our present purpose, may be ■"'^'"^^'l J"" eether and neglected, except as to their aggregate. Taxes at first sight appear to be affected by the alignment, in so far as thev might increase with the length of the road ; but taxes are based upon value and not on cost, and hence, although nominally based upon distance, are in reality much ^^r^JJ^'^ based upon low grades, large traffic, and good rates They are, moreover, too small and variable an item to justify their consid- "a ion a one of the expenses affected by any of the details of Xnment. Station expenses also, and all the other expenses me' tioned, are the same for the same business, whatever c.uinges in the alignment may be made, except as such change bungs Idditionalway business ; but even then the change will rarely be sufficient to appreciably modify tiie station expenses Fo its indirect value in such cases and others, and as a n^at^r of general information. Tables 75 to 80 give what the cos of the virions items of station and general expenses amount to on various roads and in various sections. maintenance of way. CHAP. V.—OPERATIN-G EXPENSES— RAILS. 119 the most culpable carelessness as to the quality of rails purchased ; but the difficulty existed, and was only partially remediable at best. The cost of rail wear alone per train-mile was from 7 to 9 cents, and their life on important lines was measured by months rather than years. Under these circumstances the track was constantly disturbed, the ties cut full of spike-holes, the joints imperfect and irregularly spaced, owing to the constant cutting of rails, the line and surface difficult to maintain correctly, and anything like a permanent rock ballast well-nigh out of the question, although it was occasionally used. As a further and very natural consequence all maintenance expenses for the above items varied to a very remarkable degree, in almost exact ratio with the ton- nage and rail wear— as indeed they still do, but to a less noticeable ex- tent. Some evidence of the former conditions is still preserved in Table 40. but further space need not be devoted to the discussion of conditions which no longer exist to any extent. 110. The superiority of the steel rail lies not so much in its greater strength and toughness (although it is stronger by 20 to 30 per cent) as in its greater homogeneousness and absolute freedom from grain. In other words, when of good quality it is tough enough to last until it is worn out, whereas the iron rail splits into pieces long before it has lost any serious amount by wear. The wearing properties proper of iron and steel rails — their resistance to abrasion— are not materially different. 111. The average life of good steel rails properly manufactured and inspected so as to eliminate all imperfections arising from a lack of ordi- nary care and skill, and weighing 60 to 80 lbs. per yard, according to the weight of engine, has now been determined with a considerable approach to certainty to be about 150,000,000 to 200.000,000 tons, or (what is probably a more correct way of putting it) from 300,000 to 500,000 trains. From 10 to 15 lbs. or three eighths to five eighths of an inch in height of the head of such a rail is available for wear, and abrasion takes place at the rate of about i lb. per 10,000,000 tons, or one sixteenth inch per 14,000,000 to 15,000,000 tons. This durability may be regarded as nearly a minimum for strictly first-class rails, as many recorded obser- vations indicate a much higher durability. 112. Unfortunately, it may be said to be the rule rather than the ex- ception, that American railways now buy their steel rails, as they for- merly bought their iron rails, without any effective inspection as to quality ; the so-called inspections, when there is any even in form, being confined to the exterior qualities of the rail. Unfortunately, also, a few years since the result of an investigation on the Pennsylvania Railroad into the wearing 120 CHAP. V.-OPERA TING EXPENSES-TRAILS. CHAP, v.— OPERA TING EXPENSES— RAILS. 121 5 o in -< H C/5 !> as < rt o tr\ < rt V-4 V *fx u. C/) tn 1-^ ^ ••-• • Cfl « «»4 o t) ^ C < c tf ^-4 Ci .2 .J > 1-4 -5 pa ■/-. u < b) Cd U4 H a ^ «*4 (b NH V O ;4 •-1 »n 7, a r^ I M-> on 00 < Id -< o \A (A a p o M H O 9: ••4 o » •i«iox pu«9 18 8 8 J_i_8j_§ qualities of steel rails, which showed, or seemed to show, that very hard rails did not wear so well as softer and tougher rails, was taken to indi- cate that softness in itself was a desirable quality in a rail ; and the pains- taking character of the investigation and high reputation of the road having given these conclusions wide dissemination, manufacturers for many years took them as a guide, and between 1880 and 1885 produced rails which have deformed readily under the impacts of service, espec- ially at the joints, and have also worn away very rapidly, so that their life has often been only a year or two under very moderate trunk-line traffic. In instances it has been only a few months. 113. The particular cause for this deterioration of quality, whether it is chemical or mechanical, or both, is as yet obscure. It is probable that as there has been no adequate inspection to enforce sound practice the chemical composition has suffered by the use of cheaper ores, cheaper men to supervise manufacture, and less care in all the processes. But a chief cause is probably mechanical— that the " bloom," or first rough cast- ing of the steel from the converter, out of which the finished rails are fash- ioned, is, in tlie first place, heated unduly hot for passing through the rolls, and, in the second place, is passed through them a less number of times, or too rapidly, or both. In order to roll a rail very rapidly and with few passes it must necessarily be very hot, both to begin with and when it finally leaves the rolls. Its molecular structure might be expected to be disadvantageously affected by this lack of surface compression, inde* pendentiy of the fact that, being left to cool slowly after it leaves the rolls, it is thoroughly annealed by the same process as makes the finest tool steel soft enough to readily suffer deformation from dies. The rapid motion of the rolls, moreover, may not give the molecules suffi- cient time to flow upon each other properly, and a spongy, unhomogene- ous metal is the result. 114. Whether or not this is the true explanation, it cannot be ques- tioned that there is some equally simple and easily remedied expla- nation, because certain makers do produce rails of excellent quality which are sold at the same price as the inferior ones. The remedy, therefore, lies simply in more thorough tests, especially for ability to resist deformation ; and it would be erroneous to conclude from this ad- mitted but, it may reasonably be hoped, temporary evil that the estimate of cost of rail service should be permanently increased. The reasonable cost per train-mile of rail wear may, on the basis of the facts above given as to the life of rails, be estimated at from 0.3 to 0.5 cents, as fol- lows: 122 CHAP, v.— OPERATING EXPENSES-RAILS. . $2,850 . 1.350 Cost of one mile of steel rails, 95 long tons, at $30, Less scrap value of unworn steel, say nearly half, . Leaving as net cost of wearable portion, per mile, . . . $1,500 Divided by total life of 300.0C30 to 500,000 trains, this gives 0.3 to 0.5 cents per train-mile ; but. in view of the present difficulty of getting good rails and tendency to increase the weight of trains, we may assume the even figure of i.o cents per train-mile as a maximum which there is na need of ever exceeding. No allowance for interest or discount to represent the present value of the scrap is made in this estimate, nor should there be. although at first s^ht an argument to the contrary seems plausible. The whole original cost of the steel is a permanent part of the cost of the property on which interest must be paid, like the cost of the ties and structures. The renewals for each year simply represent, in the long-run. the rail wear for that year, and no question of inter- est is involved in the cost of simply using the steel to run trains over. 115. The locomotive alone causes by far the greater portion of this- wear-how much is not positively known. Freycinet. a French engineer writer, and politician of much prominence, recently Min>ster of Public Works, estimates that the locomotive does three fourths of the damage and the train itself only one fourth. Launhardt. a German writer on the subject, after noting the fact that the locomotive and tender together constitute onlv one fifth of the total weight of train on the Prussian Stat^ railways (it would be considerably less in this country), considers that half the wear is due to the locomotive and tender and half to the train. This in all probability is a very moderate estimate. Experience on the gravity railwavs in Eastern Pennsylvania, worked solely by "^^^^^d. Pj^l^f^^-^"^ carrving a heavy coal traffic with the ordinary vehicles, and with all other usual conditions except that no locomotives run over the ra-ls. shows that the rail wear even of iron rails is very slight indeed under heavy ton- nacre. but with light loads per wheel ; but exact figures of the wear cannot beVesented. Mr. O. Chanute investigated this question somewhat by placing impression paper between the rails and wheels and determming The arfas of the surfaces in contact. He points out that the pressure of the drivers approximate, to the ultimate crushmg '^lf^''''\?^'^^ metal, and that the pressure per unit of area is very much less with ordi- nary car-wheels. He therefore reaches substantially the above conclu- sions-that from one half to three fourths of the total wear of the rails originates from the engine alone. CHAP, v.— OPERATING EXPENSES— TRAGIC LABOR. 125 116. We may assume, therefore, the cost of maintaining fairly good steel rail at 0.5 to i.o cent per train-mile; the cost of additional engine- mileage, the car-tonnage remaining constant, being only half as great. These values, although in round figures, probably approximate very closely to the facts, and the very best quality of rail might reduce them one half; but the poorer qualities which have been so generally sold of late years greatly increase it, when so poor that the rail speedily mashes out of shape, and from this cause and renewals of the still re- maining iron rails combined. 2 cents is nearer the present average (see Tables 75-80). Much of the rapid wear of rails results from the imper- fections of the fish-plate type of joint which is now universal. Its de- fects of principle are such that it seems quite certain to be supplanted within a decade by something better — probably by something closely re- sembling in principle the Fisher " bridge" joint, if not identical with it. TRACK LABOR. 117. This item includes all the considerable elements of cost in main- tenance of way proper outside of rails, ties, and frogs and switches. It has been unmistakably falling in the last ten years, the decrease on many roads having been as much as fifty per cent. About one fourth to one third of this decrease is accounted for by the decrease in the rate of wages to what bids fair to be a permanent average of about $1.25. The remainder is almost wholly due to the advent of the steel rail. Except that the joints are still so weak and imperfect a detail, it would unques- tionably fall very much more. This decrease is destined to continue, but less rapidly, for some time in the future ; and in making estimates of operating expenses for the next few years — if not for a long period ahead — the apparent indications of the statistics of other roads must be accepted with much caution. All the roads now laid with steel — with hardly an exception — are, instead of reducing track expenses to the lowest limit possible, maintaining for the time being something like the old rate of expenditure and perfecting the condition of their road by adding better ballast, dressing up the road-bed and right of way, improving their yards and switches, etc.. etc. This wise procedure is in reality an addition to the capital account, but for obvious reasons of expediency it is still called and charged to mainte- nance of way. 118. It is also very evident that the larger the business of a road, i.e., the more prosperous it is. the more likely will it be to continue this process extensively. For example, the Pennsylvania Railroad, although laid with steel and ballasted with stone throughout, still includes a very heavy charge per mile of road (although not per train-mile) in its annual 124 CHAP. V.-OPERATmC EXPENSES-CROSS- TIES. CHAP, v.— OPERATING EXPENSES— CROSS-TIES. 12$ accounts (or " maintenance of way," the reason being simply that it is encaeed in giving the last degree of finish to its road-bed. track, and rightof way!and the same is true in a less degree of many other ra.l- "^ n9 It is even possible that this practice will be continued indefinitely as a matter of permanent policy ; and when it comes to dressing up the edge^o rock ballast with u string, sodding and planting slopes, etc etc the^e is hardly any end to the labor which may be kept busily employed '■ maintenance of way," nor can it be doubted that such expenditure would be returned in part, perhaps many-fold, by its value to the me 7or its value lies not alone in the direct economy of such fine condition but n Its value as an advertisement, by making travel over the line more attract te and likewise in its eflect to instil habits of caution, neatness Tnd watchfulness into the entire force of employes. Nevertheless, such trcts should not lead us to confound advertising and landscape gardening with •• maintenance of way." nor blind us to the fact concealed from sight in the current statistics-and likely to be for some years yet-that the cost of r^aintaining steel-rail track is no longer greatly affected by the ton- nat U will for some time appear to be the case-as it came very nea to bein» actually the case during the iron-rail period-that the total cost o° mamtaining 'rack varies very nearly with the tonnage, and that it has not blen so verv largely diminished by the steel rail as was expected. Perhaps therris' more- that is permanent in this appearance than is ex- acted a cer,,in,y there is unless the current carelessness in buying bad raiTs ;; good prices is reformed; but the following estimates (par. ..4) seem reasonable and sufficient. . 120 Crossties alone cost from S.20 to S225 per mile of mam track «hout vo per year (one eighth of the total number) being required per ■I of main track at an average cost of. say. 5° cents per tie (it is often mile of mam track, at an a = ^^^.^ ^i.^^^s as many. rlr '^:^;Tt:^:^^^ side-track ties Will hardlv aver- lie in CO t, however, more than half as much per mile per year as mam- track ties, being largely "culls." or of otherwise inferior quality. T Fnol^nd and Europe generally the number used per mile is less-ordi- In England and E"'°P ^ >■ dimensions being in England some- r.ye'r:s::u;;rvrx -Hesinstead.^^^ r •" Tiin-gif h°; a": °'r '^nz::^^..... u sleepers is longer Dy aooui ^yj y nprhaos mainly— to greater '- : CeV;:;:: :^:^:::^::^^^^ .- (;- ^-p- r:;rch Tmerrcrn ro:ds are very careless), and in part to the use of cast-iron Chairs on English tracks to carry the rail and protect the sleepers from "cutting."* The differences of practice in England and America result, for the most part, from differences of conditions, and not from mistakes of judgment on either side. Where wood of any kind is dear, hard wood out of the question, and labor and rails cheap, the English and Continental plan of widely spaced ties,, with the rail carried in chairs, is at least defensible, although it may be ques- tioned if there is any real economy in spacing ties so widely. Where good haru-wood tics are cheap it would be folly to space ties farther than two feet apart, or to use a rail requiring chairs. One effect of the English plan is that, for equal stability and strength, very much heavier rails must be used than with the ties nearer together, which is the chief explanation of the fact that they are heavier. 121. The expense of cross-ties will probably be considerably reduced within the next ten years by the more general introduction of burnettizing- or other equivalent processes, and it will then be almost wholly true, as it is now in part, that the life of ties is independent of the tonnage. The only way in which tonnage seriously affects the life of a tie, under a steel rail, is by helping on that process of local rotting which is popularly and erroneously known as *• cutting" into ties. The difference in this respect between main-track ties (especially if of soft wood) and side-track ties, is- very considerable : but, given three or four trains a day over the tracks the effect of even twenty or thirty more trains a day is much less impor- tant, and the "cutting" does not take place noticeably faster. This re- sults from the fact that the only real assistance which the train gives to the "cutting" is to wear away the rotted surface, so as to leave a fresh surface exposed to decay. It is physically impossible for the rail to cut into a sound tie under existing loads, except as assisted by the greater rapidity of rotting under the rail than alongside of it. That this is true is conclusively proved by the fact that creosoted or similarly preserved ties do not cut to any important extent, even when the wood is soft. The importance of this distinction as to the cause of " cutting" is obvious; since it follows from it that the wear will not be verv g-reatlv increased by an increase in number of trains, beyond four or five per day, whereas otherwise the wear of ties would be directly as the train-mileage. 122. Putting ties into the track costs about one third as much as the tie itself, including all labor incident thereto, or about 15 cents per tie, or $50 to $75 per year. Including with this the maintenance of ballast and ditches and ordinary track-walking, but not including policing the right of way and road-bed, special watchmen, removing snow and ice, care of structures, or extraordinary repairs — the total COST OF track Labor, as thus defined, properly and necessarily chargeable to the main- ,26 CHAP. V.-OPERATING EXPENSES-MAINT.^Ay^ TT^I^aiUrack once reasonably well ballasted and in good tenance of steel-ra 1 t""="^' " ^ji^ ^f single-track mam Ime general condition. ,s not «" '-™ «300 pe ^^^^^^ .^ ^^,y ,^ ^ peryear. or say hye -" - eve,^ s,x m, e^ ^^ ^^^^^ .^ ^^^ ^^^„^^^, „, very Imuted ^-^^^^^^^J'' I ,„es not now appear probable that ,t maintenance - "° ";™ d to advantage, since it is necessary to have can ever be materially reaucea lo ° , nrudential reasons; ..at number of men ava. e o;--^--J- .^..^r the track has and work can and w.U be easily to ,^^^^j ^^^ ^^^^^ ^^<.,,. been brought ,n the course «' /[^^ '° ^^^j ^^e present rate of expen- se" nV^t'Tr l-rf rt^e r rank^nl. ^by aimin. at absolute ^Xtion. permanently i.-cur -«" "J::-^;,,,,,, ,„ ,or track- 123. About $;o per n^ileoitne above t ^^^^^^^^^ ^^^^ ^.^^ talking which - about -^ '^Tng only three or four trains per day usually be ">-"f °^"^^t /o'd that, the usual expense per annum is each way. For a tramc oeyo ^^^ fourths of ahout $5 p-.-''^':;„t;f;:aTa 3 1 o-^^^^ a cent per tra.n-m. e) up ^^-^"ZL Snow and ice is another source of which this account very rarely runs ^ amounts to about $5° irregular expense for " --menance o w^ It am ^.^^ ^^ per mile of main line. -"g'^^. ;^^^j P^^ ^Te egions-™.-ing much high- doubie-track ^-^^ ^^^^^l^f^.^ shallot cuttings are the greatest rLroTaro^r a^rpLe m Lpect to snow and ice_a consid- eration often forgotten in fixmg gradients. ^j „.„ack railways of "*• ^''^r'ra;\1'"satre: -trL'^Uo- for those items ri;::;^cr:feVa«icaUy^^:/pendent of volume of traf^c : ... $150 to $225 >j Cross-ties lo to 40 Do. for sides, , en to 200 jjo. lor siucs, ICO to Labor on track ^ Track-walking, Snow and ice Ballast, . . .• • • • • Fences and miscellaneous. 50 to o to 50 to 25 to 200 100 100 50 Per mile of main track, .not including mileage of 'sidings. Common track labor $1.25 per day. To which must be added for cattle-guards, open culverts, and crossings, about $43S to $765 Total, . . Steel rails, say . 25 to 50 $460 to $8 1 5 20 to 100 CHAP, v.— OPERATING EXPENSES— MAINT. WAY. 12/ To this estimate must be added certain allowances for maintenance of •structures, for the maintenance of large yards and terminal facilities, and for extraordinary damages and repairs, and also for the wear of steel, and other expenses, according to traffic. The amount of necessary expendi- ture which can with any propriety be assumed to vary directly with the tonnage will be — Steel rails, i ct. per train-mile, or $20 per 1,000,000 gross tons (including all expenses for relay- ing, spike, etc., connected there- with). Track labor, etc., \\ cts. p. t. m., 25 " " " Track watchmen, i " " 15 ". " " « M Total, $60 " (« «( This amount will vary almost exactly with the number of trains, inde- pendent of their weight and length. As will be seen from Table 41, the present rate of expenditure for rail renewal.s, in all pnrts of the United States, is much higher than the above, or about $200 per mile, but this can hardly continue to be permanently the case. 125. Yet it must be admitted that there are some strange anomalies in the records of maintenance of way expenses which seem to indicate that such expenditures will continue to bear a nearly constant ratio to the train expenses proper, as they have in the past. For example, if Table 41 be examined, it will be seen that in every item of maintenance of way — even those which seem most nearly independent of the number of trains, like ties, bridges and buildings, repairs of road-bed and track — it is the cost per mile of road which varies, and that the cost per train-mile or the percentage of the total remains far more nearly constant. In fact, the cost of rails, which one might expect to be almost precisely so much per train-mile, comes much the nearest of all to being uniform per mile of road. Beginning with the section of heaviest traffic, — the Middle States group, which includes Ohio, Indiana, and Michigan, — the cost of rail re- newals, in cents per train-mile, is 3.50, 4.08, 5.03, 6.08, 6.72, 3.66, averaging 4.43 ; while that of road and track labor is 9.2, ii.o, ii.o, Z.l, 16.5, 8.3, averaging 10.2. Individual roads may be compared almost at random with similar in- •dications. The following two roads, not selected in any way except as •I 128 CHAP, V.-OPERATING EXPENSESr^MAJNT, WAY.. CH. V,^OPER'G EXP.—MAINT, WAY AND ROLLG-STOCK. 1 29 ^^^pi^^^ng extremes of traffic, may serve as illustrations, the years given being fairly representative : Penn. R. R. 1883. Char., Col. & Aug. 1883. 34 Av. U. S. 1880. 6.1 Trains per day each way (main line) 64. 5 Repairs road bed and track (cts. per train. ^^^ ^^ ^^^^^^ ^^^^^ TotaTcostoi-trai>;-m"iie;;:::.:: 86.0 •• 87.5 •• 9.-o" Table 41. Maint;pnance of Way Details. Deduced from U. S. Census of x88o. See also preceding table^ Groups of States. Trains each Way Per Day. New England Middle Southern Northwestern. Southwestern, Far Western Totnl Cost Per Train -Mile Cost Repairs Road-bed and Track. Average U. S *EsumateI~The report of one road in this sm error which vitiates the total all group contains an obvious and largfr Repairs road-bed and track, p Per mile Tie renewals, p. c. . . Per mile Bridges. buildings, knd fences, p. c. . Per mile Rail renewals, p. c. .. Per mile Total, p. c Per mile Cost per train-mile. . 10.51 $374 2 64 $144 6.64 $360 4.20 $220 19.79 $1,081 $1.05 $621 2.78 $i6S 4-44 $268 3-47 $236 17-35 $1,051 %o . 906 $273 4- 30 $97 5-80 $131 I 6.16 $210 22.42 $501 $0,715 12.45 $361 3-07 $88 6.0S $176 «^.o3 $166 2 1 . 60 $625 $0.88 13-59 $480 4.21 $148 3-45 $121 3.66 $213 21.25 $749 $0,608 13.63 $382 3-48 $98 4-95 $139 6.8T $158 22.06 $619 $1.21 11.23 $450 3 -04 $121 5-14 $207 4.40 $196 19-41 $778 $0.91 Table 42t Trunk-Line Maintenance Expenses in Cents per Train-Mile by Decades for 34 Years. N.Y.C&H.R i860 1870 i83o 1884 , Erie. i860 1870 1880 1834 Penna.* 1S60 1870 l83o 1SS4 Bah. & Ohio.j i860 1S70 i83o Phil. & Read. i860 1870 looO. ..••.• 1883 Miles Run, Thou- sands. 4-493 11.430 16.654 16,453 3-475 9.326 11.452 11,305 3633 10.185 17.241 21,491 3831 7941 12,768 1.853 5.100 7.799 12,347 Expenses Per Train-Mile. Maintenance of — Way. CtS. 19.8 39-8 18.9 24. 8 24.1 39-6 20.7 18.2 21.4 30.1 14-5 15.8 15-9 26.3 18.3 II. 2 22.6 26.3 19. 1 En- gines. CtS. 9.0 9.8 5.8 5-3 9.0 14. 1 5-1 4.4 7.7 9.1 7.2 7.0 6.8 6.9 9-4 8.6 8.6 7-8 7-9 Cars. cts. 8.9 15-4 1-1.4 10.3 II. 7 12.0 8.0 8.9 8.2 II. 7 10.5 II. 4 8.7 5-5 20.6 8.9 13.5 12. 1 14. 1 Total Rolling Stock. Cts. 17.9 25.2 20. *2 15.6 20.7 26.1 I3-I 13-3 15-9 20.8 17-7 18.4 15-5 12.4 30.0 17-5 22.1 19.9 22.0 Total Ex- penses Per Train- Mile. CIS. 95-2 122.2 107.5 108.6 94.6 129.5 108.5 106.8 99-3 no. 6 81.8 81.8 51.8 68. 8 82.0 78.6 108.2 117-5 117. 2 Percentages. Track. 20.8 32.6 17.6 22.8 25.5 30.5 19.0 17.0 21.5 27.2 17-7 19-3 30-7 38.3 22.3 16 5 19-3 22.4 16.3 En- gines. 9-5 8.1 5-4 4.8 9-5 10.9 4.7 4.1 ,8 2 ,8 .6 I3-I 10. 1 II. 5 10.9 7.4 6.7 6.8 Car*. 9-4 12.6 13.4 9-5 12.4 9-2 7.4 8.3 8.5 10.6 12.91 13-9 16.7 8.0 25.1 11-3 II. 9 10.5 12.0 * Pennsylvania Division only. t Main stem and branches. In Table 42 is given a record of expenses for maintenance of way on five trunk lines for the past 34 \^ears. In this table, it will be noted, an enormous expansion of train-niileage has occurred, ranoing from four- to seven-fold, while yet the cost of maintaining track has, on the whole, decreased less rapidly than other maintenance expenses. There has been, on each of these lines, a considerable expansion of track-mileage as well as train mileage, but this increase has been of branches only, not of main line. Therefore, while due allowance for the effect of this greater 9 •srt?'-^ '^MMj^ ,30 C^. V.-O.E^C ....-MAJ^^T^^^AV^f^^^O^^ i; -rri 7::;^^^. ^y --p--" -''> -^^^ '- ^° lit^l^- , -^^o^ of thpPennsvlvaina Railroad In the following table (43) »f "P"' ^t ,e very^eg n'-g of its o„cr- only is carried back ten years f"rthcr-to t e ve y J avera:,ed ation. and every year's experience .s '"^l"''"'' * ■^^^^^;f„„, and shorten together by half-decades to eUmmate acc.denta var at-n ^^^^ ^^ the table. In this table, but not ,n tl^ P--^"^";,;"^;^.., ,, u>e single gine-wages are included wiih repairs of engines ana item •' motive-power and cars :" Table 43. OP.a.x,KO S....SX.CS OK .„. '----rtrr^oi!^.--" ^ Branches) averaged by Half Dlcades from Operation. Years avekaged. Averajje Miles Run. I = ICX30. Train Load E. only. Tons. Peu Cent of Total EXPENDnURB. Molive-powcr and Cars. 1851-55.. 1856-60. . 1861-65.. 1866-70. . 1871-75. • 1876-80. . 1881-84. . 1. 416 2,934 5- 530 8.766 14368 16.182 20.808 101.6 110. 6 146.24 158. 88 187.76 251.32 298.45 42.3 42.9 48.1 41.4 38.2 39-4 41.7 Maintrnance of Way. 13.4 23.7 22.8 27.2 23 4 i3.4 20.0 Per Cent of MiHhienancc (,f Way 10 Molive-|)ower and Cars. 317 55-4 47 5 63.6 61.3 44-3 48.0 both directions see Table 33. The drop in the last two half-decades is th^eflect of .he introduaion o, steel rails : but both in the -or^^^J^';^ 'Z^^Z^e is to in- brings this tendency out still more clearly : CH, V.—OPER'G EXP.—MAINT. WAY AND ROLLG-STOCK. 131 Table 44. Comparative Cost of Maintenance of Way to Repairs of Engines anc Cars on Each of the Five Lines in Table 42, Cost of Repairs of Engines and Cars being $1.00. N. Y. Cent. Erie. Penna. B. &0. P. &R. Average. i860 1S70 IS80 iS34 I. II 1.58 0.945 1-59 1. 16 1. 51 1.58 1.37 1.33 1.45 0.82 0.86 1.025 2.12 0.615 » • • 0.64 1.02 1.32 0.87 I.C53 1.536 1.056 1. 172 Average. 1.306 1.405 I.II5 1.915 0.962 1. 199 The contrast in the proportionate cost of maintenance on the various roads is in part genuine, but in part no doubt results from considerable difference in what items are in- cluded in " maintenance of way" or of cars or engines. Less pains were taken in this respect than to have the comparison of one year with another correct for each road sepa- rately. The last column of this table is the most instructive. With the ex- ception of 1870, which was an abnormal year, it will be seen that the tendency of maintenance of way to mcrease in relative importance, in spite of an immense growth of traffic, seems marked and clear. Table 45. Growth of English Train-Mileage and Coal Consumption of Engines Per Mile. Train-miles (i = 1000) -j ^g^ Increase per cent Engine-miles | J^73 Increase per cent Coal burned, lbs., per train- j 1873 mile \ 1883 Increase per cent Coal burned, lbs., per en- j 1873 gine-mile / 18S3 Increase per cent Great Eastern. 8.932 13.679 52.0 10,819 17.077 57.8 41.65 4596 10.35 34.39 36.81 7.05 Great Western. 19.717 31.128 58.0 22,778 36.465 60.3 41-73 37.69 — 9.8 36.12 32.17 - 10.8 London, B. & So. Coast 5.300 7.9S6 50.8 6.208 9.630 55.2 43.33 37.07 16.9 36.99 30.74 20.3 Midland. ig.8ii 330S7 67.1 57.18 49.00 14.3 II The mileage represented above is 5,221 miles, or only a trifle less than one third of ^•i H'. V.-OPIiKATING EXPENSES-FUEL. 132 ai and train-load is given only for the Great Eastern, The change in engine- F.kst-Class Gooo^^_^_^^_^^, Engine, Great Eastern Diameter of driving-wheels Cylinders Total workin? weight, lbs Working pressure Coal Train: Consumption per mile Speed, miles per hour 1873 5 ft. 3 in. 16V6 X 74 70,700 X40 lbs. 43.75 lbs. 17-4 398 tons. 43.97 lbs. 1883 4 ft. 10 in. 17^ " 24 84,000 X40 lbs. 46.68 lbs. 30 438H tons. 4^.58 lbs. Per cent increase. 8.6* xa-4 31.6 6.78 15.0 X0.3 D. 3 »7 . fHrivers The /«»^a/ increase in power of tbe- ♦ Increase per cent in /.«^.''. due to d«reasc jj d • ^^^^^^ ^^^^ becomes x08.6xXx.xa4 - engine, due both to decrease of dnvers -^J^l^^^^^.^..^ ,, ,he increase of we.ght. ,..x,or«.xpercent.ncrease.,almoste,acty ^ . a^st-class goods- The high average speed of English -^^^J^^'^:Z^':^Z^ traffic, are noticeable. prevail quite as strongly in England as ^^^^^^ ^^ j^„, ^3, 1885, which paper, how- ever, makes some vc y writer. the Railroad Gazette of Sept. n, i»5, ^7 Train Expenses. ,„. T>,e COS. of fue, per .ross - ^ A-tt^l^^^^ IC a minimum of $1.20 to ^^r" To tl at the least favored points r ^f ^Misr-ve:; a^t To^ ^ses to S^.^ or more at points nHir:;n,ption of fuensas^an average a.^^^^^^ run for heavy passenger "a-ns. J""'^- passenger engine running 30 lbs. per mile for light P='==«"S^',"^'"';„^h L this, or from 20 to 30 ight, without any train, burns nearly -"^^"^j^he" American" eight- ,bs. per mile. A heavily loaded « - ght eng ne o ^^^^ ,. wheel type will burn almost 75 'bs- P" • j^„^ ,^ t„ .^olbs. The C//^/'. v.— OPERATING EXPENSES— FUEL. 133 JCI.; and from data given there, in connection with the above, it appears that the average consumption of fuel increases considerably less rapidly than the power of the engine, as might be expected. Table 46, Motive-Power Expenses Per Train-Mile on Various English Railways. MOTIVE-FOWER EXPENSES IN DeTAIU Engine repairs — labor. . . . •' ** — materials Total engine repairs. Wages, engine crew Fuel Water Oil and stores Repairs shops, etc Gas Office and general Total motive-power.. 16.74 Great Western Railway, 1869-76. Great Southern and Western, X875. Midland Great Western, 1875. cts. 3.76 2.46 cts. 2.82 3.80 cts. 3-42 2.78 6.22 6.64 6.18 4.66 4-34 4.32 6.61 3.84 6.50 0.42 0.48 0.50 0.66 0.32 0.82 0.12 • • • • • • • • O.IO 0.32 • « • • 0.40 0.66 0.20 19.76 17.90 The above is from a paper in the Transactions of the Institution of Civil Engineers, the reference to which the writer has lost. 127i Several newly invented types of compound locomotive engine, having separate high-pressure and low-pressure cylinders, are being extensively intro- duced in Europe with, it is said, very satisfactory results. If we may judge from what has already taken place in marine engines, it is probable that they will eventually come into general use, and they promise a considerable reduc- tion of fuel consumption, but there are several practical disadvantages wiih the type which have not yet been fully overcome — notably a difficulty in starling. The burden of evidence seems to be that the coal consumption is reduced at the rate of about 20 to 25 per cent. The consumption of fuel on English railways in general, however, is lower than prevails in the United States, although very much less so than commonly supposed. It was reported by the late Howard Fry, in a paper before the Master Mechanics* Association, at from 26 to 35 lbs. per mile run, for passenger service, and from 35 to 45 lbs. per mile run, for freight service ; but the follow- ing statistics, which have been compiled by the writer from later and more ^ 134 CHAP. V.^OrERA TI NG EXPENSES-FUEL. ■ . /T Kioc AC A-*A^ SO) show that the actual difference bc- dcfiniie statistics (Tables 45. 4/- 43. 49;- =»"" En sh ana rreHcL fu., consu.pUon. The ^^^^^^^^ ^^^^ «Dlamable by a difference in the average tra.n-load; .n part also, d"""''"'; 'J* befi road bed and alignn,ents. use of copper fire-boxes, and more espec.ally ^reater"km and care in firing. The longer average tr.ps of Amcr.can eng.nes o her thn being equal, should reduce the average fuel ""su.-npuon. The oiner inin5,b uciu^ ^ u^ku, that fuel economy s subordinated m ZtiTaririlnrHlvriXtu C: trbl." herea^s in England heavy St uls, or what would pass for such in America, are the excepuon. Table 48. PASSENGER TRAIN CoAL CONSUMPTION. PENNSYLVANIA RAILROAD. ~~1 Year. 1874- 1875- 1S76. 1S77- 1S78 1879- i8ao. 1881. 1882. 18S3. 18S4. Cars Per Train. Coal Per Mile. 5- 5 5- 3 5- 6 5. 10 5 13 5 29 5 .27 5 .01 5 .14 4 95 5 02 Per Car. 9.0 8.5 8.3 8.72 8.43 8.40 8.76 10.78 9.61 10.84 10.67 Total. 49-5 45-1 46-5 44-5 43.2 44.4 46.2 54-0 49.4 53-7 53.6 The last column is not given in the reports, but is obtained by multiplying together *-';i: ^:^^i^ cen. m the coal ^^:^:-^j:^:^^, t^ZC^^Z^ZrZ:'^^^ .ileakand the much -Thir^irr^a has been selected ^;;^^^::--:^::^ftX^ ^^l accessible. It 'v--^:-o::rrro7t::::rd began o„ -^- sho« & Mrhl^rsotu :rn for example, several years before it began on *e Peansy.van.. The I'hLelphia & Reading runs about 58 lbs. per passenger tram-mde. . Table „ »a, misplaced i. maV.ng up this Pan. and i. give at the end of the volume. CHMP. v.— OPERA TING EXPENSES— FUEL. 135 Table 49. Average Freight-Train Coal Consumption, Pennsylvania Railroad. Coal BuR.NEO Per MiLB. No. Cars. Train -load Totis Fr't Approx. Toul W't Year. Per Cur. of Irani; Per Ton Per Car- Per Train- Tons. Freiglit. Mile. Mile. 1874.- 21. 1 (6.5) 327 (.646) 4.2 88.5 1875- . 21-5 (6.7) • • • • (.627) 4.2 90.2 1876. . 22.2 (6.9) • • • • (.609) 4.2 93.1 1S77.. 22.92 (7-1) • • • • (.585) 4.15 95.0 1878.. 25.06 (7.3) « • • • (-497) 3-63 91 .0 1879.. 25.60 7-55 436 .490 370 116. 7 i83o. . 25.77 8.18 • • • • •477 390 112. i83i.. 24.40 8.68 « • • • .492 4.27 109.3 1882.. 24-55 9.01 • • • • .494 4-45 104.3 1883. . 23-97 10.28 • • • • .454 4.67 100.5 1884.. 25.66 10.58 566 •430 4.55 99.2 The tons freight per car was obtained by dividing the coal consumption per car given by that per ton ; the approximate total weight by assuming the average car to have weighed 18,000 lbs. (9.0 tons) in 1874, 19,000 lbs. (9.5 tons) in 1879, and 23,000 lbs. (11.5 tons) in 1884 ; the coal burned per train by multiplying the number of cars by the coal per car. The remaining figures are direct from the report. The figures in parentlieses above are estimated, not being given in nor deducible from the reports ; but they are not far from the truth, a gradual increase of average car-load having, as is well known, been going on even in the years 1874-9, v.-hich has jrone on much more rapidly since. One of the chief reasons why the average car-load has been so small, on all the American east and west trunk lines, has been the enormous dispropor- tion (more than 3 to i) in east-bound to west-bound traffic. The increasing coal ship- ments westward, to a considerable extent in cars coming east with grain, has in recent years helped much to decrease this disproportion on some roads ; so that the increasing average car-load is not due solely to increased capacity of cars, although that is the chief cause. The proportion of switching is very heavy on English railways, the ratio of engine-miles to train-miles being almost uniformly as high as 125 to 100, and in some cases, as high as 177 to 100. On German railways the average consumption is about 50 lbs. per revenue mile, costing about six cents. 128. The cost of fuel per mile run can be calculated from the above data for any particular line. In absolute cost, it is by far the most variable element in the running expenses of railways, but its percentage to the other expenses is considerably less variable, owing to the fact that II ,36 C/fAP. V. -OPEKA TJNC EXPENSES-FVEL. .,e san,e causes which n,aUe Cue, --^^^:;^:r;::t^^ expenses to a considerable extent. The total avera e cos P ..^.ains, according " -'^^^p^slania r' ^ad . to about :o cents 5 cents as a minimum (on the Penns> '^n (g„ n Massachusetts and ,. cents on the P^<=^^,^. ^^^f; J.^ed cost runs roads in the Rocky Mountam res.o" on winch the repo ^ ^^^^^_ still higher than this-up to as mud> ^^'"Trthecttuns still lower- there are a few specially favored -^^^ -*''-' ::r„a are n.ostly due to r^r,:; ::rac\::rt:airmS':ith a^ctious .lowances. Table 50. EFFECT OF LENGTH OF TRA.K ON COAL CONSUMPTION. J ij»o«« Pa««enper Trains— Michigan Central tCoo.pa«U,= Coa, Con.u.p.ion with L.^.-^Hea„ Passenger Light Tkains. CHAP, v.— OPERATING EXPENSES— FUEL. 137 No. of Round Trips. Av No. Cars Handled. Coal Consumption, Per Mile. Av. Temp. Per Cent Correction for Temp. Corrected Lbs. Coal Per Mile. 3 1 7 2 3 I 16 7i 74 8 • • 8i 71 9 81 9^ 73 Hi • • 8.78 ,8 .6 .6 75-4 87 87 79 84-4 79-3 78.6 79-4 85.4 77-3 75.0 79-3 33 ^ 29.5 36-3° 44.2: 27.0 32.4° -3-55 + 1.55 — 0.25 4-3-15 4-7.10 - 1.50 4-1.20 77 07 79.82 79.20 88.10 82.80 73 88 80.25 The correction for temperature is by a rule deduced by the writer from records cover- ing many millions of train-miles, that the effect of differences of temperature alone^ length 0/ train and all other conditions being equals is to increase or diminish coal con- sumption at the rate o/onE per cent /or each two degrees Fahrenheit (and a small frac- tion more) difference of external temperature : a rule easily remembered and one which appears to apply fairly well to both passenger and freight service, and to be practically invariable whenever the effect of all other causes for variation can be eliminated. Since the effect of increasing the average length of train from 5.56 to 8.78 cars, or 3.23 cars, is shown above to increase coal consumption from 58.56 to 80.25 lbs. per mile run, 21.69 lbs. or 21.69 lbs., or at the rate of = 6.736 lbs. per mile per car, we have, 3*^2 Ccirs Lbs. coal per mile. For the long train, burning, , 80.25 Consumption due to cars, 8. 78 x 6. 736 = 59-14 Leaving as due to the engine alone, without cars, 21. 11 For the short train, burning, " 58.56 Coal consumption due to cars, 5.56 X 6.736, 37-45 Leaving as due to engine alone, without cars, as above, , , 21. 11 This result agrees closely with what direct expjeriment has shown to be the consump- tion of heavy passenger engines running light. Mr. Reuben Wells some years ago made a test of a liglit passenger engine, 14 x 22 cylinders, running 108 miles with six stops at 22 miles per hour, and losing about one sixth of its time only in stops, with a consump- tion of only 18^ lbs. per mile, and this test was in warm weather. Allowing for the dif- ferences of weather, size, and number of stops, the correspondence is close, and other tests, which need not be referred to in detail, have shown from 20 to 30 lbs. Mr, Wil- liam Stroudley, Mechanical Superintendent of the London, Brighton & South Coast Rail- way, alleges in a paper before the Institution of Civil Engineers (1885), that a heavy pas- senger engine was run light between London and Dover with a consumption of only 7 lbs. per mile. As the distance is only a little over 50 miles, however, and the quantity stated would amount to only a few inches over the bottom of the fire-box of 20 square feet, or barely as much as the same record shows was habitually used to get up steam, there is probably some error in this estimate. The best existing direc t evidence on the effect of length of train on coal con- sumption is given in Table 50. There is considerable difficulty in obtaining records of this kind, in which a series of trains of widely varying lengths are run with all other conditions approximately identical. The correctness of the result reached in Table 50 may be tested by grouping the various single records differently — a test which should never be omitted in computations of this kind, since it will often be found that, when grouped in one way, the records will appear to lead to one conclusion, while if grouped in another way they will indicate something quite different. Tested in this way, the correctness of the preceding conclusions is confirmed. If, instead of averaging the single tests together in only two classes, of "light" JilB I 38 CHAP. V.^OPERA TING EXP ENSES-FUEL. CHAP, v.— OPERATING EXPENSES— REP' KS ENGINES. 1 39 " ~ ,. -A ♦!,• oc rp«;ts as tabulated above into four equal and -heavy" trains, we div.de the 25 tests as tal. ^^^^ ^^^^^ .roups of six tests each, as nearly as may be, and see how ^^^^ Lned beneath the table (lbs. coal ^^^ ^^r.^^ ^oll^^^^^^ as follows: with the actual coal consumption, we find a close corresp No. of Roun.l Trips Averaged. Cars her Train Pounds Coau Per Milk. ~" r^^TTfiZr^^eciinc for difference of temperature. • Actual consumpuon afier corrccimt »"i « . f rh. rP.nlts under this entirely different grouping is The correspondence of the results ""^^J ^ \ j^ dearlv conform surprisingly close, '^^f^^^^^^^^^^^^^^ the fuel'consump. r •: -^^ct^yri^::^:^:: - ^^^^^^ - - -- ^^ ^-- - ^^ -nt^lietermined^awfor^^ by records on a large ^f ;;;';;^'^ ^^^^ , R,,road. alone among American rail- determining the ^-;^ J^^^ ^^f .^ ,,, consumption per carmile and per ways, publishes a ^^^^^^^^^'"frs oer train for every month in the year. As ^-^"■"^^"e:fthe" :::e"rAs?-^':h^ passenger tram and passenger :a^Z^c\nlm;tio:on each of its three^ramic^ Pounds of Coal— Penn«5ylvania RR. Div U. RR- N. J. Div Phila. &Erie Div : rirZir^the coal c^sumption per mile according to the Computed Coal Cons.mition. Pounds per Train-Mile. Actual. Pounds per Train- Mile. Ekkok in Fokmula. + or-. Penna. RR. Div. U. RR- N. J. Div Phila. & Erie Div The correspondence here is close, if we remember that the Pennsylvaaia Division, while making fewer slops than the Michigan Central train, whose record was used in table, has a large proportion of heavy sleeping-cars, while the New Jersey Division not only has a large proporiion of parlor- and sleeping- cars on through trains, but makes an enormous number of stops on way trains, boih into New Jersey and into Philadelphia. 129. The conclusion is, therefore, not unfair, that something like 6^ to 6| lbs. of coal per mile is added to the consumption for each passenger car of 20 tons or more moved at way-train speed, and for each sleeping- car of 30 tons or more moved in tlirougli trains making few stops, and that the locomotive alone is to be charged with rather more coal than that due to three cars. This leads to the conclusion that dead weight to the amount of 30 tons added to a train of, say, five cars, will certainly not increase coal consumption as much as to add another car, both because it does not increase air resistance, and be- cause the added load decreiises somewhat the rolling resistance per ton. If we assume it to add 5 lbs. per mile to the coal consun)piion, we are certainly not underestimating it proportionally. Adding 6 tons per car, therefore, to the average weight of a train of five passenger cars means no more than an in- crease from 55 to 60 lbs. per train-mile. If we assume this 5 lbs. of coal to be worth one cent (at the rate of $4 per ton of 20C0 lbs. for coai), if an extra pas- senger at 3 cenis per mile be attracted to the train every third trip he will pay for the loss of fuel due to adding 6 tons to the weight of every passenger car — which goes a little way toward explaining the tentiency to increase weight for the sake of luxury, which seems so reckless. This appears to neglect the efifect of the extra weight on grade resistance, and so in a sense it does as well as many other effects, but not 50 much as it appears to. since the effect of gradients is included in the records which we have used. The use of wood for fuel is rapidly passing out of date in all parts oif the United States. About i^ cords of good hard wood (a cord being 4X4X8 feet, or 12S cubic feet, and weighing from 3200 to 3600 lbs. when well seasoned) is usu- ally taken as equal to one long ton of coal. Inferior woods will average from two down to even three cords of wood equal to one ton of good coal, but some of the poorer Western coals will evaporate only half or two thirds as much as good bituminous or anthracite. REPAIRS OF ENGINES. 130. The fall in the cost of this item, of late years, has been very rapid, but it is probably now at about its minimum, unless and until some new process of manufacturing steel and iron shall materially reduce the cost 81^ 140 CHAP V -OPERATING EXPENSES-REF RS ENGINES. a/A P. v.— OPERATING EXPENSES— REP' RS ENGINES. M^ u > s o o o o V) u H (A < H C/3 O < Sll J3 Ml d 6 M oo 00 00 •♦ M o N r-- re r~ M ■♦ M M W N « M r-> t^ O f. r^ M o (A •<■ t^OO odd NO Ul O 00 rf.»Q VO 00 O^ odd"'* 8" d H >■ M f.*C • • • • • • • • « « ■ • ■ «0 ro O O N K VO r^ a >«• f rn fO fO NO M OV ro r<« Ul !>. IT) • • • . . . O lO • j 1 d»oo 00 ro N m Qvo ■ f~ •<• -"T t^ 00 ■ • • • 00 00 00 CO lO 00 w 00 ■>♦• PN NO tNOO o 6-6 6 6 1^ F- W »^ M d - ci M N M M C4 CO »»><0 lO O W N •♦ N r> looo moo t^ et (4 M M M VO NO •«■ Ul tN tx m N 00 d M M CO 01 CO fO ro VO lO M PO NO 00 two PO M •* ro ro ro ro fO CO O 0« O 00 '♦• r^ O » c« en <*> o d-^ « PI vM •- 11 00 00 i >0 O ■*■ "NO vo m o> ■>»■ t^ 1^ to N N »■< 00 M N w VO o t>, U-) lo t^ 1- O 0> Ov ro N Ov O •* ro ro Ps PN !>. Ov PN w N PS PI M M »« M o> o< "> ^ m CO - m r« ro 00 00 t^ r^>d •* w <<■ 0> r* M O ro M r<1 - >0 NO t^NO *n >d VO N 00 •* O ■«■ N fO 1-1 yr, •*■•*■ -.tirt •* VO •* M Ov On Ov ►■• f^. Ov in Ul •<«■ lo M loco <*> *! '^ 0. r 1 fi fn » « d> ^ P« M M M ►.NO OvO 00 >< On foao \d 00 •4- >o in In. t^ rovo Q Ov 00 •♦VO N lo to -«- ir> tN. VO Ul t^ O fO PN O* Ul M On mvo p^vo >0 00 o>« <0 «^ ■*■ M (^ ^ VO >0 >0 <0 VO o» 0» "A N o» 00 M ■♦ N « VO t^ tx t^ t^ M M 00 to « Ov •<»■ ro -• lo r>. w t^ t^ t^ t^ 00 •* •* VO 00 Ov PN N ro Ul 00 00 00 00 «rt «*| O. r^ O m ^ "-) " fr.oo 00 o> d 00 Q « - •* t>. M f«".>0 ■*• «0 00 M Ov ■♦ •* ■<*• CO 00 N t^ N VO -*■ lOvO t>. M M M M M PI OO vd ro ►< Ov NO 5 « ■«• Ov "' PI M ►■ N N PI O « * "O f*)00 t^ Q\ ^ v> ir»o>0 t^ f> •-< M *4 H M 00 s M M M M t-« M "o o> N lo m Pi d - N O r»l •*• M M M M C( n6 o> o o> - 00 Ov M IT) c« VO r^ O «'>vo r^ M ^ fO ro ro vf PI >*• 00 fO 00 O NO 00 VO >H •♦ t^ ■♦ in tn in C' ri U t/3 rt PO :v8 m VO PN »^ •♦ 00 ©v N •* 'T vO mvo VO 00 c u"* a « w o O uivO dvNO <*> NO 00 O •■* NO PO "♦•oo d NO NO W M N »" M I/I o > V4.4 U .«« NO PO Ov inoo CI ♦ P>. ►» - PONO 0> inoe ro I- o O r< e« n M M NO dv «^ 00 PN ci •♦ PI CI n ct ^ f« pN •♦ PI •*• Ov Ov Ul Q "^ «< p, .» 6> PI in PI d CI ro fO o> 00 c« ♦ W w PN W 8d - ui •♦ w PI •» — p> O VO moo O pN PI mvo vo CO m >♦• « tvoo m VO •♦'jO m PI 1^ Pi M PI M c« Pn 00 f» tx Px H PI d VO Ov n >o •♦ P* f1 •• ro pnoo o ro ■<*••*«■*•»» »M mvo »n in m mvo VO NO 00 p^ n8 Ov •♦00 ro pN in f» * <«• PI NO VO vO VO VO m VO f*" O PN -•F O^OO Ov NO NO IN. t^ K ►- n ro ♦• m m m m m m 00 in I in O m m m mNO 00 n8 in eo BO 00 M I x M (« PO ♦ »n NO NO NO NO vo I NO 1 «2 rvoo Ov o p^ I »• PI fO •♦• w> pN tv 1^ rs t« 00 Pn 00 NO PNOO OQ pN (s, IN »seo eo o 00 PN 00 M n ro ■♦ 00 00 00 00 eo rt o .S C a> a; ^ 5: c ^ M3 o s .S (U u lA ,42 CHAP. V.- OPERA TING KXPENSES-REP KS_ EKC1NES^___ • 1 ^'^iK, in QViflnf»s For this purpose solid steel "'Tfe'"b!e"";)on pp. .40 and ,4: shows the cost of engine repairs per en J e-, nil 0" the Pennsylvania Ra.lroad for a long senes c^ yea. and sufficiently ilU.strates the general tendency of the cost of th.s .tern, he ablX wing however, it nmst be ren.embered. nothnvg '"ore than the cos o abo.- and n.aterials directly applied to repairs and renewals proper wi ho' including any allowances or charges for -P-s. and renewals o^ Tools shops machinery, and oiher items, for which see ..ble 57 and othe,; n figures given are h. all cases for what is now known a the Pennsylvania Railro.rd Division, excluding the la.er acqu.s.t.or.s of the Philadelphia & Erie Railroad, and United Railroads of New Jersey. m F om the above table it appears that the cost per m. e on the Penn ylvlnia Railroad, at the present time, is from 5 to 6 <;ents for engme feoa^rl proper, and this may be consulered the mnunmm under the mos avor'b e cLun,stances, on roads having a heavy traffic and convement o the great iron and coal centres. Many roads-perhaps n.ost roads- .how a lower average tha.. this; but such a result, when .t contnmes for more Ua^ two or three years, is very apt to be one of the before men- Zed .niracles of booklLping, based upon running an unusually large "Mr ;Ve'Sch!.s°e«rroads average about 5* cents_a surprisingly low nv'e^aie for that region of the country, but doubtless very nearly correT U may be explained largely bv the greater proportion o pas- Tr tr, ns (more than one half the whole, as against about one fourth ::r r: : Tn^e-f the country), and also by the fact that a v^y exces ^i tViA frpio-ht iraflfic. as compared with the lest oi me :o:^r;°rn;::ely blT:ess with hght load^. a denser settW region country. 'S mere y t^ain-load heavily in th.s way. CHAP, v.— OPERATING EXPENSES— REF RS ENGINES. 143 all classes of engines, on roads with sufficient traffic to have proper facili- ties for economy in shop work. Wagesdo not vary widely in any part of the United States, and no causes exist for very wide fluctuations in this item. Table 52. Cost of Locomotive Repairs in Detail. Performance and Cost of Three Passeng^er Engines for Five Years, New York Central & Hudson River Railroad (Hudson River Div.). Per- cent- ages. Machinery (and ^ machin ihi lubur) Drivers and tires (and ^ muchinisi labor) Trucks (and blacksmith labor) Boilers and flues Wood-work and flttings, Painting Totals, cents, per mile Percentages Engine O NLV. Tendef t. • Engink and Tendek. Mat. lab. Total Mat. Lab. Total Mat. Lab. cts. Total CIS. cts. CIS. CIS. cts. CIS. CU. CIS. .214 .465 .679 — • • • • .214 .465 .679 .063 •155 .218 • « • • .018 .018 .063 •173 .236 .114 .082 .196 .150 .020 .170 .364 .102 .366 .361 .224 .48s' .021 .017 .038 .282 .241 •523 .014 .056 .070 .008 •OI.S .023 .022 .071 .093 .024 .049 •073 1.721 .012 .010 .031 .036 .068 .104 .690 1. 031 .191 .089 .280 14.0 .881 1.120 2 001 34-5 51 5 86.0' 95 4-5 44 56.0 100. % 33-9 XI. 8 18.3 26.1 4-7 100. o 100. o u M «( Average mileage per engine for the five years included, . . . 416,163 " year 83,232 •♦ " " month, 6,936 •• *• " day in service, .... 278 per cent of time »dle for repairs or otherwise, . . . t-i-"^ " for all enjrines of Pennsylvania Railroad from the beginning of its history (see Table 51), .... i7-9}( The above table represents the very lowest cost at which locomotives can be operated in actual service : First, Because the eng:ines were entirely new at the beginning; of the record, and although the record covers something over half the average mileage-life of a locomotive (which may be taken as 600,000 to 800,000 miles), yet the latter half of its mileage-life (including cost of renewal) would average three to four times as high as the first half ; Secondly, and equally important. Because of the very heavy mileage duty, which is at least three times the average of American f>assenger engines, and four to six times the average of European engines. This heavily reduces the expenses arising from frequent o> Machinery Drivers and lires (and 1 frames) f Trucks ' Boilers and flues. Wood-work and fillings. Pajnttn{j Totals, cents per mile Percentages. and renewals separately. ,34. Rep., o. cou.e ^-^^^:^£x^i:^z:t^ with a very considerable decree " «"^'f J'^^.^" "^ V^pairs of tender. About one eigl.tl. of the cost of eng.ne ^pa-^ '= ^r repa ^^^^ which is of course substantial y the --« /« ^'J ^^J^^J, \^^ „bor, as remaining cost is almost equally d'vded between ma e ^^^ will appear from Tables 5^:53-55-56. ^he cost of - > ^,. slightly afiected by the we.ght of ''- ^"g';;^ ^'J^j „,,erial will be though it is so affected to some exten Jhe cost ^^^^ nearlv In accordance with the we.ght, but not '" X ^°' ""^ ^ therefore, fpensive parts being substantially the same on aU "« - ' ' . _th ^^^^^^^ we say that half the total cost of engine J/'" (';;7^^„.,„ bably varies with the weight, and half .s •"''^P«"^'="' \*'^7°^'^e\ervle, and L very nearly exact, for engines engaged „ he same se^ ^^ ^^._ and tear from their difference in proportion and des.gn. CHAP, v.— OPERATING EXPENSES— REFRS ENGINES. HS Table 54. Details as to Cost of Locomotive Repairs. Cost Per Train-Mile of Labor and Material English Railways, Average, 1868-75. London & Northwestern Midland Great Northern Great Western Lancashire & Yorkshire Gt. Southern & W. of Ireland. Average French. Paris & Orleans. 1875 Paris, Lyons & Med., 1865-74. . Prussian Railways, 1874. State Railways State Control Railways Private Railways Increase per cent in No. of Engines. Labor. 32. a 73-6 8.1 42.3 47-2 15.0 36.4 cts. 3.04 6s 12 86 05 Mate- rial. 3.08 cts, 3 3 3 3 3 TO ID 29 58 34 382 313 1.70 2.00 Labor. R'd H'se.l General. 3-21 Total. cts. 6.14 5-75 6.41 6.44 6-39 6.90 Per cent of Labor. 6.34 3.32 3.83 0.58 1-33 0.80 1. 10 1. 16 1.03 American Railways. Phila & R'g (1869-75). repairs only " (1876-80), " ♦' (1869-75), renewals only (1876-80), " (approx.). total rep'rsand ren'ls ('69-75). ('76-8I). 390 2.38 81 60 7^ 98 1.70 1.98 0.97 2 94 1-93 1.22 0.90 4.16 3.83 4.03 483 % 49.6 46.0 48.7 60.1 47.6 44.6 Av. Total Cost Re- pairs for 31 preced- ing yrs., 1849-69. 49-3 424 41.6 6.90 713 5.87 6.73 536 .40 3.38 4.47 3. 80 6.84 431 2.03 1-5 8.87 6.81 50.0 55-5 654 I 6.7 55.) (40.) (40) (53.) (58.4) For further notes as to ratio of cost of labor to material, see Index. None of these figures include shop and general charges, maintenance of machinery, clerks, draughtsmen, policing shops, etc., which run about 50 per cent or over of labor account on nearly all railways. These statistics are supix)sed to be all per train-mile. The ratio of engine-miles to train-miles on English railways is about as 135 to 100— sometimes even 177 to 100. The same holds substantially true of American railways, reported statistics being generally computed per engine-mile. A deduction of 15 to 20 percent from the total cost of engine repairs per train-mile will give the cost excluding switching-engines, which cost much less per mile for repairs than others, on most roads. zo "S^r- Table 55. Cents Per Train-Mile. Itkms. Boiler Smoke-box, etc Wheels, frame, etc Machinery Mountings Painting ToUl Engine Tenders Total Percentages •*c to 264 cent- on renewals, to .19* credits for old material (7°»"«"f • °" "^^.^^ U^lTfor net cost, probably about *"' t:"« «;-t; constitute over thirty per cent of the labor on repairs proper, or .616 cent per mile. ^ Unaer these assun,ptio„s we are 'f -^^"^.t^'r'pef^Urrt""^ the eight-wheel " ^"^"'^^^JZ^^'^Z^Z^s proper. Heavy Mogul favorable circumstances f° "fP^'^'^f "^^;,\b„„t one tenth to one eighth or ten-wheel engines. ^!""'^; ^l J'" „'^3°', ^^ ,uh the as yet fragmentary „ore. This estimate .s l^^^^^^^Z latter do not exist in suffi- " .0 T.Bt.. S, -- ..^^r ^stuJ t. - tbe En.lUb, sbow tbe cost ^r.LTtrli'nlne'Ir .U en^nes. i.,c,uain. swUcbin,. C^AP. v.— OPERATING EXPENSES— MOTJVE.POWER, I47 Table 66. Engine Repairs and Renewals, Paris & Orleans Railway of France (1865-75). Labor. Materials. Total. Grand Total. Re- newals. Re- pairs. Re- newals. Re- pairs. Re- newals. Re- pairs. Engines .130 .040 .842 •370 .342 .106 1-238 .540 .472 .146 2.080 .910 Tenders 2.552 1.056 Total repairs proper .170 I. 212 .448 1.778 .6x8 2.990 3.608 Tools and machinery Clerks and general .074 .248 .094 • • • • .168 .248 .168 .248 Total all repair expenses. . 1.704 2.320 4.024 4.024 The proportion of renewals to repairs in this table, and in less degree the cost of pairs only, is stated to be unduly low, as appears certain from the figures. Table 57. Total Cost, by Items, of Motive-Power. Cents Per Train-Mile. re- Engine Wages. American. Penna. R.R. 1879-83. L S.& M.S.Ry 1872-81. Fuel J Co*' • • ^''- "I Wood Maint. Locs. Repairs Prober Mt. shops '* tools and mach'y Clean'g and polic'g Watchmen 5-450 4 705 .223 fOil I Tallow , <^tores. . -J Waste Other stores. tLoc. fixtures. '^ater J Expenses Supply \ Maintenance. 5.910 .612 •435 1-715 •133 5.787 [s.ss Mass. RRs. 1878-81, Av. of U.S. Census. 1880. English. Gt. W. Ry 1869-76. 7.0 5015 •255 •259 .123 .052 •358 „ (Taxes ^'«V....^ Stationery. ( Incidentals 'J'otal Motive-Power. .602 .368 •35 \- 22 xo 10.94 S-02 8.4 ^5-6 4.66 4-34 Lab. 3.76 Mat 2.46 0.22 0.40 Gt. So. &W. i875^ 4-32 6.6z iMidl. Gt. W. 1875. -I. II l. •215 .098 •415 21.928 0.6 0.48 2.82 380 0.32 0.66 2?i 6.50 342 2.78 0.20 0.42 22.6 16.74 0.66 0.82 0.50 0.32 1976 1 17-90 'i I „8 ».. ..-or^^^r^^^^J^^^^^s^^:^^ Table 68. ^xT TwPNTY English Railways, COST OF MOTIVE^POWER^^ND_CAK^^ CHAP, v.— OPERATING EXPENSES— MOTIVE.POWER. I49 «.Lareest I 4 ^-a^'ff^*^ CrrpoXns. Corporations. Mass. 1878-81. 11,005 No. of locomotives i 33.203 No. of carriages ' * ' 335.158 No. of wagons * ' ',^;«*e* * * . 17.064 Av. mileage per yearjpe^ejigine^^^^ J_ 12.46 cts. 6.17 ** Cost of working...... engine repairs. .., 18.63 cts. Total motive-power . 2.58 cts. Cost of carriage repairs ••••j ^ gg .. • • wagon 1 2«;.OQ cts. Total cost Iocs, and cars^_^._^^^j^ ^5 $1,086 133 23.41 Cost per engine.. \ pg^ \ carriage v ^^^^ \ it wagon.. ) V 6.118 14.902 171.431 16,520 12.94 cts. 6.90 •' 19.84 CIS. 2.28 cts. J-98J_ 26.10 cts. $1,148 160 20.80 $1,108 370 55.40 considered, without important error, to have tialf the weight, capacuy, *" .w ».n--. „ .,_oad the writer was on the Pennsylvania RaUroaa, m "xVconlolid'atYon locomotives are not and practice with Consolidation cn^ informed as follows by In answer to inquiry as to experience ana SrT."N.lly:Supt.M Motive-Power: ^^^^ ^^^^^^ ^^ curves than other locomotives, we think. hundred miles between a Class I .. 2. The comparative cost of ^^J^^^ ^^J p^en-wheel) locomotive is about locomotive (Consolidation type) and a Class U K as follows: 4.87 ♦' Class I ... 4-5*^ •'Class D, ■ . . . 0.37 Difference, •*•„'*' „ .,.,., «M ^ ■"■ X™ '.'.""i l...«"' " "«' ""'"""■ "" ai rule cost about twenty per cent less most favorable conditions. Table Minor Details as to 59-60. Locomotive Repairs. Deiaif items. Gt. S & W. Ry.. Ireland Cents Per Train-Mile. Detail items. Gt. S. & W. Ky., Ireland. j (Condensed in pre- ceding Uble.) Cents Per Train-Mile. (Condensed in Ta ble 55 ) Rep'rs. RenMs. Total. Rep'rs. Ren'ls. Total. Copper plates .052 .020 .062 .128 .028 .162 •034 .200 [•.260 .214 •054 .262 .416 Mountings .118 • 154 stays .272 tubes Fire-bars and brick arch Boiler sundries Clothings painting, etc .060 .058 .118 Total Engine I 542 I 724 3.266 Toul Boiler .290 .656 .946 \Tender .280 .292 • 572 Smoke-box and plat- form. .052 .092 .144 1 Engine and tender.. 1.822 1.870 3.838 Wheels Axles .114 .198 .138 .068 .164 .128 .128 .062 .092 .164 .326 .200 .160 Less credits .264 .192 •456 Tires Spririps Sundries Labor acct., as distributed in detail to gen- eral items in Table 55: Total Running GW .518 •574 1.092 j Labor, r'd-h'se rep*r. " shop " tender " .616 .976 .286 j- .704 .098 Cylinders .048 .078 .052 .010 •034 .04a •034 .054 .080 .070 .058 ■ .132 .I02 •590 2.296 Axle-boxes ■384 Axle-brasses Big-end brasses Pistons, etc Glands and bushes. . Toul Labor 1.878 .802 2.680 Slide-valve castings, brass Eccentric liners White metal Machinery sundries. Proportion of round-house repairs, Phila. & Erie R.R., about the same, viz.: 26 per cent Total Machinery.. .504 .190 .694 1 of labor. See also Table I3€ i. Table 61. Cost of Maintenance of Tires in Detail, Gt. S. & W. Ry. Cents Per Train-Mile. Date. Engines. Tenders. Pass. Freight. All. Total. 1860-64. . . 1865-69. . , 1870-74... .33 .44 .22 .57 .46 .44 .42 •45 .30 .24 .15 .23 .66 .60 •53 Average . . •33 •49 •39 .21 .60 Mileage of Tires, Iron, Steel, 4' 6" & 6" 52,300 114,500 105,700 196,600 ,50 CHAP. V.-OFEnATWG EXPENSE^-MOTIVE^FOWER^ CHAP, v.— OPERATING EXPENSES— MOTIVE-POWER. I51 w P ( • in £i CO •0 rf a> (O 3 tn «k (« '-^ 4> en U CO C U2 3 is »«-l it 4^ • <■« 3 6 4-1 in «-• 4^ c c 3 3 B B rt c& ^ ^■4 (« c« ♦J *>• H H w XJ CO • tn £ M 00 •^ tf) CO bO M c to •>> ^ in c« u c in 1 in 4>> rt «Q Ui c4 XI u 4-> *>• C c 3 3 E a rt e« . ,a « c« 'i-i <^ H K _• to to 0^ »r> 1 •-• CO vO Tf W HI to i^ 8 M < CI CI HI HI CO M • \o Tj- 0^ M rro >«t "^ Z u u *-> CO CO N r^ u-1 CJ 11 HI JT) • CI HI • td 0. 1 t^ O^ CI d in CO "4 CI rt w CO 55 J (z:] . 00 00 il- »n 0^ rf Tt • m 2 N M ^ CI i-i vr> \rt N M CO HI CI hT hT hT 0" CO M (> rC 8 HI HI 00* , •^0 »r> r> » Tt CO CO » •* CO CI u-> '^ . m «r" rt CO CO Srt VC CO 11 »H IT) CO CO r^ CO en HS HI M "^ in nO tn 'I- -J-QO O^CO CO 1 HI CO vO vO »n Q • N 00 U) rt CO CO vo r^ covO CI vO CO 2 0-9 U-> t-»i •-< HI Tj- CO in ci" CI 11 to CO • e- • • »r> in CO 00 • c« • \C\ CI r^ • . CQ c • • 1- ■* • -J- r^ • 10 «r) in • m u H • •<^ M .^ O^CI ■ r^ • 1 00 CO HI CO M • t^ 00 00 • < • m HI d 4» • -"l- "^ • • M P3 U _j • to to CI in CO • vO < 4> • CI CI CI vO u < V •«^ • fH _ ;C < ^ > * M CI h^ CO CO • •J i- M • M • • • VO >• en «" ^ ■«t CI t^ QO • HI 2; 1^3; • CO • CI CO • • in CO CO • • K > HH HI • M w • * CU • 1 ^ 1 • ~o~ T • M . c ■t ' -< V H. to CO ^ 0^ M HI to , , ja «^ CI -* ^ »n • I HI h) , CO >n • l^ M 00 M »-« •C 1- HI O^VO fO • H Tf m • • vO -< «^ M HI HI . ir> in r^ • H a M H (o Q • , h< si: H4 4 • • H c c/> w » <-• CS u •t3 c » >. 4> C bo <« b^ >.bc : c c u en u V ti D C o^u.(i4ai 4-1 -a c 4-> H It a 4-1 CJ >■ << s o m V en en O ^ o c< >.S en c bo c (J . U . (J Hn ^ He» *^ '^ CI CI CI Tj- CI 00 O^co m O II II II II iJ -> - o V) u- 4> »- u .ti 3 o - en en {/) TD C Hi 6 m 4-> o a. Ui V 4-* « •^ ^ ^ c C73 a — o c § •" ? C 3 -, « ■" ■" re u^ .£u «^^ ■" 2i c 3 O •a ^a^ = U U o cJtt o -JS <« O 1 ' 00 '^ (o «; « o cx:'C3 «J^ — - CJ= « CO t, 4> *' — cni o c: ^2 ^ C3 O 2 O O-g fvQU o-S w n.S„ C/l " CI o o -a OJ cs O «— W m CI M V o ca O .22 ctf CU > •Si2£2e > c8 *-> u to u en bo £ ll-C H W - O — *' Q a.c»^ --. e V c IS a — -w ft> , *j ,, Jr (I4 en (4 JCJH- C (O I. o : u j3 ^ Si "-sis i; V a V U.4-1 eo 4^ c 152 CHAP. V. -OPERATING EXPENSES-MO TIVE-PO WER, Table 64. COST OP A PENNSYLVANIA RAaKOAD "CLASS I" (CoNSOUPAT.ON) ENO.NE. %% Boiler Machinery Running gear Frames Fittings Painting Total engine. Tender Material. $1,877 935 1.456 200 652 47 Labor. Tot. engine and tender. $5,167 845 Toul. $6,012 $3,968 Phila. & Reading. 1881, average of 18 engines. $9,980 $10,370 See also Table 134. Table 65. R.X,0 OF COST O. MATKKUX.S TO TOTAL CoST .Oa BOTH NEW ENO.NBS ^ AND Repairs. On New Engines (or Renewals). Chicago, B.&Q.RR-, Class A.... Pennsylvania " " C... " I. • English (R. Price Williams) Gt. So. & W. of Ireland 41 »* " renewals.. Paris & Orleans. 64.6^ 66.7 60.3 78.1 72.9 69.5 71.8 On Repairs Only (,ex Renewals). New York Cent. & H. R. RR Philadelphia & Reading Av. of U. S., repairs only ii »» repairs and renewals . . Gt. So. &W. of Ireland " " av. repairs and renewals Paris &Orl.," " " 43-3 Abt., 44 " 50 45-3 55-8 58.0 CHAP, v.— OPERATING EXPENSES— MOTIVE.POWER. 153 135. The apparent cost of repairs has been kept down on all our rail- ways for the time being by the constant additions of new stock, thus greatly reducing the percentage of renewals and heavy repairs. Table 51 will show to what a very important effect this cause must have contrib- uted to reduce the apparent average, especially during the rapid growth of traffic of the last ten years. 136. The distribution of the cost of repairs to the various parts of the locomotive concerns us quite as much as its total amount. Information on this head is somewhat difficult to procure, as, so far as the writer knows, no American railways publish such statistics in a complete form, and few take much trouble to collect the information. Tables 53 to 67, however, give the cost of new " American" engines in detail, and also very full statistics of the cost of engine repairs and renewals on English railways, which latter are undoubtedly substantially accurate, and (with proper allowances) of general application to all railways. 137. From these data we may conclude that, with no very great fluc- tuations, the total cost chargeable to repairs of engines, including renew- als, may be distributed about as follows : The boiler and its attachments require about 20 per cent The running gear and frame (of which the frame consumes very little, say 2 per cent), 20 per cent The machinery proper 30 " The mountings, fittings, and painting, 12 " The smoke-box and attachments 5 " Total of engine 87 per cent The running gear of tender 9 Tank and body of tender, . , 4 « Total 100 per cent 138. Maintenance of shops, tools and machinery, and other miscella- neous motive-power expenses do not usually appear, as before stated, in statements of the cost of repairs or of running engines, although they con- stitute a legitimate addition thereto. On the Pennsylvania (Table 57) these items, including stationery, incidentals, and watchmen, but not in- cluding the item of " laborers," — the latter doubtless largely for clean ino- engines, — amount to twenty-five per cent of the cost of engine repairs, or about \\ cents per train-mile, and the item of " laborers" to as much more. This is higher than is usual, or perhaps it would be more proper to say tW^K t1> 154 ClfAP. V.-OFE,ATWG EXPENSES-MOl^yf^^^ that it is based upon a closer apportionment than is -^^1; --V jj"^^ ^•^Tarri^re-noXr^'r:!^;:^^ an^Lirect motive-power expen^s^^^^^^^^ r aK^h^rs^ieSs! U aU the e.^nses are apportioned "'^Thist an "xpense whicl, is affected but slightly by very considerable .ir:re?.^-.n....dben.^ engine repairs proper, but rareiy ib. it la « v -r .; :r r;r..« .... ■-- — rr ;2,%s one cent per mile, .but often run as low as half a cent, or even Table 66. ^r^r. rn^T OF Labor and of Material, and of the. P.KCENTACES 0;;^-J-;- ';rNBW LOCOMOTWBS. ,SHop ana .ne., e.^nses no. -udea, — in, .0 a.u. . per cen. o. U^r Items. (For amounts see Tables 6i. 6a, etc.) C, B. & Q. RR. (ClassH). St'd FreiRhi. Penna.RR./'C." St'd Passenger. Penna. RR., " I.'" St'd Freight. Lab'r Mat'l Toul Boiler and braces Machinery Running-gear Frame and bed-casting Fittings and pump, cab, etc Painting Total engine Tender Total engine and tender. Reported cost labor and mai'ls. Cylinders and weight (long fns) C//AP. v.— OPERATING EXPENSES— MOTIVE-POWER. I55 Table 67. Percentages of Cost of Various Parts for Various Foreign Locomo^ TIVES. ^ (For American, see preceding table. See also Table 131.) Itrms. Paris & Orleans (France). St'd Freight. Boiler^ smoke-box, chim- ney, stays Ask-/>an, foot-plate, cab, sand-box Wheels, bearings, frames, springs Machinery, pumps, re- verse-gear Cocks, safety- valves Fainting, brass sheathing. Total, both engine and tender Lab'r Mat'l Total 8.3 2-3 5 7 10. 1 0.9 i.o 35-2 2.9 18.2 10.6 2.2 2.6 Reported cost, labor and materials Cylinders and weight (long tons) Approx. increase per cent in cost, due to 28.3 43-5 5-2 239 20.7 31 3-6 Items. Boiler Smoke-box, etc.... Wheels, frame, etc. Gt. So. & W. (Ireland). St'd Freight. Lab'r Mat'l iTotal 71.7 100. o $9,650 (17X24)— 29.5 tons r \ brass in b'r i6.oj( .( f wr't-i. wh's ii.65< Machinery. Mountings. Painting... 5-6 3-9 3-3 9-5 1-7 I.I Total engine and tender 25.1 27.6 4-3 27.5 8.7 4.6 2.2 33 •« S.a- 30.8 18.3 6.3 3-3 74-9 100. o $9,424 17X24 — 30.0 tons. .10.0^ .i2.8)C Items. Boiler Wheels, frame, etc. Machinery Smoke-box Mountings Painting Gt. So. & W. (Ireland). Heavy Passenger. Lab'r 5.0 4.5 10.4 51 1.9 1.6 Total engine. Tender. Total engine and tender. Mat'l 23-3 28 5 7-4 3-8 6.0 2-5 Total 28.3 330 17.8 8.9 7-9 41 Great Western Railway (England). Heavy Passenger. Reported cost, labor and mat'ls Cylinders and weight (long t'ns) Approx. increase per cent in cost, due to 28.5 71,5 100.0 $9,072 Lab'r 3-8 5-6 4.9 ■9-4 23 -7 17X24 — 31 tons. (17X22)— 30.3 tons. jbrassinb'r %.o% 5 ojS { wr't-i. wh's 13.3d 10. o^ 5-8 Mat'l 25.0 19.4 3 4 II. o Total 58.8 29.5 II. 7 70-5 28.8 25.0 8.3 20.4 82.5 175 100. o $7,432 St'd Freight. Lab' 4-1 5.7 4 9 •9.6 Mat'l 24.6 16.0 3-2 12.4 243 6.5 30.8 56 2 13.0 Total 28.7 21 7 8.1 22. 0' 80.5 69.2 19.5 100. o $6, 709 17X24—30.5 tons. . 5 o< .lo.ojt The distribution to items is not precisely identical in these tables, as will be apparent 'rom the percentages. Multiplying any percentage by the total cost gives the absolute expenditure for the item. 1 56 CHAP. V.^OPERA TING EXPENSES-MO TIVE^PO WER. CHAP, v.— OPERATING EXPENSES— MOTIVE-PO WER. I 5/ ■li larger roads, especially where there is an independent account kept with "'hi" Wa'ter-supply costs about half a cent pertrain-mileas an average, son ^tnlunning below that on roads of very heavy traffic, but ofter.er runningnearer to one cent per mile. On all but roads of very cons.der- ab" trfffic one cent is the safer estimate. The quantity used ,s very con- siderable About six or six and a half pounds of water, as an average, .s evaporated per pound of coal, and a freight engine burnmg a hundred ;Zds of coal p'er mile will use some eighty gallons o --- - ;;^-- The refilling of a 2400-gallon tank within t nrty m.les ^''^e "Wnost as an averac^e. Practically the consumption of water, as of coal, is '"-egular, aid afull tank may In cases be used up within fifteen mdes; requ.rmg. for pr ctical convenience, tanks every ten miles which - th-verag^ - roads of thin or average traffic. On lines of heavy traffic tanks a e Jaced at average intervals of hardly more than five or s.x m.les. Table 57 gives considerable data as to these mmor items. 142. Switching engines constitute an enormous proportion of the total numberTr service on most roads, the average of the whole State of New Yo?k be"n/twenty-eight per cent of the whole number m service, or Larly fo"; switchLg Engines for every hundred in through servceearn- "„g money Tl.eir "mileage" is fixed by an allowance (usually s.x m> e "^ Tour, but sometimes eight), so as to bring their expenses per "mne Tr, some reasonable or desired ratio to that of through c.g.nes. The Ireat expense of this service does not tend to decrease, but rather to m- freLe w^th growth of traffic, and is with reason felt to be largely due to removable and hence discreditable, defects of admm.stratK,n. The buTden i ;omewhat relieved at the larger terminals by fixed te-^ <:har<.es allotted out of the through rates before d.v.dmg >t (at New Yo k four to five cents per hundred pounds out of through rates of twenty to hirtv cents, or even less). It is a charge but little affected by any of the details o"a ignment. so that we need not discuss it in detaU. but m cer- t!in computftions it is an element which needs to be ■•e^embered-nota- w" in computations of the value of reducing grades on old -ads whereby this portion of the motive-power expenses is not ser.ously reduced. The diagram given in Fig. 4 illustrates very fairly the .P«""f-<=y ;' I „,!„, %xoenses Alone of all the items, wages, it will be seen, have rlldprlcti ally uniform. There was a slight tendency to decrease during ZZU^^ of .877-79. but they recovered later, and remain at the end sub- ctantiallv what they were in the beginning. The cost of fuel declined sharply aher .872, but since 1876 has been nearly Fig. 4.— Locomotive Expenses, C, B. & Q. R R. I 158 CffAP. V.-OPERA TING EXPENSE^MOTIVE-POWeR. uniform Tvtq possible causes for this are indicated on the diagram both of rhich p obably had their effect. One was the increase in miles operated wh.ch Irobabrgave better access to coal-mines, but another and probably very Tportant contributing cause was the increase in miles run per engme per year Zch likewise began simultaneously, and ceased to advance sharply after the rn«!t of fuel ceased to decrease. The course of cost of repairs is very instructive. It will be seen tha the decrease has been enormous, and it is, doubtless, in great part d^'" "-'"/='' Z permanent causes, such as the decrease in cost of matenals and better shop facilities. But it needs but a brief glance at the line showmg Number of Ses on road," in connection with the cost of repairs, to detect anothe explanation, of vast importance in its effect on operating expenses, wh.ch .s too little re;embered in studying ma.ntenance charges, viz., the enormous and continuous infusion of "new blood" into the locomofve stock, gmng at all *imes a very large number of new locomotives in the stock ,n addtUon to the portion natufally required to replace old engines worn out. As new eng.nes cosHomparatively little for repairs, it is inevitable that this abnormal propo - ^n of ne'w engines should greatly affect the average -«;' ;;=P-^^^;^;'„; verv clear that it did so. The very small expense for repairs m 1875-9 "^s not rhollyd"e to economies enforced by hard times, although no doubt largely so Tut in great part to the fact that there was a greater proportion of new engmes Ts rvl e than at any time before or since. Afterwards the mevtab e .ncrease the continual additions of new stocK cease, u is v ;r ..^.^oir*" tne conu remembered also that these nommal repairs rr i^lirm^V i'dl" - - maintenance of s-PS etc. which a„ reallv a part of the cost of repairs, but not ordmanly included m .t A ch.et reason for th^ heavy decline since .866 is undoubtedly the contmued .mprove- m'tin the character of the roadbed and in the quality of the workmanship and ""Xhe'ln^rete in the average miles run per engine shows an unusually favor- able record and one not likefy to be much further improved on, since an av.r^, of near V a hundred miles per day for every day in the year and lor all engme. nearlv reaches the possible limit. It implies that single engines have more than doubed this The decrease in miles run and simultaneous increase m cost If'paTrs per mile run in x88, can hardly be an entirely accidental come '""able 68 shows the average miles run per year and the -e«ge cos. per vear of "locomotive power" (repairs, stores, wages, and fuel) on ten repre- len ative English and American lines. The latter by no means represent the Us Amerlan practice, as will be evident from Fig. 4, but are those Imes (for CHAP, v.— OPERATING EXPENSES— MOTIVE-POWER. 1 59 the most part) which are operated under the most fairly comparable conditions with the English lines. Could the ton-miles and passenger-miles per year per engine be compared, the contrast in work done per engine would be astounding -«f 'V^PP''^ Tthe cars themselves, and there is a considerable amount of >nc,d.ntal expendrre, which is really a part of the actual cost of "-"'-"'"^ ^"^t ca^s but which is yet. for very proper reasons, already suted. not gen erally included in the reported cost of car repairs. „ ,„ ,. ., ogr Such general and incidental expenses amount to from .o to 25 per cent of the total cost of car repairs proper. Table 70. Average Cost of Car Repairs on Western & Atlantic Railroad fo« Different Kinds of Cars. Cost Per Car Per Year. Passenger. Local Box. Stock. Coal and Flat. Line. Running gear Interior fittings Misceilans material.. $64.80 23-45 41.75 $6.78 12.10 $7.46 8.50 $6.76 6.50 $19.09 13. 49 Total material Labor $130.00 111.50 $t8.88 II. 12 $15.96 9-35 $13.26 4.48 $32.58 10.62 Total $241.50 $30.00 $25.31 $17.74 $43.20 Miles per car No. of cars in use.. . . 36.480 138 7.780 194 5,601 40 5,420 489 10,045 648 The above includes, whether by chance or otherwise, no charges whatever for seats or upholstery of passenK:er cars. Otherwise it includes all work done in the car department for maintenance of cars, both repairs and renewals. The cost per passenger car is very low. Tables 70. 71, 72, 73 were computed from data given in a very careful paper on car mileage and repairs by E. C. Spalding, Car Accountant W. & A. R. R., and afford about the most trustworthy data on the details of car repairs which is extant. Such information is very difficult to obtain, and even this affords no means of distributing expenses to different parts of the car body. Making a proper allowance for labor, it will be seen that somewhat over 40 per cent of car repairs arises from running-gear maintenance, and nearly 75 per cent from truck repairs. By far the larger part of the remainder is for draw-gear re- pairs. Other repairs of body are a very small expense. These statistics give the true average cost of car repairs for a stock which II „*■, t ■w*r- ,62 CH.^P_V^^0PERA^^ ~ ' ". ~ZZ^A Thev are almost the only records of is being neither increased nor decreased, l ney arc mileage per year, so ihat the rottn.g a ^_^ ^__^ ^ ^^_^^. what higher cost per mile run for such cars, for running gear only and for the aggregate of »» '^-^^ ^^^^ s„„,,„„ Table 74 giv« 'he cost of car repa.rs on the Lake Shore «. g ^__^ ^^^^ car maintenance is clear from the note to the table. Table 71. i>-t,AT„<; Pfr Mile Run by Items for Cars of Cast-iron Wrought-iron Lumber Springs Bolts Paint Labor Nails, chains, and metal- lic sundries. Av, miles run per year Av. total cost per year C//.-iP. v.— OPERATING EXPENSES-REPAIRS OF CARS. 163 Table 72. Cost of New Box Car in Detail, 1883. [Deduced from data given in a paper by E. C. Spalding. Car Accountant. Western & Atlantic Railroad.] Material. Lumber 3,987 ft. Wrought-iron...704 lbs. Cast-iron 606 " Nails, etc Draw-springs. . . .46 lbs. Tin roof Painting Total body P. c. of total cost.., $79-74 35 20 18.18 5.21 414 12. 60 3-28 f«58.35 31.2 Labor. } 20 days carpenter. $45 00 4 days tinner I'y^ days painter. 4.00 3.00 Total. $52.00 10.2 $183.33 4-14 x6.6o 6.28 $210.35 414 Per Cent. 36. z 0.8 3 3 X.3 41-4 Truck. Wheels........ 4,200 lbs. Axles 1,400 " Brasses 64 " Springs 184 " Lumber 487 ft Wroughi-iron. 1,000 lbs Cast-iron 1,306 " Painting \ $ Total truck . 160.00 14.08 16.56 9-74 50.00 39.18 ■79 $290.35 Total car $448.70 Percent 88.5 $x6o.oo 24. 08 16.56 J04-57 1.29 315 3.8 [■Carpenter Painter $5.65 •50 3-3 20.7 •3 $6.15 $296.50 58.6 $58.15 "5 $506 85 100.00 100. The weight of metal in a standard New York Central 40,000-lb. box-car is dven as follows : t, «» Wrought-iron in car body 2,552 lbs Ca.st-iron in Steel in 797 104 *' Malleable iron in " i^U •* -iron in trucks, includ'g axles, 3,144 Cast-iron in trucks, includ'gwheels, 5,366 lbs. Malleable iron in trucks 48 " Journal-bearings 80 " Wheels, each 525 Axles (M. C. B. SUndard; 347 •• The total cost per tratn-mile of passenger-car repairs and freight- car repairs is very nearly the same in the aggregate, as may be seen from Tables 75-80. although the proportion of the constituent elements differs considerably. (See par. 1 50.) «! Table 73. AVERAGE COST IN DETAIL OF KEEP.KG .N REPAIR TWCKS AH» BODIES Separately of Box Cars. Age of cars three years. Built at cost of $5.5.00 each. (Compare Table 87.) Trucks. Original Cost, ta^S- Items. Cost Per Year. Axles... Brasses Wheels. Running gear. $3 04 12.44 6.06 Per Cent j of Total. Body. Original Cost, $200. 6.3 25.8 13.6 Springs Labor Cast-iron Wrought-iron. Bolts Lumber Nuts Paint $21-54 Total $4-97 a. 7a a. 66 3.10 .67 .11 .03 .03 Items. Cost Per Year. Per Cent of Total. 44-7 $34.81 10.3 5.6 5 5 4.4 x-7 Labor Cast-iron Wrought-iron Bolts Lumber Springs Chains, nails, nuts paint, screws, sol der, tin 73.3 $5-45 x-33 1.40 X.II 1.70 1.36 X.X9 3.6 2-9 a. 3 3-5 a. 6 <.6 Total cost per car. $13.44 37.8 $48.25 lOO.O all the Western & Atlantic records. per car-m>le. tl ,s ra e havmg ^^ ^^^^ ^^ ^^^ ^^^^^^ _.^^^_ 1:Z ct"nrrn:trvice. U not ^ ^^^ ^:'^ „3e. ^^^'^Z:^T^^^::ii^lL ... road is sufficient to do tins, espec.ai y expense, any using foreign cars is ''^''^^^^^^^ deterioration which parts of the car otner inan CHAP. V.-OPERATING EXPENSES-REPAIRS OF CARS 1 65 suffer while on its lines. Nevertheless, whenever business is brisk and cars are scarce, which may be one half to two thirds of the time, the price fixed is not sufficient to cause cars to be sent home, and earnest efforts are now making to bring about a change. 145. This effort is more particularly directed to the fixing of some per-diem rate, to cure the great present evil, that when cars are kept on hand, on a side- track, instead of being sent home, sometimes for weeks, the offending road loses nothing, since it pays nothing for the car except wnen it is in motion. The most favored plan is a change to a mixed per-diem and mileage rate, approxi- mating to 25 cents per day + i cent per mile. If the car were kept faithfully in service, there would probably be no dispute that f cent per car-mile is sufficient to cover (i) maintenance and renewal charges, (2) interest on the value of the car, and (3) a fair business and punitory profit in addition. Table 74. Cost of Freight-Car Repairs Per Car Per Year, on Lake Shore & Michigan Southern Railway, for Six Years. (Average mileage of cars per year, about 12,500 miles.) Tbar. 1880 1881 18S2 1883 1884 1885 Total, 6 years Av. per year. Cost Car Per Year. Repairs only. I47.S0 43-46 38.90 30.64 21.24 35-30 New cars built for acct. " repairs." $217.34 36.22 I4.OO 2.74 1-59 5.56 3.17 1-05 Total repairs and ren'ls No. OF Cars 1x8. II 3.02 $51.80 46.20 40.49 36.20 24.41 36.35 Total in use. Built new for renewals. $235.45 39-24 12.107 14.663 16.796 16.649 16.355 16.629 107 66 58 197 108 38 15,520 574 95.7 For the ten years 1870-7C preceding this table, the Lake Shore built in all 2,233 care entirely new on renewal account, making the total number rebuilt entirely new in sixteen years, 2,807. The stock of cars, beginning with 6,077 in 1870, was increased to 10,185 in 1874, and then remained practically stationary until the middle of 1879, when the increase be^an to the figures above. Except that a large majority of cars are rebuilt piecemeal, and mamtam a kind of continuous existence, at least 10,000 cars should liave been rebuilt durmg this period instead of 2,807. It is probable that most of the latter were broken op entirely, chiefly because they had become of too antiquated design to be serviceable. Mi' 1 66 aiAP. V.-OPE RATING EXPEN SES-REPAIRS OF CAKS. 146 The repairs »hich the road using foreign cars has to pay for in addl- 146. 1 repa importance, and are determined •'°:h!: :r M vryH " n7oL there is an inspector, usually a Joint in- -:rio aiits ra!s ov°r:rrvi::i^ra:ry;r.rKire:cfr:;::.de" determined "^^ "'-- f -"y^ t p sed oi as fuifiiiing a.i the same -=ndir,::;^^^^^^^^^^^^^ rr:?:•mlaer^::a1du'^n1o.t•mrgr";ytents. .--^vayaroad ;"aVc:.^e::t'to pay for repairs due to gradua. de.^^^^^^^^^^^ "°7 r ti,:!:" rpTprtc":;": ast hi::; "pL^ i..spectio^n, it does small '°7-y/Xe Lenh: United States (or theVt twenty years, 'Z'::~Z^:iZ^^^^^^o. but be greatly affected. Table 74 the appciretiL cosu v ^ ^^^^^ ^ny Item. Few railways keep. F enormous a^^pjregate of cost of the vanous .^..^ wh^^^^^ ^.^on 'which appears in the reports. " repairs o cars, ^hat being t > ^^^,^ ,^ determine pre- or. as a rule, on the books. It is ^ner^^^ Nevertlieless. from cisely the ratio of the vanou-te- to e^^^^^ other^^ N^ ^^^^ ^^^^^^^^^ the information given m Tables 70 to 73 ^^^ especallv Table 87) we may conclude that ^^e actual cost P renewals of freight cars is divided very nearly as follows . CHAP, v.— OPERATING EXPENSES-REPAIRS OF CARS 167 Wheels 30 per cent. Axles, brasses, and axle-boxes, 30 " Springs jq Truck frame and fittings, 5 Total truck, 70 ** Brakes, 5 <• Draw-bars, jq «• Sills and attachments, 5 «« Car body, painting, etc., t «« Total, 100 " 149. Passenger-car repairs are, for wheels, axles, and brasses, but slightly more than for a freight car per mile. Exact information as to the comparative mileage of passenger and freight wheels is difficult to obtain, owing to the fact that as soon as wheels show any noticeable de- fect, which yet does not make them unsafe, they are withdrawn from pas- senger service and put under freight cars, often making a large mileage before being finally scrapped. The general tendency of the available evidence is that there is but little difference, and that difference in favor of passenger cars, the effect of the higher speed being counterbalanced by less injurious brakes and better springs. The extra cost of repairs and renewals of passenger cars is mainly in its decorations, better painting, and interior fittings; and bearing in mind that passenger cars are not exposed to anything like the rough service, blows, and shocks which come upon freight cars, we may say. without any error of moment, that the average cost per passenger car-mile is about as follows : Frt. Car. Pass. Car. Cts. Per Mile. o. Running gear, draw-bars, etc 0.3 Sills, frames, etc., o.i Painting and varnishing car body Interior fittings and upholstery, Total. 0.4 0.2 0.2 0.5 1-4 tSO. In other words, the cost of maintaining a passenger car for those Items or parts of items which are affected by differences of distance, cur- vature, and gradients is not so much greater than for freight cars, but l68 CHAP V -OPERATING EXPENSES^TRAm WAGES. iBl The average milea-e of freight cars per year, taking the wiioie miles per year, or even le=s. The tende"cy . J ^^^es e..or- J ^c« ThP mileao^e made by dittereiu cars, nuwcvci, , •• W" ^a s so called, belonging to the independent or sem.- 1 nUef^e as'is but natural: both because they are exclus.vc y looked after. The general average of all classes ol ^ 70) is about as follows : ^.^^^ ^^^ ^^^ ^.^^^ p,, y,^,. ,c to 20 5,000 to 7.500 Coal and flat cars '^5^^ ^ 9,000 to . 5.000 B"'"^?,'^ 7010100 25.000 to 35.000 '■"'^MeV : : : : '. '• 35-45 -.000 to .6.500 The average ™ilea.o. pas^.er ca. -^-^-,^1^.^. 1!^:^:TrTl^^ than this-up to. in so.e case. ,.:t^C-, are less dimcuu ^^ -rtL1':o^rrr:hi^r; „ess. The following are a close ''PP^"'''"^^^*^^^ ^i,,^. m ,^■,^^^ prevail in this country for average runs of a hundred ^^ ^hey were naturally higher than ^^'S. say 5 Per ^^^^^^^ «^„^ [,,„,, ^hey^;^;"c"oLSy iM^^l'U of the country, but less than any other item of train expenses : ^^^^^^ ^^^^^^ ^ ■ „ ftv5oto$3.75 ♦sso'o*^^ E"g'"«"='" ,\.x.o loo .75 to 2 oo 1''^'="'^" 275 to 300 375 to 500 Conductor ■=•'> ^ , co to %V> Braken,an (each. $..75). 3-50 to S-^S 3.5° to 3 5^ Baggage-men, . • • • • • • ___J_11 - — $11.50 to $14.00 $14.50 to $16.50 CHAP, v.— OPERATING EXPENSES-STRAIN WAGES. 169 153. The system by which train wages are fixed varies materially. It is sometimes strictly by the month or day, especially in passenger ser- vice—a certain run being called a day's work, independent of the time actually employed. These runs may vary anywhere from 75 to no or 120 miles; but if it constitutes ^/^/^r/^ a day's work, it is rated a day, independent both of time and distance run. This system was formerly universal, and is still very common for pas- senger service ; but with increase of traffic, and especially with the con- solidation of lines into great systems, with runs of widely var>'ing length, the practice is coming more and more into vog^e of paying strictly ac- cording to mileage, in the manner specified in par. 191. The chances are that the tendency to pay in close accordance with mileage will be- come stronger and stronger with the great organizations, especially in freight service, while the former plan will always prevail with the smaller independent lines, and even on many of the larger lines for passenger service. 154. A compromise plan, intermediate between these two extremes, is at present more usual than any other. The runs over various divisions are graduated as i day, i^ day, \-^^ day, sometimes, though rarely, \ day, etc., etc., so as to have a close correspondence with the real distance, but not to be in exact ratio thereto ; other circumstances, such as number of stops, etc., being often taken into account. This appears to be not only fairer than an exact mileap:e basis, but more acceptable to employes. The present system of handling traffic, by which the freight crews not only know no distinction of night or day or week-day and Sunday, but do not even recognize the day of twenty-four hours, tends to facilitate this basis of payment; the crews being "on" or "off " at intervals determined by the pressure of traffic, and not at all by the number of hours in the day or days in the week. In passenger service, or wherever the freight ser- vice is tolerably regular in its character, the deference paid to an exact mileage basis is much less marked. (See also par. 191.) 155. The tendency is strong to increase the length both of locomotive runs and of divisions. Locomotive runs were formerly from 80 to 100 miles. At present they range by preference from 120 to 150 miles, the gradients being often, of course, a controlling condition. The prevailing tendency is well illustrated by the locomotive divisions on the Canada Pacific, of which there are 19 on the 2445 miles between Montreal and the Pacific, an average run per locomotive of I28f miles. The shortest ^nd longest mns are : (See page 178.) I70 CHAP. v.— OPERATING EXPENSES— SUMMARY. m o 0) H H (A o H cn (A o > o Q S <§ H - in S •a ■»*• c« o Tt « M o • • - M CO M IH CO -^oo -f >^ c* 't O O r- CO • • ^ <«tco t>i y CO O \0 M O CO M N ki^ CO r>i \r\ T o , • • tn O O l>4 oo M CO o o M 6 d 6 in O «^ ^<* ^ C4 CO to n O CO M r^ ei to O O o vO >-< Q ^ ^• •O in O^ N w M 1- in CO >-> i-< O O t^ 1 o = > U CO O N CO n- >H o • • M CO vn N w N O »n . • . If. COCO ^U in CO « inW 1^ O £i.in to r~» ^4 T "^00 1 c< • • H« r4 -t •^ oo 0> in N . • • . (T. CO l-> r^ w in C0(i,0 O Tj- in CO CO vO C^ *~^ oo d 6 *n ^ CO t- r- vo C* O^ t^ \0 O O m W o »0 O CO c< vO m coco • • • • to «t O O O m t^ T t 00 W >* O O O CO •J '^ •J O rt is ►- o pi -c ^ E b. o O o fa < H P < in M C/) Z W P^ X u o %* CO O vO O CO C vO • • • CO in CO c« N . • • • "■■ vO O o o • • • in" C* inji^O w in w r^ • • • • O* O "^ o in to 00 vO CO o o O CO coo O O o COO CO -1-0 (>! »t (M in iTi O t^ N -^ O O ^ ri c> C' r^ •* (> N^ CO Qv to M O O 00 C4 O "I r^ inO CO CO in CO • • - CO to in M "to ^ in O " CO 'i-o.o r^ CI O in O c« CO i>4 O ►H m o^ in in toco N O •-••-' tovd O M o d M o '-' toco . • • • * t^ too O O oo CO oo inco <^ qn m in CO to , . . • • O CO "if O O "■ CO in N -^ OO O *•* 1 in O 00 00 w in o N4 ■^ M O M CO H^ c> 1^ • • M CO r^ CO r* oo to O . • • . »)QO O y -* o (H in OO OO w d in^O M CO o O* too ^ • • • • C* O "-• o C> O to H. ei vd d w to CO CI in ■^ too i^co O to to r^ w in O O % o in in u H < in b. O M o o in & in H U «/) .ir I/) .^ J' w IC > 5i *= o X ? S «u c: o c v< O C c u _ V. 4> D 9 CU ;X4 (A o .5 3^ O ifl^ £ w C •- w {^ rt in o «« «^ i" rt «« «; C «« vl ™ *- 4; 4; ^ *^ f -2 « 4/ "t, o rt <4 w I I lA U o.- 4> lA 4; c iS •5 ° > .ii -?; . w 4^ (J be j1 C J- CU(3b, CtJ o H 4> lA 4J C c- (A C tCrt C u rt O C//^/'. V. -OPERA TING EXPENSES-SUMMAR Y. 1 7 1 CO inoo *♦• O M O O 1- O O CO CO in CO CO fH o M 00 r^i 00 f^ r* Ct o N -^o o o o CO to in coco 00 r^ r^ M o 0^\0 C^ O "-• m coco 1^00 t^OOmTj-MOOOco 0» to ►-• r>iO c^ in O N in r^ ►* coo '^ N O O CM CO 8o 8r1 00 O c* to •^ to to odd inoco inoO O O too CD •"■r^wo^OM^-ivou-io «-• t O O M -^ l-l o o o o to in "^ r^o -Too ^ r^ O i^o o N in to to >-i O — Oi i O^ e> m CO ,£j M in T o o o m lO o O CO 8 M O oo 01 a O CO coo "^ O "t O "t -too N oo rj- -r OMMTj-rJ-OOOM'^t o eo N w O O t M o too o i-i w 00* 4 to ci d M CO CO to CI 6 too CO -I- -to M 00 r^ CO M CO •1 •<•••■.. •lO'-itoeiOOO'-'in CO 00 O O Tt 8 0^i M CO -t O m O^ N moo M 0> inloo • • • . • O t e« N to o to O in CO o f< M M tr CO O O O O O ^ r^co O O oo cooo N inO\i-i i/iTtr^rxin pjdO^coOOOO't CO O^ Tt in r^ M « CO O m M -^ •-• ^ to N N O o O O o d -^ o o o ^• ICO — o^ CO to 1 {V| N to CO I a^ O o o o p* M M r>.o OOO -tei ^CO O t->. Tt 1^ CI 1^ CO N OQiHCOcoOOOi-iO CO CM O CO d d o o c C (A in :Q rt u « a. c rt .ii lA 4) (A C V cu X V c o «A 5 ^ ti U rt rt (A (A O to «A - - 1> — lA 5 o ^ 4) (J C a £3 d o a. v> c t-« .i •= = a O 3 C 2 OQDCU. £ 111-^ £ o rt - H a* - rt « >> 4t ^ w bo 4» C lA I- 1- :« I I I 4) be a rt TJ "O C - . rt • (A lA .3 = 4; bo S rt •- e e C^ 4) c rt lA (A "rt o c _o '^ (A cQ 4> c a rt (A Q. c 2 (A C ~ — if X (A T3 C rt (A V u o C fco (A 3 O be = bo.EiS rt c rt . ^ rt - O ^ O Xi rt (A in c 41 U _c rt •01 F • £ 4) . ' ■Z, ^ ^ ;= o V- c -a 4; O C ^ "Zj jc •-^ ^ O ° 1/1 >^ y 5 O 1 :c - rt . C/) rt is 0) "O o -^ C -' T3 c > - rt HH 2 •S '!= rt* ■^ o -^ S .S (A w O ^ a; , *«- _ i« JS o Hy 1- •-^ c "^ rt S — . .2 S .9- = "^ s s C rt rt ^ i^ U w < U o rt ^ £ rS "5 o o H c - en -' i3 o c "^ u t/) -* u u S h ^ -a o 5 rt S •^ a, o- o 4; " ^ 4> 4) (A c _ aH X 4> ^ Vi_i " • O CA c rt (A 2 •« § ^ :5 53 4) 5 41 <-> > rt gj li •3 "u O 6 S - t>. — 4> t>» I- « "S iS a >v ^ v^ 'S "rt s 4) l- V It O 4> o a 4> CHAP v.— OPERA TING EXPENSES—SUMMARY. CHAP, v.— OPERATING EXPENSES-SUMMARY. 1 73 r^ o« mI r^ ■^ 1^ '!t -T q 00 »n eo O M O O ■t C4 CO O N CO m to CO 00 t-" • • • • 0> "H m !•» M 00 g^ 00 in •^ ■ -* » N m »1-cou->o O'^O N »nMl O M M M ^ M O M 1-1 to 00 ID 6 CO O N O O^ N CO CO HI 00 CO CO O — CO M d M C4 M 1 « in CO • N 1± N 1^ r^ in I-. c< in • • • • 8 O 00 o o^ O N PI ri CO rt •-• mo Tj- r^ CO O O M tJ- d o -♦• N "ff "^ t^ CO ►H 0^00 in N O *^ r^ O 1^ r^ 00 t^ "^ M m O w N 00 CO m o •1 1^ CO 'i-OO ■^ o^ O m N M M o C4 O 00 CO M rt CO a 10 80 d CO O r^ to • m t-4 . r^ N ON • • • 1— 1^ w o^ o 00 tn M N 1^ o o 1^ W m d d M ■- r^ 000 • ■ • • 000 "^00 CO o^ to O in O On M r}- Tj- • ••••♦ O M M O CO O CO M M CI TtOO O i-i t^ in to N r^O O to On N N 11 in 0^ CO CO m 8^ M -t ON to O rl- • • • 000 QO r^ IH r^ m r^O •* 'I- t-* m 00 WO O* ON m o* •^ o o o I^ N t>. O O o CO r^r^N o r^-ooo ►- '!fo^tOTtr>iM ^in>-> to NOOOMOooOr^ r^ inco COO CO N CO CI O CO to t^ t-i CI e< M o CI ool CN4 • m r>« HI 10 00 o o d o ON o O CI o «H O CI 000 00 CO ^ N O O O CO On r^O O O CO ON moo •rj- rJ-\0 CO O O O O W M CI O O O CO H. 't toco • t* 00 Tt ON • d CO On . ON CI w CI N m r^ O^ CO O o CO CO % in N CO too CO to to O O m • • • • • O CI CI o HI CI m to ^|0 CI «OI «o "^ to to "<1- O rt • • • 000 O ON CO 00 ' °o. ro to r^ ■ u « • ■ • to HI . in CI w CI nS toco Tf CO *>• M »n to o o CM o o o ii o ON 00 On •^ On ON O CO , 0>0 CI O ^00 t^l ■^ HI d d d CI CI CO r^ HI M d '^ r^ m HI r^ • • • • • O O C4 M M O O 00 00 CO CO d d CO COj CO o o o 8S- o CI 00 ONO o HI in r>. • • • M d ei HI -1- d 00 in CO O HI CO CO q in d O CO in '^ to r» too O *f^ m q d r^oo 1- CO to O HI ^ T^ O d t^ o o On d o d 00 d m O in m O r>. HI o T to ►- O HI d M CO O CO ■ O "* ON H. O 000 1^ CO On CO coo inmo ^hi m mco Onco CO to -I" O hi rf OOHIHIdOOHIHlOO CO CN* u tfl u «n o 5 ** o C r5 H J- «> ^^ /?• .^ Si 11113 w •-> H jg « !2 C "5 >- -^n« U4 I I V S c > - 1) en .5i c* 3 (4 u en .— "5. o. 3 in •O c V) bo CO c 'e5 en V V) c ti .— "O «n O en tn O (A u be ^ c u> 5 o in in C K c o 5 o "-1 = O H ^ CO 'H'f ^ u- 3 4; in TO u) k- > u. a c' a- - a; CI c C re u. O Q. in C re E "re o H o H 4-1 4^ re u •o re 12 «_ 4-> 00 U O en I- u 03 fcuCUCU I I ■ bfi re £: re •o be re E re •o c re V) v> o c to in in re «-• o H u "> V. V lA c o '5 «" •a s: c 5^ rt lA a. C.2 fcf 1. bo5 « rt en V c in &) u O ~^ . in D O C> ^ 5 c re in 'in "aJ ^ w a CUV) re «J •= o ^ in 4; c ^.v bO 2 O ^.E ^iS ^o c be W D - ;2 W O re c o bo •o c 03 c re in "re *-» o H en c u 4; re rt 4-> ka o ■" ■^ Q4 re «-> k. in o H 174 CHAP. V.-OPERATINC EXPENSES-SUMMARY. V* O O < o S'. p < 5k! in H C > '5c u u cl (A V 3 be c •5 %> u V u a o $ V «-• c c« «.< M H P U On • • O • . moo CO • • • * I Q . V* »r> O CO IH |cO IT) O CO -t • .O t^ u in . O O^ "^1 '"^ ^ '^ ^ M 0»l O O r^ ON , O O^ nO en to Woo "* w ►^ O IH IT) 3 - 1^ paSs . ♦J — ' M3 ai^ r-.co \r\ CO g. OO M •^ O •X l-t •* u M s o .2 pa o w •< o H nX H 2 Q > its <: < m OO l^ . O 0» ON t^ i-i I M to - — -- \n d CO CO 't" ON 6 d t^ to 00 8 CO CO (4 (/} U 5 a o V-l •O V ^* 9 a a o a. I I . a; • . I/) c 2h M (/) t a. WW I I ■^ V ^ Vt to c ^ c I/) c X 5 E ii)_. >>« 4) > o £ o u o u (A ft> ^ c -— ::; ±i 5- u o. 2 o ,^ ^ 9* a o 2 5*- o H eg 0« c u V ^ *- (« o -"O - Si rt tf) c c a; 15 o '^ H 1/1 a V- ^ ^ rt «^ 3 f^" '=^ f. ■= 11113 •5. ^ H C//^/>. V.-OPERAriNG EXPEl^SES-SUMMARY. 1 75 •00 ^ - ■^ "^ d* N tJ- d d C4 CO OnvO 00 r^ O^ n •H 'It tH to Onqo N ■^ to to M O 3 g NO C4 rf 0»vO N C< NO d d o GO O OnvO mo Tj- t>. IH to W CO ONO NO too N 00 i-> rj- wtHQjntoooOiHa •I- CO N -i- On O O r^ mo t^ w CO O O •t o^O in M O CO *r "^ m • • • • > O^ M to o o N N r«. IT) \r> •H to >OQO ir> N COCO O C« TT On ON'Ja On to N IH O O - r^ - 00 • o^ ^ c< 00 o CO 8 8'^ 00 •^co QO IH — M 6 6 6 o o T*-o r-* !>. 'i- -to CO O M ONwOrj-OOO M \r\ ON O" »r) to IH •* S8 IT) »A m Cl O O O u-> 4 ci d 2i8 10 CO O ON O CO in ^ I •-' o o CM f* TO ^ d d d »n r< O O CO T ^ M d to CO d On M N r>» N *^ •^ ^ O^O t^ IH On to M Tto>H o ONino O cotHOmMOOM ON vo «3 IS. 00 CM to ON O -TO t^ CO Tj- ONO >H 1-1 r>> m CO CO N m s CN| T «6 c< « O >n O CO « O O CO »H r>« d d d ^ c< O^ »n to m IH IT) <>ci ^ d M tairf in r^ cn r^ • • • r^ CO pi^ 'i- r^ c< «n • ►H h-l • IH QO M • M 1^0 1^ IH ^ CO O O On 1^ in M \f) IH 00 CO On N M in o^ o> o O IH o d d o CO CO rtco CO 1^ 1^ TO !<* Hi CO CO m T in in CO T O CO O O N On t^ CO in rf c^ Tm 'inwoodHlco <« O^r^ m O T O* m mloo *H 01 ^ O O ON 00 00 CO r^ M o T On N r^ •H O T HI O 2;iO>i On ^;CM I o "i-iCO m o o in o QO CO CO On r^ On IH HI O M ^ o o ON QO m m CO CO O CO O ON r»i CO O IH CO in tr>o M to ooiHc^Tmdddad ^s N O On hi f^ ir> IH o N T IH ON M n- N CO CO o M ho « CO in ON On f^ in m in HI to M w 2 o O ON P ON HI c< vO f-^ «00 O^O I a^ I N ON N coco 0> M O O ^ 2 o c^coOtj-noOhiOhI V V • be V c ^ C "f*. «« !2 v i* 2; " I I i ' tf) .- "5, o. p tf] •a c tf) 4^ i-i b« ■« d k. tf) V tf) c V X 2 ^ .iJ 6 CQ •H« w ■» «B ^^ tf! U • 1) V tf) .5 c 9 tf) C c« o H c "O tf) cd I O I U tf) tf) 15 .i: ^ ex c 0^0^ O N CO 2 ^ tf) 01 b£ :- "a tf)' ^ = o tf) o tf) c V o. X CI c o 4; a; u c tf5 cj rt rt bo X c i: rt ^ <_■ be <-» f ^ c o .Ef a !« o. a; o o tf) u u rs be Z rt •- E t •U tf) o CQOQu! E H tf) 'c5 . o,- I I 15 o H .-3 E: •o c - n tf) v. . 3- •o c tf) tf) o 01 *-i o H c o CQ Q^ "O CL C 3 J= CO tf} o. i2 c 2 ^ be £5 qj rt N«» I- tfj 9J i* o bo c •■- - = • 6 bfi __. c •o a *j5 o c '^ rt w tf) S (h O tf) ^-' 'J C c '-hCO O o 2 < Q > W O ti Z O < U-i en cd > a 3 o z < a z < < (d pa < ° g ^ (d U. oi, H w 8 « 5^ en td en Z Id X O < D 03 % O as (b Q Id H (d M H o < Id > Q < .2 a j= o to • Q tn tn O O O • • « • Q\ M r>« CO c^ r^ ' w U-'o t— I 0) • O ^ • O d o M o^ i* I-* o N ►^ s r* « c t: tv, SO <^JS tf" 4^ CO O • • • M ut O ! d : d GO w "* .;v bfo iC re rt ^ .in • tr> :d 6 r^ o^ o O N o W V be . fS(/3 00 ►-• C* *^ • ^ • W CO oo r* CO to O . * • . t« CO O "S^ in oo • • • oo " Q i_i 00 o o^ coo O '-' • • • • o . bCM K 01 W oo N o to CO \0 w «n r^ CI o oo M 0\ ►- CO C* CO ... e^ CO O^oo oo " CI A ' * tA O u-i CO vO 1-1 c» o T C« CO M CO 3 C V O 3 C M Ut Ut N M S ut O 't N c» f< o CO TtO CO r>» CO M t^ oo rf to rfO 1^ O^ w 00 CO O M CO CO I > 5 «-^ 23 4> B ° w.i: «« c ti ** S c — ^ Co ai (4 O .E c I I c (A bfi c *1 w> > W •» J. 1) % O E en S en Vi u in V C 8 bo o c C w- c« i", <« fcc^ £?- C r- ^ .C I I I I bo X «« 2.: .5i CO o- "cS o C//^/*. V.—OPERATING EXPENSES—SUMMARY. IJJ ut \r% ut Ut • • • • • • • • CO CO r^ r^ N N CO U) ji-^ r^ "* M • • • «o . . . »0 CO ci CO CO c<* • c5 8 O ut o o « ut -t r^oo %o rovC CO to r^ c< ut o r^ a> o o ir> *^ -* CO O^ -I" ut r^ N PI oo O ut M rj- »-• Tt CO N a co C* O 1^ t/3 M C> N CO CO 00 •^ f ^ «i- C^ W Tj- PI CM o o o O lo o o OO SI t; !:; '^^ o o o rt N ^co o r>» Tj- r>i N t^ to CI M CO CO M \0 CO C*0 oo r^ o^ N ►1 Tj- i-i CO o^oo PI Tj- to CO HI CO 8^ o> CM q -t O^O lOO PI PI O IH O C^O utO Tr^w cOPl'flO 00 0>\0 O too PI 00 M ^IqJ PI M ut CO •"• N Lis M -too ut -t <0 to l>. rj- r^ oo PI r>. to 00 00 O C» t-i to '-' o r^ O^ •^oo o ut O^ CO CO M to 00 c^ CM O CO C r^ O 00 -tot CI to ut M COCO to PI toco o •-< « • ■ • • • t^ M ut 00 u. O 00 • • ut M h« Ut O O^QO t^ w M M O^ ►-! CO O* CT> to t-t r^o M o t>» PI O M to PI M Ut CM a CM o oo o PI o o to'-/) r>> O to M IH 1-1 • ••••• M t^ CO C< »-• M ir, ut ^.rP bo /) .:* .-Q v. ^ u* a « O 3 V (A in .E = c xa w .- 'H, a 3 in •o c in bo n 5 in a 0^ u u c O H -H "o J2 in tfl •i: ^- &) u in m O in o en* fcf . OJ — '/J i- 3 oj in- ^ bfl ,« = o u c « c O 00 VO (A en c o. X M c o O tOco PI M ►H PI C^pico «r:r^o utO r»pioO>->ciai^M • •••••••. -t M N PI CI o CO O o O ut 8 5 .* 5 <« ^' ^ =0 oc Oy (; o .«a53 C i; O en in I- u cs (4 I I I en 1) 0E$ E O H o H to CJ E: •o c : (A (0 . o - E t "O in T3 = C .2 (4 «_* {/) en iS.Si — ^ o- « <« in a. O en c 5 H C.2 ^l bOiS O C5 en u C in u u o "eS en c = be V CI en 3 O .e'I 'in ^ -. ti •" ^ s s t- in o 111 •J o >" i2 bco ej C to c" *-• ^ 19 «-> ^^ o c o- in ^-^ o o o ^ I: I:- I 178 CHAP. V.-OPERA TING EXPF.KSES-SUMMARY. 6 f M2 . . 3. . .4. n6. and two of ..8 miles) under .20 miles. \ lo 12^ .25 and .26 miles) between .20 and .30 m.les. \ I'.lo, ;;;: Z. U3. .3.. .34 -.es) between .3° and .40 n-les. 1 (145 miles) between 140 and 150 miles. 2 (150 152 miles) over 150 miles. Thus the minimum is n2 and the maximum .5^ miles. This practice tends strongly to economy. „^„^„-_„ ,„ tut sliehtly affected by 156. GENERAL AND Sr..TION EXPENSES are bUSUg J any probable variations in the line and g'^'^'^^- ^° f'ns con^.ected with to'consider then, in detail. a>tboughJ°r many J -^ ^^ ^„, ^hey the operations of railways. ="='' ^"^f'',' „[^„e total operating ex- amount altogether to about "j.rty per ce"t o '^ P^ penses, ranging from twenty to forty per «"' '" ^'^'^ ^ ,„ „pendi- ^ 167. In Tables 75- 76. 77. 78 "^%f' "^"/"'""'fd ' several interior tures for the railways of the entire Un.ted Sta e and the sev ^^^^ groups thereof, for the four great trunk ""-• °^ '°"J,^'^,, „, ,„n,p„ted Ldforthe six '-ding Chi«go ln.s. T^^^^^^^^ „^^^ ,„ riat sT: f:r=ii -rrrtlticon an approximate, si.- Table 79. Operating Expenses of British Railways. 1884-85. Onts per Train-mile. Maintenance of way Locomotive power Rolling stock Traffic expenses General charges Rates and taxes Government duty Compensation: Personal injuries Damage to goods Legal and parliamentary expenses.. . Miscellaneous Totals, 11.32 16.55 6 05 19-77 2.87 3-45 0.6S 0.27 0.34 0.51 0.79 62.60 Per Cent. 18. 1 26.4 9-7 31.6 4.6 5.5 I.I 0.4 0.5 0.8 13 100. o penses has taken place since ,^=?.r?;.^:='.=tr„:riT„"..»~.. CHAP. V.-OPERA rmc expenses-summar y, i 79 Table 80. Approximate Estimate of the Details of Operating Expenses for an Average American Road. [Liable to considerable variations in individual instances, especially when the traffic is very ^reat or very small, but to much less extensive variations than might be imagined even ,n extreme cases. The average total cost per revenue train-mile is still not ven^ much below $i.oo. and by taking it at that even figure the following become either percentages or cents per train-mile, which we shall hereafter assume them XO B C J Train Expenses. 47.0 p. <;. Engines. 18.0 p. c. Road engines. 14-4 P-c. Fuel 7.6 p. c. Water 0.4 '* Oil and waste 0.8 ** ^ Repairs — cn- l gines 5.6 «( Maintenance of Way. 23.0 p. c. Train Wages and Supplies. 17.0 p. c. Cars. 12.0 p. c. Track between Stations. 8.0 p. c. Road BED. 7.0 p. c. ^ Switching engines 3.6 p. c. Switching engine wages 1.6 " Train wages and supplies. 15.4 p. c. Engine w'ges.6. 4 p. c. Car wages. . .8.5 Car supplies. 0.5 <4 Repairs and renewals.. ..lo.o p. c. Mileage (a practical equiv- alent for repairs) 2.0 <( Renewals of rails 2.0 p. c. Adjusting track 6.0 " ( Renewing ties 3.0 p. c. \ Ei "' I Yards and Structures. - 8.0 p. c. i)arihwork, ballasting, etc.. 4.0 ' Switches, frogs, and sid- p'."P •••• 2.5P.C nruJges and masonry 3.5 ^ Station and other buildings. 2.0 (t Total *' Line" or Transportation Expenses -o o p c Station, Terminal, and General Expenses and Taxes...*.*..' .*.*.' .30.0 " * Total Operating Expenses ioq.o p. c. See Table 81 for similar estimate from former edition. ,80 CHAP. V.-OPEKATINGJXPENSES-SUR^^ curred in making oyer ^^^^^^^^^^ I'^^.l^^, of comparison than the result is more ''''^'y^^fj,";',^;,^"'^ -''''>-'" ^''"'^^'"• any individual attempts to do ^he same it. . _^ ^^^^^ 'u Table 78 are '"'ew.se repeat dU- ^ ^^^^ ^^^^ ^^^^^„^^ , which the writer computed (or ^^J°J^ ^,.^^ ,„ ^en years. It seventeen different roads, ^^'^'^^avejaged for ho ^^^^.^^.^^ .^ will be seen that the <^°"«^P°"''^*"'f/Xd a pretty accurate basis for singularly close-quite euou.h ^°;° i„ Table 79 -e given some corr<^ estimating the expenses of any roaa. sponding statistics for English radways. ,i,» o-round eone over, we may estimate 168. Summanzmg the g'°""'l S° ^' ^^ Central States, 0,e operating expenses of a '-'-^y •^;';^^^^" „„,acter, about laid throughout wiU> steel, and of good ave age ^^_^ ^^,^ as in Table 80, on the P'-ous pag • W ^^^^^ ^^^^ tnble will applv to railways in any pait ot tiie ; "'c, .. c!!« «. v.™>i.~ being V. ™e . »m. _^ ^_^ Table 81- Ct.ss,.c.Tto.o.OP...T,«o EXP.WS.S A.OPX.O -N THE Fo.M.a E.mo. CLASsiFicAii ^^ ^^^^ Treatise. Train Expenses. 43 P c- Maintenance of Way. ay p.c. Engines .21 p. e. Cars Train wages. .lO 12 M lO p. C. 2 9 . lO . 6 . 6 Track — Road bed •«^ Yards and structures 7 TRANSPORTATtON EXPENSES ^^ I iFuel. ■{Oil, waste, etc I Repairs •• Repairs, inspection, etc ( Enirineman and firemen I Conductor and brakemen Renewal of rails . Adjusting track, etc i Renewal of ties 1 Eariliwork, ballast, etc .^. Switches, frofis and s.d.ngs Bridgesand bridge masonry. 2.5 „ Elation and other buildings... i-S 7 6 3 4 3 »t tt t» t* •t It It- J^I5^T;S■a.,■'an7£S^ETcns^ ana T.x«. ....70 p.^c. « ■• • • 3^ Sution, Total Operating Expenses^ 100 p. C//AP. v.— OPERATING EXPENSES— SUMMARY, I8I of the facts on neighboring roads. This table gives merely a rude average for use in the remainder of this volume for com- puting examples. Table 82. Percentage of Total Revenue-Mileage (assumed as ioo.) of Revenue- Passenger Trains, Revenue Freight Trains, "Switching Trains," and "Other" (mostly Work) Trains in the United States and' Each Group of States. [Camputed from the Statistics of the Census of 1880. For Census Groups see Table 75] Group of States. Miles Oper- aied. Revenue Train-Mile- age. Other Mileage. (Per Cent of Rev. Miles.) Pas- senger, Freig't. Total. Switch- ing. Other. TotaL New England 5,887 28,693 14.243 25,038 877 13044 51.8 35.6 34-3 31-2 16.9 34-8 482 64.4 6.V7 68.8 83.1 65.2 100.0 100. 100. 100. 100. lOO.O 12.6 16.5 7.2 16. 1 4-4 10.8 3-5 45 5-6 5-9 1.9 9.0 Middle, Ind., and Mich 16.1 Soutliern 21.0 111., la., Wis., Mo., Minn La., Ark., Ind. T 12.8 22.0 Far West and Pacific 6.3 19.8 United States 87,782 35-5 645 100 14.4 51 «9-5 It is quite certain from the statistics that the actual proportion of switching mileage is larger than the above, both because fully one third of the roads do not report switching at all, and because many include switching with train-mileage. The per cent of switching to revenue-mileage of a few single roads runs as follows : Eastern. Boston & Albany... Boston & Lowell... Cent. Vermont Ras-ern Fitchburg M.iine Central Nas'iiia & Lowell.., Old Colony Prov. & Worcester. Per Cent. 12 9 18. 13-8 29. 21. 3' 3-* 4 4 14 8 37-3 Middle. .Allegheny Valley Atl & Gf. Western Rait. &* Ohi.' CI.. C'>1.. C. & Indianapolis CI. & Pittshurg Col.. Ch. & I"d Central.... Del., Lack &> \V.--!t€rn .. N. Y., L. Ene& W N. Y. Centra! & H. R Per Cent. 35-5 21.8 5 25 33 3t 4 24 33 The two roads given in italics above are among those which show an extraordinarily Jow cost per train-mUe. The main cause therefor is clearly indicated in the above figures. l82 CHAP. V.-OP ERA TING EXPENSE^SUMMA R Y. In Table 80 o,u fif"' o( the total cost of motive-power has been allotted to switching-engines. In most cases '"«=- -^ '^ S" propom..„ than this, independent of the switching done by .eg- Zlr trains in iransUu, as is partly indicated by the following Table 82. .. ^ t* i, 1^ ©^ In Table 8. is given the table corresponding to Table 80, which was used in the former edition of this treatise as the as- sumed average distribution of expenses for computing examples. PART II. THE MINOR DETAILS OF ALIGNMENT "Despise not small thing:s, for therefrom comes sorrow and disap- pointment. Yet remember that they are small, and fix your aims and your thoughts chiefly on the great ends of life."— Horace Mann. II PART II. THE MINOR DETAILS OF ALIGNMENT. CHAPTER VI. THE NATURE AND RELATIVE IMPORTANCE OF THE MINOR DETAILS OF ALIGNMENT. 159. The three details of alignment which are properly to be classed as minor details are the following: 1. Distance, or length of line. 2. Curvature, not sharp or so ill-placed as to limit the len«h or necessary speed of trains, but Only to increase the expense of running trains. cApcuse oi 3. Rise and Fall, or elevations overcome by the engine on gradients not exceeding in resistance the maximum of the road and hence not limiting the length of the train ' 160. These are termed, collectively, the minor details for the reason that their influence is comparatively trifling upon he future o ,„e property in comparison with two other details of overwhelming importance, viz.: ciaiis oi I. The amount of traffic which the line has been or mav be adapted to secure (often very largely and even ruinously aff c.ed b> tl«. U.cat:on,for reasons discussed in Chapter III the fol lowing Chapter VII., and Chapter XXI.), and be thlr.'"''"? °«^°'^^TS or other causes, whatever thev may cl>'ef part in fixing the cost of handling the traffic. These causes lead of "Limiting Gradients and Curvature " rise^a°ndTn""''' ""■" """^ ^"''"^ '^ ^'^'''"""> "'"'^'"'■e, and -.^e pccentage certain single items of expenses, and is .eadily fac^d there.n. But they always add only a trifling pe,centage to the aggregate expenses, even when very marked diffcences exist 167. And, moreover, the important further fact must be remembered that, as respects any one line, the,e can be at most as we began by assuming (par. 162), only a "little" difference in' Fig. s. ^he minor details for the vastest expenditure cannot effect much mo e. No possible expenditure can eliminate curvature alto- gether and give a continuous right line A£, Fig. 5, of any con- Fig. 6. s^derable length, m place of the curved line shown, nor make much more reduction in it than is indicated bv the dotted line in ••■S. 5; nor can we make moie than a small diffe.ence in distance I I90 CH. VI.-RELATIVE IM PORTANCE OF MINOR DETAILS. ordinarily, nor have we more than the choice between the grade- lines b and .. Fig. 6 saving a mere fraction o the nse and fall. The grade-line „, taking out all the rise and fall between A and n is rarely a financial or physical possibility. ' 168. For these reasons, assuming what cannot always be assumed, that the engineer has first done well in putting h.s line upon the ground so as to avoid unnecessary distance, curvature and rise and fall (i.e.. that which might have been eliminated .vi.hout expense), to eliminate altogether even '< little difieiences in the minor details will ordinarily involve an immense expense. But ftrant them all to have been eliminated, without expense, from the least favored of the two lines which we began by assum- in- (par. 162), and let us see with somewhat more detail to what extent it will be benefited thereby. (For a more exact estimate ^"it wiU not reduce the interest charge, even it it do not (as it ordinarily must) increase it, and that takes, say, one third of the receipts. As respects the remaining two thirds of the receipts, which includes what are ordinarily termed " operating expenses: It will not reduce the number of trains, for the length of trains is not affected by them. Consequently, It will not reduce train wages and supplies, which are (Table io\ some 17 per cent of the expenses ; . , u - It will not reduce station-agenfs wages, nor station labor, tior the salaries of the general officers and clerks, nor taxes nor terminal expenses, and these constitute some 30 per cent of the expenses ; . •. r «i «:i It will somewhat affect repairs of engines and cars, fuel, oil and water, and maintenance of way, aggregating some 53 per cent of the operating expenses; but , r ,„, ^nd ,69. It will not affect that portion of the cost of fuel and enoiue and car repairs which is due to yard and station vvork sto^pping and starting, wear of paint and rottingof wood, natura ruling wear over the rest of the possible line, injury to boilers from cooling off, care and maintenance of shops (excep .n an indirect and trivial way), etc., etc. These causes together in- elude an immense proportion of the total of these items. CH. VI.-RELATIVE IMPORTAN CE OF MINOR DETAILS. I9I We have seen (par. 142) that something like 28 per cent of the locomotives of New York State are used for vard work only besides which a large proportion of the wear and' tear and waste of power of engines in regular service comes from yard work and stopping and starting. Precisely how much, we will not now consider ; but it will be plain in a general wav that only a minute percentage of even the cost of engine and ca'r repairs can be saved by improvements of line which do not reduce the num- ber of trains required. Then as to maintenance of way: All that degeneration which comes from the elements, from the decay of ties, from the growth of weeds ; expenses for maintaining frogs, switches, sidin-rs yards stations, bridges, culverts, crossings, signals, track-walkers (fdV the most part), track-watchmen, hand-cars, fences, etc., are virtually unaffected, or nearly so, by any modifications of line {except distance) which are within the power of the engineer to effect, as ,s likewise that portion of the wear of rails, ties, and surfacing which would exist on the best possible line, and which IS on any long line (for none are everywhere unfavorable) by far the larger part of it. oK "^'i^li^'f '■^™^'"=' therefore, only a very small fraction of about half the operating expenses, or a very small fraction of one third of the revenue, which varies directly with the minor details of alignment, whereas a full half (in round figures) of the operat.ng expenses or a full third of the revenue varies directly with the number of trains. The smaller loss is still enough to justify and require the utmost care of the engineer to avoid it, Zrll 11"^- T"^'' '" '"'"'" "• "--di"^"')'. anything but the «or t of b.d judgment to sacrifice the securing of good limiiing gradients, or the reaching of more traffic points, to get "a shorf traight and level line," which may or may not mean'a good line! for ve shall see (Part III.) that, although a tolerably •' level " line passing over low summits ordinarily means one with low ruling guides, yet that the two have no very exact relation to each 171. We may further enforce the very important moral of the 192 CH. VI.-RELATIVE IMPORT ANCE OF MINOR DETAILS. comparative unimportance of the minor details of alignment by what is reallv a close parallel from ordinary business life : Let us assume the case of a large wholesale house which sends out its "drummers" to all parts of the country to obtain business. Every time it sends one out it has a reasonable cer- tainty of sellin- something and a possibility of selling a good deal Such a house may be compared to a railway corporation, which sends out its trains to secure a certain minimum but varvins: maximum of traffic. ' Now in the conduct of such a business there are three ends : 1. To sell all the goods possible. 2. To dispense with all the miles of travel possible. ^ -K To reduce the cost of travel per mile. ^ So in planning a railway there are these three ends, precisely analogous to the former in their nature, and as nearly as may be in degree : 1 To sell all the transportation possible. 2 To dispense with all the train miles possible. X To reduce the cost of running trains per mile. _ 172. Of all the three ends sought in the drumming business, the least important-the minor detail of the drumming busi- ness-is to leduce the direct costof travelling; the expenditures for railway and sleeping-car fares and to "otels- Not tha they are unimportant, for the firm which was reckless abou theL might readily be ruined ; but they are a minor detail, of smaTl"ffcc upon the ultimate result, whether they be large or smal W the business as a whole be well planned and well con- ducted Ind the firm which should concentrate its attention upon them, giving its thought to selecting -f- where te travelling expenses per day or per mile were small, to t^e neglec of the more important question of securing more business^o reducing the amount of travel required, whether its cost per tn.le or per day were large or small, would be justly deemed on the '^NoTut many have been so ruined, for the petty end which CH. VI.-RELATIVE IMP ORTANCE OF MINOR DETAILS. I93 the dullest mind cannot fail to perceive and comprehend may fill, from that fact, an unduly large arc in the mental horizon of many. 173. And so not only some but many railways may be as they have been, ruined as productive properties by the undue importance given by engineers to the minor details of align- ment : those details which do not add at all to the traffic of the line, and which do not reduce at all the number of trains needed to handle it, but which simply effect a "picayune "saving in the cost per mile run ; a saving which is often so slight as to be imperceptible, which still more often adds to the interest charge more than it saves, and not infrequently, as we shall see, results in a negative saving, or absolute loss from the larger expendi- ture. ^ As a matter of fact, the first and most important end in the conduct of the drumming business is to get all the business possible • everything else-both the drummer's time and his expendil tures-is subordinate to that, because if the end is not secured the means must necessarily be bad. So with a railway corpora- tion : the first and most important end, when there is any great difference between routes, is to put the line where there will most business come to it. 174. And, finally, the second most important end in the drum- ming business is to obtain the most business with the least possible aggregate of travel, because avoidable travelling is expensive, not only from its direct cost, but from its waste of the drummer's time and possible earnings in more productive localities. If in any possible way one drummer can be made to do the work of two, or two drummers the work of three the economy is so great that any probable or possible difference in the drummer's expenses per mile will hardly affect the question at all. So with a railway corporation: the second most important end is to do their business with the least number of trains per rnile, because making one train do what two did before saves all the expense of the extra train, whereas cutting out some curva- ture or distance will only save a part of it— and a very small :■ i. m ,94 CH. ,I.-HBLATIVEJA^^ '"T'T^il all has been done which can be done, therefore, to part. Until an nds L.CC :, u Viardlvworth while to reduce the number of trains required, it is hardly w ort ;t a thought to reducing the -P-^J-^J^thTl tter^^^ Lrds it ^--^rSSrwTr tlJct^^^^^ on the two iriS:"--rrtrg:"t the busmess to carry and to maUe ' 'T;; The stud^nt'can do no more profitable thing to qualify Why this is so in railway business appears more in detail the three following chapters. CHAPTER VII. DISTANCE. 176/ The effect of a variation in the length of a railway on the value of the property we have seen (Chap. III.) to be peculiar in this— that, alone among all the details of alignment, it has a direct and material effect, not only on expenses, but on the reve- nue or receipts, which tends very materially to reduce its finan- cial disadvantage. As a contrary view, leading to a feeling that any longer distance between termini is an unmitigated mis- fortune, and a great one, is common even with engineers and practical railroad men, and as this view is as mistaken as it is common, and leads to much mistaken action, it will be well, be- fore proving affirmatively that this view is an error, to point out the nature and source of the error (which is easily enough seen), since the presumption is strong that any view which is widely held is a true one. 177. Its origin lies in a series of plausible nou-sequiturs, which are, in a few words, these — no one of them being true : 1. Rates are (usually and whenever possible) fixed at so much per mile, because (fallacy i) it costs so much per mile to transport the passenger or freight. Ten per cent more or less distance means ten per cent more or less fare, and " necessarily" (fallacy 2) ten per cent more or less expense. 2. But on our particular railway the service rendered is just as valuable, if transportation be furnished /;w;/ the point desired to the point desired, whether the intermediate distance be 90 miles or 100 miles, and hence (by a long but unconscious jump over a vast hiatus in the reasoning) we shall ** of course" (fallacy 3) receive the same money for it. Therefore, necessarily. I t » If W ,96 VJI.-DISTA^■CE-RELATION TO BATES AND EJCPENSES^ , All extra distance adds greatly to the cost of the service /fMHcv I and .); adds nothing to the value of the service (true int'h with ce tain limitations); hence adds nothing to revenue (falla°Jr3), and hence is among the greatest of disadvantages: ^ The truth is, not one single item of railway expenditure large or sm'l not even fuel or wear of wl.eels. varies in direct ratio with d 'tance.^ in anything like direct -tio and mo,, t an Llf of them are very slightly if at all affected thereby On te other hand, a very large P-PO''-"— --^./^ir,^ .^'fcr whole-of the receipts does vary directly with the distance. U8. The reason why rates are so generally based more or less dir cUy on distance hauled, and on nothing else except necessity i no n the least that it is a primary factor ,n the cost of e service but simply this: The sale of transportation, like the salof'any other commodity, is governed by the one universal busin - iL of selling whatever is saUd^le as "early as po-bl for at least as dearly as is prudent and wise), regardle s of the lost o production The selling price of no marketable com- modify whether transportation or houses or cotton cloth, is fixed bv the erst of production, except that if it will not bring a pro- fit on itscost it is no longer produced ; and for railways any such attempt would be particularly senseless, for the reason that, as we have elsewhere seen (par. 40, i8,), the cost of any par- dc^lar sale of transportation may be considered as varying any- Tere f-- "'o "P-rds ; depending, to a <- J-;'- -' , than in any other commercial transaction, simply upon the amount that can be sold. . 179. Thus it has happened that the distance transported as been made the basis for tariffs (when they have any basis w la - ev r other than the amount which it is possible to col le ) a measurincr in a rude wav, not the cost of the service, but the Tonsumei^s idea of its value. In point of fact, the distance trans- no" ed U but one of many circumstances-and certainly not th 1st important-which fix the cost of transportation. yi r.-DISTANCE -RELATJO^^^^^S AND EXPENSES. I97 Grades, curvature, cost of construction, ^M^^^T^^Z^^^^, ume of traffic, whether the cars return full or em^ty-al U.ese have very much more to do with the cost of service than tl ! mere distance transported, but they are entirely neglected in fix! ■ ng schedules of rates, simply because the consumer is no con- scious of receiving any value when he is transported over Lrva ZZZl '""""v '' '^"""'^"^ °^ -eiving'value whin Te s transpoited over distance. For this very humble reason only t:xes"hmf"r """ '^^"^"-"-' ^^-'y- 'Mile r^I; taxes him for the one service and not for the other, so that it mav even, to a certain extent and under certain circum tances an^so long as those circumstances continue, be a positive advantage o a line to have a few miles of extra distance" especially wl en a^ ditional way traffic is thereby secured ^ nec^Ll'Tn l'"r'""\'^°^ '"'" "'"'"' '"^•^" '' --a-ably nece sary, ,n considering the effect of distance, to consider its effect on revenue as well as on expenses, even if the former be considered only to be disregarded. To disregard it is often the Pue,rTniibr""''r°''"": "^^°" '^ "° °"^^- A^ - ^"-■°» pu.ely of public policy-that is to say, if the interests of the i:7.zz\:r '" ^""^"^"^ ^"'"'-^ '^^"''-' --^^^'^ ^^- terests of the community as a whole-tlie effect of distance upon operating expenses would be the only one which here would be need to consider, and its effect on revenue sho Id n"I Lid f" :: '' ""• '■°''^'"" '""^ ^^^' --'" rendered and paid for IS the transportation of persons or property from one erm.nus to another, the precise length of track between the two should have no more effect upon the price paid than the prec se amount of curvature or rise and fall, and much less than tlfe il es of uling grades. All should be considered or none should ie An"' - "o., on ^^*r ;i h 200 CHAP, VIL— DISTANCES-EFFECT ON EXPENSES. Table 84. Showing the Relative Cost of Wood for Kindling on the Philadel- PHIA & Reading Railroad for a Series of Years. Ybak. 1867 1869 1873 Average. Percentage of the Cost of Kindling-wood to Re- maining Cost of Fuel. Prices of Fuel. Passenger Trains. 14.2 8.8 9.7 10.9 Freight Trains. 10. 6.4 6.2 7.5 Coal Trains. 5^1 3-6 4.1 4-3 Wood per Cord. $5 79 5 50 5 94 Coal per Ton. $5 74 $3 15 3 So 3 25 Average Consumption of Wood for Kindling. $3 40 Passenger trains, .I3c'd Freight ** .15 " Coal *• .22 '• The above does not include the cost of any coal used in kindling. The consumption of wood seems very small; Mr. Trautwine (•* Engineers' Pocket Book," p. Sio) gives ^6 cord as the average consumption. When this road was using wood fuel entirely, passenger trains used 2.7 cords per too miles, or about 2^ cords per daily run of 93 miles. Allowing ^ cord for getting up steam would amount to exactly 10 per cent. Mr William Stroudley. Loc. Supt. London, Brighton & South Coast Railway, in a paper before the Institution of Civil Engineers (1885) shows that the number of pounds of coal burned to raise 100 lbs. of steam from water at 70' F. was about 450 lbs., eqi'ivalent to from 3 to 4 lbs. of coal per train-mile when kindling fires once a week, or every 650 to 8co miles run. This amounts to almost exactly 10 per cent of the total quantity of coal burned per mile. He gives also tables showing that his passenger engines spend nearly half the time that they are nominally in service either in switching or standing still (mostly the latter), and only half the time running. motive from expansion and contraction. This terminal wastage alone will average, therefore, some 400 or 500 pounds per 100 miles, sufficient to run a locomotive 5 to 10 miles, or 5 to 10 per cent of the total con- sumption. Whether the fires are drawn or not. a fire-box full of coal at least, and usually more, is wasted at the end of every trip. 185. The consumption due to stopping and starting and to standing idle in yards and on side tracks is also a heavy item, and may be considered as nearly independent of distance in the case of two nearly equal lines operated with the same number of steps and sidings between the same termini. The direct amount of loss of power in stopping a train run- ning at 1 5 miles an hour is sufficient to lift it vertically nearly 8 feet, as wiU ClfAP. VII.~DISTANCE~EFFECT ON EXPENSES. 201 be seen in Table 118. and at 30 miles an hour four times that heioht or nearly 32 feet. The roiling resistance of a loaded freight or pas^en^rer train in motion on a level being, as will be seen hereafter, equivalent to that of a grade of less than 16 feet per mile, we have, from stopping and starting only, a waste of power sufficient to run the train one half mile in the one case and two miles in the bther. causing a loss for an avera-e number of stops for stations and crossings of something very dose to To per cent of the total consumption. In such extreme cases as tlie Manhat- tan (elevated) Railway of x\ew York, where there are stations about every three eighths of a mile, very nearly three quarters of the total consump- tion of fuel has been shown to be due to this cause. As to the wastnge while standing idle, experiments made by Mr. Reuben Wells show that an engine with jacketing in perfect order, standing idle all day Ion- in a yard, wholly protected from wind and using no steam in the cylinders requM-es from 25 to 32 lbs. of coal per hour to keep up steam in the bo.ler. or nearly enough to run it a mile in service. For the short stops m actual service at least twice this amount per hour is probably wasted including what is blown out of the safety valve, owing to all paits of the engine being hot. and a surprisingly great amount of time is spent on an average freight trip, and even passenger trips, in simply standing stilL It will average over 4 hours per day. if not more, in freight service on single-track roads, not including the time lost at the beginning and end of the trip; and on the very fastest express runs experience has shown that fully one fourth of the time between termini is lost by stops. This amounts to a further waste of 3 to 6 per cent. 186. From all these causes together it is a verv moderate estimate that about one third oi the total cost of fuel is not affected by a slioht chancre more or less in the length of the line. The average consumption of fuel per train-mile in both directions is not so greatlv affected bv grade that we need consider the question of whether the additional distance is on a grade or on a level. Going up grade the consumption is greatly m- creased, but there is no consumption of steam at all in going down grade, so that the average is only slightly increased. 187. Repairs of Engines and Cars—U is exceedinqly common and for certain purposes proper enough, to assume these expenses to vary directly with distance, but for our present purpose this is very erro- neous. The wear and tear of rolling-stock, it is plain, arises from several d.stmct causes, of which the regular running wear when in motion is only one. These causes are ; 202 CHAP. VII.— DISTANCE— EFFECT ON EXPENSES. 1. Deterioration from time and age: Varying 'with time. 2. Stopping and starting: Varyittg with number of stops. 3. Terminal service, getting up steam and drawing fires, switchings making up trains, etc.: Varying with the number of trips, independent of their length. 4. Effect of curvature and heavy grades: Varying with the character /}f the alignment. And, finally, we come to 5. Effect of regular running between stations on a tangent: Varying -with distance (the additional effect of any curvature on a given distance being a separate matter). All of these causes contribute to increase the cost of maintaining roll- ing-stock, and as the whole cannot be greater than the sum of all its parts, the effect of any one of them alone must be much less than the total cost unless the effect of the other four is insignificant. Each item will be seen to vary with a different cause and only with that, and only one of these causes is the exact length of track. 188. The mere statement of these facts at once makes probable that rolling-stock repairs cannot vary very directly with distance alone when the other causes of deterioration remain the same, although precisely how much each cause contributes to the total will probably always re- main an indeterminate problem. Nothing but the most exhaustive ex- periments could settle it accurately. Hence we find that when men's attention is specially fixed upon the disadvantages of some one of these causes they are very apt. with entire good faith, to exaggerate the effect of that one cause, simply from momentary forgetfulness of how many other causes are also co-operating to make up the aggregate. If the effect of distance is under discussion, the whole cost of rolling stock repairs will be charged off as so much pei mile run. as if no other cause but mileage had any effect ; but, on the other hand, if the disadvantages of some grade crossing is in question, we shall have the wear and tear resulting from that cause spoken of as something fabulous. And so about the injurious effect of some particularly crowded yard or objectionable curvature. But starting from the premise that the total effect of all these causes cannot be more than 100 per cent, we have in Table Sj.a subdivision of this total, item by item, between the above five causes. As this has been done with great care to get the best attainable authority for each (which it would occupy too much space to give in detail), the margin for possible error is not great enough to be of moment, although no absolute exact- ness can be claimed for it. CHAP. VII.-DISTANCE^EFFECT ON EXPENSES. 203 Table 85, Distribution of the Cost o. Encne RnPAms to its Various Contrib. UTiNG Causes. Itbm. 5°'^^r Running gear Machinery Mountings Lagging and painting.*.! Smoke box, etc Tender: Running gear Body and tank Total Cost of Item Distribution. p. C. 20.0 20.0 30.0 Effect of Time, Age, and Exposure. Stopping .Terminal : Curvatu and Starling at Way Stations. p. C. I. Total 12.0 50 lo.o 3.0 4. I. p. c. 2. 4. 7. Getting Up Steam, Making UpTrains re lOO.O p. C. 7- 2. 3- and Grades. (Approx. Average.) Distance on Tangent between Stations. p. C. 4- 7. 5. 7. 15. p. c 7- 7. 14. 2. I. 6. 3. I. I. 3- 19. 4- I. 17. 42. Table 86, Distribution op the Cost ok Freight-Car Repairs to its Various Con. TRiBUTiNG Causes. Wheels Axles, brasses, and boxes Springs Truck frame and fittings Brakes ._ Draw- bars ,' Sills and attachments..'.*. Car body, painting, etc. . Total. Total Cost of Item. Distribution. p. C. 30. 30. ID. 5. 5. ID. 5- Effect of Time and Age. in- dependent of Work and Mileage p. c. Stopping and Starting. 2. 100. I. 3- 6.0 p. c 5 5 2 I 2 4 2 O Terminal Making Trains, etc. 21.5 p. c. 2. 2. I. I. I. 4. 2. 13.5 Curvature and Grades p. c. 13. 5- I. 2. 2. Distance only between Stations on Straight Track. p. C. 10. 18. 6. I. 23.0 36.0 The proportionate cost of wheels, axles, and brasses above is perhaps lar^P n.H TiTT Of brakes and draw-ba. sn^all, but it is in accordance with the ^J1^^:^,::^J^:l 204 CHAP. VII.— DISTANCE— EFFECT ON EXPENSES. 189. In Table 85 each of the smaller items is as small as it can rea- sonably be made. Consequently not more than 42 per cent of the cost of the engine repairs appears to vary with the minor changes of length. The distribution to curvature and grades will be spoken of hereafter, h will, of course, vaiy greatly on different roads. Table 86 is a similar dis- tribution of the cost of freight-car repairs based in part upon Tables 71 to 75, ajid in part on Table 87. 190i It will be seen that a considerably larger proportion of car re- pairs than of engine repairs is independent of distance, as is but natural. The cost of passenger-car repairs may be considered as not greatly differ- ent per train from that of freight trains, but the maintenance of the seats, furniture, and inside and outside ornamentation make up much more than half the cost of passenger- car repairs, so that the cost per train of all kinds of running wear is much less considerable. Table 87. Estimated Cost New, Scrap Value, and Rate of Depreciation op Freight Cars of Various Kinds. [Deduced from data published in the National Car-Buiid*r of April, 1880.] Box Cars. Labor. Material. Total. Scrap Value. Total Deprec'n. Average Life. Years. Annual Deprec'n. Wheels $90.00 4500 10.00 94-94 $35.00 15.00 4.00 25.00 $55- 30. 6. 70. 4 8 3 35 $13-75 Axles 3.75 Rras<;es 2.00 Frame. ...... 2.00 Truck Brakes Draw-bars Frame Roof Floor Sides Patntintj Trimmings.. . Trusses $227.82 7.33 26.08 52.85 25.49 10.76 36.78 5.25 13.29 5.89 $12.12 2.16 2.95 6.79 3.34 1.12 7.58 2.16 6.23 I. 13 239-94 9-49 29.03 59-64 28.83 11.88 44.31 7.41 19.52 6.02 79.00 2.00 6.00 10.00 4.00 1. 00 2.00 300 300 161. 7.50 23. 50. 25. II. 42. 7.50 16. 3- *"*6" 6 15 8 10 20 7 20 20 $21.50 1.25 3.83 3-33 3.12 I.IO 2.10 1.07 .80 .15 Total, box c. 410.54 45.58 456.12 110.00 346. $38.25 Stock cars 388.72 42.68 431.40 \ (ov< :r.) CHAP. VII.-DISTANCE-EFFECT ON EXPENSES. 205 Table 87. — Continued. Flat and Coal Cars. Total Cost New. Scrap Value. Truck (as above) $239.94 Brakes ^ j^^-^ Draw- bars. Frame . . . Floor Sides Fittings.. . . Trusses . . Painting. . . Total. 9.49 29.03 45.00 12.00 8.00 5 00 6.00 6.00 $360.46 $79 2 6 10 I I I Total Depreciat'n. Average Life. Years. 50 $103. I $161 7 23 35 II 7 4 3 6 $257-50 6 6 15 10 20 20 20 7 Annual Depreciat'n. $21 •50 I .25 3 .83 2 33 I 10 0. 35 0. 20 0. 15 0.88 $31.59 Per Cent of Total Depreciation. Wheels A.xles and brasses, Truck frame Flat Cars. I Box Cars, 43.5 18.2 6.3 Total truck. Brakes Draw bars. . . . Frame Other parts... . Total. 68.0 4.0 12. 1 7-4 8.5 36.0 15.0 5.2 Average. 100. o 56.2 3.3 10. 8.7 21.8 40. 16.6 5.7 100. o 62.3 3.6 II. o 8.0 15. 1 100. o this table is at least equally trustworthy. ^'' ^" ^^^ ^^^^e. The rule of the Master Car-Builders' Association is that 6 i^r r^nt r^ shall be allowed for depreciation in value of freLht ca^s Iwn to 1 ^' '^'^'■' '''' '"'^ ^^' cent of their original cost. ^ ' ^°'^° '° * minimum of 40 per 191. Train WAGES.-The tendency, as already stated roar ic.>» ,'« more and more to fix all train wa-esdi recti v bv th. ^i ^^^'-.'^f)' »s the larger lines made up of several di^Sl'^dut^^^ where the total number of trios a cre«r r«n r.,/ , ^ ''^^' Propcuonec a,™ost exacU, .? ^"Z^JZJZr^:':^^^ ? ! I CHAP. VII.-DISTANCE-BFFECT ON EXPENSES. 2c6 iimit is fixed varving from 2600 to 35oo miles, as =1 month's work dTv dine tltrs by the length of each division gives the number of trip to con titut a month's work, the fraction being disregarded .n favor o the employe. On a division ,00 miles long 26 tr.ps ,s a ■"""'h s wo^k o a dilision 90 or ,05 m.les long 28.89 and 24.76 tnps ^-^'^^^^^fl a month's work, but the fraction would be '^-PP^'^ "' '^.^^^/^l"' '" mil "e ™n?lnd others (including probably over half 'he mUeage o the U: -^Stat.) adopt the -P-ise P.n al^^^^^^^^ but under any orcumstances .t » " '>^ f ^^^^^^ j^,, „;„ iect trai« that slight changes of le.-^th of ^ '^ * ~/„(,^,^^„. Thecircum- and excluded. ^,„^„^, Fxpenses and TAXES.-Taxes are 10*^ Station and General ii,xpfc-Nbii.a ai^^^ „o^Lf;L.med._^^^^^ r"'"lV^reler btMng wuti Distance- Total Ana'at Per Train- Mile for Greater Differences of Distance. from 67 p. c o t( K (< << (( <( << <( << <( 2.oo per foot, more or Ip*;*: r^c i^u^ ^ , Please, , iiiuic or less as the case may be as th«^ rr^^t ^e superstructure, rig-ht of vvpa^ a„^ r • ^ ' ^^^ ^°^^ ^^ that su. Withke^o^helir/^rofeonr^,; r T^Z^^' sub-grade then enters in, to determine whether or noffh» improvement will cost more than it is wortk ^""" va>u?o; faZ; 'ra'""bv°r'"''' "T""' '" ' '"^' exaggeration of ,,e «ructing a mile oH ne comlf ! " '"' ""°'^ ""^'S' "^' «' "". like the value of everythinTelTe i, L T ' ^^ "" '"'"^ °^ <"^'^"«. n.a„e„. works beneat'h he ^k be costlv cr'n"' '" T'' ^''"-" ">= P"" that part of the length of the roaV:, "h'^ sal^'";;- L" "^ °' T"' °" same traMc. We therefore first estimate the vTl' If ,L°'' """ '"= «..mate both alternate lines to see whether »; nrt'lhMi:: e^el tt^cor and has no effect uZ ^''^"'"'"'' '^ ^ P^'^ ^o^rce of expense THE EFFECT OF DISTANCE ON RECEIPTS into ° th^lS^a^ -".f Sir,!" "-7" P-'-« roughly divided .oca. is a n^'ter^nar rg'defi'nTtio^n'^VL' tXltte" "'^' '= Of the word " through" freight would be freth ' '?'''''''''°" the entire distance between termini , .;»,/,, ^ ^ '""^ °''" other iines or not, and 2!:::^^^' ^^^^^J^^^'^ ^^ith fymg. Another basis for subdividing Z)r °"°"'f^ '" ^'assi- 'oca, is that adopted in the Ma s ch„ tf RTn^o'dp"'' """ V.Z., to call all traffic "local " which isconfined to 21 "'"'V and simply passes from one station of the road tlf' Whether those stations are the termini^r ^orand^ru^affi^ ^^ir I 212 CHAP. VIL— DISTANCE-EFFECT ON RECEIPTS, " through" which is (under this definition) not local, but passes over parts of two or more lines, although the total haul may be only a few miles between small non-competitive stations ; where- as " local " traffic may be hauled the entire length of the road at competitive rates, and be for all practical purposes what is ordi- narily understood as '* through" business. 202. Neither basis of division, therefore, is a particularly happv one for accomplishing the end sought, and the reason why neither can be is easy to see. The difficulty is that each of them is an attempt to include under only two classifications /z^^f distinct classes of traffic, each one governed by different laws as respects rates and other business considerations. These classes are Non-competitive local. Non-competive exchange. Competitive local. Competitive exchange. Partially competitive (i.e., competitive only with the disadvantage of a local haul in ad4ition). More in detail, the nature of these sub-classifications are as ^^^^^^^ * f I. Local or home traffic proper, having no choice of route and confined to- one line. 2. Exchange traffic, or (by Massachusetts classification) "through" traffic, having no choice of route, but passing from one line to another. 3. Local or home traffic, confined to one line, but having a choice of an- other route (a class of traffic once small, but rapidly increasing with the multiplication of railways). 4. Exchange or " thromh " traffic ^*^ai»er, passing between the more imoox- tant railway centres, and with a choke of twa or more routes. A. B. C. l:: I'- A. NON-COMPETITIVE. (The whole of it being what is ordinarily referred to by the term " local " traf- fic.) V r B. Competitive. (The whole of it being what is ordinarily referred to by the term "through traflac") I CHAP, VII.^DISTANCE^E FFECT ON RECEIPTS. 213 C. Partially Competitive, ■ 5. Traffic (usually exchange or "through") detween non-competitive local points and important railway centres having a choice of route only at disadvantage, by paving a local rate in addition to ' the "through." This class does not exist, practically, for passenger service. 203. Out of all these five classes there is only one-viz Class B, 3 ; traffic confined to the home road and the. J^ purely local, but having a choice of ron,^ h, tne.etoie and therefore co.petitife-on wT .L: a Zger'LT,rast^:^S whatever to increase receipts, but is a pure disadvantage This class ,s also, on most roads, the smallest class of all, anfon very CcVon":'"'v"°"r'"^"'- °" -''-•^."owev'e.asfo. Z -tance on a new hne between New York and Philadelohia it would be the bulk of the traffic. It is rapidly increasingir;™ portance, moreover, from the prevalent tendencv to confo idaTe' hnes mto great systems, and even when this consolidation not formal and complete, there is often such community of in eres from common ownership as to amount to very neady the IZ\ Receipts from ail the other classes are affected materially bv the^ d,stance ; but in different ways, which we proceed to Ln- non'?!" ^' ^°^-C°«'>"",yE (Class i and .). Traffic between 7ZT IT"" "'^ P°'"''' ^•'^"'^'- »"«« P°'nt^ are on the same or different roads. ^ -war' traffic' if '"'^'' "''f '' "''^' "'^ P°P"'-'y -eant by way faffic, .s an immense factor in the freight revenue of any II I 4 214 CJIAP. VII.— DISTANCE— EFFECT ON RECEIPTS, railway, varyinjr ordinarily from 5010 75 per cent of it; and rarelv 'falling below 50 per cent, except on lines of heavy through traffic running through sparsely settled districts. The old Canada Southern (now Michigan Central) is a peculiar and very exceptional example of a line of the latter character, its local ton-mileage having averaged, before its consolidation, below 8 per cent of the total. Even in this extreme case, however, its revenue from local freight appears to have been from 25 to 30, per cent of the total. The Cleveland, Columbus, Cincinnati & Indianapolis Railway, which carries perhaps as small a propor- tion of non-competitive freight as any other line for which precise statistics are available, and which is certainly exceeded in that respect by very few, derives, as an average of 9 years (1873-81), 36 per cent of its tonnage, 23 per cent of its ton-mileage, and about 38 per cent of its freight receipts from " local freight, which in this case includes, practically, non-competitive of all classes. In its passenger traffic this line enjoys an even larger proportion of non-competitive traffic, being at much less disad- vantage in that respect, and in fact representing as nearly as may be the average condition of the whole American railway system. This is the more fortunate as it is one of the very few lines which give statistics of the passenger or any other traffic in such form that it can be accurately separated into at least four of the five classes of traffic which actually exist, as above speci- fied. The following Table 90 gives the percentage of each of these classes (omitting fractions and distributing a trifling sum for miscellaneous receipts) for the average for the 9 years 1873- 1881. The table may be accepted as giving, in a rough way, about the general average of the whole American railway system for passenger service. 205. Table 91 gives some corresponding details for the freicrht traffic of the same road, which can hardly be accepted as so representative, and in Table 92 (as also in various other tables r —see Index) are given data as to average train loads. The variations in such matters are limited only by the number of roads, and are often very great. CH^ VII.-DISTANCE^EFFECT ON COMPETITIVE TRAFFIC. 215 There is a certain portion of even non-competitiveT^ It must alvvaysbe remembered, on which rates are governed' solely by what it will bear, without any reference to distance and on many roads a very large proportion, as where there ij miich suburban traffic ; yet in the main the rates are nominally fixed by the mile on all this traffic, and on a certain large pro- portion they are by law or fixed custom actually so fixed Before considering what weigiit should be given to these facts ,n estimating the value of distance (for which see par. 227) we will consider the conditions which exist with the three re- mainmg classes of traffic. 206. Competitive traffic, whether confined to one line or not- (classes 3, 4, and 5, above). The total through rates on all com^ petitive traffic are, in nearly all cases, arbitrarily fixed, with little regard to the mileage. For this reason it may appear, and may be too readily taken for granted by engineers not familiar Table 90, Comparative Magnitude op the Separate Classes op Through an,> Local Competitive and Non-Competitive Passenger Trapp^ o" th^ Cleveland, Columbus, Cincinnati & Indianapolis Railway Average of 9 years, 1873-1881. ITbis Uble may b. accepted, in a rude way, as not far from the general average of the whofe ^^^^^ American Railway System,] Class of Traffic as Subdivided on page 122. A. Non-Competitive. B. Competitive. 1. Local home road 2. Local or exchange between local points in different roads 3. Local traffic between com- petitive termini (only par- tially in this case) Competitive through Per Cent of No. of Pas- sengers. Partially Competitive. (Non-existent in pass, service.) 74 14 J :} 88 Per Cent of Pass. Mileage. Per Cent Contributed', to Revenue, 12 52 1 100 p. c. .3 { 48 13 6s ICXJ p. c. 26 ("39 100 p. c. 11 Si I i 'I 216 CH. VII.— DISTANCE— EFFECT ON COMPETITIVE TRAFFIC. Table 91. Fluctuations and Distribution of the Different Classes of Freight Traffic; Cleveland, Columbus, Cincinnati & Indianapolis Railway. Local Freight. East-Bound. West-Bound. Total. Year. Tons. 1,000. Ton- Miles. 1 = i,ooo,uuo. 1 Rev. $1,000. Tons. 1,000. Ton- Miles. i,cxx>,ooo. Rev. I = $1,000. Tons. Ton- Miles. Rev. 1873. .. 1875... 1880... 1885... 419 401 564 451 50.0 43-3 74.6 43.3 908.9 686.7 749-8 469.7 211 253 311 355 20.8 27.7 33-6 41.0 434.8 465.0 451.6 406.3 630 654 874 806 70.8 71.0 108.2 84.3 1344. I152. 1201. 876. Through Freight. 1873.., 870 166.5 1895. 181 37.1 I 1 496.8 1050 203.5 2392. T875... 747 145-5 1093. 209 46.8 402.8 957 192.3 1495. 1880... I189 232.0 1539. 378 80.3 588.0 1567 312.2 2127. 1S85... I140 226.9 997. 569 117.4 598.6 1 70S 344.4 1596. The above indicates the nature and extent of the fluctuations which have occurred during the thirteen years covered by the table. The following are averages for the ten years 1876-1885 : Percentages of Total Tons Carried. East-bound. West-bound. Total. Through. 48.4 17.7 66.1 Local. 19.9 14.0 33.9 Total. 68.3 31.7 100. Percentages of Total Ton-Miles. Through. Local. Total. East-bound . . . West-bound... 56.5 21.8 12.5 9.2 69.0 31.0 Total 78.3 21.7 100. Percentages of Total Revenue. Average Receipts Per Ton-Mile. Through. Local. Total. Through, Local. Total. East-bound . . . West-bound. . . 44.5 20.0 20.3 15-2 64.8 35.2 East-bound. West-bound Total .... .556 ct. .656 •' 1. 161 Cts. I.2I0 '* .674 CL .818 •♦ Total 64.5 35.5 100. .591 ct. 1. 182 Cts. .719 Ct. <'f:^^ff;^:^^STANCE-EFFECT ^ COMPETITIVE T SAFFIC. 217 Table 92. Average Train-Load of Fretpht Av.r^ d.o OF freight and Passengers in the United States Groups of Statfs Avn ^x, -r , ^^i^niiij oiates, oiAjEs, and on Trunk Lines. ^Computed from the Census Statistics of 1880.] Passenger Traffic. I. New England IL Middle, with Md.rMich..*ind. ilL Southern IV. 111., la.. Wise.; MoV, Minn*.*.'. V. La., Ark., Ind. T VI. Tex., Kan., Dak., and Far W Av. Train' Load. No. Total United States. 53.3 44.2 21.3 37.1 18.3 48.0 Av. Haul, Miles. Freight Traffic. 16.8 17.4 44.1 41.9 39.8 44.8 Av. Train Load. Tons. Av. Haul. Miles. 41.5 21, Trunk Lines. Boston & Albany New York Central... N. Y., L. Erie & W... *.;*.;*. Pennsylvania \\' Baltimore & Ohio. . .... N. Y., Penna. & 0....\.\\' N. Y., N. Haven & Hartf . * , 90.6 163. 55.7 122.5 61. 95.5 T29. 55.7 106. 1 103.7 153.3 34.6 166.9 III. 72. 65. 55. 52.4 38. 41. 90. no. 218. 211. 233. 185.5 "3- IJ^3. With operating practices, that, for this class of traffic at least anv additional distance must be a pure disadvantage inaeS "^ pense, but not affecting revenue. And this is ^^l^^^xl^^^^ i-espect to such competitive traffic as begins and end on one W, or on one system of lines with intereL wholl/in 00^^ Whole of it on the smaH^ liles is tl^lg^^t,,^^^^^^^^^^^^ '- passes over parts of several lines. On ^1 suclf t a^' 'et^^^ rate from shipping point to destination is indeed nrh! , xed without regard to mileage, and oft^n In S n n vT ^ at 00 u; but of the division of this total rate between trplr i:rrm:rsTe':;:"" '- "-^ --^^-^^ — ^ t, zi M\ 2lZ CH. VIL— DISTANCE—EFFECT ON COMPETITIVE TRAFFIC. n I ii 207. The division in all such cases is by a percentage which is regulated strictly in accordance with the relative distance hauled, although not necessarily in direct ratio to that distance ; for there are frequently " Arbitraries" of various kinds, and granted for various reasons, as for terminal expenses, to be first deducted before the final division or percentage is distributed according to mileage. 208. So, too, it is not uncommon for some line to have some strategic advantage of another, so that it can exact from it cer- tain special concessions, in excess of its exact mileage propor- tion, such as allowances for " constructive mileage," etc, etc. The Erie Railway formerly bad a great strategic advantage of this kind over the old Atlantic & Great Western Railway (New York, Pennsylvania & Ohio), the nature and efifect of which we shall shortly see (par. 2i6). 209. Again, when shipments are for extremely long dis- tances they are quite frequently subject not to one, but to the sum of two competitive rates, and the total is divided accord- ingly. All freight passing through Chicago is a remarkable example of this. It is not common to make rates past Chicago to points on either side otherwise than by adding the two Chicago rates (which latter is very common), except when, as to "Missouri River points," special circumstances make it abso- lutely unavoidable. The tendency to make Chicago a terminal point for competition and start afresh from there, is strong. There are some apparent partial exceptions to this rule, but they are hardly real ones. Thus in i886, after considerable controversy and irregularity, rates from New York to " Mississippi River points," including a large number of points north of St. Louis, were by agreement adjusted at the fixed rate of ii6 for ICO to Chicago. This was then divided between the lines east and west of Chicago (there being half a dozen or more lines interested on each side), by assuming the distance for all lines to be 220 miles west of Chicago and 970 miles east, these being about the average of the actual distances, which of course varied with each road. The total rate was then divided in exact propor- tion (as nearly as might be) to these distances, viz., i8i per cent west and Bii per cent east of Chicago. Exactly these divisions would have been 18.487 and 81.513. so that the rate on 0.15 mile of haul west of Chicago was given away to the lines east to obtain a round-numbered percentage. CH. VII.-DTSTANCE-EFFECT ON COMPETITIVE TRAFFIC. 219 arer"Jaldl!sso7H"?' '"".^"« '"^ «-"»' ^'^ ">a, through competitive rates are regardless of distance is extended likewise to a first division of those rates mto two parts. What the arrangement reallv means, however is "hat akhoulh .ntere t of peace and good-will, yet the distance was so great and the confl ct ■ ng .nterests so multifarious that it was more convenient to regard hs rate as made up of two separate and distinct through rates, than to regL i as as Lie through rate to be divided in the usual manner * Compacts of this kind may increase, but at present they are too exceptional to merit more than passing notice. / c 100 exceptional andtn °r !"'"'"' °' " ""'"■^■•y" allowances, a large part of the business from and to local points near large cities really comes under the head of ihroueh vLt L T y • ■"«»"«. being usually made the same as to New Iei:v;re"d',h:':f''^' " "" '"'''' "- P--^~ a^uany takeVtot: its effect uornth"' """"";' "°' "'"'^ ^^ ""= ""'"S'' "« '' - «•« same in Its effect upon the receipts of the connecting lines as if it were. 210. Certain considerable allowances for terminal cliarees at points where sucl. charges are heavy are very commonly and very justly deducted from the through rate before the latter is distributed, as notably at New York, where the terminal allow- ances are very heavy (4 to 5 cents per 100 lbs.), although hardiv enough to cover the direct and indirect expense to the terminal In fact the variations and exceptions in the fixing and division of rates are endless, but through them all the general law holds good that all "through" rates between connecting lines are divided precisely a^.^r^ng to the actual mileage, and to a verv large extent directly as the mileage. 211. These facts result in a curious and apparentlv contradic- tory law, as respects the through traffic of a new or old road which ,t may be highly important that the engineer should understand. That law may be thus expressed : I. It is- extremely desirable that any new line should FORM A PART OF THE SHORTEST ROUTES BETWEEN IMPORTANT CENTRES OF TRAFFIC. 2. It is not DESIRABLE, AND OFTEN THE REVERSE OF DESIRABLE, 220 CH. VIL— DISTANCE-EFFECT ON COMPETITIVE TRAFFIC, THAT IT SHOULD MAKE ANY EFFORT TO BRING ABOUT THIS RESULT, EXCEPT IN SELECTING ITS CONNECTIONS. The reason for each half of this law is not difficuh to see. 212. As respects the first part of it : The through rate being altogether independent of distance, the receipts per ton-mile or per passenger- mile on competitive traffic will be the greater the shorter the line is — a consideration plainly of immense importance. We may see a striking proof of this by comparing the New York Central, Erie, and Pennsylvania lines. The operating ex- penses of the Central and Erie, as shown in Tables 37 and 76, average continually a much heavier percentage of their receipts than on the Pennsylvania, yet they are operated with substantially equal efficiency— at least there is far less difference than super- ficial observers often conclude from this very fact. The true cause of it (with which other causes may co-operate, but only to a minor extent) is simply this : that the Pennsylvania has the short- est line from almost every point in the West to New York and Philadelphia, and hence its receipts per mile— from the same through rates — are unavoidably materially larger than the Cen- tral's or Erie's. This fact, however, does not show so much as it otherwise would in the average receipts per ton-mile of these roads, as published, simply because the Central and in less degree the Erie have an immense local business, which both pays more and costs more, thus bringing up the average receipts ; but the through business proper leaves, and must continue to leave, a very small margin per mile to both lines compared with what the Pennsylvania obtains. No ingenuity or skill will ever be able to materially decrease the large percentage of advantage for through business which its geographical position gives to the latter road ; because the total through rate will always be the same by all competing lines, and the long lines must conse- /- nai/tin^. Spending money to shorten one's own line for through busi- ness, therefore, must, except under peculiar circumstances be classed among those charitable actions for which a reward mav possibly be hoped for in the next world, but hardly in this The only important exceptions are : .» - ^ iic First, When a road reaches all important points over its. own lines, as the Pennsylvania ; or r>rofZ"'!l' ' ■'^''"" " '' """' ^°^ °'''='- ■•^^^°"^ than direct profit to the investors, as the Cincinnati Southern Railway or lines built by the State. -"vvay, or Even these exceptions are in all cases only partial. There is ways some credit side to the disadvantage of'distance, Iherea Bade, v?'"" '?"'"' ''"' '° "^^ S--^^'^"'^ °^ <='-ature. .0 themf 'k"' ^'■''"""'' ""^ '"^"-^^"y have a credit side them, from being necessarv to reach certain traffic points, but 222 CH. VII.-DISTANCE— EFFECT ON COMPETITIVE TRAFFIC, \ in themselves they are vvliolly harmful, whereas extra distance is not. 215. A notable example of these antithetic effects of distance, and of the danger of disregarding them, may be found, among many others, in the old Atlantic & Great Western (now New York, Pennsylvania & Ohio) Railroad. It enjoys the unique dis- tinction of being now, as it was when first built, the longest line in existence even between its three termini— New York in the East, Cincinnati and Cleveland in the West. It has always two, and generally three or four, more favored rivals between each considerable point in the East and every considerable point in the West. Yet even in this extreme case, if its own line had been ten miles longer between Cleveland and Cincinnati and New York it would have been better off. It would then have received — - or 46 per cent (see par. 220) instead of -— or 45 872 223 per cent on all Cincinnati and New York business, and -— or 35 per cent instead of |^ or 34 per cent on all Cleveland-New York business, assuming in both cases that receipts were divided strictly according to distance. 216. As it happens, this is, or was until within a few years (the old Atlantic & Great Western is now leased to the Erie), one of the cases in which the division was not strictly as the distance ; the Erie Railway having formerly insisted on being allowed a CONSTRUCTIVE MILEAGE of 46 miles from the junction point at Salamanca to its terminus and junction with the Lake Shore & Michigan Southern Railway at Dunkirk : an unjust exaction, which it had power to enforce because it was the only eastern connection of the Atlantic & Great Western. Whereas, there- fore, a division exactly according to distance would have given the Erie on Cleveland-New York business ~ or 66 per cent, and the Atlantic & Great Western |i| or 34 per cent, the actual <:H. VII.— DISTANCE— EFFECT ON COMPETITIVE TRAFFIC. 22'i^ division was ~^^ or -g ((^Z per cent) to the Erie and only 2 I "2 — ^- (32 per cent) to the Atlantic & Great Western. Neverthe- less, in this as in all other cases divisions were ultimately based upon, although not in strict accordance with, the precise relative hauls. 217. From this example the over-hasty conclusion should not by any means be drawn, that a road should lengthen its line of set purpose, for this end alone, for that would probably lead to acts of folly ; but it does clearly follow that whenever a better line in all other respects can be thus obtained it will ordinarily be folly not to take it. As it happens, such lines did exist at several points along the Atlantic & Great Western, affording better grades, more traffic, and cheaper work, at the cost of some distance; but unfortunately the original projectors sinned against both of the cardi-nal principles laid down in par. 211: they ne- glected the vital end of securing short and favorable connections, but exerted themselves to shorten their own road by striking an air-line wherever possible, at almost any sacrifice of gradients ; running it, in literal truth, "over the hills and far away" from' traffic. The consequences of such engineering may be read in the financial history of the road— a history which might have been anticipated with certainty in the beginning, and may be counted on with certainty to continue to the end. It has now found its greatest and only real use as a feeder and competing •weapon in the hands of the Erie, but considered as a separate property, apart from one or two profitable leases which have alone kept it in as good a position as it has had (see Chap. XXI.), it can never by possibility more than barely pay operatinjr ex- penses for any period of years ; for, however great may be the growth of traffic, and however great the future improvements tending to reduce expenses, other lines also share these advan- tages, and through rates will continue to fall in proportion, down to the lowest point which affords the most favored line 2i handsome 'but not exorbitant profit, and way rates likewise will continue to I i; 224 CI/. VII.'-DISTANCE— EFFECT ON COMPETITIVE TRAFFIC, fall in proportion down to a reasonable but not excessive per- centage (usually from 50 to 75 per cent) in excess of the through competitive rates. 218. In a certain important sense, indeed, vi'e may say that all rates are fixed by competition, for the fact that non-competitive way rates do adjust themselves quite closely to the through rates is well determined. In illustration of this fact, which has been Table 93. Statistics of Passenger Traffic, Cleveland, Columbus, Cincinnati & Indianapolis Railway, 1873-1885. Year. 1873. 74. 1875- 1876. 77. 78. 79- Local Pass. Through Pass. Av. Haul. Miles. 2q.8 27.8 27.1 1880. 1881. 82, 83. 84. 1885, 28.3 27.9 27-3 28.6 Rects. Per Mile. Cts. 3-47 2.83 2.63 2.48 2.41 2.42 2.46 29-5 27.6 28.7 30-5 295 28.9 2.39 Av. Haul. Miles. 198 185 1S8 192 183 182 186 Rects. Per Mile. Cu. 2.53 2.55 ^38^ 1.89 2.24 2.10 1.82 Per Cent Throusrh of Local Rate. 730 90.0 90.5 193 2.51 2.60 2.51 2.47 2.57 184 115 121 118 121 1.82 1.77 1.78 I. 81 1.73 1. 61 76.2 93.0 86.8 73.9 76.1 70.5 68.6 72.0 70.0 62.6 Decrease per cent in through rate in 12 years, 36.4 per cent. .4 4* 44 local " *' " 25.9 " Summary of Average Decrease from Average of 1873-5 to Average of 1878-81. 3 y'rs, 1873-75, 1.766 cts. Through Freight... -j 3 y'rs, i873-75» -979 Ct. 3 y'rs, 1879-81, .593 " Adecreaseof 38601. Or, in percenuge ViMiV- c- j 3 y'rs, 1873-751 a-487 cts. Through Passenger ^^ ^ y^^ 1879-81, 1801 " A decrease of 0.686 ct. Or, in percentage ayJiP'C- Local Freight . ( 3 y rs. I 1 3 y'rs. » 879-81, 1. 157 Adecreaseof eogct. Or, in percentage 34^ P- c- i 3 y'rs, 1873-75, 2.978 cts. L»cal Passenger. . . . -j ^ y,„^ ,879-81, a.455 "'_ Adecreaseof 523Ct. Or, in percenuge 13*3 P*** CH. VII.-DISTANCE-EFFECT ON COMP ETITIVE TRAFFIC. 225 Table 94. Statistics or Freight Traffic, Cleveland, Columbus, Cincinnati & Indianapolis Railway, 1873-1885. Through Freight. Year. East-Bound. West- Bound. Averasre Haul. Miles. 1873. 74 1875 191 215 76. 77- 78. 79- 1880 195 Receipts Per Ton-Mile cts. 1. 14 .92 Averajfe Haul. Miles. 205 214 Receipts Per Ton-Mile, cts. •75 215 202 208 203 .64 .67 •57 .52 81. 82. 83. 84. 195 1885. 193 184 185 2Q2 199 .66 .50 •59 .62 •50 223 231 223 221 217 1-34 1.24 .86 Per Cent West- Bound. 23^3 26.2 212 .44 2X1 200 202 206 .68 .88 .84 •73 207 _-73 .60 .61 •71 •59 28.7 Per Cent Through. 62.5 59-2 26.8 26.2 22.7 26.2 28.2 51 35.2 35.4 35-6 37.4 59-4 Average Receipts Per Ton-Mile. cts. I -175 .984 64.7 64.8 67.4 67.6 64.2 36.7 64.9 68.9 65.1 64.9 68.0 Local Freight, 778 650 716 613 565 68 r 532 591 652 525 463 Year. East-Bound. 1873. 74. 1875. Average Haul. Miles. 119 120 76. 77. 78. 79 • 1880. 81. 82. 83 -Jil 1885 108 106 108 116 115 Receipts Per Ton-Mile. CIS. West-Bound. 1.82 1.65 1.58 132 105 97 loi 95 1.42 1.48 I-I5 ^•15 Average Haul. Miles. 98 93 Receipts Per Ton-Mile. Cts. 109 I. GO 96 1. 10 1. 17 1. 12 1. 14 107 102 98 100 2.09 2.08 Average Receipts Per Ton-Mile cts. Per Cent Through OF Local Rate. 1.68 108 1.08 112 no 117 126 1.44 1.64 1. 61 ^•34 ,899 776 1.622 East- Bound only. 62 •34 116 1.20 1. 18 1.03 .91 1.429 i^538 1.303 1. 215 47 I. no 66 •99 1. 146 1. 176 1.079 1. 018 •039 40.8 Total. 61.9 55.4 48.0 Per Cent of Decrease, 1873-1885. -bound. West-bound. Av'e. 61.4 62.0 60.7 40.7 52.7 453 45.5 46.6 47.0 46.5 61.3 46.4 50.3 60.3 51.6 44.5 I n rough rales. . Local rates . 15 Per Cent of Decrease, 18 75-1 885. T,. , Eftst-bound. West-bound. Av'e. Through rates . 41.3 40.7 39.5 Local rates ... . 31.6 41.0 3I.9 226 CH. VII.—DISTANCE— EFFECT ON COMPETITIVE TRAFFIC. Table 95. Comparative Through and Way Rates, Lake Shore & Michigan Southern Rajlway. •m (Cents per ton-mile.) East-Bouno. West-Bound. Total. Ybar. Through. Way. Through. Way. 1868 1869 1870 1871 1872 1.56 1.49 1. 13 1. 17 1. 13 3.49 3.68 2.67 2.35 2.04 2.02 1.78 1-53 1. 18 1.49 4.07 4.05 2.84 2.26 2.01 2.43 2.34 1.50 1.39 1.37 Comparative Rates, taking Rates of 1868 as i.oo. i860 ..•••• 1869 1870 1871 1872 1.00 •954 .723 .750 .723 1.00 X.055 .755 .673 .685 1.00 .882 •758 .585 • 738 1.00 .996 .698 .556 .494 1.00 .962 .617 .573 .563 Since 1873 the rates have not been made public in this form, for through and way separately. It will be seen that the non-competitive way rates fall in close sympathy with the competitive rates, and vary more directly with each other than the East-bound and West- bound. already alluded to (par. 54), a comparison of the course of through and local rates on the Cleveland, Columbus, Cincinnati & Indianapolis Railway is given in Tables 93 and 94, and on the Lake Shore & Michigan Southern Railway in Table 95, which illustrate the fact very strikingly. Few roads publish reports from which such statistics can be obtained, but the law holds substantially true everywhere. . 219. From these examples it takes no great intelligence to perceive how inexorable is the law that the line which places itself originally at any serious disadvantage has no escape from the consequences of its folly but to remedy those disadvantages. Apparent advantages from the general progress in wealth and I.r fn tlU rt"" '° r "^"' " ^' '"• ^'"" ^" "-hare own" U ,^- u^ '""P'y "^'"« " '» hold its own, and " its divided h' ""^^ ^^^^^' "•^' "^^ ""-""gh rate is nearly always divided by some even percentage, and consequently triflinrdif ferences are not likelv tn off.„» .1 j- • . ^"'■'^y tnnmg ait- -■<: noi iiKely to affect the division either way. Thus a line entitled by its exact mileage to receive either ^27 ^^403 would probably receive 40 per cent. H i. length e'nmied I't^" 7^ It would probably receive 4. per cent. The fractional per- to hoM th^""' ^on^etimes insisted on by the line which happens iind°'ta el T:f" r'°"' "" "^"^"^ ^"^ ^'^-"-««^ "^ 'ha Kind takes the form of some terminal or arbitrary allowanr^ instead of a modification of the percentage ^""vvance ^h."'' f'"r """ ""^"'P'" °^^"y °"<= -""ad from competitive ex change traffic vary (i) with the total haul on each unifo raffiT Zt}"\r'\ '"'^ '"■°P'"-"°" "■^■•-^ - 'he homeind forS roads, the effect of any given change in the length of V.T^ ^oad wn. be different on traffic between all possif ,e t ffit^ TnTs*^ All that can be done, therefore (or all that is in the least neces: sary to do . ,s to form some rude idea of the centre oTo^^^^^^ of the initial and terminal points of shipment at each end of thi ;|ne. Which Will often be quite different for different pans 0/ tt ternale lines are under comparison in other reslTs 'he^ J„ro T° "^ ^uh the utmost caution. anotner, should be admitted only 228 CH.VII,— DISTANCE— EFFECT ON COMPETITIVE TRAFFIC. 222. The effect on the receipts of the home road from through competitive traffic of an increase in its own length only, the haul on its connections remaining unchanged, may be stated^ with adequate exactness, in this very simple way: The interpolation of additional distance by the adoption of a longer alternate line between the same termini will, for all ordi- nary and moderate changes of length (under 20 or 25 per cent of home haul), leave the earnings per mile of the original (shorter) line unchanged, and enable the home road to earn on its extra mileage as large a percentage of the average per mile on the shorter line as the percentage of the foreign haul to the total haul. This law holds essentially true, regardless of the amount of the added mileage. For example, on traffic which has 70 per cent foreign haul,. if the home road were longer it would receive out of its added proportion of through competitive freight enough to earn 70 per cent as much per mile on the added mileage as on the original mileage, the earnings on the latter remaining unchanged. 223. To put the rule in another and shorter way: With through competitive traffic — The per cent of home haul in the total haul -|- the \ = 100 p. c. per cent of average earnings per mile realized v (always a lit- by home road by extra mileage ) tie less). The maximum and minimum "limits" to this rule are: I. When the home road has 100 per cent of the haul it rea- lizes o per cent, or nothing, on any extra haul. 3. When the home road has originally o per cent of the haul the gain to its receipts from any haul it may gain is 100 per cent of the average rate per mile. 224. A simple geometric demonstration of this law is given in Figs. 7 to 12, with their accompanying explanation. The law is only approximate, and f6r very great changes of length be- comes materially in error; but the largest probable differences which can come under the consideration of the engineer are from 10 to 25 per cent in the home haul, and for such differ- *nces the law is sufficiently exact, as is evident in Table 06 which gives the exact effect on receint.OUOH (ExCHXKOK) Competitive Traffic. divine U.« ««. .ffec. and mustrating .he essentia, truth of aad amount or eLr in the approximate rule in paragraph 223. ^^''^ "f ^O A'- ^^nt Increase of Distance. Per Cent of 'Original Total Haul on the Home Road. 10 30 30 40 50 60 70 80 90 100 Corresponding Receipts of Home Road out of $1.00 Rate. If the Home Road were Ten Per Cent longer its Keceipts would be— 10 cts. 20 I ( 30 40 50 60 70 80 90 100 • < << 373- 75--- 1. 00 0-35 5-39 2.37 9.12 358. 126. 863. 133. 1479- 1871-5.. 89 0.33 4-74 2.31 827 317.6 118. 2 721.2 130.8 1287.8 1876.... 1.32 o'.29 5-79 2.52 9.92 473- 105. 915- 136. 1630, 77..,. 1.02 0.39 5-7» 2.72 9-74 364. 103. 869. 159- 1495 • 78.... 1-45 0.29 6.20 3 01 10.95 519- 103. 936. »75- 1732. 79... 1.69 0.38 7-59 4.01 13.68 605. 137. 1138. 257. 2137. 80 ... 1.58 0.49 8.51 4.79 15-36 565. 174- 1230. 329. 2298. 1876-80. 1.41 035 6.76 3 41 "•93 505.2 124.4 1017.6 211. 2 1858. 4_ 1881.... 1.64 057 10.12 5-91 18.23 586. 203. 1452. 414. 26^5. 8a.... 1.35 0.59 11.91 6.51 20.36 483. 213, '755- 430. 2880. 83... 1.38 0.56 12.47 7.27 21.67 494- 199. 1853. 451- 2997. 84... 1.29 0.53 13.33 7-43 22,58 468. 192. 1938. 484. 3082. 8s.... 1.68 0-57 13.88 7.91 24.05 612. 209. 1969. 529. 33'8. 1881-5.. 1.47 0.56 12.34 7.00 31.38 528.6 ao3.3 »793-4 461.6 2986.4 ' ^J^^'-DISTANCE-EFFECJ^ ONCOMPETITIVE TRAFFIC. 233 Table ^^, —Continued, Summary by Half- Decades. Year. Toms Carried. 1 = 1,000,000, Ton- Mileage. 1 = 1,000,000. Percentages and Average Local Haul. Year. Tons, Per Cents op Total. 1851-5 1856-60 1861-5., 1866-70. 1871-5.. 1876-80. X881-S . Through, West. East. 24.5 12.7 15.0 9-4 10.8 II. 8 6.9 Local. East, 20,5 8.7 5-9 4.6 40 2,9 3.6 34.5 44.2 55.1 57-7 57-3 56.7 57-7 West, Ton-miles, Through, 20.5 34 4 24.0 28.3 27.9 28.6 33,8 East, 22.7 23-3 31-3 West, 17-3 16,0 12.1 21.8 10,9 247 9.1 27,1 6.7 17.6 6.8 Local. East. 39-6 43-7 45-7 54-4 56.0 54.8 60.3 West. Average Haul on Local Freight. 20.4 17.0 10.9 12.9 10,2 11,4 «S.4 East, West. 30 163 141 145 151 150 145 26.0 81.0 76.5 70. a 56,6 61 9 66.0 226. From the additional receipts thus realized is to be ri^ ducted the additional cost of earning it, which we have seen may vary anywhere from .5 to 40 or (for great changes) 50 per cen^ De realized from longer home-haul of competitive frei°- would nish as much business a/,, r'' -^ f"^ '■"^■gnificant town will fur- iiiucn ousmess as that, as wil be evident frr>,r. t„ki „ The average payment to railways in the North rir J^ '* '° '*' about $.3 per head per year, an average vuL^e of ,oS to ^ 'T '""« be a sufficient inducement for such a dJlcti^l^u 5°° P^°P'«w°"l!> guides, to'be leviated from only as special reason to the con- trary "PP^^'^f = ^,,1,^^ will increase the average PER mile of ,OAD 0/ TRIBUTARY POPUI-ATION (weighing the latter, of course, m tL to thLr revenue-producing capacity) is all but certamly ex- ''TnT becluse i irmathematically demonstrable that the longer hne rugrlhentoTe fo: the Joint advantage of the community and the ra.l- ""VTve^n'tSn be considerably less than this, the deviation may easily L (and P-bably is) for the interest of the railway, although not Tthat ci ex^dient in itself, as a question of public polrcy. J38. AH the preceding conclusions as to the comparatively slight importance of distance (and the same ,s true of all the iinor details of alignment) may well lead to ruinous conse- quences If hey are stretched until they crack to support some Tended aid radical change materially modifying the cost and extenaea ,„ncoortation, and so discouragmg traffic ; for "t^lTt'^verL o t s gh of. 'that anything which tends to per- ., nLase bv ever so little the cost to the public of any SrerSre TdisSvIn^ageous to all parties, although its dis- fdvantages may be more than made up to one party by the gam , ::n1h\di«e ence .e e.^^^^^ rgVt° otinTo"! ihaTetn in extrLe cases there always .s C//AP. VII.— DISTANCE— MORAL EFFECT. 239 •a credit side of considerable importance to increase of distance —contrary to the idea which prevails to an unfortunate extent, that a short and direct line is the first desideratum, to which almost everything else must bend. On the contrary, it would be hard to put the general rule whicii should govern action about obtaining a short line in a simpler and safer form than to say that it is the one desideratum about a railway which it is a good thing to have if it costs nothing, but which must give way to other considerations in case of conflict, and is not worth spend- ing much money for. There are cases — as for instance a line between New York and Philadelphia— where it is of great importance; but the excep- tional position of distance as the one element of cost of trans- portation which is used as a basis for collecting revenue makes such exceptions rare. If the conditions were different— if, for ex- ample, we could charge the passengers we did get more, because we had sacrificed the chance of getting some others in order to carry them more quickly— all this special pleading would fall to the ground, and distance would take its true relative position with the other elements of the cost of transportation on the basis of cost alone. But the very fact that this is not the case seems to have had the effect of reversing a reasonable deduction from the premises, in the minds of the more ignorant and thoughtless, by leading to some such hazy chain of reasoning as we noted in the beginning of this chapter. 239. There is another argument, of much the same vague kind as that last referred to, but of a more reasonable and tan- gible character, which is sometimes brought up as a reason for saving distance, viz., the "moral effect" of a short line in helping to secure traffic. Nor is this argument wholly unjusti- fied, for there are numerous lines throughout the country which do apparently suffer simply from the length of their line fright- ening away passengers and fast-freight traffic. We may see that this effect is feared by the current fashion of misrepresent- ing geography in railway advertising circulars. 240. Many lines which are not particularly direct, however. 240 CHAP. Vll— DISTANCE— MORAL EFFECT. CHAP. Vir.-DISTANCE-MORAL EFFECT. 24I do not do this, and the prosperity of a single conspicuous line, the New York Central & Hudson River Railroad, will show that there is nothing in distance pure and simple to deter travel until, as in the case of the Grand Trunk Railway in competing for ' American business, the difference of distance becomes so great as to seriouslv lengthen the total time of the trip-a result not commonly to be feared from probable engineering modifica- tions of any given line. The enormous proportion of the New York-Chicago travel which the New York Central secures in spite of being the longest of three prominent lines (970 miles- against 961 by the Erie and 912 by the Pennsylvania), and in spite of taking passengers 150 miles north before they begin to go toward their destination at all, is sufficient proof that, if a line be equally comfortable and well managed, and makes equally good through time (as all lines do, for the most part, by general agreement, which ticket through at the same price and as any line can successfully insist on doing when its length is not in excess over 10 or 15 per cent), it will not suffer to any material extent from this cause alone. That the New York Cen- tral is no very great sufferer hardly needs further demonstration than may be found in various tables by referring to the Index. 241. The difficulty is (par. 51) that the lines least favored as to distance are generally less desirable in other respects. There are more connections to make, less favorable through-car arrange- ments, a less number of and slower trains, etc., etc. At the very worst, moreover, this objection only applies to a very small por- tion, and that the least profitable portion, of the traffic ot a road; and it does not apply at all to those small changes, of a f^w miles more or less, which the engineer is most frequently caUed upon to consider, and to which this chapter has mainly referred- 242. The conclusions reached in this chapter have rarely been recog- nized in the practice of engineers, but instances are not wanting where they have been clear enough to operating officers^ As one '"st^r, J the latter, on the "Pan Handle" road (Pittsburg, C.nc.nnat. &St_Lou>s^ a tunnel near Steubenville. O.. saving two miles of distance and much curvature, but costing $300,c»o. was avoided ^y^ temporary line. When at last means became sufficient to construct it. the general manager the Ime objected to its construction on the ground that, even though the greater part of their traffic was local to the vast Pennsylvania system the loss from revenue on the two miles saved would far more than counter- balance the saving in operating expenses ; and proved it so conclusively that the construction was for some years postponed. Subsequently, on account of the exceptionally commanding position of the Pennsylvania roads. It was believed that the old distance could be considered as con- structive y stUl existing so that this loss would not arise, and the tunnel was built. Whether or not this expectation has been maintained the writer cannot state, nor does it affe« the force of the example. 16 CHAP. VIII.— CURVATURE, 243 ■I CHAPTER VIII. CURVATURE. 243t It is the peculiarity of cur- vature that all its disadvantages lie upon the surface, visible to every eye and compre- hensible by every mind. A heavy grade is very un- obtrusive. The most skilful and observant eye can- not detect differ- ^ Fig. T4.*— Illustrating THAT ECONO- en ces of grade MY OF CONSTRUCTION. AVOIDANCB ^j^.^^ dCCrCaSe by OF CURVATURE AND THE SKCURING OF WAY TRAFFIC ARE NOT NECHSSA- a lafgC perCeHt" RILY IN ANTAGONISM TO EACH ^ ^J^^ operating OTHER. ^. . . ,. value of the line. But curves attract instant attention, and their disadvantages ap- peal even more strongly to the imagination of the inexpert than to the instructed judgment of the engineer. A visible defect or * This illustration the writer borrows from the heading: to a chapter on " Railway ConstTuc ion" oai English engineering work. Whether or not it is a mere fancy sketch heJanno say ; but it at least has no little verisimilitude to not a few actual works The I^f,fet;nn natiirallv arise^ what the curve in the foregrround is for, especially if the steepie ?n the middk d&e is a hint of a town, or, if a curve was deemed necessary, why it was not mlde a mUe longer There may likewise be found in the picture a hint as to Jit^v?L7^o which a larger expenditure for construction necessarily implies a better line. 'Ae f Xr moratw^^^^^^^^^ is calculated to teach may be left to the ingenuity of the reader. danger is always more keenly appreciated and dreaded than one which it requires special training to detect; and since there is always a natural tendency to correct the faults which everv one sees and to forget the faults which no one thinks of, it is evi- dent that this simple fact must always have a powerful if unde- tected influence while human nature remains what it is. 244. And when we come to consider what are the more solid objections to curvature, we find at once that a formidable and undeniably true list of objections to it may be made, consisting of many counts ; as thus : 1. It causes a considerable loss of pou>er and considerably more wear and tear of rolling-stock and road-bed, thus increasing expenses. 2. It does or may limit the length of trains, and thus still more increase expenses. 3. It causes a considerable expense for extra watchfulness and track- walking, and thus indirectly still more increases expenses. These three are what may be called the definite and positive objections to curvature. We can estimate them with some de- gree of certainty and exactness. But there are still others which are essentially indeterminate, and which for that very reason if behooves us to examine into the more closely, lest the haze of doubt which unavoidably surrounds them should on the one hand unduly obscure them, or, on the other, have a mirage-like effect, magnifying them into undue proportions. Among these causes are : 4. The danger of derailment is increased, and the consequences of such derailment when it occurs are more likely to be seri- ous. 5. The danger of collision is increased by the obstruction of the view. 6. There is more difficulty in making time, and thus passenger travel is likely to be affected. 7. // injuriously affects the smooth riding of cars, and thus deters travel. 8. // impresses the imagination of travellers with a feeling of danger 244 CHAP. VIII.— CURVATURE. « % I I even if none exists, and thus in a third way affects travel unfavor- ably; and, finally, 9. // is more or less an obstacle to the use of the heaviest atid most poiverful types of engines. This is a formidable indictment, indeed, and when it is ex- tended from curvature in the abstract to sharp curvature as against easy curvature it becomes still more so ; for there is then more wear and tear, more danger of limiting trains and more injurious effect upon the safety and speed of trains, the comfort of travellers and the reputation of the line. 245. It is therefore not unnatural that a very general course of reasoning on the question should be : " Each one of these ob- jections to curvature amounts to something ; plainly, therefore, in the aggregate they must amount to a great deal, although no one can ever determine exactly how much. If the curvature be sharp they will be several times more serious, and in fact will then become entirely inadmissible for such a line as ours..'" Thence may follow, perhaps too quickly, a conclusion in the form of an order to the engineers who are to examine the country, to the effect that "the minimum radius of curvature permitted on this line will be," etc. — an order from which thereafter there will be no retreat. 246. Notwithstanding this plausible reasoning and formidable indictment, it may be said at once that investigation seems to indicate that the prevailing error in respect to curvature among engineers is too great dislike of curvature, and especially of sharp curvature, and too great readiness to spend money to avoid it although a few go to great extremes in the other direction. This conclusion seems to necessarily result from analysis in detail of the weight to which each of the above objections is entitled; but without presupposing this, and abandoning all prepossessions in either direction, we will consider each objection to curvature as impartially as possible, beginning with what may be called the indeterminate or imaginative (but not therefore imaginary) objections, 4 to 9, which cannot be reduced to avala- ation in dollars and cents. CHAP. VIII.-CUR VA TURE^A CCIDENTS FROM. 245 THE DANGER OF ACCIDENT FROM CURVATURE. 247. Railway accidents come from a great variety of causes of which curvature is one. How great a cause it may be is made difficult to determine by the fact that accidents are rarely re- ported as directly chargeable to curvature, its effect bein u H H < < (/) < >• X u < M K O Ifa .i < o H 00 t^ « >- N 00 O fn t^ M ro 0> O ro •♦• tv tv o 3t "''2. • i** WW c^ 00 CO ** tv O^ fO flOO M « r« VO f'l CI 1000 f^ o 000 »> • • •♦ ■ PI ft • • CO <0 - o 00 ■«• ** I N >0 10 63 f 00 «o >^ M 00 rs. NO m o 00 ■♦ « M H ^ f»i o> i/> fo m CO « ►"CO ^ CO « CI 00 «0 (*» ♦m f»i n C( 00 0> •♦ >rt X ID 0« H M n 00 O M •(«<•> Ov rx « . VO e*) • « 00 'S « VO O OvvO M M vS 00 ^vo 'n !/■. 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M ^ • M • • M • • VO VO ^O fO •>•• (O OvOO M M M M ■ CO 00 Ov f) »x M M 00 m • CO M tN CO • . M Ov tx M 10 M <♦ ro M ■* trieri ertso COM M " CO O M m MOO MOO O M m VO •<(■ CXM M (f) . M CO mvo 00 ro tx M tx . . M • M M N M . . " . " VO M IX rx CO ♦ . M M . M m VO M ; M M O>00 M VO • M • M CO CO M O OlOO en M 10 • M M • M M o •-■ o o d d o' • d d • d N Ix ^ 2" X 2. *'^ 2.^ ?■ <• O 00 00 00 ^. MOv^-x^MtX MM M 5 C.C ii 2 ^-^ i: Se * c o u ^ Ct30 f2 ■a c JE '(5 u •a o z o ■J ■J o u h o X I 2 I bo c *«^ u CI c c o u u o 2 a o ■Sa OD H 2 tn O ^ tf) -J c/3 *n ^^ ' ^ fl^ H < Ox 2 i-g^u 9Q*'.^Cc3cc: ,uuetfuu cQUccosuccn ° a ■Pi, « btiih — C C C .= £-•;: o c o u 3 •" C " ° 4, 5 3 y w cB r. *- u 3 c S a u V •a u O c o o u tt^i; (A «3 3 oi.'s.y 0&,S IT. 3 ^ rt • (» 4-t Hi H n ti c 5- Q. K U c 3 «i e« O ' UVMI V o 4) •. .. .C O- >o 9v >vmov I > o CO c U (A .■H§S u •— .-> o tn— u «= 2^ <^ O C) ~ ouQO u a 3 a a c G rt == M c5 O S^'o 5 .^ ~ -^ x^ C •»" _ W <;i tS ,. o — fc» O ?J O) CO ^ ii S «3 Si o 6 «« 0^ ^^ -S S a ^ c^ 3 o 6 o ^ -S ^ w •- - -. 5J (U O !r"7! ft c - ST 3 P ^ C rt ^ o Pa *' JQ " :: E ^ - J? ., o .!- w ea ^ sS -^ o o o ii ^ S ^ ^ 3 nj i< - ^ g .22 «» S 3 o ^-s a - o o Wi g 4) 1-1 -< flj i? O O (^ V o 3 o "^ c r: in E ^ JJ PS rt a irtSe ?:;:T"' '""T °" ' ''''' '""'^ "" ^'^ ^'C this de cr n "nV but ? """''' ""■"'^ '"^ '^"°>« '"'^ - ''f descnption), but another one, precisely like it, occurred in 256 CHAP, VIII.— CURVATURE^ACCIDENTS FROM. CHAP. VIII.-CURVATURE-ACCIDENTS FROM, the immediate vicinity, ten years before, on a perfectly straight piece of track, which is something pretty hard to find in that locality. These are the two most serious accidents which have ever (1882) occurred from this cause on that section of the road. In the first instance, on a curve, 24 were killed and 80 injured; in the second instance, on a tangent, only 6 killed and 50 injured; but the difference is due, not to the alignment, but to the differ- ence in the height of the precipice — 30 feet in one case and 80 feet in the other. 259. A very common error with regard to broken-rail accidents re- quires correction heg2. There is not a particle of evidence — or certainly none of much moment or weight— tending to show that curvature notice- ably increases the liability of breakage or even the consequences thereof. As respects the former, it is almost purely a matter of the condition of road-bed and of chance defects. Thus the records kept by the Rail- road Gazette show that such accidents are nearly nine times as numerous in the winter months as in the summer, there having been of noticeable accidents caused by broken rails during the eight years 1873-80: In January, February, and March, 268 ; in July, August, and September, 32. The consequences of a rough road-bed or of the temperature of the metal, or both, being so very noticeable, it is clearly indicated that it is the hammer-like effect of the locomotive, rather than any direct pressure, which causes the breakage ; and this is not in- creased by curvature : it is rather de- ..^ creased. On a tangent a train impinges — against the rails with a great deal of force from one side to the other alternately. li \ On a curve every truck in the train tends Vyi \ rather to hug the outside rail with the \ V front outer wheel — in a manner shown in Fig. t7. Fig. 1 7, of which we shall speak more fully shortly— both the inner wheels standing clear of the rail ; while the driving wheel-base is preserved by the truck from impinging against either rail with anything like its natural force. For these same reasons a broken rail on the inside of a curve is noticeably less likely to cause a derailment than if on a tangent; while a broken rail on the outside, although it is of course greatly more dangerous than on a tangent, is not so much so as might seem— for the reason that, even on a tangent. / i KJ 4. — : 257 some one truck in the train is likely to impinge at just the ri<.ht s^^ strongly both to the imagination and the judgment curvaureUaTe a vnere is, tne more dan'^'er thfr** Jc tu^. i • . >i c ucujj,er mere is. 1 hose who mainta n that it shonlrl have the best of the argument so long as it is confined to generalities ihe,r case only becomes weak when' we consider its force in detail 260. The truth is that nothing but a standing miracle keeps e, her curvature or any other of a dozen causes of accident from be..,g a fruttful source of disaster. The marvellous safety of a.lvvay travel ,„ the face of such numberless chances for dLs- kl a!rf • ."T impressive triumphs of human care and sk.ll, and u IS th.s fact alone which gives our argument any force wuatever. No one could have foreseen it, and hardlt any one can fully realize it; but the fact being as it is, true wiLoI requ.res that we should recognize its consequences, and no^ .nsts on trusting to the imagination for arguments n a purely practical question. i^iciy safJH""' ^'^'"'"l '"" ^^"^ eff-^ctively expressed this marvellous safety ,„ a puhy sentence, by saying, that '• the chances of acci- dent ,n ra.lroad travelling are so small that thev are not materi- o LeH ""T \ ^? '"'°""' °^ "■^^'^"'"S ^^hich can be accom- plished w.tlnn the hmits of a human life." He proceeds with the followmg interesting comparative statistics: 260<,. "During the four years 1875-8 only i passenger was killed "e™ Te? d '°"' '." °"" ~""°' '" M--'husLs. and o^^ .0 ^'^ , • y",.^"""g 'he year ,878 alone, excluding all cases of n.ere injury, of which no account was made no less thnnC ^ their death in Boston alone from fani;g d w -s a rs"n'd ;Tr:Z" ^e^ killed by bemg run over by teams, and the pastime of coasting w^ carried on at the cost of ,0 lives more. During the five vears "s,!^ here were more persons murdered in the city of Lston alone hanit:! tneir Ives as passengers through the negligence of all the railroad co m ^^ I 258 CHAP. VIII.-^CURVATURE-^'' D EGREE OF CURVES," porations in the whole State of Massachusetts during the nine years 1871-8 which included the Revere and Wollaston disasters, in which 50 people' lost their lives. Neither are the comparative results here stated in any respect novel, or peculiar to Massachusetts : years ago it was offi- cially announced in France that people were less safe in their own honies than when travelling on railroads ; and, in support of this somewhat startling proposition, statistics were produced showing 14 cases of death of persons remaining at home and there falling over carpets, or in the case of females having their garments catch fire, to 10 deaths on the rail. Even the game of cricket counted 8 victims to the railways 10. 260^. All these facts agree in indicating the conclusion that although curvature is a considerable source of danger, yet it is even then so little dangerous to life and property tliat we are not justified in giving any financial weight whatever to tins argument against it, unless under peculiar circumstances, or as a makeweight when all other considerations are exactly bal- anced The case is entirely different, for reasons we cannot take space to discuss at length, from the defects in operating details which people rightly insist should be corrected even at a large immediate expenditure. Before proceeding further wilh the discussion of the question of curvature it may be well to explain just what is meant by the term •' the degree of a curve." which we shall have frequent occasion to use. for the benefit of foreign readers if for no others. , , .1 j 261. Meaning of the Term " Degree of CuRVE."-The universal method in America of expressing the sharpness of curvature is not by giving the radius, but by the -degree of the curve" or number of degrees of central angle, sub- tended bv a chord of 100 ft. ; i.e.. by the angular change in direction of the curve in the distance subtended by a chord of 100 ft. If the central angle be i . the radius is readily computed as 5729 65 ft- which is the radius of a one-DEGREE CURVE, taken in practical work as 5730 ft. , , , * .u. Except as the length of the arc bears a varying ratio to the length of the subtending chord in curves of different radii, it is readily shown geomeiru:allv that the radius is inversely proportional to the degree of curvature; and this is so nearly true in fact u? to the limit of an 8" curve (within a small fraction o a foot) that it is almost universally customary in the best practice to record the radius of a i' curve as 5730 ft., and to determine the radius of curves of otne ••degrees" by the approximate formula, (To p. 266.) CHAP. VIII.— CURVATURE— AMOUNT OF. 259 Table 101. Statistics of Grades and Curvature on the Railways op the North- eastern United States. [Computed from the Census Statistics of 1880. Sec note.] New England. Namb op Road. Miles of Road. Curvature. Curves Per Mile. 18 Roads, A. to Conn., 19 " Conn. to Nor. ^o " Nor. to Sum. Total. 57 roads Single Roads. Boston & Worcester. Boston & Albany. . . . , B. & N. Y. Airline.. Concord & Portsm... Central Vermont P. C Curved. ,027 750 982 1.859 Totals and av. 44 203 51 40 120 457 1.72 1.89 r.67 1.76 X.68 1-55 Z.62 1. 41 1.17 1.48 42.0 33-3 35-0 Deg. Per Mile. 36.i 40.5 56.0 34-0 37-2 37-8 41.1 49- 60 51.5° 38.7" Grades. 46.6" P. C. Level. 25.0" 72 '5' 76.0* 93.0° 34.5" 60. 0.0 1-3 38 Rise Per Miie.* 1-7 3.8 0.0 6.1 3-8 0.9 18.7 24.6 19. 5 Rise and Fall Per Mile.* Ruling Grades. 20.9 X0.4 9-3 13 5 19.0 15-7 12.2 15.6 10. s 12.8 3. J 13.6 2.8 »3-7 »7.3 »5.3 8.4 II. 5 30 80 60 80 42 New York. Alb. & Susq Buff., N. Y. & Phila. N. Y.&Can Hudson River....... N. Y. Central " (Syr, to Roch). Totals and av. N. V. & Harlem. Erie. E. Div.... Del. Div.. Susq. " .. W. " ... Reps. & Saratoga. #42.5 liD.5 112. 9 143-8 296.6 102.6 2.36 1. 14 2-55 1.68 0.78 o.os 9.8.9 Roch. & St;»te Line atoea te Lii To tals and av . . . . R , W. &0 Syr., Bingr. & N. Y. Syr., Gen. «k C l;ister& Del Utica & B. River. . U. Itli. & Elm Totals and av. 127.0 87 o »03 9 »39-9 129.2 79*1 107.7 773-8 1.58 1.17 1.67 3-73 1.44 1-25 1-37 1.09 36.2 24.8 34-6 32.3 19.8 34 5 30- 3 1.67 148.0 81.0 57-8 73-2 86 8 71.0 5x7-8 0.63 1.60 1.26 3.00 1. 14 1. 51 X.53 20.7 29- 3 53-8 29.6 28.4 25.5 255 54.2' 28. 6« 64.7; 28. 5» 15.1° 25.0° 36. 30- 9" •5' 46. ^» 31-3 »7-4 33-8 24.x 41.0 26.6 "•5 25.9 88. 32.0" 32.4" 28 4» 31.5' ai.3 • • • • 32.2 75-8 34-8 6 8 34.1 4' -4' 17.0" 3i.6'» 27-3* 80. 5» 24.0* 21.7* 33-7* II 9 39 31 12.8 25-3 16.8 5-9 3.8 0.0 0.0 X.8 09 13.2 9.0 7.8 X.6 3-8 90 78-56 2.1 21.0 29.4 24.8 17-5 13.6 3»-3 7.0 20.6 3-» 5-1 4-5 * 7 4.3 1.6 5-4 o 9 5-7 8.6 24.1 0.8 3-2 7-4 8.4 II. 8 4-5 I xo 7 9 39- 43 24- 34 2'- 33+ 40- 56 7.6 7.2 6.8 6-5 8.9 II. 6 12.3 II. o 9-S 40- 42 30 + 15 + 12- x8— 52- 47 53 71- S3 40- 53 52 37- 74 160-142 66 85-127 ♦ The column R.se Per Mile" gives the average excess of rise over the fall in one mile The next column gives the feet of rise and fall. Thus, if a road rose 500 it. and fell «oo in loci miles. It would be given above as -Rise Per Mile, 3.0." "Rise and Fall, a.o." The first quantity is an unavoidable necessity, due to difference of level of the termini 26o CHAP. VIIL— CURVATURE— AMOUNT OF. Table \Q\,— Continued. New Jersey. Namb or Road. Miles of Road. CURVATURB. Morris &. Essex... Phila. & All. City. Toials and av. Curves Per Mile. 83.7 54-5 X38.2 1. 16 0.43 0.79 P. c. Curved, 34 o 10. 5 32.2 Depr. Per Miie. Gradbs. 44.4' 6.3' 25- 3' P.O. Level. Rise Per Mile.* 17.8 _24_^_ 21.3 Rise and Fall Per Mile.* Ruling Grades. 2.6 0.0 1-3 16.4 10.7 >3-5 50 52.8 + Pennsylvania. Cumb. Valley... Del., Lack. & W Lehigh Valley Lew. & Tyrone Montrose No. Cent Totals and av Penna. Mid. Uiv W. Div P. & N. Y. Canal Perkiomen Phila. & Erie " (Summit Section) Pitts. & Connell Western Pa Wi lm. & No Totals and av Summary of North-Eastern States. No of Roads or Divs. 57 5 6 7 6 3 6 10 State. 99 New England. •t >• New York ** " • ■ • • • New Jersey... Pennsylvania., Totals and av Curvaturb. Miles of Road. 1,859.0 457-0 918. Q 773.8 5»7-8 1.^8.2 705.9 r,o»x.4 Curves Per Mile. 1.76 1.48 1.58 1.67 1.52 0.79 2.67 2-47 P. C. Curved, 5.372- .88 36.8 41. 1 30 31 25 22 37-8 45-3 Deg. Per Mile. Grades. P. C. Level. 6» .,0 35-5 46 60 36.0* 41.4" 33-7' 25.3' 91.4° 81.4" 55-9° 309 13-6 34- 1 21.0 20.6 21-3 U-5 24.9 Rise Per Mile.* 33.8 1-7 3« 3.1 9.8 7.3 ».3 9.3 32 Rise and Fall Per Mile.* 4-7 30 9 13.6 7-4 8.3 9-5 13-5 12. 3 13.0 Compare Summary of Table 102, with note. CHAP. VIJI.— CURVATURE—AMOUNT OF. 261 ^ntL^rlf ''''^^''^ ^P^'^' '" '^'' ^"^ ^^" ^°"°^^'"^ Tables 102, 103, 104 were com- puted by the writer from time to time from the statistics which were gathered for I iZl IT,^ T . , '^'"^ excess of average grade in the prairie States over what elts in the East is clear enough, and an undoubted fact. Table io2. Statistics op Grades and Curvature on the Railways of the North Central States. [Computed from the Census Statistics of 1880. See note to Table xoi.] Ohio and Indiana. Nams of Road. Cin., Wab. & Mich ... C.,C.,C.&L(N. End). c' »'; (Ind.End) C, H. & Ind Cid. & Mar C, Mt. V. &Del...'. C, Tusc. V. &W.... Dayton & Mich Evansv. &T. H .... Ft. W.M.&Cinc . Totals and av Miles of Road. Curvature. no 138 203 98 98 »43. 158, 139.8 109.0 104.2 Curves Per Mile. End) Ind.. D. &S J., Mad. & Ind.(S L. Erie& W L. S. &M. S vv T," (Air-Line) N. Y., Pa. &0.. v>. & Miss . . . P , C. & St. L T. H. & S. E 0.56 0.23 o 36 0.65 1.90 1.29 2.03 0.42 0.60 0.28 P. c. Curved Degr. Per Mile. t«304-5 l 0.83 152.0 IIO.O 353-0 540-5 130 8 387 -9 103 • 7 338.0 192.8 40.0 0.32 0-54 o. 19 0.41 o.io 0-74 0-33 2-3 8.1 9.0 14.3 34-7 28.5 315 7.0 151 5-4 16. 7.0 10.4 6. 12. 4- 23- 10. 21. 33- 19- .6 .0 •9 •7 .6 •7 •7 •4 1.2" 6.7» 8.9° 14.6° 5.2° 35.7° 59 f° 7.0° 17.5° 4-6° 16. 5 9" 9-5° 7-8- 1.8° 21.5° 5-2» 28.30 46.0° 24.0* 15.9° ♦See note to Table zox. P. C. Level. 27-4 8.0 8-3 13 o 48.6 I5-I 20.5 I.O 19.8 15-3 17-7 335 23-7 15.4 18.0 190 18.6 11.7 16.S 43-2 22.2 Grades. Rise Per Mile.* 0.7 0.9 2-4 I.I 32 1-3 0.7 1-3 0.0 9-7 Rise and Fall Per Mile.* 7.8 5-1 1.2 7 13 7 9 6 3 10.3 6.8 1-5 2-3 05 0.1 Z.I 1.6 4-4 0.3 0.1 0.6 7.8 6.9 5-4 7-1 5-2 4-2 11.4 5-8 8.8 10.8 10 o Z.3 7-5 Ruling- Grades. 52.8 -i- '38-"39" 65-65 79- 67 66- 66 60- 47 31- 25 43- 42 45- 50 40- 57- 37 52.8 53- 46- 21- 27 53- 60 53- 57 52.8 52.8 ! i \n 262 CHAP. VIIL—CURVATURE^AMOUNT OF. Table \02,— Continued. Michigan. Miles of Road. Curvature, Name of Road. Curves Per Mile. P. C. Curved. Deif. Per Mile. Chicago &G. Trunk... Det., G. H. & Mil 1 1 A Sat? 330.5 189.0 936.0 63.1 103.6 970.0 61.1 0.34 0.51 0.62 2.14 I.OI 61 1. 16 6.7 18.0 II. 43-4 i'-3 26.8 24.0 5 5: 12.2* 11.0° 46. 7» 8.2° i8.8» 19- 5° Marq., H. & Ont Mich. Air- Line Mirh C No. C. Mich Totals and av 1,253.3 0.91 20.2 17-4' P. c. Level. 23 5 19.0 19.9 25 8 27.5 21. 30-3 23 9 Am. Cent Belleville & Eld. C. & Alton C, B. & Q C. & E. Ill .' C, M.&St. Totals and av. Ch. & Spr Danv. &«. W O. & Miss III. Central " (N. End only) ♦' Branches. Totals and av. Burl., C. R. &N Burl.,&S. W " (Mo.).. Cent. la C. B. C.& W C, B.&Q C, M. &St. P tt •' Dub. &S. C .'.' Totals and av Illinois. 50.6 49-7 243 5 27 8 79.8 38.1 203.3 99-7 107.5 82.2 982. o 30 0.98 0.27 0.79 0.40 1.08 0.38 0.78 039 0.36 II. 8 154 a. 7 «5-3 8.0 23.0 10.8 144 10.7 9.0 4-9" 20.1° 05° 2.0» 0.9* 4.3» 8.7' 15.6° 6.2° 5 4° o 57 III. 5 100. 1 228 364.7 (252-1) 340.8 1,1451 0.30 0.38 0.21 (0.06) 0.38 13 1 5.1 7-4 149 9.0 (327) 12.0 6.9" 0.32 9.7 4-3" 8.4° 11.7° 8.3° (0.9°) 10 o 7.0 22.0 27.8 6.6 30.7 21.3 19.0 14.0 35-3 19.4 25.2 21.8 12. 1 o 9.0" 42.0 (45.7) 30.0 Grades. Rise Per Mile.* 29.7 Iowa. 252.7 59-6 82.7 189.0 35-7 280.3 3317 150.6 142.7 1,5250 0.70 1 .90 1.70 o 94 340 0.84 0.51 1-53 0.88 22.6 36.0 38.0 20.2 38.5 327 144 23 7 20.1 17. 5' 57-3° 55 •3° 15.6° 81.0° 29.2° 10. 6° 36 -S' 24.8° 1.36 27-3 36. 4« Rise and Fall Per Mile.* 0.3 0.0 1.9 0.0 a-5 0.0 4-3 1-3 7-2 7.8 6.8 93.0 7-3 6.5 8.1 9 5 5-5 1.8 0.9 0.4 0.2 5-2 0.2 3» 0.1 O 2 5-3 14.6 6.3 2.2 2 .8 4-9 6.4 0.5 2.6 0.2 0.9 (0.5) 0.4 0.9 91 8.9 9.1 5-8 (49) 9.6 8.5 Ruling Grades. 54- 51 42 + 52 + 200. 39- 45 49- 38 52.8 37- 52 100-119 43- 80 26- 35 45- 61 64- 64 38- 55 37- 49 60- 33 32- 26 57- 58- 66 58 63- 45 77- 86 18.0 2.7 9.1 66.0 13.0 12.0 5 6 12.6 68 6 2.3 17-3 68.6 II. 1-4 136 76- 73 10.7 5-5 32.0 175-160 T3-6 1.7 13-6 70- 70 22.0 0.8 10.8 58- 74 12.0 25.0 4-2 3-7 13.0 19.4 6-;- =;8 80- 81 153 1 3- 14.9 CHAP. VIII.— CURVATURE— A 2MO UN T OF. Table 102. — Continued. Wisconsin, Minnesota, and Dakota. 263 Miles of Road. c urvature. Grades. Name of Road. Curves _ _ Per P. C Mile. Curved. Deg. Per Mile. P. c. Level. Rise Per Mile.* Riee and Fall Per Mile.* Ruling Grades. C. M. &St. P 194-4 196.4 192.0 202.1 215-4 0.58 0.58 0.54 0.70 I.OO 20.0 151 12.0 14.8 237 14-9' 13-3° 12.8° 13-4° 30.2° 1 36.0 17.6 26.0 23.0 21.0 0.1 0.4 0.0 6.5 0.9 5-4 9.0 10.5 8.3 II. 4 35- 36 50- 53 69- 53 74- 63 63- 52.8 t« ti 4* »t M ii it tt Totals and av 1,000.3 0.68 17.1 16.9° 24.7 1.6 8.9 Summary of the Western States. No. of Roads or Divs. State. Miles of Road. Curvature. Grades. Curves Per Mile. P. C. Curved- Deg. Per Mile. P. C. Level. Rise Per Mile.* Rise and Fall Per Mile.* 10 10 7 10 Ohio and Indiana Michigan 1.304 5 2,348 7 X.20 . 1 0.83 0.70 16.3 15.0 90.2 13.1 9-7 27-3 16. i» 15-9° i7-4» 6 Q° 17.7 22.2 23.9 1.2 1.2 1.3 1.8 0.9 3.1 7.8 7-5 9 5 6.4 8.5 14.9 Illinois 982.2 0.57 1,145.1 0.32 1,525.0 x.36 5 7 4. Iowa 9.0° 29.7 36.4° I 15.3 49 Totals and av 8,558.8: 0.78 16 9 16.9° i 21.4 1.6 9.1 99 Ditto, Eastern States, from Table loi. . 5.372.0 1.88 35-5 55-9° 22.8 4-7 13.0 «7 Ditto. South'n States, from Table 103 3»5ii-2 1. 10 27.6 3..5» 22. 1.9 12.4 ♦ See note to Table loi. ♦ See note to Table 101. The most important moral to be drawn from comparison of this with the preceding: table is in the last column of the table, which it seemed impossible to average, viz., in the excessive ruling gjades throughout the West, which are considerably heavier than in the East, in spite of the very much easier alij^nment and less rise and fall. In lo- calities it was impossible or very difficult to avoid this, owing to a succession of long low ridges extending for great distances in each direction; but for the most part it is due to bad judgment in location, in avoiding curvature and loss of distance at any sacrifice of grade, whereas the reverse should be the rule. See Chapter XX. .1'' 264 CHAP. VIII.— CURVATURE— AMOUNT OF, Table 103. Statistics of Grades and Curvature on the Railways of the South- ern States and Missouri. [Computed from the Census Statistics of 1880. See Note to Table 101.] Virginia. Cin. So Eliz , Lex. & B. L.&N Memph & C. Mobile & O . St. L. &S. E. Totals and av . Miles of Road. Curvature. Grade.s. Name of Road. Curves Per Mile. P. C. Curved. Dejr. Per Mile. PC. Level. Rise Per Mile.* Rise and Fall Per Mile.* Ruling Grades. Atl . M. & 408.6 419.6 140.6 8. .7 1.6 2-4 1.0 36.3 47 33-8 27.0 57-5° 62.o"» 38.0° 30 0° 46.9° ^5.5 1 13s ] 2-7 4-» 1.2 2.7 I.I 13-9 135 12.4 10.2 80-70 - Ches. & Rich. & Dan .. R.,F. & Potomac 70 ± 60 116-55 Totals and av 1,050.5 1-7 36.0 10.6 1 2-3 12.5 North and South Carolina and Georgia. Kentucky and Tennessee. 335-9 102.0 "3-5 71-3 272.0 472.0 135 2 1,501.9 92 Q3 81 48 66 80 0.88 1.07 35-2 29.5 19.4 14.0 17.0 31-3 20.0 23 8 55-4- 52 9° :6.9° 13-9° 16.6° 20.2° 22.9° 28.4" 13-4 154 29.0 22.0 15.2 23-5 12.5 19.0 0.6 2.8 0.3 0.8 0.8 o 6 0.2 0.9 15-6 15-3 II. I 16.7 12. Q 7.2 17s 13-8 Missouri. C, Col. & Aug Ga.RR.&B Macon & B 191. 171. 188.0 I. OS 0.8s 0.33 40.6 33.5 16.0 36.0° 31- 3" 9.60 9-9 41.0 1.8 5-3 2.0 22.9 10.5 5-4 60-67 39-6 75 Totals and av 550.0 0.78 30.0 25. 6» 254 3.0 12.9 60 - 60-66 70-53 70-70 52.8 40-30 216-90 Bruns & Chill Burl. &S. W CapeG. & St. L H.&St.Jo 79 7 82.7 40.0 306.4 0.76 1.70 0.20 0.76 14.7 38.0 4-5 25.0 22.7" 55-3" 4.6«» 17. 8» i t 46.0 12.0 51.6 30.0 1-3 2.3 0.0 1-7 5.6 17-3 1-7 16.9 52.8 68.6 i6-ti 80-80 Totals and av 408.8 0.85 20.5 ,5... i 3a-4 1-3 10.4 . CHAP. VIII— CURVATURE— AMOUNT OF. 26s Table \^^,-^Coniinued. Summary of Southern States. No. of Roads or Divs. Statb. Miles of Road. Curvature. 4 3 6 4 ^7 Virginia .V. and S. C. and Ga Ky. and Tenn Missouri 1,050.5 550 o 1,501.9 408 8 Curves Per Mile. 3,5".2 1.70 0.78 1 .07 0.85 no P. Cur C. kred 36 30 23 8 20 s Deg. Per Mile. Grades. 46 90 25. 6» 28 4» 25. i» 27.6 31-5 o I P. C. Level. Rise Per Mile.* Rise and Fail Per Mile.* 10.6 254 19.0 32.4 22.0 2.3 30 0.9 1-3 1.9 "5 12.9 13.8 10.4 12.4 ♦ See Note to Table loi and Summary to Table 102. In Holland, which has the levellest railways in Europe, 62 per cent is level, and only 27 miles out of 945 on grades between 0.5 and 1.5 per cent. In Germany 25 per cent of the mileage is between 0.5 and 1.5 per cent, and a Utile over 25 per cent curved. , «^u a uiuc In Norway a little more than 50 per cent is curved, and 37^ per cent has grades be- tween 0.5 and 1.5 per cent. Table 104. Curvature Per Mile on Various Railxvays in the Rocky Mountain Region which have a Great Amount of Curvature. [Computed from Census Statistics of 1880.] Cent. Pac ^ (from San Francisco west.) Average. Colo. Cent Virg. & Truckee Utah& No Union Pac " " West End Texas Cent... So. Pacific 266 CH. VIIL— CURVATURE— MEANING OF DEGREE OF CURVE. More commonly yet, the radius is taken direct from a table, but nothing is ever done with it in practical field-work, and it is only of importance for recording on maps or for use in solving problems. 262i Among English engineers curves are usually defined as of so many 5729.65 chains (66 ft.) radius. The radius of a 1° curve in chains is — ^r- — 86.813 chains, so that the one method of designation may be converted into the other by the formulae, 86.813 _. ^ 86813 R in chains = — --, and D = -rr-. — r-^— . D R m chams 263. Continental engineers designate curves by the radius in metres. The radius in metres of a i" curve being - ^' ^ = 1746.4 metres, we have, forcon- 3.2804 verting the one method of designation into the other, the similar formulae, 1746.4 ^ ^ 1746.4 R in metres = V and Z> = R in metres 264. American engineers, and those adopting American practice, when working with the metric system, use, as the unit chord, a chain of 20 metres (65.61 ft.) divided into 100 links of 2 decimetres (.656 ft.) each. The radius of a curve having 1° of central angle for a chord of 100 of any unit is 5730 (5729.65) of that unit, so that the radius in metres of a 1° metric curve is 5729 65 X 0.2 = 1145.93 (1146) metres, or one fifth as many metres as there are feet in the radius of a 1° foot curve— as is natural from the fact that there are only one fifth as many units in the chord. 265. In stationing under the metric system, however, the best practice is to use lo-metre stations, setting stakes at every other station only (or i chain apart) on tangents and easy curves, and at every station (or half-chain) on sharp curves. In practice this produces little inconvenience. 266. The radius in feet of a i° metric curve is 65.61 100 of the radius of a i' " foot" curve, or a little (li per cent) less than f (.667) and a little (4.6 per cent) more than f (62.5), either of which vulgar fractions may be used for approximate inter conversions. 267. Whether with English or metric measures, on sharper curves than 8° or 10°, the chord becomes so much shorter than the subtended arc that it becomes inaccurate to assume the radius as ^-. To obviate this difficulty, it is now becoming usual in the best practice to run in curves sharper than 8° with half the usual unit chord, or 50 ft., and to run in curves sharper than 16° with one FOURTH the usual unit chord. It then becomes literally true, to the nearest even CH. VIII.— CURVATURE— MEANING OF DEGREE OF CURVE 2b J foot, that the radius of all curves, of whatever degree, is given by the formula p - 5730 R - --. It is expedient for practical reasons to set stakes thus frequently on sharp- curves, so that this practice involves no inconvenience. It is rarely necessary or expedient, in practical location, to use other than even degrees (or, at most, even half-degrees) of curvature, except in "closing curves," to connect with other lines, and except that certain degrees which con- tain an even number of minutes (as 50', 1° 40' (100'). 3° 20' (200) curves) are, for practical convenience in the transit work, sometimes preferred. ^Table 105 gives the radii in feel, chains, and metres of all the curves below 30° which are much used for either metric or English measures. We now re- sume consideration of the various objections to curvature. Table 105, Radii of Curves of Various Degrees in Feet, Chains, and Metres, Degree of Curve, Curves run by English Measures. o" 30' 0° 50' 1° 1° 40' 2° 2° 30' 3° 3° 20' 5" 6" 8' 8 •a o U c Radius in Feet. 9 10' 11,460 6.876 5,730 3.438 2.865 2.292 1,910 1. 719 1.433 1,146 955 819 717 Radius in Chains. Radius in Metres. TT° t-j •0 c u 12' D »n 14° U 16° i8» 1 20° '^J v • c k. \rt 24" D sz w 30' U 637 573 521 478 409 358 173.626 100,40s 86.813 52.089 43.406 34-726 28.938 26 . 044 21,704 17-363 14.469 I 2 . 402 10.852 318 286 239 191 9.646 8,681 7,892 7-236 6,201 5.426 3.492 8 2,095,7 1,746.4 1,047.8 873.2 698.6 582,1 523-9 436.6 349-3 291. 1 278,1 218.3 Curves Run by Metkic Meas- ures (20 M, Chain). Radius in Metres. Radius in Feet. 4.823 4 340 3-6x8 2.894 194.0 174.6 158.8 145.5 124.7 109. 1 2,291.86 1. 375-12 1.145.93 687.56 572.96 458.28 381.98 343.78 286.48 229. 19 190.99 163.70 143.24 7.519-2 4.511.5 3759.6 2.255,8 1.879.8 1.503. 8 1.253.2 1,127.9 939-9 751-9 626.6 537-1 470.0 97.0 87.3 72,8 58.2 127.33 114.59 104.18 95 . 50 81.85 71,62 417.7 376.0 341.8 313-3 268.5 2350 63,66 57.30 47.75 38.20 208.9 188.0 156.6 125.3 268 CHAP. VIII.^CURVATURE— MAKING TIME, CHAP. VIII.— CURVATURE— MAKING TIME. 26g> mi' DIFFICULTY IN MAKING TIME. 268. It is beyond dispute that the addition of a sufficiently great amount of sufficiently unfavorable curvature will seriously cripple any line. The curvature is objectionable not alone for fast passenger trains but for freight trains also, for it is fully as difficult and as dangerous to run freight trains over sharp curves at 25 or 30 miles per hour as passenger trains at 60 miles per hour, owing to the difference in their mechanical construction, and yet with each alike such speeds are often necessary. Here, as elsewhere, however, the true question before us is not " Does the difficulty exist ?" but " How great is the difficulty, and what are its limits ?" Considering the question in this light, and remembering that we are not now speaking of nor consider- ing cost, but only physical possibilities, experience seems to in- dicate that, up to reasonable amounts of 8° or even 10° maximum curvature (717 to 573 feet radius) this difficulty is not one which results in very serious consequences; for lines which are little less than a succession of such curves have as fast schedules and make as good time and connections as more favored lines. On curvature of shorter radius the centrifugal force become so great that either the speed must be checked, or the additional pressure against the outside rail becomes objectionable. 269. In the days of hand-brakes and iron rails this necessity of checking speed on sharp curves was (or would have been) a serious obstacle to habitual fast running, but since the introduc- tion of air-brakes and steel rails a train can be checked up slightly with such a very trifling loss of time — and if it should chance to be omitted, the consequences are so much less likely to be disastrous — that, within the limits of choice which are ordi- narily open to the engineer, this question of making time is much less likely than heretofore to be seriously affected by either the amount or the radius of curvature. Since the introduction of steel rails, the question now chiefly concerns passenger traffic, any curve of less than 20° laid with steel (and, in fact, with properly designed engines, much sharper curves) being safe (we are now considering nothing else) at ordinary freight-traia speed. 270. For any ordinary differences of radii the reduction of speed necessary to eliminate the additional centrifugal force due to a shorter radius is not great. Much misapprehension in this respect exists, owing to forgetfulness or ignorance of the fact that centrifugal force increases only as the degree of curva- ture, but as the square of the speed, so that comparatively trifling decrease of speed will place very material differences of radius on an equality in this respect. Thus, to obviate the effect of sharpening a curve from a 5° to a io° we do not need to halve the speed, but only to reduce it in the proportion of i : i/J, so that if a speed of 60 miles per hour be safe on a 5° curve a speed of 42.43 miles per hour [~j is equally safe on a 10° curve ; and if we again double the degree of the curve to 20% we only reduce the admissible speed of equal safety by 1^.43' miles per hour, or to 30 miles per hour. This statement neglects the fact that the same excess of centrifugal force is more dangerous on a sharp curve than on an easy one; but the difference in that respect, while it exists, is small, because the lateral flange pressure is (contrary to a common misapprehension) unaffected by the degree of curvature. 271, The precise effect of curvature on the admissible speed maybe determined as follows : The centrifugal force Cof any body of weight IV moving at v ft. per second in a circle of r ft. radius is, in the latitude of New York, C = V^v ^^-^ (log 32.16, 1.50731). (i> To determine the centrifugal force of a body moving at V miles per hour on a D° curve, we have v = ^^ = 1467 T. and r = 1^30^ Sub- 00 X 00 J} stituting these values, we obtain C= .00001167 (log 5.06722) V*D X W, (2> {i>- .■■; "l .• > > C2 J-^ 3 II ^^' 270 Cyy./ii'. VIIL^CURVATURE— MAKING TIME, Or. for the centrifugal force in lbs. per ton, multiplying the second member of the above equation by 2000, we obtain C=. 023:48 F'Z> (log 8.36825) (3) From this formula Table 106 is calculated, giving the centrifugal force in lbs. per ton of 2000 lbs. on any curve at any speed. Table 106. Centrifugal Force in Pounds Per Ton of 2000 lbs. on Various Curves AT Various Speeds. [Computed by Eq. (3), par. 271.] Speed Miles Per Hour. Dbgrbe op Curve. i«» 5« IO« 15* 20» 10 20 30 40 2.33 9-34 21.01 37.36 58.37 84.05 114.40 149-43 189.12 233.48 11.67 46.70 105.07 186.78 291.85 420.26 23.35 93-39 210.13 373-57 35-02 140.09 315.20 560.35 875-55 1.260.79 1.706.08 2,241.41 2,836.78 3,502.20 46.70 186.78 420.26 747.14 50 60 5^^3-70 840.53 1,144.05 1.494-27 1. 891. 19 2,334.80 I. 167.40 1,681.06 70 80 90 100 57203 747.14 945.59 1,167.40 2,288.10 2.988.54 3,782.38 4,669. bo The centrifugal force on any other curve is directly as the degree of curvature. The heavy division lines mark the assumed maximum limit of speed for safety;— when the centrifugal force is J4 W. 272. For the train to be overturned it is essential that the resultant of the centrifugal force and gravity shall fall without the base, which is upon the point of occurring, on a level track, as will be clear from Figs. J 8 and 19, when W cent. grav. a bove track ~C ~ half-gauge CHAP. VIII— CURVATURE— MAKING TIME. 2; I The height of the centre of gravity varies in different cars and loco- motives from as little as 4^ to 5 ft,, in heavily loaded flat cars, to as much as 7 ft. in some types of locomotives. • i(....^B^*-^ . Assuming it at 6 ft., as in Fig. j«"r":i^^vr->i 18, makes some allowance for the beneficial effect of super- elevation ; which moreover, in the extreme case of danger of overturning, does not have its full effect, because, long before the point where it is ; Sj l .°.' '..f jg. ; imminent, centrifugal force ? Hf '"L.^r"! will so act upon the springs as ■^"■— -^"--' — ""'" to throw the centre of gravity into nearly the position it Fig. 18. Fig. 19. would occupy if the cars were a rigid body and there were no super- elevation. The maximum superelevation is about one seventh the gauge, or about eight inches. This may be considered as reducing the centr'ifucral force by one seventh of the weight of the body, or 286 lbs. per ton, barring the action of the springs. 273, We have, then, assuming the centre of gravity to be 6 ft. above the rails, and half the gauge (between centres of rails) to be 2.4 + ft., C 60 2.4 (4) whence C = 0.4 ^ when the train is upon the point of overturning. But [eq. (2)] we have also C = . 00001167 V^D IV, . and from eqs. (2) and (4) we readily obtain • • (2) '=/ 0.4 _ 185.1 .00001 1 67Z> j/^ (5) this being the equation of the maximum velocity in miles per hour wiiich a train can have without leaving the rails by overturning, 274. Long before this comes the point of danger, and long before that u 1 272 C//AP. VIII.—CURVATURE-^MAKING TIME. again comes the point of more or less serious impacts, oscillation, and ap- prehension of danger. The minimum limit of objectionable speed, below which there may be said to be not only no sensible danger, but no possibil- ity of annoyance or apprehension of danger, does not from its nature admit of exact determination ; but we shall obtain a result corresponding closely with what have in fact proved wholly unobjectionable velocities on various curves if we assume this minimum limit to be when the action of the centrifugal force upon the car-body does not more than suffice, on easy curves having the usual (but, as we shall shortly see, probably too small) superelevation of about \ in. per degree, to throw it over so as to maintain it level despite the superelevation. The point at which this occurs may be determined as follows: The springs of an easy-riding passenger car have been compressed through perhaps 6 in. by the weight of the car-body from their unloaded dimensions. An addition of ^V o^ ^^e weight resting on a spring, con- sequently, will compress it through an additional \ in., and an addition of ^i of the weight resting on it will compress it through \ in. The shifting of this much of the weight to the outer springs involves a cor- responding decrease of the compression in the inner springs ; so that, as- suming the leverage of the centre of gravity of the car-body only to be equal to that of the resisting moment of the springs, as it approximately is (see Fig. 18), a centrifugal force of ^. or say o.o\W, will suffice to- preserve the car-body level. Substituting this coefficient, 0.04 for 04 in eq. (s), we obtain " 58.536. v=^ 0.04 .00001167/? /^~J) (6) this being the equation of the inferior limit of the danjjerous velocities ; i.e., that at which the car-body of the easiest-riding coaches will at the most remain level, and not have a cant toward the outside of the rail, with the smallest usual superelevation. 275. As both the possible compression of the springs and the amount of superelevation soon reach a maximum limit, this particular criterion for determining what is the inferior limit of obnoxious velocities docs not hold precisely and theoretically true when extended to the sharper curves, since it would require, for instance, on a 20*' curve, 10 in. of superelevation and 5 in. compression of the springs, neither of which are admissible ; but it has, nevertheless, the advantage before mentioned (par. 274) of correspondingtolerably closely with what have in fact proved wholly unobjectionable velocities on such curves, as it plainly should if cor- CHAP. VIIT.-CURVATURE-MAKING TIME. 273 rect for the lower curves. This appears in the tabulation of eqs. (5) and (6) given in Table 107, for curves of different radii up to a 60° curve (95 ft. radius), the latter being somewhat easier than the curve of 00 feet radius on the New York elevated railways, and hence to be regarded as about the maximum. The trains pass around these curves at 6 to 10 miles per hour without any disagreeable centrifugal force, (See also par. S65 et seq.) Table 107. Giving for Various Curves the Inferior and Superior Limits of Speed WITHIN WHICH THE CENTRIFUGAL FORCE IS MORE OR LeSS OBJECTION- ABLE AND DANGEROUS. J^v,iiuxm [Computed by Eqs. (5) and (6), par. 273.] Curve. Degree. Radius. Feet. 4" 6° 8° 10' 2.865 1.433 955 717 Maximum and Minimum Limits of Speed. Miles Per Hour. Minimum. Having no Disagreeable Effect. 573 12° 14° 18" 20' 478 470 358 319 41-39 Miles per hour. 29.27 23.90 20.70 << Maximum. On the Point of Overturning the Vehicles. 18.51 Miles per hour. 286 22" 24° 26°. 28° 30' 40' 50" 261 239 221 205 16.90 Miles per hour. 15.64 14.63 13.78 it (( it 130. 89 Miles per hour. 92.55 75.57 65.44 1 1 tt it 13.09 Miles per hour. 191 12.48 Miles per hour. "•95 II. 61 11.06 58.54 Miles per hour. 53.43 Miles per hour. 49-47 46.28 43.58 1 1 1 1 < t t f 41.39 Miles per hour. t < tt ft 1 1 tt (I 10.69 Miles per hour. 60' 143-3 1 14. 6 95.5 9.25 Miles per hour. 8.28 39-46 Miles per hour. 37.78 36.72 34-98 tt 1 1 n t( 33.80 Miles per hour. 7.56 Miles per hour. 29.27 Miles per hour. 26.18 «< 23.90 Miles per hour. col7„„ ^ , ' '"" ~'"""" ^"^ ^' 'f'"" "^ '""" "-f^'y' 'hose in the last TZ^^^ '^T K °" " "' P'"^'"^ '°'"'"" * ♦''° "' 3. .6. Multiplying or ^mg either column by a, 3. or any other factor whatever, wiU give a new column o» speeds of equal safety. "*" *« 18 274 CHAP. VIIL— CURVATURE— MAKING TIME. 276. These maximum and minimum limits correspond to a difference in centrifugal force of i to lo; yet it will be seen that the resulting veloci- ties differ only as i to 'fio or i to 3.16, as they should. It will also be seen that the permissible speed, by whatever standard, does not vary directly as the radius or inversely as the degree, as may be over-hastily assumed, but as the square-root of the radius or degree. That is to say, on any three curves having radii as I, 2. 3. the centrifugal force at any given velocity, it is true, is as 3» 2, i; but the coefficient of safety against overturning or of disagreeable or obnoxious effect of any kind admissible under any circumstances on a road operated by steam, is as 4^ i^ V7 or as I73» 1-41. i-OO- 277. We may also note that the maximum necessary loss of time from a dead stop, in passenger service, under any ordinary circumstances, is only about three minutes, and the loss of time from slowing up for a quarter of a mile or so. under the quick command of the train given by the air, is veiy much less than this, while the steel rail has materially reduced the difficulty in and objection to making up for such delays by higher speed at other points. This is shown more fully in Chap. XIX. For freight service alternations of speed by the use of brakes are still very objectionable, and perhaps will long continue to be ; but ordinary cur- vature does not require this. 278. We may, therefore, conclude (in part on the author- ity of the matter referred to above, which it seemed more appro- priate to postpone to Chap. XIX.) that any difference within the power of the engineer to effect is not likely to materially affect the ability to make ordinary express-train time. If it were a question between 2° curves or 20°, or between no curvature and a great deal, it might well make a serious difference ; but under ordinary circumstances the question is rather between say, 6° and 10° curves, or between, say, 10 per cent more and 10 CHAP, VIIL--CURVATURE -SMOOTH RIDING OF CARS. 275 per cent less curvature. In such cases, on other than trunk hnes running fast expresses, the importance of this particular question is not simply diminished pro rata, but entirely van- ishes. "^ 279. The effect of curvature on the smooth riding of CARS is a matter of more serious moment in not a few cases of lines with a large through-passenger traffic. For day travel it matters less; but tliere is no doubt that since the general introduction of sleeping-cars not a little travel has been kept off the New York, Lake Erie & Western Railroad for example, as well as other crooked railways, for this reason alone, when a straighter competing line existed. On the other hand, the number of lines to which, on account of the competi- tion of other.ft«d straighter lines, this ^ as an important consid- eration is not very great ; and even when it is or may be, this also is peculiarly one of those cases in which, although a perfect cure would be exceedingly important and valuable, the partial cure from the slight modifications which are alone within the power of the engineer, without very great expenditure, will in most cases have httle value. It is also to be remembered that ifa curve is in thoroughly good shape the motion of a car is, after it has once entered the curve, almost as steady as on a tangent. If tlie centrifugal force and superelevation could be exactly balanced the body of a traveller cither in a sleeping-car or day-coach would be unaffected by cither. Unfortunately this is out of the question; but the worst effect usually comes from entering and leaving a curve, and this again chiefly results from the fact that as roads are ordinarily located, the line instantly changes from' a tangent to a sliarp curve. The consequence is, inevitably a disagreeable lurch and "thud;" which would be much worse than it is except that the trackman with his bar corrects the errors of the engineer with his transit by "easing off" the curve at the ends, extending it a hundred feet or more on to the tanjrent, but of course necessarily sharpening the curve not a little for a Short distance beyond the technical " P. C." The latter is un- fortunate; but it is far better than to leave the curve as the en- 276 CHAP. VIII.— CURVATURE— SMOOTH RIDING OF CARS'. gineer stakes it out, and it never is so left on old and good tracks SO far as the writer has observed, but invariably flattened off at the ends by the trackmen. 280. The " easing off" should, it need hardly be said, be rather done by the engineer in proper form in ihe first place, in such manner as to avoid alsa the lesser evil of a kind in the body of the curve. A simple and practical method for putting in such transition curves involving hardly any extra work for this purpose (in fact rather facilitating the field work) is given in the fieldr book which succeeds this volume. See also close of Chap. XXX. 281i It may be added that, as more fully pointed out in the field-book re- ferred to, the use of the parabolas instead of circular curves for railways, pro- posed in the early days of railway construction and in a few cases used, would have no important effect in reducing the evil described. What is wanted is (i), to ease off the curve by a rapidly changing radius for a short distance at the ends — a transition curve ; and (2), to leave the great body of the curve of uniform radius. This the parabola does not accomplish. 282. The moral effect of excessive curvature to deter: TRAVEL — or rather, the moral effect of known excellence in that as in every other detail to encourage travel, is in not a few cases,. — as for instance the Pennsylvania Railroad — a consideration of more importance than appears. Advertising is generally re- garded by all business men as a profitable outlay, even when it is all outlay. When the advertising is of such a nature as to in part pay for itself by saving expenses, even if only to a limited extent, it becomes of course still more desirable, and in the case of railways has the peculiar advantage noted in Chap. III., that any additional sales they may thus make cost almost literally nothing. In the case of some few roads which have an immense, an almost unlimited, traffic to contend for, this consideration alone may become of such great importance as to justify very heavy expenditure. Thus, the policy which the Pennsylvania Railroad has adopted of polishing and perfecting their line in this and in various other almost fanciful ways will doubtless prove a money- making operation, and largely on this account; for even with their great traffic, which will justify almost any expenditure to effect a perceptible improvement, it might perhaps be difficult CHAP. VIII-CURVAT UR E-SMOOTH R IDING OF CARS. 277 ZLT'l\f'" ^^P-^'^— vvhich they have made to take out some of their curvature by any correct estimate of the direct saving in operating expenses. One of the •' almost fanciful " ex penditures referred to is to secure absolute perfection of appear- ance, as well as real excellence, in the track and riglit of Ty by dressing he edges of the slopes of the broken stone ballast to an exact line, stone by stone, and by elaborately neat and taste err dt IsT"^" T''' '"' ^'^ ^"^ "^^^ particularly re- fened to is the expenditure of occasional large sums in bold lines to eliminate curvature and trifling amounfs of distance Rai'!!"d fs"re"of"r"'"' •'"' Philadelphia the line of the Pennsvlvania First, and chiefly, the old line is an eyamniA «f u cu.va,ure may be in'noduced .ere,; ^^r^:! n Z^r 0^:""" "' ence, „i,„o„, .^e .,,Htest rea, necessi.y. 'm very .any ;:"„;:; Z^Z was no more expensive than the old, ^vhile materially better «ood purpose „hi,e capita, .as scarce andTrraTn^ra^T.^::;:!::;- "I^ to throw away when tWfese conditions had changed so as to justify the t^e v 1 ^e i^:^z:z:::::' '"°" '--^^ "^ -' ^ "-= -^^ '■ -- -"-- Thirdly, there are various points where the new line, however more nl,« would just.fy ,„ proportion to the end attained. The Pennsvlvan Ir i - , however, has not an ordinary traffic. ""nsylvanta R.i.l.oad, 284. But, afterall, the lines are few which have so la.o-e a con,pet...ve traffic to lose ofgain as to make the advertfslg vl.i: «f a better hne a consideration of much moment, and then it onlv ous pohcy. W.th the Pennsylvania it is so. Its track is well known among well-informed railroad men, the world over, ,0 be \ Fig. 22. II '• f'- di 1284 CHAP. VIII.— MECHANICS OF CURVE RESISTANCE, gents, the tread wears down near the flange very rapidly, and such con- ing as there may be soon disappears. We may therefore neglect it here- after, and assume the wheels to be cylindrical. The coning now put in wheels is chiefly useful as a prospective provision for wear; and experi- ment shows that whether the wheels be coned or not, the tendency of any rectangular wheel-base is to roll very nearly in a straight line. 298. As we have seen that the rear axle is always radial to the curve, the front axle. Figs. 20 to 23, stands at an angle A, Fig. 23, to the rail, ^qual to the arc subtended by the length of the wheel-base, /. With a 5-ft. wheel-base (the usual leng^th for freight trucks) this angle would be. on a i* curve, .05° or 3', and proportionately on other curves; with a 12-ft. wheel-base the angle is 0.12° = 7.2'. The distance by which the rear outer wheel. Figs. 20 to 23, stands at a distance from the outer rail (being equal to the ver. sin of twice the arc subtended by /) is readily determined to be, from what has preceded, • For a 5-ft. wheel-base, .0022 foot per degree of curvature. For a 12-ft. wheel-base, 0^0127 foot per degree of curvature. 299. The gauge of a road is the exact distance between inside of rails and the gauge of the wheels is usually set so as to allow a normal play of from f to f inch, averaging about \ inch or .04 feet. The rear inner wheel, then, of a 5-ft. wheel-base will be close against the inner rail on a Fig. 23. .04 = 17° curve +, and a 12-ft. wheel-base on a .04 ^3 curve -h. .0022 .0127 In watching ordinary cars pass around a curve, however, there will be con- siderable fluctuations in the position of the rail owing to irregularities of bot h curve and truck. 300. The slipping of wheel on rail on a curve arises from two causes: First. Longitudinal slipping, due to the difference in length of inner and outer rail. This difference on any given curve, or part of a curve, is equal to an arc of a radius equal to the gauge, and the same number of degrees long; i.e., it is, on any given distance d, i» 5" io» 20» I rear, wheel s front " .000 vheel. in moving through an infinitesimal distance ^B ' t'S: 28, IS actually rotated, yet as this takes place simul' taneously with the other sliding its' effect is simply to de- v,. « crease the velocity on one side of the center of contact bv « f creases it on the other side. ^^ ^' """"^ ^^ »' »«' 311. Flange Friction.— We have seen that :^t ^a^u • * 3...n, on the su^f^- '^fttir^- t^e 2::^ i^S^- -- mes The force which causes this rotation-the only force which e^^ts It necessarily follows from this fact that, assuming; that the coefficient till al^lvTthf sT' '' "' '^'""'^ "' '"''"^' ^''^ P-ssure f ac. IS always the same on curves. For. however easy the curve, a 292 CHAP. VIII.— MECHANICS OF CURVE RESISTANCE. minute sliding motion is continuously taking place, caused by the reac- tion of the flange ; and the static force or pressure required to slide one- body on another through an infinitesimal distance is sufficient, if con- tinuously applied, to slide it through any distance whatsoever. The- POWER CONSUMED varies with the degree of curvature, because power or energy of any kind is measurable only by a double unit, the force applied X the distance through which it acts. The latter (the distance), we have already seen, varies with the degree of curvature, and hence the power consumed does also ; but the static force applied does not vary with, the degree of curvature. This very important distinction is one which should be clearly comprehended and kept in mind. A very mis- taken idea is too prevalent that the flange pressure as well as curve resistance increases with the degree of curva- ture. An apparent contradiction to this statement is the: well-known excess of flange wear on sharp curves, but this is rather a confirmation. The greater distance elidden through produces the greater wear, not greater pressure. 312i The front outer wheel alone has its flange normally in contact witb the rail. The forces acting upon <^f^P^J^ni^-MECHAmcs OF CURVE RESISTANCE. 293 Fig. 30. the front outer wheel are, firsts the load, Z., Fig, 29, resting upon it, acting vertically downward ; secondly, a horizontal pressure against the rail sufficient to slide three wheels (see Fig. 25, page 286), each loaded with L. Assuming a coefficient of sliding friction of 0.25, this late- ral force amounts to 0.75 Z, and the resultant in magnitude and direction of these two forces is shown in Fig. 29. 313. The manner in which the various forces thus meas- ured will act is not doubtful in theory, and we have their footprints on the rails themselves to assure us that theory and practice correspond. Instead of the pressure on the rail being vertical, as in Ficr. 30. 've have the conditions and the relative I : t m 1' 294 C//AP. VIIL— MECHANICS OF CURVE RESISTANCE. position of rail and wheel shown in Fig. 31. Figs. 32 to 41 give a series of rail section selected from a great number taken by the writer on the Atlantic & Great Western (now New York, Pennsylvania & Ohio) Rail- road, showing the wear which actually results from the conditions watched. They were exact copies originally, to full scale, and are now reduced one half. Fig. 30 is a half-scale section of a new flange and rail section of ordi- nary form (they vary somewhat in outline, but that is unimportant) in their natural relative position on a tangent. Fig. 31 shows the same new Q fiange and rail section in "^ (.LATERAL THRusT.J . their natural relative posi- Ifc tion ON ANY CURVE WHAT- EVER, however sharp or flaU CHAP. VIII.-MECHANICS OF CURVE RESISTANCE. 295 Fig. 31. Fig. 42. The tread stands entirely free of the top of the rail, the surfaces in con- tact being neither the horizontal tread nor the vertical flange, but the curved surfaces which are perpendicular to the resultant shown in Figs. 29 and 31. To understand this, let the reader turn Fig. 31 around diag- onally until the diagonal stands in a vertical position, and let him con- ceive it to represent the vertical force of gravity alone. He will see that the wheel would naturally take this position— as naturally as a wheel shjiped like Fig. 42 rolls on the central curved surface instead of the side surfaces. 314. The consequences of this condition of things are these: First. The disproportion in the diameter of the wheels ; hence the necessary longitudinal slipping, and hence the curve resistance, is materi- ally increased. If the increase of radius of wheel be W '"^h, the extra distance slipped through per station of 100 feet by one wheel will be 1.16 feet; which, by referring to Table .09 on page 286, will be seen to be as TfoIIowsT"" °l '\ "'■'''^^ °^ '"^ ^^" °" ^ ''' — This increase Lh , H ^^" P'"""'''^'^' '^ '"'"'"'"' '"' =■" <=""'es. and thus tends to d,sproport,onateIy increase the resistance of easy curves But It IS profitless to inquire, because, &««y 'he same form i" the end^ Thus m some similar sections to those shown in Fi<.s ,2 t^., on he Pennsylvania Railroad, rails from 4" curves after sustai;ing nearly four times he tonnage of the rails shown in Fig. 34, were in even worsi condition than the rail from a .6' curve shown in Fig 4, whirl %r''. "'°™ ''■'I ^'"- "'• "'^ '™^ bearing surface on which the »heel rolls (compare Fig. 3,) is directly on the corner, and the mWmt urfaces above and below are revolving in a circle of nearly i-inch^on'ef radius, the average of the whole surface being nearly if not quite S It necessarily results from this, that while fhe wheel is "oiling through any distance its surfaces slip on the rail through 1^1 „^ i ^^ ^^^^ tance: = 1.51 feet in 100. * °° 316. The coefficient of friction, moreover (as well as rail wear) with such large surfaces in contact, is probably considerably larger than when he bearing is on a mere point, as in the unworn rafl. Fig 3, ^07 the formerly accepted - law" that fr.ictlon is independent of the^ar'ea's n con! ated,, f Proven untrue for lubricated and still more for unlubri- cated surfaces, as was found out practically long since with brake-sl"oei ■n u 296 C//AP. F///.— MECHANICS OF CURVE RESISTANCE, The information on friction laid down in most of the standard text-books is very deceptive. 317. This third source of extra resistance, due to badly worn rails, is reached in a much shorter time on sharp curves, and as a rule exists only on them ; but nevertheless, when it exists, the amount of the extra re- sistance caused thereby is independent of the radius. If rails be equally worn it will amount to substantially the same on all curves. When the wear has become so great that the rail has the form of Fig. 41, so that the flange bears against the rail almost down to its point, the wear, and resistance as well, is doubtless very much increased. In a lot of rails which have been all exposed to substantially the same tonnage, like those in Figs. 32 to 41, this condition will be likely to exist only on the sharpest curves, and accordingly the apparent indications of a test of such rails will be that rail wear increases very much more rapidly than the degree of curvature— in fact nearly as the square of the degree of curvature. The writer himself reached this conclusion, from the only facts then before him, in his report on these observations. 318. But if, on the contrary, we investigate the tonnage necessary to produce the same wear of rails on different curves, we shall find it to be almost directly as the degree of curvature, and this is undoubtedly the true law of rail wear ; from which it follows that the RATE of wear on any one curve increases as the rails become more worn, and this pro- duces the deceptive appearance of a rate of wear varying as some function of the square of the degree of curvature. 319. As to the wear on the inner rail, it is apparent that the effect of the flange pressure (see Fig. 29, page 292) is to increase by about one third the load resting on the front outer wheel. We might accordingly expect that all the longitudinal slipping would be confined to the inner wheel which runs (see Figs. 20 to 23) with its flange entirely clear of the rail. From this we might expect (i) that the wear of the inner rail would be wholly on top, and (2) that it would be more rapid than the outer rail. This is always found to be the case, as will be evident from Figs. 32 to 41. The excess of top wear on the inner rail would undoubtedly be much more disproportionate than it is except for this fact : The bulk of tonnage is slow traffic, and in such cases the excess of the superelevation over the very small amount required to balance the centrifugal force (i inch per degree at 15 miles per hour; see page 298) produces a slight excess of load on the inner wheels; not sufficient to counterbalance the effect of the flange pressure on the front axle, but CHAP, VIII.-MECH ANICS OF CURVE RESISTANCE, 297 amply sufficient to cause the rear axle, both flanges of which stand clear o\ the rail, to slip entirely on the outer rail on slow trains, as being the point of least resistance. 320. We thus have this condition : (1) The front outer wheel produces all the flange wear and little or none of the top wear, (2) The front inner-wheel produces nearly all the wear on inner rail —confined entirely to top of rail. (3) The rear outer wheel of slow trains produces nearly all the top wear on outer rail. (4) The rear inner wheel produces only the normal tangent wear. 321. As respects the aggregate amount of curve resistance : From all these data together we may expect it to be— (1) 0.37 lb. per ton per degree of curvature as a minimum, varying directly with the curvature, plus— (2) Upwards of i lb. per ton as a constant addition due to flange friction on new rails (assuming the coefficient of friction to be as low as 0.25. as it appears to be with car wheels. With engine-drivers it is about 0.35)- (3) As rail wear increases there will be a very considerable further addition to the" resistance due to the flange wear on worn rails. This effect will become visible very much sooner on the sharper curves, but It will occur sooner or later on all curves when the flange has cut into the side of the rail. 321^. Let us compare these conclusions with experience : I. Actual experiment on the 63° curves (90 feet radius) of the New York elevated railroads, conducted by Charles E. Emery, M. Am. Soc. C. E., shows the resistance to be 0.43 lb. per ton per degree of curva- ture on new rails with fixed wheels in the ordinary mode, and 0.33 lb. per ton with loose wheels. (If the reader will refer back to Table 109 and the accompanying discussion, he will see this to be as nearly as may be what our theory would indicate.) 2. The late Benj. H. Latrobe experimented on 14° curves, with new rails also, and found the resistance to be .40 lb. per ton. 3- French experiments with about 12-ft. wheel-bases on easy curves show about 1.25 lbs. per ton resistance. 4. The writer made, by the aid of very delicate electrical apparatus, what he believes to be the most accurate experiments on train resistance, so far as they went, which have as yet been made ; and his conclusions! •so far as relating to curve resistance, were that curve resistance is much 298 CHAP. VIII.-^MECHANKiS OF CURVE RESISTANCE. greater per degree on easy curves and at slow speeds, as shown in App. A. 322. This completes our analysis of the forces originating and acting within the truck itself, which are the only ones of importance. Let us see what, if any, effect the forces acting upon the car body and train as a wbole have to modify this result. Centrifugal force and superelevation act upon the car as a whole, and their effect is communicated to the truck through the centre-pin or side- bearings. The centrifugal force C in lbs. per ton of any body moving at V miles per hour on a Z?" curve we have already found to be (eq. (3), par. 271),^ C = .02335 F'A (I) from which Table 106, page 270, was computed. 323. The superelevation of the outer rail creates a force tending to draw the car inward and to counteract the cen- trifugal force. The weight, by a well- known mechanical law (Fig. 44), bears the same ratio to this force as g. Fig. 43, does to the superelevation e. On a 4 ft. 8^ in. gauge (say 4 ft. io| in. centre to centre of rail) it amounts, therefore,. Fig. 43. Fig. 44. in lbs. per ton per inch of superelevation, to ^g-rr x 2000 = 34.04 lbs. The maximum amount of elevation which is ever to be found on rail- ways is about 8 inches, creating a force of 272.32 lbs. per ton. Many roads limit it to 6 inches, or 204.24 lbs. ; but we may for safety assume the maximum to be 10 inches, or 340.4 lbs. per ton. Comparing this with Tables 106 and 107, it will be seen to just about balance the centrifugal forces at what is marked as the maximum safe speed, according to usual practice, on various curves. 324. To determine the effect of these forces on curve resistance, let us assume the extreme case — that the maximum superelevation is en* ^A^l ^'"—MECHANICS O^ CURVE RESISTANCE. 299 tirely unbalanced by centrifugal force. This is the utmost limit that safety permits. The first effect, with the centre of gravity in the position sliown in Fig. 43. is. by well understood mechanical laws, to throw % or about 70 outeTrail"' Th'^'" "''°" ")\ '""'' '''"■ '^^"'"^ ""'^ 3° Per cent on the H h I r !! '""'^' °' ^"""^ "'" ^°"'P'''' "'« 'P""g^ on the inside and by the further tipping of the car body cause the insfde rail to carr^ tliree fourths or more of tlie total load. The second effect is to confine all longitudinal slipping to the outside wheels as being the most lightly loaded. This, however, we have seen ta be the casew.th the front axle under any ordi„a.y circun.stances. The lateral slip of the front axle is of course not affected. The third effect, resulting from the combination of the above causes ,/rz.i .sb£. \ i40 //CO ccoo /ooo 2009 Fig. 45 —Front Ootbr Whkbl. (I he higher rectangfle shows the conditions without supereleva- tion; the smaller recungle, with superelevation.) I. i\ ^3000 I Fig. 46.— Rear Outer Wheel. ; » Fig. 47.— Both Inner Wheels, is to change the magnitude and direction of the forces acting on each wheel m the manner shown in Figs. 45 to 47, in which the solid lines how the magnitude and direction of the forces already determined, independent of the superelevation. »hi?h' '" "f'^' ™?"^'' '^'''"^ ^'■°'" '^^'''^ '°9' P«g« ^86, the slippage which^ regularly takes place in a 5-foot wheel-base on a 10° curve, we Rear inner wheel " outer " Front inner " " outer " Total amount Slippage in feet per too feet. 0.00 0.82 0.89 1.21 Increase of Load. 2.92 50 per cent, increase. 50 " " decrease. 50 " " increase. 39 " " decrease. New Slip. 15 per cent, decrease. 0.00 0.41 1-33 •74 2.4& ■ 'f fRiPa I'i '1 * -r- IN I N I I I I I I I I I I i I I I I ••13000 I I \ 300 C//AP. VIII.— MECHANICS OF CURVE RESISTANCE. The further resistance from flange friction on the front outer wheel i(as also flange rail wear) should also be diminished about 39 per cent. 325. We thus see grounds for believing that the general effect of even an extreme amount of unbalanced superelevation may be to somewhat decrease the resistance, but not to any important extent ; and with the ordinary and proper limit of 6 or 7 inches superelevation, partially balanced, as it always is in practice, by centrifugal force, the effect be- comes almost insignificant one way or the other, although still apparently to decrease the resistance so far as it has any effect at all. On the other Jiand, a similar computation to the above as to the effect of an unbalanced centrifugal force will indicate that it has a very similar and equally inconsiderable effect to in- crease the resistance. Fig. 48 shows the most objectionable effect from excess of centrifugal force. (See par. 327.) 326. Let us now see what effect such unbal- anced forces do not have. They do not alter in any manner whatsoever the position of any of the wheels, nor can they by any possibility do so, it would appear, until the centrifugal or centripetal ^IG. 48. — EfFKCT of Un- , , c ....i^-.. 1J1-J BALANCED CENTRIFUGAL force becomes a force so great that it would slide Fkon? ''ou?Eir'''w'HEEL ^^^ whccls laterally on the track if the car were AGAINST Rail. standlncr still on the rails, which would be when (Compare Fiff. 45. show- *^ •ing effect of an equal the superelevation was equal \,o\x\t. coeff. fric. X amount of unbalanced cen- ^ , u .. • i. tripetai force from super- gauge, OX at, Say, \ gauge, or about 14 inches. fir*vHScity^n*ecSar) "to ^or the force required to slide a rolling wheel on produce this amount of cen- the rail, either laterally or longitudinally, is trifugal force. j o j neither greater nor less than if the wheel were standing still (unless there may be some slight and unknown modifica- tion of the coefficient of friction) ; and so long as the force is not FULLY sufficient to do this, it has no effect at all to move the body. All it can do is to increase or decrease the pressure of the flange against the outside rail, and this (within the limits of safe and customary prac- tice) only to a trifling extent. This results from an elementary mechani- cal law which has been too readily lost sight of by theorizers on this subject, that a lifting force of 1999 pounds is as incapable of lifting a ton as a force of one pound. 327. The real objections to too much superelevation, or to too high ve- locity, is its effect upon safety. Throwing so much weight upon one rail and one set of springs, is, if carried to excess, highly dangerous, although 5 I ^V CHAP. VIII.-ME CHANICS OF CURVE RESISTANCE. 30r the resistance is not in any case very seriously affected. An excess of superelevation would appear to be the least evil of the two, however, in a^ respects, for we have seen (par. 324) that it has probably some slight effect to decrease the resistance of the slowest freight train. 328. The contrary assumption is very general, but it is absolutely unsup. ported by experimental evidence so far as the writer can discover, and it cer- tainly finds little defence in theory. The truth is, that much of the current and almost endless discussion of this topic among road-masters and even engineers has Its root in insufficient examination of the mechanics of the problem. It is ASSUMED that the two obtrusively evident forces, centrifugal force and its oppo- site, are the only ones to be considered, and that the truck is thrown against one rail or the other by these forces according as either force preponderates. Yet one has only to watch the wear of rails and the motion of a truck around a curve to find that there is some force independent of either (which we have analyzed at length) which presses the outer wheel against the rail with tre- mendous force, however high the superelevation ; and from this it follows that It is the effect of the other two central forces upon this force which is the real problem lo be considered. 329. We conclude, therefore, that the centrifugal and cen- tripetal forces have but a trifling effect on curve resistance, and that the proper rule for superelevation is to elevate sufficiently to balance the centrifugal force of the fastest trains up to a maximum of six to eight inches. This will slightly decrease the resistance and danger of accident to freight trains, and greatly improve the comfortable riding of passenger coaches, provided always that some uniform rule be followed, since almost any rule is better than none. 330. A third source of possible curve resistance, obliquity of trac- tion, affects the train as a whole. The conditions of the problem are presented in Fig. 49. ^ It may now be considered as established that, despite a prevalent impression to the contra- B_ — r _ ^ ry (which many able engi- neers have shared), no loss of power whatever occurs from this cause. Let OA, f^'g- 49. represent the trac- Fig. 49, tive force to be transmitted through the coupling O to the car B As^ there is a change of direction in the force at O, it is sometimes claimed ^^i ■^1 302 CHAP. VIII.— MECHANICS OF CURVE RESISTANCE. that no force OA can be caused to act on the following car in the changed direction OB without a certain loss of tractive force, and hence -waste of energy. This position is in both respects unsound. There is no loss of tractive force at each car due to obliquity of traction, and, even if there were, it would not necessarily imply any waste of energy. It fol- lows that the method of analyzing the strains by which such position is supported (which consists in making the angle OCA, Fig. 49, a right angle and then taking the force OB = AC, or less than OA) is incorrect. 331. The correct way of representing the action of the forces involved is by the parallelogram of forces shown in Fig. 49, which should be constructed as shown, with OB = OA, the force OA being transmitted undiminished through O as around a pulley ; the lateral stress OC having no more effect to reduce the force OB than the stress OC, Fig. 50, has to make the force OB less than OA. Both in Figs. 49 and 50, if the stress OC is suf- ficient to produce lateral motion in the direction OC by overcoming the static resistance, it will or may consume power, and the force OB may be th*»n quite different from AO, but otherwise not. In a train of cars, the lateral component has only the effect to mi- nutely increase the lateral resultant of the superelevation, which we have just seen tends to decrease the resistance (if anything), but has no effect to change the position of any wheel, or to increase perceptibly the pres- sure of the wheels against the rails. Conceive the track to be a complete circle, and the train to com- pletely fill it. Conceive the floor of the cars to be a rigid continuous cir- cular platform. There would then nowhere be a lateral resultant of the kind discussed, but no reason is apparent why the curve resistance should be either greater or less. 332. The transmission of force from car to car, through a train on a curve, is an almost exact mechanical parallel to the transmission of power by a rope or chain over a pulley ; the rope being the string of car bodies, and the car wheels the pulleys. The fact that the pulleys are carried by the rope itself, instead of in a block exterior to it, '\s a mere detail not affecting the mechanical conditions. In either case the loss from such transmission is simply the friction of the pulley. Conceive a chain made of successive links, each carrying a pulley wheel and being CHAP. VIII.- MECHANICSOF CURVE RESISTANCE. 303 dragged over a large cylinder or succession of cylinders, large or small Conceive furter, the rope to be so long and the friction of ^he pnhet so great that the whole power of the prime mover is consumed In k ep- mg the Cham ,n motion at uniform speed. We have here a perfea mecnamcal parallel to a train in motion on a curve, except for the one nnnor fact that the resultant of all the forces acting on the wheels does not, m case of a ra.lroad train, lie exactly (althoughlt does nearh) n the plane of the wheels themselves, whereas in the case of the pulley wheels 'l^o^:r:rT^r^'^ ^'^ coupling-pomts from .'chalget friction of the n^ !'" "^ '"''""' "^ ^''""^ ""^ ^^^^ — than%he fnct.on of the pulleys proper, m either case. It is, of course true that the resistance of the rear pulleys would tend to pre;s each puiley" ad vance more t.ghtly against the surface, and so produce greater f rkt on in a railroad tram it is entirely pertinent to prove that a lateral centripetal force is produced by obliquity of traction, so that the resultant of ^ ™r fl\:o" ' Th t ^^^7 ^^ ^'^ ^'^^^' ^"^ ^^- this LXod ce greater friction. The latter, however.-the only possibility periinent to discuss,-,s commonly neglected in discussions wh^h assume th a M resultants from obliquity of traction indicate /..;. //..,. Zr/^^i^^^^f. lc>ss of energy Force, i.e., static stress, is one thing, resistInce e destruction of dynamic energy, is another and quite Afferent thing We cannot figure away energy with a parallelogram of forces, but musf prove w en and how, if at all. it is lost by additional friction. As a mattero fact the e appears to be no loss, but a trifling gain, under ordinary con- d.fons. from the fact that the centripetal tendency is increased. ' 333. There .s so much misconception as to this matter that we may en- deavor to make it still dearer. In Fig. ,, let the lines OOP represent the n:.ld7 Tr7 T.^T' ^" ^^^'^^ '''^^'-'^ ■' ^^' ^'^ -' -M^^^^ F'ns, and/,, ihecoupling-hnk. Let the lines SS represent in magni- S»~-£t^__Js tude and direction the tensile force acting upon the link and tending to rupture it. As a matter of course, these forces S must be equal to Fig. 51. TctT^r' "'T ''"*''". ^""^ ''"''"" "'" ^^"^^' ^"^ ^h^" resolved into forces a t ng , ,he axes of the cars this makes the latter also equal. The losses ens.,e force from car to car occur at the centre pins O of e\ch car, and no at the coupling points P. The tension on the front end and back end of ^h. resistance of that car ; but the longitudinal strains, parallel with the respttive 304 CHAP. VIII.— MECHANICS OF CURVE RESISTANCE. axes of the cars, on the rear draw-gear of a forward car and the front draw- gear of a rear car, are always equal to each other in magnitude, although differ- ent in direction by the amount of the angle between the axes. That is to say». the diminution of tensile force from car to car is internal to each car, and not at all at the coupling-point. 334. But the point is not worth disputing, for the loss, if it were granted to exist, is very small. Assuming the car body to be 30 feet long, the deflection angle OAB, Fig. 49. will evidently be, on a Z?° curve, 0.3Z? or 18' X D, and of the tractive force F( = OA, Fig. 49) there will be an assumed loss, which let = L, at each coupling, from obliquity of traction : , ^ ,, /, = yr (I _ cos 18') Z> = o.ooooi6Z?/^. The tractive force of a Consolidation engine is something over 20,000 lbs. at the engine and zero at the end of the train, averaging, say^ 10,000 lbs. Then the loss per car will average, on a 1° curve. Z = 0.16 lb. per car, or, on a 10° curve with a 60-car train, Z, = 96 lbs. Not a very serious matter, certainly. 336. We conclude, therefore, as to curve resistance : 1. Obliquity of traction and the length of the train have no- appreciable effect to modify curve resistance. 2. Centrifugal force within the limits of practice has but lit- tle effect on the resistance, but that little is to increase it. 3. Centripetal force from superelevation within the limits of safe practice has but little effect on the resistance, but that little is to reduce it. 4. The best rule for superelevation is to elevate for the fast- est rej^ular speed up to a maximum limit of 6 to 8 inches in all. 5. Rail wear and curve resistance over rails in the same con- dition are as nearly as may be directly as the degree of curva- ture, with some minor elements which are independent of radius. 6. Rail wear and curve resistance are appreciably less with new rails than with old, and become greater as the outer rail is worn away to the shape of the flange. 7. The pressure of the flanges against the rail is the same on all curves independent of radius, but the wheel stands at a CHAR. VIII.^MECHANICS OF CURVE RESISTANCE. 305 greater angle to the rail as the curve is sharper, and likewise is shdmg faster on the surface of the rail, increasing the danger of derailment correspondingly, by some unknown amount, but not nearly in proportion to the degree of the curve 8 The lowest probable limit of curve resistance at ordinary freight speeds and in ordinary curves is about 4 lb per ton per degree of curve, with all in perfect order. With worn rails and somewhat rough track it may be as high as | lb. per ton 9. While so obscure a point cannot be considered as estab- lished by the existing experimental evidence, all the more trust- worthy existing evidence seems to combine with theory to indi- cate that curve resistance per degree of curve is very much greater on easy curves than on sharp curves ; so that when the resistance is i lb. per ton, for example, on a 1° curve, it may be 6 to 8 lbs. per ton on a 10° curve, and not more than 15 to 18 lbs. per ton on a 40° to 50° curve. (See Appendix A.) 10. It may be considered established that curve resistance is affected somewhat by the speed, and probably by a verv consid- able percentage; so that if the curve resistance in motion be i lb. per ton it may be as high as i lb. per ton on worn rails for speeds of less than 4 or 5 miles per hour, or for the first train length or thereabout in getting under way. As a stoppage on any curve is always ^onftfudrnafsiip. a possibility, this contingency should not be ^'"'"''^* forgotten when reducing grade on curves, es- pecially near possible stopping points. II. The beneficial effect of the narrower gauge is small with the same length of wheel- base. With a 3-ft. gauge as against a 4.7-ft. ^, . gauge, with a wheel-base of 4. 7 ft., it is about f,c c f ^ ' ' ^v^i^w 1*10. 52.— Effect of Dif- , 4/4 73 I . -a A<.« FERENCE OF GaUGR ON as (not exactly as) -±Z_ll±7_ _ ^047 __ , Curve Resistance, 4/ ^3 I T ~ 77T^ ~ ff Length of Wheel-base ^3 +4-7 5-570 REMAINING THE SAME. less, as outlined in Fig. 52. With a wheel-base Pi^^'of X'^S ,'„"■>» >f"ven distance is repre- Of 2^- the crai'n i«5 onl^r ^^"'72 , sented by thetwodiaeonals v'l ig ine gain is only =12 per cent less marked n. g. and sfd. g.) 97.36 If, however, the length of wheel-base decreases with the gauge _£^ iS^ ms 306 CHAP. VIII.— MECHANICS OF CURVE RESISTANCE. CHAP. VIII.-MECHANICS OF CURVE RESISTANCE. 30/ ■; i Longifudinal S/f'p the gain is directly as the gauge. All the preceding refers only to the surface friction on the top of rail, flange friction being much less affected. 12. Increasing the length of wheel-base, say, from gaug^ to 2 gauge increases curve fric- tion as outlined in Fig. 53, in the ratio of ^ = 58 per cent. 1.414 336. Perhaps the best existing experimental confir- mation of the eleventh conclusion above is to be found in some delicate experimenis on models by Mr. Reuben Wells (Rept. Am. Ry. M. M. Assoc, 1876), which have at- tracted far less attention than their merit deserves. While no one test of any kind can be considered decisive, the tests do afford an indication which is perhaps more delicate and re- liable as a test of principle than could easily be made with the actual rolling-stock. With trucks representing to yV scale a p,^ _ effect ' '- J . f. 01 ;- __ Qp DiFFERENCB OF Length ok Wheel-base on Curve Resist- ance, Gauge remaining the SAME. wheel-base of 4 ft. 10 in. and gauges of 3 ft. and 4 ft. 8^ in. on a curve representing to the same scale one of 300 ft. radius and 273 ft. long, gravity being the impelling force, Mr. Wells found — Speed. Miles Per Hour. 5-76 7-59 10.12 16.70 Resistance ; lbs. per ton (actual). St G. N. G. p. c, of N. G. 46.80 39 -H 83-6 48.96 41.66 85.1 45.76 41 -66 91-0 68.20 64.40 960 By f ormula above |/^ "^ '"'' " ^'^^ ''' ^^^^ -^ ^^^eral the passage of a curve or Weral thrust ? other cause, instead of the bearing surfaces being able to still maintain the merely Tolling contact of minimum wear, as outlined in Figs. 31 and 59, we have the ruddui^ side contact shown in Fig. 53) sure to produce rapid side wear, in addition to the usual top sliding and wear. This has actually resulted with rails of such form. On the Lehigh Valley and on the parts of the Pennsylvania laid with its new rail section of ^ in. corner radius, both rails results, however old or worn the roii; . "^' '°™ ""'^ ""« 34? « , °' "°™ "■"^'''' ^^^P'on the outside rail of curves. best ex;sUng"vide„?;::''to:h'e'':;^r?'°"^ '"""" '° ''-■ "«>• S^-^ ">« having parallel axles He ex oenle , °, T'"^ °" '"= """'"' P^" "' "-ks ." Fig. 60. To dete™" ^Z7^ ZZ'"""' '"'' ^^ ''' ^'"'"" has since constructed and tested mV., ""' ""^"' ""' "■•'■'" similar results. '"°'''' °' """"^ '^'«"«"' f"™ "i* closely Of u.. =\T, r2';,rr":e "xh: Tr '--'• -- --"^ •" ^ -■= -i«d wheels of 34i and 3 i "or a diff °" ,"'""'' «P-sented full, radii of the actual ptth Of th^ln^ddUhwtr^efaf '"■ '" T"'""' '"'' -te that a sin.i p.r of ^^^'o!:i:'z:^:z:t:s::::-::z ;:: I 3IO CHAP. VIII.— MECHANICS OF CURVE RESISTANCE. Fia 57. CHAP. VIII. -MECHANICS OF CURVE RESISTANCE. 311 in their diameters, will roll in a curve of 53i Ti. radius. Two pairs of such wheels, If the axles are held parallel, as in the model, would roll in the following curves: Axles 3 ft. apart will roll in a curve of 67 ft. radius. «< 4 i( (( 5 •< «< 6 <( «t 7 (t « 8 « •( 9 (( *( 10 (C (i « << * ""d, and an average play m the gauge of J ,n., we find abom A in. to be the difference of diameter «h,ch ordmary coned car wheels can have, assuming that both wheels stood 312 CHAP. VIII.— MECHANICS OF CURVE RESISTANCE. close to the outside rail, which they do not (see Fig. 20 and par. 294). This would correspond to results in actual practice as follows : Axles 3 ft. apart will roll in a curve of J 2.572 ft. radius. .. ^ •< 3.513 i '• 5 (< 5.107 / " 6 (« 6,700 / •' 7 « 9.638 / f " 8 •• « 12,969 " / - 9 <« 18,393 \ / " 10 •• M 24,700 / ^ A / 1 y 8 jj / j> ^ < /^ it s ^ e y^ Si S -»^-.^-"?^^• § "tfl it^ 9 «p S 0. iW 2» 2V»' 3 d»/a' ♦' 4V«' ._. ji Gauge, 2.35 in. Fig. 6i. — Radius of Path of Wheel-base shown in Fig. 60. with Wheels set at Various Distances apart, as shown along the Base-line. These figures indicate that even under the most favorable possible circum- stances coning can have little effect to facilitate the passage of curves. 343. Having now investigated the nature of rail wear on curves and the causes of curve resistance, we are better prepared to take up and estimate at their true worth the positive objec- tions to curvature, as summarized at the beginning of this chap- ter, whicb are : 1. The direct cost of curvature of various radii; that is to say, the greater wear and tear of road-bed and rolling-stock, and the greater consumption of fuel. 2. The limiting effect of curvature on the weight and length of trains. A moment's consideration will show that these two causes of expense are sharply defined from each other. For every curve, whether sharp or flat, and wherever situated, must cause a certain amount of wear and tear and waste of power, although CffAP. Vm.-CURVATURE-EFFECT ON EXPENSES. 313 it may not cause any shorter trains to be hauled,^;i;i;ir771^ DIRECT effect on expenses; but if the curvature be very sha p o very unfavorably situated, or if the line be very nearlv level so that there are no heavy grades to li^it trains in'^advance of cur! vature, there w.ll finally come a point where too much or too sharp curvature will not only cause wear and tear, but likewise cause the length of trains to be cut down. In that case the di- iue '^T"\ '''" '"'■^''"'"' '"^ ^"^^ ^'"^ '-^ ->d waste of fuel, w.l continue on as before, but there will now be a new r; d- tiLTirn:^^ '''-' " '^^' ^'^^^'^ -^^'^ - ^" --- -■^^^■ We for the present (until Chaps. XVIII. and XIX.) consider only these DIRECT sources of expense which are common to aU curva ure wherever situated, assuming that it does not require run them." ""' ''"' '"'"^ """^ " '""''^ ^"P^"^-^ '° THE EFFECT OF CURVATURE ON OPERATING EXPENSES. of ^^^'Jrij'^^ '"'? ''^'^^^ '^^" ^P^--- '86) that about 33 per cent of the cost of fuel goes for getting up steam, kindling fires runninrto and from trams, stopping and starting trains, standingldle et e"c and IS hence a constant wastage, independent of the distance run AU f th,s may be considered as likewise unaffected by cuV^lture "d in aL uon thereto there is another and important sou'ceTf ^s"' Z "nden" and hence with the distance run, but is inappreciably affected bv the po ver developed per hour. Every part of a locomoti ve,^eve„ the liein^ IS hot enough to burn the hand in the coldest weather '''^'^^Sing. whilh if ^'H°^;' k'"""^ '"'' ^""■■<=ly<=^Posed (by a mi;taken negligence «h,ch IS gradually being corrected in some few instances as onfhL 1 1 Shore & Michigan Southern Railway, on which Si th^firA agged*), and the ends of the cyli„d';rs are pL t d on ;brmetl! wt^er is shotn brr'n"' "" ■'''"''' ^"'°""' »' '-' consl^d „ cergrler than • ''"'"'"' '° "^ "^^^ ""'f"™'^ -bout 20 per o t mperatu e ^""""^^' ^-^ '"^^^ " P—« for each Jf. difference -^^s^^C:— ::-rirry".r;^^^^-^^ 314 CHAP. VIIL—CURVATURE^EFFECT ON EXPENSES. •< 345. To appreciate the full force of this fact, we must remember that the hottest summer day is cold to the cylinders and boiler. The temper- ature within the boiler is about 350'' F.; and hence whether the temper- ature outside be o'' F. or 100° F. makes little proportionate difference. Let us suppose the average fuel consumption in July, with an average temperature of if F., to be 60 lbs. per mile. In January, with an aver- age temperature of 37" F., experience shows that the consumption will be some 20 per cent greater. Then we have : Tbmpbratvkk. Lbs. Coal July, January, Interior. 350° 350'' Exterior. .u Difference. Burned Per Mile. Increase p. c, IT If 40" 273 313' 60 72 14.6 p. c. 20 p. c The cause of this enormous effect of difference of temperature is very obscure, and it would lead us too far to discuss it in detail. The matter has attracted far less attention than it should, and even the facts from which any discussion of causes must start are but little known to railroad men. It will be seen that, superficially considered, the facts seem to in- dicate that a very large proportion of the fuel consumption is due to the effects of exterior temperature ; for if a decrease of 40° F. or li per cent in the difference between the temperature within and without the boiler saves 20 per cent of the fuel, it would seem as if we had only to decrease the difference a little farther to save half or three quarters of it. This conclusion would be absurd, but all that it is desired here to show is that exterior radiation is a very serious matter. The chief causes for the great difference in winter and summer fuel consumption are prob- ably these : I. Tl?e rolling friction is considerably higher. Most of the energy destroyed by friction must take the form of heat, and as the journals speedily attain about the same temperature in both winter and summer (moderately warm to the touch) the difference in temperature of the journals and the external air is much greater in winter, and this means so much more journal friction. This theoretical deduction lacks, as yet. direct experimental evidence, pend- ing which it must be regarded as doubtful. By some strange omission, the comparative winter and summer train resistance has not been the subject of di- rect investigation, so far as the writer is aware; but that there is considerable difference appears to be indicated by the fact that it is found necessary in prac- CHAP. VIII.-CURVATURE-EFFECT ON EXPENSES. 315. tical operation to cut down trains in winter by about 10 per cent (say from 20- cars to 18. or from 40 cars to 36), for which it is riiffirnit \r. • • ''"""^^^ ,„,. , , . ^ J /• ^wi wiucn It IS dilticult to imagine any other rafonal exp.anafon. The popular explanations are : (,) That the wind ravels n,ore m.les ,„ winter than in summer, which is no true: and wTa" the track .s m worse condition, .vhich is unquestionably true to ome extend but there are very few days when snow and ice cause much trouble on the sur-' and the effect of heav.ng of the road-bed on train resistance, although impor tant. can hardly account for the difference which exists ,. ,f *■ \"'^;"^'/«'^'«i°" ^'so. from the hot stean,, when first admitted to the cylinder mto the interior walls thereof,-whence itisalmos tn- stantly returned again into the exhaust steam, as the temperature alls from reducfon of pressure, without having done anv work.-is admitted to be a very great source of waste, but is entirely distinct from the exter- nal rad.at.on, for .t is not appreciably affected by the external tempera- ture and does vary with the power demanded, and inversely with the speed ; .„ all of whtch details it differs from external radiation It IS true that a locomotive standing still and not using steam loses but a trtfl.ng amount from radiation (about 30 lbs. per ifour), bu the cond,t.ons are vastly different when working against a fierce wind w th t Lr. o°thef f • ""i " '^ '"''="" *°"^'^' the evidence that at least , of the fuel consumed goes to replace radiated heat. If so as 33i per cent goes for other causes of wastage, we have 50 per cent of ihe Pot M "". ^"^'..P""'"" -hich varies directly with the power detnanded. Possibly It IS siill less, but it can hardly be much more The correctness of this conclusion is indicated, in a measure, by the coal buned by engines running light. An engine which will burn 60 .0 80 lbs. per mile with Its full train, will burn 20 to 30 lbs. per mile only ,0 run itself. J17. Assuming curve resistance to average about i lb. per ton it is perhaps as correct an average as possible to say that a continuous M 20 curve causes an average additional train resistance of about 6 lbs per ton, or about doubles the resistance of a train on a level. A mile in length of such a curve contains 600° of curvature. We may say, therefore, that 600- of curvature will waste about 50 per eent as much fuel as the average burned per mile run 348. Repairs of ENCINES.-Referring to Table 85, page 20, it will b seen that the proportion of this item assignable to the avera^; effect wear Tr r*^ r^'' '' ^''°"' '9 ^" ""'• """"^y ^" °f " "'^"g f'om wear of wheels and tires. Experimental data as to the actual effect of em er grades or curvature on locomotive or car repairs are very few statistics of actual expenditures for such purposes on lines differing con- 3l6 CHAP. VIII.— CURVATURE— EFFECT ON EXPENSES. CHAP. VIII.— CUP VA TUPE— EFFECT ON EXPENSES. 3 1 / siderably in grades and curvature afford no assistance, except to drive us to the conclusion that curvature has little or no effect, as we have al- ready seen (par. 164). 349. We may get at the probable effect of curvature on engine re- pairs little more definitely, at least to the extent of checking any error of consequence, as follows : The ways in which engine repairs are affected by curvature are two: First, — and more important,— by the additional wear of tires and wheels. Secondly, by the effect on wear and tear of the additional power de- manded. The last is an inconsiderable element, because the additional power demanded by the curvature, even in extreme cases, is inconsiderable when measured in foot-pounds. Thus, if there be 300° in a mile, — which by turning to Tables loi to 104, page 259, will be seen to be a very large allowance, — this amounts to less than a continuous 6" curve, or 3 lbs. per ton continuous addition to the train resistance. On descending grades this is rather a help, saving the use of brakes. On ascending grades of say I per cent the normal train resistance is some 26 lbs. per ton, and 3 lbs. per ton resistance adds but 12 per cent to this. As, then, only 31 per cent of the cost of engine repairs (exclusive of running-gear) varies directly with the distance run on tangent, the increase, if in direct pro- portion, would be only 0.12 x 0.31 = 3.7 per cent for 300°, or say 7.5 per cent for 600° of curvature, so far as this cause alone is concerned. The maintenance of running-gear (including frames, which is a very small item) amounts to 30 per cent of the total cost of engine repairs, but of this, only one third, or 10 per cent, can properly be assigned to the effect of curvature and grades. We may assume that two thirds of this, or 6.7 per cent of the total cost of engine repairs, is due to curva- ture. By turning to Table 104. we shall find that the average amount of curvature on an average railway is some 30° per mile. On a contin- uous 11° 20' curve, containing 600° per mile, the curvature is 20 times this amount; and hence on such a mile the extra cost due to the curva- ture would be 6 X 20 = 120 per cent of the average cost of engine repairs per mile. This seems to be, and is, a rude process ; but it may be further checked as follows : 350. The cost of maintaining tires average on trunk lines, like the Erie or Pennsylvania, about i^ cts. per mile run, with an average cost o engme repairs of some 6 cts. as a minimum. Their average curvature per mile is some 5o^ The above allowance (of ,20 per cent addition to the total cost of engine repairs by 600" of curvature) is equivalent to al- lowing that with continuous 11° 20' curves the total cost of running-gear maintenance would be 7.2 cts. per train-mile, or six times greater than it is now, on an average, with twelve times as much curvature. While this may not be much too large, it is certainly ample. See also the fol- lowing data (Table 114) as to the wheel wear of cars and the causes thereof. Table 114. Percentages of Wheels removed in 1884 on the New York. Lake Erie & Western Railroad for Various Causes of Each One of Twenty- four Different Makes. (Out of a total of some 300,000 wheels and 18,000 removals.) Class i.-Six Best Makers-aggregating 78.2 Per Cent, of All Wheels in Service. Makers. Cracked and Broken. Shelled Out. Sharp Flange. Slid Flat. Worn Flat& Worn Out. Total. p. C. of Removals to No. in Service. Broken. Crack'd Total. 1 2 1.3 a. 7 5-3 2.0 30 7.2 6.8 14.9 10 I 23.2 20.8 8.4 9-5 15-4 25.2 23 8 0.3 1-7 0.6 0.7 0.6 0.0 4.8 1.9 1.6 4-8 2.6 1.2 9.6 32.9 259 29.7 350 "•3 76.9 64.0 56.6 49-4 36.6 63.7 ICO. 100. lOO. 100. 100. 100. 385 369 7.40 3 4 5 ^.00 6 2.28 8 97 Average 2.0 12. 2 14-4 07 2-7 22.3 60.1 100. 4-39 Class 2.~Six Next Best Makers-aggregating 17.2 Per Cent of Wheels in Service. 7 a-4 8.8 «-3 31 17.0 12.2 30.8 37.9 9-7 138 19.4 147 33-6 29.4 II. 16.9 0.0 0.1 0.1 0.1 0.3 0.0 6.9 i6.i 6.4 2.9 23.2 6.1 20.8 20.4 21.0 18.8 33-2 40.1 52.9 48.7 38.9 48.8 323 36.9 100. 100. 100. 100. 100. 100. — 8 8.21 9 14.63 9.26 10.88 10 "■ 11 *I2 22.5 8 23 Average .... 3.3 93.7 25-9 0.1 8.3 2Z.I 44-7 100. 1 TO. 94 \h m 318 C//AP. VIII.— CURVATURE— EFFECT ON EXPENSES, Table 114. — Continued. Class 3.— Twelve Worst Makers— aggregating only 4.6 Per Cent op Wheels in Service. Ta •9 3-4 10.4 0.0 6.3 4-9 16 6.0 0.2 5.8 7-5 71.9 59-3 19.0 0.0 21.9 14-5 8.6 22.9 36.2 88.8 26.4 4-5 72.8 62.7 30.0 0.0 28.2 19-4 ,6.5 24.5 42.2 90.0 32.2 12.0 0.0 0.0 03 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 54-6 21.8 24.1 9-3 4.9 4-6 I 6 1.1 22.3 83-7 II. 9 45-4 17.8 15.6 17.4 49.6 44-7 4-9 13.6 43-6 0.0 40.6 38.7 59-9 55 35-3 14 14.9 34.4 100. 100. 100. 100. 100. 100. 100. 100. 100. 100. 100. 100. 14.40 *J T^ ••.. 3-76 •• 5 ... 90 5 ♦i.:: 35-7 ♦♦•17 12.62 **i8 10. 1 ♦♦10 76.9 ♦20 14. X ♦21 28.9 22 25.2 23 .,., •....• 5 00 ♦♦♦24 2.29 Average — 4-4 37.2 41.6 0.0 12.4 20.3 25.7 100. 20.l6 Bold/ace numbers represent makers having from 20,000 to 50,000 wheels each in service. Starred numbers indicate the smaller makers, viz., * Lets than 1000 in service; •♦ less than 500 in service; ♦•♦ less than 300 in service. Summary. Ter cent of whole number in service. Broken ■Cracked Broken and cracked.. Shelled out Sharp flange Slid flat Worn flat and worn out. Total removed Per cent of number in service removed. Six Best Makers. 78.2 a.o 12.2 14.2 0.7 a 7 •a. 3 60.1 100. o 4-39 Six Next Best. 17.2 a. 2 »3.7 a5.9 0.1 8.2 21. t 44.7 100. o 10.94 Twelve Worst Makers. 4-6 4-4 37a 41.6 0.0 12. 4 20.3 25.7 100. 20.16 Av. of all on Road. xoo.o 8-4 19.4 21.8 0.4 58 21.7 50.3 100. o 6. 21 percentage of total number in service removed for each cause. Per cent of whole number in service Broken Cracked Broken and cracked Shelled out Sharp flange Slid flat Worn flat and worn out Toul removed Six Best Makers. 78.2 0.09 0.54 0.63 0.03 0.12 0.98 2.63 4-39 Six Next Best. 17.2 0.23 2.60 2 83 o 01 0.89 2. 31 4.90 10.94 Twelve Worst. 4.6 0.88 7.50 8.38 0.00 3.50 4.10 5.18 20.16 Total. 100. o 0.15 i.ao I.15 0.02 0.36 1-35 3»3 6.31 CHAP. VIII,— CURVATURE— EFFECT ON EXPENSES. 319 While the above table gives valuable and trustworthy indications of the relative quali- ties of different makers, it gives an entirely false idea 0/ the absolute qualities 0/ American chilled car wheels, unless a large allowance is made for the fact that it is modified immensely by the constant annual additions of new stock. This is immediately evident in the total number removed for all causes, which is only 6.21 per cent of those in service, indicating on its face an average life 0/ sixteen years, which is certainly more than twice the actual average life of wheels on the road in question, and would be much more than twice or even tliree times the average life in years, except that the average mileage per car p)er year has recently been very low. An average life of eight years for car wheels would require 12)^ per cent per year aver- age renewals, against only 6.21 per cent actual renewals— a discrepancy of over one half. The constant additions of new rolling-stock which are known to have been made on the road are the only apparent cause for this effect. With such an abnormal proportion of new wheels, the proportion of failures from "old age" will be decreased, and hence that the proportion of failures from acute diseases, such as cracked or broken, will be abnor- mally increased ; since in a large proportion of the wheels these are the only failures which are occurring. This table sheds especially valuable light on the cause of sharp flanges. It will be seen that there is twenty times as large a proportion of wheels removed because of sharp flanges among bad wheels as good ones, and that with good makers the proportion of wheels removed for sharp flanges (2.7 per cent, and that on a very crooked road) is so small as to indicate that bad quality of the wheel itself is the leading cause of sharp flanges. Of broken or cracked wheels, only about one quarter break in the flange or tread, and nearly two thirds of the fractures arise from the bursting strains produced by forcing the wheels on the axles. 351. Repairs of Cars.— In Table 86, page 203, the proportion of the cost of this item assignable to the effect of grades and curvature is given as some 23 per cent. Of this at least three fourths would ordinarily be assignable to the effect of grades and only one fourth to curvature. Then, proceeding exactly as in the case of engine repairs, we have 6 x 20 = 120 per cent of the average total cost of car repairs per mile as the extra cost due to 600° of curvature. This estimate is certainly large enough, and probably considerably too large. An exact distribution of the cost of rolling-stock repairs to its various causes is very difficult, because the expenses are not ordinarily kept by Items, but only by aggregates. Some recent statistics as to wheel wear, however (the chief and almost the only item of car repairs affected by curvature), given in Table 1 14, afford some valuable insight into the causes which destroy them most, and indicate that the wear from curvature is a comparatively minor element. 362. Wear of Rails.— We may take the wear of good rails on curves, as an average of their whole life, at about \ lb. per 10,000.000 tons , i: 320 CI/AF. VIII.— CURVATURE—EFFECT ON EXPENSES, per degree of curve, or certainly not more than this. Observations by the writer on the railroads of the New York, Pennsylvania & Ohio Rail- road, and some more elaborate investigations on the Pennsylvania Rail- road by Dr. Charles B. Dudley, agree in indicating this, when allowance is made for the fact that the wear is not at a uniform rate during the whole life of the rail (par. ix-^^et seq.\ but is perhaps, rudely speaking, only one fourth of the total during the first half of its life and three fourths during the latter half. As a consequence, as already pointed out (par. 315). the wear shown by an investigation of a lot of rails of the same absolute age on different curves will apparently indicate a very much greater wear on sharp curves; but this appearance is deceptive. The wear in tangents, then, being (as it is) about i lb. per 10,000,000 tons duty, the wear on a continuous 11* 20' curve will be i lb. x ii^ = 5f lbs. per mile of curve, or be increased 567 per cent over the tangent wear. But this is assuming that the tangent rails are so good that they will need renewals only from the effect of abrasion, in which case rails will cost only about ict. per train-mile. With inferior steel rails, as formerly with iron rails, the proportionate increase of wear is very much less than this, owing simply to the fact that the tangent wear is so very much greater. The additional rail wear on curves was estimated by the writer in the first edition of this treatise— and, so far as he can now judge, with very close correctness— at 100 per cent increase over the tangent wear on an 11° 20' curve. The absolute rate of abrasion is much the same with all rails, iron or steel, good or bad. With rails that fail only by abrasion, therefore, the curve wear adds a large percentage to a very small total cost. With rails that mash or split in service, the curve wear becomes a much smaller percentage of a much larger total. 353. Cross-ties.— The effect of curvature on ties has been much de- creased by the introduction of steel rails, and will be still further and very largely decreased by the introduction of creosoted ties. Still its effect on the life of ties is considerable. Several years of the tie's life must be sacrificed on sharp curves because the holding power of the spike be- comes too little. The so-called " cutting" of ties (par. 121) isalso«ireater on curves, and mainly on the outside of the rail. As the rail wears by flange cutting, moreover, it is necessary either to renew the rails prema- turely or to throw them in to gauge. The effect of all these causes to- gether to shorten the life of ties is a pure matter of fact; and considerable observation of and inquiry as to practice in this respect indicates that the following comes very near to the average life of white-oak ties oR CHAP. VIII.-CURVATURE-EFFECT ON EXPENSES. 32 1 ' I . sand or gravel ballast, imperfectly drained-the life given on cui-ves bemg, if anything, too short : On a tangent, On a 2° curve, , , On a 6° curve, . , On a 10° curve, . . On a 14° to" 16*' curve 9 years. 8 7 6 5 «< From this we may conclude that the cost for ties on an i,° 20' curve (600 per nnle) IS about 50 per cent greater than on a tangent, and t^t the mcrease is directly as the degree of curvature on any gfven distance' or, in other words, is uniform per degree, whatever the radius" ' 354. Track Labor is, as a matter of fact, but little affected bv curvacure. It is an unusual thing to see sections made shorter thai others on th.s account. If two contiguous sectionsare noticeably differ^ ent in this respect it is not unusual to take a quarter or half a mile off one and add it to the other, but any greater difference than this is un- likely. Yet comparing the conditions which would exist on a mile of tangent and a mile of 11° 20' curve, it might not unfairly be claimed that there would be a difference of 50 per cent in the cost of track labor; and to avoid that very objectionable result, an underestimate of the disadvan- tages of curvature, we may assume this, which will amply cover the facts. 355. Summing up the various Items affected by Curva- ture, we obtain the following Table 115, giving the assumed eflect on expenses of 600° of curvature. The total cost per year per daily train of 1° of curvature given below, Table 115 (43.3 cts.), divided by the rate of interest on capital, will give the justifiable expenditure to save 1° of curva- ture estimated per daily train, viz.: At 5 per cent, %^AZZ At 8 per cent, . 0.05 .0-433 0.8 At 10 per cent, ^-^33 _ o. 10 541. 4-33- And similarly for any other rate of interest; this being assumed as heretofore, not to be a precisely accurate result, but one as exact as is either practicable or necessary to avoid serious errors- 21 * , \ 322 CHAP, VIII.^CURVATUR E^EFFECT ON EXPENSES. Table 115. Estimated Average Cost Per Train-Mile of 600" of Curvature. [Being equivalent to a continuous ii* ao' curve, one mile long, assumed to double the average train resistance in lbs. per tons.] (Cost of train-mile assumed at fi.oo.) Item. (As per Table 80.) Average Cost of liem. Cts. or Per Cent. Ftrel Water Oil and waste Repairs, engines • . • Switching-engines service. Train wages and supplies Repairs, cars Car mileage Rail renewals Adjusting track Renewing ties Earthwork, ballast, etc., Yards and structures Station and general Total cost per train-mile of 600' of curvature (cts. or per cent). 7.6 0.4 0.8 5.6 5-a 15.4 10. o 2.0 2.0 6.0 30 4.0 8.0 30.0 Per Cent added by 6oo» of Curvature, as above. Cost due to Curvature. lOO.O 50 per cent. 3.8 25 " •* 0.1 25 " " 0.2 125 " " 7.0 Unaffected. • • • 1 • • • 120 per cent. 12.0 Unaffected. 300 per cent. 6.0 50 - " 30 50 " •• 1.5 50 " " 2.0 Unaffected. 35.6 per cent. 35-6 35* = -0593 <*• Total cost per train-mile per degree, -^ of !• of curvature per year per daUy train (.0593 ct. x 3*5 X 2) = 43-3 ^s. Total cost ed 356. The similar estimate which the writer made in the first ition of this treatise gave a smaller estimate for the value o curvature than this, viz.. ».s cts. instead of 35-6 fo-" the cost cer train-mile of 600° of curvature-a difference of over 50 per cent- and this in spite of the fact that the former estimate was for the most part on an iron-rail basis. The only positive reason for this difference is that the writer has seen reason to increase the estimate of the effect of curvatur-^ on rolling-stock repairs, al- though a chief reason has been to ensure that the estimate was Urge enough. According to the above estimate, the total cost of atrain-m.leshould be 10 per cent greater on a road having 100 aiore curvature, whicli is the most that the evidence warrants. CHAP. VIII—CURVATURE -EFFECT ON EXPENSES. 323 397. To illustrate how very little difference any probable error m the above estimate can make in the justifiable expenditure to avoid curvature: Assuming the case of a road running .0 dailv trains each way, the justifiable expenditure to save 1° of curva- ture, at 8 per cent, is $54. ,0, and to save 20°, $1082.00; a sum which will warrant no very large amount of work to avoid it. The ANNUAL LOSS TO REVENUE IF IT BE NOT AVOIDED will be 43-3 cts. X 10 trains X 20° = $86.60; a sum sufficient to pay for perhaps two extra trains over the road dunng the year or for running 7302 trains instead of 7300 When the effect of the most trifling difference of grade is compared with this It becomes slight indeed. 388. This example is for a considerable traffic and for a con- siderable amount of curvature, to save at one point. As such It well Illustrates the principal purpose of such estimates as we have just made. It is not to avoid errors of 10, 20, or even 50 or 100 per cent in the sums spent to save curvature; for we cannot go far wrong if we assume either $700 or $800 or $1200 or $.500 as our standard value for such an amount of curvature instead of $,058. But its principal purpose is to save us from the manifold greater errors which may so easily result from follow- ing mere guesswork and "judgment:" from spending $cooo or $.0,000 to gain something whose true value lies between $'700 and $,soo, as has been done in many cases on heavy work* or from the corresponding error of introducing 10° or 20° of curva- ture recklessly, which might be saved at trifling cost, or perhaos at no cost at all, by a little more care. 359. All the preceding estimate of the direct cost of curvature has been based upon the assumption that the cost per degree was for the most part uniform for all curves, independenf of radius; i.e., that the cost of the curvature in 100 stations of .• curve was essentially the same as that in 10 stations of .0° curve This assumption appears to be unquestionably justified bv the facts, but the reasons why it is so are considered later, in Chap. AlX., page 638. ^ if lii m 324 CI/AF. VIIL-CURVATURE-EFFECT ON EXPENSES, 360. A particular form of bad practice in respect to curva- ture and one of the most prevalent and indefensible of the minor errors of location, is a weakness for very long tangents and a readiness to spend money to secure them. A reasonably long tangent, say not less than 400 feet, is always very desirable, if not absolutely essential, in order to taper out the superelevation and afford room for proper transition curves; but beyond this there is no justification, theoretical or practical, for expending more than a very small sum to avoid any number of short and gentle curves The difference in distance resulting from even very con- siderable and frequent breaks in a tangent is too trivial to be a serious consideration on lines of small traffic (although it may look as if it were considerable, especially on the ground; see Chap XXVIII.), and the same is at least equally true of the curvature. Thus let us suppose that there is a section of a mile and a half out of one of those four- or five-mile tangents, in moderately difficult country, for which the following curved, alignment may be substituted with some economy in first cosU CURVBS. 1° Z for 300 ft. 2' 2' 2* • L '° R '" L «< 600 600 " 500 •• 200 •• Central Angle. 12° 10° Total. 38' Toul Length of Tan>;ents between Intersections. 2,500 ft. 2.500 •• 2,000 " 1,100 " 8,100 ft. Such an alternate alignment would perhaps have the effect of reducing a succession of considerable cuts and fills materially. How much does it damage the operating value of the line ? The difference in distance is as nearly as may be 23 f eet m about 8350. The amount of curvature introduced is 38 • Then to an hypothetical line running 10 trains per day each way and CHAP. VIII.— CURVATURE— EFFECT ON EXPENSES. 325 paying 8 per cent for capital the value of the difference would be — 23 feet distance at (possibly) 0.30 cts. X 10, $69 00 38 curvature at $5.41 x 10, 2,055 80 ^°^^^» $2,124 80 Many a tangent has been broken up improperly to effect less saving than this; but, on the other hand, a saving of 8000 to 10,000 cubic yards of excavation is enough to balance it; and if we reduce the estimated traffic by two thirds or three quarters, in all ordinary country the saving by breaking up tlie tangent would far more than justify doing so, even in light work, for the above figures fully represent every measurable disadvantage from a moderately curved line of that character. Especially if the general character of the work is heavy, the caution of par. 14 becomes of vital moment on such alignment if the most careful engineer would avoid error. Table 116. Sharpest Curves in Regular Use on Standard-Guage Roads. (Chiefly from a list published in the Railroad Gazette of Oct. 4, 1878.) N. Y., New Haven & Hartford. Lehigh & Susquehanna <( 14 Baltimore & Ohio. M ii Oroya Railroad. Virginia Central Pennsylvania Railroad tracks Pittsburg, Fort Wayne & Chicago Canarsie & Rockaway Brooklyn, Bath & Coney Island.. , Manhattan Elevated Petersburg, Va Springfield, Mass Upper Divisions Stony Creek Butler Branch Harper's Ferry, Md. side.... Ilchester Harper's Ferry, Va. side Y for Consolidation Engines. In Peru Over Rockfish Gap Tunnel... Centennial Grounds. Pittsburg Brooklyn New York City U. S. Military Railway. 410 383 320 310 400 375 300 136 395 300 238 300 246 175 55 to 125 90, loo, 103.5, 125, 150 50 15" i8« 18° 32' 14° 22' 15° 20' 19° lO* 43* 14° 32' 19" i' due to that velocity will lift the body against gravity only before it comes to rest. Miles Per 0. I. 2. 3. 4. 5. 6. 7. 8. 9. Hour. to , 20 30 40 5o« > • ' • • 0. 1. 2. 3. 4. 5. 6. 7. 8. 0.00 0.03 0.13 0.30 0.54 0.84 1 .20 1.64 2.14 3-34 4 05 482 5.65 6.55 7-52 8.56 9.67 10.84 »3-38 «4-75 16.19 17.69 19.26 20.90 22.61 24-38 26.22 30.10 32.14 34-25 36.42 38.66 40.97 43 34 45-78 48.29 53 -si 56.22 58 99 61.84 64-75 67.72 70.77 .73-88 77-05 83.61. .86.99 9043 93-94 97-52 101.17 104.88 108.66 112.50 2.71 12.07 28.13 50.87 80.30 116.42 Formula : h = \6o x6o/ • (in miles per hour) 0-033445 ^•. 64.32 For computations connected with the movement of trains the following Table 1 19 should be used. 374. The formula of par. 371 assumes that the body is in motion as a whole, but that its parts are at rest relatively to each other. In a mov- 334 CI/AP. IX.-^RISE AND FALL— EFFECT OF VELOCITY, ing train this is not so ; for the wheels and axles, in addition to their for- ward motion, are in rapid rotation, so that additional energy is stored up within them as in so manyfly-wlieels. To put the same truth in another way : Each particle in the wheels and axles (except on the axisj moves more feet per second through space (albeit in a curved path) than the train as a whole, so that they necessarily have more energy stored within them. The energy due to the rotation of the wheels and stored up in them as in a fiy-wheel is usually computed separately from that which they have in common with the rest of the train, when it is computed at all; but for all purposes in connection with the motion of trains for which the one is required to be known, the other may be said to be also, and in Table 1 18 the two are included together. If the wheels were not in con- tact with the rails, but were mounted like fly-wheels within the car, they would exercise no effect upon the forward motion of the train. After the train had been brought to a stop they would continue to spin around indefinitely until stopped by their own friction ; but, being in contact with the rails (or if mounted on the body of the car and connected with the wheels by gearing), they act very eflfectually to carry the train along just so much farther, in the same way as the rotating fly-wheel on the little toy locomotives, which almost every one has seen, causes the latter to move, being in that case the only motive-power. 375. The amount of energy in any rotating body is determined, as may be seen in any treatise on mechanics, by determining the position and velocity of a point called the centre of gyration, which is the point at which, if the whole mass of the rotating body were concentrated, any given force would communi- cate the same velocity of rotation as it does to the acutal body. Motion in a circular or other curved path at any given linear velocity means the accumula- tion of the same amount of energy as if the body, as a whole, were moving in a right line at the same velocity, and if the body be both revolving and moving forward, like the wheels, the two are separate and in addition to each other. 376. The manner of determining this radius of gyration it is needless to go into deuil. According to the pattern of wheel, it will vary between 0.7 and 0.8 of the actual radius, being in car wheels nearer 0.7 and in locomotive drivers fully 0.8. Assuming a minimum radius of 0.7, it will be plain that points on that circle are rotating with a linear velocity of 0.7 times the velocity of the train, and hence that the rotative energy only of the wheels will be 0.7' or 0.49 in round numbers one half that due to the forward motion of the wheels in common with the rest of the train. Really it should be a little more than this even figure for ordinary patterns of wheels, and in locomotives it is fully six- tenths. CHAP. IX.-^RISE AND FALL— EFFECT OF VELOCITY. 335 Estimating ordinary car wheels to weigh 2^ tons per 8- wheeled car, or 561 pounds per wheel, the ratio of the weight of the wheels to the total weight will be about — Weighing Per cent of weight of wheels Making an addition to the total energy of the train of about In a Passcng-er or Loaded Freight Car. 2.2\ tons. 10 p. C. 5 p. c. In an Empty Freight Car. 9 tons. 25 p. c. 12\ p. c. In Locomotive and Tender. ID to 12^ p. C 6 to 7i p. C We may say, therefore, that the rotative energy of the wheels will add about 6 per cent as a mmimum to the accumulated energy or "velocity head " of the train as a whole, in the case of ordinary passenger or loaded freight trains, which with very heavily loaded cars may be a little less, but in the case of long trains of empty cars may be some 4 or 5 per cent higher. Under this assumption, assuming 6.14 per cent for ease of computation, Table 118 was computed, which is the proper one for use in all computations concerning the energy stored in trains at various velocities. Table 118. Total Emergy of Potential Lift in Vertical Feet (or Velocity Head) IN Trains moving at Various Velocities. Including the Effect of the Rotative Energy of the Wheels for Passenger or Loaded Freight Trains^ assumed at 6.14 per cent of the total enei^y. For trains of empty flat or coal cars add about 4 per cent to the quantities below, and proportionately for mixed trains. MiLBS Per Hour. 0. 1. 2. 8. 4. 5. 6. 7. 8. 9. Vel. ft.. 0.00 0.04 0.14 0.3a 0.57 0,89 X.28 '•74 «.27 3.88 MiLBS Per Hour. .0 .1 .2 .3 .4 .5 .8 .7 .8 .9 10 3.55 3.62 369 3-77 3.84 3-92 3-99 4.07 4 »5 4.3a II la »3 430 5 II 6.00 438 519 6.09 4.46 5.2« 6.19 4-54 5-37 6.28 4.62 546 6.38 4.70 5-55 6.47 479 5 64 6-57 4-87 5.73 6.67 4-95 5.82 6.76 5-03 5-01 6.86 14 15 t6 6.96 7-99 9.09 7.06 8.10 9.21 7.16 8.31 9-3» 7.27 8.32 9-44 8.43 9-55 7 47 8.54 9.67 7-57 8 65 9.79 7.68 8.76 9-90 7-78 8.87 10 02 7-89 8.98 jo. 14 57 18 »Q 20....: 10.26 IX. 50 12. 8a 10.39 11.63 12.96 10.51 11.76 n.09 10.64 11.90 13-23 10.76 12.03 1337 10.88 12. 16 13-51 II. 01 12 20 13-64 11 13 "43 13-78 TI.26 12.56 13 92 11.38 12.69 14.06 14.20 14-34 14-49 14 64 14.78 14-93 15.08 15-23 15-38 15.5a 336 CHAP, IX,— RISE AND FALL—EFFJiCT OF VELOCITY. CHAP. IX.— RISE AND FALL— EFFECT OF VELOCITY, 337 Table 118. — Continued. Miles Per Hour. Vel. ft.. 0. 0.00 1. 0.04 2. 0.14 8. 0.33 4. 0.57 6. 0.89 6. Z.38 7. x-74 8. 3.27 9. 3.88 Miles Per Hour. .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 20 ... 14.20 14-34 14 49 14.64 14.78 14.93 15 08 15-23 15 38 15-52 ai aa as a4 «5 36 a? 38 . . . . . a9 15 67 17.19 18.79 20.46 22.20 34.00 25.88 27-83 29.86 15.82 1735 18.95 20.63 22 38 24.18 26.07 28.03 30.06 15-97 i7-5» 19.11 20.80 22.56 24-37 36,27 28.23 30.27 16.13 17.67 19.27 20.98 22.74 24.56 36.46 28.43 30.48 16.28 17-83 19-44 31.16 22.92 34.75 26.66 28.64 30.69 16.43 17.99 19.61 21.34 23.10 24 93 36 85 28.84 30.90 16.58 18.15 19.78 31.51 23-38 25.12 37.05 29.05 31.11 16.73 18.31 19.95 21.68 23.46 25.31 27.24 29.25 31-32 16.88 18.47 20.12 21.84 23 64 25.50 27-44 29.46 31-53 17,04 18.63 20.39 31. 03 23.82 25.69 37.63 29.66 3'-74 30 3»-95 33.16 32.18 32.60 32.81 3303 33.25 33.47 35.68 37.97 40.32 42 -75 45.26 47.82 50.47 53-18 55.96 33-69 33 90 3» 3a 33 34 11:::::: %::■:. 39 3412 36-35 38.66 41.04 43 49 46.01 48 60 51.26 54.00 56.80 34-34 36.58 38.90 41.28 43-74 46.26 48.87 51-53 54.28 34-57 36.81 39-13 41.53 44.00 46.5a 49 13 51-80 54-56 34-79 37 04 39-37 41-77 44 25 46.78 49-39 52.08 54 84 35-01 37-27 39.61 42.03 44-50 47.04 49.66 52-36 55-12 35 24 37.50 39.85 42.26 44-75 47.30 49.93 52.63 55-40 35.46 37.74 40.08 42.51 45.00 47.56 50.20 52.91 55.68 35.91 38.20 40.56 4300 45-51 48.03 50.73 53.46 56.24 36.13 38-43 40.80 4324 45-76 48.34 51.00 53-73 56.52 40. ... 57-09 57-37 57.66 57-95 58.24 1 58.52 58.81 .sgio 59-39 41 4a 43 44 Jl:::::: %■■:::. 49 59 68 62.62 65.64 68.73 71.89 75-12 78.42 81.79 85.24 59-97 62.93 65.94 69.05 72.21 75-45 78.75 82.13 85-59 60.27 63.23 66.25 69.36 72.54 75-78 79.09 82 48 85 94 60.56 63-53 66.56 69.68 72.86 76.11 79-43 82.82 86.29 60.86 6383 66.87 70.02 73.18 76.44 79.76 83-17 86.64 61.15 64.13 67.18 70.34 73-50 76.77 80.10 83.51 86.99 61.4s 64 -43 67.69 70.65 73.82 77.10 80.44 83-85 87.34 61.74 64.73 67.80 70.97 74-15 77.43 80.77 84.20 87.69 62.04 65-03 68.11 71.28 74-47 77.76 8t.ii 84 55 88.04 60.33 65-34 68.42 71.6a. 74.79 78.09 81.4s 84.89 88.39 50. ... Diffs... 60 Diffs .. 70 Diffs... 88.75 3-59 127.80 4-30 173-95 5-01 92-34 3.6s 133.10 4-36 178.96 5.07 95-99 3-73 136.46 4-44 184.03 5»5 99.72 3.80 140,90 4-51 189.18 5.33 103.52 3.87 145.41 458 194.40 5.29 107.39 3.94 149.99 4.65 199 69 5-36 111.33 4.01 154-64 4.7a 205 05 5.43 115. 34 4.08 159-36 4-79 310.48 5.50 119.42 4.16 164.15 4-87 215.98 5-58 123.58 4.22 169.03 4-93 221.56 564 •H , ,T , «. J I'* 'n ft. per sec. 1.467" F« (m miles per hour) .,. Formula : Vel. head = 2—^ = — ^-^ —2 ' = 0.033445 F» 64.32 04.32 To which add 6.14 per cent for rotative energy of the wheels = 0.002055 V* Giving as the final formula, by which the table is computed, Vel. head = 0.035500 ^'' The above table is exact for the even miles. The heights for tenths of a mile per hour were filled in by interpolation, and the last digit may be in error. The process of computing the result of a brake-test by the aid of this table, which may be useful for reference in connection with it, is as follows : FIELD NOTES REQUIRED FOR COMPUTING BRAKE TESTS. 1. Speed in miles per hour at instant of applying brakes. 3. Distance run after applying brakes, in feet. 3. Jiate 0/ grade, ascending or descending, in per cent, i.e., feet per station of 100 ft. 4. Proportion 0/ the total weight 0/ the train to which brakes were applied. (Except as necessary to determine this proportion, the total weight of the train, or the total weight on braked or unbraked wheels, is unessential, and does not witer into the computation.) To these essential notes should preferably be added : 5. Time 0/ stop in seconds (best taken with a stop-watch). PROCESS OF COMPUTATION. 1. Take from the table the height in vertical feet corresponding to its speed, i.e., the •• Vel. head." Divide it by the length of the stop in stations of 100 ft. The quotient (which will in all ordinaVy cases be between the extreme limits of 2.00 and 20.00) is the equivalent grade 0/ retardation for a stop on a level grade. 2. To this quotient add the actual rate of grade, if descending, or subtract it if ascend- ing. Subtract also the grade representing the average train resistance during the entire Stop, which may be approximately assumed as follows : Miles per hour. Initial speed, 25 30 and less. 40 50 55 Pounds per ton (2000 lbs.). 60 Average resistance during stop, Equivalent grade, . 8 9 10 12 14 Per cent (or feet per 100). 16 0.4 0.45 0.5 0.6 0.7 0.8 3. The resulting sum or difference is the actual equivalent grade 0/ retardation, in feet per 100 : or the effect of the brakes as a whole on the train as a whole. The figures ex- pressing this grade, as 5.00, 8.50, 12.45, express also the efficiency of the brakes upon the train as a whole, in percentages of the total weight 0/ the train. 4. Divide this grade or percentage by the per cent 0/ the total weight of the train upofi which brakes acted or were adapted, intended, or expected to act. The quotient is the actual efficiency of the brakes upon the load carried by the braked wheels, or upon that portion thereof which it was intended to rely upon in proportioning the brakes. This quotient will always lie between the extreme limits of 25.00 and i.oo, usually be- tween 3.00 and 14.00, and is the only one by which comparisons with different trains having differently distributed brakes can properly be made. By formula : Grade of retardation = Yfl-J^i^ j + rate of descending grade, or ) _ Distance I — ascending " J ^ . , «. t ' ^' J Grade of retardation grade of rolhng friction ; and 7 ; : = Efficiencv of p. c. of wt. of train on which brakes acted ^"^^^^^ncy 01 brakes in per cent of weight on which they acted. EXAMPLES. I. Train with 9^ (75 per cent) of weight braked; 20 miles per hour; 284 ft. (2.84 stations), distance run ; grade, 52.8 ft. per mile (i.o per cent) descending. 22 ■' ( 338 CHAP. IX.— RISE AND FALL— EFFECT OF VELOCITY. Assumed average grade of rolling friction, as above, = 0.4. Then 14.20 (from table) 2.84 = 5.00 + i.oo - 0.4 = S.6 + 0.7s = 7.47, being the percentage of the efficiency of the brakes or rate of an equivalent grade ; and grade of 7.47 X 20 = 159.4 Jbs. per ton retarding force from brakes. 2. Train 90 per cent braked ; 60 miles per hour ; 1014 ft. length of stop ; grade, 26.4 ft. per mile (0.5 per cent) ascending. Assumed average grade of rolling friction, as above, = 0.8. 127.80 (from table) 10.14 = 12.60-0.50 — 0.8= 11.30 -»• 0.90= 12.56. 377. The magnitude of any force is expressed (in English) in pounds or some multiple. The work done (or which has been or can be done) by the continued application of any force is expressed in foot-pounds, i.e., by the force in pounds multiplied by the distance in feet through which it acts or has acted or can act. A Consolidation locomotive has a tractive force of, say, 20,000 lbs. The work done by such an engine in runnin;? a mile is 20,000 X 5280 = 105,600,000 foot-pounds. A HORSE-POWER is 33.000 foot-pounds per minute. If, therefore, such an engine run a mile in 4 105,600,000 „ , T,.^ ., minutes its horsepower is ———--= 800 horse-power. If it run a mile 33>ooo X 4 105.600.000 , , in 5 minutes it is exerting a force of only — ;^^^^ = ^4© horse-power. If a train at a certain velocity has an average resistance of 10 pounds per ton, the power consumed by it will be 10 foot-pounds per ton per foot, or 52.800 foot-pounds per ton per mile. If, again, the resistance of brakes be added, assuming the total pressure on the brake blocks to be equal to half the weight of train or 1000 lbs. per ton, and assuming the coefficient of friction to be at 0.16 (it is in reality very variable), the re- tarding force of the brakes will be 1000 x 0.16 = 160 lbs per ton. and the work done per ton by the brakes (in dissipating energy) will be 160 foot-pounds per foot through which the brakes act. 378. The same amount of energy (in excess of all retarding forces) communicated from any source to any body moving in any direction will cause that body to move through space with the same velocity. The direction of the motion may vary. The velocity of motion will not vary, and will always be equal to that required to lift the body through the vertical height through which the body would have to fall freely in a vacuum to acquire that velocity. CHAP. IX.— RISE AND FALI^EFFECT OF VELOCITY. 339 379. From the above it necessarily results that it is a general law of motion on inclined planes that a body descending freely along any incline, regular or irregular, as AC, AD, AE, or AF, Fig. ()2, under the action of the same vertical force, as gravity, will be moving through space at any point, C, D, E, or F, which lies at the same verti- cal distance below A, with the same velocitv as it would have at B if it had fallen vertically through AB. The direction of motion will varv in each case. The time of descending to the line bd will also varv in each case, but the velocity with which the bodv is moving through space as It passes any given level db will always be the same, by whatever path It has reached that level, and always that "due" to the vertical h^\8,hx. of the plane (less the loss by friction), this being the necessary result of the fact that the same number of foot-pounds of work have been com- municated to the body in either case. 380. The time occupied in the descent, if it be a regular plane, will be greater than that " due" to the vertical fall in the ratio of the len^rth of the plane to its height. If it be a curved or broken surface, the time of descent will bear no such constant ratio, but the final velocity at a given vertical distance below A will in all cases be the same. 381. Conversely, the accelerating or retarding effect of gravity on any incline, and in the direction thereof, as on a railway grade, Fig. 63 is less than the weight of the body in the same ratio as the height ab of the plane is less than its length ac; that is to say, the force IV, Fig. 63, which represents the weight of the body O acting verti- cally downward, may be resolved — or rather resolves itself — into the force/ acting parallel with the plane and tending to produce mo- tion down it, and the force W — (al- ways less than W^)— acting in the direction /?, perpendicular to the Fig. 63. rail, ac representing the actual pressure of the wheel thereon. It is geo- metrically evident from Fig. 63 (on account of the similarity of triangles) 340 CHAP. JX.—RISE AND FALL— EFFECT OF VELOCITY. CHAP. IX.- RISE AND FALL-EFFECT OF VELOCITY. 341 ^1^ that the force / (technically known as the grade resistance, although in descending it is not a resistance but an accelerating force) bears the same ratio to the weight that the rise in any distance does to the length ac, measured on the slope, and not horizontally. Practically, however, on any ordinary railway grade the horizontal distance be is not sensibly differ- ent from the length measured along the surface of the rails ac, and hence it is customary and proper to assume dc = ac \ whence we have, approxi- mately, W~ be' or, if we let the horizontal distance be = loo, and the height ab = r = rate of grade or rise in loo (whether feet or other horizontal unit, if we use the same for both vertical and horizontal), then we have /_r_ lVr_ W 100 *^^ -^ " loo* 382. If, in this equation, we let W^ 2000 = the number of pounds in. a ton, we have /=2or. or. The grade resistance in lbs. per ton = rate of grade per CENT X 20. This rule should be memorized by every railroad engineer, preferably in the still simpler form : " Rate of grade in tenths x 2." E. g. on a I per cent or i.o grade the grade resistance is 20 lbs. per ton ; on a 0.4 grade, 8 lbs. per ton. For the long ton of 2240 lbs. it is only necessary to increase the re- sult by 12 per cent. The rule amounts to no more than saying that if the rate of grade be xb* the resistance per ton will be ^-^ ton, which is 20 lbs. 383. The trifling importance of the error in assuming in Fig 63, that, for all practical purposes, the hypothenuse ac and the base ab may be assumed equal, when computing grade resistance, is shown by Table 119. On a 4 per cent grade, which may be considered the utmost limit of ordi- nary practice, the error in the computed resistance is only o.cooS, or less than one tenth of i per cent. On the heaviest grade on which the locomotive has ever worked, 10 per cent, the error is only one half of one per cent. The error can be avoided by substituting for the actual weight. W, Fig. 63, the value of the component W at right angles to the plane; but for any grade less than the most extreme this is unnecessary trouble, as the error, what there- is of it, tends to safety by exaggerating the grade resistance. Table 119. <5.v.ng: also the percentage of excess in the comDuted ^.A. ■ . ine computed grade resistance under the rule / = 2or of par. 382. Rise in loo. («^, Fig. 63.) (= rale of grade per cent.) I 2. 3. 4 5. 6. .00 .00 .00 .00 .00 .00 7.00 8.00 9.00 10.00 Length on Slope («<^) for Horizontal Distance i^c) of 100, 100.005 100.020 100 . 045 100.080 100.125 100.180 100.245 100.319 100.404 100.499 NOTE.-This table likewise affords a good opportunity for testing the convenient rule elsewhere given for solving right - angled triangles of small altitude, viz. : B ^^ 01 I^iff. between hyp. and base = ht « iTnown'j: ^^^' "" ^""'^ (whichever is It will be seen to be correct with these triangles to within a very mi- nute percentage. ^ carat any given veocitys called ^h T^ '° "'' "'°'""« '""■•°"" °f ^"e being thLVade on wh'i h a cl/or t'"' °' 'T'" '°^ ''''' ^'"'^^y- erating force of gravity wou d t« h T "^'"^"^ descending, the accei- hence enable it to ^tC t'^^r^lTei: Itt:":" '° ""f °"' ^"^ gaining nor losmcr velocity «rhi.i, • .^^''^f ^* *''^ ^^^e speed, neither bodies to which a given vlUtv t-= o '"'k"""^"''^^' ^""^ition of all ing to Newtons firs' Zl of moUon " '"" communicated, accord- ■ootion when a train was once movinrwL t """" """ ■•«'■««"« of - "ate of rest. I„ reality a grTse;elT, 1"°"^'' '° ^'^" ^ ■"'" f™™ 'a.ter grade only can propcrfy be a led a "T .7 " "'"''"'■ """ '"is chosen tern, is still the coLon one LI ..5''' °'/«=P°^^" But the ill. ■dea in which it originated Other»i« ut ' """"^PPily. *« erroneous on limiting grades. '' ^'"^^"'y- """^ """'d be fewer station, .■O ■m^ ^ ♦, •I H 4 342 C//AP. IX.— RISE AND FALI^EFFECT OF VELOCITY. 387. When a railway train descending a grade, or any other falling body, is acted upon by an accelerating force which remains uniform, — like the traction of a locomotive or gravity, — in opposition to a retarding force which increases with the velocity, — like the resistance of a train, — the velocity of motion will continue to increase until the retarding force becomes equal to the accelerating, and thereafter the body will continue in motion indefinitely at a uniform velocity. The net resultant of all the forces acting is then zero, and consequently the body continues indefinitely in motion at an unvarying velocity, as theory requires. 388. This statement should be read over until its meaning is fully grasped. A railway train in motion at a uniform velocity is acted on in one sense by two forces, but in a truer sense by no force. The frictional and other resistances and the traction of the locomotive act upon and destroy each other within the body, without either acting upon the body itself, except to produce internal stress. Such a body is therefore one of the nearest examples in practical mechanics of Newton's abstract con- ception of a body moving on indefinitely in vacuo from original impulse, without gain or loss of energy, as do the heavenly bodies. 389. Under such conditions any new force— whether accelerating or retarding, like a change in the rate of grade or in the tractive force of the locomotive — will act upon the body precisely as if no other forces existed to act upon it; i.e., the whole of the new force, undiminished by frictional or other losses, will act upon the body to vary its velocity, and will vary it precisely as theory requires. This fact bears with it im- portant consequences. To illustrate this interconvertibility of work and velocity : Let us assume any body, as a car, weighing 20,000 pounds to have fallen freely (i.e., without, or in excess of, the loss by friction) 16.08 feet. It would then have 20,000 X 16.08 = 321,600 foot-pounds of work stored up in it, and would be moving through space with the precise velocity of 32.16 feet per second or about 21 miles per hour. If, instead of having fallen vertically, either gravity, or the tension on the draw-bar, or any other force, had been communicating to that same car body continuously a force of 20 pounds (or one pound per ton in excess of all 321,600 resistance), the car would have to move through a distance of CHAP. IX.-RISE AND FALL— EFFECT OF VELOCITY. 343 20 16,080 feet to store up within itself 321,600 foot pounds, and hence to acquire the same velocity that it acquires when falling freely through space, or, when acted upon (in any direction) by a force equal to its weight, in 16 08 ft. 390. This velocity once acquired, the corresponding amount of energy stored in the car may be expended in any one of the following ways : First. It may (theoretically) by proper mechanical appliances be made to lift the body vertically through a height of 16.08 feet, which it will do in one second of time, and bring it to a stale of rest. 391. Secondly. It may be made to lift the body up an inclined plane A, A\ A", A", Fig. 64, as on a grade of any rate, against the action of gravity.' Iil Fig. 64. this case, if there be no other resisting force but gravity, the body will rise through the same vertical height in all cases before coming to rest. The dis- tance run and the time occupied in the ascent will alone vary. The vertical elevation surmounted will not vary. But as there is a resisting force (rolling friction) which is so much per foot run, these conditions do not precisely obtain in practice. 392. Thirdly. It may be made to propel the body on a level against the resistance of axle and rolling friction. If the natural resistance to motion be 7 lbs. per ton, or 70 lbs. for the car, its accumulated energy of 321,600 foot- pounds will continue it in motion for a distance of ^li:^ ^ ^5^^ ^^^^ ^^^^^^ .^ comes to a state of rest. This "rolling friction," so called, of 7 or a pounds per ton of 2000 pounds is precisely equivalent in its mechanical effects to a grade rising 7 or a feet in 2000, or to the "grade of repose" before explained (par. 384). It follows, therefore, that any given grade other than a level is equivalent in Its mechanical effect upon the train, if it be an ascending grade, to the actual rate of grade plus the grade of repose; and if it be a descending grade, to the actual rate minus the grade of repose. 393. Fourthly. The accumulated energy of the car may be sooner exhausted by calling in the action of brakes in addition to the resistances of gravity and rolling friction. If there be brake-blocks on half the wheels only (which has until recently been the general custom for freight service), and the pressure on them be equal to the load on the wheel, which is somewhat more than that which the ordinary brake leverage is intended to give (modern experiments indicate that not more than two thirds of the load on the wheels is a safe pressure), and if the coefficient of friction between brake and wheel be \ which 's about an average (it varies in reality from i to i) then the retarding forces on the car will be— o , 20.000 Brakes, X i X i Normal rolling friction as above = Resistance of grade if on a level = = 1,667 lbs. 70 o << << Total resistances on a level = 1,737 lbs. or 173.7 lbs. per ir'H^ --"^^pfi- 344 CHAP. IX.— RISE AND FALL— EFFECT OF VELOCITY, ton of 2000 lbs. The car will, consequently, come to a state of rest on a level , . ,. , 321.600 ft. -lbs. „ , . . L 1 .- grade in a distance of -^ = 185 feet, supposing the brakes to be ^ 1737 lbs. instantly applied and with their full force, neither of which is very likely to be the case. If the car be on an ascending or descending grade instead of on a level the -|- or — resistance of the grade is to be included among the resistances. If the car stood on a descending grade of 173-7 2000 = 8.69 per cent, or 458 ft. per mile, it would continue in motion forever at the same velocity even with brakes set. This has repeatedly been proven practically on 8 and 10 per cent grades. If there were 10 cars in the train, moving at the velocity of 32.16 feet per second, and only one of them, as above, had brakes set, then we should have — Brake resistance, Rolling friction 70 X 10, 1,667 lbs. 700 " 3.216,000 ft. -lbs. Total resistances on a level. 2,367 lbs. = 1359 feet, as the distance in which the train would come and , ,. 2,367 lbs. to a state of rest.* 394. Fifthly. The accumulated energy of the car may be made to act con- jointly with the full power of the loco- motive to carry it over a particularly difficult gradient. If the full power of the locomotive is just sufficient to carry the car or train over any grade of a per cent, Figs. 65 to 67, the en- ergy of momentum will carry the car or train up a grade which rises in all 16.08 feet higher; whether that rise be by a uniform excess of rate, as in Fig. 65, or in a local excess at certain points, as in Figs. 66 and 67. In this case the office of the locomotive is simply to neutralize all grades and rolling resistances due to the a per cent grade. All extraneous forces thus neutralizing and destroying each other, the vis viva of the body lifts it through the additional rise of 16.08 feet, precisely as, and to the full extent that, theory requires; but if the power of the locomotive is completely used up on the a per Fig. 65. ♦ This calculation is not quite correct, because the wheels, in addition to their linear velocity in common with the remainder of the car, have an energy of rotation which adds some 6 per cent to the total vis viva of the car, as noted in par. 374 et seq. Nor should computations of this kind be ordinarily made as above, but by the *' velocity-heads" given in Table 118, which include the rotative energy of the wheels. CHAP. IX.— RISE AND FALL— EFFECT OF VELOCITY. 345 cent grade, the tram will come to a state of rest at the summit, which is 16.08 feet higher, m spite of the exertion of the full power of the locomotive and the aid of the stored energy jointly. Grades so operated are called momentum .GRADES. Fig. 67. 395. Sixthly. The accumulated energy in the car may. in theory, be made ofherTnd'T "r^:'''"" ^^^ ^^ ^°"^P^^^^ ^ ^P""^' ^"^ ^ P>^e. - ^o any other kind of work whatsoever capable of measurement in foot-pounds If \ spring required a force of xo.ooo pounds to compress it one inch and its resistance contmued uniform, then the energy of the car body would compress '^"^ ^P""^ 1^:;^- = 32. 16 inches. A perfectly elastic body, to which a spring approximates would immediately give back this energy to the car and repel it with equal velocity. A perfectly inelastic body, such as a bank of earth which required a pressure of 10.000 pounds to enable a body of the size of the car to penetrate It one inch, would (if the resistance continued uniform) be likewise penetrated 32.16 inches, and would not repel the bodv. The energy would be converted into heat. A pile which apposed astatic resistance to motion of 100,000 pounds would in theory be driven |^i^ = 3.21 feet, or 322 similar piles would be driven 0.01 feet, if the resistance to motion were uniform, which it is not. 396. A rod of iron of one square inch section, which would require a load of 26.000,000 pounds to extend it to double its length if its resistance to extension continued uniform.-i.e., whose modulus of elasticity was 26 000 000 -would sustain a force of only some 50.000 pounds without rupture,' and say 25.000 pounds without producing a permanent set. Therefore, if those effects are to be avoided, the stress on the rod must at no time exceed that limit- and "k""V /u^ ^^' '' '° ^^ "'"'PP^'^ ^y '^^ '■°^' 321.600 foot-pounds are to be absorbed by reaction against a force beginning at zero (since the slightest force will extend the bar somewhat) and gradually increasing to 50.000 or 25 000 pounds respectively, we have » ^ » a. 321.600 ^ ^ , -— = 128.64 feet 50,000 -*- 2 ^ as the length which the rod would have to stretch to avoid the rupture, and 321.600 25,000 -i- 2 = 257.28 feet % i ':\ ii 1l 346 CHAP. IX.--RISE AND FALL-EFFECT OF VELOCITY. as the length which the rod would have to stretch to avoid exceeding the elastic limit. But (assuming uniformity of elasticity) the rod can only stretch in any case the -i°°^ part of its length (— ^\ without rupture, and only half that 26,000,000 \i,3oo/ without permanent set. Therefore, to avoid these efifects and yet enable the bar to do (or use up) the requisite amount of work in slopping the car, it would have to be 128.64 X 1300 = 167,232 ft. long to avoid the rupture, and 257.28 X 2600 = 668,928 ft. long to avoid permanent set;— which are rather long bars. The consequences to the car body also we will not consider, but the example will serve to illustrate the laws of the mutual converti- bility of energy or work, and velocity. 397. From this ready interconvertibility of velocity and work results the undoubted fact — too little considered by engineers — that train resistance, in practical operation (i.e., as measured by the tension on the draw-bar of the locomotive, or graphically recorded by a dynamometer) bears no very close and apparent relationship to what may be called the dead resistance, as deter- mined by adding the nominal grade resistance to a certain rolling friction, without paying any regard to the effect of differences of velocity. This is well understood by all those who have had occasion to deal with dynamometer experiments, and is the greatest difficulty in deducing valuable results from such experiments. It is also well understood in a practical way by locomotive engineers, who appreciate the great advantage of a " run at a hill " and the disadvantage of a stop on it. 398. Now the object before the engineer in laying out a rail- way is, obviously, to lay out his line so that the demand on THE LOCOMOTIVE, and not the absolute grade resistance (which latter is in itself a thing of no moment), shall be as nearly uni- form as possible, under the conditions which actually exist in the daily routine of operation. If, at a certain point, the veloc- ity of the trains has certainly to be increased, in addition to overcoming the normal grade and rolling resistances, the gradi- ent is in effect increased at that point. If at a certain other point velocity can safely be acquired before reaching it and then CHAP, IX.— RISE AND FALL— EFFECT OF VELOCITY. 347 surrendered, the grades are in effect reduced. The virtuaT^ equivalent profile, including these effects of velocity, is what the engineer should study, and should consider as the true profile of the line for operating purposes, as distinguished from the nominal grades shown by the levels and the plotted profiles 399. The two are widely different even in freight service, and much more so in passenger service. Thus, when a train starts out from a station it has to acquire a certain velocity as speedily as possible-say 15, 20, or 40 miles per hour; giving which velocity is mechanically equivalent to lifting the train vertkally (see Table 118) 7.99, 14.20, or 56.80 feet. This rise, divided by the distance in which the velocity is or must be at- tained, gives a grade which is in effect an addition to the actual grade. Thus, if there be a station at A, Fig. 6%^ on a nominally level grade, and it be necessary to acquire a velocity of 21 3 miles per hour (being nearly the "velocity-head," as per lable 118, for 16.08 feet), and it be necessary to acquire that velocity in at most 2000 feet, the "virtual" grade is that shown by the solid line in Fig. (>^, or ^? = .804 per cent. _ . 20 *^ If the train then strikes a down grade, no change in the strain upon the draw-bar necessarily takes place, nor probably will take place, if the grade be short or the speed high. More probably, the same steam-power and ten- sion on the draw-bar will be contin- A uously exerted, and the excess of power over that consumed by the resistances will be stored up in the train as velocity, to be surrendered in part on the next up grade; and so on indefi- nitely. In fast passenger service, with a sufficiently good track and alignment to admit of high speed, the amount of energy required to cause even slight modifications of speed between stations is so great that the effect of undulations of gradients, even of con- siderable size, is almost wholly eliminated. Fig. 68. 348 I I /I I I I 2 S/g $ § 8 \i CHAP. IX.— RISE AND FALL. 400. Thus, Fig. 69 is an ex- ample from actual practice of a very bad undulatory profile (for freight service), which not only may be, but actually is, operated by express passenger trains almost as a level grade. To determine in practice how velocity affects the operation of this or any other similar profile is a problem of the simplest possible character. We require nothing to aid us but Table 118. Thus, let us suppose that an express passenger train approaches the point A, Fig. 69, as it actually does, at a velocity of about 50 miles per hour, the point being situated at the foot of a long gen- tle incline. This velocity being given, in order to run without a stop to the point B, a distance of about eleven miles, no further burden is laid upon the locomo- tive than to furnish the power which is necessary to keep the train moving on the " equivalent" maximum grade, which in this case is a dead level, despite the fact that the profile maximum is I per cent or 52.8 ft. per mile. The process of determming in advance whether it will be possi- ble to operate this undulating grade as a level gradient in this manner, and what the fluctuations of velocity must be to do it, is as follows: 401. The train at the point A, moving (by assumption) at 50 miles per hour, has sufficient vis CHAP. IX— RISE AND FALL— EFFECT OF VELOCITY. 349 viva or "velocity-head" (Table 118) to lift it through 88.75 ^^et verti- cally before coming to a state of rest. In running to b, it makes a rise of 130—80 = 50 feet, and if the engine is to do only the work due to a level grade all the work of lifting the train through this 50 feet must be done from the energy stored as velocity, and there will consequently be left in the train, on reaching b, only 88.75 — 50 = 38.75 vertical feet of " head," which corresponds (Table 1 18) to 33 + miles per hour. The par- ticular grade, and hence the horizontal distance, between A and b makes no difference, because the engine, if it is to operate the grade as a level, furnishes the power to overcome the frictional resistances on a level, and no more; and these alone are affected by the horizontal distances. From b X.O c the train descends 30 feet. Therefore, the engine being supposed to continuously exert the same amount of force to overcome the frictional resistances, all the additional accelerating force due to the descending grade will be communicated to the train in the form of ve- locity, and at the foot of the grade, at c, the train will be moving with the velocity due to 38.75 + 30= 68.75 vertical feet, which (Table 118) is 44 miles per hour. From c \.o d there is a vertical rise of 20 feet, and consequently the train will be moving at d at the speed due to 68.75 — 20 = 48.75 feet, or (Table 118) 37 + miles per hour. 402. So the undulations of speed continue, as shown by figures and the dotted diagram, until on reaching the points, which is neither higher nor lower than the initial point A, the train is found to be moving with the same velocity as at a, or 50 miles per hour. Whether this will be the case at any point we can determine at once, without tracing up the inter- mediate velocities, simply from its relative level compared with A. Thus, the highest point on the stretch is at elevation 140, or 60 feet above A. The train here, consequently, will have only the velocity due to 88. 75 — 60 = 28.75 vertical feet, or nearly 28^ miles per hour. The lowest point is the point n, which is 70 feet below A, and the velocity at that point will consequently be that due to 88.75 + 7° = 158.75 vertical feet, or 66.9 miles per hour. 403. Now if we had a dynamometer record of the tension on the draw-bar during such a run as this (which the writer has made many times over that identical piece of track at approximately the assumed ve- locities) we should find it absolutely uniform and unvarying, without any appreciable trace or evidence in the recorded strains that there were any undulations in grade or deviations from a perfect level on the stretch passed over. If we were to stand and watch any coupling of the train I 350 CHAP. IX.^RISE AND FALL-EFFECT OF VELOCITY. we should be led to the same conclusion. Assuming the vertical curves connecting the grades to have been properly put in. there would be no '•slack" at any time, nor crowding of one car upon another; but. on the contrary, there would be a continuous and substantially uniform tension on ever'y'draw-bar, whether going up hill or down, and the motion of the train would be as steady as if the grade were in fact level, as to all intents and purposes it is— AT THAT VELOCITY. At slower velocities, or with intervening stops, or with very high summits, the conditions are widely different. 404. To determine the effect of all these and similar facts in advance for any piece of track and any assumed speeds, we have only to construct, with the assistance of Table ii8. what may be termed the equivalent or VIRTUAL PROFILE, which is the actual profile so modified as to include these effects of probable or admissible variations of velocity. Thus at A, Piforra and unvarymg, wharever the variation of grade, the change in resistance taking the form Ifincreased or decreased velocity. The only time when the tension on 1 driw bar is not absolutely fixed and unvarying is in pass.ng from one grade to another, and this occurs as follows : ,„„,:nnouslY 415 As the enc'ine passes over station loo, Fig. 74- contmuously exen'g the same steam'power. the change in the rate of grade (rom + 2 to - 0.2) makes a difference of 8 lbs. per net ton of >ts weight, or iv 8x62 5 = oo lbs. in all, in its pull on the draw-bar, thus increasing ^ pull on the rain for the moment from i6.<»o to .6 500 lbs., or about fir cent. This increased traction will immediately begm to make he tr^n r^ove faster, and as some of it must be absorbed •" "'^'king the eng?ne"tself move faster, not all of it will be transmitted backward to ^'''me" seconds afterwards, two other cars will have Pas^^^o-r sta- tion .00 and will increase the traction on the drawbars behind them by sLme ~o lbs. more. This increase of tractive force, likewise, having no ZTa resistance to use it up. will take the form of an increase in velocity. So ^tch car in succe^ion passes over the break of grade the acul^ CHAP. IX.— RISE AND FALL— SAFE LIMITS OF, 357 ^erattng force gradually increases from zero (as the engine approaches station 100) to 8 lbs. per ton of weight of the whole train, when the entire train has finally passed over the apex. 416. The instant that this occurs the tension on the draw-bars will be precisely the same as before throughout, viz., that due to the work of the engine only, and will be employed in the same manner — in overcoming the normal train resistance on a grade of + 0.2 at the original velocity ; while the extra accelerating force from the change of grade will be act- ing upon the train independently to communicate velocity, precisely as if it were descending the same plane without resistance and with no Other force acting. The final velocity at stations 125 and 140 will be precisely the same as if it had fallen freely through a height equal to — not the actual differ- ence of level between 100 and 140 — but through a vertical height equal to the drop in the actual— 0.2 grade from the dotted +0.2 grade, on which, by assumption, the locomotive was exerting just enough power to keep the train moving at 15 miles per hour. What will be the velocity of motion, then, at 125 ? Computing it as before, we have — The original velocity of 15 miles per hour is equivalent to a fall through space of (see Table 118) 7.99 feet. The dip in the grade is 10.00 " Hence the train at 125 will have the velocity " due" to a free fall of 17.99 " which by Table 118 will be 22.5 miles per hour. This is an entirely safe and unobjectionable velocity. At station 140 the "dip" is 16 feet instead of lo.o feet, and the velocity acquired is 16.0 + 7.99 = 23.99 vert, feet = a velocity of 26.0 miles per hour, which may be claimed to approach the utmost limit of expediency for freight service. Had the dip been 20 feet, the velocity acquired would have been about 28.1 miles per hour. A dip of 20 feet may therefore be considered about the maximum which it is permissible to ride over in freio-ht ser- vice without shutting off steam, on good track and with favorable alignment. 417. These velocities would actually be somewhat less than the fig- ures given, owing to the fact (i) that the centre of gravity of the train does not rise quite as high or fall quite as low as the highest or lowest point of the track, and (2) that the resistance of the train in- III 358 CHAP, IX.-RISE AND FALL^SAFE LIMITS OF, creases with the velocity (see Table 120 and Chap. XIII.), whereas we have assumed it to be constant; but as the difference is of no great moment in the details we are now considering, and as the neglect of it tends to safety, it is not here considered. Table 120. Approximate Grades of Repose for Various Trains (as Determined in Table 166). See also Table 180. Approximate General Average. Velocity. Miles Per Hour. ID. 20. 40 50. 60. 70. Freight Trains Of- Twenty Cars. 0.30 0.36 0.46 0.5S 0.73 1. 10 Fifty Cars. 0.28 0.33 0.40 0.48 0.59 0.90 Passenger Trains OF — Four Cars. 0.34 0.40 0.52 0.69 0.88 1.38 2.02 2.81 3.74 Twelve Cars. 27 34 42 53 65 98 39 1.89 2.49 o o o o o o I Grade Per Cent. 0.30 0.35 0.40 0.50 0.65 1. 00 1.50 2.25 3.00 Feet Per Mile. 16.84 19.48 21.12 26.40 36.32 52.80 79.20 118.80 168.40 The resistance in pounds per ton is given by multiplying the above by 20. 418. Now, what takes place in the hollow at 140, when the engine be- gins to ascend ? Here, if anywhere, is the point of danger, and here is in fact a very great danger, the precise nature and limits of which should be determined. The danger arises from the fact that in the hollow of a grade where the head of the train is on an up grade and the rear of the train on a down grade, there is liable to be a momentary crowdmg to- gether of the train. This liability occurs only when the head and rear of the tram are on different grades. We have just seen (pars. 41 5. 4i6) that when the whole train is on the same grade, however great its rate of ascent or descent, the tension on the draw-bars will remain the same, being that arising from the traction of the locomotive, and the additional energy communicated to or taken from the train by the grade will take the form of an increase or decrease of velocity, which is uniform throughout the tram because the grade is uniform. . 419. In the hollow of a grade this is not so. and hence arises the tendency for the rear of the train to run up against the front when pass- ing such points under certain conditions, taking all the " slack" out of CHAP. IX.— RISE AND FALL—SAFE LIMITS OF. 359 the train and bringing the draw-bars into more or less compression. The next instant, when the hollow is passed and the uniform grade (whatever it may be) is struck, the normal condition of tension throughout the train returns, but returns with a jerk; for with the present awkward style of couplings the difference in length of a train in tension or compression is very considerable. The " slack" varies from 4 to 6 inches or more per car, according to the degree of force with which the springs are compressed and extended, so that a train of 60 or 80 empty cars may shorten as much as 30 to 40 ft. The jerk, when this slack is "taken out," is exceedingly apt to break the train in two, and it is at such hollows in grades that most of such breakages occur. 420. The reality of the danger may be illustrated by a literally truthful anecdote : In the old days of iron rails, some thirty-five years ago, when derailments were much more frequent and more easily caused than now, a certain especially poor road was having very frequent derailments, so that each conductor was having derailments every few days. One of the older conductors was singularly exempt from such accidents, for which no reason appeared. In answer to repeated questions, he at last confessed that he "always kept his caboose brake set up a little." This was con- trary to orders, but it had the practical effect of keeping the draw-bars always in tension, and at the cost of a slight waste of power prevented the more serious danger. Such crowding together is dangerous, not only for the quick jerk which must almost inevitably follow it. but because it tends to crowd the cars out sidewise against one or the other rail, and so produce irregularity of motion, causing the wheels to hunt, as it were, even more zealously than they ordinarily do. for the first defect by which they may escape from the track. Especially on curves this is very dangerous. 421. The philosophy of trains breaking in two is simply this : At the top of the grade the steam is partially shut off and the brakes put on slightly ; but before reaching the foot of the grade the brakes are almost always let off, and the train strikes the foot of the ascent " full of slack." A careful engineman will then let on steam gently, and all will be well. The more careless will " pull out" with a jerk, and. if he be careless enough, he will be almost certain to break a link or pull out a draw-head, for such parts can hardly be made strong enough (at least in the present fashion) to resist a too sudden exertion of the power of the engine. To a great extent the number of such accidents is en- tirely in the hands of the engineer. It has not unfrequently happened that, when the employes were annoyed by an increase of train or other cause, the feeling of annoyance has taken the form of a jerky fashion of pulling out the throttle, which has resulted in an alarming increase in such accidents and ter- 360 CHAP, IX.— RISE AND FALL— SAFE LIMITS OF. rifled a doubling or inexperienced superintendent. So, too, the introduction of heavier engines has had and will almost certainly have dangerous consequences, — for a time, — partly because the enginemen are really inexperienced in hand- ling such powerful machines and partly from a secret willingness to throw dis- credit upon them. 422. We will consider the mechanical reasons why a very slight set- ting up of brakes on a rear car should reduce these dangers, and how — as that remedy is objectionable as a regular reliance — it also can be safely dispensed with in passing sags. A train of cars coupled together may be considered as, mechanically, a single solid body. All solid bodies have m ore or less elasticity, and alter their dimensions under exterior force applied to certain parts only. A train has more than usual longitudinal elasticity: that is all. The motion of such a body, as respects the action of gravity, is the same as if its mass were concentrated at its centre of gravity. 423. The centre of gravity of such a train does not descend into the apex of the hollow in Fig. 74 or 75 (assuming such sharp intersections of L«vet. Fig. 75. grade to exist in practice), although each individual car does. Its path lies— for simple geometrical reasons which the student may be assumed either to understand or to take for granted— at a uniform distance above a circular arc or parabola (according to the assumptions made) tangent to the two grades at the points e.g., one half train-length from the apex. In Fig. 75 we assume, as the simplest case, that a level grade intersects an 0.6 per cent ascent, instead of a — 0.2 and + 0.4 grade in Fig. 74- The results we shall reach are not essentially varied, whatever the rates of the separate grades, if their angle of intersection is the same. Let us assume for the moment the train in Fig. 75 ^o be exerting within itself just energy enough to balance its own resistances, so that it is in the theoretical condition of a body moving in vacuo without either CHAP. IX.— RISE AND FALL— SAFE LIMITS OF. 361 gaining or losing velocity, and moving at, say, 26 miles per hour, equal to a " velocity-head " (Table 118) of 23.99 leet. For simplicity we will assume the train to be 1200 feet long and to weigh uniformly one ton per foot, and we will assume it to consist of only 8, 12, or more very long cars instead of some 40, as it probably would. 424. Under these conditions, when the train has reached the position mdicated by the black line OC in Fig. 76, with the rear car just past the apex O, its centre of gravity B will be precisely 6.00 x 0.6 = 3.6 feet higher than at A, and the train as a whole will have surrendered an amount of ^energy and of velocity corresponding to that height. The centre of H2e.o J L Leve/. Fig. 76. •^avity will have moved in the arc AOB, and the velocity with which the tram as a whole is moving at any point Oor ^ is given with absolute precision by substracting the ordinates to the curve from the base-line AA from the mitial " velocity head," as is done in Fig. 76. At B the velocity will be only 24.0 miles per hour. With the train in this position, each car considered separately would have surrendered the energy and velocity represented by the successively dimmishmg ordmates aa\ and if the train were, as assumed, a body movmg through space from original impulse without resistance or com- municated force, the inevitable effect of such conditions would be to pro- duce a uniform compression throughout the body at all the points aa' (each rear particle pressing against that in front of it) whenever the path of the body were deflected upward, however slightly. 425. But the train, although as a whole it is in the condition stated, yet internally to itself is in very different condition. A 'strong acceler- atmg force fthe engine) is acting in front at C; a strong retarding force (say 10 lbs. per ton) throughout the rear of the body. The two counter- act and destroy each other, their net resultant being zero ; but in so doing they produce, or tend to produce, a state ot tension throughout the train. 362 CHAP, IX.-^RISE AND FALL—SAFE LIMITS OF. What is required is, not that this tension shall not be reduced m passing changes of grade, but that it shall not be exchanged in any part of the train (or only in a very small part) for a state of compression. A train may be, as respects its couplings, in three conditions : 1. In tension, its normal condition, which, whether greater or less, will only extend the springs a little more or less, but make no material differ- ence in the whole length of the train. 2. In neither tension nor compression, the two adjacent cars tending for the moment to move with the same velocity, so that no force of any kind is communicated from one to the other. This condition can only be momentary. 3. In compression, the cars behind crowding upon those in front. In the transition from the first to this last condition lies the whole danger. So long as we do not pass the second (which is more properly merely a line of demarcation between the first and third) we are safe. 426. This we shall avoid if the rear car (or cars), where the tension is least, nowhere itself tends to move faster than the train as a whole is moving at the same moment, during the period of transition from one grade to another. Figs. 75, 76, or 78. The rear car, when travelling on a grade of any rate, as a, b, or c, Fig. yy, has a certain frictional resistance which will make it of itself, without exterior assistance, surrender veloc- ity as if it were moving on the dot- ted grade without friction, instead of Fig. 77. on the actual grade with friction. The difference between the dotted and actual grade is the so-called " grade of repose," marked^ in Fig. 78. By even a slight application of brakes this grade of repose may be very greatly increased. Since the train as a whole, then, is moving, mechanically, without friction, and surrendering velocity at the same rate as if its mass were concentrated at its centre of gravity and moving in the path thereof {A B, Figs. 76 and 78), at = Gr&cfe of Repose of/ctst Can^f ^ T c^. '■ Fig. 78. each point in the passage from A to B the tram as a whole is surrender- ing velocity at the rate due to the grade on which the centre of gravity is for the moment moving m its path AB. The steepest point on this curve is at the tangent point B, at which same CHAP. IX.— RISE AND FALL— SAFE LIMITS OF. 363 instant the rear car of the train itself strikes the up grade at 6^, and en- counters the same retarding resistance as the rest of the train, so that the danger of its crowding up on it is then past. 427. By comparison of the conditions just stated for the last car and the whole train we deduce this simple rule : To OBVIATE ALL DANGER OF THE REAR PORTION OF THE TRAIN CROWDING UPON THE CARS IN FRONT, WITHOUT THE USE OF BRAKES, AT ANY SAG IN A GRADE LINE: The rate of the grade on which the head of the train stands must in no case exceed that on which the rear of the train stands by more than the "grade of repose" of the last car. Otherwise the latter will crowd up upon the train. 428. The grade of repose may be increased for the time being above the normal (i) by applying brakes, and (2) by the engineman " pulling out "or beginning to exert more force upon the train at or quite near to the apex O. In the latter case, until the train has acquired a velocity corresponding to the new tractive force, the "grade of repose" of the rear car, or its resistance to moving with the train, will be considerably greater. The first of these remedies is objectionable as a regular reliance, and the second is too uncertain. Therefore the rule above may be considered one which it is desirable to adhere to strictly whenever possible. 429. Since the conclusions reached above depend on the differ- ences in the rate of grade (see Figs. yy and 78), it is obvious that they ap- ply alike to all hollows in grade lines, whether both be ascending, both de- Fig. 79. scending, or one descending and one ascending. To see this more clearly (which should be almost self-evident), tip Fig. 78 in various directions so as to correspond to all the conditions of practice. It will be obvious that although the changes in the absolute velocity of the train and every part of it will be greatly modified, yet that the relation of the motion of the rear car to the whole train will not be modified. 430. We see in what has preceded the urgent reasons why the use of long and easy vertical curves in the hollows of grade lines should never be neglected. The conditions are entirely different in a salient or rising angle in a grade-line like Fig. 79 and in a hollow like Fig. 80. In passing over the former there is only a Fig. 80, 3^4 CHAP. IX.^RISE AND FALL— SAFE LIMITS OF, CHAP. IX.— RISE AND FALL^SAFE LIMITS OF. 36s momentary increase in the normal tension. If too sudden, this is objectionable, so that vertical curves should be used in all cases; but it is the reversal of strain in a hollow which is par- ticularly objectionable, and for them the rule — The cnange in rate of grade in a train-length should never exceed the grade of repose of the last car — should be strictly adhered to when the cost of doing so is not too great. 431. From this it follows that the longer the train and the lower the grade of repose the easier should be the vertical curve, and vice versa. As the grade of repose increases with the velocity, it is evident that short trains at high speed, like passenger trains, are in little danger of any such effect, and that to obviate it altogether the longest possible train and the lowest possible resistance for the last car or cars should be assumed. The lowest probable resistance for the rear of the train at any such point is about 6 lbs. per ton. Dynamometer tests of freight trains show, indeed, average resistances of 3^ to 4 lbs. in frequent instances, but the speed is likely to be high at the particular localities in question, and there is, moreover, a certain atmospheric resistance from suction at the rear of the train (which may be estimated, by analogy, from experiments on a small scale, at about half as much per square foot as that at the head of the train) which will increase the resistance of the rear cars somewhat above the rest of the train. Curve resistance, if uncompen- sated (and still more when compensated, in descending a grade), may affect the question either way, according to its location. Grade resist- ance, as we have seen, does not in itself affect the question in the slight- est. The difference between the grades at the rear and head of the train alone concerns us. 432. The utmost length of train will depend on the ruling grade of the road. An empty-car train will have about twice the length of a loaded train ; but empty-car trains are unusual, their rolling friction is higher, and the phenomenon is not so objectionable that it may not in occasional instances be permitted, especially as it can be avoided by brakes, or " pulling out," if desired. A 35- or 40-car train will be, say, 1200 ft. long, and this may not unreasonably be taken as an average maxi- mum. On heavy-grade lines a shorter assumed length of train may suf- fice, and on low-grade lines the trains may be much longer. 433. Assuming 1200 ft. (12 stations) length of train, and 6 lbs. per ton (0.3 grade) for the resistance of the rear car or cars, we have the rule — Vertical curves in sags should be 400 ft. long, or 200 ft. on each side I \ 200 \ of the vertex \ J , for each tenth in change of rate of grade, making the change in rate of grade per station not over 0.025 per station, if ALL POSSIBILITY of bringing the draw-bars of any part of the train into cotn- pression while passing over it is to be avoided. With half this length of curve, which is considerably more than is usual in laying out vertical curves, all danger of " taking out the slack " in the front half of the train, where there is most danger of breaking in two, will be avoided. 434. A short and simple method of putting in vertical curves is given at the close of this chapter. The omission of such curves, and the neglect to make them long enough when used at all, is one of the most prevalent and unfortu- nate of the minor errors of location, for it often converts a sag which would otherwise be almost innocuous into a serious disadvantage. The bad results in such a case will very naturally be ascribed to the sag itself instead of to the bad manner of putting in the sag ; and in this way a prejudice even greater than the facts justify exists against such breaks of grade. With proper care they may be used harmlessly with some freedom, especially as it is nearly always possible to take them out in part or whole at any time when circumstan- ces seem to require and permit, by increasing the height of the fills or grading a new line. In this manner, in fact, it is often possible to provide for eventually securing better line and grades than it would otherwise be possible to obtain. So soon as an automatic close coupler shall be adopted, eliminating all loose slack from the train (and it is now clear, for reasons given in Chapter XII., that such a coupler is the only proper form to adopt), much of the impor- tance of connecting breaks of grade by extremely easy vertical curves will disappear. It is hardly safe, however, to count upon any speedy and gen- eral action in that direction. 435. Let it therefore be repeated, that so long as (i) it is not neces- sary to alter in any way the steam-power of the engine to avoid too high speed, and (2) so long as the transition from one grade to another is ex- tremely gentle and gradual, such breaks are a matter of the most trifling moment. But to this rule there are some exceptions. Thus, a sag of 10 or 15 feet might be entirely innocuous on a long tangent between sta- tions, yet at some other point on the line, where the profile is precisely the same, it might be a serious and even dangerous evil. A sharp curve at the bottom of the sag might necessitate a very low speed there, or a heavy grade near at hand make high speed desirable. A station, or a siding, or crossing, or water-tank may in the future, if not at present,, necessitate a stop there. In any such case the sag would at once change its character from a harmless economy to a serious and costly error, if it be for any reason a permanency. If, on the other hand, it can be taken f fl it 366 CHAP. IX.— RISE AND FALL— LIMITS OF CLASSES. \v-\ Fig. 8z. leve/_. --5J Fig. 83. out at any time by simply filling up the hollow, of course far greater boldness may be used. 436. It will be obvious, furthermore, that the effect and disadvan- tages of such sags are, other things being equal, the same, whatever the rate of the grade on which the ^ sag occurs. Thus in Fig. 81 there is, literally speaking, no rise and fall at all, because it is i con- tinuous up grade ; yet if the loco- motive be ascending this grade, and exerting just power enough to maintain a uniform velocity, the effect of the mere break of grade is precisely the same as the actual sag and rise and fall in Fig. 82. In each case, if the train be moving at a uniform velocity of 12 or 15 or 20 miles per hour (= velo- city-head, by Table 118, of 5.1 1, 7-99. and 14.20 ft.), the sag will increase the velocity- head by 4.0 ft., to 9.1 1, 11.99, and 18.20 ft., and the velocity in the bottom of the hollow (neglecting the fact, as heretofore, that the centre of gravity of the train does not rise quite so high nor fall quite so low as the angles of the grade) will be increased to 16.0, 18.4, and 22.6 miles per hour. After passing the bottom of the hollow the train begins to lose velocity, and on again reaching the main grade is moving at the same velocity as when it left it. 437. The above makes clear that it is a fallacy to count up the num- ber of feet of rise and fall merely from the ups and downs as shown by the differences of elevation of the profile, as one of the criterions of the excellence of a line. Ordinarily this may not prove very deceptive but the true comparative importance to be ascribed to rise and fall, and hence the limits of the three classes of rise and fall. A, B. and C, as sum- marized in par. 367, and again in par. 451, must be determined in a dif- ferent way. LIMITS OF THE CLASSES OF RISE AND FALL. 438. Limits of Class A. (The least objectionable class.)— The nor- mal freight speed may be assumed to be 15 miles per hour, but in certain locations it is not likely to be more than 10 miles per hour, and in other locations it may usually and naturally be as high as 20 miles per hour. Assuming a train to be approaching a sag in any grade line at these rates CHAP. IX.-RISE AND FALL-LIMITS OF CLASSES. 367 •of speed, we have in Table 121 the maximum velocity which sags of vari- ous depths will give to the train. Table 121. Effect of Sags of Various Depths below a Continuous Grade-Line AND having the ForM OF EITHER FiG. 8l OR FiG. 82 TO MODIFY THE Speed of Trai.ns. (Computed by the aid of Table 118, as explained in par. 400 ./ seg.) Greatest Dkpth of Sag in Feet. None. . . . 5 10 15 20 25 30 Vel.-Head in Train at Lowest Point of Sag for Speeds of Approach IN Miles Per Hour of— 10 3-55 8.55 13-55 18.55 23-55 28.55 33-55 15 7-99 12.99 17.99 22.99 27.99 32.99 37-99 20 14.20 19.20 24.20 29.20 34.20 39- 20 44.20 Maximum Speed in Botiom of Sag for Speed of Approach in Miles Per Hour of— 10 10. 15-5 19-5 22.9 25.8 28.3 30.8 15 15- 19. 1 22.5 25.4 28. T 30.5 32.7 20 20. 23.2 26.1 28.7 31 o 33-2 35-3 This table assumes that the train is approaching at a uniform speed, and that the locomotive continues to exert the same uniform power in passing the sag. The oridnaJ velocity will then be resumed after passing it. v }. ^>^. i ne original If there is an excess of accelerating or retarding force in approaching the sag both the speed in the bottom of the sag and the speed after passing it will L correspondin^v higher or lower than the speed of approach, but the table will not be essentiluy ZdifiS! The manner of computing Table I271h^ be care^T^uidied^It will be seen how little the speed of approach affects the resulting speed at the bottom of a sag in grade-Iine of any considerable depth Twice the speed of approach. 20 miles per hour instead of 10, increases the speed in the hollow only some 15 per cent, or 4i miles per hour. It will also be seen how comparatively slight is the effect of increased depth of sag. A lo-ft. sag increases 10 miles per hour to 20, but it takes 20 ft. more, or a 30 ft. sag in all, to increase the 20 miles per hour to 30 At a speed of approach of 20 miles per hour a lo-ft. sag increases the speed 6.1 miles per hour ; the next 10 ft. (20 ft. in all) only 4.9 miles per hour, and the next 10 ft. only 4.3 miles per hour. ^h^xJm^'^^^' likewise shows in part (for fuller explanation see Chap. XVIII.) why a very slight break upwards from a long continuous grade-hne .s so very much more injurious than even a considerable droo below It. Sags even of 30 ft. will not produce an absolutely dangerous speed, but a rise of even 3i ft. above a grade- line will bring a train mov- ~1 68 CHAP, IX.— RISE AND FALL— LIMITS OF CLASSES. ing at lo miles per hour to a stop, or a train moving at 15 miles per hour to a speed of 1 1.2 miles per hour. 440. The highest freight-train speed which can be regarded as reasonably safe and practical at favorable points is about 30 miles, per hour. Such speeds are ordinarily far less objectionable on long straight grades than on undulating grades, for the reason that the true objection to high freight speeds (within reason) is not the speed itself, but abrupt alterations of speed. With long and easy vertical curves (usually want- ing), and with breaks of grade so designed that their depth will not give a dangerous maximum speed if they are operated as virtual continuous grades, by making no change in the work done by the locomotive but permitting its excess of work to take the form of velocity, speeds of 30. miles per hour for the moment only on good alignment cannot be con- sidered as in the least objectionable, and are very common in present practice, and likely to become more so. (See par. 444.) If we assume 30 miles per hour as a maximum speed at certain favor- ably situated points where considerable speed is desirable, it results (see Table 121) that sags of 20 or even 30 ft. from a grade-line, according to- the speed of approach, may be operated as a virtual continuous grade. 441. We therefore conclude that, as a general rule, but with a number of modifying special conditions, a sag of not exceeding 20 ft. in vertical depth from the main grade-line, if eased off by a long and easy vertical curve in the hollow, will not require any slacking up or variation in steam-power, and that, if it does not, it is entirely innocuous, except for the greater wear and tear which may result from the higher speed. That ex- pense we will estimate in par. 452 et seq. 442. If the sag be deeper than 20 ft,, and sometimes if it be consider- ably less than 20 ft., we have a more objectionable class of rise and fall (Class B, pars. 367 and 451). It will then be necessary either to put on brakes (which is really the best practice) or to merely shut off steam and " pull out" again at the foot of the grade, which is the too common prac- tice. It is in this latter kind of sags, especially if they have no adequate apology for a vertical curve, that most of the draw-heads are pulled out and trains broken in two, in the way explained in par. 418-421. In part this is avoidable by care in running. Nevertheless, with the greatest practicable care, it is not possible to prevent frequent serious jerks to trains in sags of considerable depth, which will sometimes break tben> CHAP. IX. -RISE AND FALL-LIMITS OF CLASSES. 36^ in two. Such sags, therefore, become more and more objectionable as V:r^:Z^Tt' 7w ^^^'^" '' '' "^^ "^^^-^^^ - use^ny brats 443. ^^^ Po^nt at wh^ch zt certamfy becomes necessary to ajp/y braJ^es accel^Sforcl'r' '"^^.^"---^P-^^' -., the grades on which the acceleratmg force of gravity just suffices of itself to keep the train in either gam 01 loss of velocity, are about as given in Table 120. page 358 par o 'tt7 T ''''^^ "°' '''' '' ''' ^^"^'^^'^^^ ^-^^ -f speed^l'fny part of the line be given, any grade, however long, on a rate not exceel ^n^l^egracie of repose for that speed, may be of indefinite leng" wilho^ ever requiring the use of brakes, because all that is necessary is to shut ing the grade, will of itself either acquire or lose velocity until it attains Fig. 83. The dotted line shows the virtual gjade-line of a c^ , iSiTv" whl"h^ ^'■'"5 ''^f ^"^P °^ ^^^ ^'" ^ith a small ve- i^i^Jth ^f^"^"y increases until it becomes as On tl . ^u ''^il''^L'''" "^ ^'■^^'ty 's able to maintain, ^nd .hi oT*" .^i "-^^ ^^^ ^"^ resistance are small T-- next^sttclThtrelisreTst^t^'t!^^^^ ^^^ Ifl" - -^ocity. On the cess of acceleration. So wkh the nex? stretcS but J t h'/P^^"^; ^"' "^^'^ '^ ^'"^ ^° ^^- higherwitheachincreaseofvelo^itvthei npi'c o -I 'esistance grows higher and and acceleration bala^S eaL'Kf Is 'g?ven^^^^^ ^ ^^'"^ "'^^^ ^^^ --^^--e reslsIalTJ'" ^V^'^V'' -f erating force precisely balances the rolling tra n sneH ^^'^^^^^^ ^'" ^^ «^^" ^« ^^ ^^ry high for fast passenger train speeds, so that there can rarely or never be necessity for the use of brakes on descending grades of less than i per cent (52.8 a. per mile) in ordinary passenger service, merely to avoid excessive speed due to the orntd"h \^'^""^^"^^- U^-'^y- h— -. heavy gradi^its are accom! panied by heavy curvature, which latter will often necessitate on long grades a rate of speed but little higher than the freight maximum. ^ 444. The customary speed in freight service shows a steady tendency to increase at points where velocity is of assistance in hauling heavy trams. It is of course greatly affected by the character of the line as to 24 370 CHAP, IX.— RISE AND FALL— LIMITS OF CLASSES. CHAP. IX.— RISE AND FALL— LIMITS OF CLASSES. 371 .5 ■ *! r. i I curvature, but the idea formerly prevalent that the most economical speed for freight trains is a very slow one has been pretty thoroughly ex- ploded, both by theory, practice, and experiment. Experiments by Mr. P. H. Dudley on the Lake Shore & Michigan Southern Railway have shown directly that " with long and heavy freight trains it required less fuel with the same engine to run trains at 18 to 20 miles per hour than at 10 to 12 miles per hour." * This result— as to the substantial correctness of which there is little room for doubt— is not due to the actual resist- ances to motion being any lower, or as low, at the higher speed, but to the joint action of the following causes : 1. To the saving of power at undulations of grades, in the manner heretofore discussed in this chapter, the extra velocity serving as a reser- voir of power and so preventing waste thereof. 2. To the less time of exposure of the locomotive to radiation— a sav- ing, in all probability, of very great importance. (See pars. 344 e/ al.) 3. To the less time for radiation from the interior surface of a cylin- der into the exhaust steam ; also a very important source of loss. On the other hand, evidence presented in Chapter XIII. makes it at least doubtful if the resistance is more than a pound or two per ton greater. 445. Whatever may be the cause, the expediency and economy of m- creasing freight-train speeds, on fair alignment, up to 20 and even (at points) 30 miles per hour is very generally recognized and acted on by the more prominent managing officers. This tendency will probably be greatly strengthened in the near future by (i) the general adoption of some form of freight-train brake and of a more durable and stronger coupler, and by (2) the increase in average car-load and consequent de- crease in number of freight cars per train, with the natural attendant in- crease of care in the construction of freight cars. On lines using the "speed gauge" the usual maximum speed specified is 22 miles per hour, a rate in all probability which at some points on some lines has been ex- pensively low, and would have been still more so except that the grades at stations are usually the de-facto limiting grades, and not those between stations. 446. It will therefore be safe in all cases to assume a maximum ♦Trans Am Soc. C. E., Oct. 1876. The explanation there given by Mr. Dudley that at the higher speeds " the locomotive seems to produce its power more economically by using the steam expansively to a greater extent ihan at slow speeds" would seem to be certainly incorrect, except as the less time lor internal radiation may be supposed to be referred to. freight-train speed of about 22 to 25 miles per hour on long grades, cor- responding to a grade of repose of something under 0.5 per cent, or 26.4 feet per mile; and this, under favorable circumstances, for important ends, may be assumed to be increased to nearly 30 miles per hour, corre- sponding to a degree of repose of something over 0.6 per cent, or'32 feet per mile. On grades not exceeding these limits rise and fall on grades of any length will not be likely to require the use of brakes, or to en- danger objectionable " slack" in the train, with the most moderate care in running, 447. The point at which a grade on rates exceeding these limits be- comes so long that the use of brakes will become necessary is readily + /?' to be -^ = 311 stations for , 14.21 . an initial speed of 10 miles per hour and —^ = 23.7 stations lor an in- itial speed of 15 miles per hour. In this manner we may construct Table 122. 448. Any grade, at any given rate whatever, which does not exceed in length and vertical rise the limits of Table 122 can be operated in the routine of freight service without the use of brakes (the cost of such rise and fall being, consequently, very much less) provided that there be no excessive curvature or other special cause near the foot of the grade to require especially low speed at that point. Ordinary curvature, with a Table 122. Distance within which the Velocity of Trains descending Various Grades without Steam or Use of Brakes will exceed the Limits OF 25 and 30 Miles Per Hour, starting with Various Initial Ve- locities. Ratb of Graob. Admissible Maximum Velocity OF 25 MiLBS Per Hour. Admissible Maximum Velocity OF 30 Miles Per Hour. ■>cr Cent. Less Grade of Repose. Initial Velocity at Top of Grade, in Miles Per Hour. Initial Veloc' Grade, in Mil ty at Top of es Per Hour. + 10 15 20 + 10 15 20 0.4 0.5 0.0 Infinite Infinite Infinite Infinite Infinite Infinite Infinite Infinite o.z aaa.o 166.5 142. X 80.0 it It t« tt 0.6 o.a ZII.O 83.2 71. 40.0 3'9-5 284.0 239.6 177-5 0.7 0.3 74.0 55-5 47-4 26.7 »59-7 142.0 119. 8 88.8 0.8 0.4 5S-5 41.6^ 35-5 20.0 X06.5 94-7 79-9 59-3 0.9 0.5 44-4 33-3 28.4 16.0 79-9 71.0 59-9 44-4 t.o 0.6 37-0 27.7 23-7 »3-3 63.9 56.8 47-9 35-5 s-5 I.X 20.3 I5-I 12.9 7-3 32.0 28.4 24.0 17.7 s.o 1.6 »3-9i 10.4 8.9 SO 21.3 18.9 x6.o II. 8 3-0 a.6 8.5 6.4 5-5 3-> 12.8 II. 4 9.6 7.« Table 122. — Continued. Total Vertical Fall in Feet from Top of Grade to Point where the admissible Maximum Velocity is attained, as above. 0.4 0-5 0.6 t».7 0.8 «.9 s.o 1-5 S.o 30 Infinite III.O 66.6 51-8 44-4 40.0 37-0 30-3 27.8 17.0 Infinite 83.2 49-9 38.8 33-3 30.0 27.7 22.6 20.8 12.8 Infinite 71.0 42.6 33-2 28.4 25-5 23.7 19.4 17.8 II. o Infinite 40.0 24.0 • 18.7 16.0 14.4 13-3 10.9 10. o 6.2 Infinite tt 191. 7 111. 8 85.2 72.0 63.9 48.0 42.6 38.4 Infinite tt 170.4 99-4 75-8 63-9 56.8 42.6 37-8 34-2 Infinite tt 143-8 839 64.0 54 -0 47-9 36.0 32.0 28.8 Infinite tt 106.5 62.2 47-4 40.0 35-5 26.6 23.6 21.3 Computed as follows : At speed of 0.00 22. 20 10 3-55 22.20 15 7-99 22.20 20 14.20 22.20 0.00 31-95 3-55 31-95 7-99 31 95 Vel.-head Do. at 25 (and 30) m. p.h. 14.30 31.95 Difference 22.20 16.65 14.21 8.00 .40 31-95 28.40 23.96 Assumed average grade of repose 17.7s .50 Then the actual rate of grade, less the grade of repose, gfives the fall per station which goes to increase the velocity, and the "differences" above, divided by the surplus fall per station, gives the number of stations within which the permitted maximum velocity will be attained, as in the first part of the table above. The number of stations x rate of ^ade per cent gives the second part of the table. Toad-bed in good condition, can be operated by all trains with almost as great safety at 25 to 30 miles per hour as at any lower speed, if the speed does not require to be suddenly checked. In ascending such a grade the same conditions obtain as in descending, except (i) that the locomo- tive ascends the grade using steam, whereas it descends without steam ; and (2) that it starts or may start with the high velocity which gradually decreases instead of with the low velocity which gradually increases. We are not now considering the effect of limiting gradients, which is an entirely different matter, but assuming that the locomotive has sufficient power to ascend all grades at necessary speeds, as of course in all cases it must. The cost of decreasing the length and increasing the number of trains to effect this end, which constitutes the chief objection to gradi- ents, is not now under consideration at all. 374 ^HAP. IX.-RISE AND FALL— LIMITS OF CLASSES. 449. Summarizing the preceding discussion of the nature of rise and fall, we have found that it may be divided into the following classes, having a very different effect on operating expenses : Class A. Rise and fall on minor gradients and for small un- dulations, not sufficient to make it necessary to vary the power of the engine, but merely causing a momentary, gradual, and unobjectionable fluctuation of speed. Class B. Rise and fall similar to class A, in its effect in speed, provided steam be shut off in descending, but not requiring the use of brakes in descending, nor seriously taking the power of the engine on the ascent. Tables 121-2 give the limits of this class. Class C. Rise and fall requiring the use of brakes in descend- ing, in addition to shutting off steam, in order to avoid exces- sive velocities, and consequently, in almost all cases, more or less use of sand in ascending. 450. Rise and fall is most conveniently estimated by the number of vertical feet of it, since the cost of it (which in- eludes no limiting effect on trains) depends primarily on the length of grades and not at all on their rate, except as the rate may change the rise and fall from one to the other of the above classes. A foot of "rise and fall" is ordinarily considered as one foot of ascent with its corresponding foot of descent, so that in passing over a hill 100 feet high there are 100 feet of rise and fall, and not 100 feet ascending + 100 feet descending = 200 feet. 451. The amount of rise and fall of each kind on the profile should be determined thus : A. All rise and fall arising from hollows in grade-lines not exceeding the limits specified in connection with Table 121 (par. 435 ft seq.\ if the grades are connected by easy vertical curves and are not too near stations, 05 very bad curvature, will belong to the least objectionable class, A. If the hollows are sharp and abrupt, however, even if quite small, the rise and fall will be more objectionable than the worst class here considered. B. All rise and fall on grades too long to come under Class A, but on rates of grade so easy that the train can never obtain CHAP. IX.— PISE AND FALL— COST OF. 375 a dangerously high velocity when running without brakes with steam shut off, will belong to Class B. So also will rise and fall on any grade, however steep, which is not long enough for the train to obtain a dangerously high velocity, as fixed in Table 122 and par. 447 et seq. So also, strictly speaking, will the upper part of any grade, however steep and however long, on which no dangerously high velocity can result according to Table 122 ; but it would be an objectionable refinement, tending to an under- estimate of the cost of bad details of location, to so consider. C. Class C, therefore, should be considered to include the entire length of all grades so long and steep as to require the use of brakes in descending. The ruling grade of the line may belong to either Class B or Class C. In either case it will involve the occasional use of sand and more or less slipping of wheels, and perhaps breaking in two of trains in ascending, and thus make an addition to the cost of either class which would not apply to the same grades if they were not ruling grades, and hence did not so severely tax the power of the engine. The limit of these classes will vary in every case, but there is a tolerably sharp line of demarcation between the cost of each, which may be estimated as follows : the cost of rise and fall. 452. Fuel. — Except as wasted by brakes, there is no loss of power (energy), and except as wasted by brakes and radiation combined, there is no loss of either fuel or power, from any amount of rise and fall of Class A, if we neglect the slight difference in frictional resistances result- ing from a (so to speak) regularly irregular speed instead of from a uni- form speed averaging the same in miles per hour. This necessarily fol- lows from elementary dynamic laws. Even if there be a difference in the level of the two termini, what power iS lost in going in one direction is regained in returning. When, in the case of rise and fall on easy gradients requiring no brakes (Class B), we run a part of a distance of one or two miles (the ascent) under steam and another part of it (the descent) with steam shut off, assisted by gravity only, — or in other words, assisted by the energy ■ 37t) CHAP. IX.— RISE AND FALL— COST OF. CHAP. IX.— RISE AND FALL— COST OF. 377 stored in the train during the run over the up grade by the act of lifting it against gravity, — the total time that the locomotive is exposed to ex- terior radiation is the same, and probably also the loss of heat. The loss from interior radiation in the cylinders, a very important loss, explained in Chapter XL, is affected as follows: It is increased by the (probable) lower piston speed in ascending the up grade. It is decreased by the (probable) later point of cut-off, and hence less oscillation of temperature in the cylinder; the disadvantage of this latter very nearly balancing, as experiment shows, the theoretical gain from an earlier point of cut-off. This is to say, from both of these causes com- bined, tlie steam used for equal work in the locomotive engine is about the same at all points of cut-off less than half stroke ; which leads to the conclusion that the steam (not fuel) used to run an engine two miles will be about the same whether the work is uniform for the whole run or is all done during the first mile in taking the engine up an easy grade, down which it runs by gravity for the second mile. Tiie loss by ex- ternal radiation during the last mile will be a net loss. The fuel used will probably be much more increased, not only by possible blowing off of steam from the safety-valve, but by blowing out more unconsumed coal from and wasting more heat through the smoke-stack, owing to the stronger draft. In Chapter XI. it is shown that in proportion as the work of the engine is increased, economy of fuel consumption is decreased. From all these causes combined a locomotive running without brakes or steam down grades too steep to continue the steam-power unchanged, but not steep enough or long enough to require the use of brakes, will burn probably one fourth to one fifth more, and certainly not over one third more fuel in ascending one mile on the grade equal to the grade of repose (assumed at 26 feet per mile, or 0.5 per cent), and then descend- ing one mile without steam, than in running two miles on a level. Al- lowing one third more, 80 vertical feet of rise and fall on such grades will waste fuel equal to the average consumption per mile. 453t When brakes are required, owing to the grade being either too steep or too long to permit of operating it without them, the power used in ascending is entirely lost, except that portion of it which is just suffi- cient to keep the train in motion on the grade of repose. That is to say : The rise and fall at BC, Fig. 85, consists of two parts, the upper part, B, belonging to Class B, and the lower part only, C, belonging to Class C, which is very much more costly, objectionable, and dangerous. In laying out a line this fact must be borne in mind ; the lower portion, C, estimated at its true value and avoided if possible ; the upper portion, B, less care- fully avoided. The limit between classes B and C may be taken in round figures as the height of the point b. Fig. 85, above or below the grade of repose descending from A, although, strictly speaking, the grade of repose should be drawn in starting from the point on the grade where the limits of Table 122 and par. 447 are passed, '*^' ^' so that dangerously high speed before reaching the foot of the grade is •certain. But when this point is once passed great care in handling the train on a grade where brakes are known to be essential cannot fairly be assumed, so that it is fairer and more reasonable to assume that all the fall, C, Fig. 85, will be of the objectionable class. When an engine is descending a grade without steam, the wastage of fuel by radiation and slow combustion is at first (say for 10 or 15 minutes) very considerable — about one fourth of the usual consumption per mile. The loss of fuel on this most objectionable class of rise and fall may be taken as equal to the average consumption in running a mile for every 26 feet of rise and fall. 454. Repairs of Cars and Locomotives. — The use of brakes is excessively destructive to wheels. Table 114, page 318, will make it clear that something like one third of the total cost of wheels arises from this cause, and other data that as much as forty or fifty per cent arises from them. Brakes, however, are used even more for stopping and starting than on grades — sometimes very much more; and the whole cost of wheels is only some 30 per cent of freight-car repairs and very much less of passenger cars. The records of wheels drawn on the Pennsylvania Railroad indicate {a) that about 30 per cent of passenger- car wheels are drawn for being " worn flat from sliding," and that their life is from this cause abbreviated from one third to one half. About one sixth of the wheels are drawn for being "worn flat or hollow on tread." which class of wear is distinctly ascribed in the Pennsylvania classification to " wear from rail," If we should consider only such facts as these, we might reach the conclusion that the wear due to grades must be a very important element in the cost of freight-car repairs; but by referring to Table 86, page 203, and remembering that grades are only one of many causes for wear and tear of cars, we shall see reasons for concluding that, while it is exceed- i --t; \ I w 378 CHAP, IX.— RISE AND FALL— COST OF: ingly difficult, in fact impossible, to reach an exact estimate in such a. mattter as this, yet that it is not probable, if all grades were levelled down fiat so as not to require in any case the use of brakes, except for stops^ wheel renewals would not be reduced more than one sixth nor car repairs as a whole more than one tenth. The only item of car repairs other than the wheels affected to an important extent is the cost of draw-gear and links and pins, and the loss in this respect, as we have seen (par. 419), arises more from lack of proper vertical curves at breaks of grade than from the grades themselves. Table 123. Variations in the Quality of Water Supply, Chicago, Burlington & QuiNCY Railroad. Locality. Chicago Division : Best Worst Average St. Louis Division : Best Worst Average Lake Michigan Hudson River Croton River, N. Y . . . . Loch Katrine, Scotland.. Grains Per Gallon. Incrusting Solids. 10 666 28.8*51 16.405 4.898 20.178 11.490 7-305 7177 5.362 O.9II Alkalies and Non-crusting. 1.365 10. 788 2.853 1.458 2.449 1.678 0.626 1. 136 1. 5" 1-333 Lbs. Incrusting Matter in Tank of 2750 Gallons. 4.19 11-33 6-44 1.92 7-93 4-51 2.87 2.82 2. II 0.36 Comparative Incrusting Matter. Lake Michigaa = 1. 00. 1.5 3.9 2.2 0.7 2.8 1.6 i.o I.O 0.7 o.z Incrusting solids include silica, oxide of iron and alumina, carbonates of lime and magnesia, and sulphates of lime and magnesia. The standard tank of the road carries 2750 gallons. The non-incrusting matter may be partly deposited as mud and partly mechanically combined with the scale. According to this table, an engine consuming three full tanks of water per day would in a week's work with the average water in the Chicago Division accumulate at least 116 lbs. of incrustation. With the best water on the St. Louis Division (taken from the Mississippi at Rock Island) the result of a similar week's work would be only 34^^ lbs, of incrustation. The difference shows the importance of good water. The water of Loch Katrine, Scotland, from which Glasgow derives its supply, is about the purest and softest known. CHAP. IX.— RISE AND FALL— COST OF. 179 455. The cost of locomotive tires will be affected in much the same way and to the same extent as the cost of car wheels. The life of the boiler is likewise unfavorably affected by an intermittent instead of regular demand for power, although this effect is slight in comparison with the injury suffered from the cooling off of boilers at the end of the trip, from the effect of bad water and many other causes not connected with the grades between stations. Table 123 gives an idea of how im- portant is the effect of bad water on locomotive repairs. 456. It is, moreover, true of both engine and car repairs that, as noted in par. 164, when we search for evidence of the effect of much rise and fall, or curvature, or (as usually happens) both together, by comparing the cost of engine and car service per mile run on roads or divisions having much and having little curvature and rise and fall, we fail to find it. As respects grade, this results in part, no doubt, from lower speed and more careful handling on them ; but as this costs the company nothing except a slight delay, we may fairly regard it as an offset, to some extent. In the first edition of this treatise the writer estimated the effect of rise and fall at 5 per cent, on the total cost of repairs of engines and cars per mile, for each 25 feet per mile (0.5 per cent, nearly) which would amount in 2 per cent grades to something over 20 per cent per mile of ascent and descent. Taking an average of the mountain divisions of the Pennsylvania Railroad, this would require that a difference of at least 15 per cent should be visible, and on the Baltimore & Ohio at least 20 per cent, whereas in fact no such difference appears in either case. This fact, together with a careful estimate by items, which cannot be given more fully than above, leads the writer to believe that his original estimate was too high and it is reduced in the estimate below (Table 124) to 4 per cent, which is the utmost that the statistical evidence seems to justify. On Class A of rise and fall there cannot be considered to be any measurable increase in the cost of rolling-stock maintenance if proper vertical curves are used. On Class B (requiring shutting off steam for descending, but not the use of sand or brakes) there is very little — cer- tainly not over one fourth of what exists on the worst class, C. 457. Wear of Rails. — The effect of grades on the wear of rails is exaggerated in popular belief for want of a proper distinction between the effect of a heavy ruling grade, which increases the number of trains and the proportion of engine tonnage, and the effect of rise and fall simply, on which the number of trains and proportion of engine tonnage is the same as on adjacent sections of level track. Thus, in an able and 38o CHAP, IX.— RISE AND FALL— COST OF. CHAP. IX.— RISE AND FALL— COST OF. elaborate report on the wear of rails on the Pennsylvania Railroad, already quoted, an increase of some 75 per cent in the wear of rails on grades over which almost three times as many engines pass as on ad- jacent sections of level track was ascribed to the effect of grades as such, whereas it is in reality merely an expression of the fact that an engine wears the rails several times as much as the same weight of cars (par. 115). In so far as this is the cause of extra wear of rails it is an effect arising from the limiting effect of gradients, and not at all an inherent property of gradients as such. When we eliminate this extraneous question we are driven to the conclusion that the wear of rails due to gradients as such is almost nil, except as their rate may be such to require the use of brakes and sand. The use of sand is exceedingly destructive to rails. The writer found that at specially exposed localities (near stations for the most part), where the use of both brakes and sand was usual, the wear as measured by loss •of weight was increased some 75 per cent ; but loss of weight alone is an unfair criterion, since the wear at joints is a very important factor in the life of rails, and often requires their removal before they are fully worn •out. Such extreme use of either brakes or sand, moreover, is not <;ommon on any grade as at the points covered by the writer's tests. 458. In tlie first edition of this treatise, a considerable body of sta- tistics being presented and discussed to which it appears unnecessary to again give space, the writer estimated that the wear of iron rails was in- creased not over 5 per cent per 25 vertical feet of rising grade and the same on the corresponding descent, or 10 per cent for each 25 feet of rise and fall, making, on a 2 per cent grade (106 feet per mile) a differ- ence of 20 per cent in the aggregate of this item on both the ascent and •corresponding descent. He sees no reason to believe that this estimate is materially in error in either direction (unless in excess) as measuring the effect of gradients pure and simple, without modification in the num- ber of engines used for a given number of cars, and this latter occurs only on the worst class of rise and fall, C. For that class, a proper estimate for iron rails might be expected to still hold good for steel, since the proportions of the grade near to the level wear has not been greatly af- fected by the introduction of steel on such steep grades, where speed is slow. On Class A there is certainly no direct evidence that the wear of rails is affected at all, with steel rails. With iron rails, which failed mostly from lamination and which speedily wore to an irregular surface on top, on which any considerable increase of speed caused greatly increased wear and tear, the case was different. , 38r Class B of rise and fall likewise has little effect to increase rail wear,, but as it is apt to cause a somewhat high velocity in the hollows, it un- doubtedly has some ill effect ; possibly about one half as much as Class C. 459, Maintenance of Road-bed and Track.— In the former edition of this treatise the cost of these items was estimated as increased in about the same ratio as the rail wear, viz., 5 per cent for each 25 feet per mile (0.5 per cent nearly) of rise and as much for the corresponding^ fall. A liberal estimate in such a matter is proper, and we may continue the former estimate for Class C, although it is probably somewhat too high for average conditions. On Class A and Class B the disadvantages and advantages of the grade may be fairly considered to balance each other as respects main- tenance of road-bed and track. A great compensating advantage from the grade, besides the lower speed, is the more perfect drainage, giving a firmer road-bed and prolonging the life of ties and ballast as well as preserving the surface. Level cuts are always very objectionable, as has been rediscovered many times since one of the early English engineers laid out one several miles long, which caused immense difficulty (and still causes it), several costly tunnel culverts having to be driven to drain it. Grades of any moment are usually situated in comparatively rugged and difficult regions, and the increased expense arising from that cause is very apt to be erroneously ascribed to the effect of the gradients themselves. Creeping of rails is an annoying effect due in part to gra- dients, but has been largely done away with in recent years by improved forms of joints. 460. Train Wages.— It is quite conceivable that one or more addi- tional brakemen may be required on a line of much rise and fall, yet it would ordinarily be quite improper to include this as one of the ex- penses arising from it, for this reason : Whether or not such additional force will be required is usually determined by the general character of the line beyond hope of change by the engineer. In comparing two radically different lines, it might be an element worthy of consideration,, but the slight modifications which are ordinarily alone possible can rarely be sufficient to in themselves make any difference in this respect. 461. Station, Terminal, and General Expenses, as well as train wages and a large proportion of the other running expenses, cannot be considered as affected to any appreciable extent by any changes in rise and fall not of the most radical and extensive nature. 462. From all that has preceded we may deduce that no lead- ing item of railway expenditure is largely affected by rise and <;-« 382 CHAP. IX.— RISE AND FALL— COST OF. fall in itself, and very many of them not at all affected. In Table 124 appears a detailed summary of the aggregate effect to increase expenses of ieach of the three classes of rise and fall, A, B, and C: A. Not requiring shutting off steam nor change in the natural velocity, nor use of brakes or sand. (See foot-note to Table 124.) B. Requiring shutting off steam at the head of the grade, but not use of brakes or sand. C. Requiring use of both brakes and sand. 463. The summary of the cost per year of a foot of rise and fall at the foot of Table 124 shows its cost to be— Class C. Class B. Class A. Cost on minor gradients $2 67 $0 84 $0 28 Cost on ruling gradients 3 50 167 Addition to cost of same amount of rise and fall if on ruling gradient o 83 o 83 These sums, divided by the rate of interest on capital, what- ever it may be, will give the justifiable expenditure per DAILY TRAIN to avoid oue foot of rise and fall. Thus, if capital cost 6 per cent, the justifiable expenditure per daily train to avoid 100 feet of rise and fall (i.e., 100 feet up, with the corre- sponding 100 feet down) will be for each class,— multiplying the above sums by 100 and dividing by 0.06, — Class C. Class B. Class A. If on minor gradients $4,45° $1,400 $467 If on a ruling gradient 5>833 2,783 To reduce the ruling to a minor gradi- ent (leaving the ruling gradient else- where unchanged) IjS^S 1*383 It would be impossible, however, that there should be so much as 100 feet of rise and fall of Class A at any one point, since if there were so much, or even half or one quarter so much, it could not belong to Class A. The value given for reduction of a ruling to a minor gradient refers, of course, merely to the DIRECT saving of wear and tear by having tiie grade easier, and CHAP. IX.— RISE AND FALL— COST OF. 383 Table 124. Estimated Cost Per Train-Mile and Per Daily Train of 26.4 Feet of THE Various Classes of Rise and Fall. (Cost of train-mile assumed at $i.oo.) Item. Fuel Water, oil, and waste, . . . Repairs of engines Swiiching-engine service.. Train wages and supplies. Repairs of cars Car-mileage Renewals of rails . . Adjusting track Renewing ties Earthwork, ballast, etc. . . Yards and structures Station and general Total Cost of Item. Total. 7.6 1.2 5.6 5.2 154 10. o 2.0 2.0 6.0 3.0 4.0 8.0 30.0 Percentage of same increasing with 26.4 feet of ribe and fall belonging to — Class C Class B. 100. P- c. p. c. 100 33i 50 20 4-0 i.o Unaffected. 4.0 1.0 Unaffected. 10. O 5.0 50 0.0 5-0 0.0 50 0.0 Unaffected. Cost per train-mile of 26.4 feet of rise and fall belonging to- Class C. Class B. 9-7 PC 7.6 0.6 0.22 0.4 • • • • 0.2 0.3 0.15 0.2 p. c. 2.53 0.24 0.06 O.IO ■ « • • 0.10 0.00 0.00 0.00 3.0 9.67 3.03 Per Foot of Rise and Fall Per Foot of Rise and Fall per Daily* Train'(roundVrip). .366 $2.67 *"5 $0.84 Cxll'P'l ^''^ ^""^^ ^^ '''' """^ Maximum Grade, whether on Class B~or W r^" '"^" °^ rolling-stock and track will be so increased as to add at ^co'zzr^ '""""' '" ''' '"' °' ^'^ '''' °' "^^ ^^^ ^^"' ^--^ - '^^ f«»-- ^°' aCe*?^"^ *I"^'° ^' ^"^^ ""^ "'^ ^^ ^^" °° ^^^°^ Gradients, as' Additioritocost'ofthesan^egT^de if a Ruling Gradient due io the extra wear and tear on ruling gradients, . . "uc lu me ^''''gra'^IENTS°'' ^' "^^"^ '"^'^ ^' ^'^'''^ "'^ ^"^ ^^" °° ^^^ING Class C. Class B. $2.67 0.83 $0.84 0.83 (par 4^'' "^ ^"' '''"' ^^^^ °''^' ^ ^''°' ""^ ^''°' ""''^ '"^ correspondf^g des^nt fromtrnrt^"^- ^T ^"""^ ''\''^'' "^^ '"''"'^^ ^" *'^^ *^^^^' because, as will be seen n in anT?^"f ^'T °' ''' '"'"'' °' ^^^"^^^' "° '""^^'^ ^^ ^ ^--^ly traced Hm taLTr HH^ T' ,^^^«°^^^^""^ this apparently doubtful conclusion the strict air? tit '^ "^ '"'" '^ '" ^^'' ^-^5 '' ^eg. are to be remembered. Moreovef andTv^L^l "tr"' "'"^^"^^^^^ ^"^'"^ ^-- -^h "se and fall for this cause alone, d It W.U lead to no senous error to assume its cost at one fourth to one third the cost 0/ 384 CHAP. IX.— RISE AND FALD—COST OF. CHAP. IX.-^RISE AND FALL— VERTICAL CURVES. 38$ not at all to the much greater value which results from reducing all ruling grades throughout the line, so that the length of trains can be increased. 464. The above values are to be further multiplied by the estimated number of trains per day (round trip). Thus, if there are expected to be 10 trains per day each way, the value of sub- stituting a level for a hill 100 feet high becomes $14,000 to $44,500 for minor gradients, and $27,830 to $58,330 for ruling gradients — which are very considerable sums if we remember that they are quite apart from all limiting effect of the gradi- ents. The value of changing the rise and fall from Class C to Class B is nearly $30,000, and of reducing a ruling gradient to a minor gradient without changing the class, nearly $14,000. 465. In the first edition of this treatise the cost of rise and fall on all grades of over 40 feet per mile was found to be — On I2| feet per mile (about 0.25) grades $1 04 25 ......(.. 0.5 ) " I 56 35 •' .. «« ^ «. o^ ) .. I 8y 40 to 50 ** " " ( " 0.8 to i.o ) '• 2 g8 80 " ....(.. 15) .. 2 29 125 " •• •• ( ** 2.5 ) " 2 40 The writer has been forced to the conclusion that these estimates were too small to be on the safe side, and, despite the fact that the steel rail and other mechanical betterments have materially reduced the disadvantages of rise and fall, has increased its estimated cost as above. 466. It will be clear from all that has preceded in this chapter that the disadvantages of rise and fall are measured more truly by the number of breaks of grade than by the actual amount of it in vertical feet, except on the worst class of all, C, on which both brakes and sand have to be constantly used. Even on the heaviest grades this is in a measure true. Thus, the long i per cent grade in Fig. 86, belonging to Class C, will be considerably more objectionable to operate than a corresponding easy grade belonging to Class A or B of rise and fall, as the 0.5 continuous grade in Fig. 86; but the breaking up of the i per cent grade at frequent intervals by stretches of lighter grade, so that the descent is made half on one grade and half on the other, so far from decreasing the aggregate cost of the grade over the straight ^^4V V* w«»W«»ww«» r~~r-i — I — r~n ' Fig. 86. I per cent, will in fact make it considerably more expensive to operate. 467. Again, 1000 feet of rise and fall concentrated on a single grade is not nearly so expensive in wear and tear as when the same amount of it is scattered around in a dozen or more shorter and widely scattered grades of the same rate and class (par. 462). If its class is changed by such breaking up the case is different. Thus, the least objectionable class. A, of rise and fall can only exist when there is very little at one point. 468. We have seen (par. 414 et seq.) that long and easy verti- cal curves, properly used, very largely obviate the disadvantages of every class of rise and fall, however much broken up into short sections; in fact, properly used, they forbid the breaking it up into over-short sections. It is so extremely important that vertical curves should be sufficiently long and should be properly put in, that we may anticipate here, from the field-book which follows this volume, some notes as to the proper manner of putting in such curves: 469. We have seen (par. 426^/ seg.) that the length of vertical curves should be determined, not arbitrarily, regardless of the angle between gradients, but by the amount of change of grade per station which is admiFc.ble; the safest rule being as already given-that the difference in tb J rate of grade under the head and rear of the train shall not exceed Ihe grade of repose of the last car. A rate of change per station (100 feet) of .025 will most completely 25 386 CHAP. IX.-RISE AND FALI^VERTICAL CURVES. CHAP. IX.— RISE AND FALL—VERTICAL CURVES. 387 fulfil this condition with all kinds of trains, including those with a great deal of slack in the couplings, like coal trains : but .05 per =tat.on w.ll obviate all the more serious effects, especially if the speed be high or the °rain short, or both. After the introduction of improved f re.ght couplers oc oer station will be ample. ■ Both of these rates give a longer curve than is usual ; but more ch^^ge •" Fig. 88. Fig. 87. cer sution than that last specified should never be used in sags (Fig. 8^ . unless for high speed and very short trains. On sumnut curves (F g. 88) shorter curves are admissible ; but these also should not be shorter than o.i per station-if for no other reason, because .t is needless '° "yorCa^gle between grade-lines. .. Figs. 87. 88. is considered to be the sum or difference in the rate per cent of the ^='d«^°^;''"^ deflection from each other. In Fig. 87, a = ..4 : m F.g. 88; « " '^°-^^ If we let r = the change of rate per stat.on *h.ch is con .dered adnus^ sible, = 0.025 to 0.10 according to circumstances, then the aggregate length of any curve is at once given by the equation If the angle between grade-lines te i.o per cent, this gives a vertic^ curve 10. 20. or 40 stations long, according as the assumed value of r .s "■'•^^IZmo. that the change in rate of grade shall be uniform per Fig. 89. an this cut, which is rather poorly executed, I • :i 4. s are successive stations of too feet fiom the tangent point T. but the " curve" as drawn is supposed to consist merely of a series of straight hnes, ab be, cd, etc., tangent to the curve at these stations, thise ungents, as prolonged by the dotted lines, bemg supposed to differ from each other in rate of grade by a constant change of rate, r.) ^.u^* ««♦ sution or other unit results in the generation of a curve such as that out- lined in Fig. 89, which is. mathematically, a parabola. 471. It is to be remembered that all geometrical diagrams connected with railway location are greatly exaggerated or distorted, so that the succession of chords outlined in Fig. 89 are in fact practically coincident with the curve. Fig. 90 gives to correct scale the intersection of a 4 per cent (211 feet per mile) grade with a level, which is periiaps twice as large an intersection angle as actually occurs on any located line in the United States, even on the engineer's profile, and four or five times as much as is usual ; topographical reasons generally requiring one or more intermediate grades in cases of such abrupt change. Fig. 90 will also make it clear that in the two sketches of vertical , lsmvf€ ,11 . Fig. 90. curves shown in Figs. 91 and 92 the tangents, the chord M, and the curves themselves are sensibly of the same absolute length, independent of the fact that, all distances being measured horizontally, they are neces- sarily equal as measured in the field. 472. From the law of the parabola it results that in any vertical curve, Fig. 91 or 92, the curve bisects the middle ordinate IM in c, and from elementary geomet- rical relations we have for the distance Ic = c, by fig. 91. which the curve departs vertically from the intersection of tangents : I a la ^=7 ^4 =-8-' 'h^^ r or, as / = - (par. 470), a' ^ = 8r* 473. From this formula we can compute the following Table 125, giv- ing the first detail which it is desirable to know in laying out a vertical curve, viz. : How much vertical change it will produce in the position of the grade-line, which is greatest at the middle of the curve and thence rapidly diminishes in each direction, being only one fourth as much at the "quarter-points" of the curve or at the middle of each tangent. 474. Having determined from Table 125. or otherwise, what rate of per station will be necessary or feasible : To lay out a vertical curve, HAVING GIVEN THE RATE OF THE TWO GRADIENTS AND THEIR ANGLE 388 CHAP. JX.-RISE AND FALL- VERTICAL CURVES. Table 125. VERTICAL CHANGE IN THE POSITION OF THE ^^ADE-LlNE AT InTE^s™ OF Gradients resulting from Vertical Curves of Various Rates T AND WITH Various Grade-Angles a. (Computed by formula of par. 472.) Grade-Angle a. Figs. 91, 9«' Vertical Distance of Curve from Intersection of Gradients = Ic, Figs. 91 and 93, for Change of Rate OF Grade per Station, = r of— L 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 i.o I.I 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 0.2 Feet. .006 .025 .061 .100 .156 .225 .306 .400 .501 .625 .756 .goo 1.056 1.225 1.406 1.600 1.806 2.025 2.256 2.500 0.1 0.05 Feet. Feet. .01 .025 .05 .1 .11 .225 .2 .4 • 31 .625 .45 .9 .61 1.225 .8 1.6 1. 01 2.025 1.25 2.5 1. 51 3 025 1.8 3-6 2. II 4.225 2.45 4.9 2.81 5.625 3.2 6.4 3-6i 7-225 4.05 8.1 4.51 9.025 5-0 10. 0.025 Feet. .05 .2 .45 .8 I.2S 1.8 2.45 3.2 4.05 5.0 6.05 7.2 8.45 9.8 11.25 12.8 14.45 16.2 18.05 20.0 The vertical change in the position curve, or at the middle of the tangents, The whole length of the curve (both of the grade-line at the "quarter-points" of the is in each case one fourth of the above. grade-angle tangents) = ' = change of grade per station OF INTERSECTION ..THE RATE PER STATION r, AND THE STATION OF THE INTERSECTION OF GRADIENTS : ^ I The total length of the curve in stations is - (which let = n .tations^ one half of which is the length of each tangent, whence the sutron of the tangent-point can be determined and the elevation of the grade at that point. CHAP, IX.— RISE AND FALL— VERTICAL CURVES. 389 2. Having given the station and elevation on either grade, and the rate (which let = R) of the grade in which it lies, write successively R — \r, R— i\r, R — 2^r, etc., adding or substracting r from each (as the case may require) until n quantities have been written down, paying strict attention to the algebraic signs, as below specified. The «th quantity thus determined will differ from the rate R' of the other tangent by \r, and the addition of the several quantities thus de- termined to the elevation of the first tangent-point w^ill give the elevation of each station of the curve, to and including the other tangent- point, where the elevation will check upon that independently fixed by the tangent grade-line for the second tangent, if the work has been correctly done. When the angle between the grade-lines is upward, or on a summit, the successive additions of r are -, or subtractions; when the angle of the grades is downward, the additions are positive. Examples.— Curves to connect the gradients shown in Figs. 93, 94, 95, each "With the intersections of gradients at station 100 and elevation loo. (9«.9; o ^ .. (^.9> Fig. 93. Fig. 93. Angle between grade-lines 1.6 Rate of change of grade per station. 0.2 Total length of curve 8 sta. Station of tangent-points -J ^ Elevations of grade at do. (computed). \ ^^'2 Rafe,o.f 6 Stafhns Fig. 94. Additions. P.C. R-\r. 0.7 R — l\r. 0.5 R — 2\r, 0.3 R — 3\r. 0.1 Etc —0.1 - 0.3 P.T -0.7 Eleva- Stations. TIONS. 969 97.6 98.1 98.4 98.5 98.4 98.1 97.6 96.9 96 97 98 99 100 lOI 102 103 104 Fig. 94. 0.6 O.I 6 stations. 97 103 100.9 97.3 Addi- tions. — 0-35 -0.45 -0.55 — 0.65 -0.75 — 0.85 Elevations. TOO 90 100.55 100.10 99-55 98.90 98.15 97.30 Sta- tions. 97 9« 99 100 lOI 102 103 OoB^o) '20 stafions *• Fig. 95* I.O Angle between grade-lines • • * * q 05 Rate of change of grade per station ^o station*. Total length of curve ( go Station of tangent-poinU I I08.0 Elevation of grade at tangent-points j 102 .0 Elevations. Stations. Additions. ^^g^ ^o *^''-* Il2^ »o4.^ a - 375 "-'»5 S I *?« 102.5 '°^ I I25 102.0 102 "" 'ill 101.7 '^ - 02! 101.6 106 i^.r. t:i75 This .ethod is practically n.uch the -fj;--^^^^^^^^^ begins and'ends at a ^ "1\ ^t^^^^"' ^[^^^^^^^^ ^ZZL cases the following ing grades for half stations or otherwise. •"%7rB?t.e property of the p^^-j^ '':^,r-'^:::oTthVranc: ^ngents parallel to the " ^^^e h^-no ™ O AKD A^. Fig. 96, !.'o°'"J™rors:xs rrJrcUKVK, . .. ." at distances . «'. «' from the P- C, CHAP. IX.— RISE AND FALD-VERTICAL CURVES. 39 1 Letting iV = the length of one tangent we have, for any offset o what- ever at a distance n from the P. C, nr^ = Zi> whence o = 0-tjI N n Thus, if we divide the tangent N into five parts the first offset, 0, will be I* O O x—i, or — , and the succeeding ones will be 4, 9, 16 times the first. By this formula we may compute the elevation of any two points 100 Pro. 9(5. feet apart on any vertical curve (presumably at full stations) and deter- mine the rate of grade between them ; whence, knowing the change per station in rate of grade, all remaining stations are determined by succes- sive additions as above. To avoid cumulative error, the computation should be carried out to more decimals than it is expected to use. The entire curve may likewise be computed by determining the off- sets 0, n the sense of beine a governing element by which its power in serv.ce >s l.m.ted. On he ^ntrlry. the logicaf order of design (but not necessarily for that reason the order that a practised designer will follow) is— ,,• - ■ FM to L the total admissible or desired weight of the machine r.Ldl (U. a freight engine) the proportion of this weight which can be util'edfof 'adhesion or (in a'passenger engine) the largest boiler power which can be eotten without exceeding that weight. . , . j IhMly. to adapt the boiler power and adhesion to each other; and FZrthiy. to fix the size of the cylinders to correspond, making sure to ha^e '"^Thr^'u'rrefous disadvantage in having cylinders unnecessarily largej^or u I L L done due to external and internal radiation, which lim.K some- llt. le dtcr^tit: s'pecified. but not so greatly as to affect the substance of what has been said. 491 The boiler power of a locomotive, like that of any other source of enel^Jor dynatnll: force, is ultimately measurable in foot-pounds per Jiour, or other unit of time. So far as boiler power is concerned, there- fore, a locomotive is capable of hauling any load whatever if the speed be made low enough, or of attaining any speed whatever at the expense of the load hauled. HOKSE-POWERS or other equivalent units are merely certain multiples of foot-pounds. Whatever the name of the unit for the measurement of energy, it is always made up of the three elements of lifting a certain weight through a certain distance in a certain time against the natural force of gravity, gravity being the only constant and ever-present force with which we are familiar, and hence a natural unit for comparison. 492. The tractive power is measurable only in pounds, being a mere static or dead force, serving for the transmission of energy, like a belt or a .shaft, but not affecting its amount. The tractive power is— with impor- tant limitations to be considered— an approximately constant quantity at all speeds and under all circumstances. 493. Therefore, remembering (i) that the cylinder power is not an element in fixing the working power of an engine, and (2) that speed includes the two elements of time and space, which, with the third ele- Fig. 97.— Indicating the Manner ok adapting the same Boiler Power to Passenger or Freight Service. ment, weight or force, make up the three which are necessary for the £xact description of the amount of any kind of power, we may express 404 CHAP. XI.— THE LOCOMOTIVE ENGINE. graphically the variations which can be made in the manner of utilizing or distributing the power of an engine as follows (Fig. 97) '• 494. On a pair of co-ordinate axes intersecting at O, Fig. 97, let dis- tances on the vertical axis OA represent pounds of tractive power, and distances on the horizontal axis OC represent the compound unit speed, including the two primary units, distance and time. Then the capacity of any given boiler, which is measurable only by a productof the three units. /<^J. x //. x //;;/^, may be represented on such a diagram by a rectangle of a given fixed area (OABC, OA'B'C, OA"B"C") which may be proportioned in any ratio of height to length desired, provided the total area included within it be not exceeded. The number of such possible rectangles, as will be apparent from the figure, is infinite. As a matter of mere mathematical curiosity, of no immediate practical moment, it may be noted that if an hyperbola be drawn passing through the point B, with the axes OA, OC, as asymptotes, any point B' on it will be the apex of a rectangle of always equal area. 495. Each one of these rectangles will represent a possible locomotive;, each different from the other, which may be designed to fit the same boiler,— with this sole limitation : The tractive power in pounds of ordi- nary forms of locomotives is a limited quantity, which cannot be indefi- nitely increased ; and consequently at a certain point on the diagram A'' we reach a vertical limit, beyond which it is not possible, by any ordinary device, to increase the tractive power. It follows directly from this fact that we have a certain minimum of speed OC, below which it is not pos- sible to decrease the speed and still utilize the full power of the boiler by increasing the load hauled. As might naturally be expected, this limita- tion is at'times very inconvenient, when it is desired to obtain the maxi- mum hauling capacity regardless of speed, as in engines for yard service or for working on heavy grades. It is. in fact, practically, the most serious theoretical defect of the locomotive. Various exceptional de- vices are employed to evade it in part, the simplest and most common of which is to carry the water supply, and sometimes the fuel also, upon the- drivin--' wheel-base. A still more radical remedy is mentioned in par. 511. and yet another device is the so-called traction-increaser, throw- inga part of the weight of the tender on the drivers- for the time being by- cylinders attached to the piston, or by various combinations of levers. Finally, the device of a rack between the rails, or of a central rail which the driving wheels grip by spring power or other pressure, enables the- gravity of the engine to be wholly dispensed with for furnishing the trac- CHAP. XL— THE LOCOMOTIVE ENGINE. 405 live force, by substituting for it frictional adhesion, and thus removes all limit whatever to the load that a given boiler can move, provided the speed be made slow enough. 496. When this is done, all limits to the diagram in Fig. 97 are like- wise removed : so that it then becomes literally true that, so far as boiler- power is concerned, there is no limit whatever to either the speed of a locomotive or to the load it can haul, provided one decreases as the other increases; but since the load to be hauled can in no case be de- creased below the weight of the engine itself, a limit of possible speed is soon reached as well as of tractive force, and the limit of expediency in €ach direction is much narrower than that of possibility. A very interesting and instructive study of the differences of designs in locomotives and of the causes therefor, which the writer feels compelled to omit, may be made by constructing diagrams similar to Fig. 89 for various actual locomotives; laying off the load on drivers on the vertical axis ; taking the boiler power as proportional to the heating surface, and adding various de- tails of grate-area, etc. 497. It will be sufficiently clear from what has preceded, that in the practical working of engines a deficiency in any one of the three co-ordi- fiate forces which when combined make the complete machine will be shown in the following ways: 1. 1/ adhesion or tractive power be the smallest of the three, the en- gine will slip her drivers. 2. If boiler power be the smallest, the boiler pressure as indicated by the steam-gauge will fall, and the engine will from this fall of pressure be unable to turn the wheels. 3. If cylinder or engine power be the smallest, the engine will be stalled while utilizing to the utmost a full pressure of steam and while yet un- able to slip its drivers. 498. The last is either an evidence that the engine is out of the ser- vice for which it was designed, — as for instance a fast passenger engine hauling freight trains. — or it is an evidence of bad design. It is one of the most discreditable faults an engine can have, for the reason that it is an entirely unnecessary sacrifice of a portion of its capacity for work, and it is, naturally, a fault of rare occurrence. It has occurred in in- stances on a considerable scale, however, as an eflect of cutting down the permitted boiler pressure to 120 lbs. after copying the general pro- portions of engines designed to carry 130 or 140 lbs. The effect of such action on the pounds of tension which can be exerted is the same, and 4o6 CHAP. XL— THE LOCOMOTIVE ENGINE, as injurious, as if the boiler power itself had been reduced, which latter, however, does not at all follow from the reduction of pressure (par. 552). 499. The indication of deficient hauling power first above specified, slipping of drivers, is that which should first occur in all well-designed freight engines; for, since hauling-power and not speed is the desidera- tum in such engines, the boiler-power, however small (within limits), can be made to exert an indefinitely great force in pounds at the expense of speed, by proper design of the engine; which can hence be so designed that the boiler shall be able to exert continuously a force always in ex- cess of the tractive power when at its maximum (as when using sand) by a little at least, in order that the full measure of the latter may in all cases be utilized. 500. This theoretical principle is limited in part by this fact: Convenient operation, requires that it should not be 100 easy to slip the drivers under ordi- nary conditions but should require nearly a full head of steam to do so, or the difficulty of throttling the pressure just right (par. 527) will lead to too frequent slipping. Hence it is desirable that the cylinder power should be only a little in excess of the adhesion, and from this it may result that the ultimate maxi- mum of adhesion, when using sand on a dry rail with boiler pressure perhaps a little low. cannot be advantageously realized. There are also certain disad- vantages in an over-large cylinder, from greater loss by radiation, condensa- tion, etc., as well as some advantages. See also foot of page 408. 601. But it is probable that all these disadvantages have been over-esti- mated, or the whole question inadequately considered, in designing many of the engines now running, a considerable minority of which cannot utilize the full ultimate adhesion, and are in consequence compelled to haul smaller loads than they otherwise might ; although most freight engines can slip their drivers in ordinary working, when starting or running very slowly, and do so liberally. No well-designed engine will slip its drivers when running at speed, unless the rails are in bad order, as the average cylinder pressure is then much lower than in starting (i>ar. 594). Over-frequent slipping of drivers is an evidence of want of skill or care in the engineman. He can with ease slip the drivers with the lightest train or with no train at all. and in fact must use care not to. unless the cylinders are too small for the engine, because only an infinite force can set in motion the lightest body instantly. 502. The second indication of deficient hauling capacity above speci- fied, deficiency of boiler power, is the only one, in theory, by which a passenger engine should ever fail ; since a fraction only of its weight, if on the drivers, will give a hauling power in pounds far in excess of the available /^^/-/^w«iy of boiler power at a high speed in feet per minute. Neither do passenger engines often fail, in fact, for any other cause, be- tween stations, on moderate grades. The necessity of starting heavy trains Vf CHAP. XL— THE LOCOMOTIVE ENGINE. 407 quickly, however, and of maintaining a high rate of speed even on long, heavy grades, makes the demand for adhesion on passenger engines very unequal, and at times very great, so that it is often in practice the actual limiting cause which it is desirable to increase. It is not essential to do this permanently. Any device which increases the load on the drivers temporarily, especially for stopping or starting, answers every purpose, and a better purpose in fact than a permanent increase. Such attach- ments are now in use on extra-fast engines and to a limited extent on others, and it is probable that their use, or that of some equivalent, might be greatly extended, for both passenger and freight engines, without any disadvantage at all comparable to the gain. 503. But however well an engine may have been designed for the average contingencies of ordinary service, when the engine is once in service there are limitations to or variations in the efficiency of each of its three primary forces which have an important effect upon the load it can haul, and which we need to consider. In the following Tables 127 to 137 are given a variety of data as to the dimensions, weight, cost, and life of locomotives which we shall have occasion to use or refer to, which are here grouped together for conven- ience of reference. Table 127. Comparative Dimensions of Engines of the American Type. Weight on drivers.. Weight on truck Weight, total (lbs.). Grate surface i Fire-box Tubes... Total... Barrel of boiler Diameter of drivers Tender : I Total capacity -j (3jj^, (ibs.).... Wheel-base: DrivinsT Total engine Tender Engine and tender 17x24 Cylinders. Mason. 1873. 40.000 22.000 62,000 sq. ft. 16.38 105 906 lOII 46" 66" 2,250 8'o" 22' o" No. Pac. 1884. 54,350 iq.450 83,800 sq. ft. 16. 117 I I2l8 »335 51" 62" 27,900 29^438 57.338 3,8oo 6,105 8' 6" 23' 3H" 45' iH" Brooks. 1884. 48.000 26,000 74,000* sq. ft. 16.45 £.990. 1093. 48" 67" 2,640 S'o" 22' 7" 42' 6' C, B. &0. 1884. 53,600 27,600 8l,200 sq. ft 17.6 q8. 1 968. 1066. 49«" 69" 24,183 37.467 61,650 2,750 14.550 8' 6" 22' 6»4" 14' 11" 44' 9" 18 X 24 Cylinders. C, B. &Q. 1884. 54 500 28,^00 82,800 sq. ft. 17.7 102. 1 958. 1060. 49^" 69" 65" J 69" p. 1 65" n. 24,183 37.467 61,650 2.750 M.550 .8' 6" 22' tM" 14 44' 9 II" // Mason. 1884. 68.000 32,000 100,000 sq. ft. 18.9 £1230. 1375- 54" 68 // 3,600 9' o" 23' 4" West Shore. A. B. 64,000 32,000 96,000 sq. ft. 34- 128. E1084. I2I2. I 55" 68" 62,500 32.000 94.5a> sq. ft. 17- 12&. E10841. i2ia 34.000 30.000 64,000 3.000 10,000 8' 6" 22' 996" 15' 8" 47' aW • Weight, empty, 66,000 lbs., leaving 8000 lbs. for contents of boiler and fire-box, and two men. 408 CHAP, XL— THE LOCOMOTIVE ENGINE. CHAP. XL— THE LOCOMOTIVE ENGINE. 409 Table 128. Comparative Dimensions of Mogul and Ten-wheel Engines. Weight on drivers , Weight on truck.., Weight, total (lbs). Moguls. Baldwin 18x24. 1873. Grate surface 1 Fire-box. Heating surface \ Tubes. . . j Total.... Barrel of boiler Diameter of drivers ••••••« Tender : «,...( Empty. '*>*• (Total ^ .. 3 Water (galls.) Capacity j Coal (Ibi) .... Wheel-basb : Driving Total engine Tender Engine and tender 66,000 11.000 77,000 sq. ft. 16. 103. 948. 105 X. 50" 5^" Brooks 18 X 24. 1883. 72^500 13,500 86,000* sq. ft. 17- 114. 1141. "55- 53" B. &0. 19 X 34. 1883. N. S. Wales. (Baldwin) 18x26 1884. 87,400 60" 3,300 '5 23' 3,880 15' 6" 33' o" 79.000 17,000 96,000 sq. ff. »7 I1066. J 189. 55" 60H" 31.500 41,200 72.700 3,600 10,000 15' o" 33' 2" 14' 6" 46' 2Vi" Ten-whekl. Baldwin 18x26. 1873. 58,000 20,000 78,000 sq. ft. M-4 94- 1014. 1108. 50" 54" 3,300 Brooks 19x34. 1883. 73,100 21,400 94i5oot sq.'ft. 23.6 128.4 1422.4 1550.8 52" 5594" 3,880 13 2S' 6" 14' o" «5'3" ■45' 7'' • Weight, empty, 78,000 lbs., leaving 8000 lbs. for contents of boiler and fire-box. t Weight, empty, 84,300 lbs., leaving 10,200 lbs. for contents of boiler and fire-box. The Baltimore & Ohio Mogul carries 140 lbs. of boiler pressure, affording a maximum average cylinder pressure of some 119 lbs. (85 per cent of boiler pressure). At this rate the cylinder tractive force is 17,184 lbs., or about \ weight on drivers. In most American engines it is about J, and in some as low as 0.30. The tendency in recent years has been strongly toward increase of wei^'ht and boiler power with the same-sized cylinders, as Tables 127 to I30^and Table 142 bring out very clearly. Three concurrent causes have brought this about: (i) The material increa.se in steam pressure, which makes a smaller cylinder do much more work ; (2) the higher average speed of trains, which necessitates larger boiler power to maintain it ; and (3) the fact that the more perfect track has justified and the lower rates required loading engines up to the last limit of their tractive power, and it was necessary to have as much as possible under all conditions of rail and weather. Table 129. Comparative Dimensions of the Original and Present Standard Con- solidation Locomotive of the Pennsylvania Railroad, and of the West Shore Standard Consolidation. Class I. 1876. Size of cylinders Weight on drivers " truck Total wheel base Driving-wheel base Diameter of drivers Working pressure Boiler: Inside diam. smallest boiler-ring... •'T u.„ S No. and size (outside) TubcsJLengih i Length Fire-box^ Width (Depth •Grate surface {Fire-box Tubes Total Smallest inside diameter chimney. . Height top of rails to top of chimney Tender : 1 Empty 'Weights Load (Total capacuy]S";. .■.•.•.•.;•.•.•.•.■.•.:;: Wheel-base Engine and Tender Total wheel-base Length over all 20 X 24" 79,400 lbs. 12,240 lbs. 21' 6" 13' 8" 50" 125 lbs. 53%" 12' 11" 96" 34^'' 42 to 61" 23 sq. ft. 92 " " E 1,166 " " 1,258 " " 20" 14' 11" 22.770 lbs. 3-^.000 " 55,770 '• 3.000 galls. 8,000 lbs. 15' 4" 47' 7" 56' 9%" Class R. 1886. Increase. 20 X 24' 100,600 lbs. 14.025 (1 21' // 9 10 ji 13' SO- 140 lbs. 59" 183, 2^" 13' ^W 107" 42" 57 to 591^" 31.2 sq. ft. 167 " " E 1,564 " " 1,731 " " 18" 15' o" 23,800 lbs. 33.000 " 56.800 " 3.000 galls. 8,000 lbs. 15' 4" 48' 9" 58' M' None. 27 p. C. 14.6 " ^" 2" None. 12 p. c. 10.5 p. c. 32.6 " 11.5 p. c. 21.8 " 35.6 p. c. 8I.S " 4-5 P- C. None. 1.8 p. c. None. I' 2" 2' iW West Shore. 1883. -.1' 20 X 24" 88,000 lbs. 16.000 " 21' 7" 14' o' 50'' 140 lbs. (?) 55" 169, 2^" 13' 4%" 95%" 34H" 23 sq. ft. 120 " " E 1,340 " " 1,460 " " 29,000 lbs. 35,000 '* 64.000 " 3,000 galls. 10,000 lbs. 15' 8" 47' 7" 56' 8>^" The following; are some further details in respect to the changes in the latest Pennsyl- vania Consolidation from the earlier design : Cylinders. — Unchanged: diameter of piston-rod, size of ports, travel and outside 'lap of valves, size of slide-blocks. Piston-head, i in. thicker ; cylinders, 2 in, farther apart (7 ft. 2 in.) ; inside lap. none (in place of ^ in.) ; lead, ^ for \ in.; steam-pipe, 19.6 for 18 sq. in.; each blast-nozzle, 13.8 for 11. 2 sq. in. Journal.— All increased materially. Driving-axles, from 6i x 7J to 7x8!; truck- .axles, from 4J X 71'^ to 5 X 8 • ; crank-pin, from 4^ and 5 to 5 and 6 in. Coupling-rod and journals unchanged., 3J in. Boiler.— C/nchanged : material (steel ; wrought-iron tubes), distance between centres •of tubes (3i in.); thickness fire-box platefe Q in. outside ; /, in. inside), tube-plates (i in.). Barrel-plates, i and » in. for g in.; butt-joints, welted inside, for lap. Water grate for ■shaking grate. Tehder.— Unchanged : tank, 19 ft. x 43 in. high. The West Shore Consolidation was designed by the late Howard Fry, one of the most -eminent of American mechanical engineers, and was designed to include all the latest improvements up to its date. ! I 4IO CHAP, XL— THE LOCOMOTIVE ENGINE. CHAP, XL— THE LOCOMOTIVE ENGINE, 41 r Table 130. Comparative Dimensions of Engines more Powerful than the Con- soLiDATiON Type. Size of cylinders Weight on drivers . . " truck ... Total wheel-base . . . Driving wheel-base. Diameter of drivers. Working pressure . . Mastodon Type. (8 drivers ; 4 truck-wheels.) Central Pacific. BOILEK : Inside diam. smallest boiler-ring. T K-. 3 No. and size (outside). . . . Tubes^Lengih 4 Length Fire-box K Width (Depth Grate surface. 1 Fire-box . . "A Heating surfaced Tubes I Total Smallest inside diameter chimney. . Height top of rails to top of chimney Tender : ( Empty . Weights Load... ( Total . . -, ., j Water Capacity-! Coal.. Wheel-base Engine and Tbndkr ; Total wheel-base Length over all 19 X 30'' 106,050 lbs. 16.050 '* 15' 9f 54" 135 lbs. 54" 166, M' 12' 39>6 t?58U" 25.74 sq. ft. 182 " " I 1,076 " " X.258 ;; " 20" 15' 6^" 26,000 lbs. 37.000 I' 63,000 " 3,000 galls. i2,ooo lbs. 15' o94" 53' »«" 64' o^' Lehigh Valley. 20 X 26" 83,432 lbs. 19.264 '* 23' a" 13^^ o%" 125 lbs. 51" 199, 2" 11' 6'^ 34" 43^t0 52>^" 32 sq. ft. 179 " " 1 995 •; :; 17" 14' 7" 23,400 lbs. S3.8i8 " 2,575 palls. 8,960 lbs. 46' 9" 55' 4" " El Guber- nador" (Cent. Pac). (10 drivers; 4 truck-wh'ls) 21 X 36" 121,600 lbs 32.400 ** 28' 11" 19' 7" 57" 140 lbs Decapod (Baldwin). (10 drivers; 2 truck-wh'lsV 22 X 26" 128,000 lbs. 16,000 " 24' 4" (?) 56%'' 178. 2H" 12' o'' »7 o" 45" 50,650 lbs. 35,000 '' 85,650 " 3,000 galls. 10,000 lbs. 64'' 268.2" 12' gW' 10' i^' 39^" 65' 5' 80,000 lbs. 3,500 galls. These four engines are as yet the most powerful in the world. A Fairlie engine weighing about 85 gross tons and having two six-wheel driving-trucks, each with 17X23 cylinders, with a Bissell (pony) truck at each end, is running on the Iquique Railway, in Peru. Other heavy*locomotives are given in Table 137. The Central Pacific Mastodon (the original of the type) has hauled 20 loaded cars, weighing 422 tons, up a long grade of 116 ft. per mile. By Table 170 it should haul 421 tons At 8 miles per hour it is reported to have shown an average pressure of 124 lbs. per square inch in the cylinders. " El Gubemador," cutting off at five-sixths stroke, at a speed of 6% miles per hour, showed an average of 115 lbs. with 130 lbs. boiler pressure, or 88 per cent, which is much nearer to boiler pressure than is often possible, and de- velops the enormous tractive power of 32,039 lbs., or just 39 lbs. more than one fourth th« weight on drivers. As this is about the very utmost the cylinders can do, it indicates that the cylinders, large as they are, might with advantage be larger, or the boiler pres- sure higher. .J < s S o 3 S i O o I- rt en w •J n < H c z. o •J I-) o H s > < < z. H (A U < OS . w X Ul b. O C/3 z o z u Q Z U H H I/] S o o V) < s Q u z w O z a- • > o «> S.E ^ >. *** e Z ° o ® V) c t— .^ *«: c P« UJ o ^ • r^ •*oo ■*• •♦ PI n z" c« « ro 00 fO Oi 1 VO «^ ^0 ^^- H \0 lO "O \ VO 00 " <-• 00 00 o> o> 0. i ro m ♦ M V N IN W « M M W PI r<^ «^ 1/1 Lj • 8f; iri «n -»o ^ u in N w -^ 00 »o ■» rt n r.» •* 00 00 1- P^ m o\ r^ U ■♦^O \0 VO 00 PI •♦ PI ^0 2 M »4 »« «» Correc- tion, per cent on Mate- rials. • • ■«"«."*«. >5- ^ , tN. rrjoo •«.•«■«. NO • ■ « M « m 10 lo t^ N N « M M H M • t* ■♦00 •*■ 0> On PI PI rt M ro \0 iH so ►" ro^O "1 « in 00 N fn On rn •«- 10 00 00 r^ ■* »0 1000 fj fO M M N CO <» z. "O . 1 H S rt \r, to Ohm P~ m P« JO rt 2 ►4 10 N r^ 10 SO vO NO 00 (3 u ■ N ro ►" « o\ vo f M 00 P^ MOP* 1^ 8^ H o> t^ 00 00 t« r^ c^NO (A •-] <» CJ • 8f: m ir> u-)00 On ,_^ V . t^ P^ M 11 M H M l-l F. M ^ oco w r»^ 10 «0 \r> Wei in Serv Eng onl To f^ 1^ c t-« 1- ON ■*-f.1 M m c v. >>. T! ^'•^ >, UW «CL :i > > > ^^'^ rt cji -:X3: JIK E oi. ^. . d , -• c/5 , \ I • ■ H * • • • • J c • • • < 09 JS u ^ «• « « < a 6B- ■• c « ^ « c 2 -< M b a < a H O ca < < > H O S O U O ►J u b. O to u > O s o < CQ o; tfl CJ 73 c ^ > C — :« 2 "^ O Ul be c c/) -a S V. W X QJ O (/J *J 3 OJ tf3 4) rt O JZ rt > CO r. '-' >- in to --1 -c 'o -5 H OH Si .5 8 «« I :^ r^ CLi O 3 ^ fcC .. fli -* *^ ^ 2 -^ PCS CO 9^ bi£ a f*5 O vO < > ^ H U ■d u c at •» ^ H 3 4-1 "* '• < E CU « n po X u «0 PI Pi M M M a. a. < C H be c 10 c m t^ ro ro « M hJ «» u u ^ b. ° bO s o u 0) 00 ^1 f f 412 < (A Q < Q Z •< H W a < o 2; > 2 > H O >>% O u o 2: •< y M < c (/) < (d H •< fa O H O Q Z < H o CZr^/*. XI.^THE LOCOMOTIVE ENGINE. • SsS^JSJg ^5? ?R{?J;•8^ :S>?.s; \%^\ 'T no ONm>« ON M ftJx • s s •< -?" 5,-H":«-- :^^i^^^^i'''is>^r5s .0 'u 0. «c.^ ^ ' ^1 : :i?:«! : . : : . H4 fO ^ • ^0^0 . m • • • ■ • • w rri M M • I lis w . . . « ... : : : - . S>| S, ; ; • • , w M < u z rt ^ : * ■ : % : '. 00 ! ; * I ; ■ • • • • • » . . . . M 8 : : : f. . . . N ' i ! . . . r^ tC < Q Z3 il \o m . . . . r»^oo M f»> ^ • • • • • . . M M ... N • . . Bv • . . • • • • lol yj • • • • f^i H b^ 1** C/3 2 . : : : : • . • . M >.','.'. . . . . M M z ^ ::::.:•:: i| u b£0 • {?• eg -00 >o . * ■ ^H. ■ • 'e^ 2: • • * 00 w f' 00 • * • -ooio* -rofj' •«►. in 00 • : : in : : . : ♦ ►: • • •• •• M J* • • • • . • • • • • , , . M . . o • r»> . . .* • ■♦ • -to . * • . » 1 i • * • ! * I r I ! I ::::§ ^ i ij^^S : ::g; "8 1 03 • • • • • • • • • • • • 1 : : i i :■ M • M • : : : ;7» : : . i"^ ^ : rt : • • • . u • 6C • • • . . . . u : -i . u : . .^ . lA ; c : ! ! • . . . « : ^ * ! . « • *^ ; c« . . .^ • • . : : : I'-o . . . . c .... a : •? •a : ' pij * • • • • : •••§ :.= . 13 ; ' • : • : •• c ^ SvA ; ;.i§ :1 ■ cB ?: 4-1 _ ii "r: bcc 2 * «" w • i i{ : : : fl : ; . « : u w . . • • : S. • t s .2 ■ c a -1| : S : : : S : : : g. : S. t — . — • • • — ' V ■ .- • > ("^ • a . -b M : • „• — k W.JQ f> a - >^ ^ So CO 2 ■; 2 " :«>-.e2 ^ . c u u a s ^J«! c = p 2 ■g c iiJ< J; rt 2 u rt C.P^ 3UtdCU< • 4-1 00 f^OO (X Q 00 m c>oo 6< N .3-2 ^%^^ :^nS5>?;!;5,? ^^ :S';gjr5-8 N 11-1 •^ r»S u- 00 r«~ ■* « 00 > - 00 00 NO M • 00 u '• ; 0\ fn '•■00 • ln^O ts • . 10 • :? iagS-^ : : : M ■ . • • • • • ; : : : 010 .... . . . . rn 1»> < u iiS • • • • ■ • • • • • • • • • • • • • * • ; • ; • « N : : : : ° 8 111 t;;d •^1; i : : f- wwii . . . .«o >o. . . . . o> r8 1^ . • • • • • • ■ • ■ * » ^ fid i/5 • en be 1 . ui « . • • • • ■ • • . ' * ....MM . . . . 1^ t» •< >> Pi < z Q K • • • • M M .' e e« ^c • • • . OOk i-i CI * • • • • ^ • • • • . • • • • • : : : :2 8 H . . . hx . . . 00 . • . . . . ♦ in ...... 00 ••••■«■ 1 I i . ! •* 4-1 S : • •ojr>''r>ovo • -Ok »»> • '.JOS • w m . . f^io « • • M M H . ^ . . M 1 . . . « c n 2! 2 • •••••• • •••••• :: : :S, a 1 * • ■ • • • ••••■•• . • H M ::'*.'« . . . ro f' n • . • ■••••« • •••••« . . M : : : 1 ' • C.^.^P. XI.— THE LOCOMOTIVE ENGINE. M rfi .♦oo >{ 00 5 CO 5- 00 tx« ij- - IH ►. M lO M « 0> •■♦•V5 00 ■«- N O •«- N w 10 o r»>vo O ■>«•■♦■♦ f»i ■» H vg O N M NC I/) lO .CO : c U 3 •« ■ * »• 5 u b. (A cd ■ 111 w ^" *n V t; K C C c> C 1) w 3 ben) s: D.4' Jt >-• c vt .r, O CO u K « o O O Q. . K ►< ■ rt 2 o u a. -— ., a u a = o ~ ; Vi- i I- ■= H >Ij= 3 c cs « ♦oo o« 00 • o ro mi 00 r>. 8 : 8100 m M »o « « On ro •n m lo 10 M bi.!i= o^ ci c CB 4j c .- a ^ -:»^cauo<; O r^ m O ro m •^ t^ •♦ M lO N <;? O •*• «- ►^ On ♦ « ON ts. •.♦■ ro . M rv ^0 _ 10 . o ■♦ I O NO : W O O 00 o. ocT n O M o o ►- 10 J5 • tc : 3 to c « o^ : T «n : . — 4; O . CO ri§ '.£ c S- X ■ c ^ "n c { o 0>| NNO 00 00 ■.»- 80 tx O N ►■ O W On >»■ - N ^0 M NO f I MM M 10 O t>N t^ •*■ MOO w 00 On t^ M On tv ■♦ nB <0 I ? O On lO O '*• • 00 10 ^ M , fTN * •>«-oo - rr NO O J O o\ o> o« On rN. r^ «r> M m m 10 NO VO M n NO ro • 10 8 8 M I «n P- NO 00 O • T^ Q n . VO VO . M ITN 8 NO VO mNO M N N M M NO ■si 8 ! 00 i <^ 818 ^ o a a V tn tfl. O O, w 3 bA O O (U 3 *1 O O 3 o CO " •" >v ".. 3 (—1 nj ^ 9. a. I/: CQ rt U ■*-> U ■0 c a. Vu 4-* - T3 u a - 4) t/] a bi): C U (U <« u .2 k \i •^ of j( .4.J <;» "««« 4-> V J5^ ■V* H «o •a Vj CO 5J a> r* P-? ^N & t 4> 413 11 mi 414 CHAP. XI. — THE LOCOMOTIVE ENGINE. Table 133. Weights in Detail of an Old Illinois Central Passenger Engine, i6 X 22 Cylinders. [Abstracted from a record taken by Mr. M. N. Forney.] Boiler sheets, rivets and stay-bolts Braces, crown-bars, etc Tubes and copper thimbles .... Rin^fordry-pipe,furn'e-door,eic Dome Dry-pipes Throitle-valve. etc Steam and exhaust pipes Petticoat-pipe Blower Sm< >ke-box door Smokestack •Grate Ash-pan Weights — Lbs. Brass. Total Boiler Prames Boiler-braces Bed-casting . Total Frames ■Cylinders Sie;im-chest Valves Pistons Cross-liead guides.... Connecting-rods Crank-pins Driviny-wheel boxes. Valve-ge.ir Reverse-lever Pumt)S Purap-check valvfS. . . Total Machinery. Drivinjj-wherl centres.. . •• tires *• axles Truck-wheels " axles " frames, boxes, etc " check-chains Driver sprin'.,'s. steel *• attMchments Truck springs Total Running Gear. 40 75 38 13 10 16 9 301 no 36 18 13 117 113 3 436 39 883 7« Wrought Iron. 6,299 1,635 3»034 90 24 \o-\ no II 52 38 45 452 >75 314 12,382 3.553 628 29 4,309 6S 80 83 137 681 609 166 6 740 231 253 13 3.04a 3.360 «.033 "60; z,i8i 131 416 506 337 7.568 Cast Iron. »7 84s 93 193 377 336 300 1.333 3.394 913 913 2.795 805 133 363 340 42 430 984 »9 163 100 5.972 5.324 107 1.884 1,058 8.373 Wood, etc. 13 13 136 136 640 10 650 Total. 6,399 1.635 3.034 147 944 346 3x6 398 52 54 390 652 1,508 3M 15.989 3,552 638 941 5.i2» 3,106 921 333 389 933 768 166 548 ',724 343 853 I5» 10,033 5,964 3.360 1,140 1,884 604 2,3" »3J 416 5t6 337 16,663 CHAP. XL— THE LOCOMOTIVE ENGINE. Table \ZZ,— Continued. Safety-valve Steam gauges and cocks. ... Cylinder cocks and fittings. Injector Sand-box Bell and clapper \\'. " stand \\ Hand-rail '!.''.'.'. Running-board '.'.'.'.'.'.. Wheel-covers Cab and foot-board ... Pilot ;;: Head-light bracket .... .',*.'.' ,' Lagging and sundries Total Fittings. Tender tank Fittings for ditto .'....!.. Frame '''' Truck-wheels '.'.'.'.'.'.. Axles and collars !.'!."!!." Axle-boxes '*,",'.' Bearings and fittings for ditto. Springs Trucks and other parts Brakes Total Tender Boiler. Frame Machinery ... Running gear. Fittings Total Engine Tender Total Engine and Tender. . . , ■ Weights — Lhs. Brass. 53 73 10 66 45 80 68 63 60 139 4 Wrought Iron. 15 114 26 26 57 21 144 9 10 44 lOI 337 565 757 II 329 790 »9 2.437 64 83 3,515 37 1,124 1,272 29 880 1.330 143 8.330 Summary. 201 882 72 790 1.945 83 2,028 12,382 4.209 3.042 7.568 2.437 29,638 8,330 37.968 Cast Iron. 13 50 283 52 120 446 77 68 r,ii5 103 722 3.952 536 32 1,596 46 6,987 3,394 912 5,972 8.373 1,115 19,766 6,987 26,753 Wood, etc. 334 1,083 320 49 874 2,660 3 2,327 12 670 106 3."8 12 136 650 2,660 3.458 3."8 6,576 415 Total. 86 99 79 »37 472 89 130 107 495 596 2,098 1. 154 143 1.317 7.002 3,515 163 4.173 3»952 1,272 536 880 3-596 295 18,518 15.089 5. 121 10,032 16,663 7.002 54-807 18.518 73.325 "^^ "* hoLl* fi'lJ'K *'^'*^'!,' ^°'' "^^'^^^ °^ *^"^'"« '° working order, for contents of boiler, fire-box, and two men in cab, about contents oi And for contents of tender, coal ; ,: • • water (x6oogaiis.)::.::::::::::::::::;:::;;:: n^^^' Giving for total weight of engine in service ~ ^ „ And lor total weight of tender 60,807 40.018 Approximate total engine and tender in service Zs — 100,835 6,000 21,500 No. 0/ separate pieces, large and small (not including nails) )In engine. In tender. Tnfal . . 4.904 tender 1,366 Total 0,270 The proportion 0/ brass is now, in general practice, much less than in the above engine. 4i6 CHAP. XI.— THE LOCOMOTIVE ENGINE. CO PQ < < H Q H O O U o o w o Q < u ai H < O 1—1 u H b O H O u Q S5 •< (A H K O H CW^/'. XI.— THE LOCOMOTIVE ENGINE. j: ^ o> >nee c eo 1 1 M On lO £ £ M IT) M *^ 8 II 8 Mil " M 00 v\ b >0 O>00 to 1 <«■ « fO s o d f^ t^ "1 * 8 ■ 1 eo ^ E « lO - M 1 « =0 n o "mi c 00 C« 00 t^ lO 1 ■ 8 8 • - 1 CO M l-i 00 ■H 00 On M m oi fl On N VO O 1 • * On •- lO (A o J d» 1*1 tv »n ^ lO - « 8 S M 1 1 W <^ 8n ro < h z u u a: ■<«■ '■1 ■-> 00 •♦ 1 1 ■>»• «o ro d c c M r^ O ►< 0> to N r») 8 g M H On w 00 1 lO lO (^ < 0. N -*■ O fO 0» 8 M I w 00 w 00 00 N u 00 ■♦ ro lO . 1 0< M m • C4 C> M NO 0> 8 8 «^ 8n o ro HH M 1 H X u <« >.r. 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O r^ 00 rt 2 On O^nO ►" t>. •*■ OC 00 in 4; (« t^ ■"»- fo M fn ta r^ 00 o> o ■♦mm CO «c ir> w 1 00 • •«• ■ 00 • u«y o-^ G O On ♦NO t>» O 00 NO >noo lO On ►" t^ «o NC O NO O 0^ (/5 On c N ►. 00 z c;:? ■>«■ ^c lO M ro < 0£, O w •H 00 ►< ro On ■<»■ N On N « u U ro N CO o c h CO M rt c , lO N NO NO fO N ^ Q W 8 >: c S^ "- 00 m o> On t^ fO m L -< u ^^h' M •>< h 1^ t^ * U< cu^ n O t^ O 00 On li ■> 00 NO N rr, M fO CO ^ NO N .2 .- . 00 •-• t^ rovo in h o r^ 00 O t: J3 en K On t^ m t>> O N NO 1^ IT) ro > >N V K •o n c c c c » o o •a ^ be c c t; u •o « «» V aj c u V ^ •^ u c 3 o c 2 s be 2 ■ e o H 4a bo Si bo •IS 1/1 H -< Oi < a. S3 o u ro ^ "^ *-* ^ (« n «« (A >N 4* O k" 6 P 2 rt to .S "-» -o . ■" K ', « «* ^ O *» c p- a J: 3 o P^ «« w . — w ri u •=•0 S c "^ I/, tt C -C ^- c ** u Ph Q a- a- o "O u 3 !•; «0 «« n (J ^ 3 c "a O eS M g c ^ — _o « IS = ^ bo - c o t' o 'i °. u.S "O "O c c U C4 u c u •5' u o fc ii (A •o .5 2 w 3 ^ o t: u •a t« •o "* •a V, <« ^ ^ jQ S .!2 -^ S «■ 8 "S "5 •a T. "r bo c 3 C .:2 o c o u eo u •" O ro O u. O o .5 c ^ o .5 C O C t o « .52 i^ CO en be u ^ a o rs •r " rt •i; "a "" " 2 CO' O „ nT S S .= — -a O V CO CO y X u u o c (A .c < . Ic • u O a.c «• '^ •<-' c tx ft; u JS, V (-1 bo C tA C u O a - (J 43 C JS £ ? lA "O V CA SZ 3 CA V - ft; « -i: 2 S .2 a s a c .= J3 CO .2 » ei (A 5 3 ^ 3 •o o e« rt o %i o H c V ftj « C ft; u ftj . «ij m >i "^ *-> "(A ^ rt en *■ ft; « -a u ^ ft; a. ^ a f ^O eA *? (A O in eo 00 ''«-«0 M «noo O ro ir.NO NO o.NO NO CT M 00 NO O tv ro 00 ONr»>« M in ■ ee 00 « M M « NO « m ♦OO ♦ N M M M M 00 t-» ro m >n M *0 fO« 00 eo O" l>- M ►- in O ro- N M ♦00 1^ m ro On H O M W M w 00 ro in « « ro ♦CO- CO w 0> On in d IrtNO m ro'>i ''"IS A^^ CO w ro M NO «n tvoo M ro •-" NO ts. (N IH !& M NO m N com ro vo On rOM ro M m M m m N mom vo fO M I O^ « M ♦ ♦ N 00 N M m eT tT N 6> ro ro w ♦ W NO 00 CO w ro 00 O ro I- NO M NO « ro w I t-00 ♦ 00 00 On ♦ in N no" « w* >o NO ro moo Oi ejN " m ON «o NO 00 On W M m NO ro iH ro O ro t^ m m N rj O O ro cT m" 00 NO : : • • • • • • : : eo m « t^ « O'' in eo e« O roM a •o u C3 a 'k o u a a < C "« S r s O £ •- ^ — be lA et u be:^ •&s — N^ ^ ^3-0 ««; i! X <= «« rt t'^ 5i = o 417 (L) bo c o CO ^ CO •-■ to ^ O* 3 -« Iti -^ H S Si S ^ 8 rt o -D S £ JO c« *^ •-^ .<_> c/: ^~' ^^^^^Z^ of the working parts of engine^ on the Penn- sylvania Railroad occur immediately on starting from a stop A paper before the German Society of Mechanical Engineers showed that out of ,g engines (presumably a fair average)— "^^ 10 of shortest life were broken up after 10 of longest life were broken up after 15 were in use less than 20 years, and average of all 'was . 6.5 years. . 28.5 " The average mileage of German locomotives (Table 69) is 11,870 mUes per year indi- •eating a very short locomotive life in miles. Table 136, Approximate Life of Various Parts of the Locomotive. Part. I^ocomotives as a whole, American " " English (and Eu. rope generally) Tenders, T2in]a ** Frames, wood Authority. Life in Years. Life in Miles. • «••• •••■ Boilers, as a whole {ejc partial renewals) ** English (prob. an av. of all parts) " U. S. " " •• •♦ •• " (bad water) , Fire-box steel, bituminous coal fuel (wood, two thirds greater) Firebox steel, anthracite coal (iron or copper fire-box, about one third only).. Firebox steel {anthracite fuel, 50,000 miles less, passenger) Fire-hox steel (anthracite fuel, 50,000 miles less, freight) M. M., L. S. &M. S. Ry }r. P.Williams L. S. &M. S. Reports.... M. M. Association.. ..... L. S. & M. S. Reports. . . . McDonnell, M. Inst. C.E. M. M., L. S. &M. S Various sources 22 to 24 30 zo 7 10 to 14 M. M., L. S. &M. S M, M., Ph. & Reading... M. M. Association M. M. Association xo-f- 8 + 700,000 450,000 to 500,000 800,000 250,000 800,000 to 1,000,000 320,000 to 350,000 450,000 300.000 to 350,000 z8o,ooo z 20,000 300,000 250,000 CHAP. XL— THE LOCOMOTIVE ENGINE, CHAP. XL—LOCOMOTIVE RUNNING GEAR. 421 420 ^ Bad water estimated to reduce these last averages about ^-.000 mU^. -^ increasecost of maintenance $750 per year, or .* to 3 cents per mUe 7' ^/^f^^^^^^^,^^ J'^^ !; ^l r/Txc J^lTpel ;ea; o^ Lds^Uh L water. Z thence down to none with after deposit of scale. Nearly aU fractures (about seven eighths) are m side sheets, vertic , ^"S:"lT^^--Good water. England, every three weeUs ^^^^^^^ abo^one month, but much oftener with bad water T^^c^ness o/sU.i, almost univers ally : tube-sheet. /, to i"; sides, back, and crown, ft ; barrel, , . Mileage Life. j 74.000 I to i6i,ooo j 120,000 \ to 167.000 360,000 Fireboxes coPJer.—Gt. No. and L., S. C. & D. Rys., English (pass, and freight).. Tubes, iron, various English railways. . . . " •' entirely new sets McDonnell McDonnell ,oyrs.,L.S.& M.S. Reps Years. 6 to 7 «5 more ' ordinarily taken for entirely new sets at half ^^^1;^^:^^^^^^ piecings at end in addition, and removal o^^^^ J_^ ^^ rovrn:;b^oiSVtor^^^^^^^ 7ubes not essentially different ; require cleaning less frequently. .-Average of English returns, passenger, fair ^^^^ }^'J]^^\ Tabes, *rrt«. , ,. , , about one hall only) J Maximum reported (McDonnell, average of 10 years) \ •. T c A^ vr c: anrt T M & I. (max. before removal).. Axles, iron (.drivers). -\^. S. & M. S. and J .. M. a 1. vi«* , ♦» " (crtfw^).— English ' ,000. 4t »* truck.— L. S. & M. S n«Arinss (^r/T'*rj).— Various railways, per A" wear CesTr^o-, D , L. & W., 8..oco ; lowest, Philadelphia & Reading, X4 Tlrls .1/ -5' 6" average of U. S. ; 65,000 per turning ; 3 turnings in h;aTyserv^ce, with small drivers, near a^^^^^^^^ English reports very nearly the same, viz. -j ^/ g,. -j l>riving-wheel centres.-L. S. & M. S. Reports Cylinder8.-Same as engine. . „ ^ . Frame.-" A question of accident" (M. M. Assoc.). * ra™*'* "^^ ^* TT Q oR" to 10" wheels). M. M., Ph. & Kdg. Truck-wbeel8.-(About av. of U. S.. 28 to 30 wncc«; Teiider-wheel..-( About average of U. S., 33" wheels). vITves'-^ommon slide-valve between facings (M. M. Assoc.) " -Good balanced, several patterns, between facings (M. M. Ass'n).... scrap value, old English l-omotives (copper fire-bo., brass tubes), about p. c. of original cost of materials. Mileage Life. 200,000 290, ooo- to 437i000 300.000- 150.000- to 225,000 100,000 30.000 56,000 to aoo.ooo 100,000 196,600 106,000 to 150.000 z,ooo,ooo 34.O0O 50.0004- 30,000 75.000 to 100,000 10 The locomotives 18 to ao months. of the Pennsylvania Railroad go into shop for general repairs once in. Table 137. Miscellaneous Extra Heavy Locomotives. (A list published in the National Car- Builder.) Road. Kind. Reading Pennsylvania Baldwin Loc. W'ks. Boston & Albany. . . Pennsylvania Passenger Locomotives. Fast express. Class K. . Tank locomotive. Reading A., T. & Santa F^ Central Pacific Freight Locomotive. Consolidation Twelve wheels coupled Consolidation, tank Mogul, tank Weight. Total. 96,200 lbs. 92,700 " 85,000 " 80,000 " § 120,400 " 102,000 " 101,000 " X 115,000 •• On Drivers. * 64,250 lbs. * 65,300 " 1 35 to 45,000 lbs, 1 56,000 lbs. 88,500 lbs. 101,000 '* X 100,000 " 88,000 " Driv- ers. 68 in. 78 " 78 •' 66 " 60 " 50 " 46 " 48 " 48 " Cylin- ders. 21 X 22 in. 18 X 24 " 18x24 " 18x22 " 17x24 " 20 X 24 20 X 26 '* 17 X 24 " 16X24 " * On four wheels. t On two wheels. X Estimated. § Reported weight. THE RUNNING GEAR. 504. The distinctive peculiarities of the running gear of American locomotives, as compared with foreign, are two: the swivelling TRUCK in front (in England called " bogie"), and the equalizing levers by -which the load is kept uniformly distributed on the four or more drivers, and the effect of any chance irregularities in the track reduced to a minimum. The first was invented by John B. Jervis in 1834, before the trial of the Rocket had taken place ; the second was invented by Ross M. Winans, who also invented the double-truck railway car which has be- come all but universal in this country, only a few years later.|| 605. Both of these inventions, with much else that was novel and meritorious, had their origin in the necessities of the earlier years of American railways, which required that the locomotives should be adapted to ready passage over sharp curves and imperfectly surfaced track and road-bed. Both of them are now gradually making their way \ A crude form of double-truck car was shown to have been used in Quincy, Mass., before Winans invented it, so that Winans was unable to support his claim for patent; but he reinvented it independently, and really deserves the credit for conceiving of and introducing it as the normal type of car. m 422 CHAP. XL— LOCOMOTIVE RUNNING GEAR. CHAP. XL— LOCOMOTIVE RUNNLNG GEAR. 423 into England and throughout the world ; and both of them, beyond doubt, will eventually become universal, since they are almost equally advantageous on good roads and on poor roads, the only difference being that on poor track they are absolutely indispensable, while on good track they are not indispensable, but merely advantageous. In great part, we owe to them two advantages which experience appears to indicate that the American locomotive possesses: It can (at least it unquestionably does) haul greater loads in proportion to weight on drivers, and it is less readily disorganized, so that it can run in practice (at least it does) a great many more miles in a day and a year (see Tables 68, 69). The extent of this advantage should not be exaggerated. It does not clearly appear that on first-class track (on which alone English locomo- tives can be run at all to any advantage) the cost of locomotive repairs per mile run is noticeably different for either type, although the cost per ton hauled is enormously in favor of American engines. Nevertheless it still remains true, that wherever American locomotives have fairly come in competition with those without their distinctive features, as in Canada. Mexico, South America, and the Australasian colonies (in nearly all of which the right of decision has rested in English officials), they have in- variably obtained the preference, with exceptions that prove the rule. 506. The original type of American locomotive, still distinctively known as the "American" type, has two drivers coupled, spaced 8 ft. to 8 ft. 6 in. apart so as to include the fire-box between them, with a four-whee) truck in front. Until about twenty years ago this type was all but uni- versal in both passenger and freight service, but the name is now rapidly losing its appropriateness.* 507. At the present time there are the following types in common use in America. 1. American (Table 127). 4 drivers. 4 truck wheels ; still approved for light service, but passing out of use for ordinary freight and heavy passenger service. 2. Mogul (Table 128), 6 drivers. 2 truck wheels (pony truck) ; one of * Complete illustrations of every detail of the ordinary form of " American" engine, with outline drawings of others, may be found in the "Catechism of the Locomotive," by M. N. Forney, and drawings and descriptions of many examples of all the types of locomotives here named in " Recent Locomotives ' both published by the Railroad Gazette of New York. The catalogues of the Baldwin and the Rogers Locomotive Works also contain views and many of the details of all ordinary types of locomotives, with much other interesting matter All the above works are valuable ones for the engineer to own. the earliest modifications of the " American" locomotive and largely used, but in rather less favor than formerly. 3. Ten-wheel (Table 128), 6 drivers, 4 truck wheels; generally pre- ferred to the Mogul, and at one time bidding fair to become the standard type for heavy freight service, but now hardly tending to multiply, except as a substitute for the American for heavy passenger service. 4. Consolidation (Table 129), 8 drivers, 2 truck wheels ; a compara- tively recent innovation, invented by Alex. Mitchell, superintendent of the Lehigh Valley Railroad, in 1872. It has very rapidly won its way into public favor, and is now, it is hardly too much to say, the standard American locomotive for heavy freight service, and is fast coming into use for all but the lightest service. 507. These are the only types which can be said to be in general use for road service, but in addition there are the following in approved but more limited use: 5. Mastodon (Table 130). eight drivers, four truck wheels a very recent design introduced by Mr. A. J. Stevens, of the Central Pacific Railroad, in 1881, and said to be rendering most excellent service. Some have been built for the Lehigh Valley. It has not as yet (1886) been in- troduced to any extent on other roads, but it is exceedingly probable that it will be. While not very largely increasing the load on the drivers, which is not feasible, the four-wheel truck and greater load thereon not only makes the engine run better, but enables the boiler to be enlarged. 6. Forney, a type invented by Mr. M. N. Forney some twenty years ago, having the tender and engine combined on one frame, the tender running in front and its truck serving in lieu of an engine truck, so that the weight of the engine itself is carried wholly on the drivers. 508. The advantage of the Forney type is that it gives more tractive power (adhesion) for the same size of engine, by placing the entire weight of the latter on the drivers. Its disadvantage is that the boiler of no locomotive engine can generate steam enough to utilize its whole weight for adhesion, unless at slower than ordinary freight speeds, or in service requiring very frequent stops, as will be seen from par. 551. For such service only is the engine well adapted, and for such service only has it come into use. As this service is the exception, the quite extensive use which the type has recently been given still leaves it an exceptional type. It has been urged for use in general ser- vice, but is not well adapted for it in the respect mentioned. 509t Other types of engines are : 7. Double- Ender, with two "pony" trucks, one at each end, or 11*1 424 CHAP, XL-LOCOMOTIVE RUNNING GEAR. CHAP, XL.—LOCOMOTLVE RUNNLNG GEAR. 425 sometimes with one "pony" and one four-wheel truck; used chiefly for short-run local service. . 8 TANK engines; a type not confined to any espec.al form of run- ninggear, but available for any locomotive, whenever it .s des.rab e to have very great adhesion for short runs. As th,s adhesion can only be utuLd at very slow speeds, without exceeding the bo.ler power, there :s no economy or advantage in placing a tank on the engme. except as a temporary resource, unless for very slow speeds; and hence, naturally. veTsmaU drivers, carrying nearly the whole weight of the engme. are usual with tank engines. 510. This type, carried one step further, results i"- g FAIRLIE Engine; two boilers placed back to back wth a smgle frame and carrying on their back the entire supply of both fuel and wa r' The two "trucks" on which the whole is carried are drwmg- wheel bases, each carrying their own cylinders, which are supphed w,th Ttelm through a swivelling joint. It is siiU less possible for engmes o hlsType Ui^n for tank engines to utilize their great adhesion without exceed^g their boiler power, except at the slowest speeds. Consequently they have only found acceptance for work on very heavy grades where Irelt tractive power is necessary and slow speed no objection, and for flch service onlv are they suitable. The type is the invention of the late Robert F. Fairlie, the "apostle" of the now moribund narrow-gauge movement, and was pushed by him energetically for many years but without success, except as respects localities such as descried (_s for example the Mexican Railway described in Appendix C), where the type has done and is doing good service, although very costly to maintain 611. Finallv, in certain extreme cases, where still greater athat is all-sufficient to bring about the equilibrium of forces sketched in Fig. loi. as one might take out the slack of a chain before it comes to a bearing, and then the force O acts as before. . . , » ^.o^tiral Right here we touch upon the leading theoretical, and in fact practical, objection to the swing-motion truck, although its true cause is not always ap- preciated. We have seen (par. 516) that the force O is a constant, regardless of the radius of curvature. Consequently, whenever this force is called into- action at all, the same amount of lateral deflection. Oa, Figs. 100, loi, lo2» will take place, or tend to take place, unless stopped by the driving-wheel flange: coming in contact with the rail, which it is the object of the truck to prevent. Fig. ioi. Fig. 102. 521. This is not at all what is desired, since it correctly adapts the wheel- base to motion on only one curve, that, namely, on which the distance Oa, Fig. 102, = the offset to the curve at O from a tangent to the curve at c. This must be- on a comparatively sharp curve if the very object of the swing-motion (to enable the locomotive to pass sharp curves easily) is to be attained. On easier curves the amount of deviation which the swing-motion permits is as much too great as that of the fixed centre-pin is too small. On all easier curves the wheel-base will tend to assume a position something like Fig. 102. which is still less favor- able than the normal position of an American engine wheel-base, without the swing-motion, outlined in Fig. 100. It is true that, owing to the splay given to the links of the swing-motion, there is a certain amount of resistance to any lateral motion, however slight; but this is not sufficient to restrain the tendency lo assume the position shown in Fig. loi, and hence has little remedial effect. 430 CHAP, XL—LOCOMOTIVE RUNNING GEAR. CHAP. XL— LOCOMOTIVE RUNNING GEAR. 431 522. For these reasons the swing-motion, although very largely used, has never shown the advantage over the fixed centre which it probably would if the lateral deviation were in fact proportioned to radius of curvature, as it is often assumed to be. As orig- inally designed by Mr. Bissell (for ** pony" trucks) it was not open to this objection; two inclined planes being used, in the manner shown in principle in Fig. 103, which offered the same lateral resist- ance however much or little motion took place. But for practical reasons (rapid deterioration of bearing surfaces and impact when bearings return to the centre) this form has passed out of use, per- haps in part for lack of giving due weight to the theoretical advantages which it undoubtedly pos- jf sesses. I 523. The manner in which the two-wheeled / Bissell or " pony" truck (Figs. 104, 105) relieves the Fig. 103. driving-wheel base of lateral strain is quite differ- ent, and much less clear. Apparently it ought not to assist at all. except to the' very slight extent (especially on easy curves) by which the resistance of the swing-motion (Fig. lOi), which is directly over the axle, resists lateral motion; for it is free to swivel around its bearing at O (Figs. 104 and 98), regardless of the remain- der of the wheel-base. It is known to have in fact, how- ever, a very material effect upon the motion of the wheel- base, and theory very readily indicates to us why this should be. The "pony" truck natu- rally tends to roll forward in a right line, parallel to itself, Kl^a Fig. 105. as in Fig. 104. The rigid driving-wheel base behind, and not its own flange or its coning, as we shall see, compels it to move in a curve, to do which the driving-wheel base must exert a stress, O, Fig. 104, in the opposite direction to the arrow, of sufficient magnitude to produce motion in the direction ak. Fig. 105, and thus slide one or the other of the wheels continuously on the rail, compelling the leading axle to move in a curved path instead of a straight one. The resistance of the wheels to this sliding creates one or the other (not both) of the two forces represented by the longitudinal arrows in Fig. 104, and for the force O, resulting therefrom, we have O = (load on one wheel X coef. frict.) X f L!^' ^ , . / (Fig. 104) 624. Lest the wheels should run toward the outside rail, and from coning or •otherwise adapt their diameters to naturally travel in a curve, we have this further precaution: To enable both the pony truck and the transverse axis of the driving-wheel base to assume radial positions, the radius-bar of the pony truck should, from well known properties of the circle, pivot at the point O (Fig. 106), mid- way between c and the " pony" axle. If shorter than this, as at o. Fig. 106 (as it always is), the driving- wheel-base will throw the rear end of the radius- bar over through a certain distance (ak. Fig. 105) toward the outside rail, and thus create in it a tendency to run toward the inside rail and away from the outside rail. This tendency is increased by the fact that it is the rear and not the centre of the driving-wheel base which tends (par. 294 and Fig. 20) to assume a radial position, the front outer driving-wheel tending of itself to crowd ^hard against the outer rail. 625. These two causes together ensure that the pony axle shall always have a continuous ten- dency to run toward the inside rail and away from the outside, and if the radius-bar be made too short this tendency becomes so decided that inju- rious wear results. Thus, in a Consolidation en- pio. 106. gine of the Norfolk & Western Railroad the radius-bar was originally only 4 ft. 2 in. long, and created so strong a tendency to run to the inside rail that it was lengthened to 5 ft. 6 in. long, with very beneficial results. Even then the point O was some 9 ft. ahead of the centre of the wheel-base, c, Fig. 106, so that it was still much shorter than was apparently required to enable the wheel-base to adapt itself most perfectly to the curve. No very strong tendency in the pony axle to run toward the inside rail is necessary, but only just enough to ensure the driving-wheel base shall in fact modify its natural path in the way outlined, by however little, since if any force whatever (O, Fig. 104) needs to be applied to cause the pony axle to roll in the curve it must necessarily be adequate to slip the wheels on the rails: the stress necessary to slip them a little is as great as to slip them a good deal. 432 CHAP. XI.— LOCOMOTIVE RUNNING GEAR. CHAP. XI.—LOCOMOTIVE RUNNING GEAR. 433 From this it will be seen that xll = g (Fig. 104) the lateral force at neces- sary to alter the path of the leading wheels is just half diS great as if these were a fixed axle at O, in the English style (because there is only one wheel to slide instead of two), with the added advantage that the pony axle is approximately radial and guided by the wheel-base behind, so as to relieve the pony flanges of strain, and thus add greatly to safety. In addition to the force O, Fig. 104. the swing motion of the pony truck sup- plies any desired amount of additional lateral force, directly, whenever the engine is running on curves sharp enough to develop it fully. 526. For the forces acting on the leading outer wheel of any locomo- tive wheel-base. then, if it is in fact to perform the office of guiding the complete wheel-base on curves, we have these conditions: There is a vertical component equal to the load on the wheel, and there is a hori- zontal component equal to the forces determined for all the various types in pars. 516 to 525. These forces, as computed for a great variety of light and heavy engines of all types, have been plotted in Fig. 107, which rep- resents graphicallv the comparative degree of safety of various types of locomotives for passing curves ; and the surprising dejiree of uniformity which they show in a measure tends to confirm the correctness of our conclusions, since experience has shown that there is in fact no marked difference in safety between the engines themselves. Note to Fio. 107.— The diagram shows in magnitude and direction the resultant of the horizontal and vertical forces acting on the front outer truck-wheel of locomotive wheel-bases of all common types on curves of any radius (the same being, except for unknown variations in the coefficient of friction, uniform for all radii). The comparative safety may be considered as varying— First. With the direction of the resultant, as being more or less inclined to the " horizontal; those most inclined being the safest, other things being equal, since the re- sistance to the flange mounting the rails is then greatest. Secondly, and chiefly. With the MAGNITUDE of the resultant, or total pressure of the wheel against the rail. All American engines, embracing a great variety of designs and weights, will be seen to lie within the small quadrilateral marked out by the points i. 3, 10, 15. The more com- mon English types cause a far greater pressure against the rails, but as a compensating advantage have more nearly vertical resultants. ^^ Details as to all the locomotives shown may be found either in ♦' Recent Locomotives, Forney's "Catechism of the Locomotive" (Railroad Gazette), or Barry's "Railway Ap- pliances" (Spon). Manner of Constructing the Diagram. The vertical ordinates represent the load in pounds on the front outer wheel. The horizontal abscissa represent the lateral stress in pounds acting on the wheel, which consists of {a), with four-wheel trucks only, the flange pressure necessary to cause rotation in the truck, and (b) half the force (9, Figs. 99 and 104, required to be appUed at V * 434 CHAP, XL-LOCOMOTIVE TRACTIVE POWER. CHAP. XL— LOCOMOTIVE TRACTIVE POWER. 435 the centre-pin of the truck (or all of it in the case of two-wheel ' * pony » trucks) to produce rotation of the driving-wheel base. The various types of locomotives shown are : Mastodon. \ i— Central Pacific. (4-wheel truck.) 1 2— Lehigh Valley. Consolidation. \ 3— Baldwin. (Pony truck.) \ 4— Pennsylv'a (Class 1). Ten-wheel. < 5— Baldwin. (4-wheel truck.) \ 6— Pennsylvania. f 9 — Baldwin. Tr.— Pennsylvania. Mogul. (Pony truck.) ( 7 — Baldwin. ( II — American. (4-wheel truck.) Heavy Mogul. English. (No truck, lead ing axle.) 12— English fast passenger 14 — Pennsylvania fast pas- senger. 15— Old (light) fast pas- senger. reight type. Passenger type. ) 8— Pre ^- ^ 13-PaJ V TRACTIVE POWER. 527. The friction between the driving-wheels and rails which prevents them from slipping and enables them to propel the train is a static or mer" y resisting fdction. as distinguished from dynamic friction or that Twh^ch motion takes place between the surfaces in contact, w.th result- L destruction of energy. Its cause, beyond all question, is an absolute inferlocking of the roughnesses or projecting fibres of the surfaces in contact as cogs might Interlock. That this is essentially true of all frictTon between metallic surfaces, under the most favorable circumstances, iTs curio^^^^^^^^ by experiments of Mr. Beauchamp Tower * on the most finely polished and completely lubricated journals: a mere change m the direc fon of revolution resulted in a noticeable but temporary increase n the coefficient of friction, for which so careful and competent an ob- ervercouM ascribe no other cause than that the fibres were stroked one way by continuous revolution, as fur might be, and that on motion being reversed the fibres opposed each other 528. Our best existing evidence, by far. of the general ^^^^wmcn govern static friction between rail and wheel - -"^^^^^ '"J^/.^P^^ by Capt. Douglas Galton. giving the results ^^ JP^.^""1^" ^7/,g' efficiency conducted by him and by Mr. Geo. Westinghouse m 1876 T^ee experiments are quite unique in the completeness and accur^^^^^^^^^^ the apparatus used, and (what is still more important) ^"/he Uioj^^^^^ ness a'n'd technical knowledge with which the ^^^^^^^^J^l^^^^^ '^^ they positively contradict the assumption someumes^ made. that tne ♦Trans. Inst. Mcch. Engrs. . 1885. See Appendix B. coefficient of friction between rail and wheel is greater at low speeds "on account of less time for new surfaces to interlock." * An impression that the adhesion is less at speed has been derived, in some instances, from dynamometer records, which shows far less tractive pull between stations than in starting. This, however, results merely from the fact that the cylinders are not able to exert their full power at speed, and has no real connection with the adhesion. No error of moment can arise, therefore, from assuming that the resistance of the wheels to slipping is sensibly constant at all speeds. It is only at slow speeds that the precise amount of adhesion becomes important.! That the coefficient of adhesion is the same at all train-speeds has not been experimentally proven; but however fast the motion of the locomotive, so long as the drivers do not slip, the adhesion is equally static; and the only reason why the adhesion should be less at high speeds is that the fibres are afforded less time to completely engage with each other. That this difference may have some slight effect is possible, but as the available cylinder power falls far more rapidly with increase of speed, it is a fact which is not important, even if true. 529. When slipping has once begun, however, the conditions are very different. Chiefly from the Galton- Westinghouse experiments before referred to. which are confirmed from other sources and by uni- versal experience, we may derive the following conclusions as to the gen- eral laws which govern friction between rail and wheel ; all of which cor- respond closely with the results of modern investigations of other kinds of friction. * "The Pennsylvania Railroad Company," by James Dredge: Appendix on Brake Trials. The exact language of Capt. Galton on this point is: •* The amount of frictional resistance which determines the point at which the rotation of wheels is checked varies, it is true, in the different experiments. The ratio which it bears to the weight upon the braked wheels" varies from .29 to .35. averaging .25. " But it [the variations]clearly represents simply the adhesion between the wheel and the rail, and varies only with this, and not with the speed. " Thus at 60 miles per hour the amount of frictional resistance which checked the rotation of the wheels was about 2000 lbs, exhibiting an adhesion of about .191 per cent; at 15 miles per hour, 2160 lbs. or .196 per cent. As these two values are so nearly equivalent, it would appear that the effort is much the same at all speeds." f D. K. Clark, a usually careful authority, states (p. 724, " Man. Mech. Engr."), '* As the speed is increased the adhesion is reduced," as a result of his own tests of locomotives. The author cannot but believe, however, that this is an over-hasty conclusion by that able and usually trustworthy writer. IP 436 CHAP. XL— LOCOMOTIVE TRACTIVE POWER, 1. The coefficient of static friction between rail and wheel is not sen- sibly affected by the velocity of motion (as above). 2. It is very greatly affected by the insistent weight, increasing rapidly therewith. 3. It is very greatly affected by the condition of the surfaces as re- spects moisture or other equivalent for a lubricant, even when the eye can detect no difference, and is very considerably affected by unknown causes, so that it can rarely be determined twice alike. 4. It is greatest when the rails are very dry or (probably for the rea- son that the minute mineral and metallic particles which act as rollers are washed away) very wet, moisture or frost having the most injurious effect. 5. The coefficient of dynamic or sliding friction is very greatly less than static friction, and very greatly affected by velocity, in inverse ratio thereto. At the instant when slipping begins, the velocity of the rubbing surfaces being very small, it is sensibly the same as static friction, but as the velocity becomes greater it falls very rapidly, until it is hardly one third or one fourth as great as the static friction. Tables 112, 113, page 290, show the general results of these tests, and the evidence on which the above conclusions are based, more clearly than words. . From these laws it necessarily results that when slipping of the drivers once begins the resistance to further slipping (coefficient of fric- tion) should almost instantly fall, and hence that the wheels should almost instantly begin to "spin;" i.e., the surplus energy of the drivers. no longer required to turn the wheels against a great resistance, but only ag'ainst a small resistance, must necessarily go somewhere, and is stored in the wheels in the form of velocity, sometimes making them ••spin" so violently (when steam is not shut off soon enough) as to wear holes in the rails one-eighth to one-half inch deep. This spinning is not an evidence of overloading, since (par. 483) «n any well-designed engine letting in the full power of the cylinders will in any case give a greater tractive energy than the wheels can transmit. The proper course when it occurs is to shut off steam, let the drivers come to rest, and start more gradually. If engines are to be loaded up to their full capacity, only the greatest care can prevent this phenomenon occasionally occurring, and it does occur constantly in practice, in starting trains, although rarely when in motion, except when the train is almost at a stand-still. 630. A lonjx list of actual performances of locomotives in ser- vice is given in Table 138, and from this and the further data CHAP. XL— LOCOMOTIVE TRACTIVE POWER. 437 ^'Z^ to 0.37 (i) ^'Zl (i) 0.25 (i) o- 20 below it is clear that the following average coefficients of adhe- sion may be assumed with sufficient exactness as corresponding closely to the results of American practice. European practice (par. 537 and Table 139) shows much lower ratios of adhesion : Min. (load on TT1 • !• • r * drivers = 1. 00). 1. Ultimate limit of adhesion in practice, under con- ditions in all respects favorable, and with loads per wheel exceeding 10,000 lbs., . 2. Working limit of adhesion when sand is used, 3. Working limit of adhesion in ordinary summer weather, and maximum limit with loads of less than 10,000 lbs. per wheel, 4. Working limit of adhesion on slightly moist or frosty rail, being the apparent average of ad- hesion which limits the weight of trains in winter (as to which see par. 632), 5. After the wheels have once slipped, the co- efficient rapidly falls (see Table 112) to less ^^^" (iV)o.io 531. The first of these limits was realized by Zerah Colburn as early as 1853, and with light locomotives \io,ooo lbs. per driver), in his still famous tests on the Erie Railway, and re- peatedly since. In a large number of recorded instances trains have been hauled in regular service which demanded nearly or quite one third adhesion, but only as exceptional performances. A long list of notes as to such trains might be given. 532. The second limit (when sand is used) is less fully deter- mined, but various dynamometer records of the effect of sand to increase tractive power indicate that it increases the working limit of coefficient to about \ under all conditions of track or weather; that is to say, it makes the adhesion on a bad rail as high as on a good one. On a good rail it does not appear that the coefficient of adhesion is appreciably increased, but what is gained by the sand is to retard the tendency to' slip. Direct evidence on the subject is scarce, and there is no doubt a "liil .:''(!:' 438 CHAP. XL-LOCOMOTIVE TRACTIVE POWER. No. of Record. I. 3. 3 4 5- 6. 7- 8 9 lo. II 12 X3- X5 • x6 - 17. 18.. 19.. ao. . 31. 32. «3- 84- 95 s6. 37. s8. 89 30 31 3a 33 34 II::::; 37 38.... 39.... Cylin- ders. Inches. 13x22 14x22 15x22 16x24 tk X7X24 t k tt ii 18x24 19x34 16x24 kk - Loaded . . -j .390 -4 395.8 \ ^^^1 573-3 605 481 536 561 536 679 637 665 637 452 428 418.5 358 709 588 665 587 544-1 479 825 1 910 f 820 17 23 o± -45 25 42 28 24 60 121 78 65 o± 5-4^ -8 A% A.1% 6.6% 4-4^ 5-6^ 16.7^ 20.5^ 13.2^ ^zM Sharpsville. ti Western Ala. k * kk T. H. & Ind'olis. E. T., Va. & Ga. E. Kentucky. F. & Pere Marq. Mo., K. «& Tex. C. & Talc. (Chili). ill! I 440 CHAP. XI.^LOCOMOTJVE TRACTIVE POWER, Table 138. — Consolidation No. of Record. 40. 41. 4a 43- 44. 45- 46. 47- 48. 49 50. 5«- 53 53- 54 55- 56 58. 59- 60. 61. 6a. 63. 64. 65. Cylin- ders. Inches. 20x24 tt «> tt ti t( it ti i< (t ti it it it ti it it ti it it it ii 31x24 »i Ii it Wbight of Engine. Tons, 2CXX) lbs. En- gine. 45-8 ii ii tt it tt ti it It II It It ii it It it it It It it 60.0 ii tt tt Ten- der. 36.3 26.0 4» ti it ii ii ii it tt tl (I It ii ii II ii ti ti It tt ti 0.0 II 11 tl On Drivers 39 7 44.0 It It it it it It 11 It ii it it ii t. It ii tl ti it tt 50.0 tl ti it Tractive Power, Adhesion. Lbs. 19.850 32,000 II Ii t« it it tt it tt tt it it it tt it t« tt tl tt it it 95,000 tl It it Character of Performance. Grade. Feet Per Mile. Regular service. >i II do. (fair average work.) . Regular load Occasional load .... Trial trip Daily service Using sand Regular service (?). Maximum load Usual •' Maximum " .... Usual Maximum Usual Average of 5 years. it ii Daily service. ti 11 II tl it Maximum. + 6 96 145 -}- 10 116 -- xo 64 - - 28 96 4- »o 45 + 3 171 23 126 II If 96-t- 10 96 130 68.6 67.6 53-4 105.6 184.8 316.8 The caboose is included in the gross loads given when used on train, although not in- cluded in list of cars. ^ T, ,J . T The assumed ratio of adhesion used in this volume (as also by the Baldwin Locomo- tive Works) is M- The percentage by which the calculated load taken from Table 170 exceeds or falls below the computed load may be estimated by the following : An assumed adhesion of 1 would increase the calculated load 334 per cent. (( tl (I «» t •« decrease it 20 i( The principal cause of the fluctuations between the actual and computed loads, how- ever lies in the fact that the reported gradients are not the actual de-facto gradients for operating purposes, but are increased in effect, in some instances, by uncompensated curva- ture or stopping-points on the maximum grade, and diminished in others by the use of momentum to assist in surmounting them. No. 8 (Kansas Pacific) and No. 9 (M., K. & T.> are conspicuous instances of the latter, the loads reported as hauled being beyond all probability for de-facto grades of the given rate. Nos. 2, 4, 10, 11, 14, and 27 are prob- ably less conspicuous instances of the same use of momentum \.o practically reduce grades below the profile rate. In Nos. 27, 39. 61 this was expressly stated to be the case, and (the length of the grade being given) the corresponding de-facto grade per mile was com- CHAP. XI.'-LOCOMOTIVE TRACTIVE POWER. 441 Continued, Engines. No. of Record 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 63 63 64 65 Resist- ance. Lbs. Per Ton. zi.o 44 36 66.71 55 72 4* 85 48- 15 26.18 72.8 II 16.71 55-73 36 -79 48 15 ii 44-36 57-24 34-14 33 76 26.56 48. 78. 128. Train-Load. Actual. No Cars. Kind of Load. ^^^'•''li Loaded I 90.31 S 23 26 15 40 33 35 47 32 100 35 25 140 100 40 35 100 30 29 30 40 7 9 Loaded . Empties. Loaded . it ii Empties Load, 4-wh. . . 4-wh., coal.... II II Empty 4-wh.. 41 Ii Load, 4-wh... ti II Empty 4-wh. . Load, 4-wh... i5-ton load. .. ii Ii . . . Loads Loads . Tot. I'd, inc.eng. 1720 I 1886 f 438.4 298.6 405.2 478 375-7 393-7 1100 264 309 1 144 445-5 340.2 610. 1 458.8 498.1 445-5 457-8 392.8 752 776 1005 542 5 318.5 210.5 254 Accord- ing to Table 170. 1804 496 330 394 513 456 456 840 302 302 13*0 394 394 600 600 487 487 496 384 644 653 828 520 320 195 195 Excess of Actual Load over Table. Tons. o± -58 -31 9 —35 —80 -62 260 -38 7 — 176 52 -54 10 -141 II -41 -38 9 108 123 177 22 — I. 16 59 Per Cent. ■11.7^ - 9-4^ 2.3^ - 6.6^ ■17-4^ -13.7^ 31.05C -12.6jf 2.3^ -13-3^ 13-1^ -13.7^ -23-5?^ 2.3^ - 8.4;« - 7-7^ 2.45« 16.8^ 18.8^ 21.4^ 4-2jt o 8.2^ 30-3^ Name of Road. Ph. & Erie. Dom Pedro II. Tyrone Br.,Penn. Ii II Lehigh & Susq. Lehigh Valley. i. ii Missouri Pacific. Cumb. & Penna. ii ii Central N. J. Lehigh Valley. ti it It it it It «t ii it Chic, Burl. &Q. tl ii II II Ate, T. & S. Ftf. it it it tl puted and used in computations, the reduction being indicated by a — sign in the column* of grades. On the other hand, most of the instances in which the reported performance is less than Table 170 calls for are to be explained by high speed or by uncompensated curvature, except under Consolidation engines, where the character of the trains (chiefly 4-wheel coal cars) had no doubt equal or greater effect to diminish the load. Curvature was assumed to add only 1 ft. per mile (0.38 lb.) per degree of curvature up to 10° curves, and 2 ft. per mile per degree for sharper curves, when expressly stated to constitute an addition to the grade, and this addition is indicated by the sign -|- in the column of grades. A very low rate was assumed in order that tiie comparison of actual and theoretical loads might be more certainly trustworthy. From the above table we may conclude that if the given grade be the de-facto grade for operating purposes, with all effects of curvature and velocity elim- inated, an assumed adhesion of one fourth the weight on drivers and a rolling friction on tangent, at 15 miles per Jiour, ofS lbs. per ton {the latter being somewhat more than ample) will give very approximately TUTS, safe operating load IN REGU- LAR SERVICE. . A long list of further records of performance the writer omits to save space. Quite a number of them show more than % adhesion realized as an average of long runs, but not as every-day {>erforraances. ft 442 CHAP. XI.^LOCOMOTIVE TRACTIVE POWER, certain deduction to be made from the apparent gain because of the increased tractive train resistance caused by the sand on the rails 633. The third, and most important limit, that of ordinary working, is warranted by the all but universal evidence of mod- ern experience, as sufficiently proved by Table 138, which gives a long record of actual performances with locomotives, taken chiefly from the very abundant data given in the catalogue of the Bald- win Locomotive Works, and including all the records therein. The ratio of \ is used by them as the basis for computing the table of capacity on various grades given in their catalogue, and thus in a measure guaranteed by them, and the high character and great experience of that firm entitles this fact to far more than the usual weight which would be accorded to manufac- turers* evidence. 534. Many causes combine to make the apparent mdications •of practice very variable. One of the most important is that the nominal ruling gradient is not the real or - virtual" one, being in some cases higher than the virtual grade, because the rulin'^g grades are short and surmounted in part by momentum ; and in others (and far more commonly) lower than the virtual grade, because of the necessity of stops on unreduced gradients, or of unreduced curvature on the ruling grade, thus materially increasing the nominal maximum: so that if we assume the grades of the profile to be the virtual grades, the trains hauled will ap- pear to be only such as are due to \ adhesion, or even less. On very low gradients this is especially true; and, moreover, another cause comes in— the difficulty of starting, making up, and handling very long trains. From this it results that we very rarely indeed hear of trains being hauled on very easy grades such as are beyond all question within the power of the locomotive under conditions which are as fair actually as they are nominally. But when these errors are eliminated it will be found that in all cases, in good American practice, the actual ratio of adhesion is ^ whenever it is attempted to load the engines to their full capacity. CHAP. XL— LOCOMOTIVE TRACTIVE POWER. 443 635. The fifth ratio of adhesion, \, apparently applies to winter loads, and will actually give, in most cases, the loads which are hauled in practice in winter. It is usually assumed that this difference is due to the fact, that the ratio of adhesion is less in winter than in summer, but it appears probable that in reality, as we shall see (par. 632), it is due to an increase in the rolling friction, both because of greater axle friction and because of the poorer condition of the track. 636. In the former edition of this treatise \ instead of \ was as- sumed as the ordinary working ratio of adhesion. This was deduced Table 139. Comparative Ratios of Adhesion of American and Foreign Locomotives. Conditions. Maximum at slow speeds and under favor- able conditions Working maximum Ordinary apparent adhesion, Ratio of Adhesion. Foreign Engines. i or 0.25 ( ^ or 0.20 to \ i or 0.17 \ or 0.14 American Engines. tor 0.33 i or 0.25 ^ or o . 20 Many European engineers assume f, or even less ; but many American engineers, in like manner, assume \. From a summary by Mr. O. Chanute, in " Haswell's Pocket-Book," we may abstract the following data as to early and European tests of adhesion : Ratio of Adhesion. Mr. Wood on early English railways (per- J Slm^ormTd^y rails! :::::::::: V<^ haps the earliest tests on record) | Very greasy rails 0.04 B. H. Latrobe on B. & O. R. R. 1838 Safe working limit 0.13 (Maximum 0.20 Modern European practice •< Minimum o.ii Soemmering line 0.16 Italian Alpine road, subject to frequent Maximum in open cuttings 0.12 mists *l Maximum in tunnels o.io Dry weather -j oJo^^ciSS Damp weather \ °' j^* Prench experiments. 1862-67 by Messrs. Vuil- J | ■ 39 lemin, Guebhard, and Dieudonn^. Wet weather. 39 0.078 0.164 Light rain 0.09 Rain and fog 0.14 Heavy ram 0.16 The last records are of dubious value. Mr. Chanute gives a table of average European and American practice, which differs somewhat from the above, but seems open to ques- tion in several details. M 444 CHAP. XL-'LOCOMOTIVE TRACTIVE POWER. by comparison of the actual loads hauled on various nominal grades by the same engine. Besides the causes just mentioned, however, which tend to make this process inaccurate, within the nine years from 1876 to 1885 a very great change has taken place in the average train-loads hauled on American railways, as shown in Tables 30 to 33. and others. Much of this is due to the use of heavier engines, but a great part of it is due to greater care to load engines to their full capacity. 537. The adhesion of English and other foreign locomotives is ordi- narily stated at less than of American by a considerable percentage. Table 139 approximates closely to the difference which appears to exist. How much of this represents an actual difference of capacity and how much is due merely to difference of administration, it would be impos- sible to say ; but there is no room for doubt of the fact that foreign engines haul lighter trains, as a rule, than American engines of the same weight, or that European engineers state the limit of their ad- hesion at less than that given by American engineers for American engines. ""ines. 538. If we may assume that the loads hauled by the same engine on any two grades are affected only by the difference in the grades (which ordinarily we cannot, except very approximately), we may at once deter- mine from the records of these loads the rolling friction and ratio of adhesion, as follows ; Let L and L' = the gross load (including its own weight) hauled by the same engine on any two grades, i' and ^'. Let X = the total resistance per ton on the lowest grade g, and d - the an ference in resistance per ton on grades ^ and / (being that due to gravity only, and equal to the resistance from gravity on a grade of/ - g). Then whence Then we have Lx = L'(x-{-d), L'd Rolling friction =x- resistance from gravity only on grade g. Traction of engine = xL traction Ratio of adhesion = "^t^ ^„ driZ^' But while these formula are theoretically correct, results determined by them are to be accepted as reliable only with great caution. If the reported low grade loads are too small, as they usually are. the effect will be to greatly increase the apparent rolling friction. ^ . r- ^^ 539. Owing chiefly to some misinterpreted experiments made in France CHAP. XL— LOCOMOTIVE TKACTLVE POWER. 445 ^ome years ago by a M. Rabeauf, a chief engineer of the Corps des Ponts et Chaussies, there has for some time been some available authority to show that there may be such a thing as ** imperceptible" or continuous slip in the driving-wheels of locomotives in motion. Such a thing is really impossible, but the impression that it occurs has become widespread, and mere assertions in support of it, or allusions to it as a well-known fact, exist without number. The experiments referred to, from which this wholV' imaginary discovery seems to have originated, were described in a paper in the Annates du Genie Civil (1876), in which the record was given of tests of a fast passenger engine for the Northern Railroad of France, having four coupled drivers 6 ft. 10 in. diameter, carrying 2Jb\ tons on a grade of 0.5 per cent (26 ft. per mile), with good rail and weather, and 121 lbs. per square inch boiler pressure. The repc^rt continues: • " Under these conditions the locomotive, which was tested alone (hauling no train behind it), attained a speed on the down grade of 74^ miles an hour, corresponding to 303 revolutions of the drivers per minute. Now, the regis- tered number of revolutions was 360, corresponding to 88.8 miles per hour — a slip of 19 per cent. "Surprised at these results, the writer repeated the same observations on a certain number of locomotives of different types, comparing the speed with the revolutions of the drivers. It was generally found that the slip was slight on an up grade, but very apparent on a down grade, ranging from 13 to 25 per cent. It increased rapidly with the speed." This evidence appears pretty conclusive, especially as other articles and paragraphs to the same effect have appeared from time to time, accompanied by various reasons why the centrifugal force of the counterweights, and what not, must have the effect of producing it. 540. As a result of these tests it was concluded that " common locomotives" were 'actually unsuited for speeds of 60 to 75 miles per hour," because the slippage was as much as 20 per cent. In a specific instance (the Uetliberg road) referred to in the paper it was said that on grades of 7 per cent (370 ft. per mile; less by i per cent than is now successfully operated in Colorado, and less by 3 per cent than was successfully operated on temporary lines by the late Benj. H. Latrobe) "the slip of the driving-wheels was found so considerable that the gear system was found more economical." in spite of the slow speed. 541, On the other hand, tests of various American passenger locomotives at speeds at from 75 miles per hour down, made by Prof. Chas. A. Smith, Mr. Albert F. Hill, and Messrs. Henry Abbey and Oscar H. Baldwin (see Engineer- ing, Aug , 1885), to mention no others, have uniformly indicated that no such phenomenon occurs with American locomotives under any circumstances. There is an undoubted possibility, so far as this evidence alone is concerned, that the phenomenon might not occur with American locomotives, and might occur with differently constructed foreign locomotives; but in addition to the :grave reasons for questioning the physical possibility of the assumed phenom- CHAP. XL— LOCOMOTIVE TRACTIVE POWER. AA^ , enon, as being contrary to what is known in other ways of the laws of fiiction^ it is not difficult to see how the alleged slipping may have occurred and yet have been in no respect "imperceptible" slip, nor different in any way ixora, ordinary slipping, which is perceptible enough. 542, When a locomotive is only moving itself, especially if running down a grade, and so having little work to do, and when all possible power is put on' to run, in literal truth " as fast as the wheels can turn," whether the wheels are slipping or not will make no very conspicuous difference in their speed of revo- lution; while, on the other hand, the work required of the locomotive, simply to keep up speed, will be so small that, when the wheels once begin to slip, the loss of power will not be so great as to prevent the acquirement and mainte- nance of very high speed, although they will continue to slip indefinitely, never- theless. On the other hand, with a traifl of even one car behind the engine no high speed could probably be maintained under such conditions, for the mini- mum power to maintain the speed would then be so great that the speed would be immediately checked, and make it clear to the senses that the wheels were slipping. Whenever the locomotive was running up any considerable grade it would be still less possible; and the cautious statement quoted above, that it was "generally found" that "the slip was slight" on an up grade, probably means that, as a matter of fact, no absolute evidence of any slip was detected, or the figures for it would have been given. 543. To make the true explanation of the phenomenon clearer: Suppose, when the wheels of a freight engine were slipping, while it was standing still, that the engine were simply uncoupled— instead of shutting off steam in the usual fashion. If the grades were not too unfavorable the engine would prob- ably start ahead, the wheels still slipping; and if all the steam were put on, on a favorable down grade, a velocity of " 74^ miles per hour" might possibly be obtained, with an "imperceptible slip" of 20 per cent. These, or something like these, are probably the conditions, and the only conditions, under which the phenomenon has ever been observed, and they correspond to nothing in the worst extremes of practical operation. The only thing really proved by such "tests" is that even the wheels are slipping in ordinary fashion they will kick hard enough against the rails to make an unloaded engine move down a grade at a very lively pace; which illustrates how easy it is to draw wrong conclusions from observed facts. 544. The effect of the CENTRIFUGAL FORCE OF THE COUNTERWEIGHTS of the locomotive to modify the pressure of the wheels on the rail is con- siderable, and especially on bridges very important, but as respects its effect on the adhesion it is less important, if indeed it can be said to be of any importance. The counterweights are weights added to balance the piston and other reciprocating parts, and thus prevent serious disturbance of the CHAP. XL— LOCOMOTIVE TRACTIVE POWER. 44r Fig. 108. motion of the engine. They are either cast-iron weights between the spokes of the drivers or lead poured into hollows in the wheel-centre^ and have the effect to make the wheel lop-sided. When the counterweights are in the position a. Fig. 108, their centrifugal force will be so much added to the weight car- ried by the wheel, and increase its pressure on the rail by so much. When they are in the position a', at the top of the wheel, the centrifugal force will decrease the pressure on the rail. When they are in the position d and d' the centrifugal force will have no vertical effect. As respects freight engines, especially when the engine is working hard enough to be in any danger of slipping the wheels, the speed is ordinarily so slow that the centrifugal force of the counterweights is all but imperceptible. As respects passenger engines, the counterweights can at worst exert no appreciably injurious effect upon the adhesion, for the reason that the possible boiler tractive power decreases with speed very much faster than it can be diminished by any possible effect of the counterweights. 545. But while this phenomenon has no measurable effect upon the adhe- sion, and is not likely to have a very serious effect upon the track, it may and does have such effect on bridges. The sharp variation which takes place in the load on the rails has no effect on the riding of the engine, since it does not act through the springs. But it does give to the rail what has been not inaptly termed a "hammer-blow;" and its effect on bridges (especially on over light bridges; see Chap. XXIII.) is visi- ble in the striking diagrams repro- duced in Figs. 101-108, which show how very greatly the oscillations of bridges are increased when the period of revolution of the drivers happens to coincide with the period of oscillation of the bridge. JRWwrvvwvYy IT: 173. Figs. 109-1 16 are from observations on the vibration of bridges by Prof. S. W. Robinson. They show the vertical and lateral vibrations of the panel point nearest the middle of its lower chord during the entire passage of the train. The upper line, AB, shows the ver- tical movements, and the lower one, MNy the lateral movements. The lowest one, XY^is a. line of reference. ^r»v^l^^w^nn^^^o^ —M ^-- Figs, ioq, ho.— Effect of Passage of Fast Pas- senger Trains (40.8 and 42.1 Miles per Hour) OVER Through Pratt Truss, 148 Ft. Shan. As a train 448 CHAP, XL-^LOCOMOTIVE TRACTIVE POWER, CHAP. XL— LOCOMOTIVE POLLER. 449 T^ Figs. iii-«i6.— Vibrations Produced in the SAME BrIDCB by THE PASSAGE OF VARIOUS Freight Trains at Various Speeds. Vertical Scale three fourths of actual move- ment. [Through Pratt Truss Bridge, New York, Pennsylvania & Ohio Railroad, near Leav- ittsburg, O., 141 feet span, 24 feet deep, 9 panels, 15 feet 8 inches each. Kind of engine and train and speed given in each diagram. The scale below " Length of Train" shows the revolutions of the drivers.] T ^ 1 L »_jai.i-i-i-iJj.J. i-»-L-i j-Li-.LL.i-i. ^ approached the indicator was started, making the straight lines to the left oi AM and ^. As the train struck the bridge lateral motion of the pencils began, and it will be seen that in all cases the deflection was greatest within a second or two after the locomoUve had entered upon the bridge, or about when the whole of the engine and tender was fairly on the bridge, and long before it had reached even the middle point of the bridge. The hollow in the diagrams, which immediately follows, showing a reaction from this extreme depression, indicates clearly that the latter is a dynamic effect, the sudden depression caused by the entrance of the load setting the bridge in motion downward so quickly that its momentum carries it down far below what even much greater static strains are able to maintain. It is probable that bridges of longer span and greater weight would show this effect much less markedly. The length of train and also a scale (on the right line between A and B) on which the revolutions of the drivers are indicated has been added to the originals. It will be seen that in every instance the vibrations of greatest magnitude are almost exactly synchronous with the drivers' revolutions, but as the vibrations decreased they be- come less so, and when the vibrations become a mere wavy line there is no observable connection whatever with the drivers' revolutions. . The difference in the effect of passenger and freight trains, or of different construc- tion and speed, as shown by comparing Figs. 115-16 with Figs. 109-10, is very noticeable and curious. THE LOCOMOTIVE BOILER. 546. To burn more than 80 lbs. of coal per square foot of grate per hour is sure to decrease the efficiency of combustion, although as much as 100 lbs. may be burned under favorable conditions, with fair economy. When combustion is pushed beyond this, as it not unfrequently is, sometimes even so far as to apparently double it, it is all but certain that a large proportion of the additional coal supply will be ejected at once from the smoke-stack, unconsumed. As much as 20 per cent of the entire coal put into the fire-box has Fig. 117.— Lump of Unconsumed ,, , . ^, ^^^i,« K^v nnA Anthracite Coal, Natural Size, been actually caught in tne smoKe-oox, ana ejected from the Smoke-stack . -^ «.U„4. «,Uon m r»r^ tVl an l in OF AN EXPRESS LOCOMOTIVE WITH It IS quite certain that When more tnan 130 ^^^^ ^^^^^ ^^ ^^ ^^^^ ^^ to ICO lbs oer square foot are "burned" through the Open Window m 10 i^u lus. pci 34 a , , . THE Second Car in THE Rear. nearlv the whole of the excess of supply is (This lump was picked up by Mr. •'^ , ^ t-1 /r\ T?- ,« -4.1, Geo. W. Parsons, who handed It to thus ejected (see lable 140). fig. 117. Wltn the writer, still hot. The most sali- its accompanying note, gives a rather exag- J« »i;ffb„T'SiS?iy'""o^rar'^er gerated instance of what is continually tak- S'a^^^SJd^bmln'.l'umerabi^ incT Tulare The minimum waste of coal in smaller ones. The lump was near- ing pidCC. 1 lie . j^ ^ ^^^^ j^ partially ignited its this way is probably 5 per cent. specific prraviiy would have been . c ^ much reduced, and it would have 647, The ordinary evaporation Ot water been more easily carried out by per pound of coal burned is hardly more S^^he p'ciae'^?""'"'" "■°''" "^ than 6 lbs. in this country, and sometimes only 5 lbs., or even less, although it rises to 8 or 9 lbs. in some cases, 29 (' , t. I; 450 CHAP. XI.-^LOCOMOTIVE BOILER. and very frequently if not usually does so abroad, where the evaporation is more economical than is common here, owing in great degree to the combustion being less pushed by the hauling of heavy loads, and in part, probably, to more skilful firing. Theoretically, a fair ordinary coal (of 14000 heat-units— not by any means the best— see Table 140) ought to ev'aporate something over 12 lbs. from water at 60° Fahr. to steam at 120 lbs. pressure. Table 140. Heat-units in Various Fuels. Pure carbon — , Pennsylvania anthracite. . . Pittsburg bituminous Illinois coal (pure quality) Heat-units. Evap. Power (lbs. water) from and at 313*. English coal (average).. English coke (average). Crude petroleum Lignite Asphalt Dry wood (all kinds) 8,000 I 10,000 s 14,858 \ 13,860 f 14,150 1 13,300 \ 91834 \ I4»449 ) 14,500 i4»5oo 14.200 9,000 14.330 »3.550 30,340 11,678 16,655 7,79« X4-34^ X5-5a J ( 13.73 t 10.18 I 14.96 f 15.0a 15.03 14 69 9.30 -4.83 14.03 lbs. aO.33 ** 13. 10 •• «7.a4 " 8.07 " The heat required for evaporation •'from and at 212" (i.e., the conversion of water at ai2» into steam at 212- or atmospheric pressure) being i.oo, the heat required to turn water at normal feeding temperatures into steam of usual working pressures is as foUows: Feed- Steam Pressure above Atmosphere— Lbs • water. • Fahr. 20 40 60 80 100 120 140 160 40* 6o» 8o» lOO* 1.193 1.173 1.151 X.131 1.303 1.183 1.161 1.141 1.309 1.188 1. 167 1.147 1. 314 I 193 1.173 1.153 1.319 1.198 1.177 1.157 1.333 1.303 I.181 I.161 1.336 1.205 1.184 1.164 1.339 1.308 1.187 1.167 (Abstracted from a large table in " Steam-Making," by the late Prof. Charles A. Smith.) The lowest rates of evaporation occur with the highest rates of combustion, and vice versa ; and ordinarily it is not possible to evaporate more than 600 lbs. of water per square foot of grate per hour (say 80 lbs. coal X 7i lbs. evaporation ratio, or 100 lbs. x 6) for any length of time. CHAP, XI,— LOCOMOTIVE BOILER, 451 More may be done, but it cannot be relied on, and 500 lbs. of water per square foot of grate would come nearer to a moderate working maximum. 548. The ordinary load on drivers per square foot of grate ranges from 2500 to 4000 for ordinary types, as shown in Tables 127-130; 3000 lbs. being rather low for passenger engines of the American type and for Consolidation engines, and 4000 rather low for Mogul and Ten-wheel engines. The larger proportion of grate surface in the Consolidation type may be considered as in part a concession to the difficulty in firing such engines. 649. The steam used in the every-day working of locomotives (in- cluding the entrained water carried along with the steam mechanically) to •do 33,000 fi.-lbs. of net effective work is somewhat under 30 lbs., never, probably, running very much higher than that, and rarely quite as low as to 25 lbs., even under the most favorable circumstances; that being the lowest fair assumption for steam used at slow speeds on long grades or at other specially favorable points, except that for very short distances •considerably more than that may be shown, owing in part to drawing on the small reserve of power in the boiler (par. 553 and Table 144). 650. Then, as the production of steam is 600 lbs. per square foot of grate per hour, and the consumption per horse-power per hour is rarely better than 25 lbs. and often much worse, we have ^^ = 24 horse-power as the maximum ordinary capacity of one square foot of grate area. Tables 146 and 147 will indicate that this is, on the whole, a rather favorable showing for what can be actually realized. But to determine the very highest maximum which can be claimed in the way of locomo- tive performance, we may appropriately refer to Mr. Wm. Stroudley's paper on the locomotive performance of the London, Brighton & South Coast Railway (Trans. Inst. C. E. 1885), where we find that an average of about 600 indicated horse-power was maintained for 6 or 8 miles in succession by an engine with 17.04 square feet grate area, with an aver- age horse-power for the whole run of 50 miles of 528.5, corresponding to Indicated H. P. per sq. ft. grate maximum 600 = 35-3 H. P. average 528.5 _ 17 = 31.1 (( 2iet effective <« (10 per cent less), say, 32 and 28 H. P. In round figures, 30 effective horse-powers per square foot maybe said to be the ultimate limit. 651. The horse-power which, if it could be produced, might be trans- 452 CHAP, XL— LOCOMOTIVE BOILER. mitted through the drivers for propelling the train is very much greater than this except at the slower speeds, so that at the slower speeds onljr is it possible to utilize the full adhesion, as may be determined thus : Per Square Foot of Grate Area. Usual load on drivers, as per Table 141. 3.000 to 4.000 lbs. Equivalent tractive power for \ adhesion, 750 to 1,000 lbs. Table 141. Load on Drivers Per Square Foot of Grate Area for the Various Locomotives given in Tables 127-130. Table 127.— American Engines. Date. X873 .. 1884... 1884 .. 1884... 1884... 1884... 1884 . . Road or Maker, and Cylinders. Mason, 17x24 No. Pacific, 17x24.. Brooks, 17x24 C, B. &0., 17x24- ♦' " 18x24. Mason, 18x24 West Shore -j 3 * • Lbs. per sq. s. pel J. ft. Table 128.— Mogul Engines. Date. a.440 3.390 2,920 3.050 3.070 3.590 i,88o* 3.670 1873... 1883... 1884... Road or Maker, and Cylinders. Baldwin, 18x24 — Brooks, i8 X 24 Baldwin (N.S.Wales),i8x26 Lbs. sq. r 4,120 4,270 4.650 Table 129.— Consolidation Engines. aox 24 cylinder*. Table 128.— Ten-wheel Engines. 1873 . . 1883... Baldwin, 18x26 Brooks, 19 X 24 1875-6 1886... 1883... Penna. "Class I".. " " Class R". West Shore 3.450 3,210 3.830 Table 130.— Mastodon Engines. Central Pac, 19x30. Lehigh V., 20x26... 4,120 2.570* ♦ These engines have specially large grates to permit of slow combustion. Then the horse-power per hour per square foot of grate area which will or might be transmitted through the drivers, if their utmost adhesioa be utilized, will be — _ load on drivers ) _ 5280 ^ ^ ^^ -^^ ^^jj^g ^^ hour. Max. H. r, - T^eff . adhesion ( 33.000 x 60 By this formula Table 142 was computed, which indicates at once a truth of the first importance-that it is absolutely impossible to produce enoucrh power in the boiler to utilize more than a small fraction of the available tractive power at any of the higher speeds, and it is only as we fall below 1 5 miles per hour that it becomes possible for even freight engines to do so. CHAP, XI.— LOCOMOTIVE BOILER, 453 Table 142. Horse power of Net Effective Work required to be Continuously Generated Per Square Foot of Grate Area to FULLY utilize the Entire Tractive Force of Various Engines at Various Ve- locities. Adhesion assumed, \. Reduce by one-fifth part to correspond to \ adhesion. Pounds on Drivers Pbr Square Foot of Horse-power to be supplied Per Square Foot, at Velocities in Miles Per Hour. Grate Area. 10 15 20 30 40 «,ooo 1 Minimum for American engines. Freight types. 1333 16.67 20.00 23 -33 26.67 30.00 20.0 25.0 30.0 26.67 40.0 : 50.0 60.0 70.0 80.0 90.0 53-33 66.67 80.00 93 33 106 . 67 120.00 «.500 33-33 3.000 . 40.00 46.67 53-33 60.00 3.500 350 4,000 4.500 . 40.0 450 50 66.67 83 -33 100.00 116.67 133-33 150.00 The black line marks the limit at which it ceases to be physically possible, under the most favorable circumstances, for the boiler to produce sufficient steam to utilize the full adhesion, allowing 30 horse-power per hour per square foot of grate (an ordinary maximum being 24 horse-power) and for \ adhesion. To add a similar line corresponding to \ ad- hesion, draw the line at 37.5 horse-power instead of 30 horse-power, as indicated by dotted Ime, making little change. 652. There is, however, one more resource for eking out deficiency of boiler power — to draw upon the reserve in the boiler itself, either by pumping in no feed water for the time being, or by allowing the pressure to fall somewhat while the excessive demand continues, or both. Neither of these resources amounts to much, although both assist very slightly. As respects variations of pressure ; as the pressure of steam rises or falls, the sensible temperature of the steam rises or falls very rapidly, but the total heat per pound of steam is little affected — so little that the total heat was at one time supposed to be constant for all pressures. This is shown in Table 143. «" ^he following page : 553. A very small excess of demand for steam, therefore, will cause the pressure to fall very rapidly, and as there are only 20 to 30 lbs. of live steam stored in the boiler at any one time, what is gained by letting 1 1* 454 CHAP. XL—LOCOMOTIVE BOILER, CHAP. XL— LOCOMOTIVE BOILER, 455 Table 143. Weight of and Heat in Steam at Various Pressures. Pressure, Lbs. per sq. in. above atmosphere. O 20 50 100 120 140 160 Hkat-units.* Sensible. Total. 212.0 259-3 281.0 33S.O 350.1 361.0 370.8 Weight per cu. ft. Lbs. II78.I .038 II92.5 II99.I I2I6.5 1220.2 .086 .120 .263 .308 1223.5 1226.4 .350 .393 Full tables giving these properties of steam for each point of pressure will be found in D K Clark's " Manual for Mechanical Engineers," and in many other treatises. The pressures given above the atmosphere should be 0.3 lb. greater, and the total pressure measured from a vacuum 15 lbs. greater. These figures rest purely on experiment, from which accurate fonnulae have been deduced. Table 144. Available Energy in Heated Water and Steam of Locomotive Boilers, Between normal temperature of steam and 2I2- Fahr., or that available in case of explosion. For practical working the available stored energy is very much less than this. See top of next page. [Abstracted from a paper on " Boiler Explosions." by Prof. R. H. Thurston, Trans. Am. Soc. M. E., Vol VI., Paper CLXII.l Area of — , Weight of— Stored Energy Available— Grate. Heat'g surface. Boiler. 1 Water. Steam. Water. Steam. Total. sq. ft. IS 30 23 30 sq. ft. 875 1,200 1,070 1,350 lbs. 14,020 20,565 19,400 25,000 lbs. 6,330 6,450 5,260 6,920 lbs. 19.02 25.65 1 21.67 31 19 ft.-lbs. 1 = 1000 64,253 64,452 52,561 69,149 ft.-lbs. I = 1000 2.385 3,226 2,7U 3»9io ft.-lbs. I = 1000 66.638 67,678 55.278 73.059 mile-lbs 1 = 1 12,621 12,818 10,469 13,837 ♦ The heat-unit must be carefully distinguished from a mere degree of temperature, from which it differs much as ^foot-pound differs from a pound or a foot, or as an area differs frorar a distance. The little diagrams on the next page (Figs. 118, tiq, and 120) will make this clearer A heat-unit is a quantity of heat. What is called temperature is merely an altitude of heat A high altitude of temperature is consistent with a very small quantity, if the body be small, or even if the body be large and its capacity for absorbing or holding heat small. Different materials differ greatly in this respect. Assumed steam pressure, 125 lbs. This table gives the entire energy in the steam and water between 212" and 353<», or the amount of work which would be done if the pressure were allowed to faU to zero and there were no back pressure or other losses in the cylinder. It will be seen to be about equal to the ordinary working tractive power of a powerful engine for about one mile. Perhaps one half of this stored energy is a practically available resource in operating emergencies. pressure drop from 140 lbs. to $0 lbs. is simply this, say, for the second engine given in the preceding Table 144 : In Steam Space: Only 8.8 instead of 25.6 lbs. of steam are required to fill the steam space, releasing some 17 lbs. of steam. In Water Space: The fall of sensible temperature from 361° to 281° releases 80 heat-units per pound of water, and 80 x | (specific heat of iron) heat-units per pound of boiler, being sufficient to convert into steam a weight of water equal to about ■^ of the total weight of boiler and con- tained water, or for the given engine 728 lbs. of steam. This makes a total gain of only 745 I I ■20Fh fOFi-- Areas I lOff. "^pf. 30ff, '^OFt! « \ % I .J. Fig. X18. — Relation of Areas to Altitudes and Lengths. a I lbs. of steam, or 37^ lbs. per square foot ."^ of grate, which is about what a square ^ foot of grate should evaporate in 3f min- utes, at the rate of 600 lbs. per hour. kx I Foot Pounds ■20Fh-^ -: J— - I of WORK.t yopf-\ i \—' I Weicrhfs ToWs 20 /bs 30 lbs -w/i6i 554. As respects letting the supply of Fig. 119 —Relation of Foot-pounds water fall off. here also the gain is COmpar- °^ ^okk to Distances and Weights. atively slight, because the heat used to raise the temperature of the water, say, from 60° to the boiling-point at 120 lbs. pressure, 350°, is only 290 heat-units per pound of water, or one third f||-|) as much as is needed to change the water into steam after it has reached that limit. Therefore, even if we allow as much as 10 per cent of the whole water in the boiler to evaporate without replacing it, which Fig. 120.— Relation of Hf.at-units , . . , 1 1. ^ to Temperature and Mass. Will lower It about 3 m., we only save heat enough to evaporate ^ of the whole water in the boiler, or 215 lbs., I o I : ■ I S 40169^ CHAP, XI.— LOCOMOTIVE BOILER. 45<^ being somewhat over lo lbs. per square foot of grate, or about what is evaporated in one minute. „ . , • ^« 655. Nevertheless it helps ; but that the help is small, is clear in an- other way from Table 143. which gives the total available energy in the boiler and contents if the boiler pressure were allowed to fall to zero, and the steam thus produced used without loss (other than the heat in the steam at 212°) in the cylinders. It will be seen from Table 143 that an engme which is workmg fairly hard (as hard as it can continue to work indefinitely), and evaporating 600 lbs. per square foot of grate, will evaporate a whole boilerful of water in from 20 to 40 minutes. This, again, shows that the available reserve Table 145. Estimated Approximate Distribution of the Loss of Heat in American Locomotive Boilers to its Various Contributing Causes. CHAP. XI.— LOCOMOTIVE— CYLINDER POWER. 457 Theoretical evaporation o£ fairly good (14,000 H. U.) coal Actually evaporated in fair average practice, with such coal Maximum. Lbs. I Per cent. 12. 07 9.06 Leavinff as wastage to be accounted for, which may be divided between the various sources of loss, as follows : 1 Heat carried off in the gases of combustion (ex tremes of smoke-box temperature taken at 392 and 724°) •. Lost in the ash , Getting up steam and banking fires (about 10 per ^* cen?, but not included above, and so ueglccted.) 4. Unconsumed coal ejected by the blast 5. Imperfect combustion 6. External radiation. 7. Entrained water (a real loss but apparent gain). 8. Lost through safety-valve Total loss as above estimated ■ 3. ox Minimum. Lbs. Per cent. xoo. 75. 25- X.3X T2.07 6.04 6.04 TOO. 50- zo. 0.+ .36 «.44 — O.I3 o.ia 3. ox 19. — I. X. 25- 3.43 x.ai .60 i.8x — o.6x 0.61 50. 6.04 so. 0.+ xo. 5- 15. -5. 5- 50. These extremes are rarely reached in the same engine, but the maximum is onlr reJhrf^der favorable and the mtoimum under unfavorable condmons for economical ""^^"m'arine practice nearly all the above sources of loss except the first are avoided. An efficiency of fr'omTtoV'per cent of the theoreUcai evaporation is therefore no longer exceptional. in the boiler is a pretty small affair, and the normal generation of steam we have seen (Table 142) to be quite unequal to utilizing the full tractive power at any high speed. 556. The boiler is not an uneconomical generator of power. In the last types, from 75 to 90 per cent of the potential energy which goes into it in the form of fuel leaves it in the form of steam. Nor is the locomo- tive boiler, in spite of its great efficiency in proportion to weight, inferior to other types in economy, the very best of stationary and marine boilers alone excepted. Without going into details, for which space cannot be taken. Table 145 gives the substance of the facts in relation to its ordi- nary working when not burning over 80 to 100 lbs. of coal per hour. When combustion is pushed harder, the loss from unconsumed coal ■ejected by the blast is much heavier. THE CYLINDER POWER. 557. Since we have seen that the locomotive boiler is quite unequal to supplying steam enough to utilize the full adhesion at high speeds, it results in no serious loss, and need occasion no surprise, that the cylin- der, which is a mere transmitting agency, is in actual practice and as actually constructed unequal to transmitting such an amount of power, even if it could be generated. As the speed rises above the lower work- ing speeds for which the locomotive was designed there is a very great reduction of cylinder efficiency as measured by the average pressure in the cylinders, cut-off. opening of throttle, and boiler pressure being the same. 558. The steam-engine, even in its most perfect forms, attempts only to convert into work the expansive energy of steam, which is a very small part of its total energy. All that great proportion of the heat energy in the steam which has been required for the purpose of chang- ing it from water into steam is wholly thrown away, even in a theoreti- cally perfect steam-engine. It is hardly to be conceived of that science, will not eventually discover some radically different device for convert- ing heat into work which will be many times more effective, but at pres- ent we do not seem to be even tending toward it. 559. All ordinary forms of steam-engines are in substance similar to the engine of the locomotive, which in its essential outlines is simplicity itself, consisting only of a piston vibrating back and forth within a cylin- der to wliich steam is admitted and cut off at each end alternately by «ome form of automatically-acting valve — in the locomotive, the slide- valve. The steam is admitted for a certain fraction of the stroke (one 458 CHAP. XI.^LOCOMOTIVE— CYLINDER POWER, quarter to three quarters in the ordinary practice of the locomotive), called \.\\^ period of admission; then cut off, permitting what steam is shut up- in the cylinder to expand and do further work during what is called the period of expansion ; and then released or permitted to escape at or be- fore the end of the stroke, so that there may be as little as possible back pressure to resist the return stroke. While this division of the work done in the cylinder into the period of " admission" and of "expansion" is convenient, yet during each period alike it is the expansive energy of the steam, and that alone, which does, what work is done. 560. On the proper design of the valve gear by which the slide-valve is moved, and so the admission, cut off and release of the steam controlled, hangs nearly the whole question of good or bad working of the cylinders, and its theory is a study in itself, into which we need not enter ; contenting our- selves with determining what are the theoretical limits of efficiency, what are the results actually obtained in good practice, and how these results ought to- be and are affected by varying conditions. 561. The form of valve-gear known as the link-motion is in all but univer- sal use on American engines, and is used on a large majority of all foreign engines. It was invented almost contemporaneously with the locomotive itself, and a large part of the credit for it is due to the same man, George Stephenson';. so that it is not unjustly known by his name, although it is, properly speaking, the invention of Howe, a foreman in his shops. It has not been essentially modified or improved upon since its invention, except as advancing experience- has given better knowledge of the precise proportions which it should have, and it is with justice regarded as one of the most notable inspirations in the history of mechanism, fulfilling as it does very simply yet remarkably well all the complex requirements which a locomotive valve-gear should have. 562. Nevertheless there are certain desirable ends which it does not fulfil, and in recent years a number of valve-gears have been devised, some of them of a highly ingenious character, which are claimed, and probably with truth, to possess certain practical advantages over the link-motion, and which have met wide acceptance abroad. It is possible, although as yet hardly probable, that some of these may eventually supplant the link-motion, but none of them have yet been shown to give such radically different results from the link-mo- tion that any of the conclusions we shall reach will be affected thereby, except in degree. 563. Assume such a cylinder as that described in par. 559 to have a connection opened with the boiler, at the beginning of the stroke, which continues open until the end of the stroke. Let the connection with boiler be then closed, and a connection with the outside air opened, so CHAP, XI.— LOCOMOTIVE— CYLINDER POWER. 459 I I Frj-LBSo£.Work, stroke , as to permit the inclosed steam to escape, while at the same time steam is admitted to the other end of the cylinder and the operation is repeated. 564. In this we have a steam-engine of the simplest type, which was also the earliest type, and an indicator-diagram of such an engine, if it worked perfectly (which it would not be likely to do at very high speed), would resemble Fig. 121. The boiler, being constantly generating steam, may be considered as, for the time being, a reservoir of infinite volume, and the expansion of the steam to fill the cylinder will not reduce its pressure. Con- sequently, the cylinder pressure throughout the F'^. 121. stroke will be equal to the boiler pressure, and the diagram will be a rectangle, in which the foot-pounds of work done will be represented by stroke in ft. x area of piston in sq. ins. x boiler pressure in lbs. per sq. in. The efficiency of even so crude an engine as this is considerably over three fourths of what is actually realized in fair average practice^ and fully as much as is realized under unfavorable conditions, and may be determined thus : 565. A 17 X 24 in. cylinder has a capacity of 3.1525 cu. ft., and will hold almost precisely one pound of live steam at a pressure of 126 lbs. per sq. in. above the atmosphere — an ordinary working pressure. The work done by this- steam, in foot-pounds, if there be no loss by condensation or other disturbing cause, will be W17' -— - X 126 lbs. X 2 ft. = 57,200 ft.-lbs. 4 Dividing this amount of work by the mechanical equivalent of heat, we obtain- as the useful work which ought to be realized if there were no losses by back pressure of steam, condensation, or otherwise, 57^200 772" = 74.09 H. U. In addition to this useful work the steam has, in a non-condensing engine, tione this work against the pressure of the atmosphere on the opposite side of the piston, amounting to nearly 15 lbs. per sq. in., or about 11. 2 per cent of the useful pressure. Computed to include work done against this pressure, most of which is avoided in marine and other condensing engines, the total work done is equivalent to 74.09 X 1.112 = 82.91 H. U. Now the total heat in this quantity of steam is (Table 100) 1191 H. U., so« that all that is utilized is : .460 CHAP. XL— LOCOMOTIVE— CYLINDER POWER, CHAP. XL— LOCOMOTIVE— CYLINDER POWER. 46E Cutting off at Full Stroke. In a perfect non-condensing engine, In a perfect condensing engine 74.09 „ b s , = 0.22 per cent. 1191 82.9 — - = 6.96 per cent. Practically even this result is 7 or 8 per cent too great, owing to the steam wasted to fill the passages between the valve and the piston, which does no work whatever unless the steam is expanded after being cut off. 666. There being 33,000 X 60 = 1,980,000 ft. lbs. in a horse-power per hour, we shall have to use, in order to develop a horse-power per hour with an engine worked in this way, 1.980.0 00 " 57.20 0" ~ "^^ steam. And if we had a boiler able to utilize the full evaporative efficiency of fairly good coal, instead of only one half to three fourths of it, we should require 34.62 ^ j2 07 ~ ^'^^ ^^^* °^ *^°^^ '° obtain one horse-power per hour. 567. Only under the most favorable possible circumstances for ob- taining the last degree of efficiency out of the locomotive is it possible to obtain a horse-power per hour with 2.87 lbs. of coal, or with less than 25 lbs. of steam. Ordinarily in fact, even on long up grades which afford the most favorable localities for the economical working of the locomotive, something like 30 lbs. per horse-power is used (see Table 146). With ordinary evaporation of 6 to 8 lbs. of water per pound of coal from 4 to 6 lbs. of coal per horse-power per hour are required, and this is about what is ordinarily obtained from locomotives, the very finest marine engines running down to 1.3 to 1.5 lbs. 568. Many engines in times past have been, and in fact still are, run at nearly full stroke, as notably high-pressure engines on Mississippi River steamboats. In the locomotive this is occasionally done, but usually the steam is permitted to expand through about half the stroke. The theoretical gain from doing this is large, but the practical gain small — so small that nearly all that is gained by it is to neutralize tjie various practical obstacles to realizing the full theoretical work of steam at full stroke, 669. A theoretically perfect condensing steam-engine and boiler requires only f lb. per H. P. per hour of coal, and some 8 lbs. of water, at a boiler pressure of 120 lbs. per sq. in., utilizing a scant 26 per cent of the energy in tiie coal. A theoretically perfect non-condensing engine utilizes 16,9 per cent. 570. The very best ever claimed to have been realized with locomotives is in the paper by Mr. Wm. Stroudley before referred to (par. 550), where it is stated ilhat in a trip ot 50.4 miles at 43.3 miles per hour the average coal consumption (exclusive of coal for getting up steam, which is about 3 lbs. per mile run) was- 24.87 lbs. per mile, and the average horse-power developed 528.53 (see Fig. 123). This amounts to producing a horse power with 2.04 lbs. of coal per hour — a result which has been approached elsewhere under the most favorable con- ditions, but when alleged as the result of an ordinary service run over undu- lating grades it is all but certain that its remarkably favorable result is largely due to serious errors in the record ; in great part probably originating in the shortness of the run, in which only some 1200 lbs. of coal is alleged to have been burned, or 1.2 cu. ft. per square foot of grate. The same allowance must be made for the alleged rate of evaporation, 11. 6 to 12.6 lbs. per pound of coal, which, it is risking little to say, is from 10 to 20 per cent beyond the limits of physical possibility, in view of the fact that the gases in the smoke-box seem to have had a temperature of 600° Fahr. 571. A far better index of average practical results is that given in Table* M c 9 "o t» 4; 0< •o c 01 a. o I ^00 ^. /BO T I£0 1 \ /^O 1 \ J20 _<^ if%f% ^ ^r^ ]\ SO V^ .* k . .r4 y -\ 60 /\ A A M-iSa A ■^ f 'P I r-A \ 7:ts^ \r ^^ A 5^ 20 ^ /-» ' • 1 w lOQ A k. J ^ / \ , s tkQ / X\'^^ ^ A, r f!f tJ^ '■«' 1 -^ £0 >A_ \ ^ / v* 1 3 \l\ ^\A 1 AO f ,■ ... J ^ ^^ ' ^- 20 ^ ^* \ , «%, ^"" — • w \ • •■ V ■■ .' 5 re/c/rl 0. l^rjrf^ •-ri n iO zo 3 --lb 400 300 200 100 C/) o s* o ►<» a o n I o % Fig. 122. Diagram showing Results of a Test of a Baldwin Locomotive, by John W. Hill, M.E... DURING A Run between Cincinnati and Hamilton, 24.7 Miles. (See Tables 146 and 147.) [The abscissae represent the intervals between indicator-diagrams, which were taken in as quick succession as possible (40 in 25 miles, or ih. 26m.) and not miles.] The mean effective pressure may be considered as the equivalent of the tractive power, which should theoretically fall immediately to zero on striking the down grade, if the velocity were to remain the same, but instead of this was maintained about the same for some distance, with the effect of greatly increasing the speed and horse-power. 146 and 147, where from 4^ to 5^ lbs. of coal per horse-power per hour were required, rising, when combustion was so forced as to expel unconsumed coal 462 CHAP. XI.-LOCOMOTIVE-^CYLINDER POWER, *rf*' 1' T • ¥ • ♦ mil fin CHAP. XI.— LOCOMOTIVE— CYLINDER POWER. 463 T T T r'l I r ! 'i, \\ tons. A verage of WhoU Ji'un^iu^J^^ ° " m "" ^^'S^^t of engine and 23 carriages,,/. 7 from .h= smoke-stack (as it often is in practice), to over 7 lbs. Fig. .22 show, he fluctuafons of speed and tractive power during a part of this run in a some! what similar manner to Fig. 123. aomc- Table 146, Tests of a Baldwin 16 X 24 in. American Engine in Express Freight Service. (D..uc.a fro. R„or. "f T.„ ., M W „„, M. ^_B., ;ou. K„„. fn«.. .pH,-„.,. ..^ For details of engine and train, see below.] Boiler Performancb. Cincinnati to Hamilton. Apparent evaporation, actual r . ' , , " ^^ss 5 p. c. primage Equivalent from and at 212" Actual evap. (less primage) perVq.'ft of heating surface, per hour. . . Coal burned per sq. ft. of grate, '^x hour °_ ^ Evap'n from and at 212° per hour! Estimating coal burned per sq. ft.* of grate per hour with natural draft at 25 lbs., and one horse-power = 15 sq. ft., we have, for such an engine as above, for a Healing surface per H. P. of Ratio of effect of blast ( coal burned to natural draft, -j comparing by ( heating surface lbs. 7.44 7.07 8.36 9.96 83.9 10,586 Hamilton to Twin Creek. Twin Creek to Dayton. sq.ft. 3.24 lbs. 4-75 4-51 5.34 13.01 172.0 13.856 3.36 3.32 ■q. ft. 2-57 lbs. 6.55 6.22 7.30 12.24 117. 3 12,918 sq.ft. 2.61 4.34 4.33 4.04 4*o8 mnnu I HI I ! / 1 m M* i • I ■:' j is! ! ' j !!i>a»|i«M»|«ii*aM{ ■•■ms i ■•««•• I ! i I "I I Brighton & South Coast Railway. Speed in miles per hour is indicated by the figures at the top of the diagram and by the heavy solid line. Horse-po-wer is indicated by the d^aed line made of points. Tractive force is indicated by the light-dotted line. The dotted lines along the base show where diagraais were taken, 49 in all. The three arrow-heads at the left indicate stops. Table \^6*— Continued. Engine Performance, Miles run Speed, miles per hour Mean boiler pressure '• initial " •• cut-oflf " effective pressure Grade of expansion, incl. clearance... Distribution of Power: Indicated H. P Power absorbed by engine only above all resistances Gross load Extra friction due to load (5 p. c. of gross load) Power expended in moving train Per cent of total power absorbed by engine Cost of Power: Steam per hour to engines Steam accounted for by diagrams .... Per cent of do Steam per I. H. P. from boiler " diagrams.... Coal per I. H, P., actual •• *' ** at I to 9 evap'n... 24.7 17.23 122.0 lbs, 98.5 " .53 65.0 lbs, 2.0 H. P. 291.9 33.4 258.5 12.9 245.6 15.86 lbs. 9.424 -6 8,017.2 85 32 27 4 3 o 3 5 24 59 15.87 22.67 124.0 lbs, 107. " •515 64.2 lbs. 2.09 H. P. 368.7 41-3 327.4 16.4 311. o 15-63 lbs. 12.312 9,883 80.3 33.4 26.9 7.03 3.71 16.267 23.0 123.0 lbs. 105.5 •' .52 63 . 2 lbs. 2.03 H. P. 388.5 44.3 344-2 17.2 327.0 15.82 lbs. 12.415 10.324 83 32 26 2 O 6 5.36 3-55 These tests are perhaps as fairly representative of every-day American practice as any which exist. See details on following page and Table 147. 464 CHAP. XL— LOCOMOTIVE— CYLINDER POWER, Details of Engine and Train for Tables 146, 147. Baldwin American engine, 16 x 24 in. cylinders, 61 in. drivers, 15.99 sq. ft. grate area,, 898.7 total heating surface. Weight on drivers, 44.840; trucks, 27,380; total, 72,22olbs. Weight of tender, empty, 23,480155.; load, 24,000 lbs. Train, 35 loaded box cars and caboose, weighing 782.94 tons. Average of engine and tender 5572 " Total weight of train 838.66 tons. Engine in ordinary working order, out of shop 22 months (55,471 miles), Pittsburg No. 2 coal. Date of tests, July 28, 1878. Evaporation per sq. ft. of fire-box surface, assuming 60 per cent of the evaporation to have been from that surface, 93.53 lbs. per hour. Friction of engine was determined by series of indicator-diagrams at each speed, averaging 15.8 per cent (including the allowance of 5 per cent for extra work due to load, which is probably too large), while the weight of the engine was only 6.65 per cent of the total. This work, however, includes atmospheric head resistance as well as rolling and internal friction. 572, A more reasonable presentation of what may fairly be expected from locomotives under the most favorable working conditions for developing power economically is given in a paper on "The Consumption of Fuel in Locomo- tives," read before the Institution of Mechanical Engineers, by M. Georges Mari6, engineer of the Paris & Lyons Railway, of France. In these tests a powerful locomotive (21^ X 26 in. cylinders, eight 4 ft. \\ in. drivers, carrying some 100,000 lbs.; exact figures not given) was loaded with a light train of 167.8 to 183.2 tons, and run up a long grade on the Mont Cenis line, rising 1709 ft. in \-j\ miles, or about a two per cent average grade (the maximum being 2.84 per cent), in one hour. The total tax on the adhesion on such a grade was only some 65 lbs. per ton maximum and 46 lbs. average, or a total average traction of some 8000 lbs. With so light a load it was possible to cut off at one- fifth stroke. The author's conclusions from the tests are that with a good loco- motive and a good driver the consumption of fuel and water is as follows : Consumption of fuel per effective horse-power per hour. Consumption of fuel per indicated horse power per hour. Ratio of consumption of water to consumption of fuel... Ratio of dry steam produced to fuel consumed 3.27 lbs. 2.88 lbs. 8.88 8.08 These satisfactory result are attributed to the following causes: " (i) The total heating surface of the boiler is very large compared to the grate surface, — 96 to I, — so that the boiler absorbs the heat of the gases very completely;. (2) the cylinders of the locomotive are very large, — according to the late M. Mari6's system, — so that the grade of expansion is high ; (3) the locomotive was very well looked after, which is an important point in economy of fuel." CHAP. XL— LOCOMOTIVE— CYLINDER PO WER. » 465 Table 147. Details as to ia^ Resistances of Engine and Train in the Tests Abstracted in the Preceding Table. In three runs of At speeds in miles per hour of. The average indicated H. P.,asdetsrmined by the average of cards taken on both sides of the engine simulta- neously at intervals of two minutes, was The entire weight of the train having been, engine, 55.72 -f- 782.94 = 838.66 tons, we may compute from the above data that the average tractive eflergy of the locomotive (including its own internal friction) was Equal, average of entire train Of the above H. P., however, it was determined by actual trial that the indicated H. P. necessary to move the engine alone at the given speeds was And it was estimated that when the engine was working hard there was a further addition to its internal friction of 5 per cent loss on work done, = Making total H. P. absorbed within engine Deducting this from the work done, and deducting engine from weight of train, we find the average traction exerted on the train was Leaving as the power required to propel the engine itself, without load Add estimated addition to engine resistance when work- ing hard (5 p. c.) C. to H. H. to T. C. T. C. to D. 24.7 miles. 15.87 miles. 16.27 milesw 17.23 22.67 23.0 Average of — 40 cards. 20 cards. 21 cards. L H. P. . 291.9 368.7 388.5 -lbs. V 6,346 6,097 6,334. I lbs. per ton « 7-57 727 7-55 / 1. H. P., engine only » 33-4 41-3 44-3 12.9 46^ 6.83 727. 281. Total continuous force in lbs. to move eng. Or in lbs. per ton of engine and tender: Locomotive without load Increase d ue to load itself. 1008. Total locomotive resistance Assuming the effective end-area of the engine for air re- sistance to be 100 sq. ft., and air resistance to be \^ lb. per sq. ft., at 10 miles per hour, we have for air head resistance only . .*. Leaving as the tractive and internal resistance of the engine without load In round figures, we may deduce from the preceding, for locomotive resistances in lbs. per ton, of engines of the American type (in which head-resistance would be a larger proportion than in more powerful engines) 13.04 5.06 18.10 16.4 57-7 -lbs. per ton- 6.57 —Total Ibs.- 683. 273. 955- -lbs. per ton- 12.26 4.87 17.* 6^ 6.78 722. 280. 1002. 148 17.13 -Total lbs. 857 12.96 5 04 18.00 265 579 4*6 457 Lbs. per ton of eng. Atmospheric 3.0 Rolling friction, light ... 5.0 Internal " '* ... 5.0 " " increase due to load 5.0 Total 18.0 The average of the train behind engine is, say 6.75, Excess of engine resistance, lbs, per ton of engine 11.25 This engine excess, when distributed through the entire train (of 35 loaded cars) makes a difiter- ence, as shown above, of only (average, 0.74, 0.70, 0.77), say 94 lb. per ton. 30 466 CHAP. XT.— LOCOMOTIVE-CYLINDER POWER. Reference ,s also made in the same paper to some experiments made by M Regray. Chief Engineer of the Eastern Railway of France, on consumption of fuel m express engines hauling express trains, showing 3.01 lbs. per indi- cated horse-power as an average, and 2.48 lbs. as the minimum. These satis- factory results are claimed by the author to be due in large part to the use of large heating surfaces and large cylinders: he always built his own locomo- tives by that rule. 673. The present tendency in this country, however, is not by any means toward the use of large cylinders, but rather toward heavier engines and boilers for the same cylinders. The comparison given in Table 148 shows this very Table 148. Increase in Total Weight of Engines having the Samesized Cylinders. Baldwin Locomotive Works. Class of Engine. American , Mogul Consolidation Cylinders. 16 X 24 17 X 24 16 X 24 17 X 24 18 X 24 19 X 24 20 X 24 Weight in Working Ordbk. i = 1000 Lbs. On Drivers. 73. 42 45 51 54 58 61 87 86. 46 52 54 57 64 70 95 Inc. 4 7 3 3 6 9 8 On Track. Total. 73- 86. Inc. 1 73. 86. Inc. 23 26 3 65 72 7 25 28 3 70 80 10 16 18 2 67 72 5 18 21 3 72 78 6 19 24 5 77 88 II 20 24 4 81 94 13 9 13 4 96 108 12 Rhode Island Locomotive Works. CHAP. XL— LOCOMOTIVE— CYLINDER POWER. 467 Table 148. — Continued. Taunton Locomotive Works. 16" X 24" Cylinders. 17" X 24" Cylinders. Year. Weight— Lbs. Year. Weight— Lbs. 1848* 50 000* 1850* 57,000* i857' SS.ooof 1857 67,700 1859" 52.ooof 1S65 67.000 iS6o' 540oof 18S2 78,400 i86i 62.400 1883 80.000 1880 70,000 1884 90,000 18S3 82,000 1885 91,000 1884 83,000 * 16" X 20 ' cylinders. * 17" X 20" cy linders. t 16" X 22" See also Tables 127-130. Most of the striking change shown in this table is accounted for by the gradual in- crease in boiler pressure carried. See par. 605. Strikingly. After allowing its full weight to the effect of the increase in boiler pressure carried, it is clear that there is no tendency toward using larger cylin- -ders for the sake of being able to cut off earlier. the theoretical gain by expansion. 574i Under " Mariotte's Law" (given in any text-book on physics) the vol- time of a gas is inversely as the pressure, so that if the gas has expanded into twice the volume it exerts lialf the pressure, etc. In ** cutting off " steam at some point in the stroke, say half- or quarter stroke, the steam in the cylinder expands according to this law (theoretically), and thus continues to push the piston before it with a ■gradually decreasing pressure as the interior volume increases, until at the end of the stroke the pressure is (or ought to be, with a perfect gas) just half or a •quarter of the initial boiler pressure. A perfect indicator-diagram of such a stroke would have the form of Figs. 124, 125, the bounding curve being a iiyperbola, as in Fig. 97. The shaded portion in these cuts represents what is gained by expansion, or oujjht to be. 675i But steam is not affected in precisely the Fig. 124. Fig. 125. — The Ratio of thr Shaded Portion to the Unshaded Rectangle im- dicates the theoretical Gain by Expansion. isame way as a perfect gas by changes of pressure and volume; and, moreover, 4^8 CHAP. XI.^LOCOMOTIVE— CYLINDER POWER. Table 149. Theoretical Efficiency of Steam, Expanded in Non conducting Cylinders, involving no Waste of Heat. [Rearranged from " Steam Using, or Steara-Engine Practice," by Prof. Chas. A. Smith.] Boiler pressure assumed at 120 lbs. per sq. in. above atmosphere. Cirr-OFF. Full Stroke \ \ \ i i << • < (I << <« v much the theoretical loss amounts to it is needless to in soTr«s IfTosr" r" ^T""l'" "■' ^"'°"^ ""'" -" '" n,o:e impolnt' roTnts to • "' "^ "' '"' '""'"^ °^ '''P"-" "'- '"eir agg'regate 579. The chief sources of loss of cylinder efficiency in the locomotive engine are those numbered i to 8 below : ' "i^oniotive 1. The steam is ■wire-drawn. &o that its pressure in the cylinder is neyer equal to that of the boiler, and often ,o and even .o lbs below U 2. The steam-porls are not large e,w, • ^"/°"""«^ly- experiment seems to indicate quite uniformly conVd ""■^^;"^™'« '"- the exception for freight engines to show I consKJerable reducfon in cylinder efficiency even a? their lower workb^ rTn h '° T 'T"' "^ '°" '^ " '^ ^«f« »° "- -'thout danger of hf tram bemg brought to a stop by slight additional resistance fror^ curves grades head w.nds, or bad track, do cause a very material decreieo^ uln f UsTvXTe ult^^ T''"" '■■ ^"' "^"'^^ '^^ ^"«'"'= cannot "o'tb? uLiiize us available ultimate tract ve nower— i ^ xr^^r „^ i i- . wheels-at any practicable wor.in, s,lZL::::7^^'^^^^^^ d.fference . small compared with the effect of further inc;ease of fpel^ the lit J„Tdi;T.:^(tgr";rtt^r: r r".'""^^'^ ^^ ^" ^-^ ^'^- -^^ '•« ^ ^ ^^'^^- '3^ '° '39) of the engine whose performance is * Annales Industrie^ Feb., 1885 t " Manual for Mechanical Engineers," p. 879. CHAP. XI.— LOCOMOTIVE— CYLINDER POWER. 475; recorded in Table 146 and Fig. 123 (par. 571). The same thing appears in the diagrams accompanying Mr. Stroudley's paper (par. 570 and Fig. 122). where, With a cut-off of , At a speed in miles per hour of * - 12 m 30 m And steant-chest pressure of .'.*.' 140 lbs. 130 lbs. The average pressure was ^^g lbs. 57-2 lbs. The horse-power bemg 262 502 At 12 miles per hour, with 60 per cent cut-off and 125 lbs. steam-chest ores- sure (bmler pressure full 5 lbs. more), the average cylinder pressure was 95.4 lbs., whereas at 4 miles per hour an average of about 85 per cent of the boiler pressure was obtained in the cylinder- about the best which is ever possible. 593. That this should occur at high speeds is practically unavoidable but tiiat It should occur at slow speeds of less than 15 miles per hour is in no respect a mechanical necessity, nor does it require any radical modification of existing engines to cure it. whenever it appears desirable but merely some slight modification of the valves. Some engines do not show It, but more do. The chief reason why it is not done is that no particularly useful end would be served thereby, since the imperfections, of the gradients and of the locomotive serve to justify each other bv de- stroying to a very large extent the advantage of remedying one without the other. It is important that the true nature of the difficulty should be clearly understood. \ 594. The largest tractive pulls, by far. on nearly all railways, are ex^ erted in getting trains under way from stopping-places on unfavorable grades or curves. There are few roads indeed, and those onlv havings very heavy grades, on which the traction between stations is the heaviest So long as this is so. the need is not felt that an engine should be able to exert sometiimg like its maximum pull between stations at fair workin ; 1 rf It;). l| 476 ClfAP. XI.-LOCOMOTIFE^CYLmDEJ^ POWER. fflUHc^<^^ CHAP. XI.-^LOCOMOTIVE— CYLINDER POWER. ^'JJ Figs. 126 to 133 were taken in some tests on the Cincinnati, New Orleans & Texas Pacific (Cincinnati Southern) Railway, from a fine Baldwin passenger engine of the follow- ing dimensions : Cylmders ... Drivers Weight Jondnvers Tractive force per pound of av. press, in cylinder (Table 151)... ValvM J Allen-Richardson: vaives, ^ Lap, % in. ; lead, ^ in. z8 X 24 in. 68 in. 60,000 lbs. 90,000 lbs. zi4.4lbs. Ports, -I steam 'lexhaust Exhaust nozzle ( ^"^^ ;;.; 1,325 sq. ft J fire-box 133 sq. ft, t6 X \\ in. 16 X 2i in. si in. Heating surface, ] Grate area The train hauled consisted of 8 cars, weighing 480,000 lbs. Total 1,458 sq.fu 17 sq. f t.. Fig. lag. Fig. 130. Fig. 129. Boiler pressure Cutoff Throttle open Speed Av. cylinder pressure.. Indicated horse-power.. Loss initial pressure 145 lbs. 8 in. \ 53.4 m- 37-2 lbs. 583 32 lbs. 145 lbs. Sin. \ 45 -o m- 44-3 lbs. 608 22 lbs. Fig. 130. 140 lbs. 6 in. 54-6m. 32.5 lbs. 541 24 lbs. 135 lbs. 4 in. i 55-9m. 28.0 lbs. 477 26 lbs. Figs. 129, 130 show the same effect of speed as Figs. 126-128 very forcibly, both bv comparison of the full and dotted diagrams and (still more forcibly) by comparing the solid diagrams in Figs. 120 and 121, which may be said to be taken under precisely similar circumstances (balancing difference in throttle against difference in boiler pressure): except that Speed was ^'I.^f- '^\--^' Reducing average pressure from 61 8 to -xn 2. Yet that this does no real harm to hauling capacity is* * evident from the fact that the horse-power at which the engine was working increased from • 549 to ^g^ Comparing the dotted Fig. 131 with the solid Fig. 132 we see that the combined effect of 5 lbs. liigher boiler pressure, 4 ins. longer cut-off, and a throttle % instead of \^ open, gave only a slightly higher average pressure (6.8 lbs.), indicating that the slight difference of 0.8 mile per hour in speed very largely counterbalanced all these advantages Fig. 132, contrasted with the dotted Fig. 129, illustrates a truth which might be proved m many other ways, that after the speed gets fairly high it does little or no good to 478 CHAP, XL^LOCOMO TIVE-CYLINDER POWER. admit more steam to the cvlindpr«s tk« o,«.,* .aine. is use. „p . Uc. p^Lr.^, ^^1^. 7:iL^^^-:33r;: --'O ^ Boiler pressure Cut-oflf Throttle open , Speed Av. cylinder pressure. Indicated horsepower Loss initial pressure, 145 lbs. 14 in. f 26.3111. 83.3 lbs 668 24 lbs. 142 lbs. 14 in. 24.3 ni. 81.3 lbs. 603 20 lbs. 141 lbs. II in. 46.9 m. 37.9 lbs. 542 50 lbs. nor to indicate that the one arises from excessive demand on the tract^e^power. which is remediable only by changing theTades while r " 1 148 the other fs caused by deficiency of cylin- der power only, which is remediable for the most part by trivial changes in the valves. 696. By the use of smaller drivers, both the cylinder and boiler power are in effect increased proportionately, so far as tractive power in pounds is concerned, at the expense of speed ; so we may con-' elude, as we began (par. 483), bv saying Fig. 133 Boiler pressure, ■Cut-off, . . . Throttle open, . Speed, . . . Av, cyl, press., Ind. H. P., . . Grade, . . . I >» VI Z z. u ou u X O M (A < u H 33 O H Q oi o V) iz: o ^^ en u o Q H Ciy^/>. XII.— ROLLING-STOCK, 8 o o CO m a in a to O to O O to x: . 88 a>co d -f C CI o CO Q O O O O m N CO 1^ cT d^rA o a a •nfcoHoo it«H«i ; ^ > ^ OO MC> »n ""moVn CO M W M C4 00 r^oo t-H to o oq vO 2 2 '2 2 ""^ oio't^ "o a 9 a s (4 CO a» o»*^o* CO GO oo vo "o^ •o o CQ t^ o o o CO 0^ O^O* OO o oo 00 OO sO « OO X H O Z u O o 6o do V> "o^'wo V toco coco to conJ? 8 S3 ^co » OO M r>.00 M CO ^ 00 ^ M eo ^"m NtO NtO to tONM \n < fb o o T3 "O C C Ctt I M O ^ JS •U C I u o fa O •a cu e a o * o i5 t« ^ •" fe. ^ 12 «^ o 055fa I V it u 9 O fa V) O O u I a (U ^ ^ " J2 « c E — — o 5 "5 ^ |i rt ^ t; W JQ ^ 6/) til <" a B a to a; 0) o u o c -S .^ - '5 0) 13 V a -^ M *" « « V- ^ J3 fc/) ^ «= n« W wT TD T3 . r c c g U c = .2 S 6 •§ O ^ -o I ca H p « 2 . 4; - § J3 i: ^ c '" X o •:: in .2 .y w ♦, S -a *' «< ^ •" JH s S (A c c o u 0) 2 "O a, o "2 a o ^ ^ ^ "^ g 2 iJ ^ S3 "O c 8 ^ ^ S &3 S. ^" ^^ k^ D 2 c <" Tj- O c O >v O 4* r -rr o 2 fe ■" o ^ >: g w _C "rt ■§ _ 5 3 o -3 >^ "» ■ rt o c -S ja ^ r3 ft C H O X o o 5 i5 -' J c '^ • u.2-*^ocsr;.5 CO J* .O -5 o c ^ > I, ti J3 t« n <3 rt £ "V iuO to *- < Q < O to S CO J3 •« IC ~ _^ x: a IS ^ to «, .S X ^-4 C^ CLfAI". XIL— ROLLING-STOCK. 487 Table 155 is interesting, not only as giving the average capacity, but for the variety of dimensions appearing among the standard types of a single line. It will be seen that in these 13 classes there are 10 different lengths (not counting differences of less than an inch), and 9 different widths, ranging by jumps of a few inches each from 7 ft. 5 in. to 8 ft. 1 1 in.; all in freight service only. This diversity is in part because the cars must be adapted to many different uses, but in the main it is evidence of the fact that a process of evolution is still going on, so that the rolling- stock of the country is for the present in a transition state. The general tendency of this process can alone be stated : to increase the capacity of freight cars up to 25 or even 30 tons of paying load, and perfect their con- struction so that such loads may be handled with safety, at fairly high speeds. 602. Two changes which may reasonably be expected to come about in the next few years will greatly strengthen this tendency, and probably materially modify the handling of freight trains as well — the Table 155, Classification List of Freight Cars of the Pennsylvania Company, 1885. Kind of Car. Long box*... Box* Refrigerator, Provision Stock (standard) Gondola (standard) " (widened) " (standard, long) . . Drop bottom (standard)*. . . Hopper bottom (standard)*. Stone flat (sundard) Class. Q. M. R. M. &0. M. &0. O. P. B. P. D. P. E. E. D. C. S. Inside Dimensions. Length. ft. in. 33 ioJ4 21 5 23 I 33 10 29 A% 29 8% 29 m. 33 o 33 o 23 5 35 7 Width. ft. in. 8 4^ 7 wYi, 7 ^o^ 7 10 7 10 5 8 8 8 8 7 7 7 3 o 4 5 S 7 8 II Height. ft. in. 7 4 5 10^ 5 81^ 5 10 5 »o 7 2 6 2 3 2 3 3 " Standard Capacity. lbs. 40,000, 50,000 26, 30, 40,000 40,000 40,000 40,ocx> 40,000 26, 28, 30,000 26, 30, 40,000 50,000, 60,000 40,000 40,000 50,000 50,000 Standard height of floor from rail, all cars, 4.0^4. P. D. gondolas, built before present standards were adopted, have sides only 20 in. and 2 ft. high. The weights of these cars are substantially the same as those for the Pennsylvania Railroad, given in the preceding table, those marked * being substantially, if not exactly, the same cars. 0mm :i 488 CHAP. XII.— ROLLING-STOCK. adoption of some form of automatic coupler, and the adoption of a freight-train brake. The effect of all these causes combined will prob- ably be to assimilate the handling of freight trains more and more to the handling of passenger trains, except that the speed will be much more variable : as low as now on heavy grades, but very much higher on the easier sections of the line, where great tractive force is not demanded and where, consequently, higher speed is entirely feasible. As the ordi- nary passenger piston speed is not found to be injurious, we may expect with some confidence that at no distant day maximum freight speeds of 28 to 30 miles per hour, which would give about the same piston speed will be established in general practice. The effect of this change will be to greatly facilitate the haulin^r of heavy trains, even without considerable modification of gradients for reasons discussed in Chapter IX.. and elsewhere. With the more per- feet road-beds and track which become every year more general there is no reason to believe that wear and tear will be materially increased while the cost of power per ton-mile will certainly be rather less th in more, not only because of the less time afforded for radiation of heat from the exterior of the locomotive and journal-boxes and interior of the cylinders, but from less destruction of energy by brakes, since it can be stored in the train in the form of velocity, and afterwards used, to a much greater extent. 603. The primary requirement for the attainment of this desirable end is the adoption of a freight-train brake, and fortunately there now appears every prospect that some approved form of freight-train brake will come into general use within a few years, and thus greatly simplify the problem of ob- taming the most favorable virtual gradients cheaply, in addition to the direct advantages. The latter alone are much considered bv the public, but on cer- tain lines at least their effect on the virtual gradients will almost certainly be of more financial importance, and make the expenditure for train-brakes a most profitable one. independently of the greater safety and convenience. 604. The ultimate solution of the problem of automatic couplers is a more doubtful matter, and it may be well on toward the close of this century before automatic couplers come into use. To the highest efficiency of train-brakes they are almost essential, and the breaking in two of trains is another evil lending to discourage the hauling of heavy trains, which they will very largely remedy. The chief obstacle to their introduction is and has always been not the mechanical difficulty of the problem, but the fact that, owing to the contin- uous interchange of cars, no real benefit would be derived from such a coupler until It had come into almost universal use. whereas a passenger-coupler was as useful to the road applying It as it ever could be. as soon as it was applied CHAP. XII.— ROLLING-STOCK. 489 to their own cars, or even to a few trains. The consequence of this difference is that the usual cut-and-try process of development and survival of the fittest was impossible wii«h freight couplers, whereas the first practicable passenger- coupler was adopted by a few roads almost immediately, from which the conta- gion of example sped, each gaining the full benefit of their own expenditure as soon as made, and losing nothing by the backwardness of others. The greatest immediate obstacle to a general agreement on some one •freight-coupler, or on two or more couplers working well together, is the exist- ence of two distinct types of such couplers, which have become known as the "link" and (by a somewhat awkward and inappropriate term) "vertical-plane" or lateral-hook couplers. The link type resembles more or less closely the ordinary form of coupler, but arranged to work automatical- ly, and, in the best types, dis- pensing with loose links and pins. The hook type is model- led after the couplers which have been so successful in pas- senger service. Fig. 149 shows , ^, ^ J Fig. 140. — Ames (Link) Car-couplkr. 'One of the most approved ^^ forms of link-couplers— the Ames, and Figs. 150. 151 one of the most approved iorms of hook-couplers— the Janney. Neither of these couplers has been se- FlG. 150. Fig. 151. Janney (Hook) Car-coupler. .lected for illustration as the best of its type, but merely as fairly representative and among the best and most approved. 605. Each of these types has strong advocates, but it may be expected with some confidence that the hook type will ultimately, and perhaps very speedily, prevail, for the reason that it insures a steadier and smoother motion of the train by doing away with loose slack, which is the chief provocative of breaking in two. of trains and of broken draw-bars and other damage, while it has been proved not to be of appreciable advantage in starting heavy trains. There is wmimm 490 CHAP. XII.—KOLLING-STOCK. a general impression to the contrary, and not a little floating evidence- but in careful tests at Burlington, la., .886, it was found that there was nnth' gained by loose slack n.ore than could be secured by first bac^Th locoZ t.ve against brakes set at the rear of the train, and so compressing the sprir. hroughout the train. On the locomotive starting forward the com Pre sed spnngs g,ve a push to each car. and this push seems to be more effecUve tha^ when the same thing is done with a train having slack As several good couplers of each type now exist which will work ouiti^ well together, nothing now impedes a decision of the coupler questTon except the existence of these two types, each of which has certain Idvantages The advocates, of each are indisposed to proceed very actively with the equtpi ment of the.r cars until the vexed question of a choice is settled ^ ^ h,»: ;■ '"Z^'"''' '56 are given various details as to certain very large or heavy freight cars, and in Table 157 the leadmg dimensions of the mot usua^ passenger cars. In respect .0 the latter, the tendency is more and more towa^i the use of the heavy sleeping and drawing-room cars for a large percentage 0I Table 156, Dimensions of Certain Very Large and Heavy Freight-Cars. Furniture Car Chicagfo & N. W. Railway. Length over sills. Width over sills. . Length over roof. Width over roof. Inside length 37 width " height... Extreme height . " length. Total wheel-base Weight Capacity ft. 38 8 38 9 M. C. B. Standard 60.000-lb. Box Car. 8 8 13 in. O 6 li 6i oi 5f 8i Pile-driver Car Ga. Central Railroad. t Philadelphia & Reading Standard Coal Car. 40 Hi 31 lOf 40,000 lbs. 60,000 lbs. 32,000 lbs. +39.000 •* \ 18,480 lbs. 56,000 ** * To top of brake-shaft, la ft. lo in. ~ t Leaders to hammer, 40 ft. high, taking a pile 18 in X w ft • c« ,vv. m. moved back to let the front of the car profect Four t^u^ks in ^if 'rami "^ ^'^"''" piles to ,8 ft. below the rails. irucics in all. Hammer, 8000 lbs.; drives The Baltimore &> Ohio Railroad have a large and increasing numh.. nf . / in use carrying so^ooo lbs., and weighing loaded 3614 /^Z f "'"''" lbs. in all on ^r//. out to out 0/ bu/ers :!Tto\...l 1' .>*^^;«««'«^ >''''• 76,000 Consolidation locomotives. ^ ^ ^"'' '''' '""^ '"^ ""''^'*' P''' >-' e^ CHAP. XII.— ROLLING-STOCK. 491 the travel, and many through-trains consist of them almost exclusively — a fact which tends to make the rate of long grades and of grades at stations of almost as much importance to them as to freight trains, but owing to the fact that, by varying high velocities slightly, a great difference in tractive power on up grades results, and all but quite long grades may be operated almost as virtual levels (par. 397), the disadvantage of dead weight is very much less in passen- ger service than is sometimes assumed, and the tendency toward luxury in that respect may be expected to continue. Drawings and dimensions of a great variety of cars, and of all car details, will be found in the Car-Builders' Dictionary, as revised by the writer. Table 157, Leading Dimensions and Weight of Sundry Passenger Cars. Penna. Railroad. Standauds. Passenger* Baggage Postal Sleeper (old style). Dining KC B. &Q.).. Monarch sleeping-cars.. Mann sleeping-cars... Parlor Car (B.&O.R.R.) Woodruff sleeper Harl. & H. Co., ist-class passenger Length. Width. Height. Weight Capacity. Body. Out to Out. Body. Max. ft. in. ft. in. ft. in. ft. in. ft. in. lbs. Pass. t46 6 52 9 9 10 10 1% 14 1% *44,989 51 40 46 9 »oM 10 \% 14 1% 32,000 .... t6o ;We;n fret" phw S;;pt: net^ii^prS^r^'rcn^en - xucy were made by the " gravity method " de- CHAP. XIII.— FREIGHT- TRAIN RESISTANCE. ^gj scribed in Appendix A. the train being caused to approach the starting post at as nearly as might be 20 miles per hour, when steam was shut off and the train permitted to run over a very slight down grade till it came to a stop. It was then caused to approach a succeeding stop-post at a sharp down grade, having a slightly curved alignment, at 5 miles per hour, and permitted to acquire what velocity it would (about 35 miles per hour) for a certain distance. There was no wind; and the ther- mometer averaged about 80° Fahr. The results of the tests are summa- rized in Table 160 and Fig. 154. which maybe accepted as an almost absolutely accurate record of actual resistances * over the entire range of Fig. 154.-RESULTS OF THE Burlington, Ia., Tests of thf Resistance of Entire Trains. AS Summarized in Table i6o,Page 500 ikains, [Computed by the method shown in Table ,59, on follo^ving page, and in Appendix K? ( 1 he dotted lines eive the tests made on curved tr'^r\r mr-n-r-t ^a t * 76finJXpIn^dV:^r ''°^ -"^"^ ""• ^^^^^^^^^^^S^^'il^^^^, * As the writer was referee of these tests he was familiar with the condition Of the cars and all other modifying circumstances. Therefore be can vouca for the accuracy of the results, which seem somewhat peculiar, 32 ij— I 498 CHAP. XII I. ^TR A IN RESISTANCE. Table 169. Manner of Computing Gravitv Tests of Train Resistance of Entire Freight Trains. Speed, decreasing from «, „i,es per hour-.; mixed-' resistances mFlg. .54. Station. Elev. Track at ^fif. of Train. Speed. Miles Per Hour. Vel.-Head (by Table 118). Virtual Elevation. Differ- ences in ditto. Pounds Per Ton Resist- .1 ^^-^^- XIII.-TRAI N RESISTANCE. 499 It was found on invest^aUoi thai thT t T". ''''" ""'^ '"" '"''""^^ ^" *^^ ^-^— • had been reballi ted l^e^^:^^^^^^ ^ ",^^^^ ^^ ^ ^^^ ^^^ow of a ,rade) atnount (probably -ethl^^^leral^ot)^^^^^^^^^^^ ^f-- of the table are due to two defects of ob Nation • a) Lack of In, "'"^^^^"^'^^ track elevations, and (3) lack of exact correctness' in\he spe^Ltato^ ^ h ^'^ mometer record, which was on a scal^ of > i. •, , '^""^ *^^ ^y^^" run. TO attem;. to compr U.: SL cl^Tpara^r relctsuC "• °' T^*^^ """^ crucial test of the accuracy nf th. .^...v, ^ ^^^^^'^^^ ^O'^ each successive 1000 ft. is a very point Of view. The™:.: it Z^^^^",: TllT'^'' °"^ '""^ ^ """'-' .hat no other method can 'approach this inTecitnTn'd errtar'"^ ""''^- '""^"^''"^ The weights of the trains tested were a. follows, in tons of ^ lb. • 25 box-cars, empty weight 12 loads, at 20 tons each ....'..* .* Equalizing load, when used Dynamometer car. with 15 persons.' Way car, with 10 persons.. . . Total train Engine on drivers **, on truck Tender empty \ Total engine and train, Of which there was braked Percent braked 639.48 339 96 5316 639-71 300.16 46.90 68r.6i 382.16 56.04 Every box-car truck but one. as well as Hip t^r.A^^ 7 '. " a very unusual proportion ^^^' ^"^ ^°^'°^ ^"^^". ^ad brakes on- field^^ tt^nrih-tt^^^^^^^^ ^^-^-^ -'- « X 7 in.), except the Widdi- IN .887 (see^«^«....^^^,, May, 5...^:^z:::iL:;:?'' """ °^ ^^^^^ rrcste had not been made when the first edition of this treatise was issued.] 5cx> CHAP. XIJI.^FREIGHT-TRAIN RESISTANCE. Table 160. Train Resistance of Entire Freight Trains, including Engine. [Giving the mean resistances in pounds per ton (of 2000 lbs.) computed as shown in' Table 159, with the corresponding velocities in miles per hour.] (Each of the resistances on tangent is the average on a run of 5000 ft. Each of the resistances on curves the average on a run of 2500 ft.) Resistances on Tangent. Resistances on Curves. Tangent Vel. Resist. Vel. Resist. Curve. Resist.* Wcstinghouse (C, B. 1 & Q. cars) » 16.93 16.06 21.58 24.78 21.55 3.80 4.36 4-56 4.24 4.44 18.86 33 90 34.90 • • • • * • • • 4.56 7.56 6.41 • • • • • • • • 1.08° 2.60° 1.47" • • • • • • • • 4.02 6.26 5-68 • • • • • • • • Mean 20.51 4.32 26.33 6.07 1.75° 5-30 Eames (I., D. & S. f cars) and Widdifield -J & Button (L.V.cars) ( 8.42 18.28 19.70 6.50 6.76 7.04 14.03 24-55 30.10 9.68 9.20 936 1.08° 2.60" 1-47° 9.14 7.90 8.63 Mean 16.82 6.84 21.70 9.42 I 75° e rr 1 • /3 "-33 American (St. L. & S. j F. cars) 1 9.62 13-72 • • • • 930 7.88 • • • • 13 03 24-45 30.75 8.08 10.40 7.84 1.08° 7-54 2.60" 9.10 1.47° 7-21 Mean 11.66 8.50 21.19 8.94 1.75° 8.07 * Tangent resistance determined by subtracting ^ lb. per degree of curve from the total resistance. Average degree of curve determined by determining degrees of central angle passed over by head and rear of train on given distance, averaging the two, and dividing by number of stations. Velocities are in miles per hour ; resistances in pounds per ton. practicable freight speeds. The track was in fair but not remarkably- good condition. 618. The conditions of the trains tested (which will be seen to have shown quite different results) were as follows : I. Westinghouse\ train. — Made up of old cars in excellent running order, with well-worn journals and wheel-treads. The performance of this train should fairly represent the ordinary conditions of practice. 2. Ainericatt train. — Made up of entirely new and very heavy cars, which had only run some 300 to 500 miles since leaving the shop, and f The trains are designated, for convenience, by the names of the brakes with which they were fitted, although these brakes had nothing to do with the- tests. CHAP. XIII.— PR EIGHT- TR A nv RESISTANCE. 501 •consequently had bearings and wheel-treads still comparatively rough, and not fairly representing the average conditions of practice. 3. Eames train.— Ma.dQ up of fairly old but poorly built cars, and generally in rather inferior condition. 619. The effect of these differences in the trains is clearly visible in Pig. 154, where the Wcstinghouse train shows rather less than half the rolling resistance of the other two, or about 4 lbs. per ton for all speeds up to 25 miles per hour. The general fact that speed causes very little increase in train resistance up to speeds of 30 miles per hour is clearly indicated ; and this many other indications tend to confirm, as notably various dynamometer tests made by the Pennsylvania, New York, Lake Erie & Western, Chicago, Burlington & Quincy, and other roads, where very low car resistances, running down to from 2i to 4 lbs. per ton, have been indicated, with little variation as an effect of speed. These latter tests alone would leave the question open to much doubt, since they do not include any of the head or engine resistances, which at high speeds become more important than any other, but the tests ^iven in Fig. 154 include ALL resistances and lead to the same conclusion so clearly as to be unmistakable. 620. The peculiar manner in which the Eames and American resistance lines on curves cross each other, as shown by the fol- lowing sketch, may appear to indicate that there is ^ ' something wrong in the computed results. This is by no means so. The anomaly may be thus explained : (a) Each train was made up of 25 cars from the same road and built nearly at the same time. (6) All freight cars are roughly built. The axles are not likely to be pre- 4:isgly parallel, except by accident. To have the axles enough out of parallel to precisely fit a 1° curve requires that the wheel-base shall be only y-^ part longer on one side than the other, or ^V i"- A lot of cars built at one time are very likely to have the error all on one side. ic) Resistances a and c (see sketch above) were on curves turning to the right; resistance d was on a curve turning to the left. If, therefore, the American train curved most easily to the right, resistances /land c would be abnormally low, or very near the tangent rate, and resistance /J abnormally high: while, if the contrary was the case, with the Eames train re- sistance a and c would be abnormally high, and resistance b abnormally low, or well down toward the tangent rate. Whether this or other cause led to the variation, it is certain that it was an actual one, and the fairer plan, therefore, seems to be to take the average of both •trains. The trottlc of each engine was absolutely tight. 14 502 CHAP. XIIl.—I'KEIGHT-TKAIN RESISTANCE. 621. The experiments by the writer recorded in Appendix A were made by the same general method as those just described, and were the first in which the very low train resistances for trains in motion which are now generally admitted were observed. They indicated that the normal magnitude of the rolling- friction at speeds of lo to 30 miles per hour was : For passenger and loaded freight cars 4 ibs. per ton For empty freight cars and other light loads, ... 6 " " For street cars and other still lighter loads, .....* 10 " For freight trucks without load, ! ! ! 14 " ^ The starting-friction is very much higher, rising to over 20 Ibs. per ton in some cases. (See Appendix B.) 622. Some experiments on train resistance, both on curves and tan- gents, made in 1885 on the Breslau-Schmoltz line in Germany, apparently in an accurate and careful manner, but covering only the resistance of cars behind the tender and dynamometer car, gave still lower results than these, as shown in Table 161. The tests covered also the question of remedies for oscillation and the advantages of a device for radiating axles on curves, as to which nothing important was developed. The resist- ances are noticeable as being among the lowest ever reported for similar speeds. Similar tests on the Freiburg-Sulzbrunn line, with the same apparatus and by the same individuals, gave somewhat higher averaije. Modern evidence to the same general purport as that which precedes might be multiplied almost indefinitely, but it appears needless to do so. 623. We may conclude, therefore, as to freight-train resistance I. The particular velocity adopted is wholly unimportant, both because it makes absolutely but little difTerence in the resistance, and because, if the resistances are mounting too high for the power of the engine, the speed can always be cut down at critical points. The total work in foot-pounds done to move Table 161. Resistance of European Cars (16 to 23 ft. rigid wheel-base). [Reported in full in the Railway Engineer, Dec. 1884 et seg. Resistance in Pounds Per Ton. Spekd. Radiating Axlrs. Fixed Axles. Miles Per Hour. Limits. Average. Limits. Averafje. 12.4 21.8 28 2.0 to 3.75 3.97 to 4.19 5 -07 2.65 4.08 5-07 2.42 to 3.75 3.97 to 4.85 6.17 3.09 4.19 6.17 CHAP. XIII.— FREIGHT-TRAIN RESISTANCE. 503 the train is not affected enoueh to have any measurable effect on the cost of power (see par. 664). 2. The normal tangent treight-train resistance in summer, ENGINE AND ALL INCLUDED, is often, and perhaps usually, as low as 4 lbs. per ton, up to speeds as high as 25 miles per iiour, run- ning down in cases to 3 lbs. and even less; and, on the other hand, rising in cases as high as 6 or 8 lbs. per ton when the cars are in bad order, or against a head or side wind, or (as we are about to see) at winter temperatures; these latter figures being a fair working maximum for freight service. Four pounds per ton will make a difference of some 2400 lbs. in tractive re- sistance with an average train of 25 cars, which will use up the adhesion of 4.8 tons of weight on drivers, or 12 to 20 per cent of the total load. 624. It is entirely uncertain how much of the so-called rolling friction is journal-friction, and how much rolling-friction proper. The present proba- bilities are that most of it is journal-friction. Experimental determination of the rolling friction proper, apart from all journal-friction, is a matter of the greatest difficulty, and has never been attempted. Journal-friction has been far more thoroughly investigated within the last few years, but until then the laws of it also had been but little investigated, and what investigation had been made was largely erroneous. 625* By some singular chance, — probably the beautiful simplicity of the laws developed, which only lacked correctness to make the laws of friction very easily understood, — some experiments made by M. Morin,* a French officer of artillery, in 1831, obtained almost universal acceptation as a final determination of the laws of friction. There is even at the present day (1885) hardly a single text-book of engineering, at least in English, in which these laws are not laid down as facts, yet they are now generally admitted to be entirely incorrect. They were in substance that the coefficient of friction was independent both of the pressure and of the velocity, so that, once determined, it was universally applicable. The range of the experiments was very limited, and Morin himself disclaimed any extension of them beyond the range of his experiments; but it is clearly proven that there are no limits nor conditions under which his laws are approximately true, since the coefficient varies materially both with pressure and velocity, with both lubricated and unlubricated surfaces, and with tempera- ture and other conditions as well ; as notably with the character of the surface, which makes any general coefficient of " iron on iron," or " iron on brass," for example, rather worse than useless. * " Nouvelles Experiences sur le Frottement. Faites 4 Metz en 1831.' Par Arthur Morin, Capitaine d'Artllerie. 128 pp., 4°, plates. Seconde M6moire, 1832, 103 pp., 4', plates. Tro si^me Memoire, 1833. 142 pp., 4°, plates. 504 11 II CHAP. XIIL—FREFGHr-TKAIN RESTSTAKCE. 626. Prof. R. H. Thurston was among the first, if not the first, to discover and announce the true laws of friction, in 1876-78. having made a large number of experiments on an ingenious machine of his invention. The writer in the summer of 1878, made a series of tests of rolling-stock resistances, summarized in Appendix A, by dropping cars down grades and registering velocities elec- trically, in which he believes he was the first to discover and announce the variation in coefficient for loaded and empty cars and the aggregates of 4 6 and 10 lbs., above mentioned, which at the time appeared quite without prece- dent, as Prof. Thurston's results were not at that time generally known and were not at all known to the writer. A large number of dynamometer tests on various roads were made shortly after, and in fact were then in progress COtFHCIE«IT 0» FRiCTiON AT VARIOUS PWESSyRES. LUBRICANT PARAFFINC OH. VtLOCiT-/ 300 FEET PER MINuV| C./ M »OO0«U«T. a» 40 » i4> Lh» Per Ton TVain Resistanct. (The velocity given for the rubbinp-surfaces of 300 ft. per minute is equivalent to a train speed 01 some 34 miles per hour.) Fig. 155. Showing the same low rate of 4 lbs. per ton or even less for loaded-car resist- ances, although empty-car resistances were less carefully determined. Shortly thereafter Mr. C. J. H. Woodbury began tests of great interest for mill-work, which give strong confirmatory evidence of the above results as respects the gen- eral laws of friction, although not directly applicable to railroad practice. Finally, in 18S3-4 Mr. Beauchamp Tower made a series of elaborate and remarkable tests under the auspices of the Institution of Mechanical Engineers, which appear to have been the first made in England of a character to reveal the CHAP. XIII.—FREIGHT-TRAIN RESISTANCE. 505 •errors of Morin's results. The Germans and French do not appear to have shown their usual scientific activity in this matter. 627. All these modern results agree in essentials with each other, although some have covered results not touched by the others. Their general results and indications are summarized in Appendix B. Mr. Woodbury's results* begin with the lowest pressures, and are shown in Table 162, and graphically in Fig. 155. For the very reason that this diagram is for pressures lower than ever occur in normal railroad practice, it is particularly interesting, since it furnishes a check on the conclusions which have been reached by other experimenters operating within the limits of railroad practice only, by beginning as it were at the foundation, and showing the law of change in journal-friction from i lb. per square inch of journal pressure upwards. There has been added below the diagram a line showing the equivalent in pounds per ton of train resistance to the abstract "coefficients of friction" given, as being a unit better suited for our immediate purpose. Table 162. Coefficients of Friction with Very Low Pressures, and Effect THEREON of TEMPERATURE. [Abstracted from records of tests of C. J. H. Woodbury.] Pressure Coefficient of Friction. Total Friction at Tempera- ture OF — Per Cent of Per Sq. In. 40". IOO». 40°. 100°. 100° to 40*. I a 3 4 5 7 8 9 ID .538 .299 .211 .167 .140 .122 .109 .098 .ogo .084 .138 .080 .060 .050 .044 .039 .036 .034 .032 .030 lbs. .538 .598 .633 .668 .700 .732 • 763 .784 .810 .840 lbs. .138 .160 .180 .200 .220 .234 .252 .272 .288 .300 25.6 26.8 28.5 30.0 31.3 32.0 330 34.7 35.7 35-8 15 20 30 35 40 .063 .053 .046 .041 .038 .035 .025 .023 .021 .020 .019 .018 .945 1.060 1. 150 1.230 I -330 1.400 .375 .460 .525 .600 .665 .720 39-7 43-3 45.7 48.8 51. 1 51.5 * For complete paper, which is full of interesting information on friction, see "Measurements of the Friction of Lubricating Oils," by C. J. H. Woodbury, Trans. Am. Soc. M. E., 1S84-85. ii^i^ 5o6 CHAP. Xni.-FKEIGHT-TRAIN RESISTANCE. 628. The d.agran, is especially useful ,o afford some indication as to the comparat.ve tram resistance in winter and summer, as to which there are „" expenmencal records. Since the diagram fixes, as it were, a superior li^t for the r,ct,o„ of ratlroad journals, we might, on studying it, fairly d aw hr« conclusions : ^ » . -inj' uidw mrec I. Since friction can in no case be less than zero lines reoresentin., »11 poss.ble loads on railroad journals must lie in the narrorspae'lt h .'ft o the diagram between the zero line and that for 40 lbs. per square inch pre sure He betwe:„^ « """■ T- """' "■" ^'' -"-^■i<'-"a. friction oug.; lie Detvveen these narrow limiis : 40 100' Temperature of Coefficient of „ J""*""*'- friciio... Fahrenheit o to .035 Pounds per ton train resistance. o to 7.0 lbs. o to 3.6 lbs. Fahrenheit o to .018 froP,'! TtZ ^'^^^^'P""'^ ^^^^^ '^^ "«"!' of all the latest tests, which sho^ from 3^ to 6 lbs. per ton resistance. 629. 2. Within the temperature limits of 40° and 100°. the effect of the higher temperature ,s to decrease materially, and of the lower temperature to increase matenally. the amount of loss by friction. At 40 lbs. per square inch the friction is nearly twice as much at the lower temperature, while at still lower pressures of i to 10 lbs. per square inch it is from three to four times as much. Extendmg the indications of these tests to the higher pressures of rail- way practice, we might expect that the effect of a fall of temperature in the journals from 100°. which we may call an average summer temperature to 40° which we may call an average winter temperature, would be to make journal- friction in summer and winter railway service compare somewhat as follows : Loaded. Empty. summer, as shown by various tests, say 4 lbs. 6 lbs. Winter (not directly shown by any tests), say 5^ to 6 lbs. 8 to 9 Ibs.^ 630. Whether this conclusion be true or not cannot be proven by direct evidence, for lack of recorded train-resistance tests which have been made in- cold weather, but the circumstantial evidence that some change of this kind takes place is very strong. Among such evidence is one small fraction of the series of tests by Mr. Beauchamp Tower, above alluded to, for determining the effect of temperature on journal friction. The loads and journal-speeds in this case closely paralleled railway practice, but the lubrication was vastly more efficient, being by a bath of lard-oil. Lard-oil is affected by temperature much as are ordinary railroad lubricants, but the superior method of lubrication, in addition to giving rates of friction which are far below the possibilities of railway practice, would be likely to have the effect of exaggerating the beneficial effect of high temperature, since the more perfect the supply of oil, the greater might be expected to be the advantages of great fluidity. 4 . CHAP. XIII.— FREIGHT-TRAIN RESISTANCE. 507 Nevertheless, with these allowances remembered, some of Mr. Tower's results, as summarized in Table 163, are very instructive. Translating co- efficients of friction into pounds per ton of train resistance, as in Fig. 155, by multiplying them by 200, and translating the journal-speeds into train- speeds by multiplying by 10 (these methods being approximate only, but sufficiently exact), we have in Table 163 some very definite indications of the effect of temperature on axle-friction. 631. To draw any positive conclusions from this table we must make a cer- tain "scientific use of the imagination," by making allowances both in the temperatures and in the observed friction for the difference in manner of lubrication. As these allowances might or might not be correct, we will not attempt them; but it is clear that, be the allowances thus made what they may, these results support the general conclusion strongly, that the external tem- perature of the air may have a most important influence on the normal rolling- friction, as do experiments by Professor Jhurston and others. On the other hand, there are many experiments which, at least in appearance, would tend to controvert these conclusions, for one has only to look long enough to find experimental records to support or controvert almost anything. But such con- troverting evidence is in this case not abundant, nor of the highest class, and as a general rule the apparent discrepancies all result from two apparent, anomalies which are in no respect inconsistent with what has preceded : 1. At a certain temperature not far above 100° Fahr., and with some fluid oils below it, the law changes, and increase of temperature causes a rapid in- crease of resistance. 2. At very slow speeds, especially when combined with very high pressures, the law often changes, and a higher temperature has an injurious effect, apparently because a certain viscosity is necessary for efficient lubricatioa under such circumstances. Table 163. Effect of Temperature on Journal Friction. [Deduced from tests of Beauchamp Tower; bath of lard oil; load, 100 lbs. per sq. in. (about that of an ordinary empty freight-car journal.)] Train speed. . At 120° Fahr, At 60° Fahr. , Difference. , Pounds Per Ton of Train Resistance at Speeds in Miles Per Hour of — 8.8 0.48 1. 18 0.70 13-2 0.58 1.68 17.6 0.70 2.06 I. 10.. 1.36 21. 9 0.80 2.38 1.58 26.3 0.88 2.60 1.72 35-1 1.02 2.96 1.96 39-5 1.08 3-12 2.04 I * if ■i 508 C//AP. XII I.-FREIGHT-TRAIN RESISTANCE. 632. Zero temperatures are not favorite ones for dynamometer experi- ments, but experience in the running of trains in winter and summer indicates in the most positive manner that summer trains must be cut down by two to four cars in winter, or say 10 to 15 per cent, in order to run them at all This practice has not become universal without some real necessity; but it is more difficult to account for the necessity than is generally realized, for some of the explanations which are given will certainly not hold water, as pointed out in par. 345. It need only be added, that the loss by radiation from the loco- ^Tiotive will hardly explain any part of this need for cutting down trains since the difference between winter and summer temperatures is a small and unim- iportant one to the locomotive, though a very important one to the human body. 633. Let us see how radical is the difference in its effect on them The ■human body can manage to sustain for a short time a temperature of sav 40' below zero, or 138° below its natural temperature, and it can do this 'only when " lagged " with skins and such like, to the last degree of perfection at •every exposed point. The boiler is subjected to an equally unpleasant extreme of temperature when the external temperature is 350 - 138 = 212^ Fahren- heit, or just hot enough to cause water to boil in the open air. To get a fair parallel, we must consider how much warmer the average man would think It with the temperature 140° below zero than when it was down to 200° below zero. It is not probable that he would find that the difference was of great consequence. To be sure, the fire inside the boiler is more efficient than the fire inside the human body, but the demands on it are greater and the difference of winter and summer less. The average winter temperature of Pittsburgh, for example, is about 38° and the average summer temperature 72 degrees so that we have as the difference between the inside and outside temperature of the boiler — I"^'"^^"" 350' - 38° = 3i2« In summer 350. _ ^^o ^ ^yS' Difference «-«» _ o or about 11 per cent. This difference is far too small to explain the necessity for any material difference in winter and summer loads. Assuming that as much as 20 per cent of the heat generated is lost by external radiation, which is a large estimate not more than 2 per cent difference of load could be accounted for in this way! 634. We seem driven, therefore, as a net result of all the preceding, to this interesting and important conclusion, to directly support which there is. as already stated, little or no experimental evidence, although the circumstantial evidence in favor of it is very strong : that a difference in the rolling-friction of cars is the chief reason why trains must be cut down in winter. As this X Ir CHAP. XIII.— FREIGHT-TRAIN RESISTANCE. 509- probably results from difference of temperature of the journals, and this again from radiation from the boxes of the heat which the journals are constantly generating, and as radiation can be checked by a very slight covering whicb will hold a little dead air around a hot metallic surface, we have in these facts indications which might lead to the important practical conclusion that some very slight covering, which would merely check radiation from the journal- boxes somewhat, might have an appreciable effect on the loads which can be hauled in severe cold weather. 635. In Appendices A and B will be found further and more detailed infor- mation as to the laws of journal-friction, and especially as to the important question of starting trains. The normal journal-friction, under favorable con- ditions, as determined in various series of tests, is summarized in Appendix B as follows, for velocities greater than 10 miles per hour, or 90 ft. per minute^ journal-speed : Lbs. per ton. Beauchamp Tower, bath of oil o. 278 ♦' '• pad or siphon 1.9 Thurston, light loads 2.75 " heavy loads i-75 Wellington (gravity tests of cars in service), light loads. . . 6.0 " «• •« " *♦ heavy loads.. 3.9 " direct tests (as shown in Appendix B) j ; " Thurston, inferior oils (" Friction and Lubrication, "p. 173) \\'q Morin, continuous lubrication 6.0 to 10.8 636. The great discrepancies in these results will be seen to point directly to one conclusion— that the character and completeness of lubrication seems to be immensely more important than the kind of the oil. or even pressure and temperature, in affecting the coefficient of friction. Mr. Tower found that lubrication by a bath (whether barely touching the axle or almost surrounding it) was from six to ten times more effective in reducing friction than lubrication by a pad. By immersing the journal in a bath of oil Mr. Tower succeeded in reducing the coefficient in a large number of tests to as low a point as o.ooi— equivalent to only 0.2 lb. per ton of tractive resistance; and the general average in the bath tests, under all varieties of load and speed, is given as only 0.00139, or 0.278 lb. per ton. against 1.96 to 1.95 lbs. per ton with siphon lubricator, or pad under journal. These results are very far below any heretofore reported. 637. The overmastering effect of minute differences in the condition of the lubrication was curiously shown in two ways in Tower's experiments : I, It was accidentally discovered that with bath lubrication the bearing is actually floated on a film of oil between the lubricated surfaces, which is so truly a fluid that it will rise through a hole in the top of the bearing in a continuous *H1 9B1 510 CHAP, XIIL—FREIGHT-TRAIN RESISTANCE. stream and exert a pressure against a gauge equal to more than twice the average pressure per square inch on the bearing. This is precisely what theory would require if the lubricant were a perfect fluid. 2. Tower's apparatus required that the journal should be revolved first one way and then the other. It was found that the friction was always greater when the direction of motion was first reversed. The increase varied consid- erably with the newness of the journal. " Its greatest observed amount was at starting, and was almost twice the nominal friction, and it gradually diminished until the normal friction was reached, after about ten minutes' continuous run- ning. This increase of friction was accompanied by a strong tendency to heat, even under a moderate load. In the case of one brass which had worked for a considerable time it almost entirely disappeared." It is with apparent justice concluded that the phenomenon must be due to the interlocking, point to point, of the surface fibres after having been for some time stroked in one direction. 638. It appears not impossible, therefore, that a great further reduction in the axle-friction of trains, as well as a great saving of oil, may result, within a few years, from the adoption of something better than the crude and wasteful axle box which is now common. The objections to it are : 1. It leaks badly at the back, around the axle, letting oil out and grit in. Therefore — 2. The oil has to be frequently renewed, requiring a loose lid in front, from which more oil escapes and more grit gets in. From this it very naturally results that in spite of the large expense of about a cent per train-mile (Table 78) for oil there is often very little or it where it is wanted, and that dirty and gritty ; while, on the other hand, the ties and road- bed are saturated with it from one end of the United States to the other. 639. In Figs. 156-159 is shown a French oii-box which obviates many of these objections and has made the very remarkable record given below. The Germans have similar oil-boxes in extensive use. The oil reservoir is entirely below the axle, so that oil cannot escape, and it is supplied to the bear- ing by a pad fed by wicks. Could an oil-tight stuffing-box be used at the back of the box, and the box be kept completely full of oil, it is more than probable that even greater reduction of axle-friction and waste of oil would follow. The lower half of these boxes is furnished inside with a partially horizontal diaphragm in the portion toward the wheel, for the purpose of preventing the forcing out of the oil by violent side blows. They have proved so efficient that the consumption of oil has fallen from 2.3 ounces per 1000 miles to less than one fourth that amount (41.25 grammes per 1000 kilometres to 9.93) — a most remarkable showing, and a marvellous contrast to the results obtained here. The dust guard is formed of five to six thicknesses of fluffy woollen cloth, held between two leather diaphragms by screws like those used for shoe soles. The diaphragms are in halves, and are pressed up against the ^ •4 » i i " '. } CHAP. XIIL—FREIGHT-TRAIN' RESISTANCE. 511 .axle by steel springs behind them, and the leathers on opposite sides of each half diaphragm break joints with those on the other half. The oiling cushion in this box has its oiling plush firmly tacked to a beech I c. I ^y^i'—^X - BL . _ Section on AB Section on CO. Section on EF. j»4Aic-> — 33/4: _.i..2W — 4H.-a*»--4 Lower Part of 9ex. Plan. Front Elevjftion Lj.iM.t_JLJ*_iLJLJ_f-_/ _f_A_f -l_f ^'-~ Figs. 156-159.— Standard Journal-box of the Eastern Railway of France. block, and to this plush are fastened several little tufts projecting above its surface and keeping the plush from matting down by too hard pressure against the journal. The plush is of wool with a long silky warp. 640. Tl'.e important question of the comparative resistances in start- \t\\r trains is discussed so fully in Appendices A and B that it appears un- necessary to devote space to a repetition of the same matter here. From all the facts there given the following conclusions may, it is believed, be •drawn : 512 CHAP, XIIL— TRAIN RESISTANCE^STARTINC. I. The resistance at the beginning of motion in each journal is equal, (as before stated) to about 20 lbs. per ton, or say 15 lbs. per ton over the average friction in motion. Except, therefore, for the elasticity of the springs or the equivalent effect of the " slack" which always exists in freight trains, enabling the cars to be set in motion one at a time such trains as are usually hauled could not be started at all by the locomotive 2. A velocity of 0.5 to 3 miles per hour, or, as an average, 2 miles per hour, must be attained before the journal-friction falls to 10 lbs. per ton or 5 lbs. above the average motion. The average during this period may be taken at 12 lbs. per ton. 3- At 6 miles per hour the journal-friction is at least i lb. per ton higher than at usual working speeds. The average journal-friction be- tween 2 and 6 miles per hour may be taken as at least 2\ if not x lbs per ton higher than the normal. 4. During the period of getting up speed, the normal law of accelera- tion of velocity is so interfered with by the varying coefficient of friction that the velocity attained at any given point may be rudely taken as directly proportional to the distance run, so that the increase of velocity would be more correctly represented graphically by a right line than by the parabola tangent to the horizontal line of normal velocity in motion which theory requires. 641. Assuming these facts, we having the following conditions in a freight train which is so heavily loaded that it may be assumed to have to run 3340 ft., or f of a mile, to acquire a velocity of 10 miles per hour. 1. The average velocity will be under 5 miles per hour and the time occupif^d over 7.6 minutes. 2. The increased tractive force needed merely to accelerate the speed will be 2 lbs. per ton; since communicating that velocity is equivalent (Table 1 18) to lifting the train through 3.34 ft. vertically, and i^^^ = o. la- per cent grade = a resistance of 2 lbs. per ton. 3. For the first one-fifth of this distance, or 668 ft., the total demand upon the tractive power is — 2 lbs. per ton for acceleration. 12 lbs. per ton for extra rolling-friction. 14 lbs. total additional tractive resistance, equal to a grade of 0.70, or 37 ft. per mile. 4. For the next 1336 ft. the total demand upon the tractive power is similarly found to be 4.5 to 5 lbs. per ton over the normal, equivalent to- the effect of a 0.225 to 0.25 per cent grade, or 12 to 13 ft. per mile. , CH. XIII.— TRAIN RESISTANCE— SIZE WHEEL AND AXLE. 513 642. These grades, therefore, represent the reduction at stations or stopping-places which it is essential to make to fully and certainly equal- ize the demands upon the tractive power of locomotives while in motion and when getting under way. The fact that such heavy reduction of grade at stations may be said never to exist, while yet such heavy trains are hauled, is due in part to the use of sand in starting, in part to the greater starting traction which is realized in practice from the same average cylinder pressure (see end of Appendix B), and in part to the fact that the full adhesion of the locomotive is not used up on the open road (par. 557). To utilize to the utmost the power of locomotives, and to make the hauling of heavy trains easy, such reductions are the first thing which should be attended to in laying out a new road or in improv- ing an old one. Wherever possible the reduction of grade at stations should be liberal, since there is in no case danger of having it too great for convenience. On the other hand, when the lower grades at stations are only obtainable at the certain cost of higher grades between stations, then it becomes necessary to be more cautious, although the tendency will always be to have the starting resistances the true limiting cause. 643. Effect of Size of Wheel and Journal. — Theoretically, the less the diameter of the journal and the larger the diameter of the wheel the less the axle-friction. The standard diameter of car-wheels in America is 33 inches, with a very few only (chiefly on the Baltimore & Ohio lines) of 30 inches, and with a still smaller but increasing number of 42- inch wheels in passenger-car service. The weight of the latter is more than double that of 33-inch wheels (say 1200 lbs. against 550, as an average) and their primary purpose is to promote easy riding of cars. The Master Car-Builders' Association standard journal is 3f x 7 inches, giving a nominal bearing-surface (the horizontal mid-section) of i(i\ sq. in. A very few 4 x 8-inch journals, giving 32 sq. in. bearing, are in use for cars carrying very heavy loads, and a verylarq^e but decreasing number smaller, down to as small as 3Jx6, giving 19.5 sq. in. of bearing. The maximum loads which are carried in practice on these journals, allowing eight per car. may be estimated as follows : Journal. Square Inches Area. Maximum Load. Load Per Square Inch. Maximum, 4 X8 Standard, 3f X 7 Minimum, 3^ X 6 32 X 8 = 256 26^ X 8 = 210 19.5 X 8 = 154 64.000 52,500 38,500 250 lbs. 250 ♦• 250 ** 33 514 CH. XIIL— TRAIN RESISTANCE— SIZE WHEEL AND AXLE, As an average of the entire service of the car th.se loads will hardly in any case exceed 200 lbs. per sq. in., but they will often run up to 300 lbs. This pressure, however, is very unequally distributed, being great- est (about twice the average) at the top of the journal and running down to nothing at the sides. The bearing, in fact, for this and other good reasons, is never made to cover the whole semicircular top of the jour- nal. For example there are only 21.94 sq. in. of bearing-surface in the American standard journal-bearing against 26^ sq. in. in the section of the journal itself. 644. The only purpose in increasing the size of the journal is to di- 6. Centre of axle. (The standard axle differs a little from this, tapering more toward the centre.) 7. Flange. 8. Journal-box. 9. Journal-box lid. 46. Brass or journal bearing. Fic t6o -Usual Form of American Car-whebl, Journal, and Journal-box. Tc, i« the so-called dust-euard bearing ol the axle, surrounded by a flat, square dust-guard t ^^^ A i-tth«.r r!r vnlrlnfzed fibre which is slipped in from above throuKh a slot in the cast- s!;r« ^HS%^v^^ Sn;;fS dSiSId out^oS below^hL^rcvel of the underlfJ? of th'e axle that there is no n.ore to escape.] minish the pressure per sq. in. so as to prevent heating. Experience has amply shown this to be necessary, with such lubrication as is attained in I Cff. XIIL— TRAIN RESISTANCE-SIZE WHEEL AND AXLE. 5 1 5 America, because, although 99 per cent of the car mueage may be said to be made.with journals in good order, and in fact with surfaces in a high state of perfection, yet the inconvenience and danger resulting from possible heating of the remaining one per cent is the important thmg to obviate. In France and Germany, where much more carefully con- structed axle-boxes, insuring far more reliable lubrication, are in use than here, as shown in Figs. 156 to 159. far higher pressures are likewise in use, without evil results, up to fully double American practice, and with great economy of lubricants ; but the crude form of axle-box usual in this country, shown in Fig. 160, permits fully nine tenths of the oil sup- plied to the journal to drip out upon the track before it has done much service. 1 r • .• 645. The coefficient of train resistance due to axle-friction __ coef!. of fric. x diam. of axle ^.^ ^^^^ ^^^ ^^^^ ^ 2000 or 2240 ■~ diam. of wheel = journal train resistance in lbs. per ton. With the same axle, therefore. by increasing the diameter of the wheel from 33 to 42 in. we should decrease ^xle-friction to H of its former amount, or about |. With the same wheel, the comparative axle-friction is directly as ihe diameter of the journal. 646. If the average journal-friction in motion be taken at 4 lbs. per ton, the larger wheels, therefore, will save about o 8 lb. per ton of rolling-friction, but they will add possibly 10 per cent to the weight of the car, and therefore to grade resistance. Hence, wherever the grade resistance exceeds about 8 lbs. per ton (= that on a 0.4 per cent grade ; 21 feet per mile), the use of 42-inch wheels is a losing operation, so far as mere train resistance in motion is concerned, but there still remains as a net gain the improvement in riding qualities of the cars and in ease of starting— both very important gains. 647. Many circumstances indicate that the rolling-friction proper, between the rail and wheel, is an element of considerable importance in the aggregate of the so-called " rolling friction." One is the known and great effect of the .:ondition of the track on the resistance. It is probably largely due to this cause that modern determinations of rolling-friction, both in this country and abroad are so much below what was formerly the assumed average. Another is the ordinarily very perfect condition of railway journals and the very low co- efficients which have been obtained by Thurston, Tower, and others for journal- ^ JJSFt'ys ^/S£..> Fig. i6x. 5l6 CH. XIIL—TRAIN RESISTANCE— SIZE WHEEL AND AXLE. friction proper, as above given. Another is the high tractive coeflScients of wheeled vehicles with very small axles and very large wheels on the most per- fect roads. On the other hand, the close correspondence of the laws of varia- tion in rolling and journal friction, together with the laws of variation in jour- nal-friciion o'nly, seem to indicate quite the contrary. Thus, in both cases, as the load or the velocity decreases the coefficient cf resistance increases, and at about the saine rates (see Appendix B). 648. A plausible argument may be made to show that no theoretical loss whatever exists from the compression of a perfectly elastic substance, such as a rail may be arrumed to be, and to a great extent the permcn .nt way as a whole, under a rolling load. In Fig. 162, the compression at any point of the surfaces in contact, wher- ever it may be, is proportional to ordinates from the line CCto the periphery of the wheel P. The elastic resistance is in proportion to these ordinates, and the semi-segments FF represent in magnitude and position the total clastic forces operating to retard and to accelerate. The resultants R and R of these parallel forces must pass through the centre of gravity of these semi- segments F and F^ and must each be equal to half the total load resting on the wheel. It appears to follow clearly from the figure that the moments of these accelerating and retarding forces are equal, so that they neutralize each other. The error in this reasoning is in part that at high speeds the element of TIME comes in to modify the elastic resistances, increasing that in front of the wheel because it must be set in motion, and decreasing that behind the wheel because the elastic resistance requires time to act, and hence cannot follow up the wheel with its full force. In part the error is that any irregularity of sur- face causes an irregularity of motion which is known to very seriously aflfect both wear and tear and friction. Any attempt to determine theoretically the amount as well as the nature of this loss would, of course, be impracticable. 649. The work of Josef Grossman, Engineer of the Austrian Northwestern Railroad, on " Lubricating Materials and Metais for Bearings" (Wiesbaden, 1885), treats its subject with a good deal of elaboration, historically and ana- lytically, and among other matters discusses quite fully the question of train resistance, although not always with correctness and good judgment. His results indicate, however, that the axle-friction is at any rate a very small clement. In this connection he cites a remarkable result of some Bavarian experiments, in which by greasing the rails on the curve of 100 metres (337 ft.) radius a reduction of the total curve resistances of 96 per cent was attained; 61 per cent of the total resistance due to the curve disappearing when the inner CHAP. XIII.— TRAIN RESISTANCE— HIGH SPEED. 517 J. K V « i t \ ■idice of the head of the outer rail was greased, and 31 per cent more when the other rail was greased. The striking correspondence of these experimental results with those de- duced theoretically in pars. 301-320 et seq. is notable. THE VELOCITY RESISTANCES. 650. The best evidence that we have warrants the all but universal assumption that train resistance varies as the square of the velocity, or that its equation is of the form R =/7/» + c. This is still merely assumption, not only as respects train resistance as a whole, but as respects each separate constituent element. Air resistance, for example, is known by observations on projectiles to vary more nearly as the cube of the velocity, when the latter is very great; but at all ordi- nary velocities it appears to vary very nearly as the square, and as re- spects oscillatory resistance, we know absolutely that the amount of de structive work (or of any other kind of work) which a train is capable ot •doing, either by a dead or glancing blow, is directly as the square of the velocity. These two elements constituting together the ord in a^-y " ve- locity resistance," it is but natural to conclude that the aggregate also -varies as the square of the velocity, and all but certain that it does, al- though it may very easily be as 7/'*", or v^'^, or even z/'*', or may fluctuate between these powers at various speeds or according to circumstances. There have been various formulae pui forth, and some of them on very high authority, differing widely from this form, some of them giving the velocity resistance directl)'^ as v, and others (only one of which is known to the writer) as ^', but both of these assumptions lead to absurd results when extended to very high speeds, and are unquestionably erroneous. 651. One instance of the former (as respects the train behind the engine) is given in par. 662. On the other hand, a formula deduced from Bavarian experi- ments in 1876, on a large and costly scale, reported by the late Baron von Weber in a somewhat informal paper,* led to the most absurd results, not necessary to detail here. 652. As a rule, no attempt is made in train-resistance formulae to separate the aggregate velocity resistance into its constituent elements, although in some cases they are in such form as to assert or imply that the velocity resistance is either all oscillatory or all atmospheric. A formula devised by Mr. Wm. H. Searles, which has been adopted as the * See Railroad Gazette, June il, 25, 1880. I 518 CHAP, XIII.— TRAIN RESISTANCE— HIGH SPEED. 1 basis for the computations of this volume as having a truly wonderful ran^e of application to all speeds, conditions, and classes of trains, even if it is not precisely correct, is open to the sole serious objection (and that chiefly theoretical) that it in effect assumes all velocity resistance to be oscillatory, or uniform per ton, regardless of the form of the cars (see pars 657-8; ; while, on the other hand, formulae proposed by Mr. O. Chanute (in Haswell's " Pocket- Book ") are distinctly based on the assumption that the velocity resistance is wholly atmospheric. Both of these assumptions are unquestionably erroneous, although which is most so must remain doubtful. 653. The writer has conducted the only tests as yet made, and known to him, which have been distinctly directed to the end of determining the amount of each element of train resistance separately, and owing to the delicacy of the apparatus by which they were made, and the extreme care used in computing them, he believes them (with perhaps a natural bias) to be still the most trustworthy indication in that respect. These experiments are given in full in Appendix A, and their general results are shown graphically in Fig. 163, their most striking feature being perhaps the positive evidence that atmospheric resistance is at least a less pro- portion of the velocity resistance than is commonly assumed, and that the resistance arising from oscillation and concussion, whatever its exact cause and nature, is a materially more important element. 654. Nevertheless, there is a fact tending to disprove these conclu- sions, viz., the enormously greater indicated power of locomotives at high speeds than that transmitted backward to the train as determined by a dynamometer. Table 164 gives one record illustrating this fact— a test trip of a fast express train on the New York Central & Hudson River Railroad, made by Mr. P. H. Dudley, in which it will be seen that only some 55 per cent of the indicated power passed back of the dynamome- ter car to the train at 53 miles per hour. Figs. 164, 165, giving the re- sults of some elaborate French tests, show a still higher proportion of en- gine-friction. Other tests of the kind show, according to the speed, from 40 to 75 per cent. The whole subject is still involved in much obscurity and doubt, but Figs. 164. 165 and Table 165 will illustrate how very im- portant an element the head resistance is at high speeds. 655. According to the best evidences which the writer has been able to secure, the ordinary working maximum of train re- sistance, under somewhat adverse conditions as respects wind and surfacing of track and rail, may be considered to be not un- [^% t i As DEDUCBD FROM Fig. 163. D^c.cTAMrRsPERToN OF American RoliBng-stock, DIAGRAM SHOWING THE RESISTANCES PeR ToN oXwAV, AT ClEVELANH, OhIO. EXHERIMENO^ ON THE LaKE ShORE & M.CH.GAN SOUTHERN Ra» Conducted by A. M. Wellington, C^E. ■ reproduced in AppendU A.] c rK Vol Vlll No CLXXVll. lUe substance ol t»»c P*H^ ^ [For original paper, see Trans. Am. Soc. C.E., \ol. Vlll., wo. k,x. 30 lbs Tier ton = Qradeoft.sfteT-iOo -r / ^UJ- sv-^ e V I j^ M/Ls io HBH - ^^ ^^^"^ ^ s/tdiSxtijorxjar^olUngTf iation, (^JEm^ify Oars = 2_/ Us.]beyimi fS.o in. d^J y - ■ '' ~ \ istance formulae, and was for a long time regarded as standard. More ^'k Clark's formula, shown hereon, is one of the oldest and best known of all train-res ^^^^ ^^ ^,^^^^^ ,^, ^^tter is more doubtful. See par. 655 modem tests indicate that it is far too high at low speeds, and on the whole somewhat too Ijp g P- , et seq. [\ CHAP. XIII.— TRAIN RESISTANCE— HIGH SPEED. 5X9 Table 164. Train Resistance of Heavy and Fast Passenger Trains. Weight of Train. Engine on drivers 24.0 entruck 12.0 Tender Three day-coaches 65 . Six sleeping-coaches 185. ± ± Tons. 36.0 27.0 250.0 313 o Train started from a state of rest. Average speed in motion, 52 miles per hour. Slight undu- lating grade of 2 to 13 ft. per mile, the effect of which is corrected be- low. Total weight of train 17 X 24 American engine. 6 ft. drivers, 135 lbs. steam pressure [Deduced from records of dynamometer tests by P. H. Dudley on New York Central & Hudson River Railroad, Rept. Am. Ry. M. M. Assoc, 1882, p. 132.] Aver- age Mites. Aver- age Speed. Vel.- Head (Table 118). Wo k repre- sented by Speed . Vert. ft. Grade. Dyn. Work on Train. Vert. ft. Do. ± Effect of Grade. Vert. ft. Do. ± Effect of Speed. Vert. ft. Aver- ages Vert. ft. Per Mile. Equivalent Resistance. Grade p. c. Lbs. p. ton. I 3 20.68 38.31 15.20 52.10 -- 15.20 --36.90 + ■5*25 48.23 40.07 48.23 45-32 33-03 8.42 3 4 43.90 47-34 68.42 79 57 ■H-I6.32 -l-ii.iS 4- 5-25 35-53 31.81 40.78 31.81 24.46 20.66 20.72 .393 7.86 5 6 7 8 50.70 49-31 50.70 52.89 91.25 86.32 91 25 99-3» -I-11.68 - 4-93 + 4-93 -f 8.06 -13.0 4-18.0 4-13.0 29.74 30 -57 28.92 26.44 29.74 17-57 46.92 39-44 18.06 22.50 41.99 31-38 28.06 34-57 20.60 22.56 •427 8.56 9 10 IX 53-70 52.10 52.89 102 . 38 96.36 99 31 + 3-07 — 6.02 + 2-95 -1- 8.0 4- 5-0 23-13 23-55 23-55 3'-i3 28.55 23-55 28.48 -540 10.80 12 13 »4 16 52.10 51-43 5143 51-43 51-43 96.36 93.91 93-9' 93-91 93.91 - 2.95 - 2.45 a ■ ■ • • • • • 4- 8.0 25.61 24 78 25.61 26.85 26.60 33-6i 24 78 25.61 26.85 26.60 36.56 27-23 25.61 26.85 26.60 27.74 •527 10.54 17 18 19 52.89 52.89 52.89 99-31 99 31 99-31 4- 5-40 4- 6"o -4- 2.0 27.68 26.44 26.44 27.68 32.44 28 44 22.28 32.44 28 44 28.56 -541 10. 82 20 21 22 23 50.70 49-31 52.89 53-70 9»-25 86.32 99 31 102 . 38 - 8.06 - 4.93 -+12. 9Q + 3-07 — lO.O — lO.O -^-lo.o 29.68 28.92 24-78 24-37 1Q.68 18.92 24.78 34-37 11.62 13.99 11.79 31-30 27.72 17.18 •525 -337 10.50 6.74 Mr. Dudley found the traction in starting to be 11,000 to 12,000 lbs. for the first 100 to 200 feet, falling to 2800 to 3000 lbs. at 50 miles per hour. The consumption of steam and water per mile was : Ai 135 lbs. pressure, 300 to 333 lbs. water, 40 to 50 lbs. coal. = 7.5 to 6.67 lbs. water per lb. coal. He notes that Swiss and German locomotives carry 165 to 180 lbs. as a rule ; some- times as high as 225 lbs. The total horse-power developed by the engine is given in the same table as the dynamometer record, but computed and not observed. The computation, however, ap- pears to be one based on Mr. Dudley's own investigations. It shows a total horse-power i 520 CHAP, XIII.— TRAIN RESISTANCE— HIGH SPEED. developed of 750 to 800 H. P., and taking the average for the four miles 13-16, on which the grade was level and the speed uniform, we obtain : Average sf>eed. miles per Average horse-power expended on — hour, 51.43. Train. Engine. Total. P. c. enjf, 340 426 766 55-6i lbs. lbs. lbs. Equivalent total traction resistance 2,479 3,106 5,585 (= i adhesion.) Ditto, in lbs. per ton 9.92 4925 17.8 This is considerably lower than Table 166 indicates, which is about 30 lbs. per ton; but one possible explanation of this discrepancy is that Mr. Dudley's table does not war- rant his declaration that "at 50 miles per hour the traction was 2800 to 3000 lbs.," but indicates only 2500 lbs. This difference alone would add \\^ to 2 lbs. per ton to the resistance, Mr. Dudley's engine and head resistance, as an average of all his record (not all given here), amounts per engine to 0.83 F^ lb. The writer's tests (see Appendix A and Fig. 165) give a somewhat smaller result for the engine resistances, vir. : Lbs. per engine. For head resistance o. a8 F* For oscillation and concussion 0.35^^' Total 0.63^^* 4- 4 to 8 lbs. per ton constant. By comparison of a variety of evidences, however, the writer believes that 0.83 F« lb. comes very close to giving the actual total velocity-resistance of the engine at high speeds, and the rapid inroads which this rate makes on the power of the engine is shown in Table 165. fairly expressed by the single formula of Mr. Wm. H. Searles just referred to and given below. For the more favorable con- ditions it gives unquestionably far too high resistance ; as for example, for a train of 313 tons, as in Table 164, at 50 miles per hour, it gives a tractive resistance of 30 lbs. per ton for the en- tire train, or 9390 lbs. total tractive resistance, equivalent to 1280 horse-power, whereas the actual horse-power, as given beneath the table, was less than 800. Further evidences to the same ef- fect are given in par. 659 et seq., below ; but the ratios of the resistances at various speeds are of more practical importance than their absolute amount, and these will not be affected im- portantly by any reduction in the latter. Moreover, nearly all our experimental evidence is based on observations taken under the most favorable conditions for low resistance, and in the case of European tests with trains of much smaller cross-section and with cars much nearer together. The bounding rectangles of the average American and European passenger cars (a fairer basis of i' I m m Kf CHAP. XIII.— TRAIN RESISTANCE— HIGH SPEED, $21 Cn^nt aloiw. Fig. 164.— Variation in Resistance Per Ton FOR Various Loads. SOTons Load. 10 .1.4 J -C. %0 30 Miles per Hour. Fig. 165.— Variation in Total Traction for Various Loads. 20 Miles per Hour. French Tests of Train Resistance at Low Velocities. [From Annates des Fonts et Chaussies, May, 1886. '* Etudes Dynamometrique," par "M, Desdoint, Ing. de la Marine, adjoint a I'Ingenieur en Chef du Materiel et de la Trac- tion des Chemins de Fer de l'£tat.] The paper showed resistances at low ordinary speeds of— Passenger trains, 40)^" wheels, 3J4 X 7" axles, 4 tonnes per axle, . . , Lbs. per ton. Freight ii ii i 3-4 U 2 Temperature of axles 53.6» Fahr. At still lower velocities of 5 ft. per second (3^ miles per hour) the resistance varied from 4.4 to 5.4 lbs. per ton, this being in fact due to the lower journal speed, as observed by the writer in his tests (par. 640 et seg. and App. A and B), and not at all to their being *• valeurs toutes exagerees comme on va la voir," as suggested in M. Desdoint's paper. Trains of 300 tonnes, with 70-tonne, 4-coupled engine, showed a mean resistance of 4.4 lbs. per ton. 522 CHAP, XIIL-TRAIN RESISTANC E-^HIGH SPEED. Velocity Resistances. The following grades were found to approximately equajize the velocities at various speeds, with short trains : Grade per cent, o to o.s 0.5 to i.o Miles per hour, o to i8^ 18H to 37 37 See also par. 447. to 50 to 63 1.0 to 1.5 1.5 to 2.0 Equivalent, lbs. per ton. ID 10 to 20 201030 30 to 40 comparison than the precise cross-section area) compare aboat as follows: American, 10 X 14 ft. = 140 sq. ft. European, 8 X 12 " = 96 '^ 656. When we further remember that the car-bodies of Ameri- can cars are separated by over six feet from each other because of the platforms, and that the trucks are still more widely sep- arated ; and when we remember further that foreign engines have no cabs', and a smaller cross-section generally— the foreign evi- Table 165. Engine Head-Resistance at High Speed. [According to the formula R = 0.83 ^ » (see foot-note to preceding table) in which R = the TOTAL resistance of the engine.] Speed. Milks Per Hour. 10. 20. 30. 40. 50. 60. 70. Total Head Resistance. Lbs. 83 332 747 1328 2075 2988 4067 Horse- Power. 2.213 17.71 59-77 141.67 276.70 478.20 759-30 Lbs. Per Ton of Train (313 Tons). .266 1.06 2.38 4.25 6.64 9-58 13.05 Since the resistance in pounds increases as the sguar^ of the speed, the horse-power demanded will necessarily increase as the cuie of the speed. It takes a very powerful engine to maintain a speed of 70 miles per hour on a level for any distance, and no engine can do it long, with no train whatever behind it. As the horse-power corresponds very correctly to the conditions at this maximum speed it must necessarily correspond very correctly with the facts at the lower speeds. See end of par. 664. CJIAP. XIIL— TRAIN RESISTANCE— HIGH SPEED. 52J dence below given (par. 660 et seq.) seems to rather support than disprove the resistances given by the formulae summarized in Table 166 below, although nominally smaller. 657. It has tiierefore seemed best to use as the basis for all train-resistance computations in this volume the formula above referred to (par. 652), proposed by Mr. Wm. H. Searles in his " Field-Book," since this formula in a single simple equation seems to approximate very closely to what experiment indicates to be an ordinary working maximum for the resistance of trains of all classes, at all speeds, and with all forms and weight of cars. It is recommended, with justice, by Mr. Searles as accomplishing this end, in the following words: " It is an empirical formula, based upon a careful investigation of all such records of experiments on the subject, several hundred in number, as have come under the author's notice, and is believed to give results agreeing closely with the average experience and practice of the present day. It is designed to give the resistances per ton for all trains, whether freight or passenger, and at any velocity, under ordinary circumstances. Accidental circumstances, such as the state of the weather, and the con- dition of the road-bed, rails, and rolling-stock, may largely modify the re- sistance, but these, of course, are not taken account of in the formula." The formula (simplifying its form somewhat) is as follows for velocities in miles per hour: Average resistance of entire train in lbs. per ton of 2240 lbs., for all weights in gross tons, .0006 F" (wt. eng. and tender)'^ gross wt. of train * Average resistance of entire train in lbs. per net ton, for all weights in net tons, JP = 4.82 + .00535 7 V + •°°°4783K'(wt.eng.andtender> ' '^^^' ' gross wt. of train This formula, with a comparison of others below it, is tabu- lated in Table 166. 658. It will be seen that this formula gives the same result whether a given weight of train be made up of light empty box cars, weighing perhaps 9 tons each, or loaded coal cars weighing three or four times as- much and exposing only one third or one half the area to air resistance; ^ = 5.4 -|-.oo6r' + 524 CHAP, XIII.^TRAIN RESIS TANCE-HIGH SPEED. Table 166. Train Resistance on a Level as Affected by Velocity. A^.^ ac thP ordinary working maximum, as computed from the Giving what may be ^°"^f ^^^"^^'^'J^^^^^^^ closely with the apparent indications P-eneral formula of Wm. H. Searles, comciaing ^i / f ^^cwtanrM of the most recent tests, but possibly as much as one th^rdtoo h^gh for the resistances at high speeds under favorable conditions (par. 655 et seq.). ^^^ Resistance Per Short Ton, for Velocities; Miles Pek Hour. Freight Train*. Heavy Consolidation Engine. Engine only • " and 10 loaded cars (I it it it it 4i it 20 30 40 75 100 it it it ii %t it it it ti it Total Weight OF Train. Long Tons. 70 270 470 670 870 1070 1570 2070 Short Tons. 78.4 302.4 526.4 750- 4 Equation of Resistance. Per Short Ton. 974-4 I 198. 4 1758.4 2318.4 it it ti it i« it .0428^" .oi5iF« .oiogKa .oo928K'» .00837^' .0078 P^' . 00703 f^' .oo653r» For formulae coefficient of V^ of resistances for trains of flat cars, suitract about oox. from For resistances and formute per long ton, add 12 per cent. Pawenger Train*. 17 X 24 Americ'nEngine. Total Wt. OF Train. Long Tons. Engine only " and 2 cars. it it it o it ii it ii 4 8 12 16 50 100 150 250 350 450 Short Tons. Equation of Resistance. Per Short Ton. Resistance Per Short Ton for Velocities; Miles Per Hour. 56 112 168 280 39* 504 4.82+ .03214^'^ .01875^' .0143^' .0107 ^^' .00Q18F' . 00833 '^^ 15 12. 05 9.04 8.04 7-23| 6.89 6.70 20 25 17.68 12.32 10.54 9. II 8.49 8.16 30 40 24.91 16.54 13.75 11.52 10.56 10.03 33-75156.25 2i.7o'34 82 17.68:27.69 14.46121.96 13.09119.51 12.32 18.15 For resistances and formuloe per long »»». '"^'' " f*'/™'" Weight of cars talcen at .5 long tons, 56,000 lbs. each, loaded. Any of the formnl. compared on the following page P- P'-''""^;^^^,*;^. ^^^ e,cept^ Mr. CHanu.e. '— trfJX^X^T^^::^^^ Xh feToc'L tr^^jr:^ Z r UiL, glve^he res.ta„ce of freight trains a. high velocities at only Hi to M as much per ton as passenger Uains. CHAP. Xin.— TRAIN RESISTANCE— HIGH SPEED. 525 J pa < S O > H •< OS < (1. s o u a o c 3 a .a o . bo eo 4- o 10 00 .4 8 + o 8 + o 10 V • £f V (« rt *; bo .Si 2 c o o ^^ w bo ©■^ c b S o 00 to + + + 1 8 00 00 00 O c« + + + 00 00 00 V c 'Sb a a o c _o o 10 >o + 00 4> C U c U c o to c o o CO s .^ .§§^ V b£ K ac o .< 3 •a «> Q w en u u u u (« o en ifl W (J ..^ M c« O (3jO (A CO u u rt O « et on :\:\ ^^ ^^i. 8^ 88 8 + + 4- CO CA CO U U c« (4 U u ■a X rt o Co n c« :\^ gtO u o (4 O (CJ3 £2 (4 CO U U i4 O 10 M ■^00 l-l M 0\ iH O •^ 00 go 00 + + + o o q in % >. «-* 4-1 a a a a H H •- c E.2 k u o •> b. <3. m m u u U « E bl O e t ^26 CHAP. XIIL^TRAIN RESISTANCE— HIGH SPEED. in other words, it attaches no weight whatever to atmospheric resistance and the form of the train. The writer's experiments (Fig, 163) indicate positively that this is more nearly true than is generally suspected, but in going to such an extreme the formula is unquestionably defective. It would seem also to be theoretically defective — or if not that, certainly to go a long way beyond experimental authority — in multiplying one im- portant term of the equation by the square of the weight of engine. No theoretical justification for this is apparent. The constant for rolling- friction, 4.8 lbs. per ton, is also a little too high for loaded trains, although fair for a mean between loaded and empty. But with all these minor imperfections the formula is certainly one of wonderfully exact application to a wide range of trains, from an engine running light to the longest freight trains, and at all speeds. The writer maybe overmuch disposed to look on it with favor, since, as examination of Fig. 165, Appendix A, and Table 165 will show, it could hardly agree better with all the conclusions of his own tests, made in 1879, had it been based on them alone; yet the comparison given in and below Table 166 with the formulae given by Mr. O. Chanute in Haswell's " Engineer's Pocket-Book" shows that it compares equally well with some other modern formulae.* A variety of further evidence as to the absolute amount of train re- sistance at high speed is given below : 659i The tests of Mr. J. W. Hill on an American freight train at slow ■speeds, given in Tables 146-7 and Fig. 115, check very closely with the formula. Mr. Hill's tests were on a freight train weighing 782.94 tons in all, with an engine and tender weighing 55.72 tons. The observed and computed resistances com- pare as follows: Resistance in Lbs, Per Ton, Velocity in Miles Per Hour. 17.23 22.67 23.00 The observed resistances should be reduced 5 to 10 per cent for the internal friction of the locomotive. They indicate that the formula is substantially cor- rect at slow speeds, but increases too fast with speed. 660. Mr. Stroudley's tests on a train weighing 335.7 tons of 2240 lbs. gross, *The examples of the application of these formulae to various trains given in the above *' Pocket-Book" contain some serious errors which are liable to deceive. CHAP. XIII.— TRAIN RESISTANCE— HIGH SPEED. 527 Observed. Computed. 7.57 6.97 7.27 8.54 7.55 8.66 'With an engine and tender weighing 60.05 tons of 2240 lbs. (Fig. 114) should, ac- cording to Mr. Searle's formula, have had the following resistance: -^ = 5-4 + .012445 r« = 5'^ + 83:3i- For 40 miles per hour this gives 25.3 lbs. per ton, which amounts to 906 horse-power, whereas the average horse-power is recorded as only 529 horse- power, and the maximum shown by any diagram was 668; but then the draw- bar traction on the same train is given as an average of 4477 lbs., which at the average speed of 44.3 miles per hour foots up 528 horse-power (13.36 lbs, aver- age traction) transmitted through the draw-bar to the train alone, excluding all engine and head resistance. If the latter bore anything like the ratio to the car resistance that it does in Fig. 165, the total resistance should have been fully up to what Mr. Searle's formula gives. 661t The Engineer (April 4, 1884) states it to be a figure "accepted by lo- comotive superintendents," that with a total train-load of 336 long tons the train resistance at 60 miles per hour is 40 lbs. per ton, which corresponds closely to Table 131. 662i In a French paper on the subject of train resistance and economy of grades* we have the following formulae given, which appear to have been deduced from very carefully made tests : ** The resistance of an engine and tender is given by the formula ' 1000 ' \20 / in which E = Indicated tractive force in kilogrammes, R = Resistance per tonne in kilogrammes, V= Velocity in kilometres per hour. *' For the train hauled we have R = 2 + — ." 40 For a speed of 80 kilos, per hour, which is very nearly 50 miles per hour, and calling 2 lbs. per ton = i kilo, per tonne, as it is almost exactly, we have from this formula for the train tested by Mr. Dudley (Tables 146-7) : Per Ton. Total. For engine resistance 60 lbs. 3,780 lbs. For train resistance 8 *' 2,000 " Total (for 313 tons) 18.5 lbs. 5,780 lbs. * "Notice sur les Prix de Revient de la Traction, et sur les Economies reali- s6es par I'Application de Diverses Modifications aux Machines Locomotives. Par M. Ricour, Ing6nieur en Chef des Fonts et Chaussees," Annales des P. et ■C., Sept., 18S5. < 528 CHAP. XIIL— TRAIN RESISTANCE— HIGH SPEED. This corresponds very closely to what we have just deduced (Table 164)' from Mr. Dudley's tests. 663i Another French formula, based on the experiments referred to beneath Figs. 164-165, gives still lower results, indicating, at 50 miles per hour, For engine, tender, and rear car 31.0 lbs. per ton. For interposed cars ... . 7.1 " ** It is stated in the same paper that at about 18.6 miles per hour the resist- ance is double, and at 31 miles per hour triple, what it is at 6 to 9 miles, and that "at still higher velocities the increase is rapid." This is far from true for American rolling-stock, and probably for any other, up to 30 or 40 miles per hour, and the exact figures given may be rejected as untenable, except that they may serve as cumulative evidence that the resistances at high speeds are not so great as many formulae, including those of Table i66, give them, at least for European trains under favorable conditions. 664. A test was made in 1884, upon the Bound Brook route, between Phila- delphia and New York, to ascertain the difference in the consumption of coal between an express train running on schedule time and the same train run at a very low speed, but otherwise under the same conditions, the same five cars and precisely similar engines being used. The trains ran in each case from Philadelphia to Bound Brook and back, a distance of 119 miles. The slow trip was made in 9 hours and 23 minutes, 4420 lbs. of coal being consumed. The train stopped at the same places as the regular express trains, the only unusual feature of the trip being the funereal pace, averaging a little over 12^ miles an- hour. The performances compared as follows : Speed. Slow trip 12^ m. per h. Fast trip 50± •• " Coal burned. 4,420 lbs. 6.725 " Difference. . . 37^ m. per h. 2,305 lbs. = 34.2 per cent saved. The engine and tender weighed 75 tons, and the five cars 126 tons. According to D. K. Clark's formula, R = f- 8 (for gross tons), the com- parative resistances at these speeds should have been about 31 to 13^ lbs,, or more than double, and this gives a much less rapid increase with speed than most modern formulae. (See Fig. 163.) By Table 166 the difference should have been more than three to one. This appears to indicate very low velocity resistances. Coal consumption, however, is but a very vague guide to train re- sistance, it being quite certain that the power is developed more economically at the higher speeds. Still this test certainly tends to show that the resistances due to speed are not as great as supposed, as do also the facts presented be- neath, Table 164, Figs. 164, 165, and the tests already referred to (par. 444) as- CHAP. XIII.— TRAIN RESISTANCE— HIGH SPEED. 529 made on the Lake Shore & Michigan Southern Railway {Transactions Am. Soe. C. £., Oct., 1876, p. 344, ♦• Experiments and Tests," by P. H. Dudley), in which tests the conclusions reached were expressed as follows : " We found that, with the long and heavy trains of 650 to 700 tons it re- quired less fuel with the same engine (Mogul) to run trains at 18 to 20 miles per hour than it did at 10 or 12 miles per hour. The engine at the highest rate of speed, seems to produce its power more economically." Table 167. Speed of the Fastest Trains in England and America. [From Mr. E. B. Dorsey's paper on " English and American Railroads Compared," Trans. American Soc. C. E., 1885-6.] English Railways. LiNB. Termini. Miles. Time, including Stops. Average Speed, incl. Stops. London&N. W London to Liverpool '* Glasgow " Edinburgh... " Holyhead " Glasgow " York 201.75 406 401 264 444 188.25 397 216 118.5 50 76.5 125 h. m. 4 30 10 00 9 55 6 40 10 20 3 55 9 00 6 00 2 36 1 05 » 47 2 30 M •« 44-8 40.6 «l tt it <( 40.4 39-6 Great Northern it 43 48.1 «• '♦ Edinburgh . . . " Swansea Bristol " Brighton Dover *• Nottingham . . Great Western 44* 36 45.6 46. IS 42.6 u London, Br. & S. Coast London, Ch. & D Midland 50 American Railways. N. Y., N. H. &H. Pennsylvania it tt N. Y. Central & H. R. tt it Central of New Jersey . Baltimore & Ohio New York to Boston . , Jersey City to Phila.. " Pittsburg " Chicago. New York to Albany . . " Buffalo.. ** Chicago. Jersey City to Phila.... Baltimore to Washington 6 00 1 59 " 45 25 15 3 30 II 00 25 30 2 00 o 45 39 44-9 37-7 36.x 40.9 40.1 38.4 45 53-33 These runs are in every case/rom terminus tc *ermtnus, which makes a difference of 5 to 8 miles an hour from the speed obtained by selecting only the most favorable parts of the run. See summary on following page. 34 Va lltl 530 CHAP. XIIL— TRAIN RESISTANCE— HIGH SPEED. The aggregates of the preceding tables compare as follows : 12 English trains, averaging 240^ miles run at 43.33 miles per hour. 9 American " " 374V6 " " 41.71 " " Or, omitting the two long runs of over 900 miles from Chicago to New York : 7 American trains, averaging 214 miles run at 42.90 miles per hour. While this table correctly indicates that the fastest trains in England and America make substantially the same time, the average speed of all trains is undoubtedly consider- ably higher in England, owing chiefly to the fact that there are almost no grade crossings or highway crossings, and in part to the shorter runs, which always justify and require higher speed for equal convenience. 665. According to Table 165, the difference in the horse-power demanded to overcome the engine resistances only in the Bound Brook lest just mentioned would have been: Trip. Time V Horse-power. Slow 9.4 hours X 5 H. P Fast, .... 2.4 hours X 271.7 H. P. = 652 " Hour Horse-powers." = 47 Total difference in head resistance, 605 The total difference in coal consumption being 2305 lbs., we have 2305 605 3.62 lbs. as the coal burned per horse power per hour, without making any allowance for the increased car resistance due to speed on the one hand, or for the greater economy with which steam is used at high speed on the other hand. As 3.62 lbs. is about a fair rate of coal consumption under the circumstances (rather high), these two latter may have approximately balanced each other. 666. Table 167 shows the fastest regular trains in England and America, every train on the list probably reaching a speed of 60 miles per hour on short stretches of almost every run. The fastest trains do not haul over 125 tons to train, but even then they could not probably make the lime they do if the resistances were quite as high as in Table 166. When all proper allowances are made, however, the facts do not necessarily imply any materially lower resistance. ENGINE-FRICTION. 667. In computing train resistance it is not essential to assume any diflerent rolling-friction for the engine than for the cars. The tender- friction should of course be the same, and the engine truck friction sub- stantially the same, while for the driving-wheel base we have only to CHAP. XIII.— TRAIN RESISTANCE— ENGINE. 531 consider the rolling-friction between wheel and rail only, and not the journal friction, since the latter does not tax the adhesion (par. 608). The same is true of all the internal machinery-friction of every nature .and kind ; so that, as we have plenty of steam-power in freight service, or can have by reducing the speed, and only lack tractive force in pounds, the machinery and driving-journal friction is of slight importance for freight service, whether much or little. For passenger service it may be •of more importance, and it will at least be profitable to summarize the •evidence as to its amount. 668. The locomotive is a simple machine, and the evidence does not make it probable that more than 5 to 8 per cent of its indicated power fails to reach the periphery of the drivers. Ten per cent is often allowed. In complicated low-pressure compound engines the machinery-friction is flo to 15 per cent. In small stationary engines (Table 168) the loss /ranges from 12 to 20 per cent. In 16x24 American locomotives, the tests of John W. Hill (Tables 146-7) show that some 13 lbs. per ton of locomotive and tender was act- ually required to propel it without load at speeds of 17 to 23 miles per Table 168. Estimated Cost of Power and Efficiency of Stationary Engines. [[Abstracted from a careful and detailed paper by Charles E. Emery, Ph.D., M. Am. So. C. E., Trans. Am. So. C. E., November, 1883.] H.P. Kind. Cost in Mass. 1874. Loss per cent by Fric- tion. Indi- cated H. P. Feed- Water, per I H.P. Coal I. ffV. Evap. per lb Coal. Cost 309 days. 5 Portable Upright S645 20 6.25 42 5.60 7-5 $176.46 lo M »l 988 20 12.50 38 5- 10 7-5 109.96 «5 ii it 1,487 18 18.29 36 4.80 7-5 90.14 ao " Horizontal... 1,981 15 23 -53 34 425 8. 7328 as ti tt 2.441 14 29.07 32 4.00 8. 67.28 50 Stationary Non-cond'g. 5,331 12 56.8a 27 327 8.25 52.15 100 Condensing Single 9,207 II 112.36 23 2.61 8.8 36.02 200 (i It 16,785 10 220.99 22.2 2.52 8.8 28.64 300 ti tt 23,899 9-5 331-49 22.2 2.52 8.8 2682 400 It ti 29,958 9-5 441-99 22.2 2.52 8.8 26.01 500 it it 36,220 9-5 SS-?- 49 22.2 2.52 8 8 25.66 This table is carried out in the paper in much more detail, but the above are the most important data. 532 CHAP. XIII, — TRAIN RESISTANCE— ENGINE. hour, whereas the average resistance of the train behind it, at the same speeds, was only some 6f lbs. per ton. Assuming that, owing to the greater weight on the locomotive drivers, the rolling-friction proper, be- tween rail and wheel, was at least as much as the rolling and axle fric- tion combined of the train behind it, we may divide up this i8 lbs. ap- proximately as follows : Lbs. Per Ton. Total Lbs. Taxing adhesion : 'RoWxn^-ix'xcxXon 7 3^2 " " Head and oscillatory resistance, . . 2 1 1.2. Not taxing adhesion : Friction of engine running light, 4 224 " " Assumed addition due to load, . 5. 280 Total, 18 1,008 Actual average tractive pull (nearly | load on drivers), . . . 6,250 Maximum tractive pull in ordinary work (i weight on drivers), 11,200 This would indicate that when the engine is working fairly hard the internal friction consumes about 9 per cent of the indicated power, but it is almost certainly too high. When an engine is working light and run- ning fast a much larger proportion of the energy developed, up to nearly \, would appear to be used up by internal friction, and no doubt is — a waste well worthy of attention, but not of that ruinously injurious character that an equal tax on the adhesion would be. 669. The friction ok the slide-valve is one of the chief sources of loss by machinery-friction; but by the rapid introduction of " balanced " slide-valves, or those which have the pressure excluded or counteracted on the top side of the slide-valve, this loss is being largely eliminated. The slide-valve exposes an area of from 70 to 100 sq. in., averaging perhaps 90 sq. in., to the steam-pres- sure in the steam-chest, which may be taken to average at least 100 lbs. per sq. in., giving some 9000 lbs. pressure. With good lubrication this pressure would create no great amount of friction, but with the imperfect lubrication which alone is possible, it is far more serious. The coefficient is probably in the neighborhood of o.i to 0.2 in ordinary working, causing a resistance to motion^ in both steam-chests, of 900 to 1800 lbs. With sin. travel of valve and 50-in. drivers the slide-valve travels about ^V as far as the engine, which would make this loss equivalent to 900 to 1800 16 = say, 55 to no lbs. of tractive resistance,. amounting to something like i per cent of the ordinary work done, which in starting is no doubt often much more. Direct experiments on the Boston & Albany road gave a resistance to- motion of 2100 lbs. in starting under the worst conditions — full stroke with throttle wide open; while with the Richardson balanced slide-valve, which is one of the most approved, 325 lbs. sufficed. When once in motion it is prob- CHAP, XIII— TRAIN RESISTANCE— ENGINE. 533 able that the contrast is much less striking, but the saving in wear as well as resistance is so great that balanced slide-valves promise to be soon practically universal. 670. Otherwise than this it is difficult to account for any great loss by fric- tion at any one part of the machinery. Therefore, since no difficulty is found in obtaining correspondingly favorable results with stationary engines of equal power and more complication, we may conclude with some certainty that 5 to 8 per cent of the indicated power represents the full extent of the loss by ma- chinery.friction proper, in ordinary cases. 671. Tests at the works of Messrs. Schneider & Co., Creusot, reported by Mr. M. F. Delafield in a notable paper published in the Annales des Mines (and most other scientific journals of the world), 1885. made on a 22 X 44 in. Corliss engine, which could be worked either condensing or non-condensing, gave the following relation of indicated and effective power: Condensing engines, effective H. P. = .902 I. H. P. — 16 Non-condensing " " '• = .^45 i. h. P. - 12 This, however, is not known to apply correctly to other than engines ap- proximately similar to that tested, which developed 140 to 250 H. P. with about 60 revolutions per minute, according as it was condensing or non-condensing. 672. Tests purporting to give very high or low engine friction must be looked on with extreme scepticism. There is especial danger of error in inter- preting the apparent results of such tests Thus, tests of an apparently very accurate character by the Locomotive Superintendent of the Eastern Railway ■of France* show that of the total indicated horse-power only 42.5 and 41.6 per cent was delivered to the draw-bar, in two successive tests, out of which it was assumed that 34.2 and 35.6 per cent was consumed by the bare friction of the engine mechanism, after deducing the assumed resistance of the engine and tender considered as vehicles. The error lay in an insufficient allowance for the latter, and especially in an insufficient allowance for head resistance, which at high passenger speeds, such as that of the tests, consumes a large part of the power. 673. An investigation by the writer given in par. 128 shows that 20 lbs. X ^5 lbs. per car gives the ordinary consumption in passenger service; indicat- ing a very small loss by internal friction. 674. To get at the collective resistance of the bearings of a locomotive under steam, and to separate it into its constituent elements. Messrs. VuiUemin, Guebhard. and Dieudonn6 made some experiments, narrated in a work by Josef '^ represented by the length of any line /, which will suffice to close the triangle of forces. The direction of this force is ordinanly fixed by the conditions, and in the case we are now considlrLg It must he parallel with the plane s. as represented in the cut ; but a force Fig. 168. CHAP. XIV.— EFFECT OF GRADES ON TRAIN-LOAD. 53/ acting in any other direction, as/7", Fig. i68, will suffice for the same end, provided it will form with the forces g and w'. Fig. 167, a closed triangle ; the magnitude only of the force / required varying thereby. 677. If the body W, Fig. 167, be an angular body, this necessary force / will be supplied by the friction of con- tact between the body and the plane, and the body will remain at rest until the angle becomes very considerable, as in sliding a brick down a board. If the body be a wheeled vehicle, the journal and other rolling-friction subserves the same purpose, so far as it goes, as respects motion down the plane ; but since the rolling-friction is a very small portion of the total weight of the body, the angle of the slope on which the rolling-friction alone will suffice to maintain equi- librium must be very small. When it does not suffice for this purpose, the body is impelled down the plane by the difference between the force / of gravity and the retarding force of friction. When a body is caused to move up the plane it is obvious that the resisting friction, whether much or little, plays no part in reducing the iorce /, tending to cause the body to move down the plane ; for in that case the two forces resisting motion coincide with each other in direction, and their sum instead of their difference has to be overcome by the im- pelling force, whatever it may be. 678. These are the conditions under which the locomotive acts in hauling a train up a grade ; and in Fig. 167, if ^ be made to represent the ^weight of any vehicle W or of all the vehicles, W will represent the •force with which they press against the rails ; /, the "grade resistance" or ■force impelling them downward, or resisting motion upward ; — , the , . , . , - , 2000/ 2240/ ,. ratio of the grade resistance to the weight ; • or , according g g to the number of pounds m the ton, the grade resistance in pounds per ton,' iv — , the ratio of the reaction against the rails to the actual weight of the «body, which is given numerically, for various grades, in Table 119. 679. All grades are, in the technical work of American and Continen- tal engineers, expressed in the rate per cent, although m common American practice the words " per cent" are (somewhat unfortunately) omitted, the grades being known as a 0.5, 0.8, or i.o grade. A grade so expressed is andependent of the particular unit of measure employed, whether feet, .i:i.i \ \ 'r ' H wmtm 538 CHAP. XIV.^EFFECT OF GRADES ON TRAIN-LOAD. metres, miles, or any other. In popular American and English language grades are expressed by feet per mile, which (since there are 5280 feet in a mile) is 52.8 times the rate per cent. The use of this awkward unit, especially among engineers, is in every way to be regretted. Enghsh enc^ineers are also much given to a still more awkward habit-expressing grades as rising " i in 80," or some other horizontal distance. (See par. 683.) These may be turned into grades per cent with a table of recipro- cals. In Fig. 167 the rate of grade is given by -. If we let d = 100 (whether feet or any other unit), then r will give, in the same unit, the rate per cent of the grade. ^ 680. Since gravity.^, in the diagram of forces in Fig. 167. is repre- sented by the hypothenuse of a right-angled triangle, it follows that the pressure of the wheels on the rails. W, can never be quite equal to the weight of the body. The loss, however, is not on any ordinary grade a serious or even an appreciable one. It may be determined as follows: Ratio of pressure on rails to real weight ^^ (Fig. 167)= j;but^= ^/d^^rh\. exactly. Or, approximately (i), 7.d .y = —= + a. 2d whence (2), 681. This latter is determined by a rule of great convenience, which is too little known, and which the student will do well to fix indelibly in his memory, for the multitudinous uses of which it is capable, viz. : . , • . To SOLVE A RIGHT-ANGLED TRIANGLE OF SMALL ALTITUDE : Square the hetght or rise and divide by twice the base or hypothenuse (whichever is known). The quotient will be the difference between the base and hypothenuse, whence the unknown side is obtained from the known by direct addition or subtrac- tion. Frequently, however, in solving such triangles the difference only is- '^"^Exfmples showing the range of error in this rule are given in Table 168^. The extreme examples of the latter part of the table are intended only for lUus- trative purposes, but show that even in such an extreme case as the * 3. 4. and 5 triangle" the error is only ^ or i\ per cent. For a multitude of engineering computations, where the altitude of the triangle is below i the base, the formula is sufficiendy approximate for all purposes, the error with base 4 and altitude I being less than half of one per cent and varying as the square of the alti- tude. CHAP. XIV.— EFFECT OF GRADES ON TRAIN-LOAD. 539 Table I68|, Examples showing Range of Error in the Approximate Formula of Par. 681 FOR Solving Right-angled Triangles. Given— Hypothenuse. Error Per Cent. Base. Height. By Approxi- mate Rule. Exact. 10 xo 10 to so zo 10 I 2 4 5 6 8 10 10.05 10.2 10.8 11.25 II. 8 13-2 15.0 10.049 10.198 10.770 11.180 11.662 12.806 14.142 O.OI 0.02 0.03 0.6 1.2 30 5-7 4 (hyp.) 5 3 3 5^ (base.) 4^ 5- 4- ^ A All these examples are far beyond the range of the highest rates of grade. For exam- ples of the latter, see Table 119, page 341. 682. Comparing the two similar triangles, drs and W'tg, Fig. 167, we have, since r'.dwt: IV', W'r / = d W being, as we have seen, not the true w^eight or gravity of the body,, but the component thereof at right angles to the plane, or the force with which it presses against the plane. On any grade practicable for locomotives, however, W and g are practically equal to each other, the difference even on a 10 per cent grade being only one half of i per cent, and on a i per cent grade (52.8 feet per mile) only -r|^ as much, or ^^^ of i per cent. Therefore it is universally customary to consider that for all practical purposes r:^: '.t\g. Fig. 167, whence with suf!icient exactness, and we have the rule already given in par. 382:. The rati of grade in ft. per 100 = the grade resistance in lbs. per 100 Ihs.,^ whence, evidently, 540 CHAP, XIV,— EFFECT OF GRADES ON TRAINLOAD. The grade resistance in lbs. per ton = the rate of grade per cent X 20, or = 2 lbs. per o.i per cent. This last formula should likewise be indelibly engraven on the memory of the engineers having to do with railway work, making reference to a table needless. 683. The grade resistance in lbs. per ton on a grade given in feet per mile / grade in feet per mile\ is Isince the rate per cent = —- 1 grade in feet per mile grade in feet per mile equal to the tt^ X 20 = *• Or, since 2.64 52.80 = 0.3788, we have — 2.64 Grade resistance in lbs. per ton = grade in ft. per mile X 0.3788 = grade in sft. per mile -7- 2.64. For the long ton of 2240 lbs. we obtain, in the same way. Grade resistance in lbs. per ton = grade in ft. per mile X .4242. For a grade expressed in a horizontal distance for a rise of i, as i in 80, i in 100, or I in d, the total grade resistance is — -, , or — of the weight ; or in lbs. ' ° 80 100 a per ton, or — —, for the short and long ton respectively. This method of d d expressing grades is used nowhere in the world but by English engineers, and has nothing to commend it. 684. From the preceding it follows that the effect of grades UPON THE grade resistance is directly as the rate of grade. On a grade of i.o per cent, the grade resistance is just twice as much as on a grade of 0.5 ; and by whatever percentage the rate of grade be reduced the grade resistance will be reduced as much. To determine the effect of the grade resistance ON THE POWER OF engines, the rolling-friction, a constant element per ton on both grades and levels, must first be considered, in addition to the grade resistance. 685. Assuming, for reasons already stated (par. 623), that the rolling- friction at ordinary freight speeds of, say, 15 miles per hour is 8 lbs. per ton (=0.4 per cent grade), which is a high resistance to assume, and much higher than the ordinary resistance of the train behind the engine only, the total train resistance, and hence gross weight of trains on any two rates of grade, will be as the rate of grade per cent + 0.4, or as ^ + 04 On grades of 0.5 and i.o per cent, adding 0.4 to each, we have 0.9 and a .4 as the equivalent gradient in each case, including the rolling-friction. CHAP. XIV.— EFFECT OF GRADES ON TRAIN-LOAD. 54I The gross weight of trains on these grades, consequently, will be as 0.9: 1.4 or I to 1.556, and not as 0.5 : 1.0 or i to 2.00. With grades of 0.3 and 0.6 per cent, we have for the comparative gross weight of trains 0.7: 1.0 or i to 1.43, instead of i to 2.00. With grades of 1.0 and 2.0 per cent we have, similarly, 1.4 : 2.4, or i to 1.714 for the comparative gross weight ; whereas in this, as in the two former ex- amples, the grade resistance only is as i to 2. 686. It will be seen from these examples that as the grades are higher the comparative gross weight of trains comes nearer and nearer to the ratio of the grade resistance only, as is but natural, since the rolling-fric- tion becomes a less and less important fraction of the total resistance. Thus, in grades of 2.00 and 3.00 per cent, the comparative gross loads are as 2.4 : 3.4 or 2 : 2.833. But on the lower gradients this is far from beings the case. 687. So far, we have considered only the gross weight of train, in- cluding engine; but it is apparent that the true measure of the cost of gradients is their effect upon the net or revenue-earning load of cars and freight, and the ratio of the net loads on any two gradients^ depends upon an additional variable, viz., the ratio of the gross weight of engine and tender (or rather, of engine, tender, and caboose) to the trac- tive power of the engine. Whatever the absolute weight of the engine, if its ratio to the tractive power be the same, the ratio of the net loads will be the same on any two given grades, whether the engine be light or heavy. For the gross weight of train on any given grade is directly as the tractive power, and if the ratio of the weight of engine to the tractive- power be the same, the resulting net loads, as well as gross loads, will be to each other directly as the tractive power. 688. The ratio of the tractive power to the total weight of engine is not a constant, but varies, yfrj/, with the pattern of engine, and, secondly ^ with the ratio of adhesion, which is itself a variable quantity; but assum- ing the constant ratio of adhesion of ONE fourth, which we have seen (par. 530) to be that justified by ordinary American experience, the ratio- is readily determined for any pattern of engine, and will be seen from the following Table 169 to vary from i to 10^ to i to 4, according to the pattern of engine, the ratio for the more usual patterns of freight engines being about i to 7. In the former edition of this treatise it was assumed as i to 10, the average ratio of adhesion being taken at ^, but conditions have greatly changed since- then (1872-6). ) 542 CHAP. XIV,— EFFECT OF GRADES ON TRAIN-LOAD, CHAP. XIV.— EFFECT OF GRADES ON TRAIN-LOAD. 543 Table 169. Ratio of Weight of Engine and Tender to the Tractive Power, for Various Types of Engines, As assumed in the headings of Table 170, substantially in accordance with the data of Tables 1 27-131. Kind of Engine. Tractive Power. (^ Weight on Drivers.) Total Weight of Engine and Tender in Service. Ratio of Weight to Tractive Power. T icrht American •■••«••■ tons. 5 6 7 8 9 10 II 12 13 tons. 52 58 60 64 67 70 75 80 87 • • • • • • • • trac. power = i.o. 10.4 A verace American .*•••••••■ 9.67 Light Ten-wheel Averaffp Ten- wheel ..••«•••• 8.57 8.0 I iurht IVf ncriil ...........•■> A verace Mocul ....••■•••«•• 7-44 I lorHt f^r>n«r»liflation ......... 7.0 A vi»ra«y«» *' ...«...•• 6.82 Si'nddSS?) •« 6.67 Hpavv \f astodon. .•••••••••• 6.69 Tank Consolidation TankSwiich-engine(aU weight on drivers^ ••••• • • • • • • • • about 4 . 50 4.00 1 If any one of these constant ratios be subtracted from the fourth column of the long Table 170, it will give a column of ratios of net loads to tractive power which, when multiplied by the tractive power of any engine whatever of the same proportion of weight on drivers to total weight, will give its hauling power. 689. From the preceding it will be clear that if we know merely the RATIO of the net load to the tractive power we can determine by what per cent a given increase or decrease of grade will modify the necessary tractive power, without determining the absolute amount of either the one or the other, and tliis method was followed in the first edition of this treatise. It obliges us to assume, however, that this ratio is constant ; and as it is commonly the case that with every considerable variation in the weight of engine the ratio of its power to its weight will also vary, it is prac- tically much better to study the effect of gradients, and of the changes therein, directly from a table showing the tons of net load, exclusive of engine, tender, and caboose, which various patterns of engine can handle on various grades. Such a table is given in the following long Table 170, in which the net load in tons for nine different patterns of engines, varying from liglit American to the heaviest Mastodon engines, is shown for every 0.02 per cent of grade up to 4.0 per cent, and from that to 10 per cent at wider intervals. 690. Table 170 is computed under the following assumptions : Rolling-friction 8 lbs. per ton. Adhesion or tractive power i weight on drivers. Weight of tender (about two-thirds loaded), as noted in the heading to the table 21 to 25 tons. It gives also, in addition to the grade per cent, the corresponding grade in feet per mile, the resistance in pounds per ton on each grade due to gravity only, and to gravity and rolling-friction (8 lbs.) combined, and the ratio of the gross load to the tractive power, or 2000 total resistance in lbs. per ton' This ratio x tons of tractive power of each engine (= \ weight on drivers) = gross weight of train in tons which the engine.can haul. Sub- tracting from it the total weight of each engine, as given in the first line of each heading, we have the net load of train in tons, as given in the nine columns which constitute the body of the table. 691. This Table 170 we shall make the basis of our ensuing study of the effect of gradients on net loads. Experience has clearly shown that •only by the aid of such tables or by diagrams can the effect of gradients be comprehended, since the number of variables entering into such a table is so great that formulae become very intricate in form, and carry no impression to the mind. The weight of the caboose at the rear of the train, which is practically only another tender, and almost universally used, might well have been included as a part of the gross weight of the engine and tender in Table 170; but there are two styles of caboose in use, 4- wheel and 8-wheel, differing considerably in weight, and for other rea- sons it seemed better not to include it. 692. In Table 138 a variety of records of actual performances of en- gines has already been given, which justify the claim made at the head of Table 170, that it represents the fair working capacities of the various engines on the given grades in good American practice. The CAUTIONS at the HEAD AND FOOT OF THE TAlCE MUST BE FULLY REMEMBERED, however, that the grades must be the de-facto or virtual grades, not increased in effect by unreduced curvature or by stops on or near the grade, nor decreased in effect by the assistance of momentum (see par. 413 ^/ al.), either of which contingencies may make the nominal grades of the profile anything but the true governing gradients. Fig. 169 with its accompanying note will serve better than Table 170, perhaps, to make the effect of grades on train-load clear to the eye. ft 544 CHAP. XIV,— EFFECT OF GRADES ON TRAIN^LOAD. CHAP. XIV.— EFFECT OF GRADES ON TRAIN-LOAD. 545 (!} O "v "^ 00 vS 10 1 • • c z _ X X M ceooo> Mf^i^ 0'2'* 0>o**i w«« «m»o Ooo^»»0»'>■♦• fnn- (OMM CIMM NCIM 1 ^ fn moo •♦ - 'voo n r« M iv N 00 0^00 00 »v tv »0 NO 10 00 m 00 »0 00 •<• • ■ ♦< ca "o w e eiCIM MNN MNM g »o lAoo «rt «r »N n o> 0' «o o\ m 00 f)©© ■>•■ o» "rt •* • ►J > «« 10 ♦ ro w w 6 O-oo 00 MMM flwS MKK 00 i$< ^ 0> "T^to - ro (*i| <2\0>n Wl ♦ "T ♦fOP^ 8 M g. ^ % • e FN .Sfoiix Mft^ MOfn «««o* ro S « O»oo rv »^0 «CIM ««H MHIM IT) r^nvt m0>0« w'Oh •♦On'T O''*'* CO*- io<«"« ♦fncn weict • • • JB • ■ "a o> e Z T M 3 N 2xg:x ^ oSoo CO MMM «M« MKK lA) rx IN 0« •*! 0> IN (N ooroox m-00 ♦•««» mmci wwx x — o 00 00 • "1 '*-^'*- 7 « N ^xSx > 00 4-! tv < -J - M '«' in rr>«0 i«» 00 »p «n 1r<'>^« O-'^f^ i-i\o*< 00 r»>o *o «A •♦ <^ t*i <*> M S0>000 MO^lN rNO^M woo ♦ «- JN ♦ wflO^O MMM "OO oo>o> ' % 00 1 • ■J 4.0 1 »«.MN CQO^O »O0»^ r^*0 0> ^00 ro o> * \C>o^ (*>f»»N Www IH 0«^M OtOM^OMlN >Sf»^0 >5'*« 00«Or^ 000 O>O«O>0000 00- M M M M 00 00 CO • • c n « E < OO^M *5>«o *»>»•« « S»C.m wo'iN lorvii O>00 00 OOlNlN fNtNtx>0 M • btx 09 -^-lO 000 ♦HO moo f*^ O* ^ w h^. ^ M M^ o«o>a« 00 00 00 M n M M 00 ■♦ 0>«0 r^ « « ♦'O 0> in«0 OOVO-*- NQOO. iNiNrN «o\os} «o«o u^ 10 (A C 1 U T3 C «-• T3 ? •a c be c u 4-1 "S • 01 c 1 _>» c V c be c V j: be cn c _> 'u T3 c «^ jC J3 •a « a. • u M e beo 8 00 1^ r^ 00 Q N tr.OO N NNM WS« «MK IN <> M o> m (• *Q >o 0> ♦oo M WW 10 OoooS ►; •«» m«om rsftoc lOMOo <0>0>0 'T*'^ flfift 8 N H 8 M (4 w t; 0.0 00 •♦OO N «0 '«■ 00 c««o ooeo»o«00 gjjj; N ♦oo « '*o O-M nnr*) ro^ui ►« « fo «r m«o »^oo a 6 ^Sl'g ^^'S. 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M \o ►• \o O >- O O ©> ©"CO CO t^ «^ \n\ntrt ^00 >o>om •♦•••(»> fiM OMOO •♦O'O NO<»C 1- iH O 000 000 00 •♦■♦•* ■* '^ en ndi^. 00 "J M t^ t- r^ f) fo ro 00 •«• >- 00 m n so vo vo 10 iTi ir: ro (^ ro CI CO f»l »^ O M moo — moo N fn e« ►- w o o> mmm mmm lo ■* ■* Mso •-• mom so m m -*■ ■* rf^. o> ■*■ 9. •* o> ■*• o> 't' o sOsOm m"«-^ roforr « so « h«. f»l o> N - <-■ 000 ■♦■♦■♦ <*•■«•« m M t^ m OS OvOO 00 <*'i f^ f^ m 0mM »^««-o oor^i^sososo uiiom ro to CO CO CO CO CO CO CO fO0>O CO O ^» >*■ M 00 "•••♦CO COCOW PIN'- rococo cococo corrco N 0»S0 CO I « o e o - - CO CO CO CO CO w 800 m M o O^ Os 0^ JB » ■*•-: ■'f N g N 6 x^x C/3 x: . 4t>c-}- C« M X* X >(» w r^ < -•J - ^- *^ i> ^ r- 4) M -i'S o» N m 00 00 rx so ro O ■♦00 CO « — ««•■♦'•• g>«so "♦• o- so so m m ■^ rr CO CO 00 N rs tt ti " ■«•»■♦ r* o< 00 O>o>oo CO CO CO ro 00 CO (« t^ M SO M m M Cs 0*00 ^ '«' ^ CO COCO fO so M so CO fO CO « r^ CO so m m CO CO fO 00 ♦ ■♦ -r 2: fO CO CO so ro m t^\ ti ^ n tx (« »v t>. r^<0 *0 >o m ^ CO CO ro CO CO CO ro N 00 CO o> «»• CO CO N CO CO CO ro m0-"0O oo>o> cococo COfOCO COWW 8. JO 'Z « E < •a CO fO O CO Q^ O^ O^ e« c« M •^ COO> m 00 00 c^ r^ n N c« M ti^^ MOO •♦• MOO m « so lo m m •*• * •♦ M M e« MMM MMM M txx sS «».foo>sOMOs mwo tnm-* ♦♦CO rocoN MMM MMM MMM coot* if-oo >OcpM MMM MWO OOO MMM MMM MMM % CO rOO CO 00 ♦ « MOO C- tv 1^ so SO lO CO CO CO CO CO CO ■♦OO CO CO cO N ♦ CO oomM oo^-M oo^M COfOcOMWM ►«►<». CO CO CO CO CO CO CO CO CO CO mMOs\ocoQ t*mp« GOOs 0«0<0> 000000 COCOM MMM C»MN t* ♦ M OiSO ^ M OS tx t^t^t^soso^ \omm MMM NCtM MMM ■SO CO (O Moe^^- Mrsco o»oco COMM Mk- -OO cococo fOfOCO coc>co SOCOQ »■*"♦••» 00>ON (3sO>Os000000 txtNt* MMM MMM MMM ^ »^ ♦ M 0<0 CO M 00 sO so so so mmm m*^ MMM MMM MMM >-ior> ■^■MO oosoM- ♦ coco cococo MMM MMM MMM MMM i: so ro O 00 00 00 MMM r«. ro O r^ r^ t^ MMM »*.•«•- 00 so so so •o MMM M m M o c^ ♦ M mmm ♦ ^ ^ N M M MMM Ostx^ N t'l ^'i c^j ro MMM M o> t^ to C< M M MMM M Oee so ro i-i MMM MMM (^ m CO M OOO O MMM M Os o m ♦ M Os OS Os 8. 0><0 CO CO CO fO MMM oeo m ro M M MMM M O 1^ MMM MMM M O fv M M O MMM m ro M eoso ♦ OOO OS o> OS MMM MMM 0Q0^O ♦NO oosomico o>oo 00 000000 f^r^f^c^ M O^OO tvso so so ♦ ro so so so M O>0C \0 lo m U) c o 1 1 u u •a c u Ji *J •a •a M zi •a c o lit c :s: 1 •a c 1 ■5 I • a. bib > c V 4> c u • "O > bfi bfl a n u «-» «-t k ^ x: Xi u u •I o c c 5 ■ O M ■•-> - 663 ■go 5 w <« O a rOOO ♦ M M ♦ (^ M 00 (■» Os M moo - ♦OO M M o^eo 00 »<>>o so lOsOto mmm \rt*n%rt m mso 0> coco - M sO OS CO »«. ■♦ ♦ CO m M M mom CO M M M M o --'5 5 C ./ « it O o *-* c4 u b. s8 ro ♦ 00 M SO O ♦ 00 N >0 e«Mco ro^4- •.»-sn«n cococo COfOCO cococo ♦ 00 M so O ♦ 00 MNO so >o ^ r^oo 00 CO CO CO CO CO CO 00 o» o* CO CO CO ■OMOO ■♦OsO "<»♦• - t* M 00 ♦OS m6^ •r ♦ ''I mso <0 t^oO 00 ♦ mso vO so so tsoo 0> so so so O M M tN t> r* or«oo ♦QsO Moo^ r^ rooo ♦ O m M so N 0>00 MMM fOCO^ •♦so r«. 00 0> Q M M rp r« (^ r* t^ rxcio 00 00 eo cS <00 o- m fo M eo^O ♦ Oi OS Os 00 00 00 t^ r* fO M f* M 0\ l^sO K m ro soso VO VO M 000 o«o m m CO M O 00 so ^ irurt m ♦ ♦ Osl^so ro CO ro m ro M CO ro CO O Osoo CO N M O M •♦ mom ^ ^00 00 tx. ti so so CO t* r* rooo m ♦ m >0 00 O O >o N 00 ♦ M ♦ rv M t» CO m^^ COfOCO MMM ♦ ♦♦ ♦♦♦ ♦ ♦ •♦ M 00 m M o 00 ro 0>sO CO O 'O M o O 00 o> CO t^so so so CO r* ♦ C^ O^OO 00 CO ro r^. CO f^OO M 00 Os M •♦SO m ro t* 00 fv r^ CO CO CO f* r^vo CO CO CO O ro tv m « o^ so so m ro CO CO ♦00 M so O ♦ eo MSO OOm mmm Mror'i ♦00 M SO O ♦ 00 MSO »•■■*• so loso so «0 P- r^ ♦00 M ^0 O ♦ 00 M so 00 00 OS o> o o ^ \n>n O M M mmm ♦00 M so o ♦ 00 M so M M ro mmm ro ♦ ♦ mmm ♦ m 10 mmm li M ♦« MMM 00 O M ♦>© 00 M CO ro CO CO CO M ♦>© 00 O M ♦^ 00 O •* ■^ ■* >rmm lomm^ ■ o^ mso p« 00 Os 6 M M CO 000000 OOOOOt 9'0>0s VOCIOO ♦OSO MOO* m so N t^ rooo ♦ MM Mroro -*■ f "^ >^^ ? so tvOO 0> 0> OS 8:8 M M ro ♦ o 000 J >OM0Q ♦0»0 MOO^ mMvo Mooro ©■♦O S0txt^00000> &0M ^ ^'S Q M k« ^ M ^ v8 so M 00 M fv M M CJ ro ♦ o vo 00 ♦ OS ro ♦ ♦ O M M MMM M 00 ♦ m so mso so ro ♦ m MMM C CD M ■♦ so SO 5S JS P «» ♦»ooo »0 s^ p« (^ r«. r* (^ M ♦'O 00 00 00 00 Q OO OS ♦so 00 OS ^ O^ e M ?^ •s M N M ♦ SO 00 MMM M M ♦SO M M 00 M CO CO ♦SO 00 CO CO CO • M M M M M N MMM et M M M M M M MMM o 548 CHAP. XIV.— EFFECT OF GRADES ON TRAIN-LOAD. o o I ^ (>» M « • (I 33 V ^ 00 VO m ^ X o z CN ^mOO ■*'-'00 UINOn tN. i^vo 'O »0 "I lO 1/1 >*• (nrnM orof) mcnfi rri M 00 •^ ♦ m (*) to CO m ft O t^ ■♦ N ro f) <0 N N N m fj to CO CO ro c2 >o et «o O VO 2 "o « B O -it- vOfOO Iv^x OOlOfO '^«''<^ cocoro WNN cocoro cocoro cococo t^toN ot^ip s;CJ^ ^MM mOO OOO' cococo cocoro cocoe* J > 00 M CO «oN0 •>:«-g S5i2; MMM 000 OvO^O^ cococo cococo MWft o- f^ •* 00 00 00 M C4 M M O 00 VO CO - 00 OO r^ t^ c^ i>. « N M N N N 00 locto r^ioN 0«»vo 00 03 CO r^ rx t^ t^vo vO « c< - - - -...-. C« M M C* M « MO>^« locoo oovO"* VO>OlO lOlOlO ^ '^ ■^ NNN cietc* WPtC* ^ CO VO 00 ro N CO vS CO 00 o 9 en e •5 • . • . N 3 N ' c!? 00 C4O00 lOCOw Ovt^«OCO Sjio'* -*•■♦««■ roroco'ro WNN WNCI e«WM N MO>^» iocom qoovO CONN CICtN Si-""- Ct«« «W« WM« 7 w O r< >- xS X > 00 'W 1^ Ooovo -wMO OOVO^- NMI-I MI1>H 000 NNN NNN NWN M 5. «^ VO •♦ et 00*0* o» O* Ov M 900 OvSO 00 ^|x §v OOVOtO comO OOVOiO 00 00 00 00 00 00 t^ r^ r» « O Ov r^ t>.vo VO vO vO O VO vO VO no t^ •* 10 ro f« 1 01 E < •o t. m •o c « CO N X VO 10 loroc* oOvl^vo^oro lOlOiO 10*^ ^T^ M OvOO •*• ro CO CO CO CO CO M ■- ro !•) r^ U lO ^ CO N 00 t«.vO 2 g^'S a) • 1 c 1 1 u u tJ ^ c •a •a tf c« c c 4- S •a a a 1 > c M u u > « 0. 1 c 1 ._ 4> c Im • 1 • *• •a > 1 4-J h D ^ x: c : c "S be t, 1 « u ^ 1 w b ^ X : J3 >»* b c bs M i ^ ; 1 < > *-• o vm biC<-> V . b£0 \0 M t^ P» 00 >o o t^ ■♦ N u^ 10 "♦ CO ro ro ro CO CO w 00 VO O t^ lO ■* CO CO CO CO CO M CT-00 «- 00 vO t^vo 10 10 10 00 <£) ■«• ro«N Nftet "'!" cococo cococo cococo n u o o a V 0.0 t^ .y - u w . C u «-( rn <«-ao c« VO -r 00 C«vO -0 ID vO vO t^ 10 m lo t<.00 00 10 10 10 00 ov ov 10 m >o vS \ VO N 00 r^ rOOO 1^00 00 •*• OVO 000 «oo ♦ w vO N 1- M M \ VO N 1^00 CJv p» N N m — •' N ro ro ro ro Kl M M •♦• i/>vO CO CO ro H H H *•* < •♦00 « VO O •♦ 00 nvo OOw i-ctM wcoro \2 v£ VO vovovo vO VO VO VO « 00 ro Ov •*■ CO CO ♦ 00 O O CO ro •*• * VO N 00 •*■ O vo « rx N 00 lO lovo VO h* c^ M C« CO "»■ »AvO is 00 N "♦■VO 00 ^ 10 10 10 iO 10 N •♦VO cicici ri«w ««« M ■♦VO vO vO vO n e« n 00 O « •♦VO 00 VO ^» f* tv r^ r^ ci ei « « « ct C//AP. XIV.— EFFECT OF GRADES ON TRAIN-LOAD. 549 t^ ♦ Ov rs. 10 000 Qoo Ov 10 0- •♦ Ov O ■♦ rvvo VO vS 10 •0 lO VO ♦ t'. ro ro CO CO CO ro CO ro « Pi PI n M (M N 01 w 01 N N N 00 ■*• Ovo ro Ov "O M 00 •O <>• 0- «0 ro Ov Ov 0> rv .^ M on ♦• rn ro ro P» M « •- 11 Ov t^ M « M « M M W « « M N W P4 H M M M M M M 10 a PI -2; roOoo vO't-M Ovt^«o O- 0-00 00 00 00 t^ fv f~ NPIM CtnCI MMM f>. ■♦ C« O 00 vO O VO v5 ' \0 VO VO C4 Pt M _ lO 10 C« PI M •♦ PI O 10 VO 10 M M n Ob rooo ro 0> ♦ O vo pt vovoio io-»-'^ -croro PIPIM PIMM PlOtPI ♦ O vO ro o>vO PI O^vO PIN"" "-lOO OO^O" NPlPi MMN C4r-H t^ •♦ w 00 10 O-OO 00 00 C^ t^ ro O t^ r^ t^vo •^ o 10 •«- ro ro PI PI C« ►" VO N 00 >0 •" ro M PI M >- «. M PI P« M M PI PI M CO O P^ ♦ "I 00 O 000 00 00 t^ p ro O P^ 00 00 r^ ♦• M 00 P^ P^vo i^! ro vO VO VO lopio r«.iopo ooovo 101OU-) •* -^ -^ ■^roro fO ■♦ :r:8^ t^vO t PI •- o> 00 Ov cSoo ro VO CO P^ •♦ M 00 VO ro P^« 10 PI 00 10 CO M Ov t> 10 PI nv t^ *•* 2 2 u 2 2 <^ o> 00 00 P* t^ t^vO VO VO 10 10 10 10 ■«■ ■♦ ♦ •♦ CO C4 PI PI PI C« IN M CI n ^4 M PI P4 PI PI M M M M M M M M M M M M #« w M W IN IN M W IN IN IN M IN H M IN IN IN IN HI H «o ♦ ro M 000 tv VO ♦ ro 00 to w 00 10 PI Ov P^ •♦ 0>V0 ■♦ M o>vO ♦• N n 00 VO ■♦ PI 00 VO ■♦ CO IN 00 M 00 00 00 M M M 00 r^ r. M M t^ P^ t^ M M M IN Ovovo M IN M >o 10 10 M M M ■>»■•♦■■♦ ►* M M ro CO CO M M M CO PI PI IN M IN PI N IN M PI IN M IN IN IN M IN M M HI IN IN IN IN IN Ov Ov r^vo 10 CO W M 000 P^ VO ro P^ ■♦P< Ov ro ro « P^ •♦ w t^ m ro M Ov 1^ M 5 VO PO w Ov P>.vo ■<♦• PI M t^vo 1 ro 10 10 10 Ul 10 «o to m ♦• ■♦ •* ♦• ♦ ro PI p« PI t-t IN M 0- Ov Ov Ov 00 00 00 00 M m m *^ IN M M M M M H M M M M M M M M M M •H M « M IN M IN H •H o> 00 r^vO lO »♦■ r<^ M M 00 VO m M Z'% •♦ M 00 o> vC ♦ NO Ov 0^ Ov 00 P^ 10 ro N 00 P«. to •>•• C« M 00 t^vo ■♦ ■« PI M M M M M C« M N M M M M 00 00 00 00 00 00 t^ t>. «>. p^ t^ t^ f» VO VO VO VO m IN IN M IN IN M M IN M H M M M HI IN M Ht M -* COM HI 8 Ov o> 00 r^sO m O^ M Ox t^ 10 ro IN 000 VO IT) CO « 00 t^ VO ♦- CO P« OVOO VO 10 10 t^vo ♦ ro M IN OvOv OvOvO- O^ Q«00 00 00 00 00 00 P^ t^ tv t^ p* two VO VO VO VO VO 10 10 10 VO lO 10 U1 *. IN M IN M VO VOVO P«» OOOVO M ■♦VO OV 0\ C^ P^ 0. 10 Hl 00 CO P^ N t^ ♦ ro VO 0- K rfS-O ro P^ M 00 ■♦-00 10 ro M IN M ■* ro HI 0> e^ VO ♦ t^ ♦ VO CO 0> VO ro IN 00 10 N Ov p^ ♦ N 0> P«. lO M 00 VO ♦ 4N woo 000 0» Ov 0^ Ov 00 GO 00 pv r» p^ VO VO 10 VO VO 10 •♦ ♦• ♦• ro ro ro N PI M PI IN M — M M d d n CO ro CO CO CO rO lO M M M M M N M M M M M CI N M M M M M M M M M M M M N M M N M M M M M ♦ 00 M VO ♦■ ■"f •^ 10 lovd VO vO VO VO VO VO ^ 00 M VO VO tv. P* VO VO VO 00 VO ° ° ° d> d M VO t^ P^ q q q «' ro ♦ tx C>. tx «Ovo l>^ t^ t^ p» q 00' 9 ". ® ov d « t^OO 00 9 9 9 M CO 'i- 00 00 00 9 9 9 tovo P» 00 00 00 9 00 00 q q q q q q Ov H M CO •♦ 00 OV Ov Ov O^ Ov 9 9 9 tovo t^ OvOvO- q 00' o> ♦ «0 p^ ♦ VO NOO •♦Ovo Ov'O Q VO M t^ 00 Ov — M 00 ©• ►. M ro '«■ >«•■<»■ 10 10 VO 10 M 00 ♦ rooo ♦ M M ro lovd t^ 10 10 10 IN M IN 1 00 lO IN ♦00 pt Ovo ro M m^ VO VO vO M IN IN VO ■♦ O-vO N 00 - -i- VO t^ P~ HI IN IN 00 N VO 00 to - VO Ov N P^ P~00 IN IN IN •4- 00 •♦00 N ♦ t^ p^ d N 00 0» Ov IN M IN VO ♦ ro VO 1000 d o^o^ IN M M 00 M VO M Ov to ro 1000 000 M M M IN M ♦ 00 N VO •♦ 00 ♦ M p^ 1*- rovo 0> IN ■*■ P«» •" M IN M M M M M N M M M 00 MVO VO CO O^ Ovm' -i- M ro ro M M M p^ ro M 00 M •♦VO 00 M 00 00 00 00 Ov Ov ♦■VOOO Ov Ov 9 «t M M M M M M M M M 10 o to M HI O too M N ro ro CO CO CO PO CO CO CO col t/» tolO CO •<»• ^ i!5 eo to o to lOVO VO O 10 O P^ P-.00 to O to 00 o> o> rococo COCOCO COCOCOnIi 1^ to to O to O O HI I- M M CO to O to CO •*■ " o »0 5 so CHAP. XIV.— EFFECT OF GRADES ON TRAIN-LOAD. CHAP. XIV.—EFFECT OF GRADES ON TRAIN-LOAD. 55 1 ifi Z u > o ^ 2 ^> b] en ^ O W H S^ Id o U td > o< a f- > s <^ z" -^ Q en td > •< o ^ ctf . O Cd b Q ??^ So -Jo ^ W Z t-. o 2 g , -«f s c ^> V s? $> %l b Ui OQ < s S * • O ^S p. "^^ - «h 00 ^ § 1 |-^ hi) t» =: ft 05 -y 2^ c •V. 1: • e >"S s. m 3- S, fc X, 00 10 (*» op m ro S VO «o Moovo ■< m rx «*>vO ♦ Ov^ Ov t^ ii « gi r> t^ r^ r^ VO IT) IT IT ■♦ m (T C« 11 M o< 00 00 NO 10 FN ■ . X X M M M H M M M M 1^ M M M M M M M M M z WS 2^ • •S>^ >o N Q 00 VO VO «o to fO "• 0>VO ■>»■ w ■♦ tv •♦ 1^ w MOO l«» M tX ^• ^ m 00 64 ^'^ rt V H3 w, 1/1 10 ■«■•♦••• •♦ ro fi « Ov OvOO 00 "1 •*■ IH • w tl X M M M M M »« M IH M M M W M IN M IN M e ■ " -Scjf • c« J= « " l^ 10 fO 1- o> t^ VO CO t- Ov w iTiqo « M 5; t«. w OvOv r^ N 00 ■t m M •♦ UN "O be I- V U^ f ■♦ ■♦ ■*• ro f*> fo fl r'l N 00 00 r^ ^ r^ \r, >*. 1-4 .^U X •J > M M M M M M M M M M ►» M M M 1 1 ^ . • ^Oi N ^ « 00 VO ■* « Ovt^ 10 Ov M VO IN t^ r»i o> «r) vf 5 e fl r^) rr, ti N W « M M M M OvOO 00 vO t^ * -r tH HI M l-l M « « »< « M ►» ►* M M Ol M 1 1 N,*' •C . — ^ ?— ? r^ r VO • , T N a N 2 ^ ti„ 10 ro M M h* M 8^?^ ■* rr» w 000 8 ■♦00 f^ OVOOOO 00 >*■ Ov >0 N 00 VO VO m 10 «n >o ^ r w A « •- X g- X ^ oSoo M M M M M M m M JC • LTl x: ' a ) ^ 4be4- 1 e» N •- X * X 0- 00 VO ■<«■ ro M Ov Ov Ov 00 r^vo •<■ 0^ -*■ Qy m M K. •♦ t^> ♦ V? « ^ « c o> Ov Ov Ov 000000 00 vovo 10 «o 10 ■♦ ■♦ r « >' 00 oi r^ « < "J- 3 • — ' 5|t ^|x rn M tN\0 "1 fON w %o w rs. ro Ovvo CO l~» ir vS * 00 1 « fc» 00 00 00 t^ t^ ts. r^ t^ t^ «^ r^ vO VO >0 VO ■♦ ■♦• «•■ «♦ fO rr. ^j • <^ >•■ ro « M o- 1>. vfi 10 i/> VO 10 •* rr 0> I') M OvvO ro 00 10 m 00 10 h p CO c ^x >o vovovo 10 «n 10 m ■*•■*■•♦ CO f) CO fnw w « • CO ~ E < ^« 000 1^ VO 10 •*• ro w ►< M 1^ ♦• w OvvO ■♦ « Ov f» VO « bcx 10 ■♦*•*• 'T ■*■ f •*■'•■••• ^ e« e< M M IN H IN lA 1 N ^ M . c "^ tcZ„ . 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O •o a o u '•5 "o z a-o 3 X O 3 V c« <^. to *-• o X) a bl - 3 u 5 ^ 4-1 en c OS 5 C o u XI c «». {J rt bo o ^ o (J c t^ c 4-1 u; J t^ ♦J o c W >: c to 1 '=' x: o e« v5 jo u ea > 4.1 u 3 fc a *-* n V k. e o u «^ be c x: *-* bo c (X o 8 c tn V K be a >»■ c c« "O o E a .a 9 K •5 ^ a o Si en O (1 O en i C o o !3 U 3 u ttfl be c V •o (4 K u lA Xi (S n ♦o 3 ♦-> en 'ja c o b ^ 2 c K H u o o N bt •c k. o tn o x: Grade in Feet per Mile. CHAP. XIV.— EFFECT OF GRADES ON TRAIN-LOAD. 553 Notes to Fig. 169. Regarding the bottom of the page as the base-line of the diagram, or axis of x, as ex- plained beneath the title to it : 1. r/ie lower heavy line represents the progressive increase of train-load (behind ten- der) as the grade is reduced, for the lightest American engine given in Table 170, which begins at o at a grade of 480 ft. per mile, and ends at 1198 tons on a level, just beyond the limits of the diagram. * 2. The upper heavy line, marked A, represents the same thing for the heaviest Mas- todon engine given in Table 170, so nearly that it is not in error by more than its own width at any point. It was not plotted for that purpose, however, but was one of the lines of the original diagram, as below, made blacker to correspond with line i. Similar lines for all the other nine engines whose tractive capacities are given in Table 170 would fall between these two lines at approximately regular intervals. It has not seemed necessary to plot them. The remaining lines of the diagram give the cyhnder and adhesion tractive powers sep- arately for the three different engines below detailed, as computed by Mr. G. W. GUSH- ING, Supt. M. P. No. Pac. Ry., on the following assumptions : Rolling-friction, 6^ lbs. per ton in place of 8 lbs. per ton, as in this volume. Ratio 0/ adhesion, >4, as in this volume. The difference in the rolling-friction makes the train-loads somewhat greater than those given in Table 170, especially as a level is approached, but makes no great differ- ence on the higher grades. The three engines are as follows : Engine. Cylin- ders. Drivers. Trac. Pr. in Lbs., Per Lb. of Effective Pressure. No. Drivers. Weights. On Drivers. Total Tender, Engine. 1 Loaded. ! Total. A B C 2a" X 26" 22" X 26" 20" X 24" 49" 49" 49" 256.8 256.8 196 8 10 8 ioo,ocx> 110,000 96,000 112,000 112,000 108,000 65,000 65,000 65,000 177,000 177,000 i73i"«> The lines marked A, B, C indicate the loads corresponding to the adhesion tractive power of these three engines, computed on the basis of one fourth the weight on drivers. The remaining lines indicate the cylinder tractive powers for the same engines at various points of cut-offs, cis follows : Engine Qi, 2o"x24", Gonsolidation, 48 tons on drivers. At half-stroke the cylinder power is somewhat less than the adhesion, and at 70 per cent very slightly over. Only at very slow speed can such an engine furnish steam for running at 70 per cent cut-off. Engine A, 22" x 26", Consolidation, 50 tons on drivers, or 5 tons less than B, but iden- tical in cylinder capacity, showing that the latter is in excess. Engine B, 22" x 26", Mastodon, 55 tons on drivers. The two lines for cylinder tractive power apply alike to engines A and B. In both of these engines the cylinder power is much greater in proportion than in engine C, and cannot be fully utilized at one fourth adhesion. As the working adhesion on a good rail often rises much higher thiin one fourth 554 CHAP. XIV.— EFFECT OF GRADES ON TRAIN-LOAD. THE PERCENTAGE OF CHANGE IN THE NET LOAD RESULTING FROM A. CHANGE IN THE RATE OF ANY GRADE. 693. Assuming Table 170 as a basis, we can readily determine from it, in the manner below outlined, the two following laws,, which are the foundation for a correct estimate of the value of « reducing grade: First. When the rate of any one given ruling grade is increased or decreased^ the corresponding percentage of increase or decrease in ther engine-mileage required to handle any given tonnage varies almost di- rectly as the change in rate of grade ^ however much or little the change may be, slightly increasing, however, as the increase is greater and de^ creasing as the decrease is greater. For example, if a 0.6 per cent grade be increased to 0.8 the increase in en- gine-tonnage required is, for Consolidation engines, ^^ = 21.73 per cent in- crease, or 10.9 per cent per o. i per cent of grade ; but if it be increased to 1.5 percent, the increase is Yff^ = 103. 37 per cent increase, or 11.48 per cent per 0.1 per cent of grade ; being about 5i per cent more per o.i per cent of grade than for the smaller increase. If the entire weight of the engine be on the drivers, or if only the load on the drivers be considered the engine, and the re- mainder a part of the train, this law is exact, and the engine-ton- nage varies precisely with the change in rate of grade, as may be seen in Table 172. Second. The amount of this percentage of increase or decrease in CHAP. XIV.— EFFECT OF GRADES ON TRAIN-LOAD, 555 however, this surplus cylinder power is likely to be very useful in handling heavy trains easily, and indicates that engine B at least is better designed than engine C for the most efficient freight service. Where and why tank engines are advantageous may be very clearly seen from this^ diagram as follows : Referring to the head-lines to Table 170, it will be seen that the total weight of the' lightest American engine and the weight* on drivers of the heaviest Mastodon are the same, 52 tons. A tank engine of the same total weight, all of it on drivers, while it will be a much lighter and cheaper machine than the Mastodon, and be equal to much lower speeds only, will have a greater net tractive power on all grades by the constant amount of 35 tons (saved in dispensing with a tender and leading truck). Therefore, plotting on Fig. 169 a line for 35 tons greater loads than for the upper heavy black line, we find that on the higher grades it makes an enormous difference in the percentage of net load hauled, but as the lower grades, below 2 per cent (106 ft. per mile), are reached the two lines become almost coincident. the engine-tonnage required varies considerably with each grade, being nearly five times as much on a level as on a 3 per cent grade j and is about as given in the following Table 171, where these percentages are given for all grades, determined in a manner we will shortly review. 964. These two facts being definitely ascertained, we have, ire order to determine the effect of any change of grade upon the engine-mileage required to handle a fixed tonnage, simply to» multiply the percentage given in Table 171 (which see) by the xxumh^v oi tenths per cent change of grade to obtain the total in- crease in engine-mileage which will be required for any given? change of grade ; or, the same fact may be still better deter- mined directly from the actual load on each grade, given in Table 170. This percentage, multiplied by the proportion of the expenses which varies with the number of trains or engine-ton- nage (the car-mileage and traffic remaining constant), i.e., by the portion of the expenses which would be doubled if the engine- tonnage were doubled, will give the annual cost of a proposed' increase of grade, or the annual saving of a proposed decrease. 695. Table 171 (see p. 556) is determined from Table 170 in the fol- lowing simple manner: Taking only three types of engines, the lightest "American," heaviest Consolidation, and a tank engine of the same weight on drivers as the latter, but with no tender nor truck, and comparing the net loads given for grades of Level, 0.5, i.o, 1.5, and 2.0 per cent, we have the following net loads hauled : Light American, . . . St'nd Consolidation, Heavy Tank Engine, . Then it is evident that, whatever the total tonnage to be moved, the percentage of increase in the engine-mileage required to move it will be^ with a 1.5 per cent instead of i.o per cent ruling grade, American. Consolidation. Tank. 777 . ..„ 857 Grades of Level. 0.5. I.O. 1.5. 2.0. 1198 504 305 211 156 2920 1253 777 552 420 3000 1333 857 632 500 305 , — = 1.446, 211 ^^ 552 = 1.408, times that required on a i per cent grade, or 44.55 per cent, 40.8 per cent, 632 _ = '-357, 35.7 per cent. '556 CHAP. XIV.-EFFECT OF GRADES ON TRAIN-LOAD, 1 rf fW Table 171. Percentage of Increase (or Decrease) in the Engine-Mileage required WHICH RESULTS FROM ANY CHANGE IN THE RaTE OF ANY GrADE. [Deduced from the long Table 170 in the manner explained in Table 172.] INCREASE Pek Mileage Per 0.1 Cent in Engine- Grade DECREASE Per Cent in •J Enginb- of Change in Grade to be Mileage Per 0.1 of Change resulting from a Total Ch in Grade KESULTING FROM A Total Change of — Changec ange of — 79.2 52 8 26.4 5. 28 ■ Ft. Per Mile. \ 5.28 26.4 52.8 79.2 + 1.5 + 1.0 + 0.5 + 0.1 Per cent - 0.1 -0.5 - 1.0 - 1.5 28.68 27.62 26 64 25.9 Level. • ■ • • ■ . . • ■ ■ ■ 23.16 22.30 21.46 20.9 .10 20.6 • • • ■ 19 -43 18.73 18.02 17-5 .20 17.3 • • • • 16.80 16.15 15.54 »5.i .30 14.9 - • • • .... • • • • 14.84 14.25 13.72 13.3 .40 13.1 • ■ • • .... 13-30 12.76 12.26 II. 9 .50 11.8 11.42 . . . • 12.05 11.58 II. 16 10.8 .60 10.6 10.36 «... • • • • 11.05 10.60 10.22 9.8 .70 9-7 9.48 . • a . • • • • 10.24 9.81 9-44 9.2 .80 9.0 8.74 .... ■ • • • 9- 50 9.13 8.76 8.5 .90 8.4 8.14 .... .... 8.93 8.56 8.22 8.1 1.00 7.8 7.60 7-34 * • • • 7.91 7-59 7.26 7.0 1.20 6.9 6.76 6.52 • • • • 7.18 6.86 6.60 6.3 1.40 6-3 6.10 5.88 6.58 6.27 6.02 5-8 1.60 5-8 556 5-37 5 17 6.09 5.80 5.60 5.5 1.80 5.4 5.14 4-95 4.77 5.67 5.38 5.20 5-1 2.00. 5.0 4.80 4.62 4-44 5.35 5.01 4.86 4.8 2.20 4-7 4.50 4.31 4.14 5.05 4-79 4.66 4.6 2.40 4-4 4.22 4.07 3.92 4.85 4.58 4.44 4-4 2.60 4-2 4.00 3.85 3.71 4.68 4-39 4.24 4.2 2.80 4.0 380 3.67 3-55 4.50 4.23 4.06 4.0 3.00 3-8 3.62 3.50 3.37 4.03 3.80 3.66 3-6 3.50 3.5 3.38 3.19 3.07 3.79 3-57 3-34 3-4 4.00 3.3 3-10 2.97 2.83 3-5« 330 3-14 '■' 5.00 1 3.0 2.80 3.63 2.51 These percentages are computed /or an average Consolidation, havine 11 tons trac- ed i^s'^^'"s7 ^'°^^''^- '''' drivers, but they are substantially the same for all freight By interpolation any desired percentajje can be determined from the above very ao- -iproximately. Thus for an increase of 0.75 in a 0.75 grade we have 10.41 + 9.63 ^ = 10.02 X 7-5 = 75 + per cent increase in engine-mileage. -Exactly, it is (Table 170) ?-^ = 74.64 per cent, increase. 552 CHAP. XIV.— EFFECT OF GRADES ON TRAINLOAD. 557 total increase of engine-mileage, equivalent to an average increase A'' 0.1 oj increase of grade of 8.91 per cent, 8.16 per cent, 7.14 per cent. For an increase from a i.o per cent to a 2.0 per cent, we have American. Consolidation. Tank. 305 = I-PSS* m = 1.850, ^57 5^= '•7^4, 156 '" 420 a total increase per cent ot 95- 5 per cent, 85.0 per cent, 71.4 per cent, or an increase per o.i per cent of increase of grade of 9. 55 per cent, 8.50 per cent, 7. 14 per cent. 696. Proceeding similarly for other changes of grade, viz., o.i, 0.3^ 0.5, and 1.0 per cent of increase from a i per cent grade (making the" maximum change considered, from a 1.0 per cent to a 2.0 per cent)*, and computing also the comparative engine-tonnage required for correspond- ing decrease in a i per cent grade, this extreme reduction being to Level we obtain the following Table 172, in which the computations in the last Table 172. Showing the Effect of Various Changes in a One Per Cent Grade ON the Engine Tonnage required for Three Patterns of Engines. For a Decrease in A I 00 Per Cent Making the Grade The Per Cent of Change in Engine Tonnage needed is— And the same Per o. i Per Cent of Change in Grade is— Gradb of — Light Ameri- can Heavy Cons'n. Heavy Tank. Light Ameri- can. Heavy Cons'n. Heavy Tank. 1.0 per cent Level. 0.3 0.5 0.7 0.9 1.00 x.x «.3 X.5 »-7 3.0 74.5 53-9 39-5 24 3 8.4 8.5 36.0 44.6 64.0 95-5 73-4 52.4 38.0 23.1 8.8 7-9 24.1 40.8 58.2 85.0 71.4 50.0 35-7 21.4 7-14 7.14 21.4 35.7 50.0 71.4 7.45 7.70 7.90 8. II 8.41 8.53 8.68 8.91 9.14 9.55 7.34 7.49 7.60 7.71 783 7.92 8.04 8.16 8.31 8.50 0.7 " •' 7.14 0.5 " " 7.14 0.3 " " 7.14 0.1 " •• 7.14 And for an Increase of 7.t4 O.I percent 0.3 " ♦• 7.14 0.5 " " 7-14 0.7 " •» 1.0 " •» 7.14 7.14 1 7.»4 Computed from Table 170 n\ the manner explained in par. 695. The results of lar computations for all rates of grade are condensed in Table 171. simi' S58 CHAP. XIV.^EFFECT OF GRADES ON TRAIN-LOAD. CHAP. XIV.— EFFECT OF GRADES ON TRAIN-LOAD. 559 mm column but one correspond substantially with one line (that for a i.o grade) of Table 171. All the other lines of Table 171 were computed in the same way from Table 170, the figures only differing. 697. It will be seen in Table 172 that a tank engine which has all its -wreight on drivers gives exactly the same per cent of change in motive- power per unit of change of grade, whether it be great or small. In pro- tion as the dead weight of the engine becomes a larger proportion of the weight on drivers, the absolute per cent of change in motive-power in- creases, and likewise the irregularity of the percentage. 698. By interpolation in Table 171, the percentage for almost any kind of a change of grade can be readily determined. These percentages do not vary to any important extent with the pattern of engine, within the range likely to be used for freight service, nor even for considerable differences in the assumed ratio of adhesion. Moreover, as it is now well established that \ is the proper ratio to assume, for American practice at least, no other should be assumed. 699. Ordinarily the changes of grade which the engineer is called upon to consider are not very great. The typical percentage for any or- dmary change in any grade, for use in estimating the value of a reduc- tion or the cost of an increase, may therefore be taken to be that due to a change of o.i per cent in it. as shown in Table 178. which is practically the same for either an increase or a decrease of grade. For extreme dif- ferences of conditions, of any kind, the actual percentage of change in engine-tonnage should be directly computed from the relative train-loads given in Table 170. We are now prepared to consider the cost of changing the hauling power of engines by changes of grades. 700. Table 173 will illustrate how enormously the virtual gradient as well as the work of the engine may be increased by frequent stops and quick starts On the New York Elevated Railway the stops are so close together that it is ab- solutely essential that speed should be gotten up very quickly indeed if reason- ably fast time is to be made. Accordingly we find that the work done in get- ting up speed is equivalent to an addition to the actual grade of 2.63 per cent, or 139 feet per mile— an addition so great that whether the actual grade be i per cent up or i per cent down makes comparatively little di£ference in the working of the engine. Table 173 gives an extreme example of conditions which obtain very largely in passenger service, and which make frequent stops a very serious disadvantage. Due allowance for this effect should never b«» forgotten in attempting to determine what the actual grades are. Table 173. "Handling of Trains on Manhattan (Elevated) Railway (Third Avenue Line). [From a paper by Mr. Frank J. Sprague before the Boston Society of Arts, 1886.] Length of line 8.48miles. Toul lift, up track 144-42 ft. Lineal distance for same 13,160 ft. Total lift, down track 137.60 ft. Lineal distance of same ... 16,510 ft. Level on each track 15,100 ft. Number of stations 27 Number of stoppages 26 Average Times : Single trip 42 min. Per station 97 sec. Under way 80 " Stop ,7 " Time due to a run without stop at max. speed of 19.2 m. per hour.. 26,56 min. Total time standing still at sta- tions, at 17 sec. each 7.37 " Time lost in slowing up and get- ting under way 8.07 *• Total 42.00 min. Average distance between stations. 1,722 ft. Divided nearly as follows : Getting up to 10 miles per hour 130 ft. Thence to full speed (19.2 miles per P.ho"'') •- 495ft. Full speed 808 ft. Slowing to stop 289 ft. Average Speed — miles per hour : Getting under way Full speed Slowing to stop Mean between stations »3-4 19.2 9.6 14-7 Daily Work of One Engine : Round trips made 9 Coal used 5,760 lbs. Hours on duty 20 Hours steam on 6 Av. consumption of coal per trip, . . . 640 lbs. Total horse-power per round trip. , . 6,184 Horse-power per pound of coal -^^ = 9.66 Pounds of coal per H. P. p. h. 640 60 9.66 = 6.3X For a speed in miles per hour of. The velocity-head (Table 118) is , Divided by distance to acquire that speed , Gives as the virtual gradient due to that acceleration, in excess of the actual grade If the actual grade be i per cent up, the same speeds will be acquired in a distance of , Or if 1 per cent down, in Even so extreme a difference in grade makes comparatively little difference, therefore, in practical operation. xo.o 355 ft. 19. 2 13.10 ft. 135 ft. 495 ft. 2.63 p. c. 2.64 p. c. 918 ft. 98 ft. Sooft. 360 ft. Getting up speed to 19.2 miles an hour 26 times is equivalent to lifting the train ver- tically 13. 10 X 26 = 340.6 ft, in a run of 8.5 miles, or 40 ft. per mile, whereas the total tractive resistance in motion at that speed, at 10 lbs. per ton, is equivalent to some 26 ft. per mile only. 56o CHAP, XV.— TRAIN-LOAD ON OPERATING EXPENSES, CHAP,XV.— TRAIN.LOAD ON OPERATING EXPENSES. 561 Hi liffln CHAPTER XV. THE EFFECT OF TRAIN-LOAD ON OPERATING EXPENSES. 701, The increase in train resistance which results from an increase of ruling grade can be, and is, overcome in either of two ways: (i) By an increase in the weight and power of engines ; (2) by decreasing the weight and increasing the number of trains. The first of these— increasing the weight of engines— is by much the cheapest, but is only possible to a limited extent and under special cir- cumstances. Ordinarily, it is not fair to assume that heavier engines are used on one alternate grade than on another, because, whatever advantage may be gained by using heavier engines on one grade may be equally well gained on the other grade. It is far more frequently possi- ble to fairly assume the use of heavier engines on heavier grades with passenger than with freight service, but passing (until par. 732) the ques- tion of when it is or is not possible to adopt the cheaper expedient, we will estimate the cost of each separately. THE COST OF INCREASING THE WEIGHT OF ENGINES. 702. The following items will not be increased at all by an increase of weight of engines to suit the requirements of a higher grade, the weight of train remaining the same: The cost of (i) repairs of cars; (2) train- wages ; (3) general expenses ; (4) maintenance of way and works, exclusive of rail and tie renewals and lining and surfacing; (5) that portion of the inaintenance-of-way expenses last excepted which is caused by the cars and not by the engines. The most reasonable estimate which can now be made of the relative erfect of engine and cars upon the track is (pars. 115, 116) that consider- ably over half of the deterioration of track comes from the passage of en- gines over it, and the remainder only from the passage of cars, which may weigh ten or twenty times as much. Assuming one half only, we are led to the conclusion (see Table 175) that more than three quarters of the total expenditure is unaffected by an increase of the weight of engines in any visible and direct way. 703. The effect on cost of maintenance of track of increasing the weight of engines has been greatly modified and much reduced since the publication of the first edition of this volume (prepared, as it neces- sarily was, from records which were some years old in 1876) by the now universal use of steel rails in place of iron. The causes and extent of the changes thus brought about have been already summarized in par. 109 et seq. The most important of all, as respects the use of heavy engines. IS that the nature of the wear of rails has changed. With iron rails, the wear took the form of a crushing or lamination, which destroyed their surface long before the direct abrasion had become a serious matter. This crushing was very greatly hastened by heavy loads per wheel, and in- creased in much faster ratio— to the extent that iron rails which would sustain the passage of light engines for many years would be crushed out by heavy engines in a few months. On the other hand, with steel rails (excluding those of inferior quality, of which far too many have been and are laid) the wear is merely direct abrasion, which is not materially in- creased per ton of train either by load per wheel or speed. As respects the last at least, there is very good reason to believe that it increases in much less than direct ratio. 704. For, as respects speed, when the question is one merely of abrasion and not of destruction impact, the less the time to which the rail is exposed to load the less, undoubtedly, the normal crushing effect, for the same reason that journal and other (i.e.. brake) friction is less at high speeds or that it takes more force to rupture a specimen in a test- ing-machine quickly than slowly. Impacts proper play their part, no doubt, in the wear of steel rails as of iron rails, but so long as the p,c surface remains tolerably good (as it does almost indefinitely with the best steel rails) it is a small part. When the surface becomes seriously impaired steel rails go almost as quickly as iron; but either with steel or iron the effect of the impacts is not, as is often assumed, as Mv'^. This is true of a body impinging directly upon another; but one caused to impinge Fig. 171. upon another in jumping from ^ to ^ under conditions outlined clearly enough in Fig. 170 impinges at a different angle, which has the effect of reducing the im- pact communicated to B to the approximate ratio Mv ; and when we assume a 36 562 CHAP. XV.— TRAIN.LOAD ON OPERATING EXPENSES. case, as in Fig. 171, still more closely approaching average practical conditions, the communicated impact becomes more nearly in the ratio M \^v^. That this is so follows clearly from experience on tracks where the varia- tions of speed are considerable, as notably on the four tracks of the New York Central & Hudson River Railroad, two of which are used for passenger ser- vice only, and two for freight only. The observed rate of wear per ton is nearly constant on these tracks, in spite of the fact that the proportion of engine-ton- nage is several times greater on the passenger tracks. As respects efifect of increase of load, abrasion, other things being equal, should be in some approximately exact ratio to the maximum fibre-strain. If we assume an elastic cyl- inder or sphere to be rolling on a plane, a distor- tion of form will result from compression, rudely outlined in Fig. 172. The volume of this solid, shown in plan in Fig. 173, will be in direct ratio to the total load, but the maximum fibre-strain will be in proportion to the maximum ordinate CC\ which varies more nearly as \/L or even '4/Z, ac- cording to the assumptions as to the surfaces in contact. The subject is too obscure, and too unimportant for our immediate purpose, to consider further. 705. The observations of the Pennsylvania Railroad on the wear of rails on grades (par. 457) also tend to show that not more than half, or at most two thirds, of the total cost of rail wear can be considered to vary directly with the engine-tonnage, the car-tonnage remaining constant; whereas in the first edition of this treatise, based in the main on iron- rail statistics, the whole cost of rails was assumed (and the writer be- lieves with substantial correctness) to vary as the square of the weight on drivers, or at the rate, for small increments, of 200 per cent.* This change is one small evidence of the immense advantages which have re- sulted from the introduction of steel rails. 706. Of the remaining items of the cost of track, lining and sur- facing, in spite of apparent reasons to the contrary (discussed in par. 125), is affected by increased weight of engines in a considerably greater ratio than the rail wear, and tie renewals to a very considerable extent, although not quite so largely. We may not improperly take half the total cost of rails, ballast, ties, adjusting track, and switches, frogs, and sidings, as varying directly with the average weight on drivers, car-tonnage being * For the reason (to those familiar with the elements of the calculus) that <&* = 2xdx. See p. 90, old edition. Tfc, CHAP. XV.— TRAIN-LOAD ON OPERATING EXPENSES. 563 constant. With inferior steel rails it may be much more, but with such rails as may be had at the same cost by adequate care in inspection this estimate is a sufficient one. 707. The remaining items of maintenance of way, for bridges and BUILDINGS, are very slightly affected, certainly by not more, in ordinary cases, than \ ct. per train-mile, the whole being an allowance for interest and maintenance charges on heavier bridges. 708. Repairs of engines are affected much less than would be sup- posed by the weight of engines. Renewals constitute, as per Table 55 and others, from 40 to 50 per cent (under normal conditions, which can hardly be said as yet to exist on account of the rapid growth of traffic) of what ap- pears charged to "repairs." Table 174 affords the means for estimating that considerably less than 50 per cent of the Jirs/ cost of engines varies directly with weight, the remainder being, within moderate limits of variation, a constant. Of the remaining cost, repairs proper, it is indicated in Table ^\etseq. and a number of others, that between 50 and 60 per cent is for labor only : an item which will be somewhat, but very slightly, affected by the weight ■of engines. The remaining expenditures, for raw materials and for wheels, axles, and tires, will vary nearly, but not quite, directly as the M'eight. It would appear from these facts that 50 per cent of the cost of repairs may, with sufficient exactness, be assumed to vary directly with weight of engines, the remainder being constant, as has been already stated in par. 134. 709. The cost of fuel for heavier engines hauling the same train behind them will not be largely increased. In not a few cases there would be an actual decrease. It is to be remembered that, even if heavier -engines are used to overcome a somewhat higher grade, it is only for a short distance that the extra power is required. On all up grades below the maximum, and in descending all grades, the power required and ex- erted will be no greater than with the smaller engine, except the slight addition due to the weight of the engine itself, and this power will be somewhat more economically exerted (par. 579), owing to the heavier en- gine being less pushed. The constant wastage from radiation, stopping and starting, etc., estimated in par. 344 et seq., at 50 per cent of the fuel consumption, will remain for the most part constant. For all these reasons together, on something like two thirds of the length of ordinary railways the fuel burned per mile would be but slightly if at all affected by moderate (not over 20 per cent) differences in weight 564 CHAP. XV.— TRAIN-LOAD ON OPERATING EXPENSES. Table 174. Comparative Cost Per Ton of Various Sizes of Engines, Broad and- Narrow Gauge. [Compiled from information furnished by the Baldwin Locomotive Works.] American Type — Standard Gauge. Weight (net tons). Cost, 1886. Cylinders. Total. On Drivers Engine. Tender. Per Ton on Drivers. 12 X 22 13 X 24 14 X 24 15 X 24 16 X 24 17 X 24 18 X 24 24. 27. 295 32.5 36. 38. 41. 15. l8. 19.5 22. 245 25.5 27.5 $5,750 6,000 6.250 6,500 6,750 7,000 7,250 $950 1,000 1,050 1,100 1,150 I,200 1,250 $383 333 321 295 276 275 264 20 X 24 21 X 24 11 X 16 12 X 16 13 X 16 14 X 16 15 X 16 Mogul Type — Standard Gauge. 16 X 24 37. 32.5 $7,250 $1,150 $223 17 X 24 39- 34.5 7.500 1,200 217 18 X 24 42. 37. 7.750 1,300 209 19 X 24 45. 40. 8,000 1,350 200 Consolidation Type — Standard Gauge. 53. 59- 46. 52. $9,250 9.750 $1,400 1,400 Narrow-Gauge Engines. American Type. Mogul Type. $201 188 10 X 16 16.5 II. $4,750 $750 $432 II X 16 18. 12. 5,000 775 417 12 X 16 19-5 13. 5.250 800 404 13 X 16 22.5 15.5 5.500 850 355 14 X 16 24. 16.5 5.750 900 357 $5,250 $800 $362 5.500 850 334 5,750 900 295 6,000 950 278 6,250 1,000 255 CHAP. XV.-TRAIK.LOAD ON OPERATING EXPENSES. 565 • J-- J Table 174 — Continued. Consolidation Type. Cylindeks. Weight (net tons). Cost, 1886. Total. On Drivers. Engine. Tender, Per Ton on Drivers. 15 X 18 16 X 18 28. 34. 24. 29. $6,750 7,250 $950 1,000 $282 250 i^i-\rvk«-k'« «»■»»._ /■ it • Narrow Gauge. $182 100 ICX) Comparison of the above table shows that the cost of enHn^c Kr. ~. " rate of $250 per inch of cylinder diameter, about $'0 '^eZ f "'"''' ''" per extra truck-axle; which are builder^ aZroI^L / ^""'"^-^^^^' ^"^ $250 American engine as the standard or u^Ttypf "^""'^ '''''''* ''^'"'^^ ^^°™ ^^^ ^7^^ Comparing the lightest and heaviest engines of each tyt>e we finH th.t tT, on drivers of extra weight is but little over fxoo per ton, 1 : ^' '^^ Standard American Gauge. Mogul, ....'*****. ^^^ Consolidation, ^°° roads have been contemplated h wn .Idt. ^ "'^ *""" ■■»"°»'-S»"ge rail- CHi:t^tt:r'-'-r~ >Ae have, therefore, given much attention to the subject of your question Our . ™.v^ h, the ^ater cross.n,easu.n,ents, is <,ui.e Z^^Ledlr^^^^^^^^^ Wheel-base enables the engine to curve more readilv r.,,,^ ^^°''*^'" are offered at the same price." equivalent narrow-gauge engines, and which Of engines, and on the remaining distance not more than 50 per cent of the fuel burned would vary directly with the weight and power exerted As an average of entire runs, it is entirely adequate to asspme that 2 per ' 566 CHAP. XV.^TRAIN-LOAD ON OPERATING EXPENSES. % cent of the total fuel consumption varies directly with the weight of engines hauling the same train over for the most part the same grades, and that the remaining 75 per cent is unaffected. On this basis, an engine 20 per cent heavier would average for entire runs not over 5 per cent more fuel to liaul the same trains. The cost of supplying oil and water would vary in about the same proportion. 710. These various items are summed up in the following Table 175. As already stated, however, it is only under very exceptional circumstances and on a limited scale that it is proper to assume that differences of grade can or will be overcome in practice by the cheap and apparently simple expedient of in- creasing the weight of engines for freight service, and on roads enjoying a moderately large passenger traffic the same is very nearly true of passenger trains. The engines will in any case be made as powerful as is deemed feasible or expedient, for conveni- ence in stopping and starting, and for occasional exigencies, if for nothingelse; and anything which reduces their hauling capacity at the requisite speed between stations will be apt to result directly or indirectly in running shorter trains and more of them. This is far from an unmixed disadvantage under many circumstances (par. 89), but nevertheless it is a real disadvantage. 711. Table 175 itself makes clear why it is entirely improper to assume the use of heavier engines to meet the demands of heavier grades, by indicating that there is always a great econ- omy in using the heaviest engines which the traffic will warrant. To double the weight of engine to haul the same train will only add some 14 per cent to expenses, according to Table 175. If by doubling the weight of engine we can also halve the number of trains, we immediately effect an immense economy in train-wages, engine repairs, fuel, and maintenance of way, exceeding more than threefold (Table 176) the increased expense per train-mile due to the heavier weight of engine. It is only when the grades are so very low (approximating closely to a level) that even a light engine can haul the fifty or sixty loaded cars, which are as many as can be conveniently handled with the present bad styleof coupling, that heavier engines can be legitimately assumed to meet the requirements of a heavier grade; if even then. __ CHAP XV.-7KAINL0AD ON OPEKA IVX^ KXPENSF... 567 Table 175. EST,„ATH. AVEKACE COST Pkk Tha,X-M„.E OP DoUBL.NG THH We.GHT OP Engines to Haul the Same Train. Item. (As per Table 80, page 179.) FuqI Oil, waste, and water. . . .... . ', Engine repairs '.. Switching-engines *." Train wages and supplies. ... . Car maintenance and mileage. Renewals, rails ' Adjusting track Renewals, ties ..**.'.' Earthwork, ballast, etc. .. .. Switches and sidings ] ] ' Bridges and buildings. ....... Station, terminal, and general. Average Cost of Item. Cents or Per Cent, Per Cent Added by Doubling Weight of Engine. Total. 7.6 1.2 5.6 5.2 15-4 12.0 2.0 6.0 3.0 4.0 2.5 5.5 30.0 100. o 25 per cent. < > 50 per cent. Unaffected. 50 per cent. Added Cost. Cents or Per Cent. 14. 1 percent. 1.9 0.3 2.8 i.o 30 1-5 2.0 1.3 03 14. 1 Perhaps one further exception should be made-when thre traffic ,s so very light that it is not practically convenient to run very^heavy trains, as when it is less than three \o five freight trZ 712. Table 175 also explains why there is so great a tendency o increase the weight of passenger trains by Applying to'e luxurious accommodations. It is because— ^^ > "^ "^^^^ Hght ot7TabTe?;S' ^"^'"^ ^°"^ ''"' ""'^ -°- '° -" '•'- a 2. Coal consumption is but little increased by material differ- ences in the weight of cars (par. ,29) ^ ^^ untn ?yr^u ""^"^ ''"' ""■' '"""^"^ "P°" passenger trains unt 1 they become very long (par. 397 et seg.), and by slight re ca„r::7'°"'r"''^^'^''"''«'-^'''-«-'°f -creased Light as"te doT 'in " """"^^ ^''^"'^ '">' -""'"^ -"-'- I mi 568 C//AP. XV.— TRAI^-LOAD ON OPERATING EXPENSES. CHAP. XV.^TRAINLOAD ON OPERATING EXPENSES. 569 4. It encourages traffic to run more passenger trains (par. 89), and discourages it materially to attempt to crowd the traffic upon a few trains. 5. And more important than all, the increased luxury is a great attraction to travel, and added travel thus secured is of immense value to the property (pars. 37-40- 713. The cost of increasing the number of engines to haul THE SAME TRAFFIC, OH account of E heavier grade, may be estimated as follows : The number of trains is supposed to be increased by a change of maxi- mum grade only, which will not ordinarily extend over one third of the distance. While running over the remaining distance, the work done on the train behind the engine will vary according to the weight or number of cars. While running on the maximum grade the power exerted by the engine will be the same, since in each case the engine is supposed to be fully loaded on that grade. 714. Fuel.— For reasons already enumerated (par. 344), about one half of the consumption of fuel will vary directly with the tonnage of the train ; the other half, consisting of the fuel burned in stopping and start- ing (in part), getting up steam, loss by radiation, loss by head resistance, etc., making up in the aggregate the 50 per cent which is unaffected by the length of the train. If, therefore, the maximum grade be increased on about one third the length of the road, while on the remainder the grades remain about the same, about half the consumption on two thirds of the distance, equal to all the consumption on one third of the distance, or 33 per cent of the entire consumption will vary directly with the net weight of the train ; so that, if the grade were so increased as to take two locomotives instead of one to handle the same traffic, the fuel consumption would be as i.o to 1.67 at most, and not as i.oto 2.0, as might be over-hastily assumed. The aggregate cost of oil, waste, and water will vary in about the same proportion. 715. Train-wages will of course vary directly with the number of trains, unless the change of grade in contemplation were so great as to shorten up trains so as to dispense with one brakeman, which can rarely happen. 716. Station, terminal, and general expenses will remain unaf- fected by any moderate change, but there is nothing by which they are so quickly affected as by a decided increase in the number of trains, and a full 20 per cent of their aggregate may be considered as varying directly therewith. 717. Of the cost of maintenance of way we cannot directly account for an increase of more than one half to two thirds as a result of doubling theenginemileage, the car-mileage remainingconstant; but the facts given in par. 125 and its accompanying Tables 41-44 indicate that there is an in- direct effect from multiplication of the number of trains which seems to cause all expenses for maintenance of way to increase pari passu there- with, including some items, such as those for policing, maintenance of ballast, road-bed. and ties, etc., etc., which should be affected but little, if any, apparently, by the precise number of trains over the road. It is to be remembered, in considering the tables referred to, that during the years which they cover the weight as well as the number of trains has increased enormously, which should naturally tend to keep maintenance of way per train-mile at a high figure ; but after making all allowances for this differ- ence, the chief cause for the singularly constant ratio of increase in main- tenance of way and maintenance of rollmg-stock is probably this : A con- tinually advancing standard of maintenance is indispensable as the volume of traffic increases, and the cost of each step toward perfection increases about as the square of the number of steps. A very slight expenditure suffices to make track good enough for the passage of one train a day. A slight addition suffices for two or three trains a day, and makes a great improvement in the condition of the track. A much greater expenditure is necessary to fit the track for ten trains a day, and yet the visible ad- vance in condition is much less ; and, finally, as we get up to thirty or forty or fifty trains a day. a very great additional expenditure is found necessary— or at least expedient— although the visible advance of condi- tion is very small. At any rate, the fact seems to be that even in so ex- treme an advance as from six trains a day to sixty (see top of page 128), the cost of maintenance of way per train-mile does not decrease, but Tather the total cost per mile of road increases tenfold with the number •of trains. 718. Investigation clearly indicates this to be the fact. We are therefore not justified in going behind it, to see whether we can explain It, but must take it as it is. If we do sj, we are compelled to estimate that if by a change of grade we should double the engine mileage needed ^or handlmg the same tonnage, we should also double the entire cost of maintenance of way. Making a concession of somewhat doubtful pro- priety to the fact that the car-mileage would remain the same, we may ex- clude the cost of bridges and buildings as unaffected; but this is the most mmm mm 570 CHAP. XV.— TRAIN-LOAD ON OPERATING EXPENSES. which can be done. Statistics do not seem to indicate that the total cost per train-mile on roads which handle light trains is sensibly less than on roads which handle heavy trains. 719. Engine repairs should apparently vary directly with the miles run ; but the indications are (Table 42 et al.) that as a matter of fact it is much less likely to do so than maintenance of way, owing in part to the large proportion of incidental expenses (see Table 57), which are not by any means doubled to maintain a double number of engines. There will also- be a certain diminution of wear and tear from stopping and starting, etc. (see Table 85, page 203), from the fact that the trains to be handled are- shorter. Taking both of these causes together, it is not probable that doubling the number of engines to move the same number of cars would increase engine repairs in the ratio of more than i.oo to 1.75, and prol>- ably somewhat less. 720. Car repairs are certainly affected beneficially by having a less^ number of cars to a train. By referring to Table 86 (page 203) it will be seen that more than one third of the total cost of car repairs can be di- rectly traced to the concussions of stopping and starting and making up- trains. Much of this expense may disappear with the introduction of better couplers ; but even this is doubtful, as an automatic coupler will permit of much more violence in running cars together, since a brake- man's life between the cars will no longer have to be considered. A diminution of at least 10 per cent may fairly be estimated as a result of running only half as long trains. 721. To these expenses, properly so called, is to be added an inter- est charge on the cost of the additional motive-power re- quired by the higher grade, unless the first cost of these engines be in- cluded in the estimated cost of constructing the higher grade-line, before determining the difference in the capital investment. This should be done because the addition of the required number of engines is really so much added to the original investment. Before tiie line is ready to handle the required traffic it is as necessary to have them as it is to have the track laid on the high grade-line and not on the- other. In considering differences of distance (if not too great), orcurva-^ ture, or rise and fall, this is not so. The total amount of equipment will be the same whatever the differences in that respect. We therefore es- timate the expenses regardless of interest on the plant, and only consider differences in the cost of construction. Of the car equipment the same is true in the case of gradients. Whatever the grades, the number of cars will be the same ; but as the number of engines is increased because CHAP. XV.- TRAIN LOA D ON OPERATING EXPENSES. S7l of the grades, and not for any ^^^^^^^^^fZ^f^^^ he difference m the cost of equipment as a part of the cost of construe! t.on, or add an interest charge to expenses. On the whole, it is more convenient to add the interest charge. 722. Putting together all these items which have been lust considered, we obtain the summary given in Table 176, as the effect on operating expenses of so increasing the rate of grade as to double the number of engines required to handle a given Table 176. Estimated Average Cost Per Train-Mile, of Doubling th« Nnmh. r Trains TO Handle a Given Traffic- op p"°"°""e^ *"« Number of iKAFFic, OR Proportion of Expfk<;i?c WHICH Varies Directly with the Number of Trains the 0^1x0^ NAGE REMAIViKn- r.^vTc-.K,^ iKAiwb, THE CAR- TON- NAGE REMAINING CONSTANT [The percentage by which any i (or weight of engines) to be increased, is give^'in'TaWes "17^ 'and '178.] tl"!.^.?"*^.^^ '^ "^'^^ -y ^-- change of grade will require the number of trains- Item. (As per Table 80, page 179.) Fuel Oil, waste, and water Engine repairs Switching engines Train wages and supplies. . . . . Car maintenance and mileage. Renewals, rails Adjusting track Renewals, lies * * . Earthwork, ballast, etc... ... . Switches and si'Hngs ' Bridges and buildings. . '. *. *.*.'.'. Station, terminal, and general! Total of operating items. . Average Cost of Item. Cents or Per Cent. Per Cent Added by Doubling Number of Trains. 7.6 1.2 5.6 5.2 15.4 12.0 2.0 6.0 4.0 2.5 30.0 100. 67 per cent. 75 per cent. Unaffected. 100 per cent. 10 p. c. /ess. 100 per cent. «« «« <( << Unaffected. 20 per cent. 47-8 per cent. Added Cost. Cents or Per Cent. 5.1 0.8 4.2 • • • • 15.4 -1.2) 2.0 6.0 30 4.0 2.5 • • • • 6.0 Toth is is to be added the interest on the cost of 47.8 '^ ^^^ average passenger-engine miieaaf* tr^ k« 40,000 m.les per year, .e have, as thf interlst chT^^et'per mile? Making the grand total. 1-7 49.5 572 CHAP. XV.— TRAIN-LOAD ON OPERATING EXPENSES. traffic. When and if it can fairly be assumed that the weight of engines can be increased instead (par. 711), Table 175 gives the percentage of increase in expenses. 723. In the former edition of this work, this summary was materially dif- ferent, especially as respects the effect of increasing the weight of engines, as shown in the following Table 177. The cause of the discordance 'is simply the change in conditions, in the writer's view, and not that either is essentially in- correct. Table 177. Estimated Cost of Doubling the Engine-Tonnage for the same Car- Tonnage USED IN THE FORMER EDITION OF THIS TREATISE. [For statistics based for the most part on iron-rail track.] Total Cost. Cts. or Per Cent. For a Double Number OF Engines. For a Double Weight OF Engines. Items. Percent increas- ing with Number of Engines. Added Cost. Percent increas- ing with Weight of Engines. Added Cost. Fuel lO.O 2.0 9.0 13. 13.0 7.0 7.0 30.0 90 per cent. . 90 " " 90 " " 90 " " 100 " " 100 " •' Included above. Unaffected. 9.0 - 31. 13.0 7.0 • • • • 50 per cent. r 50 " " ] 33 " " [ Unaffected. 200 per cent. 100 " " Included above. Unaffected. 50 Oil, waste, etc Engine repairs 30 Train-wacres Track reoairs *>f\ Ck Road-bed repairs 7.0 • • > • • • • • Yards and structure General and station Totals 100. 50 p>er cent. 50.0 42 per cent. 42.0 Assumed average^ 48 cents per train-mile, or 48 per cent of operating expenses. 724. Assuming that under all ordinary circumstances, for moderate changes of grade, any increase must be met by an in- crease in the number and not in the weight of engines, we have 49.5 cents per train-mile, or 49.5 per cent of operating expenses, as the portion of the total expenses which will vary with increase of engine-mileage to handle the same business, which is not far from the cost of running an engine light, as it should be. Multiplying this amount by 365 X 2, we have $0,495 X 365 X 2 =$361.35 as the yearly sum per daily train per mile of road which varies di- rectly with an increase of engine-tonnage for the same traffic. CHAP. XV.— TRAINLOAD ON OPERATING EXPENSES. 57$ If, now, we multiply tliis sum by the percentage of the in- crease in engine-mileage RESULTING FROM AN INCREASE OF O. I PER CENT in any ruling grade, we shall obtain the cost per daily train per mile of road of such increase. In other words, we ob- tain the cost per train of increasing the number of trains to han- dle the same fixed tonnage, or the saving per train by decreasing that number; i.e., we obtain the cost of using i.i, 1.2, 1.5, or 2.0 trains, instead of one, to handle a given tonnage, or the sav- ing by using 0.9, 0.8, or 0.6. That cost or saving is given in Table 178, and when multiplied by the estimated number of the trains on the grade for which the traffic was estimated, it gives the total cost or saving. 725. The cost thus obtained is not an absolute value, inde- pendent of the length of the road, as in the case of the similar values deduced for distance (Tables ^^, 89), curvature (Table 115), or rise and fall (Table 124), but varies with the length of the road or division, inasmuch as the ruling grade increases the cost of operating the entire road, whatever the length of the rul- ing grade itself may be. Hence, to obtain the true value of re- ducing grade, it must be multiplied by the length of the road. It may appear that it should be multiplied bv, not the actual but, the equated length, according to pars. 195I9, since we have there seen that 10 per cent more distance does not by any means add 10 per cent to operating expenses. But whife this view is in a sense correct, yet the items which vary with a change of grade vary so nearly with distance likewise, that it would lead us too far to attempt any more accurate process of equating. 726. The cost per year in Table 178, divided by the rate of interest on capital, 0.06, 0.07, etc., will give the capitalized value per daily train of avoiding an addition of o.i per cent to the ruling grade. Thus, to avoid an increase of o.i per cent in a 10 ruling grade, at 6 per cent on capital, and for a division 100 miles long, we have $2927 ^ -^-^ = $48,873 per daily train, 4.V 11 574 CHAP. XV.^TRAIaW.LOAD on opera TJ AG EXPENSES. Table 178, Estimated Value per Daily Train of Avoiding an Addition of O.i Per Cent (5.28 Feet Per Mile) to the Rate of any Ruling Grade. [Cost per train-mile assumed at $1.00.] i Rate of Gkadk to Bu Changed. Per Cent of Increase in Enjf. Mileage lor Each o.i Per Cent Added 10 the Grade (from Table 171). Cos* Per Year Per O.I Per Cent Increase in Grade. Relative No. of Trains to Haul Same Traffic. Per Daily Train = Preceding Per Cent X S361.35 X icx> Miles. Per looo Ton- Miles Daily of Cart and Load as per Table 170. Relative N^t Load. Level 25-9 $9359 $17.50 1. 00 100.00 O.I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 20.9 17.5 15- 1 13-3 II. 9 10.8 9.8 9-2 8.5 7.552 6353 5.456 4.806 4.300 3.903 3.541 3 324 3.072 17-77 18.03 18.23 18.48 18.75 19.03 19 34 19.74 20.12 1.26 1.52 1.79 2.06 2.33 2.61 2.89 3-18 3-47 79-44 65.72 55-93 48.60 42.88 38.32 34.58 31.48 28.82 I.O 8.1 2927 20.38 3-76 26.58 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 7.0 6.3 5-8 5-5 5.1 4.8 4-6 4-4 4.2 2.530 2.277 2.096 1987 1.843 1.734 1.662 I 590 1. 518 20.87 21.43 22.26 23.18 24.26 25.22 26.23 27.22 28.21 4 37 4.99 5-63 6.29 6.98 7-69 8.41 9.16 9-94 22.88 20.04 17.76 15.89 14.32 1301 11.89 10.92 10.06 3-0 4.0 1.445 29.02 10.74 9-31 3.5 4.0 50 3.6 3-4 3.2 1. 301 1,229 1. 156 31.42 35 10 44.82 12.92 15.29 20.74 7.74 6-55 4.82 Comparison of the third and fourth columns will show that while the cost per daily train of a given increase of grade is much less on the higher grades, because the number of trains is so much greater, yet that the cost per unit of traffic is greater as the grades are higher, as it naturally should be. CHAP. XV.— TRAIN.LOAD ON OPERATING EXPENSES. 575 THE third column in this table is computed for a division 100 miles long. For a greater or less length, increase in direct ratio with the length. Letting C = the sum thus obtained, we have c X number daily trains (each way) x tenths per cent of change of grad e rate of interest on capital (0.06, 0.07, etc.) ' ' = capitalized value of any increase or decrease in the rate of the given ruling grade, approx- imately. For greater exactitude, determine the correct percentage for the given change of grade from Table 171 ; or, for still greater exactitude compute the percentage from the train-loads given in Table 170 for the two given grades and the given type of engine. The fourth column is independent of the length of the division, and may be de- duced from the third column by dividing it by the total weight of train as given in Table 170, X aoo + 1000. or, for the moderate traffic of 10 daily trains per day (each way in all cases), $487,833. If the division be no, no, or 150 miles long, this sum, multi- plied by i.io, 1.20, or 1.50, will give the capitalized value, as nearly as may be. If the change in grade be 0.2 or 0.3 per cent the capitalized value will be again increased in proportion! Thus, if the division be 150 miles long, and the comparison be between a i.o and 1.5 grade, we have $487,833 X 1.5 X 5 = $3,658,750 as the approximate justifiable expenditure for avoiding the in- crease, for 10 trains per day and at $1 00 per train-mile. For greater exactness see note to Table 178, above. 727. Several recent French and German estimates of the value of reducing grades might be given, which do not differ radically from the preceding except in the constants assumed; in which latter respect they do differ radically Table 179 gives one of the most recent and most nearly correct of such esti- mates. 1 here are no estimates in English known to the writer, of an at all reliable character. 728. The greatly inferior loads hauled on foreign railways compared with American practice is conspicuously brought out in this table. An American engine wiih 40 tons on the drivers will haul in daily practice (Table 170), ^ . "Toos. Tonnes. On a 0.5 grade 1041 ) Against French ( 487 On a 2.0 grade, 347 ( by Table 179. ( 131 The French loads are explicitly stated to be based on velocities of 25 kilos per hour, and indicate to an American eye very bad administration. 57^ CHAP. XV.-^TRAIN-LOAD ON OPERATING EXPENSES. Table 179. Estimate of the Value of Reducing Grades on French Railways. [By M. Ricour, Ing. en Chef, Corps des Fonts et Chauss^s. Abstracted from the pat>er referred to in par. 662.] CHAP. XV.— TRAIN-LOAD ON OPERATING EXPENSES. 577 Grade. Gross Load C. Tonnes. Price per Tram Kilo. Francs. Price per xooo tonnes gross, per Kilo. Francs. •4 568 »-54<5 2.72 Diffs. •5 487 1-465 3.00 .28 .6 .7 .8 .9 425 375 335 302 1.403 »-353 1-313 1.280 330 .30 3.60 .30 3 9» -31 4.23 .32 1.0 274 1.252 4-56 -33 x.a «-4 1.6 X.8 230 196 169 »47 X.208 1. 174 1.147 1. 123 5-25 .36 5 98 .37 6.78 .39 7-65 .46 2.0 131 1.109 8.46 .43 The last column of this table x ii7-5 (i-6i X 0.20 X 365) will give a column corre^ spending to the fourth column of Table 178. No close correspondence can be expi.cted, because the French loads are so much less and decrease so much more rapidly with grade. This table was computed for a 6-driver engine, 36 tonnes (39.67 tons) on drivers ; mean total weight, 50 tonnes (55.10 tons). The values in the last column are of a more general character. They are independent of the weight of the engine — at least within the limits of usual French practice. THE PROPORTION OF TRAFFIC AFFECTED BY THE RATE OF RULING GRADE. 729. According to the character of the road, this may vary under certain conceivable circumstances between the extreme limits of o and loo per cent, for both passenger and freight traffic. Freight traffic is by far the most affected, but there are at least occasional instances in which the freight traffic is so light and so little liable to grow that no appreciable value whatever can be assigned to reduction of grades below a cer- tain limit. For, as the whole objection to gradients, properly so called, lies in their effect to limit the length of trains, a re- duction of their rate has value only for such trains as they do ia fact so limit. One train at least, the "■ way freight," is very often not so limited on all railways, and many minor railwavs are not so fortunate as to run anything else but way freights over tlieir lines. 730. Nevertheless, as a rule, both the way freight and all other freight trains vary in length directly with the de-facto gradients, and should be assumed to do so. This does not at all assume that all trains will be fully loaded, for that is not a practicable result, but simply that the percentage of power wasted to power utilized will be sensibly the same for all grades and lengths of trains, or nearly enough so for all practical purposes. If so, it necessarily results that the percentage of increase in trains will be much the same, whether they are fully loaded or not. 731. As respects passenger business (see par. %^), although it is much less directly and immediately affected by a change of grade than freight traffic, because of the higher speed, and the large surplus of motive-power required therefor and for stopping and starting, yet in the long-run, whenever the pas- senger business becomes considerable in volume or largely com- petitive, either the number or the weight of passenger engines must be materially affected by the rate of grade. The effect in the case of passenger traffic is far more irregular, but not there- fore the less certain. A train, for example, might haul an extra car or two over any given grades, or haul the same cars over a heavier grade, as well as not, when the addition of yet another car to the train of say ten cars might require it to be cut in two, and so immediately double the motive-power required by in- creasing the load hauled only ten per cent. It is certain, more- over, that, whatever the margin of power deemed necessary for emergencies, if we reduce our grades and train resistance by any fixed amount, the weight of engines may always be re- duced, or the weight of train increased, in the same proportion, and yet leave the same margin for emergencies or anticipated growth of traffic as before, however much or little that may be. 37 578 CHAP, XV.—TRAIN-LOAD ON OPERATING EXPENSES, Hence a reduction of ruling grade has a positive and present cash value, even if every passenger train on the road will habit- ually run light for an indefinite number of years. 732. But this value will be but small when the passenger traffic will be light during the first few years after construction (par. 84) or when the traffic is not exacting as respects speed, or both, for the reason that the effect of any ordinary increase of grade, not sufficient to imply pushers for passenger as well as freight trains, may frequently be eliminated by a moderate re- duction of speed between stations. The limits within which this is certainly and readily possible may be determined as follows : 733. In Table 180 are given the grades of repose for various passenger trains at various speeds, determined from the com- puted resistances in pounds per ton in Table 166 by simply dividing them by twenty. The limits of ordinary passenger trains are from four to twelve cars, but the table extends from no cars at all to sixteen. These so-called " grades of repose " (see definition in par. 384) are grades equivalent to the addition which the train resist- ance makes to the actual plus or minus grade resistance. Sub- tracting them one from another, as is done in Table 180 B, we have THE AMOUNT BY WHICH THE GRADE IS IN EFFECT REDUCED BY REDUCING SPEED by a Certain number of miles per hour. If, then, it be admissible to consider the speed of a 4-car train to be reduced from thirty miles per hour to fifteen or twenty miles, we can (Table 181) use a grade — o. 19 -|- 0.16 -|-o. 13 = 0.48 per cent, or 0.19 + o«^6 = 0.35 per cent higher than if a speed of thirty miles per hour were essential on the grade as well as elsewhere. We shall shortly see (Table 183) that the loss of time in so do- ing is less than is often supposed. When to this is added the relief gained by momentum if the foot of the grade can be ap- proached at thirty or forty or fifty miles per hour (Table 118 and par. 408) we have considerable lee-way in respect to pas- CHAP. XV-TRAm.LOAD ON OPERATING EXPENSES. 579 Table 180. Grades of Repose for Passenger Trains of Various Ungths at Various Speeds. [17 X ^ American engine, averaging .5 ton. each. Ac»rfi„g .0 the fonnul. given in Table i66.] ^ [For grades of repose of freight trains, see Table 120.] Kind of Train. Weight Tons. Grades of Repose, Per Cent, for Velocities in ] VfiLEs Per Hour. 15 20 25 30 40 50 60 6.03 3.62 2.81 2.12 1.89 '•74 70 Engine only and 2 cars.. " " 4 cars.. " " Scars.. *• " 12 cars.. " " 16 cars.. 56 112 168 280 39a 504 0.60 0-45 0.40 0.36 0.34 0-33 0.88 0.62 0.52 0.46 0.42 0.41 1.24 0.83 0.69 0.58 053 0.50 1.69 1.08 0.88 0-73 0.65 0.62 2.81 »-74 1.38 1. 10 0.98 0.91 4.26 2.58 2.02 1.58 1-39 1.28 8.12 4.83 3-74 2.87 2.49 2.28 Table tSOB. Increase of Grade which will be Compensated for i^v a p. [Deduced by subtracting each of the grades of repose from the next higher.] Kind of Train Reduction of Equivalent Grade bv Reducing Speed from- 25 to 20 30 to 25 £ngine only and 2 cars. *' 4 cars. , " 8 cars. . «( 12 can. 16 can. 0.28 0.17 0.13 O.IO 0.08 0.08 0.46 0.21 0.16 0.12 O.II 0.09 o 45 0.25 0.19 CIS 0.12 0.12 40 to 30 1.12 0.66 0.50 0.37 0.33 0.29 50 to 40 60 to 50 1-45 0.84 0.65 0.48 0.41 0.37 I 1.77 1.04 0.78 0-54 0.50 0.46 70 to 60 2.09 z 21 0-93 0-75 0.60 054 *.^uttthr^ttn*:ri^vr^"^.--T— ^^^ "early large enough to fully .^presertl^e Zht^fn' « ''" / "'''^'" ""*' "-^^ "« "<" greater cylinder and boiler ^we^oTt;Venyn:trer1;:r(;^.;;7 58o CHAP. XV.— TRAIN-LOAD ON OPERATING EXPENSES. Wife' "I senger trains before certain differences of grade may materially affect them. 734. This assumes that there are no stops made or to be made on the grade- without ample reduction of grade at the stopping point, the train which can be started promptly being for the most part the limiting cause to the length of passenger trains. The ultimate limits of the possibility of eliminating the effect of grades by reduction of speed must be determined a little differently from the above, and may be more appropriately given in Chapter XX. 735. Keeping all these considerations in view, the effect of change of grade on passenger traffic may be summarizes as fol- lows: For roads having considerable passenger traffic, say over four or five trains per day each way, the passenger trains will be affected essentially as freight trains are, unless the ruliug grades are short and undulating, and the estimated number of each- class of trains should be added together. For roads having only one or two light passenger trains per day run at no very exacting speed, the passenger traffic may not be affected at all by a moderate change of grade. Whether it is likely to be or not, must be determined by Tables i8o and. i8i. For such ordinary passenger traffic as most new American roads look forward to in the near future, say from two to five trains per day, half the estimated number of passenger trains may be added to the freight, for estimating the value of reduc- ing grade, for the reason that at least half the trains are liable to be affected by the gradients. 736. The tendency to increasing luxury in first-class passenger travel has been already alluded to in par. 712. An opposite ten- dency has begun to show itself, which will tend to still further increase the effect of grades on passenger traflfic — a kind of third- class traffic carried at low rates but in large numbers. It is probable that before many years the mutual interests of the rail- ways and the public will compel a large extension of this class of traffic, and favorable grades for passenger service will then be a factor of great importance. 737. As an example of the great comparative importance of CHAP. XV.— RULING GRADE AND MINOR DETAILS. 58 1 Jovv grades, we may now profitably refer back to Chap. X., the iissumptions made in which we have just substantiated. While such estimates as are here made, as has been often stated, cannot be regarded as positive and exact, even when carefully revised to suit individual lines, the possible margin of error is too small to seriously modify, if corrected, the moral which they are calculated to convey, which is that wrongly directed expenditure is at the root of much of the financial difficulties of railways. In the example referred to one detail of occasional importance has been neglected, viz.: THE EFFECT OF A DIFFERENCE IN RULING GRADE ON THE COST OF DISTANCE, CURVATURE, AND RISE AND FALL. 738. While we have seen in Chap. X. that ordinarily, when two lines differing in ruling grade are to be compared, the importance of the differ- ence in gradients and in traffic advantages combined will be so great that such differences as may exist in any or all the minor details may be neg- lected without affecting the decision, yet when the comparison between two lines differing in ruling grade is so close that it is desirable to determine accurately the effect of differences in the minor details also, the difference in the rate of the ruling grades of the two lines makes it necessary to treat the minor details somewhat differently from merely subtracting the amount of distance, curvature, or rise and fall on the two lines from each other, and computing the value of the difference only, as we have done heretofore. 739. Suppose the case of two lines, each 100 miles long, and with pre- cisely the same amount of curvature and rise and fall, but with a ruling grade on one line of 0.8 per cent and on the other of 1.6 per cent. It appears at first sight as if in this case, whatever the amount of curvature or rise and fall, they might be balanced against each other and neglected ; but consideration shows this to be so far untrue that, inasmuch as more trams will be run over one line than the other, the cost of each degree of curvature and each foot of distance or rise and fall will be greater on one line than the other, so that the line having the heavier gradients will be more objectionable in proportion to the amount of curvature or rise and fall which there may be on both lines alike. In other words, just as there « a certain cost of operating each train-mile of distance, so there is a 582 CHAP. XV.-RULING GRADE AND MINOR DETAILS. CHAP. XV.— RULING GRADE AND MINOR DETAILS. 583 1 ! certain cost of operating what we may call each train-degree of curvature and each train-foot of rise and fall. If therefore, in such an instance as that supposed, the two lines had much curvature and rise and fall, the money value in favor of the lower grade would be considerably greater than if both lines alike were nearly straight and had very little rise and fall. 740. This diiference of value should properly find expression in a different assumed cost per train-mile; and in estimating the value of a projected improvement to a line already in operation it would be so ex- pressed, since the curvature and rise and fall would already have had its effect, much or little as the case might be. to increase the operating ex- penses by which we gauge the value of reducing grade. But in the case of a new road we have not this advantage, inasmuch as we cannot foresee the exact cost of each item of operatmg expense. The most feasible method therefore for approximating to what we really desire, the difference in operating expenses per train-mile on the two lines, is this: , . 741. First. Estimate the cost per year of all the curvature and rise and fall on the low-grade line for the estimated number of daily trains, according to Tables 1 1 5 and 1 24. ^ • a Secondly. Make the same estimate for all the curvature and rise and fall on the high-grade line, for the estimated increased number of trains required to handle the same traffic, as determined by Tables 170. 171. and 178. Thirdly. Subtract one from the other for the net difference. Similarly for any difference of distance : If the high-grade line be the longer, the cost of operating the extra distance on the high-grade line must be estimated for the number of trains on it; while if the low-grade line be the longer, by the same amount the cost of operating the extra distance must be estimated for its smaller number of trains, and hence will be somewhat smaller than for a similar excess on the high-grade line. 742. There is this further caution : Inasmuch as the traffic, and hence number of cars per day or per year, is supposed to be the same by either Jine, the only difference being that shorter trains and more of them are run over the high grade, the same cost per train-mile cannot, strictly speaking, be assumed the same for both lines. We have estimated in Table 176 that the cost of doubling the number of trains for the same traffic is 49. 5 cts. per extra train-mile, or 49.5 per cent of the average cost. For a change of grade so considerable as to halve the number of cars per train, therefore, the relative cost per train-mile in the two lines would be i.o-fo.48 as 1. 00 to , or I. to 0.74, and proportionately for less consider- able differences of grade. In other words, whatever wear and tear results from the number of cars moved over the line, as well as the expense of loading and billing the freight in them, etc., is unaffected by the change of grades. Whatever is due to the engine increases pro rata with the number of trains. 743. For still another reason than those just mentioned, it can rarely be essential to enter into minutely accurate calculations as to the minor details to decide on one line or the other. When the comparison between two lines becomes so close that it would otherwise be necessary, the possible effect of the two lines on volume of traffic ought alone to outweigh it, and the prudent rule becomes — 1. When the company is or soon may be poor (and it is no more than common prudence to assume that it will be embar- rassed for means at some time in the near future, when it is not backed by a great system of profitable lines in operation), take t/ig line of lo^v est first cost. 2. When immunity from financial embarrassment is assured, take the line which offers the most promising conditions for future growth of traffic. 3. Only when the two lines are substantially equal in both these respects enter into such minute calculations as these just sug- gested, and virhichever line be selected no serious harm can then result. 744. Having determined the justifiable expenditure to obtain low grades, we have only taken the first step toward their proper adjustment. Some of the worst sacrifices of gradients are made without effecting any saving of cost whatever, simply from inat- tention to its importance, or from attaching exaggerated impor- tance to losses of distance or curvature, or from insufficient study of the topography, leading to a too hasty conclusion that all has been done which can be done, when in fact a very little study would lead to far better results.* *: ■ It is an invidious and unpleasant thing to say, but the importance of the 584 CHAP. XV.— RULING GRADE AND MINOR DETAILS. This question of how to get tlie lowest grade which the region admits of, at a given cost, is discussed in Part V. and Appendix C. The four following sub-departments of the general problem of gradients yet remain to be considered: 1. The use of assistant engines with high "bunched" grades. 2. The balance of grades for unequal traffic. 3. Limiting curvature, and the proper compensation therefor. 4. The limit of maximum curvature. These questions we will consider in their order. caution thereby conveyed seems to justify saying it: Out of a hundred men putting a line through either easy or difficult country, but especially through easy country, the writer's observation is that all but four or five of them will adopt rates of grade from ten to fifty or even a hundred per cent higher than the other five will obtain at the same cost; and the same holds true as to amount of curva- ture. CHAP. XVI.— ASSISTANT ENGINES. 585 CHAPTER XVI. ASSISTANT ENGINES. 745. The general use of assistant engines, commonly called PUSHERS, is a comparatively modern innovation. So recently as 1873, Gen. Herman Haupt,* in a paper on gradients, felt com- pelled to say that he was making "an attempt to prove, contrary to the generally received opinion," that undulating gradients below the limits of the maximum do not necessarily increase ex- penses marerially, and "that the use of higher gradients for part of a given distance will often result in greater economy of opera- tion than a lower and uniform gradient for the whole distance." This statement has now become a truism. Driven to econ- omy by the necessities of competition, the use of assistant en- gines, even on lines ill adapted to their most advantageous use, has become very general in recent years and is constantly ex- tending, although tliey are even yet not used on more than a proportion of the lines which might use them with advantage and economy, so that their use is one of the most hopeful direc- tions in which further economy may be sought, especially on low-grade hues, where the trains hauled even by one engine are of fairly profitable length, but might be readily increased by nelp at a few points. What has been accomplished, however, is that whereas assist- ant engines were formerly used only in exceptional instances on very heavy grades, their use has now multiplied many.fold, and the expediency of using them when possible, even at quite fre- quent intervals, is universally admitted by skilled railway offi- cers. Some of our earliest and greatest engineers, as notably the engineers of the Baltimore & Ohio, Pennsylvania, and Erie [^l^lway s, distinctly contemplated the use of pusher sand adapted * See Railroad Gazette, July 5, 1873. 586 CHAP. XVI.— ASSISTANT ENGINES. CHAP. XVI.— ASSISTANT ENGINES. 587 their lines thereto; no doubt in part because of the topo-^ graphical conditions in passing the Alleghanies, but in part also- because of the singular foresight and sagacity which the great engineers who laid out those lines showed in many ways. But these precedents have not been generally recognized as estab- lishing a general principle until very recently, nor can it be said to be yet established as fully as it should be. 746. The presumption is strong in laying out every line, that advantage can be derived from laying out the grades for the use of assistant engines, because of the fact that topographical conditions always require more or less irregularity of gradients. The usual law is that the grades will be for long distances very low and easy, or can be made so at slight cost, but that for much shorter distances much higher gradients will be unavoid- able. By adapting the line to the use of assistant engines on. these higher grades we are enabled to utilize the full advantage of the lower grades, by making up our trains to correspond to them, so that long trains can be handled over the entire line by a single crew, without breaking it up into sections, and the full power of the motive-power actually in use at all points on the- line be more nearly utilized. 747. The adoption of the opposite policy, attempting to get a line of a low uniform gradient through a country of any diffi- culty whatever, is very apt to be enormously expensive, and to- be possible at all only by frequent undulations, considerable de- tours, and much higher gradients over most of the line than than there is any necessity for using. This results from the fact that it sets at defiance one of the broadest and most nearly universal laws of physical geography, — to which there are few and rare exceptions on the whole face of the globe, — that long stretches of easy plains or gently sloping valleys penetrate at intervals to and into the very heart of even the roughest regions,, leaving short sections only over which high gradients are un- avoidable. By following these easy routes as long as we can we accomplish over most of our line three desirable ends at once: 1. We get the cheapest line. 2. We get the lowest through grades ; and, 3. More than all else, we concentrate the resistances into the remaining more difficult section, so that the motive-power on it can be accurately adapted to the work required and kept fully at work over the distance where it is used, thus making it almost Fig. 17s too rniims - - Table 181. Comparative Work accomplished by an Engine in running 100 Miles FROM X10 Y, Fig. 175, and making a Rise of 2640 Feet thereon oVer THE Various Grades shown. Line, Fig. 17s. A O • • • • • C D E Distance Grade p.c. Net Miles. Net Load. Tons. Load. Tons. 100 05 II47 . 50 50 Level. 2675 I.O 711 } 33i Level. 2675 1-5 504 . 75 25 Level. 2675 2 383 80 { 20 Level. 2675 2.5 304 Total Ton-Miles Hauled by one Trip of Through Engine. 133.700 35.550 178.400 16.800 200,600 9.575 214.000 6,080 114,700 ^ 169,250 [ 195,200 [ 210,175 y 220,080 Total Enpine- Miles to Haul 2675 Tons 100 Miles. 233 Lis i ^38 Per Cent of Effici- ency. 100. 102. Z 104.7 106.4 109.9 The fifth column indicates that a single through engine, vrhich drops cars to corre- spond to its hauling capacity at the foot of the grades B, C, D, E, Fig. 175, will make vastly more ton-miles on the high grades than the low. This, however, is unfair. The true test is : //ozv much motive-power ivill it take to carry a whole train-load^ or a thou- sand train-loads, through, the typical train weighing by assumption above 2675 tons. The two last columns show that, from this more correct point of view, there is a certain dis- advantage in the higher grades, but a most trifling one, so long as the resistances are concentrated^ so that engines can be at all times fully loaded. But if scattered, so that it IS necessary to run short trains from X to K, because of the occasional steep grades, the disadvantage becomes enormous. 588 CHAP. XVI.^ASSISTANT ENGINES. CHAP. XVI,— ASSISTANT ENGINES. 589. a matter of indifference what rate of ascent we adopt on our more difficult sections — a fact which powerfully tends to still further reduce the cost of construction over those more difficult sections. Table 181 and F'ig. 175 illustrate fully how and why this advantage arises, and should be carefully studied. 748. Even where we are unable for any reason to follow the valley lines which usually penetrate far into hilly or mountainous regions, as for instance when the valleys are impracticable, or are less practicable than the ridges, it is still true that pusher gradi- ents will almost invariably fit the country better. The all but universal law of topography B^r~>^. is that, when the ground is not a dead level, transitions from one level to another, whether on a large scale or on a small scale, are of the form shown in Figs. 176 and 177. If on a small scale, we may simply adopt the dotted profile AJB, and make the fill at C or cut at B. If on a larger scale, say for a total rise of 50 or 60 or 80 feet, it be- comes impossible to do this, especially if the necessity occurs at many points, and we are reduced to adopting the profile ACB, making BC the ruling grade of the line, or else to one of the two expedients shown in plan in Fig. 177— either to run right over Fig. 176. / J^ jki "mv^ the obstruction with almost a tangent line, giving the dotted profile AB, in Fig. 178, or to sacrifice curvature and dis- tance and obtain the full-line profile. The first has been done to a most unfortunate extent in the prairie-lines of the West ; the last is almost always the proper course, if it saves an increase of ruling \ ■*«^..„^^ grade, even when necessary at Fig. 178. A many points on the line, 749. But when the rise to be overcome becomes more consid* erable, as 100 or 200 feet, even this course is rarely convenient. To obtain an equivalent for the full line AB, Fig. 177, we are then compelled, usually, to adopt a costly line hanging upon the slopes of such supporting ground as can be had in order to ob- tain the dotted profile AB, Fig. 176, or the solid-line profile AB, Fig. 178. When we have got it— assuming that we can and do get it — we have even then, in all probability, been compelled to use a higher grade than it is at all necessary to use on the re- maining and easier portions of the line. If so, we have not only spent a great deal of money where we have difficulties, but have injured our line where we have no difficulties. 750. The alternative is to treat the difficult ground as a sep- arate feature ; to maintain the lowest grades we can, on the ground where we have no difficulties ; to push these low grades as far as possible to some point C, Fig. 176, as near as may be to the rise; and then to adopt some entirely different and much higher grade BC, conforming as closely as possible to the natu- ral surface, with a view of using auxiliary power or " pushers"^ on it, thus not only saving our money on the parts of the line which are naturally most costly, but retaining all our natural advantages elsewhere which cost us nothing. 751. In other words, the secret of the vast economies which may often be realized by the skilful use of assistant engines is this — that as respects construction we work with Nature instead of against her, and that as respects operation we gain a like ad- vantage by keeping every engine while running fully at work, the greater portion of the hard work in foot-pounds being done on a small portion of the division, with such favorable through grades, in many cases, that there is little more need for an en- gine on the remainder of it, than to keep the longest trains moving and under control. It is a truth of the first impor- tance, that the objection to high gradients is not the work which engines have to do on them (see Table 181), but it is the work which they do not do when they are thundering over the track With a light train behind them, from end to end of a divi- sion, in order that the needed power may be at hand at a few S90 CHAP. XVI.— ASSISTANT ENGINES. CHAP. XVI.— ASSISTANT ENGINES— POWER OF. 591 scattered points where alone it is needed. But if we may give this additional motive-power its work to do once for all, and have done with it, high summits cost very little, and an increase of the rate of grade costs, practically, nothing whatever. At the points of greatest difficulty we are independent of the rate of ascent and in a great degree of the elevation attained, and are therefore at liberty to concentrate our efforts and expenditure on the more tractable portions of the line, where a few feet per mile reduction in grade (see Table 170 and Fig. 169) may be of enormous value. 752. in this way it is in every way practicable to secure lines over tolerably high summits and through difficult country which shall approximate closely in operating value to the most favor- able existing examples of low-grade lines. On the other hand, BY SEEKING FOR WHAT WE DO NOT REQUIRE, by defying the ob- stacles of nature and forcing them to conform throughout to the Procrustean standard of a uniform ruling gradient, we shall enormously increase the cost of construction, and in the end find that we have a far more costly line to operate than if we had "stooped to conquer" by boldly conforming to the topographical conditions and then skilfully forcing them to serve our purpose. This goes so far that it is true policy in very many instances in difficult country to make boldly for the "meeting of the waters" at the summit, even at the cost of a higher summit, rather than to zigzag up and down and from side to side in a costly effort to avoid a continuous succession of transverse valleys and other petty obstacles, each of which has us at great disadvantage. 753. The advantage of the use of pusher grades are not at all confined to high grades, but on the contrary are even greater proportionately for low grades, provided only that there be business enough to fill up the trains, and couplings good enough to permit of handliiiir long trains. On roads of light and irregu- lar traffic there may be no great advantage in them; but many roads having large traffic, which must be hauled cheaply because it pays little, are habitually using pushers on gradients as low as 0.5 to 0.6 per cent. For example, freight pushers are used on the Hudson River Railroad, nearly 95 per cent of which is a dead .level, and the remainder over summits a few feet high on 0.4 to ^.5 grades. THE POWER OF ASSISTANT ENGINES. 754. By the use of assistant engines the available motive-power is ap- proximately doubled or trebled ; and it is evident that economy in motive- power requires that the rates of these grades should be proportioned to each other as nearly as possible, in order that neither grade may be dis- portionately low, but that the true ruling grade maybe — not necessarily either the higher (pusher) grade or the lower grade, but that one which involves most difficulty and expense in reduction. With certain provisos which we will shortly consider, the determina- tion of a practically exact balance of gradients for the use of one or more assistant engines is a simple matter. If the assistant engine be of the same weight as the through engine, the load to be hauled by each en- gine is reduced one half. If there be two pushers, the load to be hauled by each engine is reduced to one third of what it was. If the pusher have, say, 10 or 20 per cent more tractive power than the through engine, the train is in effect cut into two unequal parts, that remaining to the through engme bemg ^ ^ ^ ^ ^^ . or ^^^ ^ ^ -, i.e., 47.6 or 45.5 per cent -of the original weight of the train behind tender. The grade on which the through engine can haul that per cent of its load on a given through grade will therefore be the corresponding pusher grade for pusher en- gines of such weight. 755. By the aid of the long Table 170, the process of determining such pusher grades for any through grade is made one of mere inspec- tion, as practical convenience requires. For example, to determine the pusher grades corresponding to through grades of 0.5 percent, we have — • Net load behind tender, on 0.5 grade... . , Half of which is , Corresponding pusher grades , if of load, for pushers 10 p. c. heavier, is Corresponding pusher grades if of load, for pushers 20 p. c. heavier, is Corresponding pusher grades , i of load, for 2 pushers of equal weight. . Corresponding pusher grades , Light American. 504 tons. 252 '• .24 per cent. 241 tons. .31 per cent. 229 tons. .38 per cent. 168 tons. .87 per cent. Average Consolidation. 1 147 tons. 573i " 1.30 per cent. 550 tons. 1.36 per cent. 522 tons. 1.44 per cent. 382 tons. 2.00 per cent. 592 CHAP. XVI.— ASSISTANT ENGINES— POWER OF. CHAP. XVI.— ASSISTANT ENGINES— POWER OF. 593 From these examples it will be seen that differences in type of en- gine make no considerable difference in the balance of grades, and we shall hereafter consider the average Consolidation type only. 756. If the pusher were a tank engine having no tender, it in effect adds the weight of the tender to the train hauled by the pusher ; so that to make the preceding calculation we should first have to subtract the weight of tender thus saved from the total weight of train, and then di- vide the remainder only between the through and pusher engines, in the above proportion, which would increase the rate of the admissible pusher grades materially. In this manner Table 182 was computed, which gives the proper bal- ance of grades for an ordinary Consolidation, or practically for any other engine, except tank engines, which are separately noted. 757. The requirements of the passenger service naturally favor the adoption of higher through grades rather than pusher grades, since un- dulating gradients, however steep, have little effect to impede hauling any trains ordinarily desired, when the rise on a single grade is not great. Owing to the decrease of train resistance at slow speeds (Table 166) and the simultaneous increase in the tractive power of the cylinders, the limit at which a high and long grade can certainly be operated without a pusher is still further increased. The ultimate limit for the operation of a pusher grade by a single engine in passenger service, beyond which pushers must be used for passenger as well as freight trains, may be de- termined as follows : The most that would be demanded of an ordinary 17 x 24 passenger engine, weighing with tender 56 tons, more or less, such as is assumed in the table of train resistance (Table 166), is that it should haul— as an average of a whole division and every day in the year, and not for excep- tional performances, — 4 cars, or 168 tons, 8 cars, or 280 tons, gross weight of train. gross weight of train. At 60 miles per hour maxi- At 50 miles per hour maxi- mum speed on a level. mum speed on a level. 12 cars, or 392 tons, gross weight of train. At 35 miles per hour maxi- mum speed on a level. 758. Now the tractive power which such an engine is capable of exert- ing in every-day practice at freight speeds of 15 miles per hour would be nearly if not quite 10,000 lbs., there being from 40.000 to 44,000 lbs. on the drivers. Therefore the engine will be capable of exerting a maxi- mum tractive force on these trains, at freight speeds of about 15 miles per hour of 10,000 lbs. -^ the weight in tons, or 59.S lbs. per ton, 35-7 lbs. per ton, 25.5 lbs. per ton. Table 182. Balance of Grades for the Use of Assistant Engines. [Correct within an unimportant percentage for all classes of engines and conditions of service, the through and pusher engines having the sam* weight and tractive power.] Net Load Grade up which the same Train CAN BE Hauled Through-Grade (Tons) BY THE Aid of— WORKED for Average Consolidation. BY ONE Engine. One Pusher. Two Pushers. Three Pushers. Level. 2675 .38 .74 1.08 .05 2370 .47 .87 1.25 .10 2125 .57 1. 00 i.4r >i5 1936 .66 1. 13 1-57 .20 1758 .75 1.26 1.74 .25 1618 .84 1.39 1.89 •30 1496 .94 1.52 2.05 .35 1392 1.03 1.64 2.20 .40 1300 1. 12 1.76 2.35 .45 1220 — 1. 21 1.88 2.49 -50 II47 1.30 2.01 2.64 .60 1025 I 47 2.24 2.92 .70 925 1.65 2.47 3.20 .80 842 1.82 2.69 3.45 .90 771 1.99 2.91 370 1. 00 711 2.16 3-13 3-95 1. 10 658 2.32 3-33 4.20 1.20 612 2.48 3.55 4.42 1.30 572 2.64 3.73 465 1.40 536 2.81 3-93 4.87 ■i-So 504 2.96 4.13 5-07 1.60 475 313 4.32 5-27 1.80 425 3-43 4.68 5.68 2.00 383 3.72 5.03 6.04 2.20 348 4.01 5.35 6.40 2 40 318 4-30 5.67 6.73 2.60 292 4-57 6.00 7-05 2.80 269 4 86 6.30 7.34 3 00 249 5. 10 6.58 763 If we assume \ instead of \ adhesion^ we simply reduce the tractive power of an average Consolidation (Table 170) from 10 tons to 8 tons. The ratio of the gross weights of trains on various grades remains unchanged, and the ratio of the weight behind tender would remain so likewise if the gjoss weight of engine were reduced one fifth, or by 15 tons. As it is not, the column headed 8.0 tons tractive power in Table 170 should be 1 1 tons greater to give the net loads, and we find the pusher grades to be— » 33 flHi '■It 594 CHAP. XVI.— ASSISTANT ENGINES-POWER OF. If we allow 8 lbs. per ton for tractive friction, and divide the remainder, which is admissible as grade resistance, by 20 (par. 682). we have as the grades on which these passenger trains can be handled, by reducing speed to 1 5 miles per hour, 2.57 per cent, 1.38 per cent, .875 per cent. On any grade up to tTiese limits, the trains which such an engine can be expected to handle in every-day practice will be readily handled at the lower speed of 15 miles per hour, if it is possible to stand the loss of time thereby. When Mogul or ten-wheel engines are used, as they usually would have to be for regular trains so long as 12 cars, the limits will be considerably higher; so that we may say in a general way. that grades up to ih or li. or even 2 per cent, are not a serious obstruction to light passenger business, except in loss of time. If pushers are used below the limits indicated, it is only for urgent necessity to keep up speed, as on fast through expresses. 759. The loss of time involved in such checking of passenger speed is much less than is sometimes hastily imagined. Table 183 gives its exact limits, from which it will be seen that a reduction of speed from 40 to 20 miles per hour, for example, loses but li minutes per mile, or 15 minutes on an incline 10 miles long. As the speed is higher the loss of Through grade for one engine. Level • 1.0. 3.0. , Pusher grades for adhesion of v ,_^. 1-5. Difference. 0.38 0.37 o.oi 2.16 a. 08 0.08 3.7a 352 °-~ 3.0 5.X0 4.75 0-35 A lower rolling-friction than 8 lbs. reduces the rate of pusher grades about 0.08 per cent on a level grade, decreasing to 0.04 at a 2 per cent grade. For assistant engines heavier than the through engines, add the foUowing to the above grades : Through Gradb. One Assistant Engine heavier by — Level I. CO.. 1.50.. 2.00.. 10 p. c. .03 .07 .10 .12 20 p. c. .07 ■14 .20 .24 30 p. c. .II .22 • 37 Two Assistant Engines HEAVIER BY— 10 p. c. .07 • 13 .17 .20 20 p. c. .14 .26 .34 .40 30 p. c .22 •39 .51 .60 It is rarely proper to assume that the assistant engines will be of greater power tl^ the through engines. Two pushers can only be assumed to be used with a large traffic or very heavy grades, and three pushers only with the very largest traffic. CHAP. XVI.— ASSISTANT ENGINES— POWER OF. 595 time becomes very much less, while the gain of power becomes very much greater— a condition which goes far to justify counting on this re- source for all classes of passenger trains, within reasonable limits. Table 183. Loss OF Time in Minutes Per Mile due to a Decrease of Speed op Trains. The table gives the loss of time per mile in minutes per mile in the column headed by the given higher speed opposite the given lower speed to which the speed is decreased. Lower Speed. Higher Speeds— Miles Per Hour. Miles Minutes Per Per Hour. Mile. 15 20 25 30 35 40 45 50 55 60 1 1 1 ■ -■ 1 Time Lost Per Mile ; Minutes. 10 6.0 15 4.0 20 3.00 2.0 30 I.O 3.6 1.6 0.6 4.0 2.0 1.0 0.4 4.29 2.29 1.29 0.69 0.29 4-5 2-5 0.9 0.5 0.2 467 2.67 1.67 1.07 0.67 0.38 0.17 4-83 2.83 1.83 1-23 0.83 54 0-33 0.16 4.91 2.91 1.91 1.31 0.91 0.62 041 0.24 0.08 50 3.0 25 2.4 3.0 30 2.0 1-4 35 I-7I z.o 40 1.5 0.7X 45 1.33 0.5 50 1. 17 0.33 55 109 0.17 0.09 It will be seen that the amount of time lost by considerable reductions of high speeds is less than by very slight reductions of speeds below 30 miles per hour, while the gain in train resistance is very much greater at high speeds. The fast New York Central Limited Express, which makes the run of 970 miles between New York and Chicago in 24h. 5m., with only eight regular stops, none of them for meals, loses 55 minutes in these stops alone. Including all slowing up through towns and yards, stops at crossings, etc., not less than 3 hours of the 24 are lost in this way, or about 0.2 minutes per mile, equivalent to an average reduction of 5 miles per hour in speed. With most fast trains the loss would be more than double this. 760. On the New York, Lake Erie & Western Railroad, having several long ■maximum grades of 60 feet per mile (1.14 per cent), passenger pushers are used only by the very heavy through express trains. At Altoona, on the Pennsylva- nia Railroad, at the foot of the 95-ft. grade (1.61 per cent), pushers are used for nearly all passenger trains, but nearly all are heavy trains. The local accom- modation trains, consisting of 4 to 6 ordinary day coaches and baggage cars, use no pushers. About 30 miles per hour is made by the passenger trains ^smg pushers up the mountains. Except for the requirement of making this «Peed, many of the passenger trains could dispense with pushers, although the 596 CHAP, XVI.-ASSISTANT ENGINES^POWER OF, CHAP, XVI.— ASSISTANT ENGINES—POWER OF. 597 -Ml heavier through expresses, consisting of 6 to 8 cars, each averaging over 25 tons, would find difficulty in ascending the mountain without an assistant en- gine even at verv slow speed. On the Middle Division, having very easy grades, not over 16 ft. per mile at any point, as manv as 12 heavy cars, but not more, are hauled by a single passenger engine, making, however, even with this train, high average speeds. Similar trains are hauled over the New York Central road for the entire dis- tance from New York to Buffalo, except that a pusher is used for the grade of about 1.5 per cent at Albany. 761. Except within the limits above noted, passenger trains as we^l as freight must be assumed to require pushers. The more certain it is that high speed will be required at all points, the moie likely they are to be required ; and wherever it appears likely that the passenger traffic will be important and competitive, it may. for moderately prosperous road be giving no more than due weight to the great and permanent value of easy gradients to assume that all trains, both passenger and freight, will probably require helping engines, especially as the tendency to increase the weight of passenger trains and cars is strong. The assumption made as to passenger helpers will make a consider- able difference in a comparison of gradients; for if they be assumed to- be used, the advantage of pusher gradients over moderately favorable through gradients will be much less; while if they be not assumed, the disadvantage for passenger service of the higher rates of grade can hardly be estimated at any considerable figure. 762. In laying out pusher grades, the effect of fluctuations in the velocity of trains to modify the apparent relation of the grades to each other must be carefully kept in mind. The effect of these differences (fully considered in Chap. IX., par. 397 et seq) will usually be that the apparent maximum of the lower (single engine) grades will be higher than it really is, while the actual maximum of the higher (pusher) grades will be greater than the profile shows, so that the latter will need to be reduced lower than an apparent balance requires in order to give a true balance. On long steep ascents slight sags in the grade-line may be per- missible (par. 414 et seq.), but otherwise no excess of momentum can be relied on to carry trains over any increase whatever above the normal rate- while any stop on the grade, if the latter be long, will increase its limiting effect far above the apparent maximum, unless care has been used to ease the grades for all stops which can possibly be required. Even if this has been done, there are always likely to be occasional irreg- ular stops, and the occasional operating inconvenience therefrom will be allowed far more than its true weight in cutting down trains. 763. On the other hand, the lower through grade will very commonly be cut up into such short stretches that momentum will, or may be made to. reduce its apparent rate very materially, and even if not, moderate improvements in the future will often suffice to accomplish this. More- over, it is always comparatively easy to foresee and guard against limit- ing effects from stops. True economy will ordinarily dictate, therefore, that the resistance ON THE PUSHER GRADE SHOULD BE AT LEAST TEN PER CENT LESS THAN AN APPARENT BALANCE REQUIRES if attainable at moderate cost, with the following proviso : If the rate of the pusher grade be. from its cost or otherwise, the fixed element beyond control, as often happens, then the rate of the lower through grade should be reduced at any reasonable cost (it is usually more at the cost of care than money) to ant/ a little below the full extent which an apparent balance requires ; in accordance with the sound gen- eral principle, that the links in a chain whose strength we cannot control nor exactly foresee should be the weakest, and not those whose strength we can control and can foresee. 764. Again, the lower the rolling- friction the greater the proportion- ate effect of gradients upon the total train resistance, and consequently the lower must be the rate of the higher pusher grade. As we have as- sumed (par. 623 and Table 170) 8 lbs. per ton rolling-friction, which is probably from 2 to 4 lbs. high for the slower working speeds, the rate of the higher grade should be from o.i to 0.2 percent less than theory would otherwise indicate, where possible, for this reason alone. 765. A variation in the weight and power of the assistant engines affords a means of equalizing minor inequalities in the balance of*gra- dients. should such be discovered, but this should be counted on with caution in original location. To count on using pusher engines lighter than the through engines would ordinarily be very bad practice. It would be preferable to save money and length of pusher grade by using a steeper rate of grade. To count on using heavier pushers is open to three objections: (i) The tendency is always to use heavier and heavier through engines, and a point will then soon be reached where corresponding increase in the weight of pusher engines would be objectionable or im- practicable; (2) It imposes a greater tax upon the rails and track at the very point where the alignment makes it most objectionable ; (3) Such gain as is possible in this respect is very apt to be required and used to make up for the inequalities in what was supposed to be a correct balance ^ gradients, the tendency always being to get the rate of the pusher grades m "TWgf— iWI" 598 CHAP. XVI.— ASSISTANT ENGINES— DUTY OF. CHAP. XVI.— ASSISTANT ENGINES— DUTY OF. 599 too high for a correct balance with the louver grades. In actual practice, at the present day, it will be found that pusher engines usually are a little heavier than the through engines, and yet that the pusher grades are no higher in rate than Table i8i would indicate, the excess being used, apparently, for the preceding and following reasons, and not to provide a true balance under normal conditions. 766. If the rate of adnesion be Ipw, the admissible rates for the higher gradients is very materially decreased, as shown in Table 183, for the reason that the percentage of effect lost in moving the engine itself is very materially greater. As on many days in the year the ratio of adhe- sion is unavoidably low, on those days the resulting inconvenience will be confined to the pusher grade, but will be very apt to lead to the per- manent cutting down of trains on both grades. The consequences of any unforeseen breakdown or other cause of accident or delay are so much more serious on heavy grades that 'a cer- tain excess of motive-power is naturally sought for and generally obtained in such localities, sometimes at the expense of sound economy. The curvature on heavy gradients is usually very much more severe. As the speed is also, usually, very much slower, and complete stoppage from lack of power more frequent, it appears probable (pars. 308, 335) that the curve resistance per ton is higher, and hence that either the rate of compensation for curvature must be made higher on high pusher grades or a lower average rate of grade than a nominal balance requires be adopted. THE DUTY OF ASSISTANT ENGINES. 767. Under the ordinary exigencies of operation, with two important exceptions, below noted (par. 770 et seg?), pushing or assistant engine service must be rendered by separate engines, specially detailed for that duty and available for no other. It is therefore not correct to assume that the pushing service will cost about the same per mile run as for through engines, or that pushing engines will make the same annual mileage. Rather, the safer basis is to assume as nearly as may be that a certain number of engines must be maintained for that service alone, at a certain cost per day regardless of mileage made,////5 the extra cost due to running a certain number of miles, whether that number be 50 or 100 or more miles per day. 768 As a general and safe rule, the mileage of assistant engmes may be taken at 100 miles per day // they will have a chance to run it, and as at least equal to, if not considerably in excess of. the mileage of ordinary through engines. As much as 1 30 miles per day is run by pusher engines on various roads, under favorable circumstances, but experience does not justify an assumption that more than this is practicable. If, therefore, the estimated traffic will require 150 miles per day of pusher service, the only safe basis is to assume that two engines with two crews will be re- quired, making 75 miles per day each. Theoretically, one engine with two crews might do the work, but practically, if the duty were too much for one engine and crew, convenience would almost certainly require and justify keeping two engines in working order with steam up for at least 12 hours per day. When the pushing service to be performed is over 200 miles per day the only safe basis is to assume one engine for each 100 miles, or frac- tion thereof over fifty. 769. From one to two months of every year is lost by engines while in shop for repairs (see Table 51), which reduces the apparent mileage per engine per year (and hence per day) by 10 to 16 or more per cent ; but this loss need not be considered in computing the number of engines re- quired for pushing service from the probable mileage to be run, or its cost, since the cost 'of these repairs is included in the cost of the miles actually run, and the engines actually detailed to pushing service can and will be always in working order. The exceptions to which the preceding general rules do not apply are these ; 770. I. When traffic is very light, pusher grades, if not too long, may be operated by cutting trains in two, leaving half the train at the bottom of the grade, placing half of it on a siding at the top, returning for the other half, which is preferably pushed up, and then proceeding, after coupling up, with the entire train once more. This is done to only a limited extent as a regular practice, although it is a resort in emergencies on nearly all roads. It might well be done to a much greater extent than it is, if it were only to run a freight train three times a week instead of daily. It is one of those possibilities of economy which are neglected until necessity compels them, because they take some trouble and some devia- tion from ordinary routine in management. Convenience requires that there should be a siding at least half a train long (preferably, of course, a full train long) at both top and bottom of the grade, the lack of which is no doubt one great reason why this expedient is not oftener re- sorted to, '71. 2. At short pusher grades near stations, yard or switching engines can often perform a part or all of the required pushing service at very moderate cost— or, what amounts to the same thing, the pushing engines can be so utilized for switching service as to greatly reduce the cost and inconvenience of using pushers. 6oo CHAP. XVI.— ASSISTANT ENGINES— DUTY OF. CHAP. XVI.— ASSISTANT ENGINES— COST OF, 6oi The instances are many where yard engines are utilized in this way, if only to help trains tlirough yards at which there would be no difficulty, except for the fact that it is a yard, because, for obvious topographical and commercial reasons, it is very common to find large yards near short stretches of objectionable gradients. When the yard is very large, so that several yard engines are constantly employed, the pushing service cannot be assumed to be added without adding its full pro raid to the number of engines, but in all cases the cost and inconvenience of the service will be decreased, and so, indirectly, the number of engines which will probably be required for the joint service, to the extent perhaps of 15 or 20 per cent of the whole number of engines. Switching engines of the ordinary type, having all their weight on drivers are not well adapted for pushing service, on runs of over a mile or two, nor much used there- for, since they are ill adapted for high speed, which is often desirable in returning down hill. 772. The convenience of the service must be considered as well as the theoretical requirements in estimating both the probable duty and prob- able cost of the assistant-engine service, as also of course in laying out the grades. Unless a station be situated immediately at the foot or top of the grade, the service must be assumed to begin at the nearest consid- erable station, if there be one within three to five miles of either point, because that is where convenience will require that it should begin in practice. Unless two successive pusher grades are more than five or perhaps even eight miles apart, they may more prudently be taken as one and the same grade, because in practice that is the way in which they will be likely to be operated. The tendency is always to consider convenience in such matters, even at the expense of economy; and it may be questioned if there is even a theoretical economy in breaking up a pusher run into two for less than a five-mile interval, or even under special circumstances, with thin traffic, for considerably more. The inconveniences of stopping and starting and of maintaining the double service and the loss of time are too great. No stop is required at the top of the grade for uncoupling the pusher, but for coupling on a stop is necessary, and a single stop of a heavy tram costs more than a five- or even ten-mile run of a light engine, which would otherwise be standing idle with steam up. 773. In considering the question of the probable duty of assistant en- gines it is further to be remembered that trains do not come at equal in- tervals of time apart, but some are likely to come so near together that two or more engines will be almost indispensable at certain times of the day, and some so far apart that much time will be lost while under steam. On the other hand, good time can generally be made down hill ; and the systems of automatic and other block signals have now been brought so near perfection that short sections at least can be so protected that little time need be lost between trains for the sake of allowing a margin of safety in time. American railways are but beginning to avail themselves of these in- terlocking and signal devices, the use of which may be expected to ma- terially increase hereafter. For sections on which pushers are used they are particularly well adapted. At such points the number of trains is practically doubled, and it may well be a question between such signals and a double track. For any considerable traffic a telegraph station at top and bottom of the grade is all but indispensable. THE COST OF ASSISTANT ENGINES. 774i This may be divided into three elements; 1. Interest charge on the original cost, special to the use of pushers, in- cluding extra engines, engine-houses, if any; sidings; block signals, if any; etc. 2. Cost per day for wages and a certain portion of the fuel and repair charge; all of it independent of the mileage run per day, as is also the cost of maintclning block signals, if any. 3. Cost per mile run for fuel and repairs, and for wear and tear of road-bed, track, and sidings. 775. When, as will usually happen, an approximately fair mileage can be obtained from the assistant engines, say 80 to 100 miles per day, it is unnecessary to separate these items from each other, but the whole cost per mile run, exclusive of maintenance of way and interest charges, may be assum.ed not to vary materially from that of ordinary through engines, unless there is some considerable difference in weight. The experience of the Philadelphia & Reading Railroad indicates that *hj intermittent service of pushing engines does not add materially to €Xf)er.ses, and much other evidence to the same effect might be given, as ^Iso for the fact that assistant engines will realize a somewhat higher yearly service than through engines, owing to the nature of their service, which facilitates care and prompt repairs. At least the difference in cost, il any exist, must in general be trifling. Assuming there were none at all, the DIRECT RUNNING EXPENSES for fuel, oil, and water, repairs and engine- 6o2 CHAP. XVL— ASSISTANT ENGINES— COST OF. wages would average, as per Table 80, page 179 (see Chap. V. for further details), 20.8 cents per mile. 776. The maintenance-of-way expenses must also be estimated at a considerable figure. There is a peculiar temptation in this case to fall into the error discussed in par. 125. and assume that, except in the one Item of wear of rails, there will be little additional expense for mainte- nance of way ; but partly for the indirect causes discussed in par. 125 — the necessity of maintaining a higher standard as trains increase, as well as of keeping up to the same standard— the cost of maintenance of way will certainly be materially increased. For reasons which may be readily de- duced from pars. 717-18, it will certainly not be excessive, and probably as nearly fair as is possible, to assume that the whole cost per train-mile of maintenance of way, excluding maintenance of bridges and buildings, is increased about 50 per cent by the pusher, i.e., is as much for the pusher alone passing up and down as for the whole train passing one way. 777. The total cost of pusher service (including the return light down grade) per mile of incline (on the basis of $1.00 per train-mile average cost) will then be as follows : Direct running expenses, fuel, water, oil, repairs, and wages per mile of round trip 41.6 cents Maintenance of way expenses per mile of round trip 17.5 cents (Table 80) x 2 35,0 " Total cost per mile of incline per round trip 76.6 " Or per year per daily train per mile of incline, $0,766 x 365 = $280.00. 778. The introduction of steel rails and the general cheapening of all railway supplies has greatly reduced within recent years the cost of such service, especi- ally for maintenance of way. In the former edition of this work this expense per mile of round trip was estimated at 94 cents, of which 54 cents were for lo- comotive expenses and 40 cents for maintenance. 779. This estimate assumes that the pushing engines are kept fairly busy, so as to make something like 80 to 100 miles per day average mile- age. If this seem impossible or doubtful, it will require to be increased correspondingly. All that the engine falls below 100 miles per day, i.e., all potential mileage not actually run, may be assunied to cost i to i as much per mile as if it had been run, and is so much added to the cost of what is run. 780. This results from the following estimate; Comparing the cost per mile run of an engine in actual service, as per Table 80, and the cost CHAP. XVI.— ASSISTANT ENGINES— COST OF. 605 of an engine standing still in the yard with steam up for an equal period of time, we have, approximately, the following: Average in service, Standing in yard. cts. or p. c. Per cent. Am't, cts. or p. c. Fuel 7.6 10 0.8 Oil and water, 1.2 o. Repairs 5.6 10 .6 Wages 6.4 100 6.4 Maintenance of way, . . 17.5 o 38.3 7.8 781. The chief loss from standing still is in engine-wages. Fuel is not necessarily wasted to any such extent as to make it an item of im- portance. The total consumption per hour of an engine standing in the yard to simply make good the loss from radiation has been determined by experiment not to exceed necessarily 24 to 35 lbs. of coal, or about the quantity burned in service in running one halt-mile. This would indi- cate that the consumption of an engine standing idle in a yard for a whole day with steam up would only be one or two per cent of what it would be in service; but an engine standing idle only between intermit- tent periods of service would, by carrying a larger fire and the cooling off of the machine, as well as by blowing oflf through the safety-valve and other effects of careless firing, waste much more than this proportion ; so that the allowance made above (10 per cent) is hardly too high. 782. The effect on cost of repairs per mile run of intermittent work is likewise slight. There is no doubt some bad effect from the intermittent and irregular nature of pusher service, but the mere fact that an engine, between its trips, stood idle with steam up for an hour, more or less, instead of immediately starting off on another trip, would of itself add little to the cost of repairs per mile actually run. Deterio- ration would no doubt be going on, but all the great causes of deteriora- tion — wear and tear of running gear and machinery, from stopping and starting, brakes and running over the track, injury to boiler and boiler- tubes by cooling off, by the fierce heat of the fire and by the mechanical action of the coal drawn through the tubes, etc., etc. — are absent. The above allowance is therefore ample, and probably excessive, leading to '^he resulting conclusion, that the cost of an engine per hour standing in the yard with steam up is little more than one fifth as much as if in mo- tion at 15 or 20 miles per hour. The correctness of this conclusion might be indicated in another way ^ 6o4 CH. XVI,— ASSISTANT ENGINES AND THROUGH GRADES. J by comparison with experience with switch engines, but more detailed ' comparison would lead us too far. 783. The interest charge on pusher engines is fairly chargeable to the cost of the service as well as the running expenses, for the same reason that the interest charge in the extra engines required to operate a heavier grade must fairly be added to the other expenses entailed by the grade, as specified in par. 721. Properly speaking, the first cost of these extra engines is a part of the cost of constructing the line of those grades, as much as the bridges or track thereon, and it should be included in the estimate of the cost of construction unless the interest charge is added to the operating expenses. 784. To accurately estimate the cost of pusher service, then, we must determine — First. The length of pusher run in miles (par. 'J6^). Secondly. The probable number of daily trips per engine, and hence the number of engines required for the given traffic. * Thirdly. Determine the annual interest on their first cost. Fourthly. Compute the cost of the mileage made, according to pars. 777 and 780. The sum of the last two items will be the total cost of the pusher ser- vice. COMPARISON OF PUSHER-GRADE LINES WITH UNIFORM GRADIENTS. 785. Ordinarily, when pusher grades are used, they will not be per- iectly balanced with the through grades, but either one or the other, whichever opposes most difficulties of con- struction to obtaining low grades, will be the true limiting gradient. The other must then be assumed, in order to give a fair comparison with a uniform gradient line, to be of such rate as to give a per- fect balance (Table 182), although the fact that it is really lower will not therefore be a wholly valueless advantage, even for freight purposes. In Fig. 179. for example, the 0.7 through grade and the 1.75 pusher grade are not perfectly balanced. The pusher grade should either be reduced to 1.65 or the through grade be assumed to be equivalent to •0.75. unless the circumstances make it proper to assume the use of heavier pusher engines than through engines, which is rarely the case 0.05 X 5 = $354,000 for a division 100 miles long. For a division 105 miles long we have (par. 740), $354,000 x 105 = $371,700 In favor of the uniform gradient AB : 10 miles saved of assistant-engine service, cost by par. "jyj $2,800, which, capitalized at 5 per cent, = $56,000 Net difference in operating value due to difference in gradients only, in favor of line ^^'^ $315,700 Value of 5 milesof distance in favor of line ^y^'^ possibly noth- ^200 ing, and possibly by par. 196, — -— x 5 = $29,000 Total difference in operating value, per daily train, in favor of low-grade (pusher) line $344,700 € 6o6 CH. ItVL— ASSISTANT ENGINES AND THROUGH GRADES, To this is to be added an allowance for any difference in the probable traffic, for any loss of time of assistant engines, and for any difterence in the probable capital expenditure for locomotives, which will naturally be least on the line which shows the highest operating value. 788. By computing various examples of this kind it will be seen how very large an economy almost invariably results from using pushers, but the condition that the pusliers must be kept busy and be always on hand to have them economical must be remembered. The larger the trartic of the road the more easily can this be assured, and consequently the more frequently can pushers be used. They are sometimes used as often as three or four times on a division, but with a light traffic this would be inexpedient. All the preceding, however, applies to freight business only. The use of pushers in passenger service is far less general (par. 757). 789. Whether for passenger or freight service, perhaps the most ad- vantageous and satisfactory basis of comparison of all for comparing alternate systems of gradients, as it certainly is the simplest, is to deter- mine the number of engine-miles which must be run per through car (or ton) — i.e., per car or ton — moved over the line for the entire distance between termini. A "car" has become in recent years such a very indeterminate thing, owing to the rapid increase in weights carried, that the ton is the best limit to use, as in Table 170, giving the capacity of engines on various grades. By this process the effect of differences of distance as well as grad- ients is included in the same estimate, and having assumed a reasonable price (see Table 143) for the cost of the additional motive-power and train-service required, the estimate is very readily completed. 790. Thus the example already given (par. 787 and Fig. 179) may be compared as follows : \J\nt^ AA' B iox pushers: 105 miles; 10 miles, 1.25 per cent (79.2 ft. per mile), 90 miles, actually 0.7 per cent, but in effect 0.75 per cent. Regular load for through engine with 11 tons on drivers (Table 170), 881 tons. Line AB^ uniform gradient : 100 miles, 1.25 per cent (52.8 ft. per mile). Engine load (Table 170), 592 tons. We then have this comparison : Line AA'B^ 881 tons x 105 miles = 92,505 ton-miles hauled by 100 + 10 miles run by engine (in one direction), or 841 ton-miles per engine- mile, or -^ = 8.0 through tons per engine-mile. 105 CH XVI.— ASSISTANT ENGINES AND THROUGH GRADES, 607 • , Line AB, 592 tons, through load, no pusher service, or i^- = 5.92 through tons per engine-mile. 8 00 We have then -- — = 35.14 per cent excess of engine-mileage on 592 line AB for the same through traffic, whatever it may be ; and estimating the cost of this extra engine-mileage at about half the average cost of a train-mile, as in par. 720 (which is not quite correct, because the excess of /r«/«-mileage on line AB is even greater than the excess of engine- mileage) the freight operating expenses over the two lines will be to each other about as 100 to 1 17.6. Estimating then, however rudely, the operating expenses over either line, we have a tolerably close indication of the difference in value between them, which will lead to almost exactly the same total as in par. 787. 791. With reference to the passenger business on this particular line, if only a moderate through traffic is to be handled, the difference in the gradients will be, with well arranged stations, a matter of little conse- quence. If only a little heavy passenger traffic is to be handled, under otherwise favorable conditions, the uniform gradient of 1.25 per cent will have a certain advantage ; but if any really heavy passenger traffic is to be handled, the pusher line will have much the same advantage for it, and for much the same reasons as it has for the freight traffic. It is a much more indeterminate problem, but the financial importance of high passenger speeds at all points and the effect upon it of low gradients and easy curvature is generally over-estimated (pars. 757-9)* 6oS CH. XVII.— BALANCE OF GRADES FOR UNEQUAL TRAFFIC, i!i CHAPTER XVII. THE BALANCE OF GRADES FOR UNEQUAL TRAFFIC. 792. An engine which has carried a full load in one directioa must return at nearly the same expense, whether the train be- hind it be fully loaded or not. There must, of course, be the same number of cars in each direction, in the long-run, or very nearly so (there being some lines over which considerable num- bers of cars run only in one direction, returning by other routes), and of course there is always precisely the same amount of motive-power available. If, therefore, the movement of traffic is permanently heavier in one direction than in the other, or there is good reason to expect that it will be, the grade opposed to the lighter returning traffic may be made heavier than that in the opposite direction by an amount sufficient to make the re- sistance of trains, and hence the requisite motive-power, the same in both directions. No advantage whatever results from reduc- ing the return grades below this, beyond the small amount which represents its value for occasional emergencies when the usual balance of traffic is temporarily disturbed, and the still smaller amount which represents the value of reducing the rate of any grade, as pointed out in par. 462; and hence great economy may sometimes be effected in construction by utilizing to the full such increase in grade as is legitimately made possible by the difference in resistance due to the lighter load in one direc- tion. 793. The determination of the proper balance of grades, under any assumed difference of traffic, is a simple matter. The determination of the basis of fact upon which the adjustment must rest is not so simple, but rather one of great uncertainty, except in some cases of roads built for carrying minerals or CH, XVII.-BALANC E OF GRADES FOR UNEQUAL TRAFFIC 609 Other special traffic. For roads of a large and mixed traffic as even our through East and West trunk lines, the problem is much complicated by the fact that changes of importance, especially in the transportation of minerals or from the construction of new hnes, are liable to occur at any time. Thus the growino- an- thracite coal trade to the West has produced and is producing great changes in the ratio of the tonnage East and West; and not unfrequently on different parts of the same line the burden of traffic IS m opposite directions— perhaps from causes entirely be- yond foresight when the road was first built. Nearly always the ratio of preponderance varies considerably from point to point. 794. On the Pennsylvania Railroad the balance of traffic is Widely different at different points, the westward preponderating greatly at the western end, and the eastward at the eastern end, as shown in Table 184, which is well worthy of study. Table Table 184. Comparative Volume of the Traffic East and Traffic West at Various Points on the Main Line of the Pennsylvania Railroad, between New York and Pittsburg. 1885. Jersey City. Trenton Philadelphia Columbia. . . Harrisburg . . Mifflin Altoona Conemaugh. Derry Pittsburg. . . . Miles from New York. I 57 91 171 196 245 327 364 398 444 Comparative Volume of Traffic (Phila. = i.oo). Eastward. 0.51 0.74 1.00 1.06 1. 17 0.98 0.77 0.72 0.56 o.3oi Westward. 1. 15 1. 13 I.OO 0.92 0.94 o.8r 1. 10 1.05 0.73 1.27 Ratio of Loaded Cars.* East to West. I to 1.47 I to 2. 13 I to 3.26 I to 3.76 I to 4.09 I to 3.97 I to 2.25 I to 2.22 I to 2.49 I to 0.78 ^L^^T^'T"'^ '" '^' """' "^^ '^" '°"^*='' '^^•^ ^*^«^ ^'■^ '»'>'•« J'&htly loaded than those East, so that the actual excess of east-bound over west-bound was greater than this tabl^ it'wT'; ^^^'"^'"^^; -^^- ^^^ -«^-^-"^ -" were presu Jbly the heav.es" tI average drsproportton over the •u>hole road, in ton-miles, may be deduced from Table 98 to be in d^ff/'^"''''"^ '° "^f " '^ " '^'■" ^' ^'" '^^' '^^ ^^"^^'°" '" the disproportion is as lawless •n different years as the above table shows it to be on different parts of the same line 39 6lO CH. XVII.— BALANCE OF GRADES FOR UNEQUAL TRAFFIC. flu ! ^ i 98, pages 232-3, shows the revolutionary way in which this dis- proportion has varied during the past forty-five years, or during the entire liistory of the road. Neither the extent nor the nature of these changes could well have been anticipated when the road was first constructed; but from our present stock of knowledge, actual or potential, as to the course of such matters in the past, we may make a reasonable and safe approximation at least to tlie future probabilities in this respect, by investigating the facts as to neighboring or rival lines. The proper manner of doing this we will shortly consider. A large body of further statistics of the same kind as to other roads might be presented, but not enough to serve any more useful purpose for any particular line than the approximate figures given in this chapter, without an inadmissible amount of them. 795. Assuming the ratio of the tonnage in each direction to be known or assumed, the admissible difference of gradients to correspond may be very quickly determined by the aid of the long Table 170, by de- termining the total load in tons behind the tender which must be hauled on the return trip, for a given disproportion of tonnage. The total load can at once be divided into paying load (freight) and dead load (cars), if we know or assume the average load and weight per car. By 1890, with the prevailing tendency to increase average load, it is probable that the total load hauled in the direction of heaviest traffic might fairly be divided as follows : General Traffic, . Total weight per car or train. . . 1.00 Live weight per car or train. 0.60 Dead weight per car or train. 0.40 Mineral Traflic, . . . 1. 00 0.72 0.28 At present this is a little too favorable ; not as respects the nominal loads, but as respects the loads actually hauled, although some of our best roads approach it. For example, the average load 0/ loaded cars on the Pennsylvania Railroad is now 14 tons, and of East-bound only 15^ tons. The average weight of the empty cars is probably in the neighbor- hood of lo^ tons. See Table 154. p. 486. Then if the return tonnage be only half as great, the total weight of return trains will be only 0.60 -f- -— = 80 per cent as heavy in tons; and having computed this weight in tons (making also an allowance which Cff. XVII.-BALANCE OF GRADES FOR UNEQUAL TRAFFIC. 6ll we shall consider in a moment) we find at once from Table 170 the cor respondmg grade. 'luic 170 tne cor- give?sufficient' dr'to'"""^? ""f ' "' ''^'°" "'^^ <=°™P"'«'^- »'>-'' ZL cond Hon, ^K f}^ *''^ P™P"^ '''''^"« ""der almost any there are a good L.y ::^CSi:X 1^0^^ ^^mlsTat ^^ wh,ch ,s probably the reason why in not a few instances oactua pic tice errors of importance have been made in it * ^ plicltld rrtrfonr"" °' *''^/'--""=-' ta-ance of gradients is com- I. The journal friction of empty cars is at least 2 lbs per ton (- o r ,r.ffi! "'^°'^«"';f balance of grade to that extent in favor of the liehtest I ptv'"Tti: hlr "h'"" '""^'^- ^""^ P-PO^io-tely if a par^ fetum tZLeHi'es '°" '" *=°'"P"'"« '^^'^'^ '«5. as indicated by the orcars''i=ert;iT;^.^^^^^ cent, win go empty even i„\he dt^ ion of he ' eavTsf traffif Th'" cars serve to increase by so much the proportion o t e ead t thi'": load of trams, and by so much diminish the admissible d^^erence in j I dients, and so also will the fact that even loaded drs do nn, K ^ means average their full nominal caoacitv Roth of ?J , ^ ^"^ ^n/f ®" ^' ^''^ ^'^P^oportion of traffic varies not only from year to vear Eg., a prominent text- book gives extrart« frr»r« ^«; • 1 -i..rcouMr.aXrr:stm:;L:Hr„r'''"'' " "^ --'-■ ''- 6l2 CH. XVII.— BALANCE OF GRADES FOR UNEQUAL TRAFFIC, Table 185, Proper Adjustment of Ruling Grades for an Unequal Volume of Traffic in Opposite Directions. [Correct within an inconsiderable percentage for all classes of engines and conditions. of service. Computed for an average Consolidation engine from Table 170, as explained in par. 795. Rolling-friction of empty cars assumed to be 2 lbs. per ton greater than that of loaded cars.] Opposing RETURN GRADES ; AN Equal Resistance to the Power of the Engine if the Gross Weight of Cars and Load returning is— (Weight in direction of heaviest traffic = i.oo) Gradb opposed TO Heaviest Traffic. .88 .76 .64 .52 .40 .28 Pet Cent. Ratio of Return Freight only to that in Direction of Heaviest Traffic. Freight Cars Returning Empty. Coal Cars Returning Empty. (See par. 802.) 0.8 0.6 0.4 0.2 Level .03 .08 .15 .29 .46 0.84 .1 .2 •3 .4 .5 .6 .7 .8 •9 .14 .26 •37 .48 .60 •71 .82 93 1.04 .21 .34 .47 .60 .72 .85 •97 1. 10 1.22 •30 .46 .61 .75 .90 1.04 1. 19 1.33 1.48 •45 .63 .81 .98 1. 16 1.33 1.50 1.66 1.83 .69 .92 1. 14 1.35 1.56 1.77 1.98 2.17 2.37 1. 14 1.44 1.73 2.00 2.27 2.54 2.79 304 3-28 I.O 1.15 1.35 1.62 1.99 2.56 3-52 1.2 1.4 I 1.6 1.8 2.0 2.2 2.4 2.6 2.8 1-37 1-59 1. 81 2.03 2.24 2.46 2.68 2.89 3." 1.60 1.84 2.08 2.33 2.57 2.80 3.03 3.26 350 1.90 2.17 2.44 2.71 2.98 324 3.49 3-74 3-99 2.32 2.63 2.94 3-24 3-54 3.82 4.10 4-37 4.64 2.94 3.31 3.65 3.98 4.32 4-65 4.97 5.20 5.52 396 4.40 4.80 5-17 5.55 5.88 6.21 6.53 6.83 3.0 3.32 3-74 4.23 4.91 5.80 7.10 3.5 4.0 3.86 4.38 4-30 4.86 4.84 5-44 5-54 6.16 6.46 7.10 7.87 8.47 Excess rolling- friction from empty cars, . r ^ . 0.4 1 0.8 [0.02 0.04 ! lbs. per ton 1 1.2 1 1.6 1 2.0 grade per cent 0.06 0.08 O.IO 2.0 O.IO CH. XVII.— BALANCE OF GRADES FOR UNEQUAL TRAFFIC, 613 missible rate of return grades by about 0.2 per cent in the " north-east comer" of the table, Its effect decreasing very rapidly from that point in each direction. A LOWER RATIO OF ADHESION (than ^) will also REDUCE the admissible rate of return grade, its effect being very important in the "south-east corner" of the table but decreasing still more rapidly in each direction therefrom. The use of tank engines will very materially increase the admissible rate of return grades, having a directly contrar>' effect to a lower ratio of adhesion. The same IS true in less degree as the proportion of weight on drivers or ratio of adhesion is increased None of these changes being proper ones to assume, it is not deemed necessary to eive ■exact figures. ** A lower assumed rolling-friction (than 8 lbs. per ton) will reduce the ad- moved at once; and since there must be more or less irregular fluctua- tions in the volume of all traffic, it may well happen, and not unfrequently does happen, that for the time being the burden of traffic shall be in the opposite direction to the normal one. Thus on the leading East and West lines of the United States, especially those of the second gfade. it is not uncommon to see engines running East light to handle an lin- usual quantity of West-bound traffic, although there is normally a very heavy excess of east-bound traffic on nearly all of them. When this occurs favorable west-bound grades are a decided economy, although ordinarily they may be unimportant. Nevertheless, the importance of this cause should not be exaggerated Marked irregularities of this kind are exceptional and short-lived! and would justify but very small expense to reduce grades on their account below what the average requires. Irregularities of 5 or 10 per cent may be expected to exist for nearly half the time, and hence to jus- tify about half the expense for reducing the grades correspondingly that would be incurred to provide for the average condition of the whole traffic. There is also a certain small economy in being able to send back some of the surplus engines and train crews light, as passenger extras. 4- For passenger traffic equally balanced grades are always desirable, as noted more fully in par. 807 et seq. 799. It is noticeable that all four of these limiting provisos tend to diminish the admissible variation in opposing rates of grade. In the aggregate they indicate that a reduction of the grades against the light- est traffic by something like 0.2 to 0.3 per cent (10 to 16 ft. per mile) be- low what the assumed average disproportion in weight of trains seems to require, is worth nearly half as much as if required by the average con- ditions themselves. When, in addition to these reasons for approximat- ing more closely to an even balance in spite of a known disproportion of traffic, the very existence of the assumed disproportion appears doubtful, I? ! 4 • ( » '1 11 ti 614 CH. XVII.— BALANCE OF GRADES FOR UNEQUAL TRAFFIC. Still greater caution should be used in assuming that anything will be unobjectionable, but an exact balance of resistances, which latter is of course the safest assumption to make when the future is for any reason very doubtful. Nevertheless, although the estimates of the probable future dispro- portion should always, for the reasons given, be exceedingly conserva- tive, it may on many if not on most lines be determined with practical certainty that a certain minimum disproportion at least will exist for the decade or so ahead, which is as long (par. 78 et seg.) as the engineer is financially warranted in looking ahead. 800i It is to be remembered also that the same assumed balance of grades which permits the grade in one direction to be made higher re- quires the grade in the other to be made lower, if possible, so that the assumption of a certain preponderance of traffic in one direction does not warrant any relaxation of effort to obtain low grades, but merely gives it a little different direction. If there be merely a probability that the traffic in one direction will be slightly heavier than in the other, with a possibility that it may be either considerably heavier or evenly balanced, and the same expenditure will substitute grades of 0.65 one way, and 0.55 the other, in place of 0.6 grades both ways, it is good en- gineering to do this, for we can only strike an average between the maximum and minimum possibilities and act in accordance with the mean. It is demonstrable mathematically, as well as clear to the reason, that this course is as binding upon us as if we had positive knowledge that the mean of our estimates (if they really are such, and not guesses) was the exact truth. Topographical considerations often make it impossible to even at- tempt a balance of gradients, at least m the way of favoring the heaviest traffic. It is, however, nearly always possible to favor the expense ac- count in such cases, somewhat at least, by not showing unnecessary favors to the lighter traffic. 801. For an exclusively mineral traffic the expediency of ad- justing the grades for the full theoretical difference can rarely be ques- tioned, and it is of course for this traffic that the greatest difference is required. At the present time the ratio of load to weight of car is con- siderably over 2 to I, so that less than ^ of the weight of a full train is cars and over | paying load. Consequently, the return trains of empty cars with less than ^ as much as the full trains, and the proper balance of grades shows a wide contrast in them, as will be seen in Table 185. CH. XVII.— BALANCE OF GRADES FOR UNEQUAL TRAFFIC. 615 802. An important fact to remember in considering an almost exclu- sively mineral traffic is that whatever general freight business there may be will probably be against the main traffic almost exclusively, and that the consumption of supplies per inhabitant is large in mining regions, and almost wholly imported. The traffic per inhabitant of mining re- gions, including shipments of machinery, etc., as also the outpur per miner (about | to Vtt of the total inhabitants), may be readily estimated by a little investigation. The figures vary too greatly to attempt any general analysis. 803. For general freight business no such difference as with mineral traffic ever exists, but something closely approaching to it exists at times on the leading East and West trunk lines, on which the normal average is only from 3 to 4 tons West to 10 East. It is probable that there will always continue to be a heavy preponderance of East-bound traffic in the United States, although whether it will continue to be as heavy in the future as in the past is a far more doubtful matter. The propor- tion of export traffic will become relatively less as the population of this continent increases, and this traffic has now a great influence in causing the disproportion of traffic which at present exists. If the East were to continue to be the manufacturing region par excellence this loss would be compensated for, but that this will be the case seems very doubtful. 804. An enormous West-bound anthracite coal-traffic, moreover, has sprung up within the last few years which is reducing and will still more largely reduce the existing disproportion. The rise and growth of this traffic is a good illustration of the great changes which may come with time, but which are for the moment not considered. It is the chief cause for the very remarkable reversal of the current of local traffic shown in Table 98. The only definite fact seems to be that the burden of traffic will al- ways be heavily toward a manufacturing or mining region and away from the shippers of the heavier cereals. Thus it is about three to one from West to East, and about two to one from the Northern to the Southern States. 805. The latter fact shows that it is not safe to say broadly that the burden of traffic is from an agricultural to a manufacturing region ; for the South, which is chiefly agricultural, ships to the North, as yet. much ess m weight than it receives ; the reason being that its exports are largely cotton, and that the current of its commercial business follows a kmd of triangular* course— from the South to New York or Europe, thence to the interior of the United States, and thence to the South I'M! 6l6 en. XVII.—BALANCE OF GRADES FOR UNEQUAL TRAFFIC. again. But the rapid development of the mineral resources of the South is bringing about a change in this respect. 806. The possibility of some such roundabout process of exchange as this, especially on a small scale, is one which must be very frequently remembered if a reasonable estimate of probabilities is to be made. Thus, when the Mexican system of railways was projected it became at once important and difficult to determine in which direction would be the largest freight movement. The central plateau is a region of great and largely undeveloped grazing and agricultural possibilities, but on the other hand is a great and largely undeveloped mining region, hav- ing no workable coal as yet known. Bearing in mind the character of the regions of the United States to the north, the writer concluded that the traffic would not probably be very unequal, but that the tonnage would be the heaviest northward. This expectation has not yet (1885) been fulfilled, but the direct contrary is the case, the preponderance being very heavily into the City of Mexico, and largely on account of the triangular process of exchange referred to. The products exported are on the coast or seek the coast, and thence by very indirect channels pay for the shipments (as yet small) which go to Mexico in return by rail. Whether or not this tendency will continue is doubtful. Proba- bly it will not. but the burden of traffic will be out of Mexico when a fuller development has come. In any case it illustrates the necessity of looking beyond the superficial and immediate possibilities, and remem- bering that great changes may come with time. 807. For passenger service grades should in all cases be equally balanced, because whether passenger cars be loaded or unloaded makes but an inconsiderable difference (par. 606) in the weight of trains, even if it were not certain that passenger travel must be, in the long-run, equal in each direction, in spite of a temporary preponderance in one direction, due to emigration. Therefore, in proportion as the passen- ger traffic is a larger and mineral traffic a smaller element, and in pro- portion as the preponderance of freight tonnage is doubtful, the expedi- ency of seeking uniform grades in each direction increases. 808. It follows also, that when an unequal freight or mineral traffic exists, combined with a considerable passenger traffic, there is always a certain advantage, and hence a certain justifiable expenditure, in reduc- ing the rate of grade in either direction, although the other be left un- changed. The passenger service is always benefited by reducing the higher rate of grade, whichever it may be (provided ft is, for passenger service, a de-facto limiting grade, as explained in par. 407) ; and after CH. XVII.—BALANCE OF GRADES FOR UNEQUAL TRAFFIC. 617 this has been done there is a certain advantage to the freight traffic only m reducing the grades against the heaviest traffic. The admissible ex- penditure for doing this is only that appertaining to the particular traffic benefited. 809. For example, suppose the grades on any line to be i.oo and 1.20 per cent (52.8 and 63 ft. per mile), and the ratio of the weight of freight in each direction to be about as on the Pennsylvania Railroads, viz ; as i.o to 0.3: IVell-adjusted grades for freight service would be Percent _ (Table 185) 0.6 and 1.2 Well-adjusted grades for passenger service would be 1.0 and i.o We can properly expend, therefore, to reduce the grade which limits the freight traffic (1.0 per cent) to 0.6 per cent, as much as the freight traffic alone justifies ; and to reduce the grade which is heaviest for pas- senger service (1.2 per cent) to 1.0 per cent only as much as the passen- ger service alone justifies, which, in case of a light local passenger busi- ness, will not be much (par. 732). 810. Even if the business of a road consists of three distinct classes of traffic, passenger, freight, and mineral, each one of which would re- ^ /I' ^^ ^ Fig. 180.— Effect of Unreduced Curvature to reduce Grades. 822. An immense portion of the heavy grade-mileage of the world- has been constructed in precisely this way, the grade being carried through at a uniform rate over curves and tangents alike. Until within recent years nearly all American railways were so constructed, and when the curves were compensated at all, low rates of compensation (0.02 and 0.03 per cent per degree) were and still are chiefly used, for which indeed much can be said (par. 834 below), although in general a less rate than 0.05 cannot be regarded as good practice. 823. The practice of reducing grades on curves appears to have been first introduced on the Continent. American engineers soon followed. English engineers have neglected and still do neglect it very generally. In no part of the world is it universal, many prominent roads in this country having neglected it wholly ; as. for instance, the Erie, Boston & Albany, Baltimore & Ohio (for the most part), Pennsylvania (for the most part), and in recent years such lines as the Cincinnati Southern, Chesapeake & Ohio, most of the Denver & Rio Grande, and a host ot other lines. 824. The argument by which a neglect to reduce grades on curves has been justified, when any attempt at all has been made to justify it, is that the resistance is averaged by momentum so that the broken grade-line of Fig. 180 is reduced by the equalizing effect of slight fluctu- 622 CHAP. XVIII.— LIMITING CURVATURE. CHAP. XVIII.— LIMIT ING CURVATURE. 623 ations of velocity to the continuous 0.75 grade-line shown below it. The general principle upon which this argument is based is a sound one, to the extent that under favorable conditions precisely that effect may result, either on actual irregularities of grade, or on equivalent ones caused by unreduced curvature. It is not true at all that any injurious effect upon the train, or any increase of virtual gradient, necessarily re- sults from the gradient like the broken line in Fig. 180 in place of the straight 0.75 grades, under certain and proper conditions. Why and how this is so, and under what conditions, has been so fully discerned in Chap. IX. (par. 397 et seq.) that it need not be repeated, further than to say that a curve may be considered as adding simply so much to the grade, and the two cases be treated alike. 825. But conditions justifying the assumption that unreduced curva- ture can thus be made harmless by the effect of momentum cannot exist on any actual maximum grade, unless by some rare accident, and conse- •quently it is a rule which should be regarded as of universal application, and rigidly adhered to, that unreduced curvature should under no circumstances be permitted on the maximum grade, and that the reduc- tion should in general be ample, especially near stations and where there is an excessive resistance. The reasons for this are three, as follows : I. The distribution of curvature even on a grade-line only a few miles long naturally tends to become unequal. Instead of being equally dis- tributed, as assumed for merely illustrative purposes in Fig. 180, it is far more likely to be concentrated in masses of perhaps several hundred degrees of almost continuous curvature, with long intermediate stretches of much better alignment, giving, if such curvature is not reduced, an equivalent profile more like Fig. 185, from which it is far more difficult to obtain a straight " virtual " profile (par. 398) by fluctuations of velocity than with a more even distribution of curvature; and when such excess of curvature comes well up toward the top of a long grade it becomes under most circumstances practically impossible to do so. 826. 2. Even if the curvature be tolerably evenly distributed, the speed on maximum grades is, with the full train which good operating management presupposes, necessarily slow. With extra heavy car-loads or in unfavorable weather — wet, frosty, misty, very cold, or windy — it is necessarily very slow. At what point on the line the most unfavorable conditions will be encountered (for there are always slight variations, from wind or differences of track if nothing more) cannot be exactly anticipated, but on the top of long grades, especially, it can be antici- pated with confidence that a very slow speed, not exceeding 10 or 12 miles per hour, will be rather the rule than the exception. At such speeds, and especially at still lower speeds, there is every reason to be- lieve that the curve resistance is greater (pars. 308, 335), while there is no available momentum to overcome it. A train moving at 10 miles per hour (Table 118) has only 3.55 ft. of " velocity-head." At a compen- sation of 0.05 per degree (i lb. per ton) 70° of curvature will destroy this head completely, since at that rate of compensation each 20° of central angle destroys one foot of vertical head. In other words, a train mov- ing at 10 miles per hour, which could just continue that speed on a tangent, would be stalled at once by seven stations of 10° curve, or, if by good luck not stalled, its speed would be reduced so low that additional journal-friction (par. 640 and Appendix B) as well as (probably) addi- tional curve-friction would come in and ensure stalling on any closely following curve. 827. 3. Stopping of trains on grades from accident or otherwise is not un frequently necessary, and then it is entirely clear that a stoppage on a long unreduced curve is a disastrous disadvantage, especially if it be on a long succession of curves so as to forbid the expedient of backing down off the curve to get a fair start. It is then strictly true that it is the grade at that one particular point which is the limiting gradient, and that we cannot strike an average with lower tangent grades before and behind, and assume it is the same thing as if we actually had a uniform average resistance at all points. 828. The rule that a grade-line should be unbroken by unreduced curvature is still sound, in spite of the fact that there are certain circum- stances under which slight and short sags below the grade-line may be introduced to save expense of construction, especially where economy in first cost is a great object, as it is so much more often than is realized during the period of construction. A sag below a grade-line and a rise above it — which is what an uncompensated curve in effect introduces — are two entirely different matters. Thus, if we have a 1.25 per cent maximum grade, up which a train can just make its way at a uniform speed of 10 miles per hour, a rise of 3.55 feet above the grade-line will, as we have just seen, stall the train. On the other hand, a sag in a grade-line -of an equal amount, as at C in the grade-line AB, Fig. 181, not only does not endanger a stall, but actually Fig. x8i. \\ f > ! I \ % 624 CHAP. XVIII.— LIMITING CURVATURE. CHAP. XVIII— LIMITING CURVATURE. 625 increases the velocity of passing from A to B. For by assumption we have at A, velocity of ten miles per hour = (Table 118) vel. head of 3.55 ft. ^' " " " = " " 3.55 ft. C, vel. head of 3.55 + 3-55 = 7- 10 ft. = (Table 118) a velocity of 14.14 miles per hour. 829. Then by the laws of accelerated and retarded motion (see par. 371 or any text-book on physics) the average speed between A and C and C and i5as well, and hence between A and B = ^QQo X HH _ ,2 07 2 miles per hour— a gain in average speed of 2.07 miles per hour, or about 3 ft. per second in passing over the sag shown in Fig. 181, the compara- tive times being about 2 m. o sec. and i m. 40 sec. This gain of time is for the same reason that a body descending from A to B, Fig. 182, over the different paths a, d, c, d, although acted on by the same force (gravity acting through CB), takes a very different time for de- scending to B, the cycloid d being the "curve of quickest descent." The re- sulting velocity at B is in all cases the same, barring loss by friction, but the time consumed in reaching B is widely different. 830. Therefore, while compensation for curvature should never be omitted, it may still be admissible, in certain exceptional cases (as to temporarily save large fills or otherwise reduce works), to introduce a sag below a grade-line, which is never the case with a rise above a grade- line. Thus the dotted profile, bbbb. Fig. 183. can certainly be operated un- der any and all circum- stances (if the sag be not too great, par. 435 and Table 121) as a virtual grade of the same rate as the average actual grade ; but with the grade-line aaaa this is not possible, unless the initial speed be very high or the points aa rise but little above the average grade-line. Fig. 183. FxG. 183. 831. The principle is the same as the one so familiar to hydraulic engineers known as the "hydraulic grade-line." If water is to be conveyed from a high reservoir to a lower point of delivery, it is an axiom in hydraulics that any lib- erties whatever can be taken with the grade of the pipes without affecting the discharge in the least, more than the same increase of length and curvature would do in a pipe laid to a uniform grade, provided the pipe at no point rises above a straight line connecting the points of supply and delivery, which is known as the "hydraulic grade-line," as on the line bbbh. Fig. 183. If, how- ever, the pipe rises above this line, by however little, as at the highest a, Fig. 183, the discharge will immediately be reduced to correspond with the new hydraulic grade-line passing through the point of supply and tangent to the now highest point on the pipe. In theory a lo-mile grade of 50 ft. per mile might be broken up into (i) 5 miles of level and (2) 5 miles of 100 ft. per mile, without increasing the de-facto ruling grade above 50 ft. per mile; but we cannot reverse the orders of these gradients, making the first last and the last first, without a theoretical as well as practical increase of the gradient to 100 ft. per mile. Even in the former case, the velocity at the end of the first five miles of level would have to be 87^ miles per hour, assuming an initial velocity of 15 miles per hour. This is hardly a practicable speed for freight trains; and it therefore should not be understood that any considerable sags below a grade-line are admissible. The only asser- tion made is that, assuming such speed to be practicable, even 250-ft. sags below a grade-line would do no harm, whereas any rise whatever above it would destroy it, theoretically as well as practically. Fig. 184. 832. A remarkable instance of the advantage thus to be gained at times occurred in tHe writer's practice, and is shown in Fig. 184. Near 40 626 CHAP, XVIII.— LIMITING CURVATURE. i the middle of a long grade-line which it was very desirable to keep down to the lowest limits, occurred a saddle between two hills, where support- ing ground was wholly lost. Consequently, although there was no ma- terial difference in the profile at any other point, both being side-hill, at this point any lift of the grade-line meant so much addition to the fill. To bring the grade-line down to within a few feet of the surface meant an increase of the pusher grade from 1.15 to 1.25, equivalent to an increase of ruling grade on a long d'vi.^on from 0.4 to 0.5. To obtain the lower grade required a very long fill, containing some 190.000 cubic yards when fully made (estimated to cost 20 cts. per yard); but by introducing a sag in the grade-line of some 25 feet (shown by dotted lines on Fig. 184), as- sumed as about the extreme depth of sag which it would be proper to at- tempt to operate as a continuous virtual profile, even temporarily,* the fill could be reduced to some 30,000 cubic yards, leaving the track to be gradually raised up to the straight grade-line when and if necessity should appear and convenience serve. To make the fill in the beginning was not justified by the financial status of the company, nor by the time at its disposal, nor could material be obtained at reasonable cost except by train. 833. There were then three possibilities, besides that of making the fill complete : 1. That the grade would continue to be operated indefinitely as a vir- tual straight grade by the aid of momentum, tolerating the necessary velocity of 30^ miles per hour in the bottom of the sag. 2. That the fill would be raised somewhat from time to time, so as to reduce the necessary fluctuation of velocity to less objectionable limits. 3. That the traffic of the line would prove so thin (it was very doubt- ful) that the trains would for the most part be light and the necessity for either expedient not be great. In this way it was possible to have one's cake and eat it too; to econ- omize as much as was otherwise possible against the contingency of future poverty, and to lose nothing (but rather gain the interest on the cost of the fill) in case the future should prove prosperous ; for at the worst the 1.15 line could certainly be operated as a virtual 1.25. So pronounced an instance of the legitimate use of sags in grade-lines will rarely occur, but the same principle may be availed of often on a CHAP. XVIII.— LIMITING CURVATURE. » Velocity-head due to speed of 15 miles per hour (Table 118) 7- 99 ft. Add for depth of sag below virtual profile [ 35 00 " Velocity-head in bottom of sag (giving speed of 30J miles per hour), 32.99 ft 627 smaller scale, if only to introduce a little extra compensation in a long curve on a high fill, returning to the original grade-line by a slightly steeper grade beyond. ^ 834. It will naturally follow from what has preceded that THE proper RATE OF COMPENSATION IS NOT A FIXED QUANTITY, but may under varying circumstances vary within somewhat wide limits. The more usual rates are from 0.03 to 0.05 per cent per degree of curvature, corre- sponding to 0.6 to i.o lbs. per ton per degree. If the precise amount of curve resistance were known, and if it were always the same, of course but one rate of compensation would be proper, but as its precise rate is not known, and as there is strong reason to believe (Appendix A) that in startmg a train it may possibly amount to as much as 2.0 lbs. per ton a compensation sufficient to equalize curve resistance in ordinary circum^ stances cannot be assumed to be certainly sufficient at points where speed may be expected to be very slow, as toward the top of long grades and occasionally at other points. 835. Under these circumstances, prudence would indicate that wher- ever there is NO physical limit to the possible reduction of grade on curves, .t should be made ample, so that the curves should certainJy offer no greater resistance than the adjacent tangents. At stations this rule would require a grade reduction of o.i per cent per degree On the other hand, when we are merely trying to equalize the tangent and curve resistance on a long ascent; and whatever is taken off the curves must be added on to the tangents and vice versa, no such practice |s proper A chain is only equal to the strength of its weakest link, and n avails httle to know which is the weakest link if we cannot strengthen It. If we come as near to an exact equality as we can, in compensating for curvature, it is of no importance whether our compensation is a little too great or a little too small. In the one case trains will stall on the tangents and in the other on the curves-that is all. Our object is simply to guard against a certainty of stalling on either. Nothing more than this IS important. 836. Hence it may well be that on a long and crooked ascent, where the curvature greatly exceeds the tangents, yet where there are one or two considerable tangents, prudence will require the assumption of a very low rate of compensation ; for otherwise a very slight loss of elevation ZZ^ '"""•■ '""'*;P"^.'^,''y -"^"y -""e^. will prevent our attaining the ^es red summit at all without a considerable increase of the normal tan- this m^H^' 1 "' r' ^"'''''' '"^'" "^ '° 'he real curve resistance, th.s may do no harm, but on the other hand, if we have guessed wrongly ' iwpv^pv 628 CHAP. XVII I. -^LIMITING CURVATURE. 4H and exaggerated the probable curve resistance, we shall have unneces- sarily increased our tangent grade. Hence, by assuring a low rate of curve resistance in such a case, we can hardly in any case lose anything appreciable, and may save a needless loss of grade. A compensation rate of 0.03 per degree of curvature may then be proper, below which the rate of compensation should never fall. 837, For the same reasons, it may well happen that at different points on the same line different rates of compensation may be proper. Where the loss of elevation by a high rate of compensation is a very serious mat- ter, because of a great amount of curvature, it may be taken at a mini- mum. At other points, where there is less curvature to be compensated and a higher compensation can be had at little or no cost, it should there- be used. The effect will be to make most of the maximum grade scat- tered over the division a little easier to handle trains on than the longest. or worst grade. This may well result in handling a car or two more than would be deemed possible were the resistance as great at two or three points as it is at one. It has been elsewhere said (see Table 1 24) that it is always worth while to keep a little below the maximum where possible, at moderate cost. This is only another application of the same principle, but, owing to the uncertainty which hangs about the question of curve resistance, it is a wiser way of attaining the same end than to reduce the nominal tangent grade, especially in the vicinity of stations. 838. To illustrate the importance of sometimes varying the rate of compensation to suit circumstances, assume a 1.5 percent average grade^ Fig. 185, nearly ten miles long (500 stations — taking a " mile" at 5000 ft.. for convenience of computation), subdivided as follows in respect to» amount of curvature : Top, Middle. ■■\ (( *« 150 stations with about 50** per mile = continuous 1° curve (with f of the line tangent). 100 stations with about 300° per mile = 100 " " " 400** " " =s (with J of the line tangent). Lcrwer X ^5° stations with about 8)" per mile = (with f of the line tangent) Assume also a stoppmg- place near B; at the foot of the grade, so that no assistance from velocity can be counted on : This is in no respect an unreasonably or improbably irregular distri- bution of curvature on such a line, nor an unusually large amount of curvature for a cheap line in rough country. In all there will be 150°-^ 6oo'* + 8oo° + 22q°=i775° of curvature on the ascent. CHAP, XVIIL^LIMITING CURVATURE. 629 At various rates of compensation for curvature the grades required on tangents for various rates of compensation would be as. follows, as ! { -J. «P. I ???. Fig. 185. the student will do well to determine for himself by a brief comou- tation ; * ^ At 0.03^ per degree, 1.50 -j- .1065 = 1.6065 per cent. "0.05 " " 1.50 + .1775 = 1.6775 " " " 0.10 •• •• 1.50 + .355 = 1.855 " " 839. If the topography were such that we had just 500 stations in which to rise 750 feet, this would mean, if we adopted a compensation of o.io per degree instead of 0.03. that our tangent grade (which would then certainly be the governing one. because we have adopted a compen- sation which will CERTAINLY bring the resistance on curves below that on tangents) will be greater by 0.25 per cent, or 5 lbs. per ton, than with the lower rate of compensation. In other words, in order to secure the wholly, or almost wholly, worthless end that trains, when and if they stall, shall stall always on tangents and never on curves, we have greatly increased the chances of their stalling on tangents, on the top or bottom sections of the grades at least, where the tangents are the lonrresf— a plain act of folly. ^ 840. But this is but one side of the question. The total rise in feet and the elevat ion of intermediate points would, under the various as- ♦ Knowing approximately the total degrees of central angle on any grade we have only to multiply the total by the assumed rate of compensation to find how much total elevation will be lost by the compensation. The elevation divided by the length of the grade, will give the rate by which the tangeni maximum must be increased to introduce the compensation. : :i ^ J ii^ I i 630 CHAP. XVIII.— LIMITING CURVATURE. CHAP. XVIII.— LIMITING CURVATURE. 631 sumed rates of compensation, have to be as shown in Table 186; and it will be seen that the middle point c of the entire grade comes at about the same elevation with either rate of compensation, but that there is a material difference in the height of the grade-line at the beginning and end of the middle sections C and A or at the " quarter points" of the grade. While the through uncompensated grade-line falls as shown by the dotted line, the effect of introducing the curve compensation, by whatever rate, is to give a profile like the solid line, the point C being from I li to 38 feet higher than before, and the point D from 9 to 31 feet lower, according to the rate of compensation. Table 186. Illustrating the Effect of Different Rates of Curve Compensation TO Modify the Elevation of Intermediate Points on Long Grade- Lines [Based on the data of par. 838 and Fig. 185.] B C. (Foot of Grade.) D E (summit) 1-5 Straight. No compensa- tion. Rise. 325 150 150 935 Eleva- tion, o. 335. 375- 525- 750- 1.6065 Tangent Grade. .03 compensation. Rise. 336.48 143.65 136.65 334.33 Eleva- tion. 0.00 336.48 379- »3 515-78 750- 1.6775 Gi Tangent Grade. .05 compensation. Rise. • • • • • • 844.13 137-75 127.75 340.38 Eleva- tion. 0.00 344.13 381.87 509-62 750. 1-855 Tangent Grade. .10 compensation. Rise. 363.35 125.50 105.50 255-75 Eleva- tion. 0.00 363.25 388.75 494-24 750. Difference in Resulting Elevations at Various Points on the Grade, from the Straight Tangent Grade. B (foot of grade) C c D E (summit) Constant 11.48 ft. higher 413" " 9;22 " lower. Constant 38.25 ft. higher. 13-75" " 30.76" lower. ■ Topographical conditions will sometimes permit, but will more usually forbid assuming that we have such leeway in the necessary posi- tion of the grade, thus depriving us in a measure of the privilege of free choice. 841. Now suppose, on such a grade, that the middle 300 stations or about 4 miles, on which most of the curvature is bunched, was so situ- ated as to make it essential to rise only some 230 feet, unless consider- able extra expense were to be incurred, while at the same time the character of the line elsewhere was not such as to admit of a lower maximum tangent grade. Under these circumstances, which may fre- quently occur, it would be a great error not to reduce grade on curves by the full amount which the topographical conditions made possible with- out loss up to even o. 10 per cent per degree of curve, in the existing state of our knowledge, even if at other points we used less. In that case, if we have overestimated the probable or possible resistance on curves, it is not likely to do harm, because the large amount of curva- ture and small amount of tangents will enable any excess of resistance in the latter to be equalized by momentum, whereas if we have under- estimated the curve resistance a similar effect is not possible, or at least not as fully possible, on account of the greater length of curves. On the upper and lower sections, where tangents prevail and curves are the exception, the opposite principle prevails. If the curve compen- sation be too little it will be equalized easily enough by momentum on short and infrequent curves, so that the result will be the same in effect as if the balance were exact. 842. Under the circumstances of the example just considered, as- suming the middle part of the grade to be fixed as just assumed, the proper course to pursue with the lower part of the grade would be to ease its rate a little, if circumstances permitted doing so at little or no expense; otherwise, to reduce its virtual rate by the simple expedient of removing the stopping point at the foot of the grade some distance from it, so as to ensure gaining something by momentum. A speed of 25 miles per hour at the foot of the grade reduced to 10 miles per hour at Cwill (Table 118) ensure a gain from surrendered energy of 22.20 — 3.55 = 18.65 vertical feet fsee Fig. 185), which will reduce the grade on the first 150 stations by — — =0.124 per cent, and so secure an equality with the virtual grade of the next section above, even with the lowest possible rate of curve resistance. The curve compensation on this lower section should in any case be small, whatever it may be on the middle section just above. 843. On the upper section DE, assuming the lower and middle sec- tion to have be^ fixed as above, an effort will naturally be made to lengthen the line a little at the upper end at the expense of a moderate amount of distance and curvature, so as to give a gradient DF instead of DE, Fig. 185 ; but if this be not possible, the disadvantage will not be very serious. Our case will be this : By virtue of an excess in rate of ' ■ 1 6],2 CHAP. XVIII.— LIMITING CURVATURE. curve compensation we have the broken virtual gradient ACDE in- stead of the straight grade BE, which is of course preferable. The dis- advantage at the lower end, which would naturally be the most serious (par. 828), since it carries our virtual gradient above the grade-line BE, which we desire, we have neutralized by momentum.* The disadvan- tage at the upper end, since it merely carries our profile a little below the grade-line, will in great measure, if not entirely, neutralize itself by momentum. In this way we have done the best which can be done to avail ourselves of every chance in our favor, whereas by assuming any hard-and-fast rule whatever, and then following it blindly (as we might be justified in doihg if we knew it was correct), we are certain to lose something, and may lose a good deal. 844. Our practical conclusions as to rate of curve compensa- tion, therefore, may be summarized as follows: 1. With short grades or under favoring topographical condi- tions compensate as liberally as possible up to a maximum at special points of o.io per cent per degree. 2. Where speed may sometimes be very low, and hence in- variably on or very near to known stopping-places, this maxi- mum rate appears, with our present knowledge, none too much. In general, however, 0.05 per cent per degree (= i lb. per ton) is an ample equivalent for curve resistance, and for fast trains alone probably 0.02 to 0.03 per cent (= 0.4 to 0.6 lb. per ton) is sufficient to balance the resistance. 3. On sections where curves largely predominate over tan- gents it is particularly desirable to have ample compensation, and if excessive it will do least harm. On the contrary, 4. On sections where the amount of curvature is small it is less important to have full compensation, and if excessive it will do most harm. 5. When the rate of compensation can only be increased at the CERTAIN cost of a Corresponding increase in the rate of tangent grades (making very sure that it is certain, and no*t an over-hasty * The word *' momentum" here and elsewhere is used in a somewhat un- scientific way, to correspond with the popular use of the word. The scientist will not be confused thereby, while the average reader is assisted. CflAP. XVIII.— LIMITING CURVATURE, 633 conclusion from inexperience or lack of care), no larger rate than vi-e feel practically certain will be required to balance the curve resistance (0.03 to 0.04) should be chosen. Otherwise, we are committing the folly of making a certain addition to the grade in one place, to avoid one in another place which is merely problematical. 6. On any minor gradients where the curvature is not suffi- cient to bring the virtual profile up to the maximum it is not important to compensate for curvature at all, although it is gen- erally as well to do so, especially at points where to do so will slightly reduce the cost of construction, as is very apt to be the •case on long curves. When not compensated, the curvature merely has an equiva- lent effect to a slight undulation of gradient (Class A of rise and fall, par. 438) which produces no shock to the train and so is not a measurable disadvantage. 7. It is not in the least essential or important to precisely -adapt the compensation to the exact length of each curve. The reduced rate may as well as not begin and end at the nearest even station, and may be made a little less on one curve and a little more on one immediately above if a horizontal slice of a foot or more may thereby be taken off a high fill on the tangent connect- ing them, but never so as to cause the grade to rise above the uniform grade-iine. 8. Curves immediately below a known stopping-place for all trains need not and should not be compensated at all. 9. The rate of compensation should be uniform per degree for all degrees of curvature, or in no case made greater for the sharper curves. It may even be made less for curves of over 10° [par. 335 (9)]- If the rate be reduced one half for the excess over 10°, making the compensation for a 16° curve thirteen times that for a 1° curve, it will certainly lead to no bad results, although a rather rough rule. This is directly contrary to the usual practice, which is to increase the rate of compensation with the sharpness of the curve, if anything; but this oractice Tests upon the assumption which we have seen to be the direct contrary of the iiil HI lif 5*1 curve. The results of experience on the New York elevated lines and numerous others with very sharp curves, both of standard and narrow gau^e is. enough to disprove this, confirmed as it is very directly by the indications 'of lo. Since we have seen in Chap. VIII. (par, 330-335) that there is no reason to believe that curve resistance increases per ton with the length of the train, or even (appreciably) with the type of engine (par. 285 et seq.) there is no reason for varying the compensation because of the grades or length of train, except for this—that It is usually easier to spare the elevation for a liberal rate of compensation with low grades than with high ones. It is therefore proper to do so. CHAP. XIX. -THE LIMIT OF MAXIMUM CURVATURE. 635 CHAPTER XIX. THE LIMIT OF MAXIMUM CURVATURE. 845. Although badly adjusted grades have a more serious effect on operating expenses, there is no detail connected with location which has so great an effect on the cost of construction as that which we are about to consider-nor any in which the ten- dency is so notable to go to one extreme or the other, without any very definite or defensible reasons. It is evident that, while circumstances will often justify and require the use of very sharp curvature or of very easy curvature, they will in no case either justify or require that conclusions should be jumped at in some such manner as that sketched in par. 245. 846. Moreover, it may be again repeated, and cannot be too fully recognized and clearly borne in mind, that both the amount and radius of curvature, like the amount and rate of grades is even more dependent upon study, care, and skill than on topog- raphy. There exists, too, a most dangerous tendency to use more and sharper curvature than is at all necessary in country of some difficulty, and less and easier curvature than is at all expedient in country of no difficulty, or in countrv whose only difficulty comes from trying to hold close to an air-line (Chap. XX.). Errors of this kind, resulting merely from lack of care or skill, are especially apt to lead to the use of absurdly sharp curvature if one has imbibed the notion that easy radii are unim- portant. 847. Recognizing these dangers, we proceed to analyze, as nearly as may be, the causes which fix the advisable limit' of maximum curvature and the cost of exceeding it. We have* seen (par. 343) that these causes may all be separated under the two following heads, sharply defined from each other: -036 CHAP. XIX.— l^HE LIMIT OF MAXIMUM CURVATURE. First. The inherently greater co?>Ti.m^ss^ not of curvature measured by degrees, but of sharp curvature instead of easy CURVATURE /£?/- approximately the safue number of degrees. In other words, the greater wear and tear of track and rolling-stock, con- sumption of fuel, danger of accident, loss by decreased speed, etc., which results from using loo feet of io° curvature instead of looo feet of i° curvature for deflecting the line through a cen- tral angle of io°, or from using 900 feet of 10°, and 550 feet of tangent at each end, for deflecting through an angle of 90°, as in 4 ■so'lan. " Fig. 186. Fig. 187. •[There is a certain loss of distance, aa, in using the sharper instead of easier curve which is not reierred to in the text. See par. 859.] ' Fig. 187, instead of using 1800 feet of 5° curve and only 50 feet of tangent, as in Fig. 186. Secondly. The limiting effect of sharp curvature on the weight and length of trains, provided it be sharp enough to have such effect. Some is, and some is not. 848. In other words, we are here met, upon the threshold of the subject, with a distinction precisely analogous to that which we have already found (par. 361) to exist in the case of gradients. All grades, without distinction and wherever situated, entail a certain additional expense per train passing over them; and in addition to this the highest rate of grade entails a certain and much greater expense which does not appear at all in the ex- penses per train-mile (except as it may tend to decrease them by shortening trains), but solely in an increase in the number of trains. In like manner, all curves, without distinction, entail a certain additional expense per train passing over them for every CHAP. XIX.— THE LIM IT OF MAXIMUM CURVATURE. 63/ degree of the curve, and this cost, it may be,~or may not be- increases rapidly with the sharpness of the curve; but in addi- tion to this, the sharpest curve (or curves) on the line // // be sharp enough, will have the further effect of limiting the weight and length of trains. In fact, if made sharp enough, it will so severely limit the weight of trains as to make it impossible to run any trains at all. At a certain definite radius, therefore, the expense and loss arising from short radii take a sudden jump. The inherent cost per train-mile per degree of sharp instead of easy CMxyj2.Un-^ continues on as before, and, in addition thereto, there is tlie large additional expense caused by the limiting effect of any shorter radius upon the weight of trains. 849. It is plain that the point at which this sudden jump will or may occur is intimately connected with and depends upon the rate of the maximum grade, because the higher the grade the greater the resistance on a tangent, and hence the sharper the curve which may be used (i.e., which it is possible to use) on. levels or minor gradients without any limiting effect on trains Hence the shorter the trains which can be hauled independent of the sharpest curve, the shorter the radius which may be freely used on levels or minor gradients without affecting the number of trains required for a given business. 850. Now, just as in the case of gradients, this distinction between these diverse sources of expense is one which must be carefully kept in mind if any correct and intelligent decision as- to the limit of maximum curvature is to be reached. In the first place, it needs no great effort of mind to perceive that the first item mentioned above, the inherent costliness of sharp curvature,— that portion which is visible in increased wear and tear and expenses per train-mile,— affords no ground for the fixing of any arbitrary and inflexible standard or limit, nor should it be considered or allowed to have any weight what- ever in ascertaining at what radius to fix that limit. For, mak- ing for a moment the exaggerated estimate that the cost of curvature per degree increases as the square of the degree of f t m 638 CHAP. XIX.— THE LIMIT OF MAXIMUM CURVATURE. CHAP. XIX.^THE COST OF SHARP CURVATURE. 639 the curve, it may easily be, and often is the case at certain points, that the cost of construction will vary as the cube of the radius, and hence a sudden sharp ravine or rocky spur might justify and require a 12° or 15° curve for this account alone, although 3° or 4° curves were the maximum on all the rest of the line. But what we then require to determine is: Will any such curve have the further effect of limiting the weight of trains over the whole line, or injuriously restricting speed ? For in that case, plainly, a large additional expenditure will be justifi- able to increase its radius. 851. This latter expenditure does not vary with the number of curves, as does the wear and tear, but is a certain fixed amount, which can alone be used to take out such curves, how- ever many or few they may be, and must be distributed to one curve or to fifty, according to their number. This fact alone is sufficient to show the essential dissimilarity between it and the sum which represents the direct or inherent disadvantage of using short instead of long radii. As the latter is always so much per sharp curve, or per degree of sharp curvature, it always has its effect — much or little, as the case may be— on the justifi- able expense to increase the radius of each particular curve, for it is to be added in each case to the proportion for that curve of the estimated value of avoiding any limiting effect from its radius; but it does not form an element in fixing the point at which limiting effect begins, and hence should be allowed no weight whatever in ascertaining that limit. All this seems clear enough when the attention is specially directed to it, but, as with many other problems which advance from simple premises, it requires a constant effort of the mind to keep it always in view. Hence, although it has no real or necessary connection with our present subject, we may first briefly consider THE INHERENT COSTLINESS OF SHARP CURVATURE. 852. For the consideration of this question all actual or possible lim- iting effect from curvature on the length or speed or easy riding of trains. or the use of any desired type of locomotive, must be disregarded. Such injurious effect as the sharpest curves may have on these details, if any, IS another matter. The question is simply— as between the two methods shown in Figs. 186, 187— of turning an angle of 90" within a distance of 1900 feet of track : Which adds the most to the operating expenses per train due to that 1900 feet— the method of Fig. 186, showing 1800 feet of 5° curve and 50 feet of tangent at each end, or that of Fig. 187, with 900 feet of 10° curve and 500 feet of tangent at each end } 853. Rigorously excluding all thought of possible limiting effect from the mind, it is very difficult to see reasons why the inherent cost of curvature, per train-mile per degree, should be in the least increased by using short instead of long radii, i.e., by using 100 ft. of 10° curve instead of 1000 ft. of 1° curve, to cover the same central angle. The wear and cost of rails appear from superficial investigations (the writer's among others: see par. 317) to indicate that rail wear increases faster than— or even (as the writer once suggested) as the square of— the degree of curvature ; but this is a purely deceptive appearance, due to the fact that the rate of wear increases as the rails become worn to " fit the flange" (par. 338), and thus expose a greater area to rubbing friction. It is plain that at any given date in a large lot of rails laid at the same time those •on the sharper curves will have fulfilled a greater proportion of their total life, and hence will have begun earlier to wear more rapidly. From a more correct comparison of all the data it appears rather as if both curve resistance and rail wear (and hence fuel consumption) increased more slowly instead of faster than the degree of the curve (par. 311). If so, the total RAIL WEAR caused by 10° of central angle will be less, rather than more, on a 10° curve than on a 1° curve. While this cannot as yet be positively asserted, it may be regarded as certain that the balance is at least even. 864. It may with far more certainty be claimed that the cost of main- tenance OF ROAD-BED AND TRACK is Considerably decreased, per de- gree of central angle, by the use of short radii, because a good portion of It IS nearly constant per 100 feet of curve, regardless of radius, such as the extra cost of lining, maintaining uniform and proper elevation, and the shorter life of ties, in order that they may be capable of sustaining the lateral reaction of the rails, which latter is theoretically (although probably not quite practically) the same on all curves (par. 311). It would be a most liberal estimate to assume that the additional cost per station for maintaining road-bed and track due to curvature increases as the square root of the degree of curvature, making it 3.16 times as much per 100 ft. of line on a 10° curve as on a 1° curve, or making i si ■ ( i • I 640 CHAP. XIX.— THE COST OF SHARP CURVATURE. the additional cost due to A" of central angle compare as 10 on a i'*^ curve to 3.16 on a 10° curve. This entire item is a small one, but so far us it goes it is distinctly favorable to the use of sharp instead of easy- curvature. 855. Figs. 186, 187 are literal copies of diagrams which the writer ^ -^CL a v^ .<^ \ Fig. 187. submitted to two or three of the most thoughtful practical road-masters of his acquaintance for an opinion as to probable comparative main- tenance expenses. The reply of one of them was as follows : •* Assuming a tie to last 8 years on tangent it will last about 6 years on a 10° curve, so as to keep gauge safe, and we will say 7 years on the 5° curve. Then— I'or 10" line— Cost of ties for eight years on looo-ft. tangent, 500 lies at 50 cts. $25000 450 ties on 900 ft. of 10° curve at 50 cts. = $225 for 6 years, = for 8 years, 300 00-I550 00 For 5° line— Cost of ties for 8 years on looft. tangent, 50 ties at 50 cts., 25 00 900 ties for 1800 ft. of 5' curve, at 50 cts. = I450 for 7 years = for 8 years SU 30-|539 3© •• Therefore there is a saving of I10.70 at the end of 8 years in favor of the 5" line, and we may conclude that the maintenance of line and surface will bear the same proportion as ties. "According to this figuring there is a saving of about 2 per cent in main- tenance in taking the 5° line. This is small, and in looking at the two lines in all their bearings I believe the 10° line is the preferable one for maintenance, as on it we get more tangent than curve, while the 5° for ihe same distance is nearly all curve and very little tangent." The fallacy in the first part of this estimate, which was perceived but not located, lies in assuming that a 5° curve will only dimmish the hfe of a tie half as much as a 10° curve: which is hardly so, the flange pres- sure being the same on both. Moreover, the extra work of Iminc and CHAP. XIX.— DISTANCE AND SHARP CURVATURE. 64I surfacing is, still more nearly, so much per lineal foot of curve, regardless of the radius. 856. The wear and tear of wheels and running gear of rolling- stock will naturally follow the same general law as the rail wear, so that it may be considered to vary directly as the degree of curvature, remain- ing constant per degree of central angle. 857. Moreover, tlie total cost of repairs of rolling-stock and track, for those items which are at all liable to be affected by the wear and tear and loss of power on curves, is very small, as thus : Per cent of total expenses. Engines, 19 per cent only of the total cost of repairs appears to vary with curvature and grades (Table 85); 19 per cent of 5.6 per cent (Table 80) _ j q- Cars (Table 86), 23 per cent appears to vary as above; 23 per cent of lo.o per cent (Table 80), _ ^ ^ Rails, say 50 per cent of 2.0 per cent, = j qo /'k^/, say 10 per cent of 7.6 per cent, = 0.76 A total per cent of only 5.13 Thus only about 5 per cent of the total operating expenses is likely to be affected at all by curvature, and a good part of that only slightly, and a good part of what remains by sharp and easy curvature of equal amount nearly equally. 858. It is also to be remembered that sharp curves lengthen short tangents, as is clearly brought out by Figs. 186, 187— an advantage which facilitates what would otherwise be impossible, the use of easy transition curves (see Index), and hence may be made to greatly decrease the unavoidable shock in entering and leaving curves. 859. The effect of a change of radius on the total length of the LINE, although apparently pertinent, has no real bearing on this ques- tion. The use of sharp curvature always increases the length of the line between the same tangents by the amount aa. Fig. 187, and has besides a marked further tendency both to increase the length of the line and to increase the degrees of central angle, because of the differences of loca- tion which naturally result. But the disadvantage of this extra length and curvature is a matter for separate estimation, because it is not an essential and unavoidable feature of a mere change of radius, and hence does not directly, although it commonly will indirectly, affect the deci- sion in favor of using easy curvature. In fact, although it rarely occur* in practice, it is not in the nature of things impossible, that the use of a 41 ' 1 'If -^:^ 642 CHAP. XIX.— DISTANCE AND SHARP CURVATURE, shorter radius should result in a decrease of both distance and degrees of central anoxic. On a small scale it very frequently does so, in the man- ner outlined in Fig. 188. Fig. 188. 860. On the other hand, it may well happen that the adoption of a location adapted to short radii would double the amount of curvature, and that the estimated cost of this would be more than the estimated saving on construction. In that case the short radii would not be used, but they would be abandoned, not because of the sharpness of the curv- ature, but because there was so much of it. Fig. 189. 861. The loss or gain in distance by connecting any two given tangents with one curve instead of another, Fig. 189, may be very simply determined as follows: To DETERMINE THE DIFFERENCE IN LENGTH OF LINE via ANY TWO CURVES OF DIFFERENT RADII, CONNECTING THE SAME TANGENTS: Let / = length of longer curve, of D" , with tangents T\ /' = (« shorter «< j)> T\ CHAP, XIX.— DISTANCE AND SHARP CURVATURE. 643 Then geometrically 77 = ~ = ~. if we assume, as for all practical pur- poses we may,-if curves of over 8° or 10° are run in with 50-foot chords -that the degree of curvature is directly as the radius. Then/'=|,/and7- = |,7', '-r' = (] D D' )r. Letting Z _ the length via any one of the sharper curves shown in Fig i8q from tangent-point to tangent-point of any curve of longer radius (from T to 2 ) we have Z-. = ..(.--)_(,_-), = {2T-l) D-D D' But the value of 2 7^ - / for a Z>° curve is to its value for a i» curve as --. Consequently, tabulating {2T - i) for a 1° curve, we have as the differencf in ilie length of the line via any two curves of D and D' degrees, connecting the same •tangents : = tabular number X — X — — — D D' D' — D = tabular number X D'D . u 1 , difference = tabular number X -~;^^ of the two degrees of curvature, 862. Table 187 gives such a tabulation for angles differing by 1° up to 130". The •• tabular number" is simply the difference between the length of a i' curve of any given central angle and the lengths of its tangents. It is there- iore given for any angle whatever by the formula 7^= tan i/X 5730 X 2 - ioo7; '" ^h'ch T- tabular number for Table 187, / = intersection angle in degrees. The problem is rarely one of practical importance, since two curves of con- siderable difference in radius rarely connect the same tangents, but is some- times convenient for determining the effect of minute changes. For the two curves shown in Figs. 186, 187, we have— Tab. no. for 90" (Table iS;) = 2459.3 x A (~4) = 246 feet loss of distance ty the :o° curve. '«)X5' 644 CHAP. XIX.— THE LIMIT OF MAXIMUM CURVATURE. Table 187. Difference in Length of Line vid any Two Curves of Different Radii, connecting the same Tangents. [To determine the required difference, multiply the tabular number below, corresponding difference to the given central angle by the product of the two degrees of curvature.] 1 2 3 4 5 6 7 8 9 o» 0.00 0.00 0.02 0.08 0.16 0.32 0.56 0.88 1.32 1.86 io» 2.56 3-40 442 5-62 7.02 8.64 10.50 12.60 14.98 17. 6a 20» 20.6 23.8 27-4 3«-4 35-8 40.4 45-6 5x2 57-2 63.6 30' 70.6 78.0 86 94.2 103.4 113.2 123.4 134-2 145-8 158.0 40« 170.8 184.4 198.8 214.0 229.8 246.6 264.2 282.6 302.0 322.4 5o» 343-6 365-8 389.0 4x3-4 438.8 465 -4 493-0 521.8 552.0 583-4 60° 616.0 650.0 685.4 722.2 760.6 800.4 841.8 884.8 929.4 975-8 7o« 1023 . 8 1073.8 1125.6 1179.4 1235.2 1293.0 »353-o 1415-2 1479.6 1546 4 8o» 1615.4 1687.2 1761.4 1838.4 1918.0 2006.0 2086.0 2174.4 2266.2 2361.0 9o<> 2459-4 2561.0 2666.4 2775-6 2888.6 3005.6 3126.8 3252.4 3382.4 3517.3 loo» 3656-4 3801.2 3951-0 4106.4 4267.2 4434-0 4607.0 4786.4 4972.4 5165.4 no" 5365-6 5573-4 5789.2 6013.2 6245.8 6487.6 6738.8 6999.8 7271.4 7554 iao» 7848.0 This table is not correct to the nearest tenth, but only to the nearest even two-tenths. As a certain small fraction only of the tabular number is to be taken, the error was not deemed of enough moment to require recomputation. The table gives merely the differ- ence between the length of the two tangents to a i» Curve and the length of its arc, for any given central angle. 863i Precisely this same method of analysis will enable us to determine at once the difference between the radius, long chord, middle ordinate, tangent, or any other function of any two similar curves if we know the value of the same function for a similar 1° curve. Thus the difference between the radii of a 5" and 10° curve is 10-5 5730 X and between a 7" and 8°, 5730 X 10 X 5 8-7 = 573.0 feet; T_ _ 5730 8X7" 56 = 102.3 feet. 864. From all the considerations which have been suggested together we may perhaps assume that the inherent cost of curv- ature per train-mile is independent of the radius, or at least does not increase appreciably with the sharpness of the curve, and this- CHAP. XIX .— LIMITING EFFECT OF CURVATURE. 645 view simplifies a decision as to the limit of radius. But whether this view be entirely, correct or not is a matter of perfect indiffer- ence for deciding the problem immediately before us, as it is hoped has been made perfectly clear. Dismissing, therefore, from our minds this confusing and irrel- evant question, we will now confine our attention exclusively to the LIMITING EFFECT of cuivature as the only cause which justi- fies the fixing of any arbitrary limit whatever to the sharpness of curves. THE LIMITING EFFECT OF CURVATURE. 865. Curvature may have a limiting effect in three ways : 1. It may forbid the use of certain types or weights of en- gines, or so impede it as to make it practically inexpedient The extent to which this cause does or may operate has been already considered (par. 285 et seq.) and found to be small. 2. It may impede the running of trains at high speeds by the necessity of frequently checking speed or maintaining a low rate of speed for considerable distances when the intervals between the sharper curves are small. 3. It may compel the hauling of shorter trains by its addition to curve resistance. The second cause has been already considered from the me- chanical side (in par. 268 et seq.) and found to appreciably affect passenger trains alone. 866. As a business question, the effect which we there saw sharp curves to have on tiie safe speed shows their use to be on many roads of heavy passenger traffic a consideration of extreme importance, justifying and requiring an extremelv low limit of curvature. Nevertheless, under average conditions, the same tacts show it to be one of minor importance. 867. It depends chiefly on a road of any given character on the amount and disposition of the sharp curvature. Thus on the ele- vated railways of New York, with, perhaps, the heaviest passen- ger traffic in the world, a few excessively sharp curves are used such as those shown in Figs. 189, 190, 191. These are not found ' ■»' CHAP. XIX.—LIMITING EFFECT OF CURVATURE. HI Fig. 189.-RHVERSED Curves of 90 Feet Minimum Radius for Turning Right Angles ok Manhattan Railway, Sixth Ave. Line. There are four rig:ht-ang:led turns on the Sixth Avenue line similar in substance to Fig. 189. In order to be able to turn within the stfeet limits short reversed curves were introduced, making the total of the central angles 134° 34', or 44» 34' over the necessary right angle. The dotted curve of 200 feet radius (or about 29° instead of 63°), shows with how little encroachment on private property the radius could be more than doubled. In Fig. 190 the dotted alignment would save 212° 30' - i44» = 68° 30', besides nearly- doubling the radius. About 800 trains per day pass around these curves. The shortest interval or " headway" between trains is only 9i minute on the Third Avenue line and \\^ minutes on the Sixth Avenue line, during the busiest hours. Counting both curves to- gether, more than one third as many passengers pass over them per year as ther? are who enter all the trains of all the 125,000 miles of railway in the United States. The gross earnings /i-r mile mount up to $230,000, and the operating expenses to $125,000. The property on the corners which is cut by the dotted curves is in no case particularly valuable, and $20,000 or $30,000 would have been the greatest net loss which would be likely to result from substituting any one of the dotted curves for the constructed curve. No accidents of any kind have happened on any of these sharp curves since the roads were opened in 1878. The curves are of standard gauge, and the cars are about 48 feet long. Their draw- bars go from truck to truck, and not between the car-bodies. CHAP. XIX.~LIMITING EFFECT OF CURVATURE. 647 : H J] Fig. X90.-REVERSED Curves of no Feet Radius on Manhattan Eletated Railway Third Ave. Line. """'f Line oF Unifor/n Speed. y_ 1.414. i^ !>. ?^_ _ Pi^T/f /fiL'^i —Speedl — , . i— -^<^^^t^gfo' - I I Slowinffhp I Increasinrr Speed, Fig. Xgi.-lLLUSTRATING THE EFFECT OF LONGER RaDIUS ON COMPARATIVE SpBED. .i^. 648 CHAP. XIX.— LIMITING EFFECT OF CURVATURE, to be a measurable disadvantage as respects limiting speed (for if they were, a few thousand dollars would take them out), be- cause, although every moment of lost time is of great import- ance, the speed between tlie frequent stops is slow (not over 30 miles per hour) and the motive-power between stations (because of the frequency of stops) abundant. Therefore the speed is checked to a safe limit almost instantaneously on approaching the curve, and resumed again on passing it almost as quickly, and the total loss per curve does not exceed 20 to 30 seconds for each curve; only a small of part which ( .— or 39. 3 per cent, on curve and ^ or 50 per cent in approaching and leaving the curve, as a brief analysis, which the student should make, will show) could be saved by doubling the radius of curvature. Fig. 192 and Table 107, page 273, will indicate the method of determin- ing this. 868. If, however, there were many of these curves, the loss of time would not only increase pari passu^ but, by frittering away the time and nervous energy of the engineman, obstructing his view ahead, and similar indirect causes, cause a still further de- crease in the practicable speed, and likewise decrease the admis- sible frequency of trains, thus causing an unwarranted loss, if any ordinary expenditure would avoid it. As the line now stands, an avoidance of all curves on the line would have a con- siderable money value, but to simply double the radius would be worth little or nothing — as is sufficiently evidenced by Figs. 189- 190. The management is not unintelligent nor unduly parsi- monious, but it is not thought of, simply because it would not pay- 869. So on the various railway lines connecting Boston, New York, Philadelphia, Baltimore, and Washington. The value of avoiding any considerable amount of curvature, and especially curvature sharper than 3" or 4°, is to be measured only by a vast sum, under the growing business advantage of very fast trains. Its existence in large amounts would make quick time impossi- ble ; but the same is not at all true of a small amount of curva- ture at some one point, even of very short radius, for reducing CHAP. XIX^-LIMITING EFFECT OF CURVATURE. 649 speed for one tnile only from 60 to 30 miles per hour means only the loss of li to 2 minutes time (Table 183). The justifiable ex- penditure to avoid it would certainly be far less than one tenth of what would be justifiable on the same line to avoid ten times ^s much curvature and delay, both because (i) more than ten limes as much time would be lost thereby, and because (2), even if not, the loss would be more than ten times as injurious. ' Two minutes more time between New York and Philadelphia might not place a competing line under measurable disadvantage. Twenty minutes would not simply decrease, but destroy its chance for competition on equal terms. 870. When we come to long trips, of 500 to 1000 miles, we have already (par. 240) seen that any probable loss of time which is remediable by any expenditure within bounds for easing curv- ature is not likely to have any effect whatever, measurable in dol- lars and cents, upon competitive equality. The most trifling differences in neatness of stations and equipment, courtesy of em- ployees, character of "lunch counters," etc., would be far more important for that purpose, as well as far more cheaply obtained. 871. The true principle in regard to this matter w^uld there- fore seem to be: To estimate the total loss of time which is likely to result, on a given line, from the location naturally re- sulting from one radius of curvature instead of another, and the probable money value of so much competitive business as is likely to be lost on account of this loss of time. While this is an exceedingly delicate and difficult matter to estimate even approx- imately, and an impossible one to determine with exactness, vet (par. 21) "what we can do is to fix a maximum and minimum limit, somewhere within which lies the truth and anywhere out- side of which lies a certainty of error. Due judgment and cau- tion require that we should do so." 872. As a general rule, the limiting line between the traffic to which every minute is and is not important lies at the point where It ceases to be possible to make a round trip in a day, with some time to spare at destination. For distances under 100 or 150 miles this is possible, as for instance between New York and i: 650 CHAP. XIX.— LIMITING EFFECT OF CURVATURE. Philadelphia, and time is valued greatly. For longer distances,, as from New York to Boston, this is not possible, and fast trains^ are not run, nor are they likely to be until over 50 miles per hour can be made, when there will be demand for several daily. Be- tween New York and Chicago, until it finally appeared possible to shorten up the time to 24 hours, quicker time than 36 hours- was not important, and was not made. To St. Louis, which is only 200 to 250 miles further from New York than Chicago, or some 20 per cent, the time is still eight or ten hours longer, for the same reason. The effect of sharp curvature on safety and the comfort of travellers is con- sidered in Chap. VIII., pars. 247 and 279. 873. We will now analyze the extent to which the third and chief cause for limiting effect from curvature operates — that it may compel the hauling of shorter trains by its addition to the train resistance : We have on the tangent maximum grade, whatever it may be, two» resistances to overcome : 1. The ordinary rolling-friction. 2. The resistance of gravity — a known and constant quantity. In the case of curvature on a level we have also two resistances : 1. The ordinary rolling-friction, as before. 2. All additional resistance which may or can arise from the curve. In either case, it is evident that the resistance from the rolling-fric- tion proper, being the same in any case, whatever its amount may be, may be entirely neglected. In any case, also, it is obvious that the grade on any curve may be reduced to a level, if desired, so as to eliminate all grade resistance. 874. The normal rolling-friction being eliminated, what we require, in order to determine the proper limit of maximum curvature so far as length of train is concerned, i.e., the point at which a LIMITING EFFECT begins, or should begin on a properly laid out line, is simply the curve on which, in all cases and under the most utifavorable circumstances, the same engine can haul the same train on a level as it can haul on a tangent up the maximum grade. It is not sufficient to determine merely the curve on which there will probably be no greater resistance on a level than on the tangent maxi- mum grade, nor the curve on which, under average or favorable condi- tions, there will be no limiting effect. When there is even a possibility that under any circumstances whatever, exceptional or unexceptional. CHAP. XIX.— LIMITING EFFECT OF CURVATURE. 65 1 the resistances on a level maximum curve may exceed the known and invariable effect of gravity on the actual tangent maximum grade, that curve is in a sense a limiting curve, because there is a certain disadvan- tage in even the possibility that curvature may at times limit the trains in advance of gradients, and hence a certain money value in avoiding it. 875. Viewed from this standpoint, with our existing experimental knowledge of curve resistance, all that can safely be assumed is that an allowance of 2 lbs. per ton per degree of curvature is none too great to cover the highest possible curve resistance at very low speeds, with well- worn rails and long trains of empty cars, especially on easy curves. So high a curve resistance is. we may be very certain, rarely reached in practice, but that it is sometimes reached is at least possible. On the other hand, the very lowest limit for the resistance on ordi- nary railway curvature, under the most favorable circumstances, at high speeds and with new rails, is probably about (somewhat less than) \ lb. per degree of curvature, falling on the very sharpest curves, such as on the elevated railways of New York, to something less than \ lb. per ton per degree ; but the latter curves are out of the range of ordinary expe- rience. 876. The assumed 2 lbs. per ton of train resistance is equivalent to o.i per cent of grade, and o. 5 lb. to 0.025 per cent of grade. Multiplying the former, therefore, by the degree of any curve, gives a rate of maxi- mum grade which will certainly oppose more resistance to all trains under all circumstances than the given curve will on a level, while mul- tiplying the latter by the degree of curve, in the same way. will give a rate of maximum grade which will certainly not oppose more resistance to any train under any circumstances than will the curve, and hence the latter will be, in the fullest sense, a " limiting" curve. In between these limits sometimes the curve and sometimes the grade may offer the maximum resistance. 877. From the above simple data we may construct the following Table 188, showing the proper limits of practice in respect to maximum curvature : Table 188 assumes that the most which can possibly be done to elim- inate curve resistance is to reduce the grade to a level, which is the case with an evenly balanced traffic and with long stretches of level or undu- latmg gradients having a great deal of curvature. It is evident, how- ever, that under the three following conditions, at least, this is not the case, and hence that the table will not then apply: Mk. .652 CHAP. XIX.— LIMITING EFFECT OF CURVATURE, CHAP. XIX.— LIMITING EFFECT OF CURVATURE. 653; Table 188. Maximum and Minimum Limits for the Degrees of Limiting Curvature ON Various Grades. [Being the degrees of the curves which certainly will and certainly will not cause a greater resistance on a level than a given tangent rate of maximum grade. Subject to the limitations of pars. 878 et seq.\ Tangent M AxiMUM Grade. Degree of Maximum Curve on a Level which will which certainly will have a limiting effect on all Per Cent. Feet Per Mile. certainly have no limiting effect on any train under trains under all any circumstances. circumstances. O.X 5.28 1° 4" 0.2 10.56 2" 8** 0.3 15.84 tT 12* 0.4 21.12 4' i6' 0.5 26.40 5" ao* 0.6 31.68 6' 24' 0.7 36.96 7' • « • 0.8 42.24 8" • • • 0.9 47.52 9' • • • I.O 52.80 lO" • • • etc. etc. etc. _ Fig. 19a. 878. I. On a long maximum grade, of any considerable rate, we can, if necessary, not only reduce it to a level, but break the grade to a de- scent, as at BB\ Fig. 192, and in this way completely eliminate the limiting effect of the curve resistance of any curve, however sharp ; for we have to consider trains in one direction only. To descending trains the break of grade can (ordinarily) do no harm. On such a grade, therefore, there is no reason why any curve whatever should not be used, so far as the limiting effect of its resistance is con- cerned, and the other two causes alone (par. 865) justify fixing a limit of radius. 2. When the grade is level or slightly undulating for a considerable distance, and the percentage of curvature is not too great, some little assistance at least from momentum may be relied on, to eliminate a por- tion of the resistance of very sharp curves. 3. When the burden of traffic is heavily in one direction, as in min- •eral traffic, even with nearly level grades and with no assistance from momentum, quite sharp curves can be used wherever the necessary com- pensation to equalize the curve resistance for trains moving in one direc^ Hon can be made, because the loaded trains return light with a surplus of motive-power. * 879. Summarizing our conclusions as to limit of maximum curvature, we have found: * 1. That there is rarely (although there is sometimes) real difficulty in using engines of any desired power, of types approxi- mate for efficient service, on any probable alignment, and (par. 285) that on curves below 10° or 12° there is no difficulty what- ever. 2. That those railways are the exception (although they do exist) on which any probable loss of time from the necessity of slowing up at sharp curves will be a matter of much financial importance, and that the gain in this respect by any modifica- tion of curvature ordinarily possible is much less than is sup- posed. 3. That all danger of limiting effect upon the weight of trains from sharp curvature, within the limits specified in Table 188,. can ordinarily be avoided, and that these limits afford sufficient range for using those curves which best fit the ground under all ordinary topographical conditions. 4. That the difference in danger of accident which is liable- to result from any modifications of curvature ordinarily possible is too small for estimation, as an element justifying additional, expenditure. 5. That the effect of any difference of radius on the expenses^ due to wear and tear and consumption of fuel per train-mile, the degrees of central angle remaining the same, is probably either nil Qv in favor of sharp radii; but that whether this be so or not (par. 252) is a question which should be allowed no weight what- ever in fixing on a limit of radius. 6. That the effect of shorter radii, if they have any, to lengthen the line or increase the degrees of central angle, or ^ both, through the different location which naturally results, is likewise a matter which does not directly affect the question,, although it often may indirectly. 880. We may likewise close, as we began, with another very- important conclusion: ' 1" 654 CHAP. XIX.— LIMITING EFFECT OF CURVATURE. CHAP. XIX.— LIMITING EFFECT OF CURVATURE. 655 7. That the natural tendency of inexperienced engineers is to go to extremes in the matter of curvature, either spending too much money to obtain easy curvature^ or^ when convinced that that is impolitic, going to the other extreme, introducing recklessly more and sharper curvature than there is any real necessity for ; in both cases alike failing to perceive and utilize to the utmost the topographical possibilities, 881. It may at first sight appear to follow from the aggregate of this summary that there is little reason to fix any minimum limit whatever to the radius of curvature except the physical limit of the capacity of the locomotive, and this is so far correct that it is entirely indefensible to start out upon surveys with .a limit determined in advance, or to adhere to a limit at every point because at all but one or two points there is little difficulty in so doing. If at such exceptional points a large expenditure is necessary to adhere to it, the expenditure should not be made without a correspondingly good reason. In such a case we are justified in making a moderate additional expenditure for the mere sake of a uniformity which may prove advantageous for operating certain engines or for certain high speeds; but it should in general be a very moderate one. 882. In view of the ever-present danger of overloading the capital account of new enterprises, the better course in such cases is to build a light bold line for a sliort distance, laid out with the idea that it may be subsequently improved if desired, and if means exist for doing it, in the manner elsewhere dis- cussed (par. 283 et al.). Nevertheless, it is not true that the conclusions summarized above do not warrant, under all ordinary circumstances, the maintenance of a reasonable and moderate limit of curvature ; considerably more favorable, if their spirit be closely adhered to, than has been adopted without adequate necessity on many lines. For, although each of the conclusions specified, taken separately, does not warrant the fixing of arbitrary limits to be adhered to at large expense, yet they do in the aggregate indi- cate, as common-sense also indicates, that reasonably easy curva- ture is a matter of much absolute although possibly of small rela- tive importance. 883. The true conclusions to be drawn may perhaps be better put in this way : 8. That A standard harmonizing with the natural topo- ORAPHICAL characteristics AND READILY ADAPTABLE TO THEM is the only right and proper one, until the topography becomes so rugged that the physical limit of the capacity of the locomo- tive, of the class and at the speeds practically required, begins to be approached. This is true both in letter and in spirit, and should be rigidly adhered to. When so adhered to it will rarely cause embarrassment, for there is usually a certain natural limit of radius which can be obtained without much difficulty or expense, and except in extremely rugged mountainous regions this limit will rarely be a high one. This implies that the limit should be varied from point to point along the line, as the general character of the topography varies, and the sharp curvature, so far as possible, bunched. 884. In proportion as the natural limit of radius is favorable the justifiable expenditure to obtain a still more favorable limit decreases rapidly, and it can never be amiss to bear in mind that there is no case on record where a railway has been brought to bankruptcy by the expenses resulting from sharp curvature, nor is there any likelihood that there ever will be such a case, while the instances are many where companies have been bankrupted by their expenditures to obtain easy curvature. Hence, since the money of even the richest corporations is limited, and in the case of new roads almost always more limited in proportion to its»needs than its over-sanguine projectors have any idea of, true wisdom requires that the available capital should first be devoted to the really important ends — getting close to and well into the large towns, getting suitable terminal facilities, getting low grades, building what is built well, protecting the public and the railway company at once from danger and loss by proper inter- locking apparatus at grade crossings, or by under- and over-cross- ings, rather than by expenditures for some fanciful standard ot curvature, which probably makes the largest addition to the cost of construction of any detail and (for any change within the I \.\\ ^ ( 656 CHAP. XIX.— LIMITING EFFECT OF CURVATURE. power of the engineer at any cost whatever) the smallest additioa to either the safety or economy of operation. 885. The argument in favor of adapting curvature to the nat- ural topography of the country is greatly strengthened by the fact that sharp curves frequently, if not universally, render pos- sible LOWER RULING GRADIENTS IN DIFFICULT COUNTRY and often permit the use of otlierwise favorable routes wliich, witiiout this concession to natural conditions, would be wholly impracticable. The writer could readily mention a number of important in- stances of the kind from his own experience. 886. But because other ends are more important, this is not therefore unimportant. Becauseit is unjustifiable to expend any- large proportion of the available capital for this end, it does not, follow that a very large proportion of the time given to surveys should not be devoted to it. Almost invariably it should be, and the engineer who finds himself in rough country devoting little thought and time to saving every degree of curvature possible may be tolerably sure that he has fallen into that most danger- ous fault — blindness to its undoubted and great disadvantages. 887. It is so important that the proper course in respect to fixing ar- bitrary limits of curvature should be so plain as to be fully understood, that we may profitably add a word as to the specific manner in which these conclusions are frequently violated, and the error in doing so. Many thousands of miles on this and other continents have been built on standards of grades and curvature closely approximating to this : 1. No grade shall under any circumstances exceed 60 ft. per mile. 2. No curve shall under any circumstances exceed 6". But, 3. These limits may be freely used in combination with each other; i.e., 6° curves may be inserted in unreduced 6o-ft. grades. This precise standard has been perhaps more used in this country than any other one combination. It was used on the Erie, the Cincinnati Southern, the Chesapeake & Ohio, the Blue Ridge of South Carolina, and a long list of other roads of less engineering pretensions ; having been copied from one to another, apparently, without much regard to topo- graphical requirements — perhaps because the round fij^ures and the al- literation of the 6's had a certain charm. Far less defensible combina- tions have been the rule throughout the vast expanse of the Mississippi Valley from the causes alluded to on page 6 — such as 2° or 3" or 4" limits. CHAP. XIX.— LIMITING EFFECT OF CURVATURE. 657 of curvature with 40 to 80 ft. grades (0.8 to 1.5 per cent); but it should be added that in general the topography favors long radii, and the chief error has been, not the radius of curvature, but the reckless sacrifices of gradi- ents to save degrees of central angle. 888. We have already determined (par. 825) that the use of unreduced curvature on a maximum grade is never defensible. Except that it has been done in such repeated instances and on so large a scale, it would seem incredible that any one could spend large sums of money to keep curva- ture down to 6°, and grades down to 60 ft. per mile, and yet pile one upon the other freely, giving in effect a 75-ft. grade. We may more clearly see the folly of it by an example from humble life. Suppose some plain coun- try farmer should find that his team could just draw him up a steep hill through mud a foot deep, and should forthwith draw two conclusions— that it could not draw him up any steeper hill without any mud, nor through any deeper mud without any hill : should we not think the man less intelligent than the beasts he drove } Yet this is precisely what has been done, and to some extent is still done, on thousands of miles the world over, by engineers of standing. 889. Passing this error as no longer likely to be committed, let us consider the propriety and effect of the joint standard of 60 ft. per mile and REDUCED 6° curves maxima: A 60 ft. per mile grade is 1.14 per cent. If we may use 6° curves on such grades by reducing them to 0.96 or 0.84 per cent (0.03 to 0.05 per cent per degree compenstion), which is the largest compensation used by those who adopt such standards, why should we not feel free to use some sharper curves with more compensation, or on a dead level, if we can thereby save some money to put where it will do more good } 890. The answer can only be one of four reasons : 1. A 7° or 8° or 10° curve of equal angular length will be so much more costly in wear and tear, that on no single curve can the saving m cost for construction pay for the loss therefrom. Or, 2. A few such curves, even if fully compensated, will in some unex- plained way so limit trains that the same engine cannot do the same work. Or, 3. They will cause such loss of time from slowing up (and certainlv require slowing up) that a loss of speed involving greater loss of traffic than the value of any possible saving will result. Or, 4- They are so exceedingly unsafe to operate, compared with a 6°, that in no case can the additional danger therefrom be repaid by an ade- quate economy m construction. 42 I I 658 CHAP. XIX.-^LIMITING EFFECT OF CURVATURE. 891. There is no escape from accepting one or more horns of this double dilemma if such a standard is to be justified at all ; and probably no man would have the hardihood to attempt to maintain any one of them for explicit reasons given. It is not thus that such utter and evident blunders as this — which simply to state their nature clearly is to con- demn — have come about ; but rather by the vague process of jumping at conclusions outlined in par. 245 — that "the Railway is to be first- class ;" that " nothing over 6° curvature is generally considered first- class ;" ergo, etc. etc. The fact that most of the great trunk lines have 8* to 10° curves (Table 116), and that the lines which have set up such purely arbitrary standards have been to a very large extent lines of a secondary class, increases the obviousness of the error committed. CHAP. XX.— CHOICE OF GRADIENTS. 659 CHAPTER XX. THE CHOICE OF GRADIENTS, AND DEVICES FOR REDUCING THEM. 892. We have seen clearly enough in preceding chapters that the gradients are the one thing among the purely engineering details on which the engineer should concentrate his attention, subordinating them only to the end of reaching the sources o traflic, if even to that. We have seen also, in Chap. XVII., that the use of assistant engmes for short distances with low ruling grades elsewhere, is generally preferable to a uniform through grade, both topo- graphically and financially; for the reason that, do the best we can, a uniform grade must usually approximate pretty closely to the rate of the pusher grade if it passes over the same summit and by adopting it we throw away the advantage of the low grades on all the rest of the line, which may be had, as it were, for nothing. 893. Having recognized these abstract truths, however, the next thing IS to apply them, and here we pass beyond the point where specific instructions can be easily given, since the circum- stances will vary on every line. A great part of the danger of error has been overcome when the comparative importance of he various details has been realized, but even with that advan- tage the inexperienced engineer is almost certain to conclude that a certain grade is the lowest attainable, when with longer practice or more skill, or harder work, or less self-confidence he would readily obtain grades a third or a half lower at the same cost, and not unfrequently at less cost. .nl.ff' ^^^'u ''; '''^"'^^«'' ""«' g-^neral rule, which directly re- annfirK,'' ..'"■'"''''' ""'^ ^^'''^'' ~"'«^ ^° "««^ to being an nfallible guide for the correct projection of lines in the fielf om > ^ 7 ; ^"^'""'' '''°"''^ ^°"°^ " ^'"^"y. deviating "om It only for very good reason, viz.: ^ : I \ I 66o CHAP. XX.— HOW TO PROJECT LOW GRADES. Follow that route which affords the easiest possible grades for THE LONGEST POSSIBLE DISTANCES, using to that end such amounts of distance, curvature, and rise and fall as may be necessary, and then pass OVER THE intervening DISTANCES ON SUCH GRADES AS ARE THEN FOUND NECESSARY. This law is to be applied with intelligence and not pushed too far, but so far as there can be said to be any universal and fundamental law for location, this is such a law. 895. When the higher grades are in danger of exceeding 2 per cent or 2\ per cent, it is to be accepted only with great cau- tion, and anything beyond 3 per cent will be probably bad prac- tice, except in very mountainous country. As a line falls below 100 miles in length the economy of using pushers decreases, and the practical advantage of a uniform gradient increases. Accepting this general rule as an axiom, our problem then divides itself into two parts: 1. How to obtain the lowest possible low grades. 2. What to do as to the rates of the high grades. HOW TO PROJECT LOW GRADES. 896. Considering only a naturally low-grade country with no long- continued ascents to encounter, but only a more or less rolling topog- raphy, three fourths of almost every line, or of the part thereof lying in such low country, will naturally admit of an extremely low gradient, if some considerable lateral deviations to throw the line into a generally favorable country are considered admissible, as they ought to be, so that such alternates between any two points as those sketched to a rude scale in Fig. 193 are considered as prima facie equally eli- gible. To obtain the same grades on the remaining fourth will often involve some disagreeable sacrifices, especially when, as so often in the Western States, we can take an air-line by accepting i per cent or \\ per cent grades, if we are foolish enough to do so. These disagreeable sacrifices, however, ought ordinarily to be met, even to the extent of doubling the distance on one quarter of the line if we can thereby reduce the grades to half as high a rate. We shall then CHAP. XX.-HOW TO PROJECT LOW GRADES. 661 simply have a line 11 2i miles long with 0.5 per cent grades, as against a line 100 m.les long with i.o per cent grades. The former is immensely preferable from every point of view. But usually a smaller sacrifice will make a greater gain. 897. Let us consider, for example, the case of a long, low ridge or swell m a generally flat country, wliich cannot be run around at all, by ,^ any device, since it continues indefinitely. Assume Bv^ this swell to be three miles across and 50 feet high \ by the grade-line, after making as large cuts and %^^ fills as seem expedient at A, B, C, and D, Fig. 194. A tangent over this ridge will give the profile shown in Fig 195, with two miles of i per cent grade and a mile of level interven- ing. The exaggerated vertical scale makes ■P, « ^'°- '95. i-LAN AND Profile of a Break in a Long Tangent to pass over a Long, Low R.dgb in Flat Country. the rise seem considerable, but on the ground it will be hardly percep- tible to the eye as an objectionable feature to the railway line. ^ This is especially likely to be the case because the ground approach- ing such a rise will not ordinarily be on a dead level, but is more likely 662 CHAP. XX.— HOW TO PROJECT LOW GRADES. to have about half as steep a rise, perhaps for a long distance back, giv- ing a long 0.5 grade approaching the ridge. This we will assume to be the case, as also that except for this swell, and a few others like it, the 0.5 grade might be the maximum of the whole line. Such conditions have existed on thousands of miles. 898. Now to the eye of a country farmer, and to the eye of many an engineer, perhaps, who may inspect the line during construction, as it runs over the surface of an apparently flat cornfield, this whole region will seem practically a dead level. In the first place, the long o.s^'ap-^ proach will invariably be taken by the eye to be a level, or perhaps even (by well-known optical illusion) a slight descent. This at least takes off a full half of the apparent vertical angle, and hence of the apparent height of the ridge; and, more probably, there will seem to be a slight dip of the ground toward the ridge and merely a corresponding rise be- yond it. In the second place, even if the approach were a dead level, a rise of only i per cent in a natural surface seems to the eye a very small thing, especially before the track is laid, so that it would seem ridiculous to turn four right angles " for nothing" and lose two or three miles of distance, at the cost of four such ugly curves through the cornfields as are shown in Fig. 194. 899. Nevertheless, under all the given circumstances, THAT is pre- cisely THE THING TO DO. The Very fact of the long 0.5 approach, which diminishes the visible necessity, makes it the more essential to do so, because it forbids us to resort to the assistance of momentum to sur- mount the ridge, which otherwise, by approaching the foot of it at 30 miles per hour and reaching the top at 10, would take off (Table 118) 31-95 - 3-55= 28.40 vertical feet, and give us, out of our i per cent grade, a virtual profile of 0.5 per cent, with something to spare. 900. On arriving at the pointy^, therefore, even if it be with a 30- mile tangent which might be continued for 30 miles more by running straight over the ridge, a sharp turn to the right of something over 60* should be made in the fiat cornfield, on about a 3' curve, for the sole purpose of lengthening out the one-mile ascent into two miles, so as to give half the grade. To start the curve A farther back, as shown by the dotted line A', so as to diminish the central angle, would do no good, but rather destroy the very purpose of the curve, which is xo gain dis- tance between A and B and not to reach B'. When the line reaches B\ another curve of 60° + , in another corn- field, brings it back again parallel with itself, but nearly two miles off. In a mile more, a third curve of 60°+ enables it to descend the ridge on the 0.5 maximum by losing another mile of distance, and at D another <^^-^^» XX.-HOW TO PROJECT LOW GRADES. 663 curve of 60° + brings it back to its proper position ; giving in all 2 miles mterpolatea distance in a distance of 3 miles. 250° of curvature wher^ before there was none, and-what would sometimes be the hardest blow of all-utterly runnng the 60-mile tangent which had been run in ex^ actly straight by foresights only ; and all for the sake of obtaining a line so ugly that numerous fingers of scorn may well be pointed at it 901. And, no doubt, the same end might ordinarily be accomplished in such a case m some more pleasing and economical fashion , as bv dot^liie^^^^^^^^ ""^'^^ ^" ^"^»^ --"- ^^atthe dotted Ime C B" Fig. 194. m.ght be used for the descent, so as to utilize most of the otherwise waste distance. Or. by going further back and swmgmg the Ime at this point loor 2omiles to the north or south, beuer ground may be obtained with less aggregate loss of distance (Fig. 10,) than on this three miles alone. The instance has purposely been made somewhat extreme in this respect to enforce the principle. But in an! other sense it is not extreme. If none of these things can be done to ad- vantage. IF there is nothing to be gained by deviating from an air-line be- tweentwopo.nts ioomilesapart,andiFthis air-line will admit of o.5grades each way except for one or two or three or five or six such ridges as that described, then, as between the air-line AD, which will give a surface-line hundred-mile tangent on i per cent grades and six breaks like AB'CD F'g. 194, which will introduce 1500° of curvature and lose 12 miles of distance, and break the hundred-mile tangent into five-and-twentv pieces but give 05 percent grades-the ugly and crooked line is beyond a^l possibility of question in every instance the line to take, as of ve'ry much- greater operating value, unless the line be an exception to most Ameri- can roads, by having a preponderance of passenger traffic, which is both large and competitive. Almost every general principle connected with laying out railways admits of more or less doubt, and requires exceptions lliis particular example admits of no doubt and requires no exceptions.' 902. For, computing the values of the losses and gains, we have- Yearly saving by avoiding an increase of 0.5 per cent in a 0.5 grade, by Table 178, per daily tram, $4,300 x 5 = f . . . ft2i coo 00 Per contra : .... ?>2 1,500 00 Cost of 1500° of curvature by Table 115, per daily train. $0,433 X 1500= $640 co ^ostof 12 miles of distance, by Table 89. per dailv tram, $290x12= \ ZA^o oc^ 4,12950 Difference, being excess of value of the low grade- " line, with six such breaks of tangent as is' shown in Figs. 194, K)^, per daily train, .... $17370 50 HI 664 ff CH^P- XX.— I/O IV TO PROJECT LOW GRADES. This IS equivalent to the addition of a capital sum of nearly $350,000 (at S per cent) to the value of the property, or $3500 per mile, per da.fy tra.„. For en daily trams each way the line will pay interest on $,5,000 per mile larger valuation. '^ Tliis assumes that all trains are affected by thedifference in gradients as by the difference in other details. No passenger train, however, would under atiy circumstances be much benefited by the reduction of ffrade so that ,f one quarter or one half the trains are passenger trains the estimate should be corrected correspondingly. On the other hand, no credrt side whatever has been assumed for the loss of distance, whereas there must always be some (par. 227 et seg.) and often enough to wipe out the debit side altogether. How the account will then stand is worthy of careful study. ' 903. This example makes it clear that the assumption may be still Figs. i,«, ,„._Plai. and Profile op a Break in a Long Tangent to obtain 0.4 rer cent INSTEAD OF l.o PER CENT GRADES. more extreme, as by assuming that the attainable through grade, except at a few such points as this, is 0.4 per cent. We then have the' condi- tions of Figs. 196-7. if we are to obtain 0.4 per cent in the same way; CHAP. XX.-HOW TO PROJECT LOW GRADES. 665 the lateral deviation from the air line being 2.39 miles and the loss of distance at each such point 3 miles, in an air-line of 3 miles Even L that case three or four or even five such points might be s ood before t was concluded to give up the low grade, but at six the loss of dis'ancl^ .8 miles-would be too great, threatening to discourage traffic and the indication would be very strong that a different gener!. route should L low'°r!dJr' *^'""^' P''"''P'^ ^^'""^ '''°"'<^ «°^«"' the laying out of ow grade-lmes or sections of lines cannot be made much clearer than by confineT,'"'' ;• '' '"^'""'"^ °' °''^'"'"8 ^ '"^ g^^^e are ordinarHy confined to a few points on the section. Adopt, then, the rate which can be obtained without much difficulty on three fourths or four fifths of ^e iTh^he'dT °^. ='=«''^"- r <> concentrate attention on the remainder MERr All T'" '"'' ™' "-"^ ^'^^"^ "^"ST BE PRESERVED THERE ALSO, if ,n any way possible. A way will generally appear after careful^ study, and a very much neater one than tL sket^che^ni f£ 909. Much of the lamentably prevalent bad practice in such details as we or bit bTh-r h"'"^ '°"'" '"™ '"^ '"=' ""' '"^ "- « ''""-d i" det^l onr; or bit by bit, and not as a whole, as ^' it should be. If we allow ourselves to think only of the three-mile stretch AD, Figs. 194, 196, 198, and think of the consequence of throwing the line out to C B' to pass from A to A the mind revolts from it at once. The rectangle CCB'B, Fig. 198, ob- trudes itself upon the mind while "" the project is inchoate, and thus the rJseel'.T'" T'"'^ ""^ •' '^"" "^"" '^" ^"™P^^^^ ^'"^ '' »-'d down, as may be seen at once by comparmg Figs. 198 and 194. which are really " similar" to ^ach other, although they do not look it. If the mind were able to "ke n n due proportion the vastly greater distances on each side which are not injuri osy affected at all, while they are made passable for twice as heavy trains ther" ^ nd "n'rr^ T' ''"■""" "°"^' '' °"^^ '^^'" ^° '^'^ -^>' B- this the less of ^ u '''^'' '^''""^ P'"^^'"^ ^^°"^^ b« kept up during the prog^ less of surveys with even greater care than those on working scales / '■\ 666 CHAP. XX.— PROJECTING PUSHER GRADES. I ■•1 HOW TO PROJECT PUSHER GRADES. 906. Suppose that instead of there being five or six such low- ridges as that shown in Figs. 194 or 196, scattered irregularly over the division, there is only one, but six times as high, as sketched in Fig. 199. Fig. 199. Fig. 196 may still serve as a map of such a point. As between the air-line and the bowed line, IF EACH IS to be operated in THE SAME WAY, the case is not affected in the slightest by the greater height of the ridge and length of the lines AB' and CD. The bowed line is much the best. The bunching of the obstacles at one point does make this difference, however, that there is now a rational choice in favor of assistant engines. For any considerable traffic the short line with pusher grades will be very probably the better. The volume of traffic makes a difference in two ways: First, the as- sistant power can be more exactly adapted to requirements ; second, a heavy traffic is almost sure to be largely competi- tive, thereby diminishing the credit side to the value of dis- tance, . Pusher grades may be divided into two classes, each of which requires different treatment and will be considered separately : T. Those surmounting low elevations by the easier gradients. 2. Those making long ascents (say over 700 or 800 feet) on rates which must be conspicuously more severe than the through grades on either side, as where li per cent grades or over are required. PUSHER GRADES ON EASY GRADIENTS. 907. When it is seen that the use of pushers is unavoidable if a low through grade is to be obtained, the first question which arises is : Which is to be the limitinjr gradient.-the low through grade operated by one engine, or the pusher grade operated by two engines? Ordinarily Jt will be the pusher grade, for two reasons : I. The lower pusher grades must be reduced in rate nearly twice as CHAP. XX.-PROJECTING LOW PUSHER GRADES. 667- fast as the through grades to keep the balance equal, as is evident from tiie following figures, taken from Table 182 : Through Grade.... Level o.i 0.2 0.3 0.4 0.5 0.6 l^f^^^^^^- 0.38 0.57 0.76 0.95 1.12 1.29 1.47 ^'^"^'^""^ °-^9 0.19 0.19 0.17 0.17 018 I-or a uniform difference in through grade of o.io. It will usually be very much easier to reduce the through grades compl.cated by no high elevations, from 0.6 to 0.4. than to reduce the corresponding pusher grade from 1.47 to 1.12. especiallv as the through grade, from the nature of the case, will be mostly in short undulations • and hence, *■ 2^ The influence of momentum (par. 397 et seg., and see also close of this chapter) will frequently assist greatly in reducing the virtual through gradients below the nominal maximum, or can be made to • whereas long pusher grades must be taken at their actual rate. 908. Assuming, therefore, the pusher grade to be the one that fixes- the virtual gradient of the whole line or division, all that has been said above about reducing through grades applies to it in an intensified de- gree. The saving of distance or curvature should be wholly subordi nate to the end of reducing the rate of grade to the lowest limits, taking care, however, not to introduce development which adds so much to cur- vature that the compensation destroys nearly all the gain. A resource in extreme instances may be to introduce a temporary sag in a grade-line. sL M K Tu^^'- ^^'- ^^"^P ""'^^'"^^' ^^ absolutely unavoidable should be used here, if nowhere else. In this way reductions of grade which are far beyond the apparent seltd ''r "J r''? 'u' '''"'"''• '' ''^ ^"^'"^^^ '^^'^^ has at last secured what he thinks the best the country admits of. will then throw aside all his preconceived impressions, and start in afresh with the idea tha he IS all wrong, and might reduce his grade o.i per cent or more as ITZ "^''k .' ''^'''^''''''' ''' ^•^»^^' ^he chances are many to one that ne will not be disappointed, and reductions rising to even 0.3 to o c per cent may sometimes be obtained without a dollar of extra cost, by ab- u.dly simple means, as in the instance described below, and illustrated omf ''^•', "^^'"^ "^^^ '^^ ''"y-"^'^ ^^^ ^ reduction of a 2 per cent grade some ,5 miles long to a 1.5 per cent grade, with a cheaper line. run^r* ^" '^^ '^'*' illustrated in Fig. 200 a located line aaa had first been ^.alT A ' ^'',""' ^'^"^"^ '^'""^^ ^ "^^^^ attractive saddle A over which the highway already ran, requiring a short tunnel of about looo ft. The sura 1 668 CHAP. XX.— PROJECTING HIGH PUSHER GRADES. CHAP. XX.— PROJECTING HIGH PUSHER GRADES 669 mit of the grade was but a short distance back, and A was approached by a much lighter grade; but accepting /i as a finality, it was utterly impossible to find sup- porting ground for the grade at a saddle about 4 miles below A with a less grade than 2 per cent. The grade was in all some 20 miles long, in two suc- cessive sections of 9 and 6 miles, respectively, with some little broken grade in- termixed. Fig. aoa Examination indicated (i) that except over this stretch at the head of the grade there would be ho serious difficulty in reducing the whole grade to 1.5 per cent, and (2) that the only chance for reducing it above was by gaining develop- ments around the hill DG. The very capable and experienced engineer who had made the first location was therefore instructed that the hill must be turned if possible. He ran the line bbb, accordingly, to the point Z, turned a maximum curve K, and reported it absolutely impossible to turn the hill, without two very high viaducts over the deep gorge H and a tunnel at K, This looked plausible on the ground, if it does not on the map. Standing at L there was an abysmal gorge below, a precipitous knife-edge, G, of soft Tock above, and the smoother side of the hill, M, wholly invisible and almost inaccessible, but known to be very steep. Really, however, there was no diffi- culty. Running an approximate line EM from below, and connecting across the top of the hill, it was found that the entire line could be fitted closely to a steep side-hill except for one deep rock cut at G so very narrow in proportion to its height that a single heavy blast would remove it all at once. This threw the line nearly 100 ft. lower at E, saved the tunnel A, and gave much better ground below as well, while enabling the 1.5 grade to be easily obtained. It is especially important to exhaust all such possibilities on low and short pusher grades (down to the limit which balances the lowest attainable through grade), because the use of two pushers, or still less the breaking up of trains, i& rarely expedient, as it often is on the longer and higher pusher grades, which we will next consider. LONG PUSHER GRADES ON HEAVY GRADIENTS. 910. This second class of pusher grades should ordinarily be studied by tliemselves, quite apart from the remainder of the line. Their cost, both for construction and for operation, will be a leading factor in the finances of the line, and hence should be a controlling factor. They are sufficiently prominent features in the operation of the line to enable the motive-power to be well adapted to the requirements of the gradients, whatever they may be. 911. These causes favor the adoption of low rates of grade for such a line: I. As the gradients rise above 2 per cent the loss of net haul« ing capacity becomes more serious, owing to the weight of the engine and tender, and (for freight trains) caboose, becoming a larger and larger factor, as shown in Table 189, p. dZZ. From Table 170 we see that on grades differing by i per cent the net hauling capacity is — Grade per cent. I.O 2.0 30 Net tons load for St'nd. American engine. 192 118 Per cent (2 per cent grade = 100). 193.2 ico.o 61.46 Net tons load Per cent Grade for St'nd. (2 per cent per cent. American engine, grade = 100). 4'0 7^ 40.62 50 SZ 27.60 6.0 36 18.75 2. The lower grade (if obtained by development) not only re- duces the cost of operation, but increases the revenue somewhat, by giving a larger mileage. On some costly lines of thin non- •670 CHAP. XX.— PROJECTING HIGH PUSHER GRADES. CHAP. XX.-PROJECTING HIGH PUSHER GRADES 671 competitive traffic this may justly be regarded as an additional advantage from a low grade. On other lines it might be an al- most unmixed disadvantage. 3. As grades rise above 2 per cent or 2^ per cent, such great caution has to be used to keep trains under full control, both in going UD and down, as to add considerably to the theoretical disadvantage, both in loss of time and danger of accident. 4. A lower grade will often be found to lie on such ground as to decrease rather than increase the total cost per mile to sub- grade (as we have just seen in par. 909), so that the difference in cost of a low-grade or high-grade line will be at the most not great. 5. A large portion of a continuous descent will often not ad- mit of using a higher grade than a certain rate. It then becomes a regrettable sacrifice to use a higher grade elsewhere on the same descent, although if the grade be long, traffic small, and difference of cost great, it should be done. 912. The Jalapa line between Vera Cruz and Mexico, described in Appendix C and its accompanying plates, is a good example of the effect of every one of these causes favoring low grades. On the first 30 kilo- metres (20 miles) of the descent from the summit, although a slightly steeper than 2 per cent grade might have assisted somewhat, a 4 per cent grade would have thrown the line so low as to bring it on much worse ground. 913. The descent from Tepic (see par. 917). on which the spiral oc- curs, shown in Figs. 207, 208, is a good illustration of the fifth cause above. From the summit down to the foot of the spiral more than the adopted rate of 2.6 per cent could not possibly be used, except by throw- ing away elevation with level stretches, since that grade brought the line down to the very bed of the stream under the viaduct. The same grade, in the main, fitted the bed of the stream very well, although for 5 or 6 miles it was necessary to hold up above the bed somewhat at some expense. As, therefore, there were only some 5 or 6 miles out of the 30 miles of 2.6 grade (broken by some short unavoidable levels below) in which the descent of 3000 feet to sea-level was made, it would have been an un- warrantable sacrifice to break the grade on the short stretch, where (only by raising it to about 4 per cent) some appreciable economy might be realized, even for the thin traffic expected. 914. The following causes favor the selection of high rates of grades for such sections of line: 1. It usually very much reduces the cost of construction which IS probably high at best— a consideration of great impor- tance (par. 29). ^ 2. If the rate of a higher grade can be maintained unbroken. so that Its length is decreased in proportion as its rate is increased the total motive-power is not increased (Table 181 and par 747) ^ven if the total length of the line between termini is not de- <:reased by the higher grade, i.e., if the respective profiles be- tween the two termini are as in Fig. 201. If the lower grade IS only to be obtained by interpolated distance, so that the foot of both the low grade and high grade falls at nearly the same point, the advantage in motive-power needed is still more in favor of the high-grade line. 3. The loss by multiplication of trains and train-wa^es which IS otherwise so very serious ' on high grades, is obviated in part by using two or three engines per train, which it is not practicable to do with heavy through trains over a whole division. This advantage is to be assumed with caution, however, as within the extreme limits of choice which the engineer has ordinarily before him (say not over i per cent in most cases) the same number of engines per train can be used on either the highest or the lowest rate. 915. 4. The case is much stronger in favor of high grades when the low grade is only to be obtained by hanging on a rough side-hill as against lying in the bed of a stream, or with other great contrasts in facilities of construction, as in the bt. Gothard Railway, where a low grade was obtained onlv by the desperate expedient shown in Figs. 202 to 2o6:-~turning spiral tunnels into the solid rock and thus introducing so much pure development between the same termini, so that a hio-her ?:rade would have shortened the pusher runs almost exactly/r^ >ata, and left the same amount of motive-power required for the passage between termini in either case. On the Italian side of t'le mountain, indeed, these spirals appear to have been an en- Fig, 30I. 6/2 CHAP. XX.— PROJECTING HIGH PUSHER GRADES. CHAP. XX.— PUSHER GRADES tirely superfluous luxury (see note to Figs. 202-206 on page following them), not even serving to reduce the grades. Apart from the cost of these spirals, had the grade been higher it would have lain for a considerably larger portion of its length nearer to the bottom of the valley, and hence on better ground. The St. Gothard line, therefore, furnishes a good example, although certainly not an extreme example, of unjustifiable adoption of low grades. It is mag- nificent, but in this detail of its loca- «^ I r lion it is not engineering, because it ^ '^ ^* does not accomplish the desired end in the most economical way. assL 7""^ Figs. 202-3.— Profile of St. Gothard Railway, Swiss Side 43 6/4 CH. XX.^REDUCmC RATE AND COST OF HIGH GRADES. Figs. 202 and 204 are profiles of the bed of the valleys approaching the St. Gothard tunnel, with the scale shown in miles. On the Italian side of the mountain the bed of the stream was broken by cataracts, and it will be seen by the dotted grade-lines plunging below the river-bed that by simply developing the spiral tunnels into straight ones, adding nothing to their length, the same grade up the mountain would have been obtained with a material saving of dis- tance and curvature, and hence, of course, of cost. Such a straight tunnel would start in at the lower portal of the fifth rising curve, near K, Fig. 205. and take a straight course through the words " Fig. 205" to a point beyond the limits of Fig. 205, where it would again emerge into the valley, requiring a tunnel of a trifle over 3 miles long, or about what there is nos^ of tunnel oxv the same stretch, saving all the other work and distance. The same is true in substance of the two lower raising curves, or of the upper one at least. The fact that this throws the grade-line below the bed of the stream looks bad on the profile, but should not be allowed to deceive. The tunnels plunge into the bowels of vast overhanging mountains of solid rock, and can be kept as far away from the stream as desired, if there were need to consider it at all. The only visible gain from the spirals, therefore, was to have the same engi- neering curiosities on one side of the mountain as on the other. On the Swiss side of the mountain, Fig. 202, the spiral developments shown in Fig. 203 were essential for the purpose sought, to reduce the grade to 137 ft. per mile. To have followed the natural grade of the valley would have required from 197 5 to 237.5 ft. per mile grades, according to how closely the bed of the valley was followed. By the aid of the long Table 170 we may see how much real economy in motive-power was effected by these developments in taking the traflSc from Silenen to the St. Gothard tunnel. Neglecting the actual distance, which it would be unfair to consider, we may say that the length of the moun- tain grade in miles should be about inversely as the rate of grade. Then we have, for a standard Consolidation: Grade. Ft. Per Mile. 137 219 237i Comparative Length. lOO.O 693 62.5 57.7 Comp. Net Tons. 319 210 184 165 Load of Eng. Per Cent. lOO.O 65.9 57.7 51.7 Comp. Enor. Miles Per Through Ton. 100 105 108 In other words, comparing the constructed grade with the 197.5-ft. grade only, in a valley distance of 10 miles. 44 miles {~\ of tunnel development vi?,s introduced with the effect of saving only 5 per cent of the engine-miles necessary to move a car through, and perhaps 2^ per cent of the cost of movement. Such errors result from lack of study of the economic side of railway location. There could be no better illustration of the broad distinction between reducing the rates of through grades and of pusher grades stated in par. 747. CH. XX.-REDUCWG RA TE A.VD COST OF HIC II GRADES. 6/5 EXPED,E.XS POK KEOUCNG THE RATE AND COST OP HIGH GRADES TION AND WORK EACH WAY FROVf it ;nc^o A c THIS SEC- i'KUM IT, instead of eoino- alwav« tr^ tK^ What are or ought VZTlZ^Llll^.^l''::^- '"''''' '"' °"' be the summit, and work from them 7n f ""^^ °' ""^^ "°' nar, . U or.narU, .est toTa^tl tt r:Xhut LTsfX'it .t ,s rather the rule thau the exception that it should not be dTne VU. F,g. ao7 shows a remarkable example of the advantao-^, of ,w. from the location of the lower end of the pLific Branl o ^ m- ^-Tetai Radway. onr the descent from the citv of Tenir tr. ru ^^^^ a" Central efforts were made by various engin:!; i ob't „ . pj,-::; ^T JT""' d>sting>.ished as first, second, and third lines in Fig "TL witl, "' very satisfactory result, until, aided by the knowledge gained L th. ""'' surveys, the idea of the spiral line w/s conceived an! pushed - a s^erul .a,r z:^ r sr: — — - — hy- - -e - to be rade ' 7 '"' ^'"^^ '"^ ^^^' =° ""'' ""= -"- "- wou^d have h'd Destn-fn To^ tpTc ';:T^'t;i:';''''TiT "' -- -- --« Tepic River until it dleL .h^re;rt ^ il'l^ L^ Tn^^ ^ 7g 1^ .on and becomes impracticably rough) and strikes across into the vallev of 7hJ subhmuy and beauty over the rugged and abrupt descent to the coast flats •igiy snarp. in an air-line distance of two miles frnm m- ^ . m- :r ^f r: irLr;- ^ '--' r "-^ --' ^ ^- -" "^-" - practi<^breTor Hn^ '°'"' "■' '""'^ °' '"= '"K^"i°. «""'= "tirely cfcable for a hue .n or very near to the bed of the stream, had, for many (>^^ CH. XX.— REDUCING RATE AND COST OF HIGH GRADES. miles below the spiral (to near B, Fig. 207), abrupt and rugged banks several hundred feet high, of the same impracticable character as those shown imme- diately below the spiral bridge, Fig. 208, although below B the valley became more tractable. 918. Under these circumstances, since it was impossible to descend into the bottom of the valley on any practicable grade, and since, unless this were done, the line must be, for a long distance below the spiral afterward adopted, entirely above the immediate slopes of the valley ; to avoid the most excessive work, a comparatively light trial grade, 2 per cent, was not unwisely adopted 0« tourist traffic, and much of the renainde ^f^he'r" k"'"' " ""="' "='"« beauty, this alone was deemed a dccis.ve consLra.ior ""^ °' «'"' "^"'^ WhV 'T'"' ''""^'°" °' "' ^'""' ^""^ "^''"" "- - '°"°-: 1-ength of spiral, 2,637 metres. . . _ „ , (405 -f 60 = 66g + 30. with io-m;tVeV ^i^^ ~ '^" ^"' = ^•^•* °^""^ Descent in spiral, actual. . . . ^' Descent in spiral, on 2.6 grade.. !*.*.. ;*'.*.*.*.* ^'^ "'^J''^^ = '73-9 feet. Loss of elevation in do "I 7 * 15.56 metres. Utilized as follows: ^°' degrir™^'"''''""' ^""^ '^'^'''' ^^' °*^ P*^' Spare elevation.' u'tiliVed VoVa station 'g;ound'a'r; d ^'^^ """''"'* water station at south end of spiral ^o 00 - Viaduct: Length. 200 metres Height, 53 " —656 feet. =173.9 The height is above the grade-line Ahr.tr. i more. ** "*"' ^^°^^ low-water it was some 7 feet Other resources for reducing the rates of Ion, ascents are : point'L^h^Hn^'^ornT^a^f!:,^^^ ^^ «"^^"^ ^ favorable mensely facilitate a favorable result e„Hr J"" "^^^ '''''^' ^^^^" ^"^- vorable section of a lon/de cen "o We "t " P^-^iiities of any fa- the line to .eep away fr^^t^ ^re^t ^ dTf.^^^^^^ ^^^'^"^ ment on the Jalapa line, Appendix C i, a „^ J ? develop- The privilege of using a shafrctve occLrali; u"'''' °' '"" '^^'^^• this end, and often ^si„.fua„a„ """'^'""'"'J' '' » g™at assistance ta 100 ■ I ■ I ■ I ■ I ' I METERS. 200 300 Fig. 208. I 7%e topography of this map is minutely accurate. The curves are Aotm off sett ed for transit (ton curves.) ibo 2(iO 300 46o 5^0 Mexican Central Railway - Branch to the SPIRALoFTHE BARRANCA BLANCA BETWEEN SAN BLAS AND JAN. 1883. (First three lines passed around and near the limits of the map in this direction.) • Reiueed one-fifth scale from the original field ^kteU on a scaU of j^ or 83i ft. per in. Co:rroiTBS. 2 Meteks (6 56^1.) apabt. iLinefrom here nsrerds the tmail ttream abort.) I V'ltHfii c»iiiinue.s of this nenernl character to p.. Fiff. 20T ) (First three lines ran near here.) CH. XX.^REDUCING RATE AND COST OF HIGH GRADES. 679 SAN JUAN Fig. 209 is another example to scale of such zigzag or horseshoe develop- ment, on the Lima & Oroya Railway, in Peru. The distance from A to B hori- zontally is 570 feet, and vertically is 365 feet. The horizontal distance from C to D is 495 feet, vertical dis- tance 360 feet; length of line from A to D is 4 miles. The usual rule on this road was to use switchbacks for such developments, as SACRAPE Fig. 209. shown in Figs. 218-21. In all these cuts the dotted lines represent tunnels. The curve at Sacrape is 14° 30'. 922. 3. Spirals might be used to great advantage much oftener than 1 i ,y-y\- '' I hill II- Fig. 3IO.— Bridge Shral. Fig. 211. — Tunnel Spiral. they are. A spiral, also sometimes called a "loop," is a doubling back of the line upon itself so that it returns under itself at a lower elevation. They are of two classes : bridge spirals. Fig. 210, in which the upper end of the spiral is carried over the lower on a high viaduct, and fS 68o CH. XX.— REDUCING RA TE AND COST OF HIGH GRADES. m CH. XX.— REDUCING RATE AND COST OF HIGH GRADES. 68l TUNNEL SPIRALS, Fig. 211, in which the lower end of the spiral passes under the upper end with a tunnel. Figs. 215-217 show one of the most •extensive applications of the principle of spiralling (made possible only by very peculiar topographical conditions) which was ever attempted, but a better line was afterwards found. In the typical bridge spiral the line swings around the slopes of a valley or basin, and in the typical tunnel spiral the line swings around the slopes of a central hill. The tunnel spirals of the St. Gothard line (Figs. 202-206) are also tunnel spirals, in a sense, but of a third class, which does not swing around any- thing. 923. The bridge spiral on the descent to Tepic, Figs. 207, 208, illus- trates the advantage gained by them, which is to make a sudden and great drop at one spot. They are, when well laid out, not costly feat- ures, and bridge spirals especially facilitate that most important end of sUi Half MM Fig. 213. — Map of Spiral on Union Pacific Railway, shown in Fig. 212. getting down into the bed of a stream as soon as it has descended so far from its source that it may be said to have a bed. It is to be remem- bered in laying out bridge spirals that the height of iron viaducts is a nimor factor in their cost (par. 102). They are a rare feature in location, and must always remain so, but might sometimes be used to advantage where they are not. Figs. 212-214 show the only bridge spiral in the United States. ft i? ' Ml 682 CH. XX.— REDUCING RATE AND COST OF HIGH GRADES. ts) X H >• » O U < I H Z D O a H .J <: u H z z So O J X u (A > o z o X < K eu (/) H X H •Z u ^^ c9 w Z> •o « "^ Ji o Sl u u y w^., « OJ-- 4)— «J -, m ™ > c •» V W u ^^ •> o"5 o g_<«.S _ (« u a.>^> o ^ a< »; bo i^ i a |ii £-;:.!2"3 w - «J ««^ i i I 924. 4. In making » descent into a river val- ley it is an almost invari- able rule to DESCEND against the slope of THE VALLEY, even at the cost of turning a half- circle as soon as the bot- tom is reached. The length of the side-hill descent is much de- creased. It is still bet- ter, if possible, for the same reasons, to descend against the slope of some- tributary valley, turn a half-circle, and then de- scend in its bed to the main valley. Figs. 215- 217 give an actual in- stance on a large scale. In Fig. 215 a descent was to be made from E, at an elevation above sea of about 3000 ft. (910 m.), to A, into the valley of the Ameca River, at an eleva- tion of 1120 feet (340 m.) above sea, a drop of some 1880 feet, to be made within an air-line distance from E to A of only 5 miles. The Ameca River lies along tht bottom of Fig. 215, flowing to the left with a sharp descent of over one per cent, so that beneath the spirals EG, shown in detail in Figs. 216, 217. the bed of the river was only 1020 feet (310 m.) above sea. The tributary AB had a CH XX.^REDUCING RATE AND COST OF HIGH GRADES. 683; still sharper descent of over 2 per cent, and the circumstances of the locatioa made it clear that the ruling grade on the descent must beat least 2f per cent. The location shown in Fig. 216 is 3 per cent compensated, about 2.6 per cent actual. At the left of Fig. 215 was another tributary, EG, falling far too fast for any line to follow it directly, but making a very high and steep backbone or knife- edge at EG of solid basaltic rock, overlaid for the most part with a thick surface deposit of volcanic tufa, or tepetate. This knife-edge had excessively steep slopes on both sides, as will be seen from Fig. 216, extending down to the river- bed 1000 feet below, and had the further remarkable peculiarity that the sides- swelled in and out, making it very thin at points and thicker at others. These unusual topographical features made conveniently possible such an unparalleled series of spiral developments as are shown in Figs. 216, 217, which took very kindly to the natural surface, so that they could be executed at very moderate cost, as the minutely accurate topography of Fig. 216 will show. 925. Under these circumstances there were two possibilities for the de- scent from E\o A: First, the line EDCBA, which subsequently proved to be by far the best; and, secondly, the line EEGHA. Influenced by the ease with which great development could be obtained in a small space and at small cost at EG, Fig. 215, as shown in detail in Figs. 216, 217, the latter line was examined first; the only useful result of this work having been that it is possible to present to students the instructkre study in location shown in Figs. 216, 217, where six successive spirals are shown (the lowest one finally abandoned), accomplishing a descent of 613 feet (187 m.) within a hori- zontal distance of about 1800 feet, measuring from the highest to the lowest points shown on the map. The developed distance between these same points was 4 45 miles (7.18 kilos.). Measuring from the nearest points of the first and fifth spiral, a descent of 426 feet and a development of nearly 3^ miles was obtained between points only 5 58 feet apart horizontally. The lowest (abandoned) spiral gave a further development of .855 mile and a descent of 125 feet within a horizontal distance of 263 feet. A striking feature of the development was the two-story iron viaduct outlined on Fig. 216; a precipice over 200 feet high for a short distance at one point enabling the line to pass twice over the same viaduct at elevations 100 feet apart. The value of such a feature as an advertisement and attraction to trave. for a line which must in any case be largely dependent on tourist travel, was an element not to be despised; but it was all but certain that the true loca- tion must have been by the northerly route, as was found to be the case: for (i) the stretch ED lay along the natural surface; (2) the stretch AB, accom- plishing nearly one fourth of the rise, lay in the bed of a tributary stream nsing nearly as fast as the desired grade. All that was necessary by this route, therefore, was to find ground on which the descent from D to B, and the II li I i * 684 CH. XX.— REDUCING RATE AND COST OF HIGH GRADES. turn at B, could be made. In other words, granting that a turn at B could be made, more than half the descent could be made on very easy ground. Ex- amination showed favorable points at B and C for^the turn, and a very favor- able location was obtained for the entire descent. This line also had engi- neering and scenic features of great interest; chief among the latter being a gigantic natural obelisk of stone, produced by erosion, 572 feet high, and pierced through the centre of its base by a tunnel 279 feet long. 926. Besides these four, which may be called normal expedients, there .are the following, as difficulties multiply : 5. Switchbacks: the proper laying out of which, and the arguments in favor of using them when so laid out, are described in Appendix C. Fig. 3x5. When descents of over 1000 feet are to be grappled with, and often with less, the writer believes they should be used much more freely than they are. if laid out in the way described, so that the stop and reversal of the direction of motion involves no loss of time or power, either theoretically or practically. If laid out in the ordinary way they are far more objec- tionable. Their effect to reduce the cost of construction is very great, and there is no necessary loss of time or power from the stop. Figs. 212-214 show a locality where well laid out switchbacks would have been vastly more economical, and have given better results in other ways. REDUCTION RATIO 14:1 > J^^ Ca) O 3 3 — •»o 3 X 8S go •^ in ^-< OOM O 8 3 3 ^** CjO cn 3 3 Q) O > Is o ^ < CO c O X o ^ ::d M en cr>x ^-< OOM VD o ,,5^ - ^. "&> '** 3 > 0,0 o m CJi3 ^ ^ O o X ..^^ > a^' Ui O 3 3 € i^ : bo 2.0 mm ABCDCfGHIJKLMNOPORSTUVWXVZ C CO I TJ ^ ^Ooo 0(/) 5 m O m ■^1 2.5 mm ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghiiklmnopqrstuvwxyz 1234567890 ^ fo •— » N> IN> en o UI 3 3 3 3 3 3 > fli 0> 0,0 cr2 n > ri?^ o m <§.o Q-Z! S< sj ^1 00^ no cco tub: OX CTlX < -H OOM l< >J-< OOM ^^ S X -< i Fig. ai6.— Topographical "Map of the Spirals at thk "Cuchillo" (Knifb-edgk) ok Huavacan, J-G, Fig. 215, [Reduced to ,„'„, (^^^4 ft. per Inch) from the original field-maps, to a scale of io\re.] Fig. ai7.— Section of the Crest or the "Cu- chillo" OK Hlavacan, pkujected onto a yEknCAL Pla.ve, showing iHE Spirals in PosnioN. Kyurticai Scale exaggerated only three times, so ihai ihe pruulc dot* not in ilie leasi exagj^cr- aie the cffcci upon the eye of the slopes mcm- selvcs. 1 he siOc-slopcs will be seen 10 be much Sleeper than ihc siopes on the ciest or ridge.) 60i Note to Figs. 216. 217.— The base-lines for the topography (which is minutely ac- curate) are shown by dotted lines covering the hill. The whole body of the ridge was basaltic lava, which is solid underneath, but cracks on the surface in cooling into loose blocks. The elevations of the contour-lines are not put on in the best manner They should be written across the lines, or across gaps in them. The degrees of the curves are for metric curves of 20-metre (65.6-ft.) chords. Thev should be increased about one half (53 per cent) to be correct for loo-ft. chords. The facilities which a judicious sys- tem of transition curves offers for conducting location is apparent from Fig. 216. The curves are all projected at an offset for introducing transition curves, making no effort to obtain any particular offset, and any curve or tangent on the map can be shifted, re- gardless of the rest of the line. The grade-contour is shown throughout the map, from which it can be seen at once that minor improvements are possible at a number of points. Including the lower spiral, shown by dotted lines. 4.45 miles of development and 613 ft. of elevation were here gained, practically at a single point, without anv loss of distance whatever The localities are few on the face of the globe where such a result would be so conveniently possible. In this case it was probably cheaper than a system of switchbacks such as suggested in Appendix C / REDUCTION RATIO 12:1 v. Ca> -(!' Ol ai 3 3 3 3 > Q> OD ABC bcdef o m ^o Q-Z! -m (D O OQ X 3 X 3" J~" 3 r: hO '=-:'s ■S^ 00 fi CJl 3^ ^z CTi 13 "Z. i o osj o o 5 "^ 00^ ^ J^O o ^1 < H ^ c o^x X < N < O X M .-v^' .^. A: CO c > JO O m 0) I Ul o 3 3 > Ul !^j ^^. ^^- ^,. a? o o 3 3 <^^' X-^ ky •^ ^ -i. ¥p f^ o lelsfs r« N3 GO o^ s ig to In 1.0 mm 1.5 mm 2.0 mm ABCDEFGHIJKLMNOPQRSTUVWXYZ »bcdefghi|klmnopqrstuvwxyzl234567890 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyzl234567890 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 ■^> -^Z**- '^. 'iM^ 4^ 2.5 mm ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 ^o r V ^<^^ i ;cr fc> ^c. ?CP f^ ^^ m O O ■o m -o I TI ^ m 30 O m fS s| «< JO *■< 00 INI 8 4, ^f^ 1— » to CJl o E 3 cr o >> Wo ^i *< ::xj cnx ^-< OOM O A Fig. 3x8. CH. XX.-REDUCING RA TE AND COST OF HIGH GRADES. 685 T • ^^l' ^^^ ^°"°^'"g F-igs. 218 to 221 are examples of switchbacks from the Lima & Oroya Railway in Peru. They give an idea of the advantage which they give for location, uvauiagc wnxcn but they were not ^/\C properly laid out to 00 ^ ^ reduce the disadvan- tage of a stop 10 a minimum. Fig. 218 shows a rather unusu- al and unfavorable method of laying them out, the switchbacks being usually in pairs, as in Figs. 219-221, and as near together as possible, so as to reduce the distance on which the train runs backward to a minimum. From A to B IS 3i miles by the line. In an air-line they are 855 feet apart horizontally, and 545 feet apart vertically. From I to 2, Fig. 219, is 5 miles by the line and i^- miles in an air-line. The horizontal distance between- A and £ is 985 feet, vertical distance 625 feet. The horizontal distance between E and F is 465 feet, vertical distance 535 feet, showing an average slope steeper than I to I. Many such places were entirely inaccessible to bipeds, and the line was only located by making as careful • topographical maps as possi- ^pA^ ble, projecting a location, and ff'^ triangulating in points on it for beginning construction. At the "Infiernillos,"or "Little Hells," Fig. 220, the river passes for some distance, with a succession of falls, between two walls of rock that rise perpendicularly to a height of 2000 to 250c feet. In passing under these high points the line leaves one tunnel, crosses the river on a bridge of 160 feet span at a height of 165 feet above the water, and enters another tunnel. From I to 2, Fig. 220, by line of road is 4f miles, comprising eight tunnels. An air-line from The horizontal distance from A to B is 445 feet, vertical Fig. 2x9. ' to 2 is If miles, distance 310 feet. 6S6 CH. XX.— REDUCING KA TE AND COST OF HIGH GRADES. Fig 221 shows another very peculiar development— a combination of switchbacks and horseshoes. From ^ to ^ by line of road is 4-9 miles, by air-line 1.6 miles. This portion of the line has 1776° of curvature— an aver- age of 362° to the mile. From C \.o D the horizontal distance is 730 feet, ver- tical distance 570 feet. The profile in this vicinity was not inappropriately known as " Gothic." These maps taken together will in- dicate, what is the fact, that even in the roughest country there are certain locations where zigzag developments are more economical than switchbacks, and others where switchbacks alone are practicable, without the heroic ex- pedient of spiral tunnels. 928. 6. Inclined Planes and Cable Traction.— This device, in a crude form, antedates the loco- motive itself, and was at first the almost universal resort for dealing with what were then considered high grades. It is still used to some extent, but early passed out of gen- eral use as an accredited auxiliary to railway transportation. We may admit that this at the time was wise and right, and still regard the device as one deserving of a recognized standing at the present day. In all probability, within a few years, it will be much more used than it is now for moving large traffic over high eleva- _ . ,. . tions. A' *^^^^ "^ ^^ "^"^ "**^ 929. The argu- ments against the use of planes are these : I. It introduces a break in the continuity of the movement of traffic— an argument of minor importance which must always exist in some degree. aao. CH. XX.— REDUCING RA TE AND COST OF HIGH GRADES. 68/ 2. The power and working force necessary to operate the planes must always be on hand and available, at nearly the same cost whether work- ing or idle, and possibly a good part of the time idle. This was a very serious matter in early days when traffic was light, but it grows less so as the movement of traffic becomes so great as to approximate to a steady stream of cars — a condition which exists on many lines now operating steep grades with locomotive power. It was a, leading factor in causing the abandonment of planes in the early days of^ railways ; hardly subordinate to the following, which was perhaps alone decisive : 3. Formerly, planes operated by stationary power were necessarily short, straight, and on a uniform gradient. This made it essential topo- graphically, even if it had not been mechanically, that the planes should not be long, but that a number of them, separated by intervening stretches of " level," should be used, greatly increasing the awkwardness, delay, and expense of the process. 4. A certain element of danger from runaways and breakages existed and still exists, which was, however, not a serious nor governing consid- eration, even when the only cable was a hemp rope, as in the early planes at the Alleghany Portage on the Pennsylvania State canal and railway svstem, and it is still less so now. 930. On the other hand, besides the advantage of the vast increase of traffic which would enable stationary power to be constantly employed at many points, the perfection to which the cable system has been brought in recent years has greatly changed the conditions of the problem, and favored the use of well-designed inclined planes in connection with railways. Passing the question of how they should be designed for the moment, the arguments favoring the use of inclined planes of whatever type are these : 1. The great expense is saved of lifting the ponderous motor itself up and down hill. Assuming every engine to be fully loaded, and assum- ing a light Consolidation engine with tender and caboose to weigh 80 tons, we may deduce from Table 170 the following Table 189, showing the proportion of the total power exerted which is thrown away in non- productive work on the motor. 2. The power is not only wasted in the proportion shown in Table J 89, but is more costly per horse-power for several reasons : {a) The fuel burned per horse-power is much greater than in a good and powerful stationary engine (Table 168, page 531). (^) As one stationary engine does the work of from five to thirty MM I 688 en. XX.— REDUCING RATE AXD COST OF HIGH GRADES. locomotives, there is a corresponding saving in maintenance of machinery and in wages of engine- and train-men. Table 189. Proportion of the Dead or Waste Weight (of Engine, Tender, and Caboose) to the Total Paying Weight (of Cars and Freight) on Various Grades. [An addition of $ tons has been made to the weight of an average Consolidation in Table 170, cis better corresponding to the more recent practice (Table 129), and a corre- sponding subtraction of 5 tons from the load given. In addition, a deduction of 20 per cent has been made from the load given, as an allowance for the lighter winter loads, the scant loading of many trains, and light trains in one direction. As an average, this allow- ance should be larger.] Weight in Tons. Per Cent Weight Engine Grade Per Cent. Engine, Train Do. Average to Average Tender, and by of Paying Weight. Caboose. Table 170. All Trains. I.O 80 706 565 14. 1 1-5 499 399 20.0 2.0 378 302 26.5 2.5 299 239 33-4 30 244 195 41.0 3-5 202 162 49.4 4.0 170 136 58.8 50 124 99 80.8 6.0 92 74 1350 {c) The wear and tear of track due to the locomotive is saved, which is about half of the whole cost of running them (par. 780). Against this is to be balanced the loss of power by the friction of the rope or cable, but this is comparatively a small percentage on a grade plane, although a very large percentage on level cable railways. The cable friction being constant per mile decreases in relative importance as the grade is higher. {d) The modem cable system possesses several advantages, as notably that of being used on curves, which none of the older and simpler forms of inclined planes possessed. 3. Apart from the cost of the mechanism for operating the planes (which may be balanced roughly against the cost of locomotives), the use of inclined planes will ordinarily cheapen the cost of construction ma- terially, although this may not be invariably the case. CH. XX.— REDUCING RA TE AND COST OF HIGH GRADES 689 931i If we conceive the normal type of a passage over a summit to be that shown in Fig. 222, the manner of adapting the %ame summit to the use of in- clined planes may be that of either Fig. 223 or Fig. 224. In Fig. 223 the cars are hauled directly up an inclined plane (or, q if necessary, up two or more) at A and B to some point a and h which is high enough for the cars to descend thence over the entire . ^ ^ p distance aCB or bCA, presumably in short " ' trains in charge of one or more brakesmen. Fig. 222. The power stored in the cars is thus not lost, by having to be shortly after destroyed by the brakes, but in great degree utilized for propulsion. 932i This economy of power may, under favorable circumstances, be carried still further by the construction of the auxiliary lines r^/and ce. Fig. 224, so as to extend the plan in Fig. 223 to that shown in Fig. 224. By these auxiliary lines, after the cars have as- — >. .^ .^— - cended the planes A and B \o a [ ~^^yn^^ \ or b, they run by gravity to the fj y^ ' \^,^ 1* points e or d, where they de- / y^ ^^^Aj^ scend the plane, thus assisting 5J — ^ by their gravity to pull other Fig. 223. cars up it, and making the only motive-power required (in excess of cable-friction) — that necessary to lift the cars through the distance da or eb, which Is necessary to enable them to run by gravity to the opposite plane. If the distance ab were great enough to make it desirable, a nearly level track might be laid, and loco- motive-power used, but this involves the disadvantage that the location is more difficult and costly, because the gradients have to be considered in both direc- tions, whereas the duplicate gravity tracks may be laid out on different routes, each of which need be favora- ble to motion in one direction ^ q^ h 933. Theoretically, the sys- tem sketched in Fig. 224 com- | ^ ^^^B pletely eliminates the disad- - „ , , , Fig. 224. vantage of the elevation sur- mounted, however high, leaving the only loss of power that which would result if the track were vertically projected onto the plane AB. Practically, it will of course fall far short of this, but may be made to give some approach to it, and with the privilege of introducing a few easy breaks of line and grade on the plane, which is practicable by the cable system, no great difficulty is likely to arise in laying out long planes advantageously. 934. The modern cable system has not yet been used to any consid- erable extent as an auxiliary to ordinary railway traffic, although it is tending in that direction. It originated at the city of San Francisco, 44 690 CH. XX.— REDUCING RATE AND COST OF HIGH GRADES. from the necessity of supplying street-railway transportation on high grades. In its essence it consists in using a continuously moving and endless wire cable to which the cars are attached by friction-grips, instead of winding up on a large drum a rope, chain, or flat band of metal of the length of the incline, requiring that the engines should start and stop again after taking up each load. The modern system has been brought to great perfection for street use, and has spread very rapidly in spite of the difficulty and expense involved in covering up the cable below the street level. It has been described with remarkable fulness, in all its details of construction and working, in various papers before engineering societies and in the leading technical journals. 935, Circumstances favoring the use of this particular form for rail- way traffic are : (i) The cable would not need to be covered up and gripped at some disadvantage through a narrow slit; (2) being primarily re- quired for vertical and not for horizontal transportation, the incline could be made steep at the expense of length and speed, reducing the chief source of loss in street service, friction and wear of cables ; (3) the grips having to be applied only at the bottom of the plane, and released only at the top, could be made very powerful by duplicating them, or other- wise ; the grades at the bottom of the plane could be made favorable for getting the cars quickly under way, and with speeds of not exceeding three or four miles per hour, which would be quite fast enough for economy, the grips could be applied and released by men jumping onto the grip-car for that purpose, so that there would be no necessity for any one riding up or down the plane with the cars. The system is certainly one of much promise for such localities and qonditions. and the. necessity of the utmost economy in transportation warrants its careful study, and will probably bring about its gradual adoption, with details adapted to the peculiar requirements. 936. A final expedient for reducing the disadvantages of gradients is the RACK RAILWAY, the most perfect form of which, and the only one promising general usefulness, is the Abt system. The Mt. Washington Railway, in New Hampshire, designed by Silves- ter Marsh, was the first example of a rack railway.* The device con- sists, as its name implies, in a pinion operated by a separate cylinder on the locomotive, which engages in a fixed rack laid between the rails. It * The Rhigi Railway, M, Richenbach, engineer, was an almost exact copy of every essential detail of the Mt. Washington line, but in a not particularly cred- itable way was labelled the " Syst^me Richenbach," and is so known through- out Europe. CH. XX.— DUPLICATE TRACKS FOR PUSHER GRADES. 69I thus eliminates what we have seen to be the most serious theoretical defect of the locomotive— that its tractive power cannot be increased in- definitely at the expense of speed, but only within narrow limits. In its original form it had many defects which the Abt system eliminates, but its practical utility as an adjunct to the normal operation of railways has not yet been fully demonstrated, and must for the present (1886) be re- garded as somewhat doubtful. 937. The salient features of the Abt system are these : The ingenious en- gaging rack by which a locomotive may approach the foot of a rack grade at some considerable speed, with certainty that the pinion will engage quickly and without shock with the rack ; the improved manner of constructing the rack of parallel bars with the teeth staggered ; the pinion or driving-wheel, which is constructed in sections, each capable of a slight spring, so as to ensure perfect and smooth contact with the rack ;the use of the ordinary adhesion cylinders continuously to lend what aid they can. On the other hand, there is the complication of the machine, and the diffi- culty of keeping the rack in working order, especially in the winter in cold cli- mates.* 938. A device for accomplishing the same end as the rack railway in a dif- ferent way, which has not proved equally meritorious in practice, is the fric- TION-GRIP RAILWAY. In this device two friction driving-wheels engage with a central rail, being pressed against it with any desired force, regardless of the weight on the engine itself. While the device has been used successfully in several special locations, it possesses no features to make it of general utility. It is generally known as the Fell System, and was used at the Mt. Cenis Rail- way. DUPLICATE TRACKS FOR PUSHER GRADES. 939. In the main, all climbing done by train^ on pusher or high grades is so much clear loss. The power thus stored in the train by lifting it up not only does no good, but costs more money to destroy by means of brakes. It is a peculiar advan- tage of the use of pushers that this need not be invariably nor A^ necessarily the case, for under certain fa- voring circumstances It is possible to utilize a portion of the work thus wasted by securing Fig. 225.— Typical Profile of a Gravity Railway. * The Abt system is more fully described in a paper by W. W. Evans, Trans. Am. Soc. C. E., March, 1886. I %fe,. 1 692 CHAP. XX.— DUPLICATE TRACKS FOR PUSHER GRADES, from it something of the advantages of a gravity railway, a typical profile of which is shown in Fig. 225. The gravity railway does of set purpose and to secure an advantage what the ordinary railway only does of necessity as an unmitigated dis- advantage ; viz., it seeks out certain high elevations, and ascends to them as quickly and by as steep a grade as possible. This it does for precisely the same reason that coal is put on the tender, viz., to store power in the train ; only, in this case, the power is ready for instant application without change of form. It is utilized for propulsion instead of being thrown away in wearing out wheets and brake-shoes, by laying out from the high elevation, to which the train is lifted by a plane, a continuous descending gradient, on a 0.7 to i.o per cent grade, until the lowest possible point is reached. The train is then hauled up to another high elevation, and the same process continued, giving a profile like Fig. 225. The ascent is made by sta- tionary power; but that does not affect the principle, which is, ^hat, as high elevations must at points be surmounted, it is better to do so by a sys- tem which utilizes the work thus done for propulsion instead of wasting it destructively. 940. There is one serious drawback to this system, that cars can pass over the line in only one direction, so that it necessitates an entirely in- dependent return track, however light the traffic. Nevertheless, it has been and is still used to some extent. It originated (in this country) at Mauch Chunk, before the locomotive had fairly been invented, and was afterward embodied in two prominent lines in Pennsylvania, and in a number of smaller ones. One of these lines has recently been abandoned ; but for reasons largely independent of the engineering merit of the sys- tem ; the other is still in operation. These two lines are: Pennsylvania Coal Co.—\l miles double track; 4 ft. 3 in. gauge; 36-lb. rails; 23 stationary-engine houses and as many planes, or about one for every four miles. Average speed of passenger trains, 15 miles per hour; freight trains, 10 miles per hour. Delaware b* Hudson Canal Co.— 2,2 miles of double track; 4 ft. 3 in. gauge; 45 to 56 lb. rails; 30 stationary engines and as many planes, or about one every two miles. The advantage of the plan is that it puts the undulations of the sur- face which cannot be avoided into the harness, as it were, by making them a necessary part of the system of operation. Moreover, motion in only one direction has to be considered, so that, so long as the train keeps de- CHAP. XX.-DUPLICATE TRAC KS FOR PUSHER GRADES. 693 scending, we are in a measure independent of the rate of grade, and econ- omy of construction is promoted. To balance the disadvantage of having to construct two independent tracks there is a certain economic advantage in a double track even when traffic is light. 941. The extra cost of having to construct two independent lines has undoubtedly been in years past a leading factor in impeding a more general use of this plan, until now engineering practice seems to condemn It, but that under certain exceptional circumstances it might still be ad- vantageously used, hardly admits of doubt. The merits or demerits of the gravity system in its entirety depend chiefly, it is plain, on whether or not inclined planes operated by stationary power are economical as compared with the locomotive. But whether or not the plan as a whole be advantageous, it is plain that, if we have lifted a train by any kind of power to a high elevation, that feature of the gravity plan is economical which utilizes the work thus done instead of throwing it away, and this may often be done with pusher grades, provided the traffic be sufficient to make certam short sections of double track in the immediate vicinity of the pusher grades a desirable feature; which is veiy apt to be the case since the mere existence of those grades practically doubles the demand upon the track. • 942. Thus, supposing a summit is to be passed over from one valley to another or a plateau of some width to be ascended to and descended irom. Ordinarily the pro- file over such a section would •-•-"^ be something lilce the solid ' '^ line in Fig. 226, there being certain natural difficulties in getting favorable grades in /^ \ £ more than one direction be- tween B and D so that the whole stretch AE is practically a single pusher run. If in such case, the grade ^5 can be prolonged to some Mgher po.nt and from thence carried on a favorable grade for trains go- mgto £• to a junction at some point A the expense of running pusher engmes both ways over the distance BD will be saved, at the expense of constructmg the short section of duplicate track BFCD. 943. Again, let ussuppose a common case, that we are carryingaline 1 rough a valley, a part or all of which has an irregular descend so that vallevrh ' T" k"^ "'^ '^ """" '"' '^^'"^ ™""'"8 down the valley such as Fig. 227. but favorable grades for ascending it can only be '1 1. i 694 C//AF. XX.— DUPLICATE TRACKS FOR PUSHER GRADES. had with some difficulty and expense. In some cases — not by any means in all cases — it would be possible for a return track to make at once for some high point C on a ridge or crest, and thence to make for the point A with level or descending or but slightly ascending grades, by a ridge line or a different valley line which would be for the most part lights CHAP. XX.^DUPLICATE TRACKS FOR PUSHER GRADES 695 Not only is lighter construction per mile of track almost certainly attain- able, when this is possible at all, but economy of operation is much pro- moted, because, instead of having to run short trains both ways between A and B, because of the opposing grades aa, our motive-power is only taxed appreciably on the pusher grade BC, throughout the round trip. Nevertheless, if there be not traffic enough to require or justify twa tracks any attempt of this kind would probably be uneconomical. 944i But after all, a plain continuous descent from a summit to the plain below will ever remain the normal type for location, such devices as spirals, switchbacks, and others being the exception. In all but the most rugged country, say wherever most of the surface to be built over is not bare rock, good and cheap lines can usually be obtained by following these two rules : First. Do not attempt to secure too low a grade-line by more than a moderate amount of development, remembering that on pusher planes the RATE of grade is comparatively unimportant (par. 747 and Table 181). Secondly. Do not adopt a limit of curvature too easy for the topog- raphy, unless the importance of the line and its probable revenue will certainly warrant it. (See, however, par. 883). 945. The railway system of Colorado is a splendid example of what may be accomplished by the application of these two rules. The fact that it was laid'to narrow gauge probably gave courage for adopting such alignment, but it was not at all necessary for its success, as we have else- where s^n sufficient grounds to believe (in Chaps. VIII. and XXIII). In fact, it is only a question of time when these lines will be relaid to- standard gauge without any essential change in their alignment. 4 w • It lU i 696 CJ/AP. XX.— DUPLICATE TRACKS FOR PUSHER GRADES. There is probably no system of roads in the world which are so well Worthy of the study of engineers, because of the marvellous cheapness with which it has been carried through the most forbidding regions, and certainly as good an illustration as any of what has been done in this way is the " High Line to Leadville," on the Denver, South Park & Pacific -dRnwIioH oioM &• < yj > O <» z u (O S y y CO O CD lu UJ. »- Z X << -J _i •T. 00 5o 03 ^ .00 UJ 9 00 o O O w p 8 111 VT Mk ^ miles, 132 ft. per mile (2.5 per cent) maximum grade ; 1 14. 6 ft. average. « *< ■r 700 CHAP, XX.— DUPLICATE TRACKS FOR PUSHER GRADES, In the United States there are : Southern Pacific— ^is^^ 2674 ft. in 25.4 miles; 116 ft. per mile (2.20 per cent) maxi- mum g:rade; io» maximum curve; 11 tunnels, including a "loop," or more properly spiral or helix, j8oo ft. long and rising 78 ft. Denver &> Rio Grande, Marshall Pass .—^xsfts, ^75 ft. in 25 miles, 4 per cent (211 ft. per mile) maximum grade ; 24° maximum curve. Height of summit, 10,852 ft. above the sea. Also, La Vela Pass.—mses 2368 ft. in 15 miles ; same grades and curves as above. Height of summit, 9339 ft. The lines over Fremont Pass, 11,540 ft. above the sea,— the highest point reached by the locomotive anywhere in the world except in Peru,— and the Tennessee Pass, 10,418 ft. high, are of the same general character. Another very notable heavy grade on this same road is : Calumet Mine Branch, Denver &> Rio Grande.— Rises some 2700//. in seven miles on an eight per cent grade (nearly 406 ft. per mile) with 25° maximum curves. This unparalleled line is used to bring ore to the Bessemer-steel works at Pueblo, and is operated by one train per day each way. It is undoubtedly the heaviest grade on any regularly operated railroad in the world, although 10 per cent temporary grades (528 ft. per mile) were successfully operated for over two months over the Kingwood Tunnel of the Baltimore & Ohio Railroad by the late Benj. H. Latrobe as early as 1852.* These latter lines are narrow-gauge, but need not remain so unless they choose. Mexican National.— Kxs^ 2628 ft. in 17 miles; on 3.8 per cent (201 ft. per mile) max- imum grade; 15° maximum curves; with a descent of 1325 ft. in nine miles on a 3.5 per •cent grade on the other side of the summit. Laid to narrow-gauge, but expressly built throughout to be adapted to standard gauge. On same road : Mexican National, Northern Division.— UoTiicrey to Saltillo. Rises 3465 ft. in 54 miles, at an average rate of d» ft. per mile, most of the rise, however, concentrated on a short portion of the distance on grades of 2M per cent. Less important inclines which are for one reason or another notable are ; Tyrone &* Clearfield.— A little branch of the Pennsylvania Railroad. Rises 1064 ft. in 10 miles. Tangent maximum. 138 ft. per mile. Central Pacific— Rises 992 ft. in 13 miles; 2 per cent (105.6 ft. per mile) maximum grade; io» curves; eight tunnels. Northern Pacific— Rises 1668 ft. at 116 ft. per mile (2.2 per cent) in an air-line dis- tance of 13 miles. Mexican Central.— Rises 1750 ft. in 19 miles at San Juan del Rio with easy grades and curves and 1650 ft. at Zacatecas. Among lines located, but not yet built, may be mentioned : Luckmanier Pass (near the St. Gothard).-Rises on a development of 29^ miles between two points six miles apart, on a maximum grade of 132 ft. per mile (2.5 per cent) implying a descent of something less than 3900 ft., with maximum curves of 084 ft. radius (5" 49'). "^ Mexican Central.— Two lines ascending from the coast to the central plateau of Mex- ico, one from the Gulf of Mexico at Tampico and the other from the Pacific at San Bias, fcoth of which rise some 4500 ft. on 2 to 3 per cent grades. ♦ Fora full and most interesting account of these and other works by Mr. Latrobe, see Railroad Gazette, December 5, 1874. CHAP. XX.— D UPLICATE TRACKS FOR PUSHER GRADES. 70I Vera Cruz to City 0/ Mexico, via Jalapa.— The line more fully described in Appen- dix C. Rismg 7323 ft. (2232 metres) in one unbroken 2 per cent (average) gradient for 72.64 miles (1 16.9 kUometres) or from an elevation of 600 ft. to an elevation of 702^ ft above the sea. /^ o ». 948. The great effect of fluctuations of velocity to modify the nom- inal rates of short gradients may be illustrated by the following tests made by Mr. C. H. Hudson, a prominent and able railway manager. The tests are thus described :* ••Recently, for the purpose of testing a new engine of the Consolidation pattern just received by the East Tennessee, Virginia & Georgia Railroad we weighed a train of 30 loads, caboose and private coach, and took it with' the engine to a heavy grade about a mile long, averaging 67.1 ft. per mile The- grade was not even, but undulating ; some being more and some less than the average. In one place, 100 ft. were at the rate of 98 ft. ; another, spots of 300 ft. at the rate of 91. and, of course, to match it other spots were less than the average. ^ Before reaching the grade, there were about 1600 ft of level- mostly on a 3 curve to right, which curve continued 800 ft. up the grade Then k)llovved [curves and tangents for 4800 ft. in all] when the summit was reached I he day was warm and dry, and circumstances favorable. The weight of train was as follows : ^ X AT^^SfiK^' '??'?^^ ^^^-^ tt"'^^''.. 55.000 lbs.; 32 cars. 1.453.160 lbs.; total, 1,617,160 lbs. Cylinders, 20 by 24 in.; diameter of drivers, 59 in.; weight on drivers, 97,000 lbs. ^ '' First Test.— The engine stood at start at water tank about 1500 ft from foot of grade, and when grade was reached was making about 18 miles per hour At a point 3700 ft. from the grade the engine came to a stand, unable to taki tram through. It was then backed down and two cars set off, weighing 123 500- lbs., leaving weights as follows : ' 6 ti, -«.j.ow I ' 66o*lbs' ^^'°°^ ^^^■' '^"'^^''' 55.000 lbs.; train, 1,329,660 lbs.,- total. Second Test— This time the engine started from the same place as before struck the grade making 22.3 miles per hour, and in seven minutes turned the summit, making 4.5 miles per hour. The engine averaged 145 lbs. steam was worked most of the way in the second notch from bottom, or at aboilt an i«-inch cut-oflf. the last 1200 feet being in lowest notch, or what was called full stroke (22-inch cut-oflf). Very little sand was used ; engine did not slip^ any. ^ •• While this grade was undulating, it seemed fair to take the average —which has been stated 67.1 per mile, or 1.27 per cent,— giving a resistance due gravity per ton of .0127 X 2000 = 25.4 lbs. & J' The locomotive- power indicated by these records is then computed in the following manner— correct numerically, but wholly incorrect in its apparent indications : "Train resistance Lbs. pej ton. Curve resistance on 6° curve ....*....*.* .V.V. * 60 Grade resistance (1.27 per cent) ...i ...!...!!.*.'!..'.*...* . 25 4 Total resistance t o be overcome 36.4 lbs *Jour. Assoc Eng. Societies, 18S6. I [ I il l^Hi 702 CHAP. XX.— DUPLICATE TRACKS FOR PUSHER GRADES. ** Weight of engine and train being 747 tons ; 747 X 36.4 = 27,191 lbs. But about icxD ft. of the train will be on a 10° curve, where the resistance per degree is .05, or, for the 10°, .50 percent ; theesti mated resistance on a 6° curve was .30 per cent : here is an ex- cess of .20 per cent, or per ton, 4 lbs. Now, three cars are all of the train on this curve, and we have 69 tons, which gives 69 X 4 = 276 lbs. Making a total resistance to overcome of 27,467 lbs. ** You will note that here we develop a tractive force of 28.2 per cent of the weight on drivers ; not so great as in other cases, but much over ordinary prac- tice. •'The theoretical power of the engine would be as follows: 50 X cylinder pressure = 192 X 130 (assumed) = 24,960 lbs. " The estimated resistance per ton is, including the correction for the lo" curve, 36.8 lbs. " Divide the theoretical power, 24,960, by this resistance 36.8, and we have : 24,960 -t- 36.8 = 678 tons = 1,356,000 lbs. Being the theoretical amount the engine would move up this grade, or about 137,000 lbs. less than the actual amount moved. 7'Ae actual work exceeds the theoretical by about the weight of the engine and tender.'" 949. The true explanation of this apparent anomaly is that the en- gine in reality did no such thing as to develop a tractive force of 27,467 lbs., nor is there any real discrepancy between the actual and theoreti- cal v^rork done. The true way of computing the tests is as follows : Per cent. Nominal average rate of grade (that of the profile) 1.27 Correct for curvature at 0.03 to 0.05 vertical feel for each degree of cen- tral angle, which is in effect an addition to the grade of 0.12 And we have as the equivalent nominal grade, including effect of uncom- pensated curvature 1.39 Where the curvature is makes no great difference, unless it stalls the train, and we need not now go into that detail. Then to compute the first test we have : * Train struck foot of grade at velocity of 18.0 miles per hour, and stalled in 3700 ft. Vel.-head for 18.0 miles (Table 118), 11.50 ft.; 111? = 0.311 vert. 37.00 ft. per station as the work done by momentum. 1.39 — 0.31 1 = 1.08 per cent as the virtual grade, or the one up which the unassisted traction of the engine hauled the train. Miles per hour. Vel.-head. Second Test. — Speed at foot of grade (4800 ft. long). . . . 22.3 17.67 ft. ** •' top ♦• 4.5 .73ft. 16.94 * For strict correctness the distance travelled up the grade by the centre of gravity of the train, and not the engine, should be used in this test, but as the initial velocity was taken from the engine it is impossible to do so. CHAP. XX,— DUPLICATE TRACKS FOR PUSHER GRADES 703 16.94 vert. ft. _ 48.00 stations ~ °'^^3 ^^'*'- ^^' P^*" station as the assistance derived from mo- mentum, and 1.39 -0.353 = 1.04 per cent as the virtual grade in the second All this is shown graphically in Fig. 233. At the foot of the grade the vertical head corresponding to the given velocities is erected, and 5tf Z j 1600' -also at the head of the grade, although it is so small as to be hardly visible. 1 he dotted Imes show the virtual grades. The two tests coincide, it will be seen, almost exactly in the virtual grade which they indicate, espe- cially ,f we remember that the engine used a little more steam on the upper part of the second run. This virtual grade includes the effect of curvature, and for the power developed by the engine we have : Train resistance ^**^- P^*" ^°"- Grade worked by engine powVrYsaV" i!(i6peVcem)V.V.V^*. '.*.**.* .*.';;*.*.;; 2?;2 Total per ton ~7~~ 26.2 lbs. per ton X 747 tons 'L ^^ Against Mr. Hudson's computation oVactual work o'f . .* .* *. .* .' .* *. .' .' .* ' ~ 2?'467 - And of theoretical work with 130 lbs. pressure of .i 24:960 " ,^ 5'^J^ ^^^"^^ ^""^^ ^°"^ requires an average effective piston pressure of ~~- = a fraction over 100 lbs. per square inch, which is coming down within the bounds of reason (and barely that) for a Consolidation engine ""^'oiJo^Axf ^^'' ""^ ^''''^' P'"^^^"''^ ^"d rnnnm^ over 15 miles per hour. 950. We may see how these variations of velocity may tend to in- crease grades, and how nearly our process of computing them will check by considering what took place between the starting-point and foot of 704 CHAP. XX.^DUPLICATE TRACKS FOR PUSHER GRADES the grade, 1 5cx> ft. off, over a nominally level grade. The virtual grade may be tlius determined : Speed acquired in 1 500 ft Corresponding vel.-head, ft Then we have, as the virtual grades per station.. In first test. In second test. 18.00 22.30 11.50 ii.ro = 0.77 17.67 15.00 15.00 In other words, in the first test the engine started off lazily and did not do as much work as after it struck the grade. In the second test the engine succeeded in doing somewhat more work than it did after it struck the grade, as is but natural from the fact that its average velocity was less and (probably) it used more sand and had a somewhat higher boiler pressure. But the correspondence is close without these allowances ; quite sufficient to indicate, what is beyond question, that the method is essentially trustworthy. Now, had this grade, instead of being only 4800 ft. long, been 48,000 ft. long, it will be evident that the same initial velocity would have done very little to help out the engine. To derive equal aid from momentum we should have needed to have a vertical head ten times as great in that case, or 176 ft., which would have carried the necessary initial speed up to the impracticable limit of nearly 71 miles per hour. Consequently, while short grades and short sags may be operated almost as levels with speeds of 30 to 50 miles per hour, long grades or bad sags can be but little helped out by momentum. In the one case the profile tells the truth, and in the other it does not. PART IV. LARGER ECONOMIC PROBLEMS. *• The rich man's wealth is his strong city : the destruction of the poor is their poverty." — Proverbs x. 15. •' For whosoever hath, to him shall be given, and he shall have mor« abundance : but whosoever hath not, from him shaU be taken away even that he hath."— Matthew xiii. 12. •♦ For which of you, intending to build a tower, sitteth not down first, and counteth the cost, whether he have sufficient to finish it ? Lest haply, after he hath laid the foundation, and is not able to finish it, all that be- hold it begin to mock him, saying, This man began to build, and was not able to finish." — Luke xiv. 28-30. 45 ^1 PART IV. LARGER ECONOMIC PROBLEMS. CHAPTER XXI. TRUNK LINES AND BRANCH LINES. 9«. That the most elementary conditions on which the suc- cess or failure of railway enterprises depend are often radically misunderstood, almost necessarily follows from the fact that the world IS so full of examples of misdirected enterprise-of lines built with great hopes of profit which have proved miserable failures; while, on the other hand, there are so many examples of roads built for local purposes, or otherwise without particular expectation of a brilliant future, which have proved magnificent properties. Among innumerable examples which might be men- tioned we may take the West Shore Railroad of New York as an example of the first class, and the parallel New York Central of the last: the present New York Central & Hudson River Rail- road having been made up by the consolidation of six or eight different local lines, built with little or no reference to the forma- tion of a great trunk line. These two lines are, in their different ways, striking examples of the fact that the conditions which con- trol the future prosperity of such properties are often wholly misunderstood. ""ii>- r.. f"; It seems for many reasons probable that by far the larger part of this very general misunderstanding_of the blundering into unexpected success on the one hand, and into dismal and ^ li'^l"^ I ilili mith» 708 CHAI\ XXI.^TRUNK LINES AND BRANCH LINES. M *!H ':1| m utter failure on the other— arises from a single cause, viz., an- imperfect understanding of certain elementary facts, wh.ch we will now consider, as to the effect upon the productiveness of the property of any increase in the sources of traffic. The unex- pectedly good or bad fortune of hundreds of properties can be traced, in part or whole, to this single cause. 953. Let us suppose a railway to be projected, say loo miles lone, to connect t*wo traffic points of some importance. A, B, !• ig. ^' 233. We will assume for ^ ?-t simplicity that there is Fig. ^33'. little or no intermediate local traffic, as often happens. We will consider^ and ^ to be equal, not necessarily in population, but in traffic-contnbut.ng capacity to this particular line. The traffic which the railway has to support it may be then represented by the combination AB, being that which naturally exists between two traffic points of the importance of A and B. 954. Let us now suppose that another alternate route may be chosen, which by a slight detour will stake an i"t«""^, E, F, ETC., Figs. 233 to 237. For any larger number of points N we have similarly (3) CHAP. XXL— LA IV OF LNCREMENT OF TRAFFLC. 713 whence the ratio of increase is V _ N{N- i) T n[n — i) (4) As n becomes a larger number, the ratio of « to « — i becomes more and more nearly unity, until finally the ratio of r' to T becomes sensibly n 3 ) (5) which is THE EQUATION GIVING THE GENERAL LAW OF INCREASE IN EARNINGS DUE TOAN INCREASE OF TRIBUTARY TRAFFIC POINTS ON THE SAME LENGTH OF LINE ; i.e., the productive traffic varies as the SQUARE of the number of tributary sources of traffic. Table 191. Showing the Effect upon Aggregate Traffic of Interpolating Additional Traffic Points in the Line. [See Figs. 233-238.] Per Cent Absolute No. OF Traffic Increase of Increase of Traffic Relative Per Unit of Traffic Traffic Points. Traffic. Population. by Addinif by Adding One Traffic One Traffic Point. Point. 2 I 0.5 • • 3 3 I.O 200.0 2 4 6 1.5 100. 3 5 ID 2.0 66.7 4 6 15 2.5 50.0 5 7 21 30 40.0 6 8 28 3-5 33.3 7 9 36 4.0 28.6 8 10 45 4.5 25.0 9 II 55 5.0 22.2 ID 12 66 5.5 20.0 II 13 78 6.0 18.2 12 14 91 6.5 16.7 13 15 105 7.0 15.4 14 etc. etc. cts. etc. etc. It will be seen from the last column of this table that the absolute gain from a given addition of tributary population is greater in proportion to the amount of other tributary population, but that the addition per cent is very much greater on light-traffic roads. ;il! 714 CHAP. XXI.— LAW OF INCREMENT OF TRAFFIC, CHAP. XXI.— LAW OF INCREMENT OF TRAFFIC. 7 1 5- II Table 192. Growth of New York City Internal Passenger Traffic [Compare tables noted below.] In the years 1871-72-73, the report of a committee of the American Society of Civil Engineers shows 3,000,000 to 5,000,000 more passengers per year than above, probably by inclusion of some omitted line above, but it has not been attempted to correct thfr- error. * Actual population, 1885, 1,439,037. Summary. City Passbnger Traffic 1 Ybak. Estimated and Actual Population. (Thousands). Per Inhabitant. ■ EIcTated Roads. Horse Cars. Toul. Blerated. Horse. Total. 1853 581. None. 6,836 • • • II. 8 II. 8 54 605. 6.817 II. 3 11.3 1855 629,810 18,488 29.4 29.4 56 663. 23.153 350 35.0 57 698. 22,190 31.9 31.9 58 734. 27.900 38.0 38.0 59 773- 32,889 42.7 42.7 i86o 813,669 (Same as 36.455 44.7 44-7 61 826. 26,272 31.8 31.8 62 838. next 35.878 42.8 42.8 63 850. 40,412 47.6 47.6 64 863. column.) 60,900 70.6 70.6 1865 876. 82,055 93.8 93.8 66 889. 88.953 100. 100. 67 903. 100,542 III.O III.O 68 915. 105.817 115. 6 115. 6 69 929. 114.349 123.5 123.5 1870 942,292 115.139 122.0 122. o* 71 962. • • • • 133.894 139.4 139.4 72 982. 136 143.561 143,697 0.1 146.0 146. 1 73 1,003. 644 144.715 145.359 0.6 » 144.4 145.0 74 1.024. 796 151. 131 151.927 0.8 147.8 148.6 1875 1,045,223 921 165.997 166,918 0.? 1 158.8 159.7 76 1,076. 2.013 166,401 168.414 I.^ ► 154.5 156.4 77 1.107. 3.012 160,924 163,936 2.7 135.3 148.0 78 1. 139. 9,291 160,899 170,190 8.1 131.0 149.1 79 1,172. 46,045 141.939 187,984 39.4 \ 121. 4 160.8 1880 1,206,299 60,832 150,390 211,222 50.5 124.7 175.2 81 1.242. 75.586 155.801 231.387 60.8 125.4 186.2 82 1,278. 86.361 166. 511 252,872 67.6 • 130.8 198.4 83 1.315. 92.125 176.625 268,750 70.1 134.2 204.3 84 1.354. 96,703 187,413 284,116 71 5 138.2 209.7 1885 1.393* 103.355 193.762 297.117 74.2 139.0 213.2 1 Year. Popula- tion. Trips per Inhabitant. No. OF Lines. No. Trips per Inbab't Horse. Elevated. Total. Horse. Elevated. per 100,000 of Popula- tion. 1853 1855 i860 1S65 1870 1875 1880 1885 1890 581. 630. 814. 876. 942. 1.045. 1,206. 1.393. • • • • II. 8 29.4 44-7 93.8 122.0 158.8 124.7 139.0 • • • • 0.9 50.5 74.2 • • • • II. 8 29.4 44.7 93.8 122.0 159.7 175.2 213,1 . . • • 2 4 6 12 12 19 23 25 • • I 4 4 • • 2.03 4.67 5.5 10.7 13.0 15.3 14.5 15.4 • • • • Since 1885 a further and great increase has begun, so that there is every prospect that it will be more notable in prof)ortion than heretofore. While the growth of city travel is in some respects a special problem, since its increase results in great part from the increasing distances which larger population brings, yet it is mainly but one expression of a general law brought out in Chap. XXI., that traffic tends to increase about as the square of the population or sources of traffic united by con- venient means of communication. Quite as forcible an illustration of this law is obtained by studying the growth of traffic of States and the United States as elsewhere- presented. Compare Tables 14, 15, 16; also Tables 2, 3, 7, 21 to 28, 34, etc. 960. It is plain that we cannot always, nor ordinarily, count on any series of points A, B, C, D, E, etc., each of which is ex- actly equal to each other, but we may push the generalization a little farther. Taking the entire population of a country, or of a continent, or of the world, and conceiving it to be made up of a great num- ber of units, either of single individuals or of groups of 10, 100, 1,000, or 1,000,000 individuals, it is plain that each one of these units has potential traffic relations with every other unit. The components of each unit visit those of the other socially ; they buy and sell from each other ; they visit each other in the hope of buying and selling; they produce more (this is an invariable law) for the especial purpose of supplying the necessities of others with whom they have or finally secure traffic relations. Until such traffic facilities exist, these relations are inchoate, or merely potential. As the facilities are extended they become actual'; ^ 716 CNAP. XXI.— LAW OF INCREMENT OF TRAFFIC. and they sliould tend to become actual, if our reasoning has been correct, about in proportion to the square of the facilities afforded and of the population served. Experience seems to show that they do tend to increase about in this ratio, some evi- dence of which fact is contained in Table 192, as also in Table 14, 15, 16, and others referred to below Table 192 ; but however this may be, that they increase in very much more than direct ratio is beyond all question. It is therefore unnecessary to take each individual town as a traflSc unit, as we have done heretofore. We may regard €ach individual person as the traffic unit, and while it will be by no means literally true that he will have actual traffic rela- tions with all those for whom the facilities exist, but only with ■every tenth, hundredth, thousandth, or millionth person, accord- ing to his character and occupation, yet practically the result is the same. His aggregate contributions to railway traffic will vary in close accordance with the total population connected with him by traffic facilities, and his payments to any particular line will be in direct proportion to that fraction of the total of the whole population connected with him by traffic facilities which is reached by him over that particular line. 961, We have thus only to consider the points A, B, C, D, E^ Figs, 233-237, to represent single individuals instead of towns or other traffic points, and to consider their number n to be indefi- nitely multiplied, when precisely the same process of reasoning we have just applied to towns leads to precisely the same conclu- sion as respects individuals. We then have n{n — i) = «' [Eqs. (4) and (5)] almost exactly; whence, if 7^= the actual tributary population on the line and p =^ 3. possible additional population, the percentage of increase in traffic Z, all other things being equal, will be, (6) CffAP. XXI.— LA PI' OF INCREMENT OF TRAFFIC. yi? In other words, if we have 1,000,000 tributary population and can add 100,000 more, each unit of which is of the same traffic- producing capacity, the increase will be (10 +1)' 1 — —1 = 21 per cent. 10 ^ If our original population were 500,000, we should have, all other things being equal, (5 + i)' — Ti ' = 44 per cent. This is really a more correct way of arriving at the theoreti- cal effect of additional sources of traffic than that used in Table 191, since it takes each individual as the unit, instead of a group of 20,000 or 100,000. It gives a somewhat smaller percentage, but the difference is not great enough to make a material difference in what are at best merely illustrative computations ; not sus- ceptible, nor supposed to be susceptible, of exact application in practice, except as indicating the comparative probable revenue, all other things being equal, of alternate routes between the same termini. 962. In any actual instance, of course, all other things would be more or less unequal, and hardly any of them equal, so that it would be quite impossible to make any very precise estimates- by the formula given. In the first place, it is impossible to more than guess at the true tributary population. That which is ap- parently tributary, from being on the line, is decreased by the competition of other lines, so that only a fraction of it is really tributary ; while, on the other hand, there may be an immense population beyond the limits of the line itself which is indirectly tributary to it through the medium of other lines, as in the case of the trunk lines from the sea-coast to the west. In the second place, a mere enumeration of heads is a very rude index of the traffic value of those heads. A great mining or manufacturing or commercial point will contribute vastly more traffic per head than other more inert communities, and a large town, almost al- ways, more per head than a small town. mw^. I ( 7i8 CHAP. XXI.— TRUNK LINES. 963. Nevertheless, when we connect Smithville with our line we get the New York-Smithville as well as the Smithville- New York traffic; and the traffic of New York is made up only of the aggregate of that to thousands of Smithvilles, of which we get those which we reach in one way or another by our line. Thus the discrepancy on account of the difference in the traffic- producing capacity of individuals is less than might be supposed, and Tables 14, 15, 16, and 191, with various others in this volume, show that the law holds tolerably well when applied on a large enough scale to eliminate sources of irregularity, while there are innumerable examples of single lines whose prosperity or ad- versity can be directly shown to imply the existence of some «uch law. These fundamental truths being granted, therefore, it leads very directly to certain conclusions as to the proper manner of laying out both trunk lines and branch lines ; conclusions which, while they may be difficult to apply so exactly as to avoid a con- siderable percentage of error, will yet be so definite that the radi- cal error of mistaking black for white, so to speak — taking that for the best course which is rather the worst course, — is not likely to occur. TRUNK LINES. 964. Trunk or main lines may be roughly divided into two classes: those which are, and those which are not, liable to be subjected to close competition at almost every important point. Almost all lines in the United States belong to the former class. Their only permanent protection against competition, in most cases, is to throw out a skirmish-line of branches and par- allel routes so as to cover securely a considerable territory; and this is one great reason for the tendency in that direction which is so notable, and which has already gone so far that more than half the mileage of the United States is controlled by a dozen managements, with every prospect that the tendency to consoli- dation will grow still stronger. Table 193 shows how far this tendency has already gone. Another and still stronger reason, however, directly results from what has preceded — that every CHAP. XXI.— TRUNK LINES. 719 Table 193. Length of Road and Gross Earnings of Fourteen Great Systems of Road in the United States, 1881. [Abstracted from a Paper by Wm. P. Shinn on «' Increased Efficiency of Railways for the Transportation of Freight," Trans. Am. Soc. C. E., November, 1882, with the addi- tion of the Baltimore & Ohio, Atchison, Topeka & Santa Fe, and some minor details.] New York Central & Hudson River. Lake Shore & Michigan Southern ... Canada Southern Michigan Central Total New York Central System . . Ne%v York, Lake Erie b' Western. Pennsylvania, Eastern System Western " Total Pennsylvania , Baltimore & Ohio, Eastern System. '* Western " . Total Baltimore Ss* Ohio Total Four Trunk Lines , Per cent of total United States. Wabash St. Louis & Pacific Chicago, Burlinerton & Quincy Chicago, Rock Island & Pacific... Illinois Central, Northern New Orleans line. Chicapro& North-Western Chicago, Milwaukee & St. Paul Missouri Pacific, Main System Leased and controlled lines. Louisville & Nashville, Owned Leased lines Louisville, Cincinnati & Lexington Nashville. Chattanooga & St. Louis Georgia Railroad System Atchison, Topeka & Santa F^ Union Pacific, Proper Lines in interest , Central Pacific Southern Pacific *.!!***! i ! Total Ten Systems othsr than N.Y. Trunk Lines. Per cent of total United States Miles. 993 403 950 3,523 1,020 3,041 2,529 5,570 595 959 I.5S4 11,667 12.35 P- c. 1,320 571 3,348 3,160 1,335 1,891 3,276 4,260 X,OI2 4,773 1.438 I 434$ 272 521 641 ,5,785 1,821 2,449 3,034 2,240 2,874 1,281 4,270 4,155 36,754 38.90 p. C. Gross Earnings. $29,322,532 17,880,000 3.369,259 8.8cx>,486 $44,224,716 31,058,790 159,372,277 20,715,605 75,283,506 18,463,877 Per Mile $14,900 23 -97 p. c. $8,640,957 19.087,484 $14,467,790 21,176.455 11,956,907 10,793,105 »9,334,o72 17,025,461 $10,911,650 1,196,112 2,256,186 2,543.032 $24,258,817 7,608.936 $24,094,101 3,435 945 27,728,441 16,906,980 ",584,509 31,867,753 27.530.046 $211,371,510 Per Mile $5,751 29.14 p. c. " I ^:ll t 720 CHAP. XXI.— TRUNK LINES. CHAP, XXI.— TRUNK LINES. 721 Table 193. — Continued. • Miles. Gross Earnings. Total Fourteen Great Systems 48,431 51.25 p. c. $385,206,784 Per Mile $7,956 53" p. c. Per cent of total United States Total of Minor Lines of the United States, under 300 to 400 different managements Percent of total United States 46,065 48.7s P.O. « „., •340,118,335 Per Mile $7,383 46.89 p. c. Total of the United States in 1881, of which earn- incTS were rei>orted 94,486 Per Mile $7,677 Since 1881 there have been many changes in the details of the above table, but the great sjrstems given probably cover in the aggregate a still larger proportion of the total mileage of the United States. There were in 1881 a total of 104,813 miles reported built, 10,327 miles of which did not report earnings, being largely newly built lines. addition to the tributary population makes the revenue per head from the previously tributary population greater. This may not often, perhaps never, be more than dimly felt, but that it is the true course and justification for many such extensions we cannot doubt. Nevertheless there are certain mountainous or sparsely popu- lated and poor regions, in this and all other countries, where reasonable freedom from competitive lines is assured, as in Mexico, the lines in which afforded some instructive examples of the right and wrong way of laying out main lines. 966. Bearing in mind what we have already seen as to the small expense of operating extra distance (par. 197), the appreci- able additions to revenue which may be expected to arise from it (par. 230), and the small effect of moderate additions of dis- tance to discourage traffic, there can be no question that the fundamental rule for laying out such lines — deviated from only for good special reasons — should be to link together the largest possible population, regardless of minor losses of distance, pro- vided THE AGGREGATE POPULATION PER MILE OF ROAD is not diminished (par. 237), or even sometimes if it is. An ultimate limit, beyond which it would certainly be unwise to go, and hence which should not be closely approached, is that the in- crease per cent of distance should not exceed the increase per cent of probable revenue, according to eq. (6), par. 961. 966. The most marked exception to this rule is when the dif- ference of distance becomes so great as to seriously discourage traffic, or encourage the construction of a more favorably situ- ated competing line. A further exception is when, by passing midway between two traffic centres, neither of which can be reached readily by the main line, both may be served fairly well by branches or other- wise (par. 66). Any marked difference in grades or costs of construction may of course make a difference ^xlh^r pro or con j but entire disre- gard of the rule, by deliberately neglecting intermediate traffic points for the sake of through traffic, usually means financial failure. 967. Several instances of the application of these general rules may be studied on any map of Mexico, showing the existing railway lines Ihe most pronounced is the choice between the route from the City of Mexico to the United States {via the Mexican Central or the Mexico National routes), either of which could be chosen by the Central at the time the concessions were granted. The longer line, passing through the heart of Mexico, and thence con- nectmg at El Paso with the Atchison. Topeka & Santa Fe. was chosen. The grounds for this choice, beyond question, were that (i) railways in Mexico were lo be profitable ; (2) the more railway controlled the more aggregate profit, even if the less per mile ; (3) a long line through the heart of a country must in the long-run be the best line. On the other hand, the choice violated two of the fundamental rules which have been laid down. First, it seriously discouraged traffic be- tween Mexico and the United States by burdening that which passed over It with nearly 500 miles of extra haul : this practically insuring that the National line, when completed, would be. or might easily make •tself. the leading through line. Secondly, it very materially decreased the average tributary population per mile over what it would have been nad the Mexican Central line been followed as far as Celaya. in Central Mexico, and the Mexican National from there north ; especially had the i 722 CHAP. XXI.— TRUNK LINES. CHAP. XXI.-^TRUNK LINES. towns of Silao, Guanajuato, and Leon been linked to this main line by a branch, as they might have been later. Had the Mexican Central been built by this line there can be little doubt that it would be to-day (1886) a most flourishing property, both because its investment would have been smaller and its traffic larger. 968. On the other hand, leaving the flourishing town of Durango on one side, although it saved distance in what was already a disastrously long line, was probably an error, although this cannot be asserted with much posiliveness. The loss of perhaps 50 or 60 miles more would have taken the line through a much better country, actual and prospective, for nearly 400 miles, the country through which the line was actually run having been almost the poorest possible ; while saving that loss of distance did not materially improve its already bad case as respects through traffic. 969. The National, for its part, fell into an error which has often been committed before, and never without loss— attempting to start a new terminal port at Corpus Christi, instead of making for Galveston direct. Such projects for changing the established course of trade seem to have a peculiar fascination for sanguine projectors, but it is always all but certain that they will end in failure. The more instructive example to be found on the National lines, how- ever is a striking instance of how, when traffic is at best thin and prob- ably non-competitive, connecting the largest possible population by the main line is almost surely the wiser course. Fig. 239 shows this instance, the dotted line being what had been projected, and the full line the route finally chosen by the company on the writer's recommendation. The full line seems a most roundabout course for a main line, espe- cially as the total mileage to be constructed was not diminished, but rather increased. It was to be remembered, however, first, that the traffic was thin and non-competitive; secondly, that the number of trains *'could not be great; thirdly, that reasonably good facilities for continu- ous traffic between every one of the many points connected by the line was desirable ; and, finally, that with a traffic thin at best the mainte- nance and separate operation of branch lines is very burdensome. It was therefore decided, as respects the line from Morelia to Zamora and La Piedad, that it would be better to make the branch to Patzcuaro a part of the main line, thus accomplishing the double end of decreasing the aggregate mileage to be operated and maintained, and facilitating Patz- cuaro^Zamora traffic and (by more trains) Patzcuaro-Morelia traffic, while gaining more revenue from through traffic by not materially heavier through rates. 72Z 970. Beyond La Barca. although the line had alTeady been runout of Its course from Patzcuaro to the Pacific, it was decided to run it still farther north to take in the important city of Guadalajara, the second city m Mexico (about 80.000 inhabitants), whence the line started almost due south for Colima and the coasts. This change alone much more than doubled the probable traffic per mile of the road, and it would have been, from an economic point of view, a very great error not to do it. Fig. 239. oni"ff^'^'"yI" ''"^ '"'° '''°-°"^ f™" Guadalajara to the coast, and one from Guadalajara to Mexico ; but all the more it was desirable. The Sharply accentuated topographical cond.tions. which it is impossible to describe with more detail, made this particularly clear. 971. Trunk lines open to destructive competition, and able to command only a narrow belt on each side of them as their natural tributary territory, nor that, unless they afford almost as good accommodations as it is possible to give, can of course 724 CHAP. XXI.^TRUNK LINES, CHAP. XXI. -TRUNK LINES. afford no such sacrifice as this. As the subject is a large and complex one, the conditions of success and failure may perhaps be more usefully indicated in a small space by a few notes from the history of the actual trunk lines, and notably of the four trunk Wn&s par excellence — the New York Central & Hudson River, Erie, Pennsylvania, and Baltimore & Ohio— than by a more gen- eral discussion, 972. The New York Central is probably the most striking example in the whole world of two truths: That lines connecting the largest aggre- gate of population will be likely to lie on the most favorable route for easy grades, and that easy grades give an overwhelming advantage in handling low-rate traffic especially. As a through line the New York Central was not made, — it grew. Some fifteen different corporations built its New York-Chicago line, each without a thought of doing more than connect- ing its own particular termini. Consequently it did connect them effec- tually, and the magnificent string of towns from which the New York Central has drawn its chief prosperity was the result. Its intended rival, the West Shore, was built in a very different way. It was— unfortunately— planned. From attaching exaggerated impor- tance to through traffic and to the effect thereon of accommodating way traffic, or from other cause, several of the most important local points,, as notably Albany and Rochester, were left at one side, and others ill served, there being hardly a competitive point on the line, not even its two termini, as well served by it as by the Central. This may have been unavoidable. The expense alone of doing otherwise would have been enormous, and had the expense been incurred it might not have insured the success of the line ; but the fact that it was not, foredoomed failure— for the two reasons, that the line which is only half as convenient as another does not, therefore, get half as much business, but none at all (par. 51 et al.)\ and for the further reason (par. 959), that the value of a line is as the square of the population best served by it. 973. From the through business proper the New York Central has derived comparatively little benefit. Its greater length reduces its aver- age receipts per mile on competitive traffic materially below those of the Pennsylvania, and the magnificent water-way which is immediately adja- cent to it for the entire distance from New York to Chicago has tended powerfully to still further curtail its rates. But its unequalled grades (by much the most favorable in the world for a line of such length), and the 725 indirect benefit of its immense local traffic, which alone required and supported all the staff and plant of a great railway, enabledTts thigh busmess, vast as .twas, to be handled as so much extra business the onlv expense for which was the direct outlay for wages and fuel and a smaH amount for wear and tear of track. Of no other trunk line was this so nearly true, but the lower rate per ^^k Centrlf hir ' 'T f ^ ^"^(--P^-^ly) raw material on t^New .food T^ f '"^ P'^"^""^ ^"^ ^^^"^^ ^h'^h is not always under- Cn hilh onTt""\^^'"''^"^^^P^"^^^^^ ^^^^'P^^ ^^ -^ ha's always been high on it. as shown more clearly in Table 37, page 1 10, viz. : New York Central. Erie Pennsylvania, . . Baltimore & Ohio, 1876-80. 61.3 70.0 557 53-9 -AVERAGE- 1881-85. 67.9 69.7 56.0 This contrast is immutably fixed by tlie nature of the traffic and th^ operatmg conditions, and gives no indication of relative efficiency of operation, as has often been carelessly assumed. emciency of ^JJX ^'^"'"7 '" "" P^'""'^^'' °' °P--«n8 expenses which is visible above m the figures for every one of the three lines but the Erie is due <:in,ni„ tothe enormous reduction in rates in recent years, the later Tei g at " "' a cause and effect of the still more enormous increase in volume of traffic The astoundmg and almost incredible figures for this change are shown in Table lo. an graphically in Fig. .40. The history of the worfd affords no parl^^^l t^^ " andu,soneof the strongest proofs that we have not erred far in our colclu sions in the first part of this chapter. conclu- V Tn "^"^i P^.^f ^^^^ANIA is in many respects a contrast to the Ne«r York Central. L,ke the latter, it grew, rather than was made, as a Ne" West t'piXdlT'' T"' 'r- ''™^'^"'^' *° ■'■•'"^ '-<«= f™- 1"! west to Philadelphia only, ,t chanced to lie in the most favorable Dosi .on for a short low-grade line between New Vork and the Wes "^he .rresistible tendency of events, and of its situation, linked with ita Pe^t sylvan la-New York line on the East, and a branching network of Hnes" hrough the West. In comparing it with the New vfrk Central one !s ■mmediately struck by the contrast in this respect which it poLv ^ffords. and while much of this may well be due.'and no dou^ is' to a ZC-:Zltl'' r"°r' ^''""'""" °' ^"^ "^"^Sers, an underlying r^a! son for it-of which, perhaps, no one was conscious-is that the Pennsyl- ;;i 726 CHAP. XXI.— TRUNK LINES. Table 194. Increase of Traffic and Decrease in Rates on Various Groups of American Lines, 1865-1885. [The last part of this table is shown graphically in Fig. 240.] Seven Trunk Lines. Six Chicago Roads. Twenty-one Leading Lines. Year. Ton- miles. ^'= ^ 1,000,000.) Rate. Cents. Ton- miles. (I = 1,000,000.) Rate. Cents. I — 1,000,000. Freight Earnings. 91000.) Rate. Cents. Tons. Ton- miles. 1865 ... 1.654 2.900 a. 546 2.306 1.951 1.715 5»3 3.642 22 2,370 $69,825 2.945 1866.... 1867 — i868.... 1869... 2,044 2,258 2,651 3.159 893 1,054 3-459 3-»75 3.154 3.036 a8 30 35 39 2,981 3,223 3.743 4.408 77,003 75,381 80,141 87.426 2.582 2.338 3.140 1-983 1870 . . 3.744 1.585 1,234 2.423 39 5.IH 88.488 1.731 1871 187a 1873... 1874.... 4.341 5.»8i 5.782 5.879 1.478 1-475 1.470 1-342 1,233 1,337 ».749 1,851 2.509 2.583 2.188 2.160 50 59 67 65 5.937 6,973 7.885 8,020 8,380 97,186 112,408 127,045 108,598 1.636 1.612 1. 611 1-354 1875 ... S.937 1. 161 1.904 1.979 63 107.657 1.284 1876.... 1877.... 1878.... 1879 ... 6,739 6,536 8,853 10,T20 .983 .971 .807 •725 1.994 a,2ii 2,823 3.470 1.877 1.664 1.476 1.280 69 73 9,072 9.131 10,433 »3.033 102,009 100,804 105,973 114,255 1.124 1.103 1. 015 0.876 1880 ... XO.544 .840 4.544 1.266 106 14.085 139,331 0.988 x88i.... 1883.... 1883... 1884. .. 11,659 11,189 11,141 10.719 .759 .665 .842 .740 4,435 5,04» 5,768 5.940 1.420 1-364 1.308 1.251 126 134 14a 144 16,074 »6,075 17.307 17.501 18,837 146,699 147,719 167.564 153.735 0.912 0.918 0.968 0.878 1885 ... ".331 .636 6.287 1.200 151 144,562 0.767 This table is from data compiled by Mr. Henry V. Poor. The seven trunk lines are the Pennsylvania ; Pittsburg, Fort Wayne & Chicago ; New York Central ; Lake Shore; Michigan Central ; Boston & Albany ; and New York, Lake Erie & Western. The six Chicago lines are the Illinois Central ; Chicago & Alton ; Chicago & Rock Island ; Chicago, Burlington & Quincy ; Chicago & Northwestern ; Chicago, Milwaukee & St. Paul. These thirteen roads, with eight others of most prominence, are included in the last part of the table, from which Fig. 240 was constructed. vania had more to gain by extending itself in all directions, and more to lose by not doing so. Additional traffic we have seen (par. 41) to be that on which railways grow rich. With the greatest city of the country only ninety miles off, it was mdispensable, to secure the utmost traffic from it, to reach it by its own lines, even with a friendly independent connection as an alternative. The futility of terminating a line at any CHAP. XXI. -TRUNK LINES. 727 other than the largest available city was never better illustrated, unless by the experience of the Erie at Dunkirk on a smaller scale. Perhaps Fig. 241 is as good an object-lesson as could be found as to the folly of such attempts, even when circumstances seem to especially favor what sanguine projectors look on as a " fair divide" of an enormous traffic. 1 728 CHAP. XXI.— TRUNK LINES. CHAP. XXL— TRUNK LINES. 976. A larger reason, which includes the first, was that the Pennsyl- vania was so situated 729 12s Fig. 941. — NoRiHWKSTERN Grain Reckipts at Various lead- ing Shipping Points, 1876-1885. as to form a very short line between almost all points on the West and the sea-coast. This in- sured good average rates per mile, while the abun- dance of coal and iron on the line, and the large amount of favor- able grades insured low operating expenses. The Pennsylvania had much to gain, therefore, from handling additional through traffic OVER ITS OWN LINES, according to the law laid down in par. 211 — that the only conditions under which a line could reap the full benefit of being a short line was that it should reach all its im- portant traffic points by its own lines. The Penn- sylvania was such a short line ; it proceeded to satisfy the other half of the true, and too little considered, conditions [One nf many illustrations of the prrsistency with which O* prosperity, aS it WaS ..affic flows to leading and well-established centres, as com- pared with the irregularity and uncertainty of traffic at minor traffic flows to leading and well-established centres, as com- j^g natural policy tO do. points] Until it did so it was, by its existence and facilities, making the fortunes of other lines in- stead of its own. Moreover, the additional through traffic, which it could secure by controlling its connections, was a great object to it, for it made, and must always continue to make, a comparatively large profit on it, while to the New York Central it was a small object, because it made a small profit out of it. The New York Central's chief reliance has been on its iocal trafiic ; its through rates per mile being necessarily low at best even on that traffic so situated as to come to it most naturally while its expenses were higher because of dear fuel. Had it gone much out of Its way to seek more through traffic, its average fates per mile would have been lower yet. and un remunerative. Therefore it has not done so. 977. In part, this likewise explains why the unfortunate Erie has never tended to ramify throughout the West ; but the Erie is an example of a line which has succeeded in spite of this disadvantage, for four reasons • ^ I. By terminating at the greatest city of the East, and (after correct- ing the error of attempting to make a new great city at Dunkirk) at the chief traffic point at the eastern end of the great lakes, making two ad- mirable termini. 2. By its skilful location, most of its line being on very low grades mdeed. although it has some high summits and bad sections. 3. By its local coal traffic and cheap supply of fuel. 4. By its large and growing local traffic— less than the New York Cen- trals. but larger than the Pennsylvania's, and until very recently little subject to competition. These gave it great powers of offence against the New York Central and It has been able to command at all times a fair proportion of the traffic wh.ch lines in the Central interest brought to Buffalo. But the Erie s prosperity has been injured by three causes quite as potent • I. Of ail the great Eastern cities, the Erie reached advantageously ^nly ONE, whereas the New York Central reached two. New York and Boston (in fact, all New England and a large part of the Canada trade has been almost monopolized by the Central), and the Pennsylvania reached four; the two greatest directly. New York and Philadelphia and Boston. Baltimore, and Washington fairly well. This has been the pnmary difficulty with the Erie. " To him that hath shall be given " It might pay the Pennsylvania well to control a line to Smithville in order to secure thereby its traffic with the whole Atlantic coast, when it would not pay the Erie at all to own a line to it which would secure onlv its New The Smithville-Pittsburg traffic, the Smithville-Boston traffic, and the bm.thville-jonesburg traffic naturally gravitated to the line which com- manded Its other traffic East; and so the owners of lines in the West were naturally drawn most to that line which offered the most widely \\ K rT" 730 CHAP. XXI.^TRUNK LINES. CHAP. XXI.— BRANCH LINES. 11 «IK il ramifying connections, and could both give and ask better terms. Hence it has happened — * 2. The Erie has never been able to secure good Western connec- tions. The only serious attempt in that line, until 1881, was the old At- lantic & Great Western, one of the most ill-judged enterprises which has ever been constructed in tjiis country, whose failure was foredoomed from the beginning, as pointed out in par. 215 et seq. We may be tolerably as-^ sured that the Erie never will have a great system of connecting lines,. for it is not planned to secure them. In this respect the history of the road is full of instruction. 3. The Erie has been peculiarly unfortunate in its past management — in part from lack of comprehension by its foreign owners of its necessi- ties and conditions. 978. The Baltimore & Ohio is somewhat of a contrary example — of a line whose judicious and consistent management has given great financial strength to a property under many disadvantages. It has obeyed the irresistible tendency of the times by extending its lines X.o Chicago in the West (as well as to the Ohio River tier of cities) and ta Philadelphia and New York on the East. The effect of the latter it is as yet (1886) impossible to foresee; but unless the laws of railway pros- perity which prevail elsewhere are to fail in its case, it will result in a very great addition to its traffic, giving it what it has never had before — what may be called a continental traffic. For the Baltimore & Ohio, as it stood up to about 1880, was merely an example of the financial strength which may be secured by locating between considerable local sources of natural traffic, and holding strictly to them. Between Baltimore and Washington on the East and Pitts- burg, Cincinnati, Louisville, and St. Louis on the West, the Baltimore & Ohio was the natural channel of communication, and as good a one as could be secured. A large coal traffic was also assured to it. On this it prospered, avoiding dissipation of its means on many branches and con- nections. Nevertheless, it was economically impossible that it should fail for long to reach out to the other large cities mentioned, and to transfer itself from a local line to a national one. Had the Pennsylvania chosen to restrict itself to its main line between Pittsburg and Philadelphia, with a few only of the most necessary branches, it also would have been, and might have indefinitely continued to be, a prosperous local line of the kind that the Baltimore & Ohio was. It might even have earned as good or better dividends than now, but its cost and value, and its earning capacity likewise, would have been far 73 r less, and its aggregate profits vastly less. It was therefore not to be ex- pected, nor for the public interest, that it should pursue this policy. 979. In the history of these four trunk lines, could we afford space to consider it in detail, we have warning of almost every possible danger which can arise in the laying out of trunk lines —meaning by the latter term not necessarily lines of enormous traffic (see par. 981), but lines the main part of whose traffic is complete in itself, so that they are not mere branches or feeders of other lines. We may summarize a few of the more important conditions of success in such lines as follows: 1. They must reach by their own lines the largest traffic- point at each end which is at all within reach by an extension of 20 or 30 per cent of their length, and there must stand on equal terms with their connections as respects benefits and injuries to- . be given and received. Failing to do this is pretty sure to result in great loss, and generally in insolvency. 2. They must reach without fail every considerable inter- mediate traffic point along their line which can be reached by any reasonable detour or even sacrifice of grades, their prosper- ity being about as the square of the tributary population. 3. They can in no case attempt to create new channels of trade, as by attempting to make a seaport out of some neglected roadstead, without the greatest risk of failure. The attempts ia this direction have been many ; the successes as yet none. 4. Nearly or quite half of their traffic must practically begin, and end on their own lines, either because it goes no farther, or because it is delivered at some great competitive distributing point. 5. It is of little avail to run a line even from a great city to nowhere. The apex to the pyramid in Fig. 238 is eloquent and truthful in this respect. Without a good traffic-point at each end of a line the conditions for great prosperity are not present. BRANCH LINES. 980. That branches are in the main profitable investments is^ evident from their very rapid rate of increase, which is largest, 732 CHAP. XXI.— BRANCH LINES. up to a certain point at least, on the most prosperous lines. That they are rarely very profitable when considered by themselves, and apart from the main line, and as a rule do little more than pay operating expenses, is abundantly shown by the reports of almost every line which has branches and reports their traffic in detail. This fact is so clear and so generally admitted, that it hardly needs statistics to prove it. As a rule, the earnings per mile of branches range only from a fifth to a tenth of the earnings of the main stems. 981. The only considerable exceptions to this rule are branches which are in reality main lines, having a very considerable traf- fic which is complete in itself. A striking example of this kind of branch is what is knov^rn as the Mahoning Division or Cleve- • land Branch of the New York, Pennsylvania & Ohio Railroad, which runs diagonally across the main line from Cleveland to Youngstown. This nominal *' branch" was really a subordinate main line, built by a separate company and projected on rational principles, according to par. 979. It had and has a very consider- able traffic, both freight and passenger, which is complete in itself. On the other hand, the nominal "main line" is in reality a mere branch, violating conspicuously every one of the condi- tions for the success of main lines specified in par. 979. It is not surprising, therefore, that the " main line" was a financial failure and the " branch" a financial success, which has largely helped to support the main line even after paying a very heavy rental (10 per cent dividends per annum) to the lessor company. 982. The reason for the continued and rapid building of branches in spite of their apparent unproductiveness is simply this : They contribute traffic to the main line which, as it is merely an increment, costs always comparatively little to move, and often nothing at all. The company, therefore, receives from its contributed traffic rates for a haul of perhaps 500 miles at a cost for hauling due to only 100 or 200 miles. This follows directly from what we have seen in Chapter XV., par. 181, and elsewhere. Rudely speaking, if we call the average cost per tor? or passenger-mile 100, we may say : CHAP. XXL— BRANCH LLNES. ^33 Average cost per unit of traffic = 100 Extra passengers, singly, cost o -|- ** " in car-loads cost 51030 " " in train-loads cost 50 f^xtra freight in small lots costs often in both directions and usually in one direction , + ** •* in car-loads 51020 *• " in train-loads (and all car-loads must ordinarily be con- sidered to be made up into extra trains in the direc- tion of heaviest traffic) not over 60 Not unfrequently when a large part of the traffic of a branch j^oes over the main line in the direction of favoring grades it is Handled over the main line at no appreciable extra cost by simply tilling up trains, and the branch is then enormously profitable. To these direct and evident advantages from a branch is to be added the vivifying effect of increasing the tributary population from the causes discussed in the first part of this chapter, the prosperity of the line increasing in something like the square of the tributary population. 983. It is not to be wondered at, therefore, that branches and extensions are much sought for by prosperous companies, even in regions where there is not the likelihood of rapid increase of traffic which prevails throughout the United States. Neither is it to be wond^red at that the seeking for them is often overdone, so that the branches become a burden which threatens to swamp the main line, and often does so. For there is this to be said against branches : Their traffic is usually thin, while they cost as much or more to build and not much less to keep up than the main line. Therefore it is easy to lose all that is gained on the main line by the extra cost of handling the traffic on branches and paying their rentals ; although it still remains universally true, that branches are far more profitable than appears on the face of their returns, separately considered. 984. These facts make it easy to see what should be the gov- erning rule in laying out branches. The one universal rule, to be deviated from only when special reasons to the contrary ap- pear, is this : Strike the main line as soon as possible. In 734 CHAP. XXL— BRANCH LINES, laying out a branch to A from the main line ED, Fig. 241 (which represents to scale an actual instance), B is in all ordinary cases ^. the point to strike the main line, if possible, even at \- — T"^ some disadvantage in grades and construction. It \) is not correct to compare the entire line ABCD with "C\ the alternate ACD, Were we building a line to >r handle a main-line traffic between A and Z>, that would Fig. 241' be the proper course to pursue ; but with a branch- line traffic, when we have gotten it to the main line we may say, for preliminary and approximate purposes, that we shall handle it thereafter for nothing. If the branch traffic be nearly all toward D and the grades favor it, this will be almost literally true. Therefore the true question is : How will this traffic be moved to the main line most cheaply and advantageously — via AB or via BCl In nine cases out of ten AB will be the best, for these reasons : 985. Branch-line traffic is light and fragmentary. Grades and curves then become minor considerations within pretty wide limits, especially when one, two, or three engines must be kept on the branch anyway. On the other hand, the extra cost of ■keeping up the track on AC instead of AB is so much dead loss. Any traffic AE is seriously burdened by the additional dis- tance via ACE over ABE^ while the gain to the traffic AD is but trifling. Passenger traffic is almost invariably better served if deliv- ered on the main line with the shortest possible haul. It is therefore bad practice to lengthen out branches to get ■cheap construction and good grades, even when the difference favors most of the traffic of the branch, unless the extension is justified by the cardinal rule laid down : By which route is the traffic delivered on the main line at any point, most cheaply and advantageously, regardless of where ? 986< To the preceding is to be added another still more im- portant and sometimes conflicting rule : Strike the main line at A considerable town, if possible. If there be a town of some size at either B or C, Fig. 241', that will be the point to termi- CHAP, XXL— BRANCH LLNES. 735 nate the branch at, or to consider it to terminate in comparing the alternate roiites, for the traffic of the branch will be very apt to be delivered at this town even if the branch strikes the main line elsewhere, if it does not add more than 20 per cent to the haul. The purely local traffic of two neighboring towns, A and B or A and 6*, will ordinarily be found a very welcome addition to the traffic contributed to the main line by the branch, and it depends greatly on facilities. If a train has to be taken from B to C and then another from C to -^ to get from A to B^ the A-B traffic will be practically killed. Only the necessary travel (par. 45) will remain. 987. The preceding has been on the assumption that the branch is to reach a point A. When the purpose of the branch Fig. 342. is not to reach any particular point, but to develop a tract of territory, the conditions are of course somewhat charged, but even then the same general principles apply. It will as a rule be more economical, and more convenient to the traffic, to con- centrate it upon the main line as soon as possible. Therefore it — ^^ Fig. 243. is not as a rule good practice, even when the purpose of the branch is to develop a long strip of parallel territory which has traffic relations mostly in one direction, C, Fig. 242, to construct branches along parallel lines. The method outlined in Fig. 243 736 CHAP. XXL— BRANCH LINES. CHAP. XXII.— LIGHT RAILS AND LIGHT RAILWAYS. 72,7 is far more likely to accomplish its purpose advantageously, even when branches like DEF become necessary; the governing rules being, first, to link together neighboring towns having natural traffic relations as directly as possible, and secondly, to reach the main line quickly. 988. This policy is the correct one, not only because it handles a given traffic most economically, but because it tends to unify the district served by the railway and aggrandize points on its main line. The two lines AC and DC, Fig. 242, are practically two separate roads having no interrelation with each otlier whatever. A less amount of road in Fig. 243 gives equal traffic facilities from the district AB to C at less cost to the railway, and likewise promotes traffic relations with other points on the main line and to the south of it. When the traffic of the branch is equally divided between East and West, or nearly so, as respects destination on the maia line, then Fig. 244 gives what is abstractly by much the best Q system for laying out branches, other things being equal. Other things rarely are exactly equal, and hence considerable devia- tions from this plan are oftea required in the laying out of such branches, but in all cases branch traffic needs to be quite differently considered from what it would be if we were laying out a main line to the same point. The writer is compelled to omit a number pf concrete examples of the lay- ing out of branches, especially a most interesting one having reference to the Pacific branch of the Mexican Central Railway, ia order to keep this volume within more reasonable size. i 7^^ Fig. 944. CHAPTER XXII. LIGHT -RAILS AND LIGHT RAILWAYS. 989. A FACT evident enough in the existing railway system of this country, and indeed of the world, is that, taking it as a whole, distinctively light railways do not prosper nor multiply. The apparent field for them is great — many times greater than for railways of tho ordinary type. The need for them is keenly felt in many regions where it would appear as if cheap light lines would answer every requirement which the traffic justifies. Such lines can admittedly be built, and in many cases have been built, both of standard and narrow gauge, for but little more than the cost of a good turnpike ; some of them even following the turn- pike, using low speed, light rails, light rolling-stock, sharp curves, and little or no grading beyond a mere smoothing of the sur- face. Yet it is a significant fact that out of the 125,000 miles of rail- way in the United States (1885) very little of it is of this charac- ter, or anything closely resembling it. Absolutely there is a large amount, no doubt ; but comparatively there is very little, and that little shows a constant and strong tendency to approxi- mate to the general standard. In spite of enormous differences in traffic there may still be said to be a certain average standard to which the vast majority of the roads approximately conform, or begin to do so almost as soon as the track is laid. Between the 12,000 to 14,000 miles of trunk lines or sections thereof, which make nearly half the earnings and carry far more than half the traffic of the country, and the 113,000 to 115,000 miles which manage to live on the rest of it, or on less than one tenth as heavy an average traffic, there are indeed considerable differ- ences of condition; yet the resemblances — in rails, in ties, in bal- 47 i 738 a/AP. XXII.-LICHT RAILS AND LICIIT RAILWAYS. um ( last in rolling-stock, in alignment-are still more striking, prov- ing almost to demonstration that the law (to which there are of course exceptions) is that distinctively light railways do not prosper, or if they prosper, do not stay light. We need not search far to find some strong reasons why this should be so, and it is well that every one should do so who is concerned in projecting a light line before finally deciding on its details of construction ; not because so doing will necessarily induce him to abandon his intention,-very light lines are often justifiably built and are the only alternative to none at all,— but because it is always desirable that the consequences of an intended course of action should be fully understood in advance. 990 The first and greatest question in connection with alight railway is, What weight of rails shall be chosen? This is so for two reasons : First, because the rail is the largest single item of expense on such a line, and secondly, because on the weight of rail hinges the character of the rolling-stock, the ties, the ballast, and so to a greater or less extent almost every other detail of the line. The rail question is therefore a very fundamental one, which we may well consider with some care. Cutting down the rail section is almost the first point of at- tack for a certain large class of economists, much as cutting ten percent off salaries is liable to be at a later period in the history of a railway There is probably no other way in which anything like as large a saving can be effected with so little demand upon the time or thought or skill of the manager ; nor does it admit of doubt that either or both of these economies may at times be both expedient and necessary. Nevertheless, they would not we may be certain, be resorted to nearly so often as they are if the full extent of the sacrifice made were realized. 991 That it is not more fully realized as to rails is probably due in\he main to a not unnatural impression that in buying rails what one wants is steel : That if light and heavy sections are the same price per ton, buying a 30-lb. section instead of a 60-lb. is like a poor and hungry man buying a one-pound loaf at five cents instead of a two-pound loaf at ten cents. CHAP. XXII.-LIGHT RAILS AND LIGHT RAILWAYS. 739 Tins is not at all the case. In buying rails we are not buying steel ; at least we do not care to buy it. We are buying three im- ponderable qualities: (i) stiffness, (2) strength, (3) durability If we get our money's worth of these qualities, it is a matter of complete indifference (except the future scrap value of the steel which a poor, light traffic road cannot afford to give mucli thought to) whether we get much or little of steel. If we do not get our money's worth of what 7ve want, our bargain is just as bad, how- ever much steel we get. 992. To determine whether we do or not, one must, unfortu- nately, use an intelligence somewhat higher than that of a hay- scale. Any absolute measure of the qualities mentioned is es- pec.ally difficult. Thus, it may be hardly necessary to say here that to estimate exactly our stiffness and strength we must de termine the position in the rail section, Fig. 245, of two little points which lie at a distance called the radius of gyration from the centre of the rail (meaning simply the points where, if all the steel in base and head were concen- trated, it would have the same power to resist gyration , i.e., bending, as it now has) and we must then make a "^, number of other assumptions in regard to the character of The load and support which we well know are not only doubtful but will not be even approximately true in practice, unless bv ac- cident. But for comparative purposes all this is unnecessarv The support given to the rail from below by the road-bed and ties may be assumed the same for any section of rail, whatever it may be absolutely. We may assume that any two or more sections re- quiring to be compared will be practically - similar" to each other. I.e., with the same proportion of base to height, etc etc so that Fig. 245 may, by simply varying the scale, be'taken to represent a section of any weight from 10 to 100 lbs. per yard and yet be tolerably well designed even for these extremes * ^ established mathematical laws we also know that the xCwT^^^^ designed in having a head flaring outward "artheboVoin^^t inat IS a detail we need not enter into. A »••»*" w 740 C//AP. XXIT.— LIGHT RAILS AND LIGHT RAILWAYS, weight will, under these assumptions, vary as breadth X height, and that the stiffness will vary as breadth X cube of height. That is to say, if we multiply every dimension by two, we increase the weight of the section by 2 X2 = 4, but the stiffness by 2 X2' or 2 X 8 = 16 or 2*; in other words, tiie stiffness in that case varies as the fourth power of the increase in linear dimensions, whereas the weight varies only as the square. 993, An algebraic demonstration of the simplest character, which it is unnecessary to give here, would prove this result to be in accordance with a general law — that the stiffness in a RAIL VARIES AS THE SQUARE OF ITS WEIGHT PER YARD. If We increase the weight 10 percent, 20 per cent, 30 per cent, we shall increase the stiffness to 1. 10 = 1. 21, or 21 per cent, 1.20* = 1.44, or 44 per cent, 1.30* = 1.6'^j or 69 per cent. Mere formulae have a hazy, indefinite sound, which, it is evi- dent from what we see around us (for these general facts are welP enough known), do not produce much impression on the mind r but let us reduce them, in the accompanying Table 195, to the plain, practical basis of how much stiffness we get for a DOLLAR with light and heavy rails, and we shall have some more forcible, because more readily comprehensible, evidence as to- why light rails are sooner or later avoided as the plague by all railways ; admitting the evident fact, that for light lines especi- ally stiffness is not only by much the most important quality a rail can have, but (as we shall see more fully) by much the cheap- est stability to be had in the market— far cheaper than tamping- bar stability, which roads of heavier traffic can afford to rely on more extensively. In Table 195 a so-lb. rail is taken as the unit of comparison, as being about the maximum for distinctively- light railways and the minimum for those of ordinary type, and the cost of rails is taken at the even figure of $30 per ton. CHAP. XXII.— LIGHT RAILS AND LIGHT RAILWAYS. 741 Table 195. Comparative Amount anp Cost of Stiffness in Light and Heavy Rails. Weipht of Rails. Tons Cost Per Mile Comparative Cost Per Unit Comparative Value Lbs. Per Mile. at $30 Per Ton. Stiffness. of Received Per Yard. Stiffness. for $1. 10 16 I480 .04 $12,000 20 cts. 15 24 720 .09 8,000 30 cts. 20 32 960 .16 6,000 40 cts. 25 40 1,200 .25 4,Soo 50 cts. 30 48 1,440 .36 4,000 60 cts. 35 56 1.680 .49 3.429 70 cts. 40 64 1,920 .64 3.000 80 cts. 45 72 2,160 .81 2,667 90 cts. 60 80 2,400 1.00 2,400 $1.00 55 88 2,640 I. 21 2.182 1. 10 60 96 2,880 1.44 2,000 1.20 65 104 3.120 1.69 1,846 1.30 70 112 3.360 1.96 1,714 1.40 75 120 3.600 2.25 1,600 1.50 80 128 3.840 2.56 1,500 1.60 Tons of rail per mile taken at 1.6 tons per lb. per yard, allowing for a certain mini- mum of side track. Main track only requires \^ or 1.571 tons per pound per yard. Comparative stiffness (4th column) is as the square of the weight per yard, 50 lbs. being taken as the limit of comparison. Cost per unit of stiffness (5th column) is given fcy dividing column 3 by column 4. Comparative value received for $1 (last column) is given by dividing column 5 by $2400. 994, This table should be carefully studied. It will be seen from it that the lighter the original section of a railroad, the more it loses by using a light section, because the more would be its proportionate gain from a given increase in weight of sec- tion. The sacrifice of value in buying light sections is precisely the same as if in buying rails we were, in fact as well as in form, buying steel instead of stiffness, and were to choose light sec- tions in spite of the following market quotations: Per ton. Steel in 20-lb. sections, ^75 00 30 " " 50 GO 40 " " 37 50 50 30 00 60 " " 25 00 70 " " . .' 21 43 80 " " 18 75 742 CHAP. XXII.— LIGHT RAILS AND LIGHT RAILWAYS, #1^ Or, again, our loss is the same as if we were offered a certain amount of steel in 25-lb. sections at $30 per ton, but were told that if we would take twice as many tons in the form of 50-lb. sections we could have the remainder at $10 per ton. That is precisely what we are told in effect, as respects the quality we are really buying — stiffness— when we are offered rails of such sections at a uniform price per ton. 995. The ultimate strength of rails is a less im.portant quality than the stiffness, because it is never expected to be called fully into use. Nevertheless, it often is so called into use and even exceeded, especially as the rail wears out, and it is therefore an important quality. The strength is less affected by the weight of the rail than the stiffness; for, referring to Fig. 245 once more, the strength varies only as the square of the height, whereas the stiffness varies as the cube, both varying directly as the width. Therefore, in a similar way to that employed for Table 196. Comparative Amount and Cost of Strength in Light and Heavy Rails. Weight Cost Per Mile Cost Comparative Value of Rails. at S10 Comparative Per Unit Lbs. Per Ton. Strength. of Received Per Yard. Strength. for $1. 10 I480 .089 I5.365 44. 7 CtS. 15 720 .164 4.380 54-8 * 20 960 .253 3.796 63.2 • 25 1,200 •354 3.717 70.7 ' 30 1,440 •465 3.091 77.6 • 35 1,680 .586 2,870 83.6 • 40 1.920 .716 2,684 89.4 • 45 2,160 .854 i.^'\o 94.8 • 50 2,400 1.000 3,400 100.0 • 55 2,640 I 154 2,288 104.9 ' 60 2.880 1. 314 2. 191 109.5 ♦ 65 3.120 1.482 2,105 114. ' 70 3.360 1.656 2.028 118. 3 ' 75 3.600 1.838 1.959 122.5 ' 80 3.840 2.024 1,897 126.5 * The different columns are determined in substantially the same manner as in Table 195, except that the third column is as the 9 power of the weight per yard, taking 50-lb. rails as the unit of comparison. CHAP. XXII.— LIGHT RAILS AND LIGHT RAILWAYS. 743 determining stiffness, we may determine that the strength varies as the square root of the cube (or ^ power) of the weight, and thus obtain Table 196. This table also should be carefully studied. The loss of strength obtained with light sections will be seen from Table 196 to be far less striking than the loss of stiffness. Nevertheless, it is as if strength were a ponderable element, and we bought it in spite of the following prices per ton: Per ton. Rails of 2o-lb. section ^7 c© " 30 " " ! .* 38 60 ** 40" « 3230 5^ 30 00 o<^ 27 40 7° 25 30 °^ 23 70 If steel were quoted at these prices per ton, it is a tolerably safe hypothesis that light rail-sections would not be in much favor; yet this is an unduly favorable showing even for the item of strength, for if we were to compute the comparative strength after the sections have received a certain fixed amount of wear, we should find the apparent disadvantage of light sections as given above very much increased. 996. It is a little difficult to determine a standard by which to measure durability, because, as a rule, light and heavy sec- tions are chosen for very different duties, i.e., are approximately proportioned, and necessarily must be, to the kind of locomo- tives running over them, so that no rational comparison can be made between the durability in a 10- or 20-Ib. section and that in a 70- or 8o-lb. section, as there can be in the items of stiffness and strength. What we can do, however, is to compare each section with one 5 or 10 lbs. heavier, since there is a rational and practical choice between such sections, for any one given service. Taking a rude yet tolerably approximate average of rails as they are now designed and chosen, we may say (i) that half the total weight is in the head, and (2) that half, or nearly half, of 744 CHAP, XXII.— LIGHT RAILS AND LIGHT RAIL WA YS. the metal in the head (or i of the'whole weight of the rail) is expected to be worn away before the rail is finally condemned as unsafe, although it rriay be earlier removed to a less trying location. That is to say, a 40-lb. rail has 10 lbs. of wear in it, and a 50-lb., 12^ lbs., making their weight when finally con- demned 30 and 37i lbs. respectively. 997. But when comparing two \dJ\\'s> for atiy one given service it is obvious that this is an unfair basis of comparison, since, what- ever the original weight per yard, a rail for any one given service may be so designed as to utilize most of any additional weiglit in wear, leaving the weiglits of the worn-out rails when scrapped nearly the same. This is, of course, not fully possible without using very ugly and distorted original sections, but it is at least a moderate statement that, even if any two rails of dif- ferent weights are designed precisely "similar" to each other (as, say. Fig. 245), so that they have the same proportion of waste metal (as respects wear) in the base, yet the head can in all cases, in any one given service, be worn down to an equal ulti- mate weight before condemnation, so that a 40-lb. and 50-lb. rail would compare as follows: 40-lb. rail, . 50-lb. rail, . •Whhn Nrw.— > , When Worn Out. ead. Base. Head. Base. Head. 20 lbs. 20 lbs. 25 lbs. 25 lbs. Head. Base. Total. 10 lbs. 20 lbs. 30 lbs. 10 lbs. 25 lbs. 35 lbs. A 50-lb. rail worn down to 35 lbs. may fairly be said to be at least as strong and safe as a 40-lb. rail worn down to 30 lbs., althougii that is rather an extreme illustration as respects the absolute amount of wear for either of the rails specified; but by proper design it is realizable in sections sufficiently strong for their duty. 998. If, however, we are practising the last degree of economy in first cost, clioosing the very lightest section which is con- sistent with the duty laid upon it, as we have already admitted is sometimes expedient, it is obvious that we cannot count on any such rate of wear as that. Wearing off half the head means reducing its ultimate strength by something like 45 per cent, and CHAP. XXII.— LIGHT RAILS AND LIGHT RAILWAYS. 745 Ok < _] < > .X Q < H X o pa < oi :3 Q u. o H en O u Q -< h Z. o < > < < o U •Z.^ 0) < E^ 3*0 •a .53 V .a c tn *.» '■^ '^ r4xtdHt o*e-+#H«-^»"-Hi ocH" I.H M hH M 000000000000000 r^ ~ ~ "^lT^ r^ I" Oi^u^ «<^MCi\r> u~. c4oou->c<)M »nvO N 00 i~>.o u->»0 ^ \n\0 O t^.fc»oooo O^O^d O ^sO CO O N "^vO 00 © N •<^<0 (» d CI XT) \f> \rt Wi xr> \r> \n t-i M N N CO CO '^ '^iO "^^ O t>i t>.oo in \n \r> \n ir> \n \n m t^ ^ u^ t^ MiQr^ c^mt->i N CO »rt\0 t^oo O I-" W CO mo f^oo d '-'•-'^•-''"'•^'-''-'Ci \n \n «r> »n »r> »nr».OW»nt^Oc^^r^ONtr)r>.d MMMMNNO^NCOCOCOCO^ O *n o «n o u-> o in© tn O tn O tn O •-I i-i N c< coco^^»^ mvoo r^t^QO tn O ^ (A > VI a o u a > lA V JC *J biO c s T3 a; C C 6 28-3 «» u 00 '.-• r^ u '0 U en J3 15 c _c » « ^ 4J lac '!-> cu Jj u 43 '-' • 2, or more directly from the follow- ing Table 198, which explains itself, and will probably make it very clear that whether a new project as a whole will pay or not, it is almost sure to return a heavy profit on the additional capital invested, obtained at any probable cost, to buy reasonably^ heavy rail-sections, for the sake of their durability alone. Table 198. Years of Wear which a Light Rail-Section must Outlast before thk Durability obtainable by adding Five Lbs. Per Yard to it will BECOME A Losing Bargain, costing more than that of the LiGHr Section.* Weight of Light Section. Lbs. Per Yard. Present Cost of Capital. 5 per cent. 30 30 40 50 60 70 80 Years. 450 49-1 52.0 55-5 58.1 60.3 62.4 10 per cent. Years. 23.0 25.2 26.6 28.4 29.7 30.9 31.9 15 per cent. 20 F>er cent. Years. Years. 15-7 12.0 17.2 13.1 18. 1 19.4 20.6 139 14.8 15-5 21. 1 16. 1 21.8 16.7 ♦ For the ultimate value, U, of a certain sum/ invested at compound interest for « years at » per cent, wc have :/ = /(. + »-)": ^•bence log £/ = log / + log (i + r) x «, and log (1 -I- r) Letting the numerator (1) of the vulgar fractions in column 9 of Table 197 = p (the log of which is o and may be dropped), the denominator of the same fractions will = U, and we have log n = log of log U - log of log (1 -I- r). 1000. In these facts we have reasons enough, and to spare, why all roads should tend, as they do tend, to use what project- ors of new roads call a " heavy ' rail, and think they can't afford. It is because, for a poor road as well as a rich one, the best is. ■1 1 ■J i I 748 CJIAP. XXIL— LIGHT RAILS AND LIGHT RAILWAYS. THE CHEAPEST, and a poor road, even more than a rich one, must have the cheapest to live at all. It is because, with railways as with men, ''the destruction of the poor is their poverty," in that there are not as many cents in a poor man's dollar as in a rich one's, because of the bad bargains which his poverty drives him to — or he thinks it does. While it may still be right to buy the light sections, if we must have something and cannot pay more^ it should at least be realized how great a sacrifice is made, in order to make sure that there is no other direction in which a less costly economy can be exercised. Of course, as has been already stated, there is another side to this question — a certain legitimate and advisable use of light rails. If a man needs but three yards of cloth to make a coat, and only needs one coat, there is no particular economy in his buying four yards, simply because he can get it cheap; and then, besides, there is always the open question whether his great- est need is for a coat or a pair of breeches. That part of the ques- tion we may now consider. We have merely found so far that if a man is going to buy a coat, there is a fearful loss which a poor man cannot afford in buying one which is too small to fit and too flimsy to wear. Of all directions for economy, cutting down the rail-section is the most costly in the end. 1001. If attempted economies in all other directions were equally disastrous, we should be led directly to the conclusion that it was not worth while to build light railways, and that they could never reasonably be expected to prosper; but such a con- clusion must be, in part at least, fallacious; for there is evident need at many points for just such lines, which, when built, do prosper, or at least answer the requirements. Hence there must be certain directions in which, within certain limits, it is expe- dient to economize in their construction, and there are, in fact, many directions where economy does little harm. If we exam- ine in detail the cost of even a moderately important line, we shall find that an enormous proportion of it is for items which a light, cheap railway either has no use for at all, or can dispense with at slight inconvenience, in part or whole, or can postpone at , moderate sacrifice to some indefinite date in the future. CHAP. XXIL— LIGHT RAILS AND LIGHT RAILWAYS. 749 1002. Terminal facilities, for instance, are an immense item in the investment in large railwa)^s. In the Buffalo (N. Y.) yards alone there are 650 miles of track (Table 201), representing an in- vestment of millions. Station and other buildings are other large items, which may be made small on a light road; but the chief of all directions in which a rigid yet intelligent economy- may be exercised to reduce largely the construction account with- out undue effect upon earning capacity is in the construction of the road to sub-grade. 1003. This is best seen by considering how much (or rather how little) the cost of 5 lbs. per yard extra weight in the rail, which We may take at the even figure of $30 per ton, or $240 per mile, will do to construct the road to sub-grade. We have seen how very advantageous is the effect of this expenditure upon the rail-section. If expended on grading and masonry, the same amount will only do the following: Cubic Yards.. Earthwork, at 20 cents per cubic yard 1,200 Equal to a continuous fill 5 in. deep, or a cut 10 ft. deep and 100 ft. long. Rock cutting, at $1.50 per cubic yard i6a Equal to a cut 100 ft. long and 2.3 ft. deep. Culvert masonry, at $5 per cubic yard 48. Or one small box culvert. Bridge masonry, at $10 per cubic yard only 24 Far more than these quantities can usually be saved by aban- doning the attempt to fit the line for high speed and long trains, and judiciously economizing in these three ways : (i) By using sharp curvature; (2) by using trestling in place of masonry and heavy earthwork; (3) by moderate undulations of grade; to which may be added (4) sacrifice of distance to obtain easy work, and especially to reach towns. 1004. Whatever conclusion may be just as to the proper stand- ard OF CURVATURE for Hnes of fair traffic, it is certain that for a road to which the last degree of economy in first cost is essen- tial, and which does not expect more than a very light traffic, the intelligent use of sharp curvature offers one of the simplest, most 750 CHAP. XXII.^LIGHT RAILS AND LIGHT RAILWAYS, effective, and most expedient methods of economizing in first cost. We have seen tliat since the introduction of steel rails and air-brakes both the operating cost and the danger of sharp curva- ture have been greatly diminished. The New York elevated rail- ways run 800 or more trains of four cars each per day around the 63° curves (shown in Figs. 201-2) with perfect ease and with only a moderate slackening of speed. Another much-used curve of 50 ft. radius is described on page 326. In Table 116 full details are given of other sharp curves in use on standard-gauge lines, ranging from 410 to 175 ft. radius, over many of which a very heavy traffic passes. While these extremes are to be deprecated {nor are they often required), they do make it an absurdity to say that a cheap light-traffic railroad may not use almost any curvature which the nature of its route calls for in order to re- duce first cost, whatever its gauge. In a country offering any difficulty, the reduction which can be effected in this way is very large indeed, and it will in gen- eral be found that no excessive reduction of radius is needed to give a line closely approximating to a surface line, and fitting so well that any further reduction of radius will save but little (par. 883). This disadvantage is far less than that of light rails in almost every instance. 1005. Moreover, if the profile of almost any line be studied, it will be found that the expenditures are largely concentrated AT SINGLE POINTS. Four or five cuts in a mile, eight or ten miles in a hundred, are what bring up the average; so that in seeking the last degree of economy at these critical points the line as a whole is not, after all, so seriously modified as would be imagined, A further advantage, or rather a bright side to the disadvantage of so economizing by sharp curvature is that at many points the works may assume a mere temporary character for present ne- cessities, while being adapted for ready improvement in the fu- ture, when and if means exist for doing so. In this way the ne- cessities of both the present and future are better provided for than if a compromise line were chosen in the beginning which did not fully insure either present cheapness or future excellence. Par. 283 gives a notable instance. CHAP, XXII.—LIGHT RAILS AND LIGHT RAILWAYS. 75 1 1006. Here the question of gauge naturally comes up. Among the many advantages which have been so loosely claimed for the narrow-gauge system, perhaps none has been so insisted on, or so affected the popular imagination, as this one of being able to use sharp curves readily which were all but impracticable with the standard gauge. A few years ago, when the first edition of this treatise was is- sued, no discussion of the question of light railways could have been adequate without entering pretty fully into \.\i^ pros and cons of the gauge question. This is no longer necessary. The irresistible logic of events has practically settled the question, and the belief in the narrow-gauge as an expedient and defensi- ble system of construction, which was from the beginning founded chiefly on illusion and delusion, is rapidly passing away, and all but gone. We may therefore merely summarize briefl'y file leading points of the question. As respects curvature, we have already seen (pars. 335-6) that while the gain in curve resistance from a narrowing of gauge only, with no other change, is very slight, yet when the wheel- base is reduced correspondingly the curve resistance is probably diminished about in proportion to the gauge. As this is what is usually done in practice, we may consider it from that point of view. 1007. But the question then arises: What is saved thereby ? If It be to increase the hauling capacity of engines, a very slight ad- ditional curve compensation will neutralize the extra resistance of the wider gauge, and we have already seen (par. 290) that any radius which is likely to be desired is readily practicable foV properly designed standard-gauge engines. If' it be to save the extra wear and tear and loss of power, a small reduction in an Item the whole of which is so small (Table 115, page 322) is not worth any^considerable sacrifice, nor can it be taken for granted (nor is it probable) that there is any such reduction. 1008. As respects rolling-stock, there cannot be a question that there is absolutely no practical advantage in the narrower gauge. Any reputable locomotive-builder will contract to build I 752 CJ/AP. XXII.— LIGHT RAILS AND LIGHT RAILWAYS, • • — — — -♦ ■ engines of the same weight and power for either gauge, which will traverse the same curves, for. the same price. The standard- gauge engine, in fact, will or can have enough shorter wheel- base, because of its greater width, to make it take curves a little better — a very important point which narrow-gauge advocates and opponents alike have almost wholly lost sight of. The same is essentially true of the cars. The car-bodies may be exactly the same, and the trifling loss from the extra width of trucks, if it were worth discussing at all, may be fully made up by a slight increase in the weight and capacity of the car-body,, while car-bodies of the ordinary size and capacity can go safely over any structures or track which will carry a light locomotive — whether standard-gauge or narrow-gauge — and carry as large a proportion of paying load as is customary in narrow-gauge cars. 1009. The bridges and trestles are, of course, not affected hf the width of the gauge, if rolling-stock of the same weight and width pass over them; besides which, we shall shortly see evi- dence (par. 1039) that the cost of bridges is but very little affected by the load per lineal foot they are built to carry, so that there is little real inducement to build such structures to carry less than the common loads. The earthwork and masonry is affected only by whatever dif- ference there may be in the width of the road-bed, which cannot properly be more than the difference of gauge. The ties, we shall soon see (par. 1056), may be made somewhat shorter, or about three quarters of the usual width, but only at the expense of de- creasing the stability of the track and increasing the labor re- quired. Fencing, right of way, buildings, frogs, switches, side-tracks, shops, etc., etc., are not affected at all, if the standard of excel- lence and weight of rolling-stock be the same. 1010. There remains, therefore, as the net gain from the nar- rower gauge, only the slight saving in grading and ties, which may amount to one to four per cent of the total cost of the line. On the other hand, there are several very serious losses. The CHAP. XXII.-LIGHT RAILS AND LIGHT RAILWAYS 753 one which is alone of decisive importance is the great loss from not being able to exciiange traffic in bulk, but having to trans- ship all freight and passengers. The loss from this is far more than its direct cost. The resulting inconvenience, delay, and damage to freight drives away much traffic. The cost of maintaining track to a given standard of excel- lence is likewise greater, the cost for track-labor being in about inverse proportion to the length of the ties. The less bearing area of the ties on the ballast increases this disadvantage ma- terially. ^ The maintenance of rolling-stock is decidedly more costly in proportion to work done, and the train resistance higher, because of the smaller wheels. The speed is necessarily lower,' and the passenger cars less comfortable. Tiiese facts are now admitted by all intelligent managers, whether of broad or narrow gauge, and the reconstruction of narrow to standard-gauge is now going on with great rapidity, Several thousand miles of narrow-gauge lines have already been changed, and it is plainly only a matter of a few years when prac- tically all the remaining lines will be changed 1011. It is often apologetically admitted by those otherwise opposed to the narrow-gauge that for certain mountainous re- gions it is best adapted. This likewise is an error, except for such few lines as are not likely to either have or desire traffic relations with other roads. An example is the great system of narrow-gauge lines in Colorado. The Denver & Rio Grande was projected in the early days of the narrow-gauge movement, and did much to extend it, if indeed it may not be said to have been the origin of It, as it certainly was the source of its temporary strength. It >s by much the most considerable narrow-gauge system in the world, and for many years was a great financial success; nor are Its later troubles to be ascribed primarily to its gauge, but to bad judgment in extensions and other expenditures. Nevertheless, the success of this line had little or nothing to do with its gauge, but was due rather to the fact that it was 48 % 754 C//AP. XXII.— LIGHT RAILS AND LIGHT RAILWAYS. cheaply built, and was assured a monopoly of a remunerative and growing traffic at very higli rates— rates from three to eight limes higher than were usual on lines farther east. The disadvantages of a break of gauge were likewise reduced to the minimum by its location. Its narrow-gauge system was com- plete in itself, and connected with standard-gauge tracks at but a few points, where transshipment was often no disadvantage. Yet even under these circumstances — the most favorable under which any large narrow-gauge lines have ever been placed — the disadvantages of the gauge have proved so serious that it is now (1887) only the lack of means which prevents the immediate widening of the gauge on all the more important lines. To do this involves little expense. The ties are rather short for the purpose; but the 20° and 24° curves can, in the first place, be passed without difficulty by the standard-gauge engines, and, in the second place, the cost of reconstructing such curves as are objectionable, while it may be a considerable absolute sum, will be a very trifling one in proportion to the total investment, and probably far less than the present yearly loss from the narrower gauge. 1012. The use of a narrower gauge to cheapen construction has been proved by actual experience, therefore, to be in all cases inexpedient for any road handling a general traffic, or' having any reasonable chance of wishing to exchange traffic with other lines. 1013. Returning to the more hopeful directions for economy: the free use of wooden trestling and the practical abandon- ment of the (immediate) use of masonry is another legitimate and wise device for reducing first cost. There are not a few engineers who decry the use of wooden trestles, nor can it be denied that they are often ill and danger- ously built, and then neglected so long that they become a fre- quent source of accident. But when properly built and properly kept up, they furnish a safe and cheap method of avoiding or postponing the more costly features of construction, so that, even for roads of considerable traffic, it is far wiser to preach CHAP. XXII-LI GHT RAILS AND LIGHT RAILWAYS. 755 the gospel of sound construction than to decry their existence Fortunately, under existing conditions in America, most of the localities where very light railways only can be supported are near enough to local timber supply to obtain pine, hemlock or other suitable trestling timber at very low prices; and with split stringers, and split sills and caps, it is easilv possible (with- out going into fuller details, which would be inappropriate in this volume) to erect substantial structures, without mortises in which each individual stick is renewable in detail, and which will be as safe for the passage of trains as any bridge, so long as they are properly maintained. The great majority of the trestles now erected in this country, however, are ill-designed, especiallv as respects the floors. 1014. At somewhere from 10 to 15 feet of height of fill such a structure becomes cheaper in first cost than even a plain earth fill- and when, in addition to the fill, there would have to be a ma- sonry structure, or when, if it were not for the trestle, the grade would have to be dropped or the line swung in so as to give a rock cut (or even a heavy earth cut) at each end of it, the trestle becomes very much cheaper, and its free use affords us a solid and safe roadway for immediate use which can be continued in the same form indefinitely, if poverty requires it, or which can be advantageously and economically replaced by more perma- nent structures at any time, using trains to make the fills and supply the stone, 1015. It is also allowable to use wooden box culverts to be replaced in time, as they begin to decay, by iron pipes placed inside of them. Many great roads where stone is scarce build these in place of open culverts or trestles as a regular practice and much can be said for it. No road, of course, would use wood for box culverts when stone could be obtained at reason- able cost. 1016. The use of moderate undulations on gradients affords ^nother means by which the first cost of a line mav often be largely reduced, and we have seen (par. 397) that if the track be good enough to stand a certain moderate increase of speed at 756 CHAP, XXII.— LIGHT RAILS AND LIGHT RAILWAYS, special points, it involves no injury to the hauling capacity of engines. The limits within which momentum can be relied on in this manner has been already considered (par. 441) and may, when economy is urgent, be closely approached, as in the in- stance of par. 832, because, should such undulations prove seri- ously objectionable, they may be taken out at any time. This is certainly a far wiser way of economizing than cutting down the rail so light that it will barely carry the engine, as is often done. 1017. Finally, one remaining device will complete all that is possible, or probably necessary, in the way of reducing the first cost of the road-bed. A great deal of money is spent by many roads which can ill afford the luxury in getting a short line. In the light of the facts brought out in Chap. VII, it is unquestion- able that, how^ever it may be with roads of large or of fair traffic^ a cheap light-traffic railway which spends money to get a short line is burning its candle at both ends, ai»d the engineer of such a line cannot too carefully remember that, although on the one hand its length may be the ruin of it, because it has to operate it. vet on the other hand it is its salvation, because its revenue depends on it. 1018. Especially is this true when, in choosing the easiest line regardless of distance, we not only obtain an easier line to construct, but one which will take us nearer to the various SOURCES OF TRAFFIC. Howcvcr it may be with lines of larger traffic, a poor railway certainly cannot afford to pass by on the other side even quite small traffic points which, by going nearer to them, will add a little more traffic to the slender aggregate; not only because every little helps, but because the revenue per head of that population is also smaller, as we have seen in the preceding chapter. 1019. The truths which have been stated are not to be taken *' neat," nor recklessly twisted to mean more than has been said; as, for instance, that it is ever expedient to lengthen a line merely for the sake of lengthening it, or that it is not worth while to try to avoid curvature, or that wooden trestles are as good as per- CHAP. XXII.-LIGHT RAILS AND LIGHT RAIL WA YS. 757 manent works. It has been merely intended to show that, for a road which must practise the last degree of economy and which has little more than a turnpike traffic, the construction of the ROAD TO SUB-GRADE is the proper place, and the most hopeful place, for J' cutting to the bone," because an amount sufficient to give a decently solid superstructure can usually be saved out ^f the first construction with far less risk of injury and loss This IS apparent from Table 199, showing the percentages of Table 199. -Showing the Percentage of Cost to Sub-Grade on Various Items of Construction on Various Lines. Length, miles Total cost per mile.. . Clearing I. trading, | ^^''^h. Masonry, ] Bridging Rock . . . Culverts. Bridge.. Trestling, etc. Fencing, etc. . Tunnel 60 Is. 073 2.1 71.0 • • • • 14.3 12.6 11. 100 $7. 490 • • • • 61. g • • • » 6.1 13.7 2.0 II. 7 4.6 III. 14-5 I18.260 0.2 51.0 7- II, 13- I. 9- 5 .0 5 2 I IV. 100. o 100. o 6.5 100. o 46 118.920 2.0 35.1 5.8 12.4 31.8 12.9 V. 100. o ^ 15 $83,854 • • • • 25.7 50.3 5-4 9.8 1-5 7.3 100. o Character of Lines : stone- work, many structures. ^\r T ,M,f c. / j^ . very numerous structures. V' n.S .f^h ^l-ading:, two costly bridges only ; much hijjh trestling- V. One of the costliest sections of mountain line in the Unitid Stated AwJ^A 7' u '"^^ ""'' ""^ ^""'^"'' "^^' ^^^^'"^" ^°^^' ^-^'•^' hundred miles lon^ was divided as follows, mcluding all items, and not those to sub-grade only : Engineering ^j^* Grading, including tunneilW!!.'."!.*"" 2,6 "ridge masonry \f^ Culvert masonry \ Temporary trestling j ^ Superstructure, bridges and trestles .■.".'.■ 45 «allast. and settling of embankments. . . ,7 ^ressmg up road-bed after winter. i 7 K'ght of way. fencing, cattle-guards and ' road -crossings ._ -Kails and track-laying, complete".*.!.*.* .*.".■ 179 Cross-ties (very small) '^\^' Engine-houses, shops, stations, water supply, pumps, etc g „ Locomotives and cars iq^ Interest on bonds to opening e 8 Discount on bonds 7,. f° Taxes to opening '^'' Office expenses, salaries, etc.',* "t*© 'o^n- ' ingof line ^ Incidental to opening of line .......'. 03 Total to opening of line 100. o per iw 758 C^AP. XXII.— LIGHT RAILS AND LIGHT RAILWAYS, CHAP, XXII.— LIGHT RAILS AND LIGHT RAILWAYS. 759 th*^ cost to sub-grade of various items on different railroads, all of them of comparatively light (although not the lightest) traffic, and varying in character of work from moderately light to the very heaviest. The prices on all of them were from 25 to 40 per cent higher than now (1886) obtain, under favorable conditions; but in each case alike it will be seen how much less injury a sav- ing of $240 per mile in some 'or all of the items given would probably have done to the road than if 5 lbs. per yard were cut off the rail-section. 1020. Nothing has been said so far about gradients, because a very light traffic road cannot afford to spend money to obtain more favorable gradients than careful study of the country will afford at the minimum cost, which (par. 894) will generally be quite reasonably favorable. At any rate, while the temptation for the locating engineer to magnify his office may be great, until provision has first been made for a reasonably substantial and well-maintained track, it may be taken as a tolerably safe general rule, that the same amount of money expended on track will add far more to the hauling capacity of the line than if ex- pended to reduce gradients. 1021. Cutting the work down in the various ways suggested, with due care to do the minimum of injury to its efficiency, $3000 to $5000 per mile may be made to grade a very light railway through tolerably broken country, and this, of course, under fa- vorable circumstances, may be reduced much lower. For such lines, intelligently planned, there is and will probably always be a very wide field. The trouble is that the economy is too often given a wrong direction, and the item which is ordinarily the first attacked — the rail-section — is one of the last of all to attempt to economize in. 1022. This may, perhaps, be made still clearer if we revert to the rail question for a moment to consider a little more exactly the RELATIONS OF RAIL TO TRACK-LABOR. Where is money for improving track best expended— in increasing the rail-section or in more track-labor ? The stiffer the rail the less perfect need be the supports of the road-bed for equal excellence ; but it is sometimes claimed that this needed support can be more cheaply obtained by putting a little more work into the sur- facing, especially when extreme economy in first cost seems necessary. It hardly needs more than a few contrasting figures to see that this is more an impression than a well-founded belief. 1023. To increase the weight of rail 10 lbs. per yard requires, in round numbers, 16 tons per mile, costing, at the even figure of $30 per ton, $480 per mile, the interest on which is, At 5 per cent, $24.00. At ID per cent, 148,00. At 20 per cent, ).oo. Equal to a cost in cents per train-mile, assuming various numbers of trains per day each way, of . Cents PER Train-Milr , At 5 p. c. At 10 p. c. At 20 p. c. I train per day 3.29 6.58 13.16 104 329 6.58 *° 0.33 0.66 1.32 ^^ o-i6 0.33 0.66 1024. The common expenditure on raising and surfacing, ballast, etc., IS about 10 cents per train-mile, as an average, and from that to 15 on 8 cents per train-mile on roads of very light traffic ; and contrasting this sum with the figures above, we see at once that on a road of any consid- erable traffic, which is a kind of road we are not now considering, the stability gained by adding 10 lbs. per yard to the weight of a rail would give far more for the money invested, at any probable rate of interest, than the expenditure of an equivalent sum annually on additional track- labor for lining and surfacing. On a road running 20 trains per day. even if it cannot get money at less than 10 per cent, the interest charge of $48 per year per mile amounts to but 0.33 cents per train-mile. There- fore the extra 5 lbs. per yard has only to save less than 3^ per cent of track-labor to be a paying investment. It is unquestionable that far more than that might be saved, and yet maintain equal condition, even when the rail was a tolerably heavy one. 1025. As respects the extreme of light-traffic roads, especially those built at great cost for capital, it must be admitted that the case is not so clear as that. In fact, for the extreme of thin traffic and scant capital, say one train per day and 20 per cent cost of capital, it seems at first sight clear that it will not pay to increase the rail-section beyond what safety requires, as the cost of interest on even 5 lbs. per yard extra weight of rail will in that case be 6.58 cents per train-mile. ■ 76o CHAP. XXII.— LIGHT RAILS AND LIGHT RAILWAYS. ■^f ' ! 1026. But, premising that this extreme case can but rarely be ap- proached in practice,— because (i) there are few even of the lightest-traffic roads which do not run more than one train each way per day; and (2) few roads are so poor that, if the case is properly presented, they cannot raise a moderate ar/iil// Zona/ capital for betterments which, whatever the profit on the enterprise as a whole, will return 20 per cent profit on their own separate cost, — it may be reasonably maintained from the result of experience that even in this extreme case the extra weight of rail is the best use which can be made of the money. The very least which can possibly be spent on mere track-surfacing and maintenance (par. 124) to keep it in fairly safe condition for the passage of one train per day, is from $100 to $125 per mile, with $80 to $100 additional for ties, or, say, $200 in all, excluding perhaps $100 more for yards and miscellaneous. The cost of the 5 lbs. per yard extra weight, even at 20 per cent interest on capital, is only $48 per year, for which slight increase of one fifth or one sixth in the interest charge on rails we have just seen (Tables 195, 196, 197) that we obtain an average increase, in a very light rail, of fully 50 per cent in the three elements of strength, stiffness, and durability. Granting a road to be so poor that no increase whatever in total charges can be borne for any betterment, however great, beyond absolute neces- sities, is it certain that so great a difference in the stability of the rail will not enable one fourth of the otherwise minimum track expenditure to be saved, while yet leaving the track as safe and good as before ? It is fairly even balance, indeed, under tliis extreme supposition. Unless the rails were very light indeed, it probably would not pay to increase their weight; but it is difficult to escape from the conclusion that under any ordinary conditions, with the lightest traffic, it plainly will pay to use a tolerably heavy rail before relying on track-labor to make up by better surfacing for its deficiency of strength, simply to save a slight ad- ditional investment of capital. 1027. If so, then as the traffic increases up to a comfortable average, as to six or eight or ten trains each way per day. there becomes plainly an immense economy in using heavy rails to save track-labor, so much so as to indicate strongly that the very curious similarity in weight of rails used on all roads in this country above the poorest class, despite the great difference in volume of traffic, is due, not so much to the use of too heavy rails on light-traffic roads, as the use of far too light rails for true economy on our more important lines, as, for instance. 60- or 65-lb. rails on trunk lines which would be acting more wisely to use 80- or 90- or loo-lb. rails. The difference is, however, that such lines are rich enough CHAT. XXII.— LIGHT RAILS AND LIGHT RAILWAYS. 761 •to stand the resulting loss, whereas a poor road which permits its poverty to destroy it by buying an over-light rail, cannot. Some of our more prosperous lines have recently begun to break through this rule by using what are now called very heavy rails, but the exceptions are not yet so numerous as to do more than prove the rule. It is in every way prob- able that within a few years 8o-lb. or 90-lb. rails will be the rule and lighter rails the exception. The inertia from past precedents, which have come down to us from the days when rails were several times more costly than now, will in time be overcome. 1028. We are, therefore, again and more strongly driven to the conclusion, that the one thing on which it is dangerous to economize is the item which is often cut down first of all— the weight of rail. On the other hand, we are led to these conclu- ^sions as respects the details of alignment: 1. As respects the minor details, distance, curvature, and rise and fall, their effects to increase expenses are at best small, and when the traffic is very light become very small. They are, therefore, one of the first directions in which close economy is warrantable for very light roads. 2. In less degree the same is true of ruling grades. Much increase of expenditure to obtain lower grades than a careful study of the ground shows to be possible at a minimum expense is not warrantable. 3- Both the above conclusions are especially true when the objectionable details may be readily corrected later, when and if the traffic warrants it. 4. Temporary wooden structures to decrease the immediate outlay are the next most judicious direction for economy. 5. Economies which decrease the stability of the permanent way are the most objectionable of all. 6. Sources of local traffic which can be reached by any rea- sonable sacrifice should in no case be neglected. • ii 4 ft 762 CJ/AP. XXIIL—THE ECONOMY OF CONSTRUCTION. CHAP. XXI I I. — THE ECONOMY OF CONSTRUCTION. y6^ CHAPTER XXIII THE ECONOMY OF CONSTRUCTION. 1029. We must necessarily assume, in considering the /r^r and cons of many of the details of construction (as in par. 13), that, the construction of the road once entered on, a little more or less money will not be a serious question, but that means will always be forthcoming, at some rate of interest or other, if only it can be shown that the additional investment will be profit- able. But while this is so far true in a small way that it is the only proper guide for planning the details of a line, yet it is undeniable that, when extended to larger questions, affecting considerable sums of mone}'^, it does not in all cases, nor in many very prominent cases, correspond with the facts; which are rather that a certain gross sum only is available, and when that is exhausted, if it has not been so expended as to com- plete all the more essential details of the line, the company be- comes bankrupt, and the line passes into other hands — perhaps for lack of only a small fraction of the sum which has been al- ready lavishly expended. So many prominent instances of this have happened, that it is no more than common prudence to assume that there is immi- nent danger of it in the case of every new line, to the extent of guarding against it so far as is legitimately possible. 1030. This is the more true because of the fact alluded to on page 34, that money for new lines of importance or for extensive additions to old lines can, as a rule, only be raised in "good times." " Good times" are times of high prices, as Fig. 246 il- lustrates very forcibly, and are naturally followed within two or three years by '' bad times." By that time the new line is per- haps nearly built, and needs its last instalment of money, which latter is often a sum which it was not expected to need, and which was even refused when offered, for fear of letting in toa Fig 246.-PRICES OF English Iron and Steel Rails (shown by Shaded Lines) and of American Steel Rails, Refined Bar Iron, and No. i Pig Iron, from 1855 to 1886. many "on the ground -floor"— and this money very often indeed has to be raised at great disadvantage, if raised at all. Unfortunately, the order of time in which the various expen- ditures are incurred is such as to rather increase this danger. Many of the most essential expenditures come last of all, and many of those which may be most harmlessly curtailed or post- poned come first. The locating engineer is in particular danger of overloading his company in this way, because, from the order of time in which his work is done, he in effect hypothecates a large part of Its funds to meet expenses which are not fully defrayed until near the very end of construction. Prudence indicates, there- fore, that whenever there is even the slightest doubt of securing the money necessary, the work should, from the first (par. 7)^ ■li % It 764 C//AP. XX///.— TJ/E ECONOMY OF CONSTRUCTION. be conducted on the assumption that only a given minimum sum will be certainly available, and that from it enough should be reserved to cover the most necessary items at least. The question then arises : In what direction will close economy do least harm ? So far as it goes, the preceding chapter is an answer to this question, for the economies least harmful to a light road are likely to be also least harmful to a line of fair to large prospective traffic. It is, however, not a complete nor entirely pertinent an- swer. 1031. Perhaps the first of all directions in which economy should be sought, or rather the last one in which expense should be in- curred, is in the building or purchase of branches during the period of original construction. There are exceptions to this rule, as there are to all rules ; but as a rule, a point so important tliat a branch to it cannot be legitimately postponed until the main line is finished, is so important that the main line should be carried through it. Only in the event that all other expenses are certainly provided for, should the construction of main line and branches be undertaken simultaneously. To give only a single example of the importance of this rule, the Canada Southern Railway Company, while it was building its main line to Chicago, ■carried on simultaneously the construction of the St. Clair branch, 62 miles, and an extension into Michigan from St. Clair; the Toledo and Detroit branch, 52 miles; and also involved itself in expenses to control an existing line to Ni- agara Falls. Had the money which went into these desirable but subordinate lines been concentrated on its main line, the latter would probably have been completed to Chicago, and would then, probably, have secured enough traffic to have saved its projectors from the almost total loss which the panic of 1873 brought upon them, in spite of certain unfavorable circumstances. 1032. Allied to the question of building branches is that of double-tracking during original construction. If there is any reasonable doubt of securing funds to carry through the entire enterprise successfully, opening a single track only at first is cer- tainly the next most reasonable method for a temporary econ- omy, to insure that the means on hand shall not give out before the line is in working order, and on a business footing. If it be CHAP. XXIII.— THE ECONOMY OF CONSTRUCTION. 76^ reasonably certain that a double track will be needed in the near future, all masonry structures may be built at once for double track, which will involve but a small addition to the total cost of the road— ordinarily not over five per cent, and often much less If It appear still more certain that a double track will be speed- ily needed, even the grading may be done in the first instance for double track, and grading and masonry together will not or- dinarily increase the immediate capital required more than la to 15 per cent. But as both the grading and masonry for double track can ordinarily be done to somewhat better advantage, on the whole after the track is laid than before, the expediency of doing even this much immediate work to provide for the future is question-^ able, unless the financial condition of the line is very strong- and tiie following items for double tracking, at least, can always be postponed to advantage till the line is opened,— even if it is fully expected to immediately proceed with double tracking, and funds for if appear to be certain,— viz., the bridging, ties,'rails and ballasting. ^ 1033. In IRON bridging there is not, contrary to what is gen- erally imagined, any economy worth taking the slightest chance for, in building double-track bridges instead of two parallel single-track bridges. The weight of a double-track bridge is. increased about 90 per cent over a single-track bridge of the same span, and for the same live load ; and although the cost of the structure is not increased in quite the same proportion, yet when we take into consideration (i) even a year or two's interest at ordinary cost of capital ; and (2) the depreciation and possi- ble great need of the invested capital in the dark days of the hrst operation, the petty saving is not to be considered in com- pan son. There is also a certain considerable operating advantage in 'Wing independent bridge-spans for each track, although the single structure is unquestionably the most pleasing to the eye An accident to one structure leaves the other one available. The superstructure of the double track complete, on a line I;- 'j(^ CHAP. XXIII.— THE ECONOMY OF CONSTRUCTION, requiring double track, will ordinarily cost $10,000 per mile — a sum which has repeatedly made all the difference between suc- cess and failure. If any line could be justified by the nature of its expected traffic in laying a double track at once, it was the West Shore Railroad, but had this policy been adopted by that line in respect to the double track and some similar matters, it would probably have saved it from bankruptcy. 1034. In Fig. 247 is given a diagram prepared by the writer from va- rious data, but chiefly from formula for estimating the weight of bridges given in a valuable paper by Geo. H. Pegram, C.E., a bridge engineer of large experience (Trans. Am. Soc. C. E. 1885), which shows graphically several things of importance in respect to bridges. It shows, first, how nearly a double-track bridge comes to being double the weight; secondly, how little saving is effected by building bridges to carry light loads; thirdly, the point at which the saving effected by using steel instead of iron becomes important; SL.nd, fourthly, the comparative weight of various spans by inspection. If the truths which the eye readily grasps from this diagram were more generally understood and acted on, there would probably be less bad practice in railway-bridge construction. 1035. The third least objectionable direction for economy is the bold adoption of temporary lines where permanent works of great cost will otherwise be required; meaning by "tempo- rary lines" not those intended merely for construction purposes or for use until the permanent works can be completed, but lines good enough for several years' use at least without any great loss, leaving the better permanent line to be constructed only when it is certain that the traffic justifies and requires it, and means are available. Considerable amounts of distance, curva- ture, and rise and fall will not cause a dangerous loss in opera- tion for a few years, if used only on the rougher sections as a substitute for more costly works later, and will enable the im- mediate outlay on the usually short sections (par. 1005), where the most costly works are concentrated, to be very materially reduced in many cases, as well as enable the line to be opened before an impending crash comes. The same is true in less degree of the use of TEMPORARY PUSHER GRADES of an objectionable character, but not so bad as to prevent the handling of through-trains. THE ECONOMY OF CONSTRUCTION. 767 This diagram shows the shipping weight of iron, including an all- iron floor, except ties and guard-rails. The narrow-gauge bridges are for quite light engines, as shown in Fig. 248. The slight effect of rolling load to increase weight is perhaps more strikingly shown in .^ Table 200. The formulae on which it was constructed are given near "rp" '^^ ^"<^ of the last chapter. Fig. 247 — Diagram of thb Compara- TiVF Weights of Iron in Fridges OF Varioits Spans and for Varioi's Rolling Loads shown in Fig. 248. (See also Table 200.) [The base of the diaffram for spans of less than 200 feet is at the side.J n 51 ■ 768 CHAP. XXIIL—THE ECONOMY OF CONSTRUCTION. 1036. The fourth least objectionable economy, but one which,, like the preceding, from its coming among the first in order of time, is apt to be one of the last practised, is the adoption as a standard, for the entire line, of a systematic economy (in' money, but not in time or care) in respect to the minor details of align- ment. The pros and cons of this question have been discussed so fully in the preceding chapter that we need not further en- large upon it. In these five ways (with which perhaps the use of timber STRUCTURES, such as are shown in Fig. 249, might make a jixth) a very large economy may be practised which will almost assure that any project with any merit whatever will be so little bur- dened by its capital account that it will be able to live on what it can get to live on, even if, as it usually is, it is far below its ex- pectations. 1037. Beginning now at the other end of the question, the most objectionable of all ways of economizing is much the com- monest of all, for reasons already sufficiently discussed in Chap. III., omitting to go into, as well as to, the terminal cities, and other important traffic points on the line. This error very largely arises from the fact that it is an expenditure which comes late in the history of construction, or can be made to do so. Probably the next most serious injury which can happen to a line is neglect to secure best possible ruling grades, but this more often happens from a lack of care and skill than from a de- sire to economize, since the expenditure is incurred early in the history of construction and the importance of favorable grades is more generally understood than the best manner of securing them. 1038. Barring this error, the next worst form of economy which can afflict a line is what is more emphatically than ele- gantly called a "cheap and nasty" style of construction: Light RAILS, POOR TIES, THIN BALLAST, NARROW ROAD-BEDS, POOR MA- SONRY, and LIGHT BRIDGES. These defects really save but little money, while the expense and the bad name which has resulted from them have sapped the life of many a line. It is far better to economize closely in all the details of location but the grades,. CHAP. XXIII. -THE ECONOMY OF CONSTRUCTION. ;6^ :m and sometimes even in the grades themselves, than to do this. The difference between a thoroughly adequate and solid road- bed, and a' mferior a one as it will seem possible to tolerate, will \ •^ '''»''"Mm Fig. m8.-Enc.nb Loads used in Computing th» Ws.chts for F,g. ,„. Sv ^™°7i''r f'°°° '° ^^°°° P" ""^^ ^"'^ °" ^"--k at all eavy ,t .s not d.fhcult to save that sum by economizing in loca- t.on us.ng temporary but solid wooden structures, and theothe- expedients noted above. These latter economies will not add 49 t;© chap. XXIII.— the ECONOATY OF CONSTRUCTION. ^i..sLi)'^ Jt'.fl'ia' rr-i as c o w 0, ^ in C u rt C *- A. H W D < STANDARD TRESTLE BRIDGE .- IS*. 9' BENTS ..«.f . ■ ■ .4. ■ ■ ■¥» J£ £ tt a£- tfitmt. FLAN OF WING PANEL. STANDARD ^LAM OF CATTLE GUARD. C.M.* Sr.P. RT. Li l.«J tt»»«. . ■■<»■■ ■•»■■■■ !"■»>*« lU- tTMml. ;3HT o o 9,^ : o o o «i o o o ^ o o o J Q O O -J o o a ■ o o o o .:<3 STANDARD PLAN Or PILE PIER AND A.UTNENT FOR HOWE TRUSS BRIO. 4. CM. u sr. p. RT. ^f,...f.M.f . « — L__ae . ae — ' — « — _^JV#». *- k X (^ >» C I > o 3 g W gat X u •5 0>^ z s n < .J O < o < C E .2 o c c O rt ii *-' 2 c tJ s c o V, - •o c c 0) 3 < U K .J (/! b! K H z ti! O O c % 3 cr o dj C X E rt d C < Z < c O II (A I £^ 01 £ 3 tjO C^^A XXIII, ■THE ECONOMY OF CONSTRUCTION. 7/1 materially to expenses during the first ten or fifteen years on operation, whereas a poor and flimsy superstructure entails a large and constant addition to maintenance expenses 1039. The loss which results from light bridges* is propor- tionately quite as great as from light rails, as is made evi- dent enough, without further discussion, from Figs 247-8 and Table 200. The proportionate loss from poor masonry is even greater it is far better to put up temporary wooden structures altogether, than to put up such flimsy masonry as is often built That so very large a part of the masonry put up on new Ameri^ Table 200, Comparative Weight and Cost of Bridges, taking Bridges of "T" (Typical Consolidation) Type, Fig. 249, as Unit. Class of Load. (Fig. 249.) Minor Spans of— 30 ft. T. C. M. 100 98.74 97-73 50 ft. Soft. 100 98.05 96.47 100 97-IO 94-56 104 ft. 150 ft. 100 96.33 93.16 N. (Uniform at 75.00). 100 94.98 90-75 20lj4j ft. 100 94.00 88.61 Larger Spans , T. C 201^ ft. 100 93-34 320 Feet. Iron. 100 91. II Steel. 100 89 -55 420 Feet. Iron. lOO 88.77 Steel. 100 89-55 516 Feet, Iron. 100 88.21 Steel. 100 89-55 ^rc^I^Ltr^^ n °"' '' M, "^'^"'^ '^'' *^' '^^ °f ^°'""S ^«^d «" --i^ht of bridges is small, and the followmg will perhaps more fully show how petty is the economy . For engines weighing (tons) Y"^ 'n the proportion of •0?in th.* '°*'* behind engine, per fi^'t of'(Ibs.) •^r in the proportion of ' I "kB 772 CHAP. XXIIL—THE ECONOMY OF CONSTRUCTION. Table 200. — Continued. Giving a loss percent in rolling load over the strongest type of bridge of The saving per cent in weight (not cost) of bridge is otily - for spans of i Per Cent. Engine, Cars, 30 ft. 50" 80 " 104 " 150 " io\\^ ft. 6.3 14.6 1.26 1.95 2.90 367 5.02 6.00 Per Cent. 19. 27 3. 3 5 6 9 o 27 53 44 84. 9.25 11-39 Beyond these spans the comparative difference becomes g^-eater, so that we have for the difference between a rolling lt)ad of the *' typical " and ordinary Consolidation type (neglecting the Mogul type) the following : Iron. Steel. ft. 6.66 . • • • It 8.89 10.45 i( 10.23 10.45 tt 11. 79 10.45 Thus even the largest spans do not increase in weight as fast as they increase in- capacity, and on the shorter and more common spans an increase of only 3 to 6 per cent in weight gives 15 to 25 per cent increase in carrying capacity. can lines should give out within a few years, as it does, either because the foundations were inadequate or were not properly protected against wash, or the stone poor, or laid dry, or the spans inadequate, reflects little credit on engineers. 1040. A still less reasonable and creditable mode of economy is CUTTING DOWN THE ROAD-BED, especially in cuts. The saving is but trifling, and tlie effect on maintenance expenses very un- favorable, since it forbids proper ditching, impedes access of the sun to the road-bed, and makes difficult to apply a proper coat of ballast and leave any ditch at all. The narrowest road-bed in earth should be 20 ft., especially in light work, or on light grades having many long low cuts on them, which latter are very difficult to drain. In fills, a 15-ft. or i6-ft. road-bed is none too wide, and will rarely be found to be much wider than is necessary to hold the ballast when the track is laid. 1041. Cutting down the coat of ballast is likewise one of the most costly economies in which a road can engage. Sometimes it is necessary, because ballast is not readily available, and tO" some extent good ditching may be substituted for it, but econ- omy requires that both ditching and ballast should be good. ^-^-^^^^^^^^-T^^C^^V^^^ OP CONSTRUCTION 77^ It was a saying of the late Charles Colli^i^^^i^ented chi7 two feet of ditcli is worth one foot of ballast," and this has a foundation of truth at least, as was shown by the results of fre^ hltth'en^VrSd'^-^'^ '"^ ''''' '' ^^^ ^^^si^^^^^l^ d Tmount of to "" n "'" '''''^' "^^ "^" ^^"^^^^ ^ li- lted amount of money Will accomplish more good if spent for h all the necessary delays ^aitnTfo r .h , r'""'" ^'■'^'' °'"" ^^«"'-' "-'"'' time/' and fo 4 doub n^ al trX" 'T ''''• '^ ^" '"°'""'"^ P™P°"-" °' '-' '-^ P- I 774 CHAP. XXIII.— THE ECONOMY OF CONSTRUCTION. m\ m Nevertheless, this limitation of privileges is natural enough and well enough as a matter of permanent rule. A ballast train cannot be anything else than an irregular train, and cannot safely be given any rights whatever, except by spe- cial order ; but therein lies the difficulty. Trains are, as a matter of fact, almost all run by special order, and when giving such order, it rests entirely with the discretion of the dispatcher, within wide limits, to favor one train or another as he sees fit. This discretion, however, is rarely exercised to prevent delays of ballast trains, which cost money, rather than delays of regular trains, which do not directly cost money; but the ballast train gets from the dispatcher, improperly and unwisely, much the same kind of treatment that it necessarily and properly has in the printed rules and lime-tables. Now a regular freight train is earning perhaps $1.50 per mile run and cost- ing $1, but it will earn no less and cost no more (barring a slight loss of fuel) for being a quarter or half an hour more or less upon its trips. On the other hand, the total expenses for running a steam-excavator with perhaps three or four engines at work to handle the cars, are from $100 to $150 per day. A delay to any one of these trains is to a considerable extent a delay to all and to the excavator as well, and a delay of three hours per day to these trains (which is about a minimum) means the loss of $1200 to $1500 per month. Under these circumstances what ought to be done, if true economy is to be considered, is to prepare something like a regular schedule for the movement of these trains, from day to day and from week to week, for the use of the dis- patcher ; to provide as good facilities as possible for communicating orders to them, and to require that, whenever and wherever it is possible without too great delay, the gravel trains shall be favored at the expense of the ordinary freight train. 1043. Supposing the delays to gravel trains to have been re- duced to a minimum, there are few expenditures so directly profitable as to procure a steam-excavator and ballast plows, and keep two or three trains at work for a good part of several seasons increasing the depth of ballast. Half a cubic yard per cross-tie will raise the track some 8 in., and where the road-bed is wet and the haul not too great, this would not be so very bad an investment, simply as a preservative of cross-ties. An additional economy for this kind of work on many lines,, and one deserving of more frequent use, is the hauling < side- dump cars loaded with ballast on regular trains, especially way freight, whenever, as is frequently the case, eight or ten addi- tional cars can be hauled over a portion of the division as well as not, owing to more favorable gradients. Many types of cars CHAP. XXriT.-THB ECONOMY OF CONSTRUC TION. 77S suitable for this purpose exist which are readily dun,ped by one n.nr^ ^"' °^ '^^ ^"^ ^°''' P'""^ ^° economize in, but for- tunately not a common one, is in the cross-ties. Th; number of these cannot be too great for economy, until they become so ttele-lh If rraTre^- ;-- T," ^^ ^ -""' ^ crease the t,e support, as may be speedily shown. Some "rop^^Jti^n^'V^^ "°"""' ^'^ """''"^ ""'^- ">« '^s. each of these must be used to maintain a sta- ble track, but in pro- portion as the stabil- ity from one of them less track labor U ^ ' '' '"'' "^ ™^-^ "^^ '«^= ''^^ -^ iess track-labor. If we have more or better ties, we may use a Fig. 250. Fig. 251. The different modes of yielding, outlined in Figs S and ! r' which occur more or less on all trark ,^, k ^ ^ ' and will arise from H fi ' ^"^ ^^ assumed to arise, will ause, f.om deficiencies in any one of these three re 1 1 'J'J^ CHAP. XXIII.^THE ECONOMY OF CONSTRUCTION. quirements, either the rails or ties or tamping, and may be cured, in part or whole, by spending more money on either one of them. Assuming as a standard of comparison a 6x8 in. tie 8 ft. long, spaced 2 ft. apart, or 2640 per mile, the following com- binations of spacing and width will afford an equal bearing-sur- face of ties on the road-bed and of rails, but will be seen to afford a very unequal support to the rail : Ties per mile 2,640 3,000 3,168 3,520 Distance apart, centre to centre 24 in. 21.12 in. 20 in. 18 in. Average width of face Sin. 7.04 in. 6.67 in. 6 in. Clear space, tie to tie 16 in. 14.08 in. 13.33 in. 12 in. Comparative stiffness of same rail for each span i.oo 1.47 1.73 2.37 Comparative weight of rail to give same stiffness i.ooo 0.825 0.761 0.650 The method of determining the comparative stiffness and comparative weight of rail in the last two lines is the same as used in par. 992 for rails, and need not be repeated. Whether we compute the comparative stiffness of the rails for spans from centre to centre of ties, or for one clear span between ties, or for spans omitting one tie, as in Fig. 250, the result is the same, al- though the absolute stiffness will of course vary greatly. 1045. Taking the extremes of the table above, we see that the addition of 880 ties, or one third increase, gives so much addi- tional support to the rail that (assuming the support to each tie to be the same) a rail only two thirds as heavy will distribute the load as well from tie to tie. Not forgetting that stiffness is only one of the three qualities in a rail which are gained by in- creasing its weight, this great difference still indicates that in- creasing the number of ties to the extent of practical possibility (their dimensions remaining the same) adds much more to the aggregate stiffness of the track than the same amount spent on rails ; as thus: The cost of 880 more cross-ties per mile, more than doubling the stiffness of the same rail, amounts — At 25 cents, to $220 = 7.14 tons rails at $30 = 4.5 lbs. per yard. " 30 " " 264= 8.80 " " " =5.5 " " " " 40 '- " 352 = 11.73 " " " =7.3 " '* " " 50 " " 440=14.67 •• " " =9.1. * 1.51 2.12 35 lbs. I.oo 1.27 1-57 50 lbs. I.oo 1. 19 1.40 CHAP. XXrn.-THE ECONOMY OF COl^STRU CTION. 777 Comparing this with the figures in Table 196, giving the comparauve st.ffness of light and heavy rails, we have the fol! ow.ng companson for various light rails-for which rails ol the comparison is at all close: ^ Original weight of rail, . . <,^ i^ Stiffness in do. taken as ^^ ^"• Addmg 4.5 lbs. per yard (= cost of' 880 'ties at 25 cents each, as above) makes stiff- ness Adding 9.1 lbs. per"yard'(= cost' of' 880 'ties at 50 cents each) makes stiffness . Whereas the same sum spent on ties inl creases the stiffness, as above, to . . . deciralYS- ''^1'^'''°" °^ - '-g^ - ""-bar of'iies, without deceasing the.r wdth. can rarely be practicable, and while the companson ,s not strictly exact for other reasons, this does indi cate clearly the genera, fact, that increasing the'numberoffes iilitv't " — enience is a cheaper way of increasing a! bd.ty than .ncreasmg the rail-section, even for very light rails On the other hand the total stability which is obta'^nab ^ from t.es IS I.m.ted by the number which it is possible to use. so that what these figures in fact indicate is that, in endeavoring to ge he utmost stab.hty at .he least cost, the first essential it to use t>es as free y as ,s possible, and the next essential is to decide mT T. : oh:, " I r' """-^'^-P-^ - -PP-y the deficU 1047. The physical hmit to the increase in number of ties of The r7, K, 1:' """'''' " P^^^'^'y ^«°° P^-- ■":'-; but if as t Xhe fi,-st table above, we consider the width of the ies to be di w£ use ,:oc r '""' ' """'" °' ^^'^ '" '""^ United States wh.ch use 3,00 to 3300 narrow ties per mile with very satisfac- tory results. Remembering that the stiffness of a rail decreases as the cube of the span, it is obvious that by dividing up the beanng-surface among a greater number of ties, so thaf Z Ig! gregate area remains the same, we measurably obtain two desi^. able ends at once-we give much more effectual support to a w aU .a.l, and we in general reduce, instead of increasinl the total cost of t,es, since the cost of ties will usuallv increase fester i ii 27^ CHAP. XXIII.— THE ECONOMY OF CONSTRUCTION. than the required minimum face. As, therefore, the necessary space between ties varies approximately with the width of face, and is about twice the face (so that full-width ties cannot be used with very narrow spacing), the utmost economy would seem to require that narrow ties spaced close together should be given a decided preference at the same cost for ties per mile when a light rail is to be supported, and there are few rails indeed in this country which cannot be said to be light in proportion to the duty imposed on them. It could not rationally be expected^ indeed, that 6-in. ties spaced i8 in. apart, instead of 8-in. ties- spaced 24 in, apart, would increase the stiffness of a light rail from 1. 00 to 2.37, as the figures above indicate; yet we may justly conclude that it will be increased very greatly, with a pos- sible decrease in the total cost of ties as well, where the supply of large timber is small. In not a few localities ties of 5- or 6-in. face can be had for but little more than half the cost of ties with 8-in. face. 1048. A great error is often committed in making ties too thin. A cross-tie is an inverted cantilever. In Fig. 251 we have a tie yielding, as they all do, more or less under a load; and by inverting Fig. 251 it will be seen that we may consider the tie as a cantilever beam, supported upon two piers (the rails) and loaded with a more or less uniformly distributed load. If the tie were perfectly stiff, it would be an evenly distributed load, and the pressure of the tie upon the soil would be uniform for every square inch of its bearing-surface. If the tie be very thin, the conditions of the exaggerated sketch will literally obtain. The middle and ends of the tie will then be able to transmit but little pressure to the ballast, and (since the total pressure trans- mitted must in any case be the same) an excessive and destruc- tive pressure will be thrown upon the road-bed directly under the rails, causing rapid deterioration therein. This may be shown by the load-diagram below Fig. 251. Let us suppose that a tie be so thin, or the nature of the support so unyielding, that the load per square inch directly under the rail is three timeT as great as at the ends and in the middle, as shown by the full CHAP. XXIII-THE ECONO MY OF CONSTRUCTION. 779. line in the diagram below Fig. 25i^a very co^n differen"^. If not, indeed, one almost universally exceeded in occasional in- stances, even on a very good track. An increase of stiffness which would double the load on these lightly loaded extremities would produce, as will be seen from the diagram, an absolutely uniform distribution of pressure, and although this can never be fully realized, yet it is plain that it may be approached 1049. Now the stiffness of any beam, however supported or oaded IS in proportion to the cube of its depth (or thickness of tie) and of its lengths between supports (or the gauge) Anv attempt to compute from these facts the absolute requirements, or distribution of load, with a given tie or gauge, would be pre- posterous. There is no absolute requirement, since, however well maintained the track, occasional ties are badlvor unequallv supported; and since the load is far more than sufficient to break any tie in two at the middle if only supported at that point (a dead load of 14,000 lbs. per wheel would probablv break such ties the first time it was imposed), it is for these maximum de- mands, and not the average, that we must provide. Therefore speaking comparatively only, and taking a tie 6 in. thick as the' basis of comparison, we have the following: Thickness. 5 in. 6 " 7 " 8 " Comparative Stiffness. 0.58 I. GO 1.59 2.37 Thickness of Narrow (3 ft.) gauge Tie of- Equal Stiffness. 3.18 in. 3.82 " 4.46 " 5.10 " Equal Strength. 4-30 in. 5.16 " 6.02 " From this it is clear that although the nominal bearing-sur- face of a tie IS not increased by increasing its thickness, yet that the effective bearing-surface is likely to be very materially in- creased by a very moderate increase of thickness. By increasing the thickness from 5 to 6 in., we nearly double the stiffness • bv increasing it from 6 to 7 in., we increase the stiffness 50' per cent, giving the effect outlined below Fig. 251, in which the full iine shows the assumed distribution of pressure with a tie 6 in thick, and the dotted line the effect on the latter of thickening^ -,^^nk.A 78o CHAP. XXIII,— THE ECONOMY OF CONSTRUCTION-. the tie i in. Economizing in the thickness of ties, therefore, would seem to be one of the poorest ways of saving money. 1050. This is more fully seen by comparing the effect of differ- ence of length. It cannot be attempted to consider the matter in detail, but a tie which is under fair conditions to permanently fulfil its office of distributing the load may be considered to curve into the three circular arcs shown in Fig. 251, from which it will be apparent that, under whatever assumptions as to the curve of flexure, there is a clear limit to the useful increase of length in ties at a point considerably within a length of twice the gauge,//'. If the tie be made longer, as, for instance, ex- tended to//', or, still worse, to^ ^', either the extra length will carry little or no load (which is most likely), or, if the support nearer the rail has given way so as to throw load upon it, it will be very liable to break the tie. If the tie be made shorter, the load thrown on the middle of the tie will be disproportionately increased until, if we conceive the tie cut off close to the outside edge of the rail, the load per square inch will, in the first place, be very greatly increased, and, in the second place, the strength of that portion of the tie between the rails, considered as a beam, is diminished by about one half and its stiffness about seven eighths; because the effective span of the beam has, by cutting off the projecting ends, been almost doubled, i.e., increased from b b\ Fig. 251, iocc'. 1051. For the most efficient service from ties, therefore, we have a certain quite narrow limit of length, the minimum being about 7i ft., and the maximum about 8^ to 9 ft., for the ordinary gauge of 4.71 ft. It is clear from the above that any increase of length above 8 ft. gives a far less effectual way of disposing a given quantity of wood (to obtain an approximately uniform pressure on the ballast, and so keep down the maximum), than to increase the thickness, provided the nature of the timber per- mits it. The apparent gain of bearing-surface by increasing the length of ties from 8 ft. to 9 ft., and the apparent absence of gain in bearing-surface by increasing the thickness from 6 in. to 7 in., will be seen to be precisely the reverse of the true conditions, CHAP. XXm.-THE ECON OMY OF CONSTRUCTION. JU and we may well believe that this deceptivT^trast hn<= h the chief cause for such awkward combination as ansl^r .ft" t.e w.th only 6 in. thickness, which prevails with 6 i pe.- cent of the ties in the United States. ^ °^ Neglecting the widths, as an indeterminate element not defi nitely fixed, the percentages for the entire United States of t£ various lengths and thicknesses of ties in use is as follows Lengths, . . 8 ft. 8 ft. 6 in. 9 ft. ,0 ft Total Percentages,. 63.5 .7.6 8.., o+' To.o 6| in. Thickness, Percentages, 6 in. 54.4 7 in. 41.4 8 in. 0.4 lOO.O erneTbv thT' ^:".^"°"^ ^-^^ - P^"- and perhaps chiefly, gov- at least, we may safely assume, from mistaken views as to wh.t .s, abstractly considered, the best proportion for a" T^^bes dimensions for a tie are about 7 in thick 8 U /, , . 7 to 9 in. face. , ' "• ^ '"' '°"S' a"^ 1052. There is another side to the question of masonrv struc ures which may be briefly noted. While a structure, if bui at' a 1, should be well and solidly built, it does not follow tha be cause a certain proportion of the structures of a line Ivlntuallv wash out that they were therefore ill-designed. " The „! "l end of a tutor," say the Autocrat of the Brfakfast-Table "' s To die of starvation. It is only a question of time just as with ,h burning of colleee librar;« " <;„ ■ ■" "" ""^ «nc« »-""egeiibraiies. So in a certain narrow and limited sense we may say that the natural end of a culvert and evTn of ".any bridges, is to perish in some excessive flood tL Ixceo t'onal storms which come but once or twice in . / . ^' ardlybe fully provided for, for tl.rreas r at" t is"iSt": build any large number of structures with such an ample 2 '^ of safety as to insure that many of them will not eventualirwfsh chance7"S ml"/''' ''f" '""' ^""^ """'-' ^'°™^ -h-b anced to fall most severely on some of the Boston roads which a.e about the oldest roads in this c6untry, having beeVb:ilt 782 CHAP. XXIIl.^TIIE ECONOMY OF CONSTRUCTION'. 8 from 40 to 50 years, and had rarely suffered much from floods and washouts heretofore. As a consequence structures were washed out in considerable numbers (on the Old Colony there were 40 washouts), many of which were "supposed to be strong enough to resist any current," and had succeeded in doing so for half a century. 1053. Such occurrences will and ought to make engineers cautious; but we may remember, on the other hand, that to have insured that these structures should not have washed out, their original size and cost would have had to be nearly if not quite doubled, and a simple computation in compound interest will show that had this been done in the first instance the additional investment would have amounted at 6 per cent to 19.50 times the actual first cost. It follows that in 1835 even a certainty of saving the cost of duplicating the original structure in 1886 would have warranted barely 5 per cent additional expenditure. It is true that the bare cost of renewal does not cover the whole loss, for there is a loss from delay and danger of accident incurred by the washout in addition thereto ; but on the other hand, to guard against all the contingencies which might arise in 1886, it would have been necessary in 1835 to have about doubled the ■cost of all the structures, since all may be assumed to have been laid out with equal care, and it could not have been foreseen which would be most tried thereafter. All of which goes to show that when structures have been skilfully laid out to stand the ordinary contingencies of 20 or 30 years it is about all that is either practicable or justifiable, and that the remarkable storms which come only once or twice in a century are not in fact, and hardly can be, successfully guarded against. This is especially true because the worst effects of even the greatest storms are localized within quite narrow limits. The storms referred to were not by any means the worst for 50 years, except at a few spots. But those structures which washed out chanced to be at those spots, while the really greater storms which have washed out others in past years did not chance to fall so severely on these. CHAP. XXIII.— THE ECONOMY OF CONSTRUCTION, ^83 1054. Tiie same is, in substance, true of inundations of rail- way lines. Every year we hear of miles of line of important roads being under water, and every year it is, to a considerable extent, in different localities. It is a tolerably safe prediction that within reasonable and justifiable limits of expenditure no rail- way can be carried for any long distance through that place of all places foreconomi- ■cal operation, a river valley, without being at some time and at some point under wat- er. The conclusion that whenever this oc- curs it is evidence of bad engineering is not justified. There are lines in all parts of the country which are overflowed for consid- erable distances every three or four years for a few days, and find it cheaper to suffer the evil than to cor- rect it. Prominent examples among in- numerable others is the main line of the Pennsylvania Railroad in Trenton N J various points on the Erie, Philadelphia & Erie, and Baltimore & Ohio, and various roads in the vicinity of Buffalo, N. Y. Without going to the length of saying that this'is ordinarily justifiable, which would be going too far, it is an entirely safe Fic. 259.— Annual Rainfall in Inches at Lake CocHiTUATE, Mass., 1852-1883. I 1 784 CHAP, XXIII.^THE ECONOMY OF CONSTRUCTION, CHAP. XXIV.-IMPROVEMENT OF OtD LINES. Statement that when the works endangered by such overflow are not of a very costly character, it is far better to risk the chances of overflow and damage at a few points every eight or ten or fifteen years, and often still more frequently, than to sacrifice the advantage of easy gradients and light first cost to avoid the risk, especially as it is often impossible to avoid it without aban- doning the valley altogether. This latter has been done in not a few instances, and by no means to the advantage of the prop- erty, although of course there are many valleys which are so. frequently subject to excessive floods as to make them unfit for any permanent railway line. 1055. Very great fluctuations in rainfall occur in successive years, as shown in Fig. 252, which likewise strongly indicates that there are periods of great or small rainfall of ten or fifteen years' duration. It by no means follows, however, that the years of greatest rainfall are the years of greatest floods, but rather the contrary. 785 CHAPTER XXIV. THE IMPROVEMENT OF OLD LINES. 1056. It should follow from what wp h-,„-> ,i j respect to the errors which ..ay be committed ■„'."?'' "" '" ^f new lines, that many existing lines buTf\ ^^'"^ °"' adequate study of conditions "o'^ate co ' "t """°"' .capable of material improvement af a co., T J' "'""''^ ""^ ments mav in ravipc h« ^^^ * 1 vvuac gieat improve- readilv tlfe' possibi 'itts fn thft'd' "''/"'""^ ~^'' ^"^ ''°- Without elaborate a.ld cost"yt" evl "^^ '^ ^''''''"'^^^ The subject is one which usually requires carefnl .t ^ so much for determining whether or nrir. ^' "°' vantageously be entered'on, whiC. .^ trZ^Tord" t as for determining precisely how and whpre U,e ml "' ment can be effectpri f.>r \% i """ere the most improve- •dangerthat if^h! '^'' "'°""-''' ^° ^^ '° ^^oid the «»igcr mat, it the improvements pr^ ^nf«.-^^ 1 will not be given the nVhTn ? ' "'^ «^Pe"diture only Of wha^ n^hM^atletra crphtheVrTn":;: ^ ''h" '■and. will include much that was not essentLl and "" '"terest on the capital invested '° "°' "■""'"" 786 CHAP. XMV.-IMPROVEMENT OF OLD LINES. CHAP. XXIV.— IMPROVEMENT OF OLD LINES. 'J%'J for estimating the possibility and value of any change therein We know or may know precisely how much locomotives do and can do on the line, how much they are now assisted by momen- turn in passing over their heavy grades, and where they are most taxed. Above all, perhaps, we have time to fully consider and investigate all the conditions. Usually, moreover, there are certain members of the regular staff who can devote a moderate amount of time to investigations and minor surveys without serious interference with their regular duties. 1058. On the other hand, we have the disadvantage that any changes of line or grade, or of positions of stations or water- tanks, etc., etc., involve the throwing away of a certain amount of work already done, instead of the mere addition of a new red line to the maps and a new line of stakes on the ground, l^or this reason, a change which might have been in every way ex- pedient in the beginning may not be expedient when loaded with the cost of' two lines instead of one. We have, moreover, the disadvantage that the value of property and number of bml^. ings are liable to have greatly increased, often to a prohibitory limit, especially near stations and large towns, where changes are most likely to prove expedient. Moreover, in cases of con- siderable changes, involving the abandonment of certain sec- tions of line or even the moving of minor stations or sidings, legal difficulties may arise, with expenses of unknown magni- tude resulting, perhaps, from the mere whim of a jury, and re- nuiring the maintenance and operation at heavy cost of work intended to be abandoned. It has been successfully disputed in some instances, at least for a time, whether a corporation has the right in law to abandon sections of unprofitable lines to the detriment of vested interests without payment of heavy damages as compensation for contingent as well as actual injury. On the other hand, instances have repeatedly arisen where the right of such abandonment has been successfully asserted and main- tained. Much depends, no doubt, both on the importance of the case and the rigor of the opposition, but in general it seems reasonable to expect that moderate changes for which necessity or good reason can be shown will not be accompanied by a re- fusal of legal authority to make them, or by more than reason- able and actual damages. It constitutes an element to be always remembered and weighed, but not to be exaggerated without weighing it, as there is some danger that it may be. 1059, The disadvantage of having to build a line twice over is one which, while undoubted, is liable to affect the imagination far more than its real importance warrants. The constant loss from operating a bad line, on the other hand, being so gradual and continuous that it does not affect the imagination at all, the two causes may unite to indispose responsible officers to think of entering upon a policy in which the outlay is certain and seems larger than it is, while the gain is problematical, and even its possibility does not force itself upon the attention. To construct, say, lo per cent of a long line over again, for example, inevitably impresses the imagination as very much like adding 8 or lo per cent to the capital invested; and as the ship is nearly sinking under the load it carries, what may happen to it with that load added ? The chances are, however (Table 199 and 14), that it will not really add more than one to three per cent. On the other hand, what can seem more improbable, a priori, to a manager who is only hauling 25 or 30 cars per train, than that 50 or 60 cars can be drawn over the same road with- out, say, doubling or at least increasing one third the cost of the line ? Yet this has been repeatedly accomplished, and can be again accomplished on many thousand miles of road, at far less cost. 1060. The defects which are most conspicuous in old lines which it is desired to improve are, in general, these: 1. The passing by of large towns or other sources of traffic which should have been approached more nearly. This defect, although a great one in the laying out of old lines, is ordinarily not one for which alone it is expedient to change the main line, but it is often an element in considering changes which are de- sirable for other reasons. 2. Excessive curvature; a defect which forces itself with HM 788 CHAP. XXIV.— IMPROVEMENT OF OLD LINES. CHAP. XXIV.— IMPROVEMENT OF OLD LINES. 789 quite sufficient force, as a rule, upon the attention of all con- cerned, so that there is some danger that expenditures may be incurred in efforts to remedy this evil which might better have been given some other direction. Nothing further will be said on this subject than has been already said in Chapter VIII. on curvature; but it is beyond question that on important trunk lines large expenditures may often be usefully devoted to this, as to almost any other improvement. 3. Improvements in gradients, which are generally at once the cheapest and the most important to effect, and to which this chapter will hereafter be devoted. 1061. The defects in gradients, of a remediable character, which are most likely to exist in old lines, are as follows: 1. Stations on heavy grades, including as heavy grades not only those which appear heavy on the profile, but those which are sufficient to prevent starting a full train, although easily enough passed over by trains under normal headway. The number of lines is great on which several limiting stations of this kind exist on a single division, so that, as the trainmen put it, " it is harder to start the trains than to pull them up the grade." Very frequently these bad grades at stations are the only obstacles to a considerable increase of train-load. 2. Grade-crossings of other railroads, which have often been added in great number since the original opening of the line and seriously modified the handling of trains, especially in the West. 3 Needless undulations of grade, avoidable by slight de- tours and originally introduced only because the importance of low grades in comparison with a short line or cheap construe tion was underestimated. 4 Failure to use pushers, or assistant engines: in some cases from mere oversight, but more generally because the line Is ill-suited for their use without modifications elsewhere. It is unfortunately true that in the original location of most Amen- can railwavs this possibility has been little considered; part y because the amount of future traffic was not foreseen; partly because the grades seemed too low to make the possibility worth considering (it being only in recent years that the use of pushers on low grades, to handle very heavy trains, has become common), and partly, in some instances, from mere lack of thought. 1062. On very many lines it has happened that there was some one short stretch on a division where a 50 or 60 ft. per mile grade was unavoidable. Grades approaching this limit were then used on other parts of the line which were easily avoidable and can easily be taken out, from an idea (correct enough if the «se of pushers is not considered) that they were of no importance if not exceeding the maximum. Consequently, when the line was opened, trains had to be quite short. Stations were laid out or have been added from time to time, without reference to the use of any other than the short trains then handled, and new roads have from time to time put in grade-crossings, at which all trains were compelled to stop, with similar indifference to consequences, provided the new Stop did not require a still shorter train than was then handled. 1063. Thus it may have come about, in the course of years that there will be a dozen or twenty points on the division where the demand upon the power of the locomotive is almost as great as, and frequently greater than, the resistance on the maximum grade, so that no advantage, or very little advantage, would be gained by the use of pushers anywhere, and the character of the hne seems fixed, without entire reconstruction. Yet the whole may be often remedied by some among the following simple ways, at very moderate aggregate cost: I. The point or points offering most original difficulties and having, probably, the heaviest work and grades (say 60 feet) may be in some cases avoided altogether by a detour of a few miles, but in general can more advantageously be operated as it stands with a pusher, thus about doubling the possible train over it. 1064. 2. The points of next heaviest grades— there may be six or eight of them, having grades of 30, 40, and 50 to 60 feet per mile— will in some instances be so short that they are now, or can well be, operated as momentum grades, with or without i 790 CHAP. XXIV.^IMPROVEMEXT OF OLD LIXES. CHAP. XXIV.— IMPROVEMENT OF OLD LINES. 79 1 some slight modification. The feasibility of this can be deter- mined simply and easily in tlie manner explained in par. 408. In other (and frequent) cases short sections of new grading will be required, to wliich the track complete can be removed. In some cases the regrading of considerable sections will be necessary, enabling the line perhaps to strike some new town by a detour, but endangering legal complications for damages unless both lines are maintained. Very frequently, however, such double construction may give all the advantage of a double track, for a certain distance, since the objectionable gradients may be op- posed to trains going one way only. 1065. 3. The disadvantageous effects of grade-crossings may now, happily, be immediately removed in all cases by taking ad- vantage of the laws already existing in some States (see next chap- ter), and to be easily obtained by effort where they do not exist, permitting such crossings to be operated by interlocking signals without requiring trains to stop at them regularly. It is now universally admitted by intelligent and well-informed men, that this is a much safer and cheaper safeguard than the stopping of trains. Exceptional crossings no doubt exist where (as some trains must stop when another happens to be passing) this rem- edy would not be a perfect one, and an overhead crossing prefer- able, especially to effect at the same time an improvement of grade, but in general dispensing with a stop by interlocking would be all that was practically necessary. The expense of do- ing so is considered more fully in the next chapter. 1066. 4. The unfavorable gradients at stations— very often the chief evil to be cured, although none but the trainmen may fully realize the fact — can be remedied by one or the other of numer- ous wavs, as follows: (a) By moving the station or the freight tracks only a little ahead or back, so as to reach a more favorable point; if neces- sary, at important stations, by completely separating the freight and passenger yard and station, and incurring some extra ex- pense for extra operators, switchmen, etc. {J}) By modifying the gradients of the station, or of one or two tracks thereat in the manner indicated in Fig. 254, viz., rais- ing the track a, at the lower end of the yard, so as to gi've a lower grade for starting trains, at the expense of a somewhat higher ^rade for stopping them, the latter having no other disadvan- Fig. 254. tageous effect than to check the speed of a passing train, acting in place of a brake, to some extent, if the train is to stop. {c) By stationing a switchman to open certain switches, and thus saving the necessity of a train stopping at an unfavorable point to open or shut them. On large roads and at large sta- tions this is not a difficulty, but at other points it is one which must be fully borne in mind. 1067. (d) By breaking through, if necessary, general rules as to which trains shall take the side track, and even (in effect if not in form) which trains shall have the right of way. The latter, of course, cannot safely be done in form, but the 'desired end can be accomplished by taking care in despatching, to have the lightly loaded trains, or those which the grades favor, held for those which cannot well stop at certain stations or only with difficultv. A general rule on this subject is commonly established and put in force over all divisions of large roads— as for instance that east- bound trains have right of way over west-bound, which latter, consequently, are by custom always obliged to take the side track at all stations, and by custom of the despatchers are com- monly held so as to favor the cast-bound trains. But while such a rule may work well enough on most divisions, it may work very unfavorably in others. 1068. For example, on the New York, Pennsylvania & Ohio Railroad, the general rule that east-bound trains had the right of way, which was well enough for the remainder of the road, had {and probably still has) the effect on the Mahoning Division to •compel the heaviest-loaded trains to stop and take the side track. \^^M^ 792 CHAP. XXIV.—IMPROVEMENT OF OLD LINES. on a curve, when half up a long maximum grade, to let trains always more lightly loaded pass down hill at full speed past them. Such cases are not infrequent, and come to be looked upon as matters of course; but it is needless to say that they can, when occasion arises to make it expedient, be modified if necessary (i) by reversing on one division the usual rule as to which trains have right of way ; (2) by giving, at some given station or stations, trains going in one direction the right to hold the main track and require an opposing train to take side track, regardless of which has right of way; (3) by favoring trains in dispatchers* orders, as before suggested. Thus, in one way or another, it may generally be effected that trains passing in one direction past some one station on a division, at least, with unfavorable grades which cannot other- wise be remedied, shall not be compelled to stop at it. 1069. {e) At large stations, where there is most likely to be diffi- culty or great expense in adopting any of the preceding meth- ods, a switch-engine which it is found necessary to keep at the station, but which is not kept very busy, may be utilized to help trains through the yard, and perhaps also over some uhfavor- able grade-crossing, which is particularly likely to come near to such a station. If the traffic of the line be very heavy this may not be possible; but in that case, as a last resort, an engine may be stationed at the yard for the sole purpose of helping trains through it. By modifying the position of the tele- graph office it may in general be arranged that the use of such an engine shall cause no extra stoppage of the train. In fact, on manv lines of heaw traffic, as for instance the Hudson River Division of the New York Central Railroad, pusher engines are used to help trains over short gra'des without stopping trains at all, the pushers coming up behind the train as it passes a switch, running two or three milles, and returning on the same track, protected by a flag. 1070. The best method of determining how much can be ef- fected in these various ways is by observations of the variations of velocity in the handling of heavy trains on the present line in CHAP. XXIV.— IMPROVEMENT OF OLD LINES. 793; a manner shortly to be described. In this way we eliminate the necessity of considering and allowing for a long list of doubtful elements — whicli throw a haze of uncertainty over any computa- tion in which they must be separately estimated or guessed at by simply determining by direct observation the resultant, so to speak, or net effect of them all. For lack of definite knowledge on a number of variable elements, it is difficult, if not impossible, either to compute or to observe, separately, either the power of the engine or the whole resistance of the train, but we can de- termine, very accurately and simply, the relation which the one bears to the other— which is all that really concerns us— in this way : I. When the engine at any given point on the open road LOSES SPEED, it is proof that working with the given steam-pres- sure and point of cut-off it is overloaded, and the amount of velocity lost can be made a measure of how much it is over- loaded (par. 400 et al,). II. Conversely, if the engine gain speed at any point on the open road, under given conditions of steam-pressure and cut-off, it is a proof that it is underloaded, and the observed variations of velocity can be made to accurately indicate how much. III. If an engine acquires speed in starting very quicklv, under given conditions, without slipping the wheels or using sand, etc.; or, on the contrary, IV. If the engine start very slowly, or not at all, without slipping the wheels or using sand, or both— the observed facts may be made a measure for accurately determining what train it could start under similar conditions with fair working efficiency. 1071. By velocity observations of the nature above indicated under varying conditions of wind, weather, temperature, longand short trains, loaded and empty cars, etc., etc. (all of which can be observed on trains by simply waiting for suitable opportuni- ties without affecting or interfering with normal operating prac- tices), we have a positive basis for determining from what is done under those conditions whether or not the comparative ratio of power to resistance on various parts of the line is seri- ously imperfect. 794 CHAF. XXIV.-^IMPROVEMENl' OF OLD LINES. CHAF. XXIV.— IMPROVEMENT OF OLD LINES, 795 j4.s respects the engine. . . - In other words, we can, by the simple observations suggested and to be described, construct a virtual profile of the road under all extremes of external conditions. We can then com- pare these virtual profiles and determine whether or not a given set of improvements which produce a desired uniformity of re- sistance under one set of ponditions, as fair summer weather and heavy-loaded trains, will have as great comparative value in stormy winter weather with long trains of empty cars. Positive determinations of any one of the following doubtful elements we save the need of altogether : The ratio and amount of adhesion. The cylinder-power. The steam-power. The head resistance. The rolling-friction and friction of machinery. The gain from using sand. The rolling-friction. The wind resistance. The effect of number and load of cars. The effect of temperature, state of rail. The extent to which momentum may be re- lied upon to help trains over short heavy grades. 1072. To accomplish these ends the system of observation should in detail be as follows : The only apparatus or previous preparation necessary is a series of distance-stakes along the line, a stop-watch, and a note-book, with an observer on the engine (at times), also provided with a note-book. The stakes are set at various governing points on the line where speed observations are desirable. They should be of a size and color to be easily visible, and should be set throughout the road at some fixed and uniform distance apart. Boards fastened to the fence may be more convenient than stakes. It is unimportant to place them with ref- erence to mile-posts, but they should be set at top and bottom of every doubtful grade, and at the up-grade starting-point at every station and stopping-place which either is or may become in any way a difficult point, requiring consideration. It can do no harm to place them at all stations, as comparisons may be instructive. A train moving at lo miles per hour passes over 14.67 feet per second. As our time observations must be in seconds, it will be more As respects the cars . As respects the train as a whole convenient to set these stakes at some multiple of 14.67 feet apart, thus makmg all velocity records throughout readily convertible into miles per hour from speed notes in seconds. A suitable distance is 14.667 x 20 or 293.33 feet. If set at that distance a train which passes over the distance between any two stakes in 20 seconds is moving at 10 miles per hour. 15 " " - 13I - *^ .. f5 10 5 << 15 20 if << 4( (< 40 i< « 200 A (< « In other words, reciprocal of A seconds X 200 = vel. in miles per hour between the two stakes; a very simple computation from a table 01 re- ciprocals which the following Table 201 will save the need of. Table 201, Speed in Miles Per Hour corresponding to the Time in Seconds in PASSING OVER A DISTANCE OF 293^ FeET. Seconds. Speed. 66.7 Seconds. Speed. 3 6i 32.0 3i 61.6 6i 30.8 3i 57-1 6f 29.6 3* 53.3 7 28.6 4 50.0 7i 27.6 4i 47.1 1\ 26.7 4^ 44-4 7f 25.8 4f 42.1 8 25.0 5 40.0 8i 24.2 Ik 38.1 8* 23-5 l\ 36.4 81 22.9 51 34-8 9 22.2 6 33-3 9i 21.6 Seconds. 9i 9f 10 loi II Hi 12 12\ 13 I3i 14 15 16 Speed. 21. 1 20.5 20.0 19.0 18.2 17.4 16.7 16.0 15.4 14.8 14-3 133 12.5 Seconds. 17 18 19 20 22 24 26 28 30 35 40 50 60 Speed. 11.76 II. II 10.53 10.00 9.09 8.33 7.69 7.14 6.67 5-71 5.00 4.00 3-33 The disposal of the stakes at stations, where speed is slow may be advantageously modified by putting in half-stations so that they are only 146.67 feet apart, thus giving more accuracy to the observations ; but this is unessential, and does not modify the principle. if I''" >■: 796 CHAP. XXIV.—IMPROVEMENT OF OLD LINES. 1073i Stop-watches suitable for this purpose may be bought of any dealer for %i to $io each. They read to quarter or fifths of seconds, being stopped and the hands fixed at any instant by the movement of a little button. Pres- _ sure on another button, B^ Fig. 255, restores the hand to zero, ready for another start. They are generally durable and reliable. Two stop-watches may advantageously be pro- cured and mounted together on a board, the starting buttons being connected to a single lever, as shown in Fig. 255, in such manner that a single motion of the lever will start one watch and stop the other simultaneously. This will throw the buttons for turning the hand to o on the outside, so that they can be readily used without danger of mistaking one Fig. 955. for the other. It is not, however, essential that in taking a series of say five or six observations we should return the hand to zero each time. We may simply start one watch and stop the other at each station and note the actual readings, as below noted. The attachment of the lever should be so devised that there is a single point in a central position of the lever where neither watch will be started, which is a simple matter to do. A single "split-second" watch will answer the same purpose, but is more expen- sive. Some brass clips, C, for inserting a memorandum slip near to the watches may advantageously be placed upon the board to which they are attached, and brackets or angle-plates may well be provided for readily screwing the whole firmly to the side of the car. It is convenient, although not essential, to have an observer to watch and call off the instant of passing each stake, so that the attention need not be distracted from accurately taking the time observations. A little stand or hook to carry an ordinary watch for time records may well be added. 1074. The records of a series of six or eight successive observations at any desired point may then be jotted down on the memorandum pad, to be worked up later, or on the spot, since they are likely to be needed at infrequent intervals only. It answers every useful purpose of a dyna- mometer record, for the fluctuations of speed are such a record. In starting out from a station the intervals of time will be consider- able, even when taking half-stations of 146.67 feet each, and there is no difficulty under any circumstances in taking readings with all essential accuracy. 1075. The simple preliminary preparations required having been made, the method of conducting the observations of the actual working of trains should be as follows : CHAP. XXIV.— IMPROVEMENT OF OLD LINES. 79/ Before beginning the more careful and accurate work a series of com- paratively rude observations may well be made in which exactitude is not desired or attempted, solely for the purpose of observing the varia- tions of velocity in the ordinary routine of service, and to learn what to expect and where to observe most carefully. No observer on the enoine IS needed for this purpose, and it is as well, or perhaps better, that'ihe trammen should know nothing of the particular purpose in view. For the more formal and careful observations an observer* on the engme is necessary ; and it is desirable that the train should, ih several mstances at least, be run on an accelerated schedule, and that the engine- man should have full liberty, and indeed express instructions, to get over the ground (and especially to pull out from stations) as rapidly as is con- sistent with due caution and safety; in other words, to see how quickly he can run over the division, remembering always that the cylinder tractive power of locomotive is very different at high speed and low speed (par. 557 et seg.). 1076. The duty of the observer on the engine is to take notes from pomt to point of the following details; not for the purpose of making any absolute estimates or computations, but simply to have a full record of the work of the engine : (1) The steatn-pressure, by record of fluctuations of the steam-gauge It depends largely on the skill of the fireman ; how much, can only be determined by trial of different men, or by their record, if on a road which has a fuel premium. (2) The point of cut-off , or " notch." (3) The slipping of wheels and the use of sand. The record as to the last depends very largely (par. 501) upon the skill-and even in some cases on the good-will-of the engineman. It should be remembered that he can, if he chooses, slip the wheels almost anywhere, and he will slip them, whether he wishes to or not, if he have not the requisite skill, or is not disposed to be careful. Starting is ordinarily effected by set- ting the valves in full gear ahead and regulating the admission of steam by the throttle. If a full pressure of steam be admitted too suadenly, slipping of the wheels is certain to ensue, even if the engine be haulin'c^ no train whatever. ** 1077. Too much importance must not be attached to such slipping-, therefore, since it is more or less a regular incident to handling heavy trains by locomotives, which cannot be wholly avoided without cutting down trains to an uneconomical point, nor perhaps even by doing so, as is witnessed by the slipping which goes on constantly in yard work, result- ■f M 798 CHAP. XXIV.— OLD LINES— VIRTUAL PROFILE. CHAP. XXIV.-OLD LINES-VIRTUAL PROFILE. ing not from the excessive load, but from too great haste to get the load under way. 1078. The duty of the observer on the caboose (or at any other con- venient point on the train) is confined to taking the time records. He- should know the points at which they are to be taken very thoroughly. He should also, before starting out on the trip or after completing it, note the following details : Number and class of engine and name of engineman and fireman. Number and gross weight of loaded and empty cars, and whether box or fiat cars, and how many ends of box cars are left exposed in the train, by being preceded by flat cars, to cause extra air resistance. Temperature, condition of rail, and direction and velocity of the wind. The latter may well be determined by an anemometer and wind-vane on the caboose, which will give directly, what is really required, the resultant in magnitude and direction of the wind caused by the motion of the train, and that otherwise existing. With a head wind the resultant will lie in the direction of the train and have a velocity equal to the two combined ; with a rear wind, it will have a velocity equal to the difference of the two, which may be zero; with a side wind equal in velocity to the speed of the train the resultant will lie at an angle of 45° therewith, and have a velocity 1.414 times greater, etc. It is not really essential that very accurate wind observations should be made, since we are not after abso- lute but comparative results, and it is easily estimated whether a storm or wind is or is not about as unfavorable as is often encountered. 1079. The records having been taken, the velocities at various points are taken from Table 201 and the vertical " head " in feet corresponding to that velocity taken from Table 118, in the manner which has been dis- cussed in par. 397 et seq. on virtual profiles, which we are now ready to- construct, preparatory to entering upon the interpretation of the obser- vations taken. In these latter steps lie the delicate parts of the work. CONSTRUCTION OF THE VIRTUAL PROFILE. 1080" Taking an actual profile (which need not necessarily cover the whole line, but may show only the important points; a common profile to working scales is the best), lay off at each point where time records have been taken the vertical height in feet corresponding to the velocity which the train had at that point. By an assumption which is practically correct, the aver- age speed which a train has between any two stations is its actual 799 !hriH\'^^ ^f"""- "^^d^^y between them. Tl^rtical hei^ should therefore be laid off at corresponding points on^the In this way we obtain our virtual profile, parts of which may be sornething like the dotted line on the following Fig LZ solid line being the actual profile. ^' ^ ' Fig. 256. 1081. Tins Virtual profile, as we have seen, is that which alone needs to be considered. It represents a line over which if it were actually constructed, a locomotive, exerting at everv point the same energy and overcoming the same frictional resis'tances would move at every point without either gaining or losin<^ speed. O,. tins profile what appears to be and what is coincide! M the vntual profile shows a low enough rate of grade we need not be disturbed if the actual profile below it shols a consider ably h.gher grade. On the other hand, if the virtual profile shows a short heavy grade in pnlling out from a station, which cannot be reduced by taking more time in starting trains its disadvantage is no whit less because it is short or because 'the actual grade below it is almost a level. The virtual profile will differ according to the direction the but from all these notes together a safe average is supposed to have been determined at each point. 1082. Studying how to reduce this virtual profile, we recoe- nize three ways: ° in ^^X H "'^ T'''T'^' ^° ^^""^ ^"' "^^"^"^ by increasing it llimin«, ' g'-!«Jes and decreasing it on the summits and by eliminating or taking longer time for stops. By carrying this Stfn r"" T^'* "" ""'' '■^'"•^^ '"^^ ^''•'-' P-fil^ °f - un- dulating hne having very heavy grades to a level, as we have 8oo CHAP. XXIV.— OLD LINES— VIRTUAL PROFILE. seen (par. 399); but, practically, only minor variations of this kind are admissible. Secondly (and next simplest), by using pushers. Thirdly^ by reconstruction or amendment of the actual profile. 1083. Let us suppose, as examples are most readily followed, that these observations have been taken and the virtual profiles made over a given division with the results at various points outlined on the following Figs. 257 to 264. Some long hard pull on a 1.2 per cent grade {d^-Z'^ ^^et per mile) shows that the given engines can handle 25 cars, more or less, on this grade with great ease, except in very unfavorable weather. Under fairly favorable conditions the velocity gained without overtaxing the boiler capacity is such as to indicate a virtual maximum grade of 1.4 per cent, or even more. The same is true at a number of minor points on the same •division. In pulhng out at stations, by comparison of many observa- tions, it is found under average conditions that the virtual grade was 1.3 to 1.5 without using sand (being somewhat lower be- <:ause of the greater journal-friction, and lower because the full adhesion was more nearly used and there was less air and other velocity resistance), while when sand was used the virtual grade was raised to r.6 or 1.8. On the other hand, with very unfa- vorable weather and a bad rail, the virtual profile in starting is 1.2 to 1.4, even with use of sand. ' 1084. Under these conditions we have, in the first place, an indication that the trains now handled on the road as it stands are somewhat smaller than they might be — an indication which is alone worth the trouble of an investigation of this kind, and can in no other way be so accurately determined. Passing that question, however, as not now under consideration, we have a very positive indication that we shall be safe in assuming that by using a pusher of equal power over the worst grade, we shall in effect reduce it to the equivalent for a single engine of a pusher grade of 1.2 per cent, which is (Table 182, page 593) 0.45 CHAP. XXIV.-OLD LmES-VIRTUAL PROFILE. 8or try for over the remainder of the division. If vve find it ea.sv nf accomp ishment, we may consider reducing it stiU lot and by use of san^d may' l^ZZ^:;:^:: t r^'ditLrs'."^ Fig. »57- fl^*!i-- Over the remainder of the division we are liable at various points, to have cases like the following- 1085. A station grade at ^, Fig. .57, on an actual grade of 0.6, ,s operated very easily now. the train quickly getting under way even without the use --.^ .y gcLLiug unaer of sand. By taking more *"**'-»-. time for starting heavy trains (say attaining full working speed at ^) the p,,.,,,. -^ 4 virtual grade might be reduced, perhaps, to 75, but it is nTces sary to reduce it to 0.5 at least, and if possibi" to o 4 tl e actual' grade needing to be considerablv less. ' The neatest and most effectual method is to remove the sta t on at once from A to £, this alone having the effect to favlr ably modify the virtual profile far more than was de 'ir d 'fwn. that shown in Fig. .58. If this be impossible, thlnex? be"! m thod ,s to take out the bad gradient in the virtual profile bv aising the grade at A on the actual profile to A', giLlhiZ orm shown in Fig. .5,. Changes of this kind 'a^apV to be expensive because of their locality; but, on the other hand, they 'III 8o2 CHAP, XXIV.— OLD LINES— VIRTUAL PROFILE. are inexpensive in that they are seldom very long. The effect is to substitute (in the lower half of the diagram) a broken actual but good virtual profile, in place of a good actual but bad virtual profile, as in the upper half'of Fig. 259. 1086. A modification of the same case may be as follows: A station originally well situ- ated, as Sy Fig. 260, but which has been complicated by subsequent additions of grade-crossings for other lines C and C, at which all trains have to stop and ^'°' "59- start again on a grade. The first and best remedy for this evil is the use of inter- locking signals, saving the necessity of a stop except to let another train pass; but as that is a contingency which may hap- pen not infrequently, it can never be a perfect, nor in some cases sufficient, remedy. The evil may also, in cases, be reme- CIIAP. XXIV.-OLD LINES-VIRTUAL PROFILE. -fti. Fig. 260. died by raising the grade of the track approaching the crossing as outlined at C and C\ provided the virtual grade of the approach be not increased thereby to an inadmissible rate. The only remaining course is either to use a yard engine as a helper over the crossings or to boldly lower the grade by passing under each road, and grading a new road-bed or lowering the existing one, for which room may be so scant as to require retaining- walls. This will make the improvement a costly one, and yet the cost will probably be small in proportion to the gain, unless it is only one among many costly improvements required for the desired end. 1087. At large towns it is a very common thing to find the station located at some point, like 5 or 5', Fig. 261, which was Fig. 261. S03 originally fixed more with reference to the c^^ience of the town than to the grades. This is of course the proper thing to do, and a decrease of station ^ facilities, or a change causing inconvenience to the patrons of the line, will in general be inex- pedient. Such large stations, moreover, are generally well provided with side tracks, so that the result is that they are largely used by train-dispatchers as passing points. The proper remedy in such cases is to establish sidings For F, to serve as passing points for through trains only with a :separate telegraph-office, leaving the local facilities undisturbed Ihis requires the services of two operators to do the work of one' and perhaps one or two other otherwise needless employes but' the wages of one train crew for a single trip, it should be re- membered, will pay the wages of a good operator for a week. 1088. The case sketched in Fig. 261, moreover, is one of those where the whole difficulty in handling heavier trains may be made to vanish by a modification of the system of dispatch- ing, to the effect that only trains going down grade, or say east shall be held at this station and compelled to take side track '(except, of course, in emergencies), especiallv if there be another regular station near to it, as For K', which may be used as a passing point, by holding one or the other train, in case it is im- possible for the eastward train to reach ^ or S' first. It is not essential, although it is convenient, that a dispatcher should feel at liberty to hold any train, bound either way, at any station in the regular routine of business, provided that to do so interfeVes with a material addition to the train-load. It is the rule and not the exception, however, that he can and does do so. 1089. The decision as to what course to adopt for modifica- tions of gradients on the open road is a much simpler matter than at stations. The vital point to be determined in the begin ning, before studying the details of the various difficult points at •ail, IS what rate of speed is practicable and allowable at the foot mu rt' % 8o4 CHAP. XXIV.— OLD LINES— VIRTUAL PROFILE. CHAP. XXIV.-OLD LINES-VIRTUAL PROFILE. 805 of the grade, which largely depends on tlie alignment. The modern tendency is very decidedly to permit of higher speed in handling freight trains, and it is essential to do so at points to handle the maximum train on all undulating gradients. The probable introduction in the near future of freight-train brakes and more mechanical coupling devices than are now in use will, when accomplished, greatly increase the admissible maximum of speed for equal safety; but even as freight equipment stands at present it is probable that 30 or 35 or even 40 miles per hour, for short distances at special points (the writer must not be understood to recommend the latter speed), are quite as safe as 50 to 65 miles per hour for passenger trains. It has been tolerably well determined (par. 664 et al?) that higher speeds than 15 miles per hour are more economical for freight trains; and the not un- common feeling that any speed of over 15 or 20 miles per hour verges on the dangerous is in part a relic of the old days of iron rails, poor ballast and road-bed, and less solidly constructed roll- ing-stock. 1090. Therefore, when required for reducing virtual gradients by taking a ** run at them," as part of a general system of im- provements, a speed of 30 miles per hour (which takes 31.95 ver- tical feet out of the depth of a hollow; Table 118) should be freely permitted and counted on, with fair alignment; and with a tangent in the hollow of the gradients this limit may in gen- eral be safely increased to 35 miles (43-49 vertical feet), if that speed seems essential. These speeds and even higher ones are now frequently used in handling freight trains on many lines. Whatever the limit adopted, however, it should be determined in advance, by reference to the records obtained as already de- scribed, and especially with careful consideration as to whether the assumed speed can with certainty be counted on as attainable at the given point. Unless there be a descending gradient in the approach so as to give the required speed quickly, the high speeds mentioned cannot be counted on safely. 1091. This preliminary being determined and the present and desired gradients being the same as already assumed, viz., 1.2^ Fig. a62. actual and 0.45 desired. Figs. 262 to 265 will serve as types of all the cases which can arise on the open road. In Fig. 262 let AB be a long i.o per cent grade with curved alignment at B so that more than 30 miles per hour is not deemed safe at that point, but that or even higher velocity is easily attainable. With the .. short trains heretofore in use the grade has"not'"been a difficult one, so that the virtual profile obtained in observations on trains as now run has been nearly parallel with the grade, the speed bemg lower at B and higher at A than was necessary It is de- sired to determine to what extent (i.e., for what length) such a grade can be operated as a virtual 0.5 gradient. 1092. A certain speed at A, not less than 10 miles per hour {3.55 vertical feet), must be assumed, as a margin for error whether there be a stationatA or not (par. 1095). Then 31 95 ~ , c J = 28 4 vertical feet, as the maximum through which momentum can be relied on to lift the train. Moreover, the actual grade i o -- 0.5 (assumed virtual grade) =0.5 feet per station as the defi- ciency in power of the locomotive which must be made up bv — - 28.4 ^ ^ — 50.8 stations, or over 9 mile. 05 momentum. We have then Fig. 263 Zf ^^ °^ "'*'' ^' "'" '""»"' °f 'his grade which it >s possible to operate in this manner. If the grade be longer or ^horter than this, the overplus, but the overplus only, must be ^ruJT- I "^": ~"^'™«'°". either by raising the grade at B or (what .s better) lowering it at ^. If the grade were ten stations ^'\* ■ i.: 806 C//AP. XXIV.— OLD LINES— VIRTUAL PROFILE. longer, those ten stations, but those only, must be reduced to- 0.5 actual grade in one or the other of the methods outlined in Fig. 263. If the change be made at the bottom of the hill, as at B, we shall have the disadvantage that on the whole of the new 0.5 gradient a speed of 30 miles per hour must be maintained to- have the desired effect. As this may be or may seem objection- able, the modification may need to be more extensive to effect the desired end, and should be, wherever possible. 1093. The same is true, in less degree, of the change at the top. The train, under the assumptions, will not be able to move faster than 10 miles per hour until it has passed entirely over it. Therefore the maximum figures for the gain by momentum should be used only for determining whether or not any vwdification of the grade will be required. If it is even then found necessary, 3 more liberal margin should at once be adopted, if attainable at moderate increase of cost, as it generally will be. In fact, when some construction in any case has been once found necessary it may often be best and almost as cheap to take the whole hill out at once by a detour; perhaps making the new and old lines together serve as in effect a double track. 1094. It is to be remembered in considering what allowance it is safe to make for assistance by momentum, that in many cases an error in the estimate of the possible gain from that source will have no disastrous consequences, since if it be found that the assumed speed was too great to be relied on it is pos- sible at any time to raise the grade three to five feet in the hol- low, as outlined in Fig. 264, and thus materially reduce the speed required. To do this is in most cases a comparatively simple matter, since the fills need not be very long to p,j3^g raise the hollow between two gradients by a considerable amount. If the two gradients are i per cent, the total length of the fill is only 200 feet per foot of lift ; with 0.5 gradients, 400 feet per foot of lift; and with 1.5 gradients, 133 feet per foot of lift, etc. To make fills by train in CHAP. XXIV.— OLD LINES— VIRTUAL PROFILE. 807 Fig. 265. such locations, even if of considerable magnitude, is rarely ex- pensive, and it can be done at any time when found convenient and essential. Therefore, when it is seen that a not excessive fill will, if made, fulfil all necessities, it is proper to rely quite largely on momentum for the time being, if by so doing the fill can be dispensed with for a time at least, and perhaps forever. 1095. On the other hand, there is a danger connected with the study of such virtual profiles, which has been alluded to above, but which should be still more explicitly pointed out. When the question whether or not we can keep within a certain virtual gradient is at stake, as in Fig. 265, it is in no case safe, even when there is a station at .->>_ the top of the hill at A, to assume that we can arrive there with no velocity, and can consequently lay the virtual gradient directly on the actual. It seems plausi- ble that we can do this, as we are certain that we shall need no velocity at A-, but what we are not sure of is of never falling below the desired velocity at B, and if we do, our virtual gradient is at once increased. If we assume a certain moderate velocity at A, say 10 miles per hour (3.55 vertical feet), and any maximum velocity deemed reasonable at B, as in cases where no stop is contemplated, we are safe, because our velocitvat ^may then fall quite a little below that assumed without endangering our arriving at A with some velocity, so as to float the train over It; but if we assume we are to arrive at A with no velocity, sim- ply because the train must stop there, we are liable not to reach there at all. No advantage can be assumed, therefore, from the fact of a stop at the top of the gradient more than would exist if there were to be no stop there at all. In either case we must be sure of reaching the top, and in neither case is it important to be sure of more than that. 1096. The temptation may be great to fall into this plausible error, when an estimate, perhaps, must be kept very close to have the work go through at all, and when there may be an expensive 8o8 CHAP. XXIV.— OLD LINES— VIRTUAL PROFILE. bridge at B, making it difficult to lift up the grade at that point; but if a reasonable velocity at B and some velocity at A will not suffice, there is nothing for it but either to raise the bridge, lower the station, increase the distance between them, or give up the desired virtual maximum as unattainable. 1097. By attacking the work of improving old lines in the method here outlined, halving the more formidable and inevi- table grades at once by using a pusher on them, without spend- ing a dollar on them, and spending all our money on what were before the very easy grades, and hence are usually in light work, the average train-load may be doubled at small cost on thousands of miles in this country ; whereas by merely attacking the heav- iest grades which show on the profile with force and arms, so to speak, a great deal of money must be spent, and there will be comparatively little to show for it. CHAP. XXV.—GRADE-CROSSINGS AND INI^ERLOCKING. 809 CHAPTER XXV. GRADE-CROSSINGS AND INTERLOCKING. 1098. The multiplication of grade-crossings has become a •great and serious question, especially in the West. The topo- graphical conditions in the East greatly restrict the danger from such crossings, as well as their frequency; but throughout vast regions of the West there is absolutely nothing to prevent a railway being built from anywhere to anywhere in very nearly an air-line by accepting "moderate" grades of 40 to 80 ft. per mile. As a consequence, many important lines have little or no assurance that crossings may not be demanded of them sooner or later on any single mile of their track, and it becomes of great importance to determine how strenuously they should oppose ^uch crossings, what expense they may and should incur to avoid them, and what can be done to reduce their disadvantages to a minimum when unavoidable. The problem has been greatly simplified in recent years by the fact that the disadvantages of grade-crossings may be largely •diminished, and sometimes almost destroyed, by the use of inter- locking apparatus, as we have seen in par. 1086 and elsewhere; but while there were in 1885 some 60 railways in the United States using interlocking more or less, the total amount in use was considerably less than on the London & Northwestern alone. 1099. There are 18 different sizes of standard signal-cabins on the London -& Northwestern Railway, which are : A. 5 levers, 6 X 6 ft. D. 20 levers, 16 ft. i\ in. X 12 ft. B. 10 ** 9 X 9 ft. (and so on to—) C. 15 " i3i X 12 ft. T. 180 levers, 96 ft. 6 in. X 12 ft. The usual rule being that the cabins are all 12 ft. wide and are 6 in. long per iever, plus about 6^ ft. There are 1344 of these cabins on 1753 miles of road. 8lO CHAP, XXV,— GRADE-CROSSINGS AND INTERLOCKING. containing 26,500 levers. The annual average cost for maintenance is $187,000,. which, divided by the number of levers in use on the line, comes to $7.07 per lever. This amount includes not only the renewal and repairs of the lockingf^ apparatus, but that of the signal-cabins, signals, and all subsidiary apparatus, and also the cost of providing any new and additional apparatus, when under $50. The amount of work to be maintained has increased 80 per cent since the year 1874, while the cost of maintenance has only increased 5^ per cent. In the whole United States there are, of all systems (1885), somewhat less than 250 cabins and 3000 levers, or but about one fifth as many cabins and about one ninth as many levers as are in use on the London & Northwestern alone. 1100. In England there are practically no grade-crossings- of railways, and this apparatus is used chiefly for yards and junctions. In America there are a great many grade-crossings^ even on important lines; but the clumsy and costly precaution, of a full stop of every train at every crossing is still the rule, al- though it can hardly be that such an absurd relic of barbarism- will linger much longer, now that there is. a considerable and increasing number of grade-crossings operated without a stop* by the aid of interlocking apparatus, and always with perfect safety and success. 1101. In part, the slow progress in this matter is easily ex- plained. The great loss and delay from grade-crossing stops- goes on quietly and silently, sapping the life-blood of the com- pany, as do the consequences of bad location (page 2), without interfering much with the routine of operation, and at points- removed from the managing officers' immediate observation, whereas the difficulties at yards obtrude themselves on .atten- tion, and many of tlie most crowded yards have passed the limit of their capacity without some such mechanical aid. 1102. Nevertheless, from an economical point of view, abol- ishing the stop at grade-crossings is by far the most important,, especially when, as is so frequently the case, they reduce the num- ber of cars hauled below what it otherwise would be. To reach* this conclusion we need not adopt any of the wild estimates which give the cost of a stop at anywhere from a dollar up. Without going elaborately into the details of the estimate, to- discuss which properly by items would take considerable space,. CHAP, XXV.— GRADE-CROSSINGS AND INTERLOCKING, 8ir ^rom 30 to 60 cents may fairly be taken as the cost of a stop apart from all effect on length of trains. An estimate of 40 cts' per stop for average trains on lines doing considerable through busmesscan hardly be considered excessive, and at this rate the cost per year of each train per day stopping at the crossings is 365 X 40 = $146 per year. If therefore there is an average of ten trains per day each way for each of the roads which cross (and the average at grade-crossings would probably be more rather than less than this), we have $146 X 10 X 2 X 2 = $5840- as the annual loss to both roads from the fact of the existence of this crossing. 1103. The cost of saving this loss by constructing a new line or by interlocking, will vary more or less with the locality and in less degree with the system of interlocking adopted • but the variation in the latter respect is not important, and the outside limit for a complete system of interlocking switches and signals for either single or double track (it makes little difference which), by one system of approved excellence may be stated to^ be from $2500 to $4000, averaging $3000. This includes ei^ht signals (four -home" or near signals, and four distant signals two for each track), four derailing switches, one for each track' which throw the train off onto a graded road-bed (having no rails and ties for only a short way), if the signal be carelessly run by, and (for a separate sum of $400), electric locking apparatus which renders it impossible to change the signals after a train, has once passed the first distant signal until it is over the cross- ing. The cost of the building and of erection is included in the above. One man only is required to attend to the signals as is re- quired without interlocking, and his wages need be little if any higher, so that this item may be considered unaffected. 1104. Even with the lightest ordinary traffic, therefore the lowest reasonable estimated cost of stop, and the highest prob- able rate of interest, the sum saved annually is far more than enough to cozier the additional expense of thoroughly protecting a grade- crossing so that no stop need be made, without considering the Si« ^12 CHAP. XXV —GRADE-CROSSINGS AND INTERLOCKING. greater safety and convenience. At more important crossings it would be hard to find a clearer case of an expedient improve- ment, even if the stops do not cut down the length of train. 1105. If the length of train is cut down, so as to take, say, 21 instead of 20 trains per day to handle the traffic, the very lowest cost for which the extra train can be run is (Table 176) 35 to 40 cents per train- mile (for an average cost of 70 to 80 cents), or say $38 for a trip of 100 miles, amounting to $13,870 per annum, or $693.50 for each of the 20 trains, or $1.90 per stop (if only one stop causes the decrease of train-load) in addition to THE DIRECT COST of the Stop. In such cases, of which there are many, it is culpable folly to delay availing one's self of so cheap and easy a remedy for such losses as interlocking affords, if the <:onditions are not favorable for the still better and in the end often cheaper remedy, an over- or under-crossing. 1106. A fact which explains rather than excuses the prevail- ing negligence in this matter is this, — that the protection of grade-crossings requires the joint action of two roads, usually under different and often under antagonistic management, and it requires no little negotiation, and a conciliatory spirit on both sides, to arrange the details of the distribution of tiie expense. It can hardly be doubted that this difficulty is a serious one, and it is largely the fault of the laws which authorize the use of interlocking as a substitute for stops. By some singular over- sight, all these laws as yet passed (1886) authorize roads to "agree" on putting in interlocking, but do not provide a way by which one road, anxious to act under the law, can compel an- other road to accept a reasonable settlement by arbitration or otherwise, unless it chooses to. 1107. The provisions of the State laws as to dispensing with crossing stops may be briefly summarized as follows : The Massachusetts law passed in 1882. after somewhat urgent recommen dations by its Commission, which were at the time regarded by many as some- what heretical (because the public knowledge of interlocking was much less then than it is now, even among railroad men), provides that "The approval of the Board shall be required for a system of signals to be established and maim stained in concert" by railroads which cross each other, but that a full stop shall CHAP. XXV.— GRADE-CROSSINGS AND INTERLOCKING. 813 not be dispensed with " unless a system of interlocking or of automatic signals approved m writing by the Board, is adopted by both corporations." Ohio, at almost the same time, provided by law that "any works or fix- tures" approved by the Commissioner of Railroads and Telegraphs as render- ing it safe to dispense with stops, plans having been filed with him shall dispense with the necessity of a stop; and if the Commissioner shall fail to approve the plan within twenty days, -such companies' may apply to the Court of Common Pleas, where appropriate action will be held. This enactment seems to require not only that both companies shall consent passively but that they shall unite in active legal proceedings to avert a decision which might be not unwelcome to one of them. Michigan (1883) passed first a very absurd enactment that "authority is- hereby given to said Commissioner, and it shall be his duty, if he shall deem it practicable, to prescribe the use of the interlocking switch and signal svstem provided that at crossings where all trains come to a full stop no other system, than that requiring such stop shall be prescribed." The absurdity of thus cutting oflf one of the chief advantages of interlocking signals struck the Legislature almost immediately, however, and another act of the same session provided that "whenever there shall be adopted and used at any such crossing an interlocking switch and signal svstem. or other device " wh.ch the Commissioner thinks makes it safe to dispense with a stop, he may authorize it in writing, with any regulations as to speed or other matters which, ne deems necessary, and with power to revoke his action In the strict letter of these laws, the Commissioner may prescribe automatic signals without dispensing with a stop, but can only authorize the stop after the apparatus is adopted and in use. Neither is he-what is a more serious matter -given any specific power to say what part of the expense each of the twc companies concerned shall bear. These provisions come the nearest, however, of those o any State to providing means by which one railwav which is anxious to escape from the burden of stopping at a crossing can compel the other bene- ficiary to bear its fair share of the cost. The Indiana law (1883) is merely permissive, authorizing the Auditor of State to approve interlocking or automatic signals at crossings, from plans submitted by -two or more railroads." which have erected or are about to erect them and thereafter to authorize the omission of stops. It is specifically pro- vided that such signals shall not be " used or put in" at any crossing " to the detriment of any other railroad company," unless with the consent of that com- pany ,n writing^ Under this provision, the manager who wishes to dispense ^v.th twenty different crossings must first undertake the interesting task of persuading twenty different companies that it will not be " to their detriment" to do so. The New York law (1884) provides that the requirement of a full stop may be dispensed with whenever the Board of Commissioners "decide it to be- I ■ S14 C//AF. XXV.— GRADE-CROSSINGS AND INTERLOCKING. impracticable" or where "interlocking switch and signal apparatus is adopted and put in use by the railroads there crossing each other at a level," of a form approved by the Board. Illinois passed through one house in 1S86 an act essentially similar to that of New York, which was expected to become a law at the following session. 1108i It is easy to see how, under any of these laws, a manager attempting in good faith to benefit his company and benefit the roads crossing and the public as well, by perfectly fair and equitable arrangements for dispensing with slops at crossings, might find it an irritating and almost hopeless task, and might feel compelled to give it all up in disgust before he had fairly begun. The difficulty of agreement is precisely the same as would exist in cities as respects party-walls, without the law which authorizes any man to build half his wall on his neighbor's land and compel his neighbor to pay for it when he uses it. The equities, and the great advantage to both sides, are here exceedingly Jso^onTcoafperiay @l^. J^ ^^ ^ Total 9i.o 546 loao ■CM o CI ca < O en c o *5 « i o >, u V ^ >« V) Xi .•3 o u a •o c t " ►J o < a ^ JQ 2: s o c ee V o u H < < B •^ JS C U u 'a o 2 < S % < m O •o •mm o. B o o u u o > h O S o u o Z < Q U C/«^4P. XXVI.— TERMINALS. ■a " O O Q O O ^ I-" a O »/^ t^ O M M M -Cl O u 2 A •^ " « U 4* W ;», ' 8000 000 5r f^ c^ O c^ M l-l l-i ^* CO O O w O O »r> • \rt 2; O O a o o Sii N vO CO CO O 2; •^ IT) t2ws oe "^ mo IT) o 25 ^3 00" '^ *-* «r w ^ •^ <= i» o t c:r.o« CJ .888 « o o 5 • o o o O" ,n c> m w en c< 11 > c o •u 3 c o *c B u rt Urn S S 8 r ^0000 ''^ 6 o' q" o" • in 'O O "^ ,5^ en CO en u-» 8 o 8 o m 2 o S ° o • 8^'^ 00 8"^ d ° O • CO rt i- V3 -^ 8 000 O o m o 5 en c< vo vo §8 o • O u u rt T3 •-* ^ rt u en 00 M o -f r^ t^ r^ O 00 •^8 en o U rt to .CO o O Tj- e« j« N N en ■^ M l^rt-H .00 CO M en rj- m tn en 8" a vO ' o vO e* 8 d 8 10 o o 8 o o CO 9 O u c i5 w CO a bo .rt be 819 tj .s c u t ^ >> c JH rt A c m^ cn •o "H to rt >* iA u u JS & a «J rt ..J CO rt a cr •a 9> HJ u •0 01 a h rt t> u c *M CO •a rt (90 C 2 s CO CO « .2 bo V ••• w «... ._, x: bo rt to o a o t> CO "D rt 2 •a c rt bo c •a v. oj aj cr.5 ° s o < o I UJ .2 ^ f^* PQ ^ :z: ^ :zi ci :z; :2i ^ J o H • C« ' 73 ' JS E — ;'o "o c w o _; u 4; cn '^ CJ (« c ' ex O V CO *^ CO rt O CJ en u •a _3 U c SI § c "2 V M ^rt' U O Si - O CO O a JS s o o u u rt JS o c 8 a u «^ C a 0/ eft" C o 3 « Si to CO u o o c rt « •a rt §2 *-■ 55 a. o ^ 10 — • c o ^ 5 cr •o c 3 <-• « E c; CA cn 4> « -g li o »-i ^ o -2 *? rt -"= "O V c <= .c J2 to CO en OJ U V •O -D "O .2 pH .2 U U U c c c 11 ';i.^H HI' 820 CI/AP. XXVI.-TERMINALS. The only direct return received from tlie merchants by these railways for tliis work, tlie plant of which represents an aggre- gate capital of at least $35,ooo>o°0' and the power and force em- ployed an annual expenditure of at least $3.5oo>ooo, are the charges collected for long-distance lighterage. There is, how- ever, a considerable fixed terminal charge of five cents per cwt., more or less, which is credited to the terminal road before the division of rates is made according to distance (par. 210), so that the roads terminating at New York are, perhaps, less burdened than the average by the terminal expenses. Assuming 6 percent interest, this estimate shows a total annual expense of $5,500,000, and taking into account clerk hire, management, repairs, taxes, light, stationerv, insurance, and all other expenses, the total is probLbly not far from $10,000,000, or an average burden on each road of $2,000,000 every year. 1117. If we include the terminal expenses paid by the indi- vidual shippers, as well as by the railways, the above totals, large as they are, sink into insignificance. It was estimated in 1875 by a committee of the American Society of Civil Engineers that on some 4,632,000 tons of the freight delivered at New York the total terminal expenses were $3.07 per ton, or about three fifths of the then rate (25 cts. per 100 lbs.) from Chicago to New York. The total receipts at New York in that year were about 15,000,000 tons of all kinds of freight, and on half of this the cartage charge alone was estimated at $1.60 per ton. Inasmuch as so much more for cartage means so much less- available for freight rates, and vice versa, on a large proportion of the freight, and more or less so on all of it (par. 47), we have in these figures some indication of how serious a deduction the total terminal expenses must make from the amount available for railroad transportation proper, and how important it is to have terminal facilities of the best. New York, however, is a true terminal, in the strict sense of the word. Some of the ter- minal points, which are really only yards of interchange, are of even greater magnitude, if not cost. Lest the great error be fallen into of assuming that the terminal facilities at New York are as much greater than those at other cities, as New York is as is O b U W3 C B. H X ao to <0 atf O u; o n O < - o < b. h. 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Ov J-. « 00 00 00 en « d ▼ fn ro M ^CU'^^jbd t/) , ,C/)JC , ,?j — VO «o £n8?:888888 ; lOMt>.IOIOlOl->MM ' m fO VO M 00 00 O 00 v8 o> o> 10 w o ro 10 10 10 ro vd O N 00 CM o VO O in VO o 00 8 10 o C« 8 6r 821 «-> o c c "z: t..2 ? o CO Cq ..^ ^ M W_i «~ o o >';: ^^ -^ o B! o c V u a c I (A <% V c u u o tc Ctf nH c 2 CO O V a u .a a 9 o u 01 'a a 2 c« uS = vg U7 m 15 o > -^ OS d " K A, •c 2 u > (A "5-^ "3.52 ce y t:-* V u C o u c 3 ' c c CA 4> -S >v « (S £ W wJtJ •— _. ce « ^•C iiJS is. 822 CHAP. XXVI.— TERMINALS. greater in population, some notes may be added as to what is really only the largest of many examples of interior yards — those at Buffalo, N. Y. So far from there being anything exceptional in the New York terminals, they are probably smaller in extent and cost per head of population than at most important termi- nals, and vastly smaller than at a number of them. 1118, The statistics presented in Table 203 of the yards in Buf- falo leave no reasonable doubt that, of its kind, it is the greatest in the world. How much of this abnormal magnitude is the healthy and natural result of peculiar traffic conditions, and how much of it is mere fungous growth from diseases of management whose existence is universally felt, it would be useless to inquire here, because as things are it is all necessary, and there is no im- mediate evidence of any probable change. The headings to Ta- ble 203, in which fourteen different kinds of side tracks are spe- cified, will at once explain in part why so much of some of them is necessary. In the aggregate there is a total of some 300 miles of side track within an area of some eight square miles (about i^ by si miles, 5.63 square miles being actually owned by the rail- ways within the city limits), which it is expected to increase im the near future to some 450 to 500 miles, mostly by accessions to* the trackage of the newer lines entering Buffalo, and required by them — as will be seen by the detailed table — to afford to them no- greater facilities than the older lines already enjoy. The lease of the West Shore to the New York Central saved, it is estimated (somewhat liberally, it would appear), the construction of as much as 50 miles of track which would otherwise have been ne- cessary, but, barring that, there is — , M iles. , Single track. Tracks of all kinds in city limits of Buffalo or immediately ad- jacent thereto 436. i And to be laid by the new roads (chiefly) now imperfectly sup- plied 176.0 612.I Of this there is main track, including three double-track lines swinging around the city to a connection with the Interna- tional Bridge 155- 1 And projected (minor extensions) 5-7 100^ Leaving as side track 45iS CHAP. XXVI.— TERMINALS. 823 Of the main track a considerable portion is only nominally main track, but really more in the nature of track for yard use only, which may be estimated as at least 50.0 50.0 T • V • , . (Main.) (Side.) Leavmg as the true proportions of mam track and side track ac- tual and projected. uo.S 501.3 Of which there was laid, October, 1884 100.3 326.8 An d projected, a considerable fraction of which has since been constructed j 5 174 e 1119. If we compare this with the figures for the yards of New York City, as given in Table 202, we shall have a better idea of the magnitude of the Buffalo yards. The total miles of track, main line and sidings, at the two points compare as follows : New York Buffalo New York Central 28 ^sV P't ••• 49 116 Lackawanna 50 b*? West Shore (and Ont. & West.) *...*!'..*.* 34 23 Pennsylvania og Other roads 'm\ Total 200 436 It will be seen that, with all the immense traffic of New York, there is less than half as much track at New York as at Buffalo. In the yards of Boston there are 150 miles of side track, on 568 acres, with 26 acres of buildings; the total side track on all the nine roads centring there being 765 miles for a total of 814 miles of main line. 1120. The New York tracks are also different from those at Buffalo in not being all bunched together, so as to be in fact, if not in form, one vast yard, whose different parts are constantly interchanging business with each other. The New York yards are miles apart from each other, and have comparatively the most insignificant interchange relations. Most of them, in fact, could be most fairly compared with the thirteenth class of Buffalo side tracks, those for "local city freight" alone, of which there are in Buffalo 2o| miles, with as much more projected ; for, al- though there is a very large— in fact immense— coal, steamer, and stock-yard traffic at New York, as well as the usual shop 824 CHAP. XXVI.— TERMINALS. and coaling tracks, yet the business of New York is carried on under such different conditions from that at Buffalo that the same traffic requires, as is apparent from the figures, several times less track room. For example, there are 39 miles of shop and coaling track at Buffalo, and 35 miles more projected, of which the New York Central and the Erie have each some 13 miles, which (without being able to present the exact figures) is undoubtedly several times greater than the same roads have for the same purposes at New York, the reason being that sick and wounded cars from all over the continent tend to accumulate at Buffalo, while they are kept away from New York so far as pos- sible. The same contrast is visible in the 16 miles of transfer tracks at Buffalo, which it is proposed to double ; and the enor- mous aggregate of 87 miles for the direct use of trains from the East and West and Canada, and for distributing West-bound freight (columns 3, 4, 5, 6, 7, Table 203), to which it is proposed to add over 40 miles more, mostly by the newer roads, is in itself something for which there is no very exact parallel in New York, either in quantity or quality, although, of course, the mileage devoted to similar uses is very great. 1121. The same contrast exists to an even larger extent in the areas of land occupied in the two cities, which compare as fol- lows : In New York, land 378 acres. piers . 5 •' 383 acres. In Buffalo, land 3,600 acres. Land in Buffalo is, of course, a very different and much cheaper thing than land in New York, and this area, moreover, includes several hundred acres of what is more properly main- line right of way, not properly chargeable to yards. But after making all allowances in this respect, the immense proportion- ate magnitude of the Buffalo yard, due to the nature rather than to the absolute volume of the business transacted, which makes Buffalo a point where innumerable side tracks naturally accumu- late, is clearly indicated. CHAP. XXVI.-.TERMINALS. 825 1122. While Buffalo seems to be far ahead of any other one point in Its yard facilities proper, yet that it is only the leading example of a general tendency may be indicated by the figures given in Table 204 of the total side-track mileage of the foads entering there, which well illustrate the immense aggregates o s.ce track which even ordinary yard demands produ^.^T ere seems to be what might almost be called a rude law, that trunk ines proper as distinguished from roads of the next grade beow, will have at least as much sidetrack as the length of then main line. Thus, the Boston & Albany, in additfon to •being somewhat more than double-tracked, has almost exactly Xhis amount of sidings, viz., .03.2 miles against 201.6 miles of main line. Exceptions, no doubt, exist; but Table 204 indicates that the assumed '' law" has at least some foundation in fact. Table 204. Mileage of Sidings in the Aggregate and at Buffalo and New York ^^ '^"E Leading Lines entering Buffalo. Road. "New York Central. Lake Shore Miles Main Line. • Miles op Sidings. Total '^'^ Lackawanna B.. N. Y. & P Rochester & Pittsb'jr. West Shore N. Y., C. &St. L.... 442 540 Buffalo. 982 460 413 430 213 426 512 94.1 9-3 103.4 77.2 30.8* 19.0* 4 9* 16.3* 3.5* N. Y. 28.0 Else- where. Total. 418.9 539-7 490 50.0 34-0 958.6 430.8 442.2 129.0 48.1 91.7 85.5 541.0 549 -o 1,090.0 557.0 523.0 148.0 53.0 142.0 89.0 Per Cent of all Sidings in Buflfalo. 17.4 16.9 9.5 13.9 ♦ These roads have completed less than one half of their pro^BC^^^^^^^^^, The immense aggregate of capital expenditure represented ^y these aggregates of side track, and the still larger capital -um represented by the annual expenditure to "operate'' tte ^de tracks, are plainly factors in the future of new and old lines Which can never be safely forgotten. 1 I If I 826 C/fAP. XXVL— TERMINALS, 1123. It is estimated that fifteen miles alone of the local tracks at Buffalo have cost, or would cost to replace, $350,000 per mile, or $5,250,000, tliis particular fraction of the local track- age being, as is often necessary, on exceptionally expensive land, where it is readily salable at $300 to $500 per foot front. The railways own strips varying from 60 to 100 ft. deep, and on them are laid three to five tracks, giving the following estimate for four miles of track : 5280 ft. of land at $250 per front foot $1,320,000 Planking, 60x5280 ft. X3 in. = 1050 M. ft., or with sub-sills 1200 M. ft. at 18 cts 21,600 Grading, averaging 3 ft. deep at 25 cts. per cu. yd . . i i.75o 4 miles of track at $6000 24,000 Total $1,377,350 Per mile of track 344»34<^ Add for approaches of paved streets, paving many of the tracks themselves, and incidentals 5,66a Total per mile $350,000 We need not attempt the difficult task of estimating the total exactly, but for the other items : At $10,000 per mile the 300 miles of side track, more or less, in the Buffalo yards represent $3,000,000. At $5000 per acre for the 3600 acres of land owned and used for railway purposes, the capital investment would be $18,000,000. The shop facilities alone, with the tracks for their use, represent $3,000,000. Vast as these sums appear and are, the interest on them represents but a small part of the addition to the cost of haulage which the terminal facilities cause, and still less is the bare trackage required any fair criterion. This will be clearly indicated by referring back to Table 202, where it will be seen that at New York the bare cost of the track, esti- mated at a very liberal figure, and exclusive of land, amounts to but 2.2 per cent of the total cost of yard work, and that this total is as great a tax upon the five lines concerned as if they had $91,000,000 invested, say in three thousand miles of idle, un- operated, and tolerably costly railroad, at $30,333 per mile, on which they had to pay interest, but which contributed nothing to revenue. CHAP. XXVI.— TERMINALS. %2J 1124. Nothing equal to this in degree exists in Buffalo, but the analogous tax at that point is very great indeed, and is in ad- dition to the New York tax, as is likewise the yard tax at Chicago, and all other intermediate points. Therefore, vast as is the tax of maintaining within the city limits of Buffalo enough track for local purposes only to build a new line to New York, that direct expenditure is but a small part of the total burden repre- sented by those facilities, even if a many times larger part than at New York, as no doubt it is. At no other point in this country, not even at Chicago, do so> many conditions combine to bring about such abnormal growth, and the same is still more true of even the largest cities of the old world. Buffalo, therefore, although outdone by many other cities as a traffic point, will doubtless continue to be the greatest yard, properly so called, in the world, even after that consider- able fraction of its trackage, which is with reason felt to be due to profligate and discreditable imperfections of management, has been done away with. But its interest for our immediate pur- pose lies in the fact that, large as it is, it is only the largest out- growth of universal tendencies; and that road which attempts to compete with another without having approximate equality in such terminal facilities, competes on about as favorable terms as it would in crossing a river by some new bridge in which every span but the last had been built, and was of very superior quality. Much greater sums have been spent in Europe than here in building stations in the trade centres of cities close to the warehouses and wholesale stores. In Liverpool (600,000 inhabitants), the London «& Northwestern Railway up to 1881 had expended $9,300,000 in providing freight stations alone. In London it had expended $11,200,000. Interest at the rate of 4 per cent on the cost of these stations, less rents received for warehouses, etc., amounted at Liverpool to 14.6 cents, and at London to 32 cents per ton of freight handled. Thus the mere payment of interest on the terminal facilities, excluding any charge for handling the freight, would, on a haul from Liverpool to London, amount to- 46.6 cents per ton, or nearly \ cent per ton-mile. These figures do not include the cost of collecting, distributing, and sorting sidings, of which there are 38^ miles at Edgehill (Liverpool), and proportionate lengths at other places. The f' 828 CJ/AP. XXVI.— TERMINALS. London & Northwestern is in no way exceptional in this respect among the great English railways. The total actual average cost of loading and unloading freight per gross ton, exclusive of interest, was given as under for the year 1880, at the following places : London 70-i cents. Manchester 4i-0 Birmingham 34-0 Liverpool 39 4 This total cost includes everything incidental to carrying on the business of the station, but no charge for risk, breakage and pilferage, or for cartage. PART V. THE CONDUCT OF LOCATION. r X " O, what a precious book the one would be That taught observers what they're net to see!" — O. W, Holmes: A Rhymed Lesson, •• Some things can be done as well as others."— Sam Patch. *ii *.^ i PART V. THE CONDUCT OF LOCATION. r CHAPTER XXVII. THE ART OF RECONNAISSANCE. 1125. An art, as distinguished from a science, is something which, :although it m part can be taught, yet cannot be written down in definite fixed rules which have only to be followed with exactness. A science, correctly so called, however difficult or intricate it may be, is always m' its nature susceptible of rigorous and exact analysis. An art is not. Thus we may speak with strict propriety of the science of bridge-build- ing, but only of the art of reconnoitring. Nevertheless, just as there is no scientific branch of the practical work of life so purely a science that it is possible to dispense with a certain apti- tude and tact which is outside of and beyond written rules, so, on the other hand, even in what is so purely an art as discerning the physical possibilities of a given region by the aid of the eye alone, certain general rules and cautions will greatly diminish the danger — which often rises to certainty— that without such aid an inexperienced engineer will fail to discern the possibilities which lie right before him, and reach wholly mistaken conclusions as to v»rhat he can and cannot do with the region brfore his eyes. 1125. For there is nothing against which a locating engineer will find it necessary to be more constantly on his guard than the drawing of hasty and unfounded conclusions, especially of an unfavorable character, from apparent evidence wrongly interpreted. If his conclusions on reconnais- sance are unduly favorable, there is no great harm done— nothing more at the worst will ensue than an unnecessary amount of surveying; but a hasty conclusion that some line is not feasible, or that further improve- 832 CHAP. XXVII.— THE ART OF RECONNAISSANCE. ments in it cannot be made, or even sometimes— often very absurdly — that no other line of any kind exists than that one which has chanced to be discovered— these are errors which may have disastrous consequences. On this account, if for no other, the locating engineer should culti- vate and habitually preserve what may be called an optimistic habit of mind. He should not allow himself to enter upon his work with the feeling that any country is seriously difficult, but rather that the problem before him is simply to find the line, which undoubtedly exists, and that he can only fail to do so from some blindness or oversight of his own,, which it will be his business to guard against. 1127. The chances are greatly in favor of his ultimately finding this assumption to be correct. Occasionally he may be deceived, but the young and inexperienced engineer cannot proceed on a safer hypothesis than this : That however forbidding the region, a line exists which is conspicuously better than any other, and which will in all cases be found to be — in comparison with what was expected — a line cheap to build and economical to operate; and that, on the other hand, the line which he, as an inexperienced man and acting without special training for the work, will be likely to first select as the best, is perhaps twice as costly in first cost and considerably less favorable in gradients and operating value than that which he can secure by greater care, attention, and study. Although this may seem a sweeping generalization, it is so near a general average of probabilities in both easy and difficult country, that in a rude way it may be assumed as truth. 1128. For the reason that there is so much danger of radical error t'u the selection of the lines to be sun>eyed (or, rather, of the lines not to be examined), it results that the worst errors of location generally ORIGINATE IN THE RECONNAISSANCE. This truth once grasped, the greatest of all dangers, over-confidence in one's own infallibility, is re- moved. 1129. The most fundamentally important technical qualification for entering upon the reconnaissance is an understanding of the economic questions considered in the first parts of this volume, especially as to what a railway should be from a business point of view, and what the relative importance is of engineering (or geometric) and commercial ex- cellence ; for if the engineer cannot correctly distinguish between the financially important and unimportant, as well as between the practically feasible and the practically impossible, he will be almost as liable to go astray as if he were physically blind, by omitting to examine as worthless the very possibilities which he should look into most carefully. It fol- CHAP. XX VII. -THE ART OF RECONNAISSANCE. 833 lows also that he should be well posted as to the relative cost and diffi- culties of construction. 1130. These qualifications being presupposed, before beginning the reconnaissance, as well as during it and after it, the nature, extent" and probable sources of the traffic, and especially of wav traffic, should be carefully looked mto. as a consideration which will "be often— it might almost be said usually-so important as to fix the general route in de- spite of quite important engineering disadvantages. The small effect on profit and loss of even considerable differences of distance, and the small effect on distance of even considerable and "ugly" swerves from a straight Ime. may well be especially studied up, not to make one reck- less of sacrificing distance, but to enable one to sacrifice it and save it mtelligently. 1131. On the other hand, the engineer should with especial care dis- abuse his mind of the very natural feeling that what mav be called his own particular and especial department-getting a cheap line to sub- grade-is of much relative importance to the future of the company He should remember that it requires a continuous cut or fill of about 7 feet or say an average maximum cut or fill of 10 to 12 feet, with its ordinarv^ accompaniments of mason r>^ to equal the cost of superstructure readv for operation ; that the total investment for rolling-stock, machinery buildin-s. and miscellaneous purposes will, on a line of active traffic ve^ry nearly equal that for road-bed and track complete, and that, finally' and more important than all. the interest on the total de-facto invest- ment for all purposes rarely absorbs more than from one sixth to one fourth of the gross revenue. Broadly speaking, therefore, we may say m general terms that— ^ ^ To increase gross revenue \ we may double the whole investment •nr " cost of road-bed and track. ^ " " grading and masonry. These percentages, of course, are subject to important fluctuations but the fact still remains in all cases that, for obvious reasons, the tendency Of an engineer is to concentrate his attention unduly on the work below suD grade. self?'" ^^ n"'°''^ '"'■^" qualification, the engineer sl>ouId prepare him- nrl ir"" 'f 'u""'""'" •" ^°™ ■•«^^°"«''Iy accurate estimates of the probable cost of the work per mile on various lines and grades The feculty of making tolerably close approximations of this kind, assisted t>y the eye alone, is not so very difficult to acquire, but can only be gained «* 834 CHAP. XXVII.— THE ART OF RECONNAISSANCE. CHAP. XX VII.- THE ART OF RECONNAISSANCE. 835 isiii '!=* I by careful observation. The best^manner of obtaining it is by noting the general appearance of as many lines as possible, either before or after their completion, and then comparing a guess based on this appear- ance with the actual cost or quantities. Experienced contractors can guess in this way within a very small percentage of how many yards per mile a given piece of work will run. The engineer should by previous practice and study have at least so far perfected himself in this art as to have some idea as to his "personal equation" or probable range of error. 1133. The danger with most young and inexperienced engineers in making estimates of the cost of work is decidedly that they will make too small estimates, influenced by a natural hope and anxiety to show good results. But, on the other hand, there are some who, especially in preliminary estimates, go to the other extreme. Just as it is the mark of an untrained engineer to make estimates too low, so it is the mark of a half-trained man to persistently make estimates too high, especially on work involving difficult or doubtful points, which it may be in question whether to attempt at all ; a practice which some of them adhere to through life, from an idea that they are being thereby more prudent and " practical." Each error is equally discreditable. An estimate should lean in the direction of excess, but a moderate error in either direction is a pardonable fault (par. 21). 1134. To these qualifications is to be added— not by any means as least important, but as last in order of importance, if the intended dis- tinction can be grasped— what is generally known as an "eye for coun- try," the nature and importance of which has already been considered in par. 18. Such rules and cautions for acquiring an "eye for country" as can be committed to paper (which are not a few) will be given in the fol- lowing chapter. The fundamental rule is to have an abiding conviction that a much better line than at first sight appears can be found by open- ing one's eyes. 1135. Undertaking a reconnaissance with a reasonable measure of these qualifications, it will require, often, nothing more than careful ob- servation and one or two trips over the line to definitely determine, once for all, which is the proper general route to adopt, and so save all necessity for running any duplicate lines whatever except for short alter- nate sections of 2, 10, 20, or 30 miles, which are almost always necessary at points, and which may be called matters of detail. It would be dan- gerous, perhaps, to state that it is a general rule that only one line will need actual survey, but the writer's experience is that this is far more often true than not, and that it is true, perhaps, of a larger proportion of heavy ines than of Jight Imes. When all the traffic and business considera, tions, as well as engineering difTerences. have been dulv considered the writer has never known an instance where there seemed the slightest need to survey more than two general routes, althouoh such instances may well occur. In any case the reconnaissance should be conducted always with as much care as if it was expected to make by its means a final selection of route. In conducting the reconnaissance, while individual habits of mind no doubt differ greatly, and with them the direction in which error is most to be feared, the following rules and cautions are believed to be of uni- versal application, the first one especially being fundamental : 1136. I. The reconnaissance must not be of a line, but of an AREA, including at all times in the mind as wide a belt on each side of an an- line between the two fixed termini as there is the remotest pos- sibihty of the Imes reaching to; "remotest possibility" being considered for the time being as only bounded by some marked and decisive topo- graphical feature or traffic centre. Thus, in reconnoitring a proposed line, AB, Fig. 266, supposed to be about 100 miles long, we may reasonably take the valley line V to the right or the town C to the left, as the lateral limits, but nothing less than this, and the whole area between them should be studied as an area, and a topographical map •• m the mind's eye" made of it all ; exact comparative knowledge of all the various passes and other governing points being obtained on leconnais- sance, or by subsequent survey or spur-lines. This simple rule is one rarely thought of or acted on until repeated blunders have enforced it. Error is particularly liable to follow from neglecting it as will be shown later by a few examples from practice. We may surz'cy lines but we must never reconnoitre them. If we do. it is not a reconnaissance. ' 1137. 2. All prepossessions in favor of any particular line must be aban- doned, especially in favor of that line which seems most obvious The importance of this is too, obvious to need dwelling on, yet it is one thing to admit it in theory and quite another to do it in practice. Not to do so is a dangerous and frequent error. 1138. 3. A tendency to see with undue clearness the merits of LINES LYING CLOSE TO HIGHWAYS or the more settled and open districts must be carefully guarded against. This is another dangerous and frequent -error, which is always imminent, partly because it seems too obvious a danger to be a real one. The writer now recalls no less than thirty in- stances, some of them of the first importance, in which the deceptive conveniences of highways alone were responsible for serious error as 836 CHAP. XXVII.— THE ART OF RECONNAISSANCE. ,1; . \'3 «:.] in the instances of Chapter XXIX. and Appendix C. Allied to the above are : 4. Lines hard to get over on foot, or overgrown with timber or tangled undergrowth, seem infinitely worse by comparison than they really are ; and, 5. Raggedness of detail, sharp rocky points, steep bluffs, and the like, exert an entirely undue influence upon the mind as compared with long rolling slopes spread out over a longer distance. These two dangers are so imminent where ihe conditions specified exist at all, as in comparing many valley lines wiih ridge lines, that they will be sepa- rately discussed (par. 1162). The disadvantages of a route for a railway must not be measured by its disadvantages as a foot-path, even after all brush and iimber have been removed, yet it is hard not to do so to some extent. 1139. 6. A complete mental map of the watercourses should be made as the reconnaissance proceeds — sufiiciently exact, at least, to enable the engineer to state positively where the water of every stream crossed ioins another, and what streams run in together, until they have passed off the limits of the area under examination. It is not always convenient to do this for each stream as it is passed, with- out undue delay ; but wherever a stream is passed without dping it, there, it should be noted, is a gap in the necessary knowledge of the country, which may be dangerous. A skeleton framework for this information can generally be obtained from maps. It is in respect to the minor streams that the caution is particularly necessary, and it is even more important to adhere to it in the smoother than in very rough country. Neglect of it often carries one off on a false track. 1140. 7. False summits, or those which appear to interpose between two water-sheds, when in reality they are only between different parts of the same water-shed, are very liable to deceive under certain circum- stances. The latter, fortunately, do not often occur; but when they do occur the deception is often very perfect, introducing an apparently im- possible obstacle to the progress of the line which is only apparent. One of many reasons for the preceding rule is to avoid this danger. See also overlaps (par. 1161), which are a kind of imaginary false summits. 1141. 8. As a very necessary safeguard acjainst error, the engineer should MAKE IT A RULE to invariably discredit all unfavorable reports, from whatever source derived, which do not accord with what he expects. This merely means that if he has. or thinks he has, any reasonable shadow of ground for hope that certain things are possible at controlling points, he should go there and look for himself before he finally abondons hope. Not un- CHAP. XXVII.-T H E ART OF RECONN AISSANCE. 837 necessanly co„,p,eted all at once. On the contrary, shodin';e"se oe made in part while a party is running some first experimental line but as broad a belt should ZLuLT "'"""«^ ""= '"P^' possible to keep ,n mind Th.fr ' ? ""=«'"'"'°" « '^^'^ as it is mind of the en«i„eeTthat l^l t'"^ k""""* ''""^^ "^ P''^^'" '" '"e -.h. !,„ • ^"S'neer that he ought to be somewhere over the pricrp ^f the horizon, or on the other side of the valley or ridge instead of fnf Jowmg his nose where he is. instead of fol- field!ru"tItn'ontTm°:ir'""'' " "°' ordmanly camed on in the Ill f 838 CHAP. XXVII.— THE ART OF RECONNAISSANCE. tnat an aneroid barometer will be of assistance to fix the approximate elevation of points, if too great confidence be not placed in it, — may be supposed to be understood. A hand-level is a more important tool, which should always be at hand. In looking through it do not close one eye, but while one eye looks through the tube of the hand-level let the other look at the na- tural landscape. The bubble will then be seen superimposed on the latter. Hand-levels are very often out of adjustment, and still more often have very dull bubbles^ which read quite difTerent- ly if the tube has been raised or lowered to posi- tion. A guess should al- ways be made first, before using the hand-level, but no man ever acquires a very trustworthy faculty of guessing at a horizontal line. In ordinary locali- ties a practical eye will estimate elevations and a horizontal line with a good deal of precision, but there are peculiar topographical conditions which make the evidence of the eye worse than worthless (par^ 1160), and no one can tell where they are in advance. An odometer may be fastened to the wheel of the carriage, if a vehicle be used ; but distances can usually be guessed or as- certained, by time esti- mates or otherwise, nearly enough for preliminary purposes. A pocket compass is a necessity, and a succession of travelling companions with a local knowledge of the country are very desirable. More outfit than this and the best attainable maps will not be particularly useful. C^^P' XX VII.— THE ART OF RECONNAISSANCE. 839 1H5. As a preliminary to starting out to explore, say from B to A, Fig. 266, one should strike an arc mentally across the country with B as a centre, and with a radius of 2 to 20 miles, according as some definite topographical feature may indicate. In country at all rough this arc should be at least 200° long. In smoother country it maybe less. A pass through a range of hills at e on the direct line to A may determine where to strike this arc. Before allowing himself to pass by this arc at any point the engi- neer should mentally ask himself this question, and either answer it posi- tively and definitely on the spot, or note that he must find an answer: How many different routes are there, and what are their comparative merits, for passing from B to beyond THIS arc at any point in its whole extent? If there be some point like ^ or/ which is, in the first place, out of the proper direction ; secondly, difficult of access ; and, thirdly, highly un- promising in appearance,— it must not be passed until it is known that it is not feasible, or else noted as a point to be continually remembered as of unknown and presumably great capabilities. Usually there will be three or four routes for crossing this first arc, which will appear distinctly better than any others, and perhaps be the only possible ones. Noting every one of those which have not been ex- amined, and assuming that everything is possible which is not clearly seen to be impossible, the imaginary aVc may be crossed to the next belt. 1146. Here, at some fixed topographical feature where obstacles occur, or at some town, a second mental arc may be struck, likewise with B as a centre, but it is no longer necessary to make it 200° long, but merely long enough to cover a route to A from every possible pass of the first arc, and the method should be the same. The question should be : In THIS ANNULAR BELT what is the best way to pass from some attainable point in the first arc to beyond the second, and which will give the best complete route from B} By thistime we shall be so far away from B that we cannot really cover mentally, eren in the rudest way, all the area we should investigate, and we must drop the furthest half of it entirely from mind for the time being. Remembering that it is dropped, however, the method is the same, so far as it goes. By assumption, all the most hopeful chances are in the region beyond the horizon, but it is necessary to leave them for the time being. 1147. As the reconnaissance approaches A it will be more natural that our work should be carried on with that as a centre, and as soon as pos- sible the examination of the whole possible area at once, in a cursory ,^' 840 CHAP. XXV IT. — THE ART OF RECONNAISSANCE. way at least, should be resumed. On reaching A, before the territory passed over is again examined, all the remaining possible area should be gone over in the same way, and it should not be regarded as completed until the limits of the water-shed of every stream in the whole area are well understood, and the lowest passes through the ridges. It is not by any means the roughest regions which require the most care in this re- spect. Thus, in Fig. 266, if the country were very rough the chances would be very strong indeed that the valley-line BVA would be the best, and a very cursory examination of sonie cross-line VD might suffice to prove it. In moderately easy country the line BCDA would be far more likely to be the best, and there might of course be considerable variations in it; or the valley at be might be so low and the town Cso small that the preference clearly lay with the most direct line. It does not by any means follow that the whole area should be examined with equal care. If one part is positively known to be worse than another, it matters little to determine liow much worse ; only, it must be known, and not guessed at. By following strictly on the line of these suggestions serious over- sights are not probable ; otherwise they are exceedingly probable. Such assistance as it seems possible to give for training the eye to take in the meaning of what it sees before it, is given in the following chapter. One general caution may be added : " Rough country " is a purely relative term. To the tyro, the rolling hillocks of Ohio, Michigan and New Jer- sey are rough. The same man, with a little experience in really rough country, will take the worst the Rocky Mountains or the Andes can offer with equanimity ; and equanimity is in every calling essential for success. No country in which most of the surface has a layer of soil over it de- serves the name of rough. It needs but little study and care to get several lines of reasonable cost through it. The art of location consists merely in making a judicious choice, — not in getting a line, which is always easy in such regions. 1148. An accomplishment which is not very difficult to acquire, and which is constantly useful on reconnaissance, is to estimate the rate of fall of streams from their general appearance. No general rules can be laid down, because so much depends upon the volume of the stream. A fall of 4 to 8 feet per mile will give a good-sized stream or river a very rapid current, with many stretches where it will seem to the careless eye as if there were nearly that fall at a single point, succeeded by pools above and below. On the other hand, a fall of 30 or 35 feet per mile does not necessarily give to a small-sized river the character of a torrent, and large brooks or small creeks must fall 100 feet per mile or more before they have any violent current. _ ^"■*''- ^Xl'Il.-THE ART OF KECO fJNAISSANCB. 84I II49. A special report on .he Water-Power of the United States in the T=n>h Unued States Census gives a tabular statement of the slopes of he pnncpal strean,s flowing into the Atlantic and the Eastern Guf,th7ch might pretty much the same per tu.le from the Merrimack to the Chattahoochee- the average slope of twenty one main streams being 5.4 feet per mile with the Sus feefpT^lle! ""'"'■ " "' '" "'"^' """' ''' ""''^°" ""-" '"' "sCs' af .0 The slope of some of the southern tributaries of the Ohio River is verv lieht rang,„g from 0.41 foot per mile for the Green River to 2.84 feet for the AUe gheny as a maximum. The falls in these streams generally take the form o long shoals. As an example, however, of the rapidity which some of tise Jon LITZ T o'"' '■"'''' ^°""" '" '"' «=""= ^'°P= of 'heir subsequent course. Mr. Dw.ght Porter mentions that the Cheat River, in West Virginia falls 2400 feet m the last eighty miles of its way to the Monongahela, while the latter nver descends but 75 feet in the ninety miles between the mouth of the Chel and Pittsburg. The northern tributaries of the Ohio have usually steeper slopes but the average ,s far below the rivers on the upper Atlantic coast. The Ohfo R.ver uself, from Pittsburg to its mouth, a distance of ,67 miles, falls 430°.^^ T^o mrs"'' °** ' '" """ ^' ^""'^"'"^ '""^ '^ ^ '-" of = ''«' in The Upper Mississippi, from its extreme sources to St. Paul, 500 miles by .he r,ver. falls 1000 feet. The Missouri River falls 2464 feet in he 2644 milel o ,ts course below Fort Benton, being navigable to that point. The ritltarie ■of the M,ss,ss,ppi from Eastern Iowa have a general slope of about 3 feet per mile, rangmg from 1.84 to 3.83 feet per mile. '^ f..,?* ^'^^"^^^ River, from its source to Pueblo, Colorado, averages 34.1, fee per mde. In the upper ,20 miles the river falls 40 feet per mile the" flattens out .0 8 feet per mile for 500 or 600 miles, and at .50 miles above its mouth Its slope is only 0.46 foot per mile. The Niagara River, in its short course of 37 miles, descends 333 feet to Lake Ontario w.th a vertical plunge of 160 feet at the Falls, discharg ng avo ume of wate ear,, half as great as the Mississippi River, or t66.6<^ cubic f eT pe ZZ. Z, , " '° ' ■""" ^""^^ '"^ ^^"=' '"^ "^■" ''««"ds 20 feet, or ir^nk of ZfT, :• '" '"' '"■"'" " '"""'"y "^''S^''"^: f^-"" 'his point ,0 the *nnk of the Falls ,t descends about 53 feet, or 18 feet per mile. 842 CHAP. XXVIII— OCULAR ILLUSIONS. CHAP. XXVIII.— OCULAR ILLUSIONS. i 14^ < CHAPTER XXVIII. OCULAR ILLUSIONS. 1150. The natural eyesight is readily deceived even where the ap- parent differences are so great as to seem clear and positive. Among- the more serious ways in which this danger may make trouble are : I. The eye foreshortens the distance in an air-line and materially ex- aggerates the comparative length of a lateral offset, so as to greatly exag- gerate the loss of distance (and hence of curvature) from any deflection. A deflection which will not in reality add more than lo to 15 per cent to the length of a line will seem to the eye to double it. This marked ten- dency to great exaggeration results from the effect of two concurrent causes: (i) the foreshortening alluded to, and (2) the tendency of the mind to exaggerate the distance lost by lateral deflections even when looking down upon a map— as Fig. 13. page 237. where the loss of distance in C might be easily estimated at four or five times what it is. These two causes combined, both of them having much effect in the same direction, make the judgment of inexperienced men on this subject almost absurdly deceptive. 1 1 51 . 2 . The eye exaggerates the sharpness of projecting points and spurs, and the degree of curvature necessary to pass around them : an exceed- ingly common difficulty, leading to serious consequences. It results from. a combination of natural causes, viz.: (i) The eye, in looking at all nat- ural slopes, from any point of view whatever, greatly exaggerates their steepness. A 60° slope seems almost vertical ; a 45°, fully 75°; a i^ to i slope fthe rate of the very steepest mountain sides), at least i to i ; etc., etc. This tendency is especially strong in looking at slopes from above. (2) Such points are generally looked at from above ; but whether looked at from above or below, the eye instinctively searches for something fixed and definite to start from, which is usually found in the crest or ridge line, especially if the latter runs nearly to a knife-edge. Likewise the eye al- most invariably tends to exaggerate angles, from whatever point the view is taken on which the judgment is formed. If formed from the side (Fig. 267), it exaggerates the distance C in comparison with AB\ making: 845. it seem half as long, for example, when it is only one fourth as long, thus making the point seem to require a curve of 180° where perhaps no' only will suffice. If formed from in front of very sharp points. Fig. 268, the tendency is to look upon the two range-sights, B, C, as at a much sharper angle U to each other than they really 2iV&,because the eye ranges along both slopes at once— an unusual circumstance, the more common case being that of Fig. 269, in which the tendency is in the opposite direction. In Fig. 268 one tends to approximate r I I o Fig. 267. the angle V to 180': or, in other words, to think of B and C as nearly par- allel to each other, as if we were looking from £ at an infinite distance. 1153. From these causes combined, the eye at £ first fixes on the crest-line and then exaggerates, say. a li to i slope into a i to i slope • in other words, makes the chord-line A. Fig. 268. one third shorter than it IS. This alone gives a 15° curve where 10° will suffice. But having fir^t got our chord-line too short, we then proceed to mentally exaggerate the angle to which it is a chord, and thus still further shorten the supposed radius, so that we may easily picture a 20° curve where 10° would prove on .-survey all-sufllicient. Whether this explanation of the philosophy of the tendency to error be correct or not, the fact of its existence in about the degree stated is beyond question, especially with those who are for the first time con- fronted with "rough country." They are almost sure to exaggerate greatly the difficulties of such localities. 1154. 3. An opposite tendency-to decrease the probable an^rles re- qu.red-exists in looking at smooth gentle slopes, especially 'from a distant point of view, for reasons hinted at in part in Fig. 269. Smooth- ness and gentleness of slope mean that we must either go out a loner wav to gam a little difference of elevation, or must put up with very \on^ if not very deep, cuts or fills. In order to bring down the work to reason- N «44 CHAP. XXVIII.— OCULAR ILLUSIONS. CHAP, XXVIII.— OCULAP ILLUSIONS. 845 y ^ble lightness, therefore, we must often adopt a quite crooked alignment on the smooth and (for foot travel) very tractable slopes, and even then have pretty heavy work. This error is especially liable to occur on the long gentle rolling slopes which are met over vast areas of the far- western United States, Mexico, South America, and (the writer believes) much of Asia, Africa, and Australia, in all of which regions Nature seems to have planned all her works on a vast scale and taken plenty of room to spread out in. In the Eastern United States and in Europe west of Russia it is less immi- nent. When we happen to be comparing two lines, one of which lies, say, in a valley, where the tendency is to exaggerate the sharpness of curves and angles, while another lies on a smoother and higher region, where the tendency is in the other direction, these two opposite tendencies may combine to cause most calamitously mistaken conclusions, one line being made up in large part of points like Fig. 268 and the other like Fig. 269. 1155. The unassisted eye is also liable to be deceived in many ways as to gradients and elevations, as noticeably in the following: 4. A slope looked at from a distance always appears steeper and higher than it really is, especially if we are standing on ground descend- ing towards it, when the eye tends to look on the slope where we stand as more nearly level than it is, and to exaggerate, often to an absurd ex- tent, the steepness of the rising ground in front. This is a familiar ex- perience, which most men have learned to allow for, more or less. The best training for the eye.to check the danger, is to study the phenomenon on highways or constructed railways, where the effect of a given vertical angle is far more marked than on a natural unbroken surface, for the reason, probably, that where the mind looks for uniformity, as on a rail- way or road, it is forcibly impressed by a deviation from it, but where, on the other hand, irregularities are looked for and, as it were, "discounted" in advance, the very same surface angle produces less impression. 1156. Another and perhaps truer explanation of this and many other ocular illusions is that it is simply lack of practice and training of the eye under those particular conditions. The child had absolutely no per- ception of distance or perspective, and hence of size, but puts out his hand to touch everything he sees within his field of view, even on the distant horizon. To measure distances and sizes as accurately as we do by the aid (,) of the short base-line of 2i inches between the two eyes and (2) of our gradually acquired knowledge of the probable sizes of ob^ wh rh'' '" ,^ '' ""'"'".^ P'""'"'' ""^ extraordinary difficulty and delicacy, wh.ch IS only acquired by the incessant, unconscious practice of years Under the conditions in which we have been most trained we do tolerl ably well ; but whenever we strike the unfamiliar and unusual, then the eye reverts to its original untrained tendency to bring evervthincr in the distance up into its own vicinity, with an inevitable LtortC effect on what the mind makes out of the picture seen. Thus it is thft the sun se" tirr'^'H" '' '''. ''' ' ^"^' '''' '^'^'^ -^-" ^^-y -^ -i"/or forced to do so by seeing them beyond the immediate horizon Thus rather than by the common explanation that there are no intermediate objects to fix on, distances across water are always under-estirted by fZJrZTT' "h % ^^^ ^'^ ^^"^^ ^^^^°"' ^^'^'^'^y' ^h^ ^ye brings forward the farther end of a long line of rails beyond a hollovv untill a ded son^ewhat by the further assumption that we are standing on a level-they seem almost to stand up and down. For the same reason the steepness of the slopes of mountains are exaggerated ; and possibi; for the same reason, in part at least, the immense scale on which the topographical features of the great West, Mexico. South America, and P^lG. 270. Similar regions are laid out. deceives as to distances the Eastern man or Jiuropean, accustomed to a pettier topography. 1157. A comparison of the different effect upon the eye of railway gradients and natural slopes of the same rate, wherever two descending ■846 CHAP, XXVIII.— OCULAR ILLUSIONS. gradients can be found nearly following the natural surface, is an in- structive training of the eye. By standing first on the track and then a few hundred feet to one side, the difference in the degree of the decep- tion is marked ; but trial from various points of view will show that it always exists, even on tlie natural surface. Fig. 271. 1158. 5. Allied to the above, but operating more obscurely and on a larger scale, is the deception which comes from the propinquity of LARGE MASSES OF HILLS OR MOUNTAINS when looked at from a dis- tance, or even from a mere general slope in one direction of the whole foreground within view, especially if it be much broken up in detail by minor hillocks and ridges, so that the general trend of the surface is not readily detected. The best-trained eye is quite incapable, under these circumstances, of estimating horizontal ity so as to detect the lowest points with the same success as under ordinary circumstances. Fig. 212, page Fig. 272.— A Distant View of an Overlap. ^80, reproduces admirably an ocular illusion of this kind. The grades against the stream seem enormously steep, and those with it nearly level. The reverse is the case at the viaduct in the background, and elsewhere the rate is the same. In Fig. 270 the pass A, which seems to the eye of a distant observer to be slightly lower than B, may be counted on with great certainty to be considerably higher. To be in fact on a level with it, it must appear to the eye very much lower. Fig. 270 was sketched CHAP. XXVIII.-OCULAR ILLUSIONS. 847 from an instance where half a dozen skilled men under- estimated"^ height of A, and over-estimated B, by nearly 200 feet, from a point of view less than 3 miles off. over an apparently level plain, on a line of sight nearly parallel with the slopes of the mountain, and with A and B hardly more than half a mile apart; the pass having been looked at, likewise, from both sides. 1159. Another, the most extraordinary ocular deception which the writer has ever encountered, and for which he could not then or later imagine an explanation, is badly sketched from memory in Fig 271 In a gently rolling but much •• accidented •' country, through a little pass with (seemingly) long gentle slopes on each side, the little hut appeared only /t°j!f « r l^ "^T"" °^ "^"^ "°"^'' '^^^ '"="' 400 ft. off. when in fact It was 80 ft., there being in this case no preponderance of large masses on either side of the field of view to unbalance the eyesight. tL de';^ corn- InT""', ""' """7°" '° "^"'^ '"^" °' ^ '='^8^ ''"'' experienced and ,:, h" ^^' ""'' ^'■°"' "" "^^""'^ '■""'" «f association with a sharp and tremendous descent a short distance back (1500 feet in a six mil^ view), which might have been seen in part by ejes in the back o on ' head while looking at the hut. but which neither existed in fact nor an! peared to exist in the view taken in by the natural eyesight, as rudely and very inadequately sketched in Fig. 27.. The hut look! far too high m the cut, and the very bottom of the valley was in sight 1160. Similar ocular illusions, and perhaps more remarkable ones ^ay be seen wherever there are irrigating or other nearly level ditches >wmdmg around the slopes of n,ountains above rapidly descending vat Fig. 273.— The same Overlap— Near View. leys. They invariably appear to run up hill, and often in a very marked and extraordmary way. as with many of the irrigating ditches of Colorado. These examples are but pronounced types of frequent topographical rregulanties, which make the eyesight utterly worthless for measuring mportant elevations and slopes in certain localities; and where those localities are, unfortunately, cannot be determined in advance. The aneroid barometer, altazimuth, or hand-level, consequently, should be « I ' S4S CHAP. XXVIII.— OCULAR ILLUSIONS. I constantly used on reconnaissance, and, in general, all such points, if important, should be actually visited, for another reason: 1161. 6. Overlaps of hills or elevated ground at a distance are a frequent source of deception and error. Views which from a distance appear like Fig. 272 are found on nearer acquaintance to be more like Fig. 273, with an easy, open valley, and perhaps a running stream pass- ing through what seemed to be, " beyond question," a solid ridge. Illu- CIIAP. XXVIII— OCULAR ILLUSIONS. 849 Fig. 274. — Better Country than it Looks. sions of this kind are often very perfect, even in the near vicinity of the observer. An example on a small scale (small, because the mind realizes that it must be a deception) may be seen in ascending the Hudson River when approaching Peekskill, especially in the early summer evenings, when the lights and shades are such as to produce a very vivid feeling that it is a closed basin without further outlet to the north. It is said to be on record that it deceived Hendrick Hudson himself, and almost induced him to turn back. The great safeguard against errors of this kind is: Form a complete picture of the water-shed over the area to be reconnoitred, so that it is known where water falling on it anywhere will flow to r.^T' ''l^^^ ^^^ "^'^" ''^"'^^' ''"^" '" estimating quantities, for reasons wh.ch m part result from what has preceded. Most serious con- sequences flow from this, leading to the abandonment without survey of Imes-especially valley-lines-which should have been regarded as the Fig. 275.— Worse Country than it Looks, most promising of all. The root of the difficulty, in addition to the various causes of deception which have been noted, lies in the inability of the mind to distinguish (i) between what seems rough and what is and (2 between what is rough for foot or horse travel and what is rou»h tor railway construction. " hv 1^^ ^"^"'^°f the first cause for deception will be better appreciated thev^niLt" "u ':' ^"y -"-derable experience in consfr'u ctio U they will but recall what a tremendous reduction in the apparent diffi- f CHAP. XXVJII.-OCULAR ILLUSIONS. { 850 li^f work follows from the mere act of thoroughly clearing the eround even if there were nothing on it before but light undergrowth Td brush. To a thoroughly trained eye this should make no apprec- able difference, yet the unconscious feeling of every one .s "well begun. half done." . , , 1,63. When to ordinary timber we add tangled v-es and unde - „!!ih makin" progress on foot exceedingly slow and difficult, this ^Jt is "crea;ed We are apt to measure distances by time under such Jances so that if we went over an aggregate of .0 miles at one nule "''hou and of i r^ les at five or six miles per hour, in exploring .00 !" es w; shallfinTsh with a feeling that fully a third of the line has been Te ;ough On the other hand, when we strike a highway and go along mIv over the ground, we at least never exaggerate the difficulties T. , we wVk over the hill to take a glance at. and the long stretches ;tt coltry are what we have been most conscious of and remember "In ^^''74 we have a sketch of a jagged rocky point in a river valley; in FilTs a sketch of a line on a gently rolling side-h.lK Nine mn in :e7b^«"::;;'::rb: rc^p^st. i/additio^i to having the best grade^^ ««i Tl,l, results from the fact that in following a valley-line it is . -T Hffiru to make due allowance lor the fact that Nature exceeding^. difficuU to „ake^ du ^^ ^^ ^^^^ ^ ^^^^ ^,^^ H^S ^.ADE OUR F.LLS^ It m y ^^^^^ ^ ,_^^^ ^^^^^^ ^^^,, r donele%mucrlrk on it we have excavated enough material have done ve y muc .^ ^ ^^^^^^^, ^„^ ^^„^, to carry t^!^ j'"^ J^"' ".°^„ .^e point, as on ordinary ground, to avoid a,enotoWigedtoliug mto p^^^, ,^ ^^^ ^^,,^^ ^^^^^ running our line aDove ai vy g t. ^^ THere "« - j- ow^^^^utl ^^^^^^^^^ Ltom-land, already come, probably, to a "a ^ ^^^ ^, ^„ y,,,^^, do (when rip.rapped "f ^^Sf/'''°";^"°J ^hat'pictured. just above the ordinary r^i^rhl^wlteTso t^h^^^^ level of h'g>'-»at^^' =° ' else when they are overflowed, are not sub- "■^^d^ra^lXt'e c„ n't The more violent and rapid the ordi- " ^.nt the less likelihood there is that the bottoms are often de- Tcriy ove^ow:^ If overflowed, the current cannot be rapid, or the nteX! wrefwXe passed the rocky bluff in Fig. .74 we have CHAP. XXVITL— OCULAR ILLUSIONS. 851 comfortable running, and can get a good alignment until we come to the next similar point. At every one of them, although we are thrown out to and into the water, Nature has provided the material to resist the water on the spot. The profile of such a line is very apt to be quite light ; rather deceptively so in fact, since there will be a great deal of workin protect- ing banks and working very steep slopes, which will not show on the profile at all. 1165. On the other hand, in Fig. 275, gentle as is its general effect, we must cut into our hills far more than the eye will appreciate in order to avoid enormous fills. If the slopes be at all steep (they might well be steeper in the view to bring out the effect desired), the eye when reconnoit- ring will underrate the depth of these fills, especially from a distance, by taking a mental section of them on a plane Jiormal to the slope instead of on a vertical plane. The loss from the side-hill slope of the ground, likewise, will be very likely to be under-estimated: not that the eye will not exaggerate the slope of the ground relatively to the horizontal, for it will, but, by a seeming paradox, the angle of the ground with the side- slopes of a cut or fill will be rather underrated, because the mind men- tally exaggerates the latter also, and still more. It is almost an invariable rule that fills turn out deeper than they are expected, and on a side-hill line most of the water-ways are in fills of considerable depth. The water channels are also more ramified, and hence more numerous, on high slopes than lower down in the valleys, where the total discharge is more, but the water has collected in larger streams. Much expense can be saved on side-hill lines, and danger of washouts as well, by catching the water in a ditch at or a little below grade and carrying it under the road-bed in a small structure, with the foundations of the discharging end of the structure properly secured, instead of putting the structure in the very bottom of the gulch. 1166. Cul-de-sacs are another incessant source of deception and error, al- though rather due to negligence or inexperience than to ocular illusion proper. It constantly happens that men walk into them as a mouse into a mouse-trap, and for the same reason— blindly following one's nose; or rather, from recon- noitring a LINE, foot by foot and mile by mile, instead of an area as a whole. A man sees a beautiful open area ahead of him as far as the eye can reach, prob- ably with a highway through it. He is satisfied, and looks no farther, until he comes to the end of it. Then it is too late. He has accepted his line so far as a finality, and knows no other. He assumes that he can do nothing better behind, and " therefore" must get out of his trap ahead as best he can. Unless he is confronted with very great difficulties, he is likely to do so. To read in It V V C//AP. XXVIIL— OCULAR ILLUSIONS. 852 cold print, this seems an improbable bit of stupidity. It is one of the common- est of faults. 1167. A single instance on an important survey, affecting 40 miles of line, will illustrate how it happens. In a very broad flat valley which extended for six or eight miles farther a dry run was encountered. It was assumed to drain to the west, and passed as of no moment. It really drained to the east, through a small rocky overlap about two miles off, which opened out half a mile be- yond into a broad open valley leading directly to the desired terminus. The ruUe-sac gave a fine line as long as it lasted, and then over 2o miles of rather heavy work, with bad grades and bad curves, yet it was run by an engineer of large experience, and came very near being built. 1168. Of all these types of ocular deceptions there are many varia- tions To thoroughly guard against them comes with experience alone, and rarely with that. Until they have been learned by experience, and the engineer's "personal equation' determined, very wide limits of error alone can be safely assumed. Nevertheless, provided the danger of error be realized, it is not a particularly serious one, because errors of the eye will be checked by surveys. The greater danger is that the untrained eve will tell such wholly delusive tales as to make the worse appear the better course, and cause that line or part of a line to be rejected without survey which was really the best. To guard against this danger, and not to advise substituting the eye for the precision of surveys except within known limits of safety, this chapter has been written. 1169. A single example of the way in which ocular illusions and some of the causes mentioned in the previous chapter may combine to lead to wron- conclusions by errors of reconnaissance, pure and simple, may be of vaFue to save the student from underrating the magnitude and .m- minence of the dangers against which he has been cautioned. It surn- marizes the facs of a very important piece of Ime on which a number of causes combined to bring about calamitously wrong conclusions. Those particular causes for wrong conclusions against which cautions have been given are printed in italics. The map is modified somewhat, but the other conditions are in no way exaggerated. Appendix C con- tain another example, and the writer bad made a list of nearly a dozen others which he ha,d intended to annotate similarly, but -^-^J^^'^'^ The line was about loo miles long from A to G. Figs. 276-7. through a region of much difficulty after reaching the crucial point B ot B. there an exit was to be found from an easy open basin surrounding CffAP. XXVIH.— OCULAR ILLUSIONS. 853 A. An established and much-travelled highway followed the general route selected. ABCFG. The pass B was a little easier than B', and seemed for. special reasons much easier than it was. The difficulties of construction were distributed over almost the entire line ACG, so that, •^{i;"">:=-y^. •//, I. "^ c« 'f' iv^ •y«&5. '-'l^A -^fv '# .vl//^ ^■ '^U/., 'I%l! 7^- c>% Wr l/A> % %V^i 7/(» W. ^i^i'i^' %. % -^^ './/<./. "^"^./^i'^' C ,0 V; — .c? v° *% N \ *^ %^ *^ * \ •- *- -. C----V-.S % V Mr ''•.. f *% • % *.. ' Vv* Fig. 279. Fig. 380. trifle in length while its operating advantages are materially greater, unless its grades should be decidely against it. 1181, In such cases as Figs. 279, 280, the line running through BC should likewise be always run. This is more likely to be done with Fig. 279 than with Fig. 280. In each the distances AB, BC, and CD are precisely the same; but the angular deviation from the desired direction is greater in Fig. 280, making it correspondingly repellent. By varying^ the intermediate distances, leaving the aggregate the same, much greater contrasts can be obtained, as the reader can find out in a rather in- structive way with a piece of black thread and a few pins. 86o CHAP. XXX.— THE FIELD-WORK OF SURVEYS. CHAP. XXX.— THE FIELD-WORK OF SURVEYS. 86 r ■*^( S' '^ r*^- CHAPTER XXX. THE FIELD-WORK OF SURVEYS. 1182, In general, the economical manner of making surveys of a route which it has once been decided to survey, and which offers any appreci- able difficulties, is as follows : The surveys should be planned from the beginning with the idea that not less than three, generally four, and frequently five, successive lines will be run over the route for the purpose of fully completing the final location, viz.: An exploration line, first preliminary, second PRELIMINARY, FIRST LOCATION, FINAL LOCATION. The attempt tO do with less than this on lines of any considerable difficulty is false economy; or rather, it is an attempt at economy which does not usually result in any real saving of either time or money, even in the mere direct cost of the survey, while it does seriously endanger the excellence of the com- pleted work. Running what may appear to be so many lines does not necessarily involve devoting much more time to surveys, but only dis- tributing the work somewhat differently. 1183. First, the exploration line, or what is popularly called a "shoo-fly" line, should be run as rapidly as possible over the entire route which it is contemplated will ultimately constitute the road. In the case of very long lines, circumstances may make it necessary to carry on and complete the surveys by sections, but this is to be regretted and avoided. The purpose of this first line should be merely to get a general idea of the topography of the countr>% and especially of the gradients, and it should be passed over all alternate routes which it is proposed to survey later as tliey are encountered. No attempt to study the location in de- tail should be made, except to make sure that the line being passed over is certainly feasible, and probably on the most favorable ground in the vicinity, especially in respect to gradients. For this line a mere compass line will not only answer as well, but is in general decidedly preferable to a transit line, except in easy open coun- try, for reasons discussed in par. 1185. It gives a mere string of distances and elevations from which to construct a scheme of grades and lay out the line as a whole. The following line is not guided by it in any ac- curate way, nor is even a map of it to a large working grade generally worth the making. The limit of speed will lie in the levelling, and accordingly two rodmen should be used if there be only one leveller, or better, two complete level parties (especially if the country is at all rough), to be jumped over each other's heads. This extra force does not expedite the work enough to pay if the levelling only were to be considered, but as the time of the whole party is to be considered, it does pay, and it is to some extent a safeguard against errors, as the levellers are not so hurried. Sometimes an e.xtra man to keep notes, with two rodmen, may be preferable to two level parties. A full-scale profile of the ordinary form mayor may not be made: it will probably be a waste of time to make it for the entire distance; but a small scale profile, to about one tenth the usual horizontal scale and one fifth the usual vertical scale (par. 905), should by all means in all cases be made. Fig. 281 shows one form of such profile for a completed road, to a scale of about one inch per mile, as engraved, which was origi- nally 4000 feet per inch, or ten times the usual profile scale. It is un- necessary to encumber a similar profile for location purposes with details of the minor structures. Following this line comes — 1184. Secondly, THE PRELIMINARY line proper (which may be two successive lines), which is to serve as the basis for the final location. On this line, in all but very easy country, careful topography should be taken, and taken in the field, in the manner considered in Chap. XXXI. The purpose of the preliminary is to serve as a framework for this topog- raphy and the located line, and it is run to follow closely the ground where the location is likely to lie, as nearly as the eye can estimate it„ using any angles which come handy for this purpose. Fig. 282 shows how a very well located preliminary is apt to lie with relation to the lo- cated line, being very close to it, and yet entirely independent of it. The average preliminary will diverge from the location more than that shown. This line also may, without any serious disadvantage, and with cer- tain considerable advantages, be a compass line, if any time is thereby saved to be devoted to more important matters. The only advantage of a transit line (and it is a slight one) is that it enables the map to be some- what more accurately made. The located line does not coincide with i CHAP. XXX.— TRANSIT vs. COMPASS LINES. 863 3 P •O — f6 3 W W 2 5 "^ a -• rt P 3 » *^ - 2* the preliminary at any point, unless by accident, nor is there any inten- tion that it should, nor is the location checked by the preliminary, to any great extent, but by the profile and topography. Fig. 282. — Preliminary and Located Line. TRANSIT 7/J. COMPASS LINES. 1185, An unreasonable prejudice exists in the minds of some engi- neers against compass lines, because of a false assumption that, because there is a certain lack of precision in it, the work is therefore inaccurate. On the contrary, the chances of substantial accuracy in the final result, considered as a whole, are better with the compass than with a hasty transit line (it being assumed that no local attraction exists), since large cumulative errors cannot occur in the one case, while they can in the other. This is evident if we consider how the two lines are run. A compass line, strictly so called, is run entirely by foresight, guided by the needle alone. The chief of party goes first, accompanied by the " back flag," who is now a front flag, and picks out the points to which to run (unless a straight line is being run, where the line is given from the instrument as soon as the compass has come to rest). The chain- men follow, the head chainman behind, chaining in a straight line as nearly as the eye can determine from the point where the instrument is standing toward the flag. As the line is sighted in by foresight this is near enough for all practical purposes, since more than two or three inches deviation is not probable. The transitman, or rather compassman, is at the rear of the whole party, and simply takes the bearing of each line by the needle, or, if a given line is to be continued, gives the proper line to the flagman in ad- vance as nearly as it can be determined from the needle. If a tree or other obstruction is met, the instrument is simply moved to the other side of it. placed on the same line prolonged as nearly as may be (it may be a foot or even two or three feet off), and reset to the same bearing. If accurately reset, it will give a line, not the same as the original, but par- allel thereto. Usually there is a few minutes* error in each bearing to 864 CHAP. XXX — TRANSIT vs. COMPASS LINES. < one side or the other. On the other hand, when the line behind is* visible, it is very common, even in running compass lines to run by back sight for considerable distances, as on a transit line, or at least to check, the bearings thereby. This practice does not especially conduce to real accuracy, however, but rather the contrary. 1186. A transit line, on the other hand, is run entirely by back sight, from an accurate sight on a plug, and all angles are measured exactly by the vernier. It is very much more precise than a compass line, and is the only suitable method for running in location lines, and the only method now practised, although it was not used in the earlier days of railways. It has these disadvantages : 1. It requires the cutting away of all obstructions, or tedious offsets around them, thus causing great loss of time and needless destruction of vegetation. 2. Any error in measuring or laying off an angle is cumulative, or continued indefinitely in plotting the notes. To guard against this, the angles in well-conducted transit-work are always checked by the needle,, but nevertheless this danger causes frequent annoyance in practice. 3- The angles measured are never used as such in properly conducted mapping, but have to be reconverted into bearings. This, however, is a small matter, and may and should be avoided in the manner described in par. 1242. 1187. On the other hand, there is this to be said for the transit line — that it is not unfrequently the case that no time is saved by using the compass instead of the transit, since the level limits the rate of progress in any case. When this is so, it is undoubtedly as well to run the more accurate line, and wherever there is danger of local attraction it is the only proper one to run. But it should be clearly recognized that the transit line is to be preferred only for these reasons, and that wherever they do not obtain, the true engineer will immediately adopt the compass instead. The not infrequent notion that the use of the compass is de- rogatory to his skill and unworthy of him, simply because it is less pre- cise, is absurd. Under the doctrine of chances, which is as well estab- lished as the law of gravitation, the probable average error in a series of observations decreases as the square root of their number. If in a single observation it be 10 ft., in 100 observations it will be only i ft. each, and in 10,000 observations only o.i ft. For all the legimate uses of preliminary lines (they are sometimes used illegitimately) such errors- in no way detract from its value and utility. CHAP. XXX.— TRANSIT vs. COMPASS LINES. 865 1188. The writer has not foqnd that, even when the imperfections of mappmg are reduced as they should be by the use of large scales the superior precision of the transit is of much practical moment, and he feels a preference for the use of the compass on preliminaries, other things being equal, believing that it is easier for all concerned, and that there is less danger of giving thought to splitting tacks with the cross- hairs which might better be given matters of importance. It is well for the locating engineer to be frequently reminded, especially in acquiring his traming, that instrumental accuracy is not an end in location as in ordinary surveying, but simply a means to an end; that a thoroucrhly excellent location may be made with the level and chain alone with- out other instruments, and that a bad line is not a whit better for bein^ mstrumentally precise. No angular or lineal error which is not great enough to affect the riding of the locomotive over the track is of ulti mate importance, while on the other hand errors of judgment, or unwill- ingness to disturb an accurately run line with a " good " profile are evils of great importance. As it is always easier and in the end less costly to be accurate than inaccurate, the good engineer always will be accu- rate in all essentials, but he will not waste time in attempting unneces- sary precision which does not add appreciably to the final value of his work. 1189. The levels should, on the preliminary lines, be kept correct by checking on the exploration-line benches and re-running all doubtful sections, at any seeming cost to the progress of the survey No time is saved in the end by doing otherwise. No time should be wasted in try- ing to keep the stationing continuous. 1190. Whenever the country becomes quite rough, and especially where a grade-l.ne is to be fitted to the ground, the preliminary line should from the beginning be divided up into two by running a first and second preliminary. It might seem a better way of expressing the same truth to say that whenever it is found that any section of the preliminary does not come sufficiently near to where the final line will be it should be run over; but that is not true, and that plan of conducting'surveys is more likely to result in loss of time and bad work. The true way of conducting surveys.from beginning to end. is to recognize in tiie begin- ning where there is likely to be difficulty and to run additional preliminary lines COMPLETE over those sections, thus gaining opportunity for more careful study and more thorough knowledge. Even then, there will be occasions enough when it will be necessary to "back up" and correct false steps from time to time on all the lines, to doing which occasionally. 33 866 CHAP. XXX.— TRANSIT vs. COMPASS LINES. CHAP, XXX.^IWNNING IN THE LOCATION. 867 I of course, it is not intended to object; but in cases where there seems more than an even chance that the "backing up" will be a large fraction of the advance, it is always good practice to give up from the first all idea of completing the preliminary work with one line. 1191. When two preliminaries are thus run in succession, they should in general be frequently tied together and plotted on the same sheets so as to give continuous topography, all errors in the plotting (which with good work should be small) being left in the tie-lines, and the angles and distances of the second preliminary not distorted to make a fit. 1192. In extreme cases, as in that shown in Fig. 216 and others, the difficulties of location are so great, for short distances, that all idea of determining the final location from lines must be abandoned, and a com- plete topographical study of the difficult section made, after the fashion of what was formerly customary on surveys for English railways. But such cases are very rare, and, in general, working from single lines is all- sufficient. 1193. Thirdly. The location line.— This line also should in general be divided into two and done twice over, complete. It will save time often and money always, and is the only safe way to insure good work, especially where it is necessary to entrust a part of the work to men of little experience. The first location should be made ap- proximately correct as it goes along, by backing up to correct the more serious and evident defects, but it is far better that all minor changes and modifications should be merely studied and thought over as the first location advances, and that, after completing the first line and taking adequate cross-sections of it or of a considerable part of it, the party should be recalled to run the whole of it over again, aided by its plotted cross-sections. 1194. This results not only from the direct advantage of having the details of the whole line at once to study, but from the fact that the problem is studied more coolly and dispassionately, with the aid of more extended knowledge and experience (the whole party being now skilled in their work), and without that strong inducement to tolerate bad work and "let well enough alone" which is derived from the tedious and fret- ting process of " backing up." A little consideration of the weaknesses of human nature will make it clear why, for many reasons, this should be so ; and the writer cannot urge too strongly that really good work can- not be otherwise secured, under the conditions which usually prevail. Unnecessarily sharp and frequent curvature will be left in the line; side- hill work on steep slopes will have its centre line a foot or two out of its proper place, and be unnecessarily heavy • rock cut<; w.li k. save fills, and many similar imper'fection's' be left n T hneThlch ar^ no , mdeed of great comparative moment to the line tsel sLe thev do not rnpre Us earning capacity, but which are often o'f se L momen't to 1 itrfTh^mTarso^h^^^^^ \i '---'-^ ''' ^- -- ="th: uneir means, so that it finally passes out of their hands. ORGANIZATION OF PARTY. ranks'^'r^.n"'!!!^''^"^.'''""''^ "" f"l'-handed, especially i„ the lower ranks. To do otherwise s false economy tk« ^ • • lower general be as follows : ^^onomy. The organization should in I. Chief of Party, with nothing to do excent tn t^^r. u- even where there is no clearing ^" " ^""''"''"y ^~"°'"y. 3- The level party, consisting of leveller rf>Hmo„ ^ a ■ ..its the Jee. . the wloTetrS^to" r^tercaT.et^lirhVr ployed to advantage since they expedite the work someXt ' """ 4. I he topographical Party, varying from one to tlir^« ^ t according to the country. This pa^yl usuairno" ri'lTno^glrLr; in/of rtr;rr o': roiTis itV:'' ''-'' -^-^"^ '^°-'^'- after all can.p movements and Censes '^°'"™--y- -'- 'ooks conSt^^uI^a^yTsttlr'"" T' '" "'''="" ^°"""^ -" °''- ...regionsan^ea-c— :.-^^^^^^^^^^^^ RUNNING IN THE LOCATION. nne"'!/h"erarupro:r^:::f ::!? '•',^ "°'- forthe,ocatio„ -thout capping th^e. at ai^r^Iii^ w^i^il'va'arr^gtS 868 CHAP. XXX.-KUNNING IN THE LOCATION. CHAP. XXX.— RUNNING IN THE LOCATION. 869 Ordinarily, however, a narrow belt of topography is both expedient and necessary. If the preliminary work has been skilfully conducted, it will need to be but narrow. On this topography a " paper location is made, in the manner we shall consider later; full notes of the projected alignment, and of the points of curve and tangency taken off, and a pro- file of the paper location made. The purpose of the location field-work is,/rj/, to put this paper loca- tion on the ground so as to afford at least as good a profile as the " paper" profile, and, secondly, to study the line thus put upon the ground in more detail than was possible before the precise position of the line had been so accurately fixed. , In running in the notes of such a paper location, the most experienced chief of partv never expects that the notes can be followed in the held without some slight correction at almost every curve. The profile will be found to be running too high or too low ; errors in the field-work and the topo-raphy will be discovered ; new changes of alignment will sug- crest themselves, and in other ways changes will be made. Nevertheless The correspondence in general will be very close ; so much so that it will be difficult to distinguish the paper and actual location profile. They may both be wrong and bad, but they are apt to agree with each other quite closely. . 1197. No new topography should be taken with this line, but instead of it cross-sections only, extending from 30 to 100 feet on each side, according to locality. These cross-sections should be plotted as closely together as clearness permits, WITH THE even stations at uniform DISTANCES APART, even at the expense of crowding the sections so that they overlap each other greatly, which does no particular harm. The character of the material, and especially the precise limits of the rock, should be carefully determined. Boring tools of many different forms (the simplest of which is the common post-augur) are readily obtained,, by which it may be positively determined where the rock lies, at no great cost, and much perhaps needless expense saved. It rs »very common thing to have shallow rock-cuts turn up in the bottom of excavations, which are always disproportionately expensive, and often might as well as not have been avoided altogether. Aided by these cross-sections, the location should be carefully re- studied, not' by the construction parties, who have other things to think of and are often incompetent for the work, but by a location party who re-run the entire line complete. There will still be chances enough for the construction engineer to improve on it. 1198. This last work especially, and in fact all running of curves and tangents, is greatly facilitated by the use of a proper system of transition curves. What transition curves are, and why they can never be omitted if an easy-riding road is to be obtained, have been already stated (pars. 279-81). and the proper method of running them in is given in the field- book which follows this volume. It would lead us too far to attempt it in this. The nature of the advantage which they give in making a good location is this : Ail transition curves, by whatever method they are run, must, from their very nature, have the form shown in Fig. 283. The actual tangent must lie parallel with and outside of (at a given offset from) what would be the tangent if the main curve were prolonged to include the whole angle turned. In all the systems of transition curves which have been put before the public by others than the writer, so far as he knows, these offsets are Fig. 283.— Typical Transition Curve. «-„.^^ .„u-^u i nxed, which makes run- ning them in a considerable addition to the field-work, but even then they are likely to have a certain beneficial effect on the construction, for the reason that the curves of natural slopes generally ease themselves off in this manner. 1199. But in any entirely satisfactory system of transition curves any offset, great or small, within wide limits, should be capable of use with any curve, because it will very materially add to the flexibility of the line and facilitate its adaptation to the topography. If we consider the tran- sition curve as a cubic parabola, the only difference which the offset makes in the curve is to increase its length in proportion to the square root of the offset, so that if the latter be four times as great the curve will be twice as long. In any case, the curve remains a cubic parabola, and is readily put in, either directly with the transit, as the line reaches it, by methods similar in their nature to. and quite as simple and easily remembered as, those for running circular arcs, or by offsets, after run- 8/0 CHAP. XXX.— K [/NAMING IN THE LOCA TION. CHAP. XXX.— RUNNING IN THE LOCATION 871 I ning in the full circular arc from an offsetted tangent, as indicated in Fig. 283. Tlie former of these methods is generally preferable for large offsets, and the latter for small. The immense advantage which the method' gives for making the finer adjust- ments of the line may be made evident by one or two illustrations, but it should be remembered that the chief object of the curves is not to facilitate location, but to obtain a line which trains will run over smoothly. 1200. Example i. It is found to be desirable to swing a located tangent. Fig. 284, in 2 ft. at a and out 3 ft. at b. The angle between the old and new tangent can be at once calculated. Then the two adjacent curves must be extended (in Fig. 284— or cut off, had the change of tangent been in the other direction) by the same angle. This can be done at once; the offset determined by measure, whatever it may be. and the corresponding transition curve put in by offsets from the curve and the new tangent; or the tangent points / and / of the new curve may be determined and the transition curve run in by the transit. 1201. Example 2. It is desired to take out a " broken-back" curve. Fig. 285. Governing points which it seems desirable the curve should Fig. 984. -^■~ I I pass through are a and b, at any off- set from any point on the tangent. The angle between the new and old tangent can be calculated as be- fore ; the curves extended or retraced by an equal angle, the actual offsets measured, and the proper transition curves put in. If the change has been well planned and the conditions are at all favorable, the two curves will come very near to meeting at some point near the middle of the tangent. If it leaves a little tangent between the two curves it will not greatly matter. The two desired ends will have been accomplished, viz.: Fig. 185. I. The two shocks to the train in entering and leaving the tangent will have been avoided. 2. The ugly appearance of a broken-back curve, which, owing to the abrupt transition from curve to tangent, always has the appear- ance of being out of line and somewhat re- versed, will have been corrected. If the two transition curves of the required lengths for the offset chance to overlap each other even by a considerable distance it will not much matter. It simply introduces (for reasons which cannot be given here without discussing the whole theory of the curve) a short CIRCULAR ARC of very long radius be- FiG. 286. tween the two transition curves. 1202. Example 3. A curve is found not to lie on precisely the right ground. It is desired to throw it out two feet at a, and in 3 feet at b^ Fig. 286. This implies that there will be a certain point c, at which the new and old curves will coincide. The whole curve, radii, centres and all, will be practically rotated around c. The distances ca and cb can be deter- mined by the proportion « ca \cb w offset a : offset b. The angle of rotation is readily calculated by computing the change in position of the chord ab, and from these notes we may either start at c, and run in the new curve, or start at a or b, or compute the new posi- tions of the original P. C. and P. T. If the new curve is found to crowd too closely upon or to overlap the tangents we must change the latter also. This we do. however, entirely independent of the curve, if it appears desirable to do so ; putting the tangent upon the ground which will suit it best, measuring the actual offset which the locations chosen give, and then putting in the corre- sponding transition curves. 1203. These examples will illustrate, as well as more, the peculiar ad- vantage of transition curves, thus used ; that they enable each part of the line to be studied and modified in detail, independently of the rest; and the new and old lines to be then connected together in what is at once the very best possible and the simplest possible way. without any of the puzzling geometrical problems and the confusing field-work which 872 CHAP. XXX.-^RUNNING IN THE LOCATION. CHAP. XXXI.— TOPOGRAPHY: ITS USES AND ABUSE, 873 1 1 # \ I are as apt to result from slight changes as great, if certain geometrically exact connections at all points of circular arcs are taken as essential. Differences of offsets of 20 ft. or more are readily admissible under this plan, and in projecting location it is unnecessary to consider what the actual offsets will be. Figs. 208, 216, and others illustrate how this is done. The advantages of the method in such rough localities are evi- dent from those engravings, and these advantages become even greater if one knows how to save unnecessary trouble in field-work, which will not - tell beneficially in the final result. 1204. As a single example, if one has a curve formerly terminating at T, Fig. 287, which is to be extended to T' in order to connect with the tan- gent 00 ;— to determine the offset O it is quite unnecessary to run in T' with Fig. 287. a transit. The offset Oo to the old point T may be measured instead. Then will 0=00 — 0, and |^"o -^ ^D, in which D = the degree of the curve, n = the distance in stations from the tangent point T' to the point where the offset to the curve is de- sired, and O = the desired offset. • 1206. This latter formula is one of the most useful of all location formulae, being almost indispensable for the correct and expeditious conduct of field-work. It is closely approximate (in all cases sufficiently so for what is required) within the widest possible range of values of D and n, and it is one of the few formulae which should be indelibly en- graven in the memory of every locating engineer, ready for instant use. It applies equally well for offsets from one curve to another having a common tangent point, letting Z>= the difference in the degree of cur- vature. CHAPTER XXXI. topography: its uses and abuse. 1206. Topography, in the limited technical sense of the word which is given to it in railway location, is the representation upon a map by "contour lines" of the comparative or absolute elevations on the area covered by the map. In a broader and more literally correct sense, it in- cludes the representation of all the details of the surface by any method whatever, including its form, character, and artificial structures. Topography, in the broader sense, may be represented approximately either by hatchings or " hacliures," or by washes of color. Very beauti- ful effects may be produced in this way by skilled and patient work but the results are only of pictorial value, to give a general idea of' the region, and are of no assistance for the details of location. Topography when spoken of in connection with the latter, means an exact repre- sentation of the form of the surface, so that the elevation of any point can be determined from the map, and hence a line be drawn on the map and a profile of it called off, as well (barring a margin of error) as if the line had been run in, and levels run over it, in tlie field. Figs. 208, 216 and others are representations from actual practice of such maps, re- duced photographically from the working scales. 1207. The nature of contour lines may be thus explained : Conceive a certain area, the topography of which is to be taken, to be entirely flooded with water. Conceive the level of the surface of this water to be lowered by a certain fixed distance, say ten feet at a time. At each lowering of the water a new shore-line would be developed : The con- tour lines are these imaginary shore-lines. If the slopes be very steep these successive shore-lines will be at small distances from each other horizontally. If the slopes be flat they will be at greater horizontal dis- tances, and if the slopes are very flat they will be at very great distances apart, and only a few will appear on a moderate area. Thus the lower part of Fig. 288 shows a contour map of a slightly oblique cone, and the lower part of Fig. 289 a similar contour map of a hemisphere. In each case, if the nature of contour lines has been grasped, they enable the mind to form a very correct picture of the form of the surface. I* 874 CHAP. XXXL— TOPOGRAPHY : ITS USES AND ABUSE. S-: i\ 1208. It will be obvious that working with such topographical maps has both advantages and disadvantages. The advantages are : I. The eye is able to take in a large surface at once, with exact in- formation as to the form of every part of it, and without those confusing optical illusions which result from looking at a natural surface horizon- tally instead of from above, and in successive bits instead of all at once. ,,T-'-"--"^ Fig. 288. Fig. 289. 2. Various projects can be studied with great ease, and the effect of different changes considered at once. A curve can be struck in with a compass in a moment, and three or four different ones in as many differ- ent positions almost as quickly, each one of which would take perhaps a day's hard work to run in on the ground, with the chance after they were run that they would lie considerably out of the position intended. 3. By dotting on the grade-contour (pars. 1246-8) or line where the plane of the road-bed cuts the natural surface, it can be seen almost at once whether the alignment is as favorable as the topography permits, or not. 1209. Each one of these advantages is a great one. On the other hand the disadvantages of working from contours are : 1. The making of good contour maps is expensive — which is a very weak objection, even if their cost were much greater than it is. 2. It is difficult to insure accuracy. C//AP. XXXL— TOPOGRAPHY : ITS USES AND ABUSE. 875 3. They afford no evidence of material. 4. They do not impress upon the mind the magnitude of the works^ projected, as it does to study the actual surface. 5. They are of assistance only for doing the least important part of the work, making the first approximation to the detailed location of the line. These and other difficulties which we shall shortly consider are like- wise great and valid ones. They indicate what is the fact, that topog- raphy has both its uses and abuses, and which predominates is often, the subject of heated discussion. 1210. In such discussions one is reminded of the old fable of the two- knights who fell to fighting over the shield which seemed gold or silver according to the "point of view ;" for the disputed question is emphati- cally one of the same kind. It is only by losing sight of one side or the other that one becomes a strong partisan of either view. The difference between the two views, in fact, is more imaginary than real. On the one hand, there are no engineers of any standing or ex- perience who believe that location offering any difficulties can be made to advantage in any other way than from topographical notes embodied in a more or less elaborate topographical map; while, on the other hand,, there are no engineers of experience who would think of claiming that more topography than is really necessary for intelligently completing the location, and making sure that it is correct, should be taken. The true question to be decided, therefore, is simply how mucft topography should be taken, and where the line should be drawn. There is no such difference of opinion as would appear from an error into which many have fallen— an error which well shows how completely the views of those who take one side of this question are misapprehended by those who think they disagree with them ;— that is to say. there is no class of engineers who attempt to make a final location assisted by the natural eyesight alone, or in any other way than by working from a preliminary line as a basis, which is intended to lie, and if skilfully run does lie, very close to the line on which the final location is placed, as in Fig. 282. 1211. To mark the limits of the debatable ground still more closely, it cannot be reasonably questioned (i) that in proportion to the skill of the engineer the preliminary line (often at difficult points, necessarily, the result of two or three trials) will approximate more and more closely to- where the final location will ultimately lie; (2) that it should, and in general will, lie nearer than 300 or 400 feet as an outside limit; (3) that the placing of this preliminary line upon the ground is and must be 4 ^7^ CHAP. XXXI.-TOPOGRAPHY. ITS USES AND ABUSE. r purely a matter of individual " eye for country" and good judgment; and (4) that the really vital and dangerous errors of location, the selection of the general route, the system of gradients, the going to or passing by the local towns, etc., etc., are committed, if committed at all. before any to- pography whatever has been taken, in locating this preliminary line • the usefulness of the topography beginning only after the more momentous question of where TO PUT THE PRELIMINARY has been decided, and serving only for the more ready and perfect adjustment of details-de- tails which have an important effect upon the cost of construction, in- deed, but do not otherwise seriously modify the earning capacity of the line. 1212. The remaining ground for difference between extreme advo- cates of either view is this : The extreme believer in topography is indif- ferent to getting his preliminary very near to its ultimate location, look- ing upon 400 or 500 feet average distance apart as near enough, and takes or causes to be taken a wide belt of accurate topography to save the need of a new or a better preliminary. But the advocates of the other view say. "No; the engineer who can be trusted to put a preliminary line within even 500 feet of the true location can and ought to, in gen- eral, put it much nearer ; or if not. it is cheaper to put a new line through 5till closer to the ultimate location than to take so wide a belt of topog- raphy. By one method or the other, the good engineer can and will bring the line so near to where his location should lie, that the topog- raphy which he will really need will be only a very narrow belt— usually tio more than a few series of cross-sections, and hardly amounting to a topop^raphical map at all." 1213. The truth lies between these two limits. Since the amount of topography ultimately needed and used (when its use is not abused by making it serve as a substitute for the careful placing of the preliminary) can be seen on any location map to be very little, covering a map all over with accurate topography is a sign of weakness and not of strength. On the other hand, accurate topographical contour lines for a reasona- ble and moderate distance on each side of the line are an immense as- sistance for the ready projection of lines, and at points can hardly be dispensed with. It is also an important truth that the usefulness of tO[)ography is not confined simply to that portion of it which is used to project the line adopted, but extends also to the portion which enables one to make sure that no other and better alignment might have been adopted. However confident an engineer may feel that he has in fact studied his work to the best of his ability, he owes it to himself and to CHAP. XXXI.— TOPOGRAPHY : ITS USES AND ABUSE. 877 his employers to have the ocular evidence of that fact before him, to be placed before others if need be; and it is but reasonable that no study of the ground alone, unassisted by accurate maps, can be as complete as one which has been so assisted. Yet, on the other hand, it is even more emphatically true that no study of maps alone, unassisted by study of the ground in detail, both before and after the making of the maps, can be as complete as it should be. 1214. No skilled engineer, even among those who are strong believers in the proper use of contour maps will approve of such elaborate reli- ance upon maps alone, as is sometimes taught and advocated ; such as; taking the nicest precautions for computing notes for 8 or 10 miles of location at once, so that it shall fit geometrically onto the preliminary,, and so dispense with renewed and more detailed study of the ground. Not but that the field-work and mapping might be done so accuratel5r that this would be all that would be necessary, and not but that much of a location so made may prove on examination to be beyond improve- ment, at least by the same engineer ; but that for practical reasons it is- inexpedient to rely so largely upon paper location. Among these rea- sons are — 1215. I. As above suggested, the length and depth of cuttings, and especially the classification, do not impress themselves upon the mind so forcibly in studing a topographical map as in studying the ground, and hence as great efforts will not be made, practically, to avoid this danger when the principal study of the details of the line is made upon the maps as when the paper location is looked upon as at best nothing more than a close approximation, and the last study of the ground is made with, the rock-cut staring one in the face, or on large scale cross-sections. 1216. 2. A very dangerous error, which the best engineers find it hard to avoid altogether, is especially hard to avoid in making paper loca- tions, which is, to regard a certain horizontal approximation to the GRADE-POINTS as about the proper thing, thus leading to altogether too> much curvature and respect for the contours in easy country, and alto- gether too little of both at the more diflficult points. The watchful en- gineer finds himself drifting into this error continually, guard against it as he will. It results in part from a natural, but evidently erroneous, tendency to look on a certain percentage of decrease of curvature, for example, as worth a certain percentage of increase in the work (pars. 14, 15), instead of being merely worth a certain absolute sum, which on easy work justifies great disregard of contours, and on heavy work requires, close accordance with them. - '1; jmjmM- I 878 CHAP. XXXr. — TOPOGRAPHY : ITS USES AND ABUSE. 1217. 3. The best topographical maps wliich it is either expedient or, in general, possible to make, with the time, money, and men at command, cannot by any means, as is sometimes foolishly claimed, be relied on within a foot, nor even 5 or 10 feet, at critical points, especially if extend- ing to any great width on each side. Over most of their area, if well made, they will be trustworthy, but minor irregularities of considerable importance, if nothing more than a few big boulders, get smoothed out of the map or misplaced or exaggerated, so that tlie only safe rule is to look on the iirst location, however carefully studied, as still open to much improvement — an expectation which will rarely be disappointed. But if frequent minor changes are to be made, much of the advantage of computing field-notes from a paper location so precisely as is often at- tempted is lost. It is not in fact good practice to do so. 1218. 4. To run in long stretches of location successfully without further topographical tests, but only the geometrical test of a "tie" to a preliminary, requires the nicest field and office work from the beginning to the end of the survey. It is, of course, only a question of degree. No one would advocate anything but good work of the kind, but it is obvious that less precision is required, if it is fully understood and expected that the paper location will be topographically tested throughout, than if it is expected to be, in the main, a finality. This saving of needed precision means some corresponding saving of time and money, which, as Mark Twain said of his profanity, "can then all be saved and devoted to some other end, where it will do more real and lasting good." 1219. Another objection, which is perhaps the strongest of all, against too great reliance on contour maps, is founded rather on the foibles of human nature than on any purely technical reason : It encourages a dis- position in the higher engineering officers to throw the field-work of location into incompetent hands, and to assume to themselves the func- tion of fixing the petty details of location, and hence (since the whole is only equal to the sum of all its parts) to control the whole location from their office chair, without giving to it that careful, thorough, and con- tinued study on the ground which alone will qualify the ordinary man to wisely exercise such control. This practice works injuriously in several ways: I. It deadens the perceptive faculties of the engineer in charge of the party and transforms him into a mere machine. He may, if an unusually skilful and faithful man, go over the paper line with a microscope and improve its details, but he will not be watching out for and thinking of the larger details, especially as — CHAP. XXXI.-TOPOG RAPHY : ITS USES AND ABUSE. 879 2. The practice leads to the engagement of poorer men for the field- work ; and 3. The engineer who puts in the paper location, and conirols the work, never qualifies himself by familiarity with the ground to do well even that minor duty, and is so little in the field that the far more im- portant end of avoiding the larger errors is not duly insured. 1220. The "conclusion of the whole matter" therefore is, that accu- rate topography for a certain narrow strip is a highlv useful adjunct to practical location, which should never be omitted altogether and should generally be very carefully taken and studied ; but that it is in no way a safeguard against anything but minor errors of location, and is not a safe nor expedient reliance for giving the last degree of perfection even to the -details of alignment. Great differences in natural aptitude for location exist, and among the strongest believers in the absolute necessity of elaborate topography may well be some who have less of this natural aptitude, and hence will not make very good use of the best of maps. In fact, although we should not allow this to prejudice us against topography, it is beyond doubt that those of least natural aptitude for location rely most on topography, and are the most helpless without it. On the other hand, those who have or thmk they have such aptitude may be led thereby to be over-confident, and commit errors which good topography would reveal to them. It is certain that the better natural qualifications a man has for the work the less topography he will take, because he will see in advance where it is and is not important. He will always take some, however, and what he does take will be correct. 1221. Another truth may appropriately be added here. It is easier to put A line, of some kind or other, on a topographical map than on the ground ; but to do the best that the ground admits is almost as hard, and takes almost as much study and skill, on the contour map as on the ground. This the inexperienced projector, of good natural parts, will soon find out if, after having put in a paper location, which he thinks is very gpod. he will start in over again on the assumption that it is all very bad. and give two or three times more thought and care than before to finding out wherein it is bad. He will probably soon be satisfied that his assumption was correct, by finding his curvature and quantities simultaneously diminishing. 1222. There is a tendency in discussing this question, as in many others to fall back upon the singular, yet in a sense natural, argument which seeks to defend some one way of doing things by showing that some of those who take 83o CHAP. XXXI.— TOPOGRAPHY : ITS USES AND ABUSE. CHAP. XXXI— TOPOGRAPHY : ITS USES AND ABUSE. 88 1 another way do work badly. On the one hand, we have pictured the "born- engineer" spending days in fitting a bad line to the side of a hill with his- •' practised eye," when hours would have sufficed with the assistance of a little well-taken topography; and, on the other hand, a man studying over topographi- cal maps of a line in the wrong place, missing the salient features, and perpet- uating on the ground errors of the maps. Either picture may well be drawn from life, for out of a hundred men doing anything which requires skill, more than half will do it but indifferently well, a considerable fraction wretchedly ill, and only a small proportion thoroughly well. This fact insures a supply of ready weapons for supporting either side of any argument, yet it is strange that they should be so often chosen, since it is clear that they prove nothing. But as evidence of this inconclusive character seems sometimes to carry undue weight, we may add a few words further as to certain details. 1223. The fact that the actual profile of a line run from a "paper location" agrees so precisely with the latter that the two cannot be told apart, is no proof of the excellence of the system, for both profiles may be bad. It proves the- geometrical excellence of the work, but it also proves, or tends to. that the whole process is too mechanical, unless the " paper location" has been at least so improved or modified in detail as to be distinguishable from the other. 1224. On the other hand, fixing the details of the alignment in the office, to be put on the ground by other men of less skill, while never a desirable, is. not necessarily a wrong, way of doing things. We are often compelled to do, not what we would, but what we can. If there be but one skilled man to look after half a dozen parties, and perhaps look after other work as well, it is im- possible that he should do much more than put the line on paper, and he is far more likely to project a good line in that way than an inexperienced man is to reach the same end. either on paper or on the ground, or both. When, how- ever, one ceases to look on this practice as merely a necessary evil, and begins- to look on it as an ideal state of things, so that on a difficult line it is " re- quired" that the projected location should be " strictly followed" and "no cut- and-try permitted," as is sometimes done, then the abuse of topography— and a dangerous abuse, sure to waste more or less money— has begun. The better course in such cases is to require the engineers in the field to make the first, projection, which is simply sent in for examination and revision if necessary, so as to compel them to rely on their own intelligence and not on another s, and especially to give an indication of the extent to which their own skill can be relied on. For if unequal to making a tolerably correct projection in the first instance, they will probably be still more unequal to the more responsible duty of putting in the final line. 1225. To mention one instance among many, of the evils of too great re- liance on maps: an unusually accurate paper location, on a very steep side-hill,, gave a beautiful profile, which no one could delect in the office to have any fault. The cut averaged about a foot, which was what prudence seemed to require^. \ and what no one, certainly, in the office would have thought of objecting to. But just below the earth was rock, as a " practised eye" might have detected in the field, and the earth itself was such as to make an unusually solid bank, so that when the line came to be constructed there was an ugly shallow rock-cut on the inner edge and a broad solid platform for the road-bed nearly twice too wide, due to the unnecessary amount of excavation, which involved a loss of some $8ooo in much less than a mile, all of which might have been saved by throwing the line out three or four feet beyond the paper location. Such cases occur so frequently that the engineer who does not feel the limi- tations of the map and wish that he had the ground before him in making a paper location, and who does not feel that it may be, and probably is, suscepti- ble of further improvement by further study in the field, will probably be wise to leave " topography" alone, both in the field and in the office. 1226. In some cases the larger errors of location, such as putting a line on the hill-side with a short tunnel, instead of in the bottom of the valley with a long tunnel, are very unreasonably advanced as an effect of neglecting topog- raphy; whereas it is precisely such errors which over-reliance on topography is apt to lead to. The result depends chiefly on the man. A good man will use every tool that will serve his end, and one of these tools is topography. Another one, at least equally essential, is shoe-leather. 1227. If topography is to be taken at all it should be taken accurately, and to combine this end with reasonable rapidity the limits within which accurate topography is taken should be restricted as closely as possible. Beyond these limits a skilful topographer will sketch in by the eye the general form of the ground, with sufficient accuracy to give a better general idea of the form of the country, and occasionally to serve a use- ful purpose in a rough study of some considerable change of line. 1228. Topography is taken from the preliminary line as a base-line, with the elevations on it given, by determining the slopes on each side as far out as seems necessary. Four methods for taking slopes are more or less practised : 1. By a slope-level and board straight-edge, with or without a tape- line. 2. By a hand-level and tape-line. 3. By cross-sectioning rods. 4. By using a stadia telescope and rod to measure distances in place of a tape-line, in either the first or second methods. To these may be added— 5. By using an altazimuth in place of the slope-level or hand-level in the first or second methods. It may also under special circumstances be used to advantage with cross-section rods. 56 882 CHAP. XXXL— TOPOGRAPHY : ITS USES AND ABUSE. CHAP. XXXI.— TOPOGRAPHY : ITS USES AND ABUSE. 883 Fig. agow 1229. In rugged and broken topography, as where there is much rock and large scales are to be used, the third method, by cross- section rods, is much the best. These rods are in principle nothing more than a horizontal measur- ing-rod of a fixed length, sometimes 10 but better 12 ft., carrying a level bubble, so that it can be set exactly horizontal. This is carried by one assistant while an- other reads with a light vertical rod, B, Fig. 290, the rise or fall of the ground in the given distance. In practice, to prevent warping of the rod A, it is usually made in one of the forms shown in Fig. 291. These rods are convenient to have with a locating party in rough country, and they are especially suitable for cross-sectioning a located line, but the pro- cess' is much slower than any of the others specified, which are in general better for ordinary topography. 1230. A wise choice between the slope- level and hand-level methods, also, depends a Fig. 291. good deal upon circumstances, and the character of the topography to be taken, although each method has its partisans who will rarely use any other. By the use of the altazimuth either method can be used at will, which is one of the distinguishing merits of that instrument. Much more depends, however, upon the individual skill of the topographer than upon the use of any particular method. Where the country is rough, with irregular slopes, the hand-level method is to be preferred, since it is more positive. Otherwise, the slope-level is best. 1231. The topography based on these slope-notes, by whatever method taken, should invariably be drawn in the field directly UPON the working maps of the line, which should be the first and only direct use made of the cross-section notes. As a safeguard in case of doubt, the rodman may well keep a note-book record of them, but this should be strictly restricted to such use only. The habit of taking the cross-sections in the field and drawing in the topography in the office cannot be too strongly discouraged. It is certain to result in more or less imperfect work, as well as loss of time. After a little practice a skilled topographer ought to be able to keep up with a transit and level party without much difficulty, unless circumstances require a wide belt -of exact topography to be taken, when he should be furnished with a double cross-section party. The main requirement for doing work quickly and well is to train the eye and judgment so that needless cross- section work need not be done while yet taking all that is essential. 1232. The topographer is provided with a thin drawing-board, hav- ing a leather or oil-cloth pocket on the back, in which are carried the sheets, about 19 X 24 inches in size (par. 1240), on which the line has been plotted the night before, the stations marked of!, and the elevation of each station and plus, as taken by the level, lightly pencilled on it. The topographer must thus work behind the level, but a good topographer will endeavor to keep very close up to it. One sheet at a time is pinned upon the board for use. A 6-in. scale, preferably of paper, lead pencils, and rubber complete his outfit. His two assistants (or four if need be) have nothing, necessarily, but tape and hand-level, with a small hatchet. A small compass for taking bearings is in general desirable. 1233. In taking cross-sections, the elevation of each station is given to the rodman (or has been previously taken off by him), and an offset measured off to a point, as indicated by the hand-level, where the contour next above or below the eleva- tion of the given station falls. Thus, in Fig. 292, with contours 10 ft. apart, elevation of station 704.2, contour 710 is 5.8 ft. above it, and contour 700 4.2 ft. below it. The distance out in which the ground rises or falls these amounts should in general, on rough ground, be directly determined, and then the distances to a suc- cession of other points, fall- ing 5 ft. at a time, as far out as accurate topography is taken. On smoother country a little trouble may be saved as below spoken of. The points where the contours cut the centre-line are also, at the same time, noted by the topographer. He then makes a light pencil guess at the course of the contour lines ahead, and passes, perhaps, two stations ahead, to " 17.4," Fig. 292. and repeats the process, the rodmen in the mean time cross-sectioning the intermediate station if it seems Fig. 292. 884 CHAP. XXXI.— TOPOGRAPHY : ITS USES AND A BUSK. I essential, or more properly speaking, unless it seems unessential. Until the topographer has acquired well-founded confidence by practice he will save nothing by taking chances.and be liable to throw discredit on his work. Here the previous guesses are checked by the cross-sections and the course of the contours sketched in backward, exactly and finally, and lightly ahead, with further pencilled guesses. In this way the topographer trains his eye and his hand, and forms an idea of where accuracy is and is not essential, and if he be once properly instructed, and has a capable: assistant, it is not at all difficult to take a mile or two of topography a day in ordinary country. When he has to take more than 200 to 300 ft. on each side it becomes a different matter, and progress is much slower. 1234. If slopes are determined by a slope-level it is still simpler work. A scale is then constructed, showing for a series of different slopes from. 1° to 20°, the horizontal distance apart of lo-ft. contours, which is 10 x cot 5. From this the contours can be put down upon the map at once, at the proper distances apart, or as far out as the slopes are taken, 1235. Time is lost and accuracy sacrificed in many surveys by using too small scales. The standard working scale may be said to be 400 feet per inch, or jnrW (nearly the same thing) when the metre is used ; but this scale is adhered to far too strictly. In rough country it should be at once doubled, and in very rough country should be increased to 100 ft. per in. or ^-^Vo (83i ft. per in.). These latter are the only suitable scales when there is any considerable proportion of rock-work. It rather saves work in taking topography, adds but little to the drafting work, and adds immensely to the practical value of the maps when made. 1236. The following cautions will assist in taking topography correctly : I. One contour line can never run into another and either disappear altogether or afterwards depart from it, in the manner shown at AA, Fig. 293, but must always be everywhere a separate, distinct, and continu- ous line until it either runs off the map or closes on itself so as to form an irregular ring or circle,- as at B, Fig. 293. There is, indeed, one case in which two or a dozen contours may so run together into a single -line, viz., when an absolutely vertical slope is to be represented. There is even a possible case- that of an overhanging cliff— in which the con- tour lines may cross over each other and back again, as in Fig. 294. But both of these cases are so rare, although they do occur, that it is unnecessary to coneides them as normal types of topography. Fig. 293. CHAP. XXXI.— TOPOGRAPHY : ITS USES AND ABUSE. 885 1237. 2. It is impossible for a contour line to split into two parts which sooner or later reunite again, in the manner shown in Fig. 295. It is a frequent error of young topographers, and an immediate evidence of inexperience, to be- r^^^_ _^^ lieve the contrary. It is indeed theoretically conceivable that a surface should have such '°* ^^' form as to make a sketch like Fig. 295 topo- graphically correct. Thus, if we imagine it to be a representation of the .crest of a hill, it might come to so sharp and regular a ridge, if made of dressed stone for example, that only a single mathe- matical line at the peak or ridge of the slope should appear above the water, and yet that the ridge should so appear above the water for a considerable distance, being precisely level, and should at a certain point swell out into the " island " AA. But practically, with natural surfaces as they actually exist, this is plainly impossible, and the true method of representing the natural surface, which is erroneously presented in Fig. 295, would be as shown in Figs. 208, 216. 1238. Topography, more largely than almost any other mechanical detail of engineering work, is a mat- ter of practice. The young engineer who ends his first day's work at topography discouraged, with but a few stations taken, and that so badly taken as to be worthless, can by even a few days' de- termined effort to understand it, and do what he does do well, learn to go over as much ground as an ordinary transit party. It is a valuable drill for cultivating the faculties most needed for location, and good to- pographers generally make the best chiefs of party. In country at all rough the topographer fills the most responsible position on the party below its chief, and he should so rank.* Pic. 295. * The art of taking topography should be taught in schools more thoroughly than it is. There is no better drill for cultivating those faculties of mind which make the engineer. y •M mmmmat 886 CHAP. XXXII,— MAPPING AND PROJECTING LOCATION ^) \ CHAPTER XXXII. MAPPING AND PROJECTING LOCATION. 1239i But two methods of mapping railroad surveys are to be com- mended, which are : 1. For large-scale working maps : plotting lines by bearings with a large paper protractor and parallel ruler. 2. For small-scale maps : by latitudes and departures. Plotting lines of any length by laying off successive angles — a favor- ite way of laboriously making a bad map among inexperienced men — should never under any circumstances be permitted. All work should! be plotted by bearings from a constant North and South line, which is transferred from sheet to sheet by prolongation or with a parallel ruler. Cumulative errors are thus avoided. 1240. Except in cases where fully 8o per cent of a line is tangent, and there is little topographical detail, a survey-line should never be plotted on long strips or rolls of paper, but always on small sheets, about 19X 24 inches in size, or larger if there be little curvature and topography — say^ 19X 36 inches. These sheets are added one after another as the plotting progresses, lapping one side or corner always under the preceding sheet, and giving its axis any random direction, compared with the other, which will best serve to keep the centre line of the survey in the middle of the sheets, as shown in Fig. 296. The two sheets are pinned together with thumb-tacks, and two or three X marks made at the lap, so that they can be replaced at any time in exactly the same position. A North and South base-line should then be laid down the full length of the sheet, nearly in its middle, and a consecutive number for the sheet and the name of the line pencilled on, always in the same corner. 1241. The large paper protractor should then be laid down in the middle of the sheet on the North and South lines, from a clearly-marked permanent centre-point, and the computed or actual bearings of ALL the lines which are likely to fall on the sheet laid off at once. If omis- sions are discovered, the same process should be repeated ; lightly CHAP. XXXII.— MAPPING AND PROJECTING LOCATION. 88/ pencilling in the degrees and minutes of each bearing laid off, and per- mitting the points thus marked to remain permanently, except as they interfere with the mapping. Should any subsequent error be discovered, they may then all be checked at once, saving much time. With a good parallel ruler (not the cheap and poor ones which are most used, but a heavy metal rule about 18 inches long), or, failing that, a couple of triangles, it is then but a few moments' work to transfer each bearing in succession to its proper point, draw in the line, and plot its length. The angles should then be roughly checked with a small protractor to guard against the large errors which are alone likely to occur. The bearing of each line and the plus at each angle should then be pencilled on. Every station should then be pricked off and indicated by a light check-mark, and every fifth station should be numbered. Opposite each station on a di- agonal line should then be lightly pencilled in the elevation, and also the elevation of any pluses taken. The sheets are now ready to turn over to the topographer. This work should be done every night. It takes but a short time after a little practice. The lines may be inked in on rainy days or at any convenient time. The centre line should be in red. 1242. For the same reason that Fig. 296. plotting should be done from bearings, it is well to do all the transit 888 CHAP. XXXII.^MAPPING AND PROJECTING LOCATION. work, on preliminary lines at least, by reading BEARINGS instead of ANGLES from the vernier. In starting the survey the vernier is set at o, and the lower limb clamped on a North and South line, or as near to it as possible. Unclamping the upper limb, we may then read the bearing of the line eklier with the compass or the vernier, and the two should approximately correspond. Retaining the verniers at the same reading for talcing a back-sight at the next angle, and unclamping above to take the next sight, we obtain the bearing of the new line, likewise either by the compass or the vernier— the one approximate, the other exact. Thus we may continue throughout the survey, with the advantage (i) that we can check our work at any time by simply dropping the needle, since the needle and vernier readings should always correspond, and (2) that our *' computed bearings" are already computed. We should work, how- ever, by 1 80° on each side of the North point, and not be troubled by the transition from N. E. to S. E. This is the best way to do in any case, and it is easy to read the needle so. 1243. In inking in the topography, every fifth line should in all cases be made heavier or a different color. Black or brown for every fifth line, and brown or orange for the intermediates, does very well. Where possible, contours should only be five feet apart, although ten feet is usual. The values of every fifth line should be frequently written on them, in rows one above the other, preferably by leaving a gap in the line for inserting the figures, or otherwise by writing them directly over and across the line. Much of the prejudice against working with con- tour topography arises from the prevalent neglect of these simple direc- tions, which seem almost too simple to mention. Such a map as Fig. 297, for example, is an abomination. It reflects just discredit on any engineer to turn in one in that condition, which makes it almost worth- less to the engineer and incomprehensible to the mere observer. It should be finished up as shown in Fig. 298. A light case, provided with three or four drawers of the proper size to hold the sheets, should be provided for field use. Light-yellow de- tail paper makes very good sheets, and is less trying to the eyes than white. 1244. Experience has clearly shown this system of mapping survey- lines to be far better than any other. Its advantages are : 1. But a small amount of paper is in use at once in plotting, while any number of sheets that there is table-room for may be put together if desired. 2. A very small table is all-sufficient. "~r~niiM F.G.ag7.-AN IMPROPERLY FINISHED CONTOUR MAP. (A spiral located on the Connellsville & Southern Pennsylvania RaHroad.) 'lilt (A map left in this condition is almost wholly useless for practical work, or for giving a definite idea of I I I, J 1000 FT. the line to a casual examiner, while it is nearly as much work to make it as to finish it properly, as shown on the plate which faces this one.] Fig. 298.-THE SAME MAP, PROPERLY FINISHED. J 1000 FT. I added on a full-scale map. Centre line and radii of curves should be in red.] v' CHAP. XXXII.— MAPPING AND PROJECTING LOCATION. 889 3. No time need be lost in studying how to keep the line on the paper, or in rubbing out, or in pasting on extensions. 4. The map need not be covered over with prolonged lines for laying off angles, but only the actual length needed is drawn. 5- Great accuracy is secured without effort, and cumulative errors are impossible. If an error is made on one sheet it in no way injuriously affects the work on the adjacent sheets, except that two of them will have to be re-matched. 6. If matched properly the greatest precision is possible in laying them together again whenever desired. For all practical purposes they are as -a single sheet. 7- There is no waste paper, and the line is always in the middle of what is used, readily accessible for office work. The awkwardness of working with wide rolls is entirely saved. 8. The paper is never rolled, but always flat and clean, in good con- dition for working on. 9. For projecting location, the ease with which any part of the line desired can be worked with, without annoyance from what is not wanted and from change of scale due to rolling, gives it very great advantage. 10. The maps are readily stowed away in dust-tight boxes or drawers and in very small compass, instead of taking up a great deal of room and getting into a practically unserviceable condition in a short time, as rolled maps usually do. ^45. For making small-scale maps, plotting by latitudes and " DEPARTURES is the most satisfac- tory way. The latitude and de- partures should not be computed, however (or the labor would be prohibitory), but read off mechanic- ally from a diagram similar to Fig. 299, which shows the principle of an apparatus for the purpose de- vised by Mr. Chas. Francis. Chief of Office on the Pacific Branch of the Mexican Centra! Railway. Any one can readily make it. The base is a sheet of accurate cross-section paper, 10 or 20 squares per inch, ^ff .- , , on which angles are accurately laid Off, either around the ^d.^^, as shown, or on a circular arc of as large a • i^ Fig. 299. ..-mmK. f 890 ClfAP. XXXIT.^PROJECTING LOCA TION. radius as possible. Values are given to the lines from zero to 100 or more. The straight-edge is laid off with the same scale. We have then only to set the edge of the straight-edge at the angle corresponding to any bearing ; place a needle-point or sharp pencil at the point on it representing the length of a given line, and we read off from the sheet below, at once, latitudes and departures for the line. Lati- tudes and departures for miles of line can thus be called off and tabulated in a day by two men, and the absolute position of every point on the survey, by rectangular coordinates from any fixed origin, determined once for all. From these notes as many or as few points can be trans- ferred to the map as seems desirable, according to its scale, and the re- mainder sketched in. When several alternate lines are to be mapped together this method is especially useful, as the trouble of closing ac- curately is so greatly reduced. PROJECTING LOCATION. 1246. To make a really good projection on a topographical map in- volves a great deal of work and study, and errors are almost as easy as they are on the ground. In fact the writer has no belief that any one ever projected a location on paper which could not be materially improved by study on the ground. The most difficult case is projecting a final grade-line in which curve compensation is to be introduced as it advances. In very difficult coun- try a first projection on an estimated average " straight " grade-line is often advantageous, saving time and giving a better final result because of the double study. The lower (dotted) spiral of Fig. 216 was projected in this way. The projection should begin at the summit or other fixed point which the line must make. Assuming a starting-point and elevation, take in a pair of dividers the distance on the map which the given grade- line takes to fall 10 ft., or better yet, 5 ft. When curve compensation is introduced this distance will be different on a tangent and on every curve.^ and should be laid off on a strip of paper so that the dividers can be set and reset without trouble. With the dividers thus set, step off a distance of 10 or 12 inches on the map, following as nearly as may be where it is thought the line will lie. On favorable topography this will be very closely along tlie GRADE CONTOUR, or line where the plane of the grade strikes the natural surface. In that case we can step off quite a distance at once, stepping CHAP. XXXII.^PROJECTING LOCA TION, 891 down a contour or half-contour at a time, and marking by a small cross- mark wiiere the grade-line crosses each. 1247. The grade-contour should then be very lightly pencilled in, and a curve or two, or a long tangent and the beginning of one curve, pro- jected. Then, setting the dividers for the proper distance for a L\\ of I, 2, or 5 ft. on the given curve or tangent, and starting from the fixed point, step along the projected location to the first point of curve and determme and write down its elevation to the nearest foot and tenth ; paying no attention as yet to stationing, but simply to determining points where the grade-line reaches certain even elevations, and to determining: the grade at the points of curve. Having reached a curve from a tangent, reset the dividers for the proper distance for the given fall on the curve ; start from the P, C. cor- rectly by straddling the dividers over it according to its fractional eleva- tion ; step around the curve to the P. T., and determine and lightly note Its elevation. Reset the dividers for the next tangent or curve, and so on to the end of the section projected. 1248, Then return and correct the grade-contour according to the precise points at which the elevation of each contour or half-contour is reached on the actual projection, sketch every bit of it in, and see if the projection corresponds to the corrected grade-contour as well as is possi- ble. Consider everything : the material (above all); the surface slope ; the water-ways ; whether the line should be preferably in cut or fill, whether the tangent or the centre of a curve cannot be slightly changed so as to fit the grade contour better, or avoid a rock-cut ; whether the form of the gulches is correctly represented and there is not a crossing point slightly more favorable above or below, which the topography does not clearly show ; whether the tangent cannot be broken up by a slight curve and save work which will be more conspicuous on the ground than on the map ; or, on the other hand, whether the line cannot be thrown out here and in there, so as to take out curvature and yet give as good a pro- file. Probably some little modification, at least, will be at once seen to be desirable, and the whole work will have to be done over, perhaps three or four times. If not. it may be for the time being left behind. 1249. A short stretch more should now be projected in the same manner as before, and now only will it be possible to give proper study to the first section ; for the whole relations of the line to the ground can- not be taken in until the projection is complete for a considerable dis- tance on each side of the point studied. It is now more likely than be- fore that modifications will suggest themselves in the first section. The tr.}- — - I «92 CHAP. XXXIL— PROJECTING LOCATION. reader who is quite satisfied with his first or second or third trial may justly fear that he is doing bad work. The projection in Fig. 216, for example, while good enough for an approximation, is by no means good for a final one, being capable of considerable improvement at several points. After completing several miles the whole should be studied over again, and corrections unnoticed before are pretty sure to suggest themselves. Very, often long stretches of the grade can be raised or lowered somewhat to advantage, at the expense of a slight break. It is difficult to point out every danger in advance, but it is a fact that men will differ in their projections almost as much as in field location, and the most obvious im- provements will not suggest themselves until some one else points them out. Without an accurate personal knowledge of the ground, it is folly for any one to attempt to make a really good final projection, although contour maps have the great negative merit that glaring errors or gen- eral incompetency may be detected at sight by any one of experience. Before the projection is considered final the corrected grade-contour should be made exactly right, and sketched in clearly and complete. It is very bad practice to sketch in only certain grade-points. A great check acfainst error is thus lost. 1250. The line should now be stationed and a profile and field-notes called off. The latter are readily made up, since the length and degree of each curve is known, but they should be checked and corrected throughout by determining the bearings of every projected tangent from the original North and South line. Except when errors are seen to be compensatory the bearings thus read will be more trustworthy than the stepped-off lengths of the curves, and the latter should be modified to correspond. 1251. Curves may be projected either (i) by compasses, (2) by wooden, rubber, or metal curves, or (3) by a curve- protractor made on a large clear sheet of isinglass by scratching on the curves and rubbing ink in the scratches. The latter is a very convenient and desirable adjunct to the work, but not essential when the radii are not too large for compasses. With cut curves it is far more important. The writer personally prefers a pair of compasses to anything else when the radii admit of their use. The transition curves should be projected at the same time as the curves by drawing in the latter not quite tangent to the tangents, but at a slight offset to them, as in Figs. 208 and 216. What this precise offset may be does not matter. It may vary from 0.5 to 3.0 or 4.0 feet per degree of curve. 1252. Having made the profile, the GRADES should be put on it. Re- CIIAP. XXXII.— PROJECTING LOCATION. \ 895 member in putting grades on a profile that it is a great deal easier to- stretch a thread to cover two or tliree feet of a profile than to execute with shovel and crow-bar tlie work which it calls for. Long shallow cuts are generally a mistake of judgment. The grade sliould rather be broken and thrown up into fill. As a rule, apices in grade-lines should never meet on a fill nor a hollow in them appear in a cut, since the extra depth of the cut or height of the fill is so much work thrown away in order to do a bad thmg-bring grade-lines to a sharp intersection ; but there are exceptions as respects fills, when it is desirable (as it alwavs is) to give abundant water-way for streams without carrying the whole fill on too high a bank. It is a common error of inexperienced projectors to lav the grade-lme too near to the supposed high-watermark. It is not worth while to take chances, and it should be several feet above all the an parent possibilities. P 1253. It is always desirable, except on steep side-hills, to have the fills exceed the cuts. Heavy fills can be gotten at from a good many points, or temporarily trestled and filled by train, but large cuts are very apt to delay progress (they are generally the last work finished), and give trouble for maintenance later. Long, low fills should never be laid out to average less than two feet high. The temporary economy is a dear one. Grades can in general be laid out just as well as not at some evea rate and starting from some even station, but the trouble often taken to this end IS perhaps rather worse than thrown awav, as it is a simple matter to compute the grade elevations, and economy is very apt to be sacrificed to no real advantage. Full allowance for vertical curves should IooITh ff' .. progresses and the grades for stations carefully looked after, especially m projecting long grades. Table 125, page 388 ■ will facilitate doing so. The original grades should be studied ovi and revised, aided by the cross-sections of the final location. It is costlv business to attempt to make the latter without accurate knowledge of the material under the surface, but this trouble is too frequentiv not taken Simple boring and drilling appliances for investigating the material now exist in plenty, and the expense is very slight. Whenever and wherever or 1',% T^^""- ^^'"^'J '""^ "^"""'^ "'^ ^"^f^''^^' *ere is little excuse for not determining its depth and limits, as it can often be avoided with ease. the'f *; T''"'}^^^. ^'^t' '>>= P™fi'^ and field-notes of the paper location he final location is proceeded with. The profile is kept close up to the chert'/ ,' r""°". °/ "'' ^°'^ ^' ^"'P^^^'^ ^'* '"^ projection checked mainly by it. A few tie-notes with the preliminary are usually 894 CHAP. XXXII.— PROJECTING LOCATION. % mt taken off for each day's work, but it is not worth while to attach much weight to them. The question is only : Does the line as run on the ground give as good a profile as was expected and desired, and can any improvements be made in it ? That chief of party is not a very good one who will not see many improvements as he progresses. Aided by the system of transition curves referred to in the previous chapter, these changes are rapidly made; but if there be any doubt at all about them, they should be left for a later revision. In fact, the better way is always to run the whole location over twice (par. 1193). The money spent will be well invested. \ \ CHAP. XXXIII.— THE ESTIMATION OF QUANTITIES. 895 CHAPTER XXXIII. THE ESTIMATION OF QUANTITIES. 1255. The purpose of preliminary estimates is. first, to arrive at an approximate idea of the cost of the work ; secondly, to compare alternate lines together; and thirdly, to assist in fixing the grades. For neither of these purposes is any great exactitude necessary, especially if there is certamty of having the quantities at least large enough. For estimating the cost of the work an excess of two or three per cent is rather an ad vantage. For comparing alternate lines the error, whatever it is. will make no difference unless there are causes why it should exist on one Ime and not on the other. For fixing grade-lines a slight percentage of error ,s equally unimportant, since it is rarely good engineering, under modern "methods of construction, to attempt any very exact balance of cut and fill, the fill bemg always laid out in excess, and long cuts avoided as much as possible. The only exceptions to this rule are when both the cuts and fills are short and heavy, so that the haul will not be long or on a steep side-slope, so that throwing the line in to decrease the ci^ts will increase the fills, or vice versa. Even then the possibility of using temporary or permanent trestles, the size of water-ways required, and the .differences in classification will ordinarily have more effect on where the hne IS laid than the mere question of balancing the profile. 1256. For these reasons it is an absurd waste of time to use the pris- moidal formula, or any other method but that of averaging end-areas for making preliminary estimates, and this method should be used in the simplest way of ail-that of determining centre-heights directly from the profile, unless the ground is quite rough and irregular. In that case des^rable^ '^ ^^^ ™^'^''^^ ^^ '''''^' ^^"""^"^ cross-sections may appear In working merely from the profile centre-heights, without takin & In any wooden trestle, the caps and all the floor system above it as also the minimum length of sill and all wooden parts below it are directly as the length of the structure and independent of its height The same is true of the cost of digging foundations, and the piling or masonry if used (as one or the other always should be). At a certain distance below the cap, say 10 feet, there is a system of longitudinal, transverse, and diagonal ties and sway-brace running the entire length of the structure on a line about 10 feet below the caps and ^constructively) a certain addition to the length of the sill. All this* may be expressed at so much per lineal foot on a horizontal line 10 feet below the grade-line. Ten feet farther down there is a similar system, nearly duplicating the first, but a little larger, which may be all expressed at so much per lineal foot on a horizontal line 20 feet (or whatever the distance may be) below the grade-line. So we may proceed until we have provided for the highest trestles likely to occur on the line of the given type, and we shall have expressed the feet board measure in any width in an equation of the following lorm : ^ F/. B. M. =/L +fL' +f'L" -f etc., w\ I f a I 900 C//AP. XXXIII.— THE ESTIMATION OF QUANTITIES.. in which L, L', L" = the respective lengths of the structure on the* grade-line and on parallel lines 10, 20, 30 feet, etc., below it, and /,/*,/"=. the corresponding measurement per lineal foot. 1268. The length of each of these lines below the grade-line ought, in theory, to be measured a little short on the profile to allow for any bents which may extend below one system and not quite down to another, but such nicety may be neglected. At the bottom of the trestle there will be an irregular area of greater or less extent. To include this in the estimate, transform it by eye into a rectangle 10 feet high and of equal area. Any one familiar with the construction of trestles will do this with great accuracy; and the results of this method, in which no account is taken of the particular number or position of bents, come surprisingly close to the ultimate measurement, as the writer has tested on many structures. 1269. Trestles should invariably be built with side stringers and ties- about 12 ft. long, capped with a guard rail, as a safeguard against de- railed trains, foot-passengers caught on the structure by a train, and the- insidious effect of decay, as well as for its material addition to the strength, of the structure even when new. " Split " stringers, breaking joints with each other, are invariably used in good practice, and split caps and sills- boxed into the posts and bolted through make a far stiffer, better, and more easily renewable structure than the common form of mortise joints. " Cluster-bent" trestles made of 8 x 8 inch timber are the best- for high structures. The ends of all trestles and bridges should be protected by Latimer's rerailing safety frogs, a cheap cast-iron watchman which may be relied upon to put derailed wheels back upon the track, if not too far displaced, as has been proven by many instances. 1270. Iron Trestles.— Iron trestles may be estimated in much the same way as wooden trestles, and it is of practical value to do so to bring out how little the height of trestles has to do with their weight or cost, — a fact which, if it be fully realized and taken advantage of, may often be an immense assistance in obtaining a favorable line, by enabling it to be carried high above what are apt to be the most serious obstacles — the deep gorges. Iron trestles, for some occult reason, are usually planned for bents 30 feet apart, each successive pair of bents being braced together into a kind of pier. Sometimes the intermediate spans are made 45 or 60 feet, and occasionally the bents are 60 feet apart, continuously. Sometimes* the intermediate spans are mcreased to loaor more feet. \ 'CHAP. XXXIII.— THE ESTIMATION OF QUANTITIES 9OI 1271. However these details are varied, there is wonderfullv little dif- ference m the total weight of the structure, which usually comes out much the same, barring a slight percentage, as if the simple type of 30-foot bents had been used throughout. What is gained in the bents is lost in the floor-system, or vice versa. This is strikingly illustrated even in so widely different a structure from the ordinary trestle as the Kentucky River bridge. The total weight of iron corresponds very closelv with what would have been required to cross the gorge with a trestle with 30-ft bents— not equally safe by any means, but of the same average weight per lineal and vertical foot as in the minor structures on the same road built to sustain the same rolling load ; so that in estimating structures for large and small gorges, by the same rule, we do not go far astray 1272. This fact has led Mr. Geo. H. Pegram to propose the followin^r lornmla for the weight of iron trestles, which he states that he has found to give close results when tested on a considerable number of actual structures : IVt. in lbs. = (3Z + 2H) no for Mogul engines and 1820 lbs. per ft • m which L = the total length of the structure between centres of end- pins and /r= the sum of the total bent heights from top of masonry pedestal to top of columns, taken as 30 feet apart, whatever they may actually be. For Consolidation engines we may take W=(xL + 2H) 125 to 130. ^ These formulae give the total shipping weight of iron, and will ordi- narily approximate within 5 to 10 per cent. They will be most in error er ft.) 724,000 lbs. Pier, 130 ft. 4 in. (1304 lbs. per ft.), lyOjCxxj Total of pier and cantilever span, 894,000 lbs. Additional per ft. extra height, about, 1,500 '* or \ of one per cent. CHAP. XXXIII.— THE ESTIMATION OF QUANTITIES. 903 their cost. Singularly enough, it appears from comparisons of the con- tract prices on that road that it has more effect on the cost per foot horizontal than per foot vertical, which latter were very little affected ; in part, no doubt, because erection is much more expensive per pound with low trestles. Fig, 301 will show how little the height has to do with the cost of even the largest structures. 1275. It is probable that pedestals of very superior concrete would be cheaper as well as better than masonry. One difficulty in the use of concrete which is a very serious one with masonry also, is that under the usual form of contract the contractor furnishes his own cement. He is therefore under a con- stant temptation to^ skimp the work in that vital detail, both in quantity and quality. The true way is for the company to purchase its own cement, furni«;h It to the contractor liberally, and require him to use it so. He will then be as anxious to make the work good in that respect as he is now to make it poor. Much dispute and inspecting annoyances will thus be saved, the cost of the work little if any increased, and its quality materially benefited. 1276. Bridges.— In Fig. 247, page 767, there has alreadv been given a diagram prepared by the writer, mainly from the formula determined by George H. Pegram. C.E., and given in a paper before the American Society of Civil Engineers. In addition to what is stated in connection with the diagram, it may be added that the West Shore specifications called for rolled I-beams up to 20 ft. span, plate girders from 20 to 50 feet, lattice girders from 50 to 75 ft., and thereafter pin-connected trusses. There was naturally a slight jump in passing from one to another. The weights of bridges of various spans were computed to be of first-class construction, without any additions of doubtful utility, so that while a bridge might weigh more than that given through some special excel- lence, it should not weigh much less. The following are the formulae deduced by Mr. Pegram, in all of which 5 = the span centre to centre of bed-plates or end-pins, as the case may be. W rr the total or " shipping" weight of iron or steel in pounds. For iron bridges under 200 ft. span : in which c- 7 for Class T, Fig. 248, page 769. <^ = 9 for Class C, a = 12 for Class M. " " For Class N, three fourths of the weight as given for Class T was taken — a very rough process. if I I ] 904 C//AP. XXXI1I,— THE ESTIMATION OF QUANTITIES, For iron bridges over 200 ft. span : »-= (5 + 1)5-. in which b — 100 for Class C, • ^ = 80 for Class T. For steel bridges aver yooft. span : W = cS\ in which c — d for Class C, ^ = 6.7 for Class T. 1277i The type of bridge assumed was as follows : For spans below 75 ft. : deck-plate girder bridges, 8 ft. wide, con- nected with angle-iron bracing, and with cross-ties resting on the top chords. Above 75 ft. up to 150 ft.: through truss bridges, Pratt or single quadrangular trusses. Over 150 ft.: Whipple or double quadrangular trusses. The widths assumed were: For standard-gauge spans under 255 ft., 14 ft. in the clear; for 320-ft. span, 18 ft. centre to centre of trusses; for 420-ft. span, 21 ft. centre to centre, and for 520 ft. span, 25 feet centre to centre. The floors of the spans consisted of cross floor-beams at the panel points, with a line of iron stringers under each rail, except for spans over 300 ft., which had three lines of stringers. Differences in depth affect the weight less than would be supposed. Thus in a 6o-ft. girder span, for Class T, the difference in total weights between depths of 5 ft. and 5^ ft. was practically nothing, and for an 80-ft. girder span, calculated for Class C, with depths of 6 ft., 6^ ft., and 7 ft., the difference was less than i per cent. In a 1 80-ft. truss span, the difference in weights between depths of 26 and 28 ft. was less than 2 per cent. In a 520 ft. steel span, for Class T, the difference in weight between a depth of 50 ft. and one of 58 ft., was about 3 per cent. ; a depth of 56 ft. was finally taken in this case. 1278. Modifications for other conditions than those specified may be made as follows : If wooden stringers are used, deduct 195 lbs. per ft. for Classes; M. and C, 210 lbs. for Class T, and 140 lbs. for Class N. For safety stringers add 100 lbs. per ft. for all classes. CHAP. XXXIIL ^THE ESTIMATION OF QUANTITIES. 905 For deck-truss bridges add 10 per cent, and for double-track bridges 90 per cent, to the formula weight. Through-plate girder bridges will not differ materially from deck bridges m weight, where the cross-ties are made to serve as floor beams. When an iron stringer floor is used, it will be a close approximation to add 200 lbs. per foot to the weight given by the formula. For bridges of less than 150 ft. span, the only part of the rolling load which affects the weight of the bridge greatly is the engine load. For spans of over 200 or 250 ft., an average of the engine and car-load per loot will come nearer to expressing the ratio by which the weight of the bridge is affected. 1279. The weight of a drawbridge, including turn-table, wheels and machinery to turn by hand, will be very nearly the same as for a fixed span of the same total length to carry the same live load. This rule is stated by Mr. Pegram to have been remarkably exact in tests on a num- ber of drawbridges of 150 to 400 feet, both single and double track. 1280. The cost of bridges per pound is far from fixed for all classes of structures, but may be said to be made up as follows : •n . . Cts. per lb 1. Raw material, rolled and plate iron 2^ to 3 2. Work on same in shop ' b |.q j 1 3. Transportation by rail 1 ^^ 1 4. Falseworks and erection i to i <;. Profit and administration i to i4- "^^^^^ 4""^ The lowest of these prices are sometimes cut under, especiallv in dull times and for large orders of a simple class of work. For example on the Manhattan Elevated Railway, involving immense weights of a very simple class of work, contracts were let at 2 to 3 cents per pound while on the other hand, fat contracts at much higher rates than those given above are not uncommon ; but these are fair averages for average work in moderately good and bad times. It will be seen that only items i and 3 above, and not always even those, increase directly with the weight of the bridge. We may say in a general way that 10 per cent increase iri weight, with its several times greater increase in safe rolling load, will mean not more than 5 or at most 6, per cent in the cost of the bridge to the company, and propor- tionately for greater or less differences of weight. 90^ LHAP. XXXIII.^THE ESTIMATION OF QUANTITIES. 1281. Station buildings, yards, track and track-laying, and many other minor details of construction, must likewise be included in any complete estimate, but to consider them here would lead us too far from our sub- ject, which has had to do with those details only which are connected with and affected by the location of the road. In all such details, it has been intended to go far enough, and not toa far, to at least fairly prepare the patient reader to make a decent approxi- mation to the true economy of alignment. To do more than this can only be a happy accident with any one. To do less than this the writer hopes he may have rendered unnecessary. He has not spared his own labor to do so, and for wherein he may have fallen short he can only say with the heroine of " A Winter s Tale : I speak as my understanding, instructs me, and as mine honesty puts ii to utterance.' APPENDICES. APPENDIX A. ] EXPERIMENTS ON THE RESISTANCES OF ROLLING-STOCK The mode of test was by what may be termed the " drop test •" start- ing car^ from a state of rest down a known grade, and deducing t^e resistances from the velocity acquired. The principle of this method ht! of en been employed before, sometimes merely to determine comparati^ resistances, w,thout attempting to measure their absolute amount and wi r^it^ " °" ''"'"'• '" '"^ P^^^^"* ^-'^ ■' »- "temped! with entire success, to extend this method to the determination of a serie^ pa h of the vehicles, dunng which their velocity varied /rom o to ,o miles per hour Great accuracy in time observations was necessa^ for tSTT,u "^' ""^ '^""'^'^ "y "'^ ^'d °f electricity, so Tully m fact that the margin for error in the latter half of the experiment I luVr "'^" ^'^ '"• ^' *°"- I' ™"^' be added, however that about half the tests were made before the apparatus was ully Trfeaed and are, hence less minutely accurate, but the maximum erro'^s'Tn these atter can hardly exceed i lb. per ton in any case, as will be evident from the record plates, and all errors of any kind in this mode of test ar" necessarily compensatory, any excess in one resistance causing a corri! spond.ng deficiency in the succeeding one, and v^ce versa. It IS believed that equal accuracy is unattainable by any other mode of test, sirfce it is plain that every step in this process'^is free from any ^nsible source of error other than carelessness. The accelerating force (gravity) is uniformly applied, and exactly known from formula without measurement. This force is necessarily all consumed (.) in ov;rI^ming he resistances to be measured, or (2) in communicating velockyThf amount of force represented by a given velocity is known by fo;muli without measurement, and the velocity itself is exactly record ^ tl \. ] 910 APPES'DIX A. electricity, beside a synchronous record of seconds, from which intervals of time may be easily read off to ^V second. Errors from carelessness in computation are always possible, but three checks existed against them: e average resistance of a 1° curve to 4-wheel trucks having » 5- oot r,g,d wheel-base, and to 6-wheel tn,cks haying aToliVL t:t'r?ScaK '"^ ^'^^ °^ "^^ "--' - ''^ Peistal-AsrlpS 9tli. It appears possible that the act of coupling together cars hv a loose hnk slightly decreases the axle-friction, and hence presuLblv the oscllating friction at high velocities. The ave age reducS observed from coupling four or five cars together appeaf^d to be a^ much as i lb. per ton. [The tests appeared to indicate this but th^ author now regards it as very doubtful.] ^ loth. There appear to be good grounds for suspecting that a shVht superelevat.on of one rail on a tangent may have the effect of appre .TewV:!ir"p!rtur'^"^^ '° '"°"°" -- - ->-''- °^ - :; • This, of course, does not include, nor in any way refer to th- ,h^-,- ^i power demanded to get up speed, which is . lbs. per oV to g "; a peed' "70 miles per hour n 3340 feet or 4 :; lh«5 n*.r r«„ » • ^ ° hour in the same dfslance '^ " '° ^"' " '"""' "' '^ ™''«^ P" 912 APPENDIX A. ij 1 I \ nth. Roller-journals of various forms appear to be very effectual at velocities of o +, but lose nearly all their theoretical advantage as the velocity increases. Such journals appear to be more effective as the load is decreased, and reduce the resistances of empty horse cars by about one half. 1 2th. Forty-two-inch wheels seem to be even more effectual than theory would indicate in reducing extra friction. 13th. The equation of resistance for average trains (twenty cars) of loaded box cars may be taken, approximately, as APPENDIX B. -ff = + 4; 130 or, for trains of forty empty box cars. ^ = 106 + 6. The velocity resistances of flat cars increase somewhat more rapidly^ being for twenty loaded flat cars — , and for forty empty flat cars -x— . These formulae are believed to be closely approximate up to velocities of thirty miles per hour. No tests were made at higher velocities. 14th. The coeflicient of axle-friction is about .02 for loaded freight cars and passenger coaches at speeds of over five miles per hour, about .03 for empty freight cars, about .065 for horse cars, and about .12 for freight tmwks without load. The coefficient is two to three times greater at the instant of starting. It decreases rapidly as the load per journal increases. 913 APPENDIX B. EXPERIMENTS WITH NEW APPARATUS ON JOURNAL.FRICTION AT LOW VELOCITIES. [A Paper by the author, read before the American Society of Civil Engineers Tune . x8g. Abbreviated from Trans. Am. Soc. C. E., Dec, 1884.] ' '' Of iLT 1''"''''T experiments were undertaken by the writer in the winter of 1878. pr.manly to test the correctness, especially in respect to initial fnct.on at low velocities, of a series of other tests of rollin^stock e t ances (see Appendix A) made in a totally different manner, on the Like bhore & M.ch,gan Southern Railway, under the directi;n of Charles lame. Member and ex-President of the Society, who kindly furnished the writer all necessary facilities. ^ ^urnisnea The apparatus used is shown with sufficient clearness in Ficr ,0" It is extremely cheap and simple, but fulfils its purpose as perfectTy as" could be desu-ed. and is believed to be entirely novel.' The axle To b tes d IS placed ,n an ordinary lathe, having as great a variety of speeds as possible. The testmg apparatus, as actually constructed, consisted of an oak beam. 6. about 4"x4" in size, and about 5 ft. long, carrying he com pound ever. LU, each of which multiplies the load applied about i timl or. m the aggregate. ,25 times. The yoke E encircles the axle and bea^ agamst the brass B underneath it. thus furnishing the necessary resTs" ance to the action of the levers and throwing the same load upon he ower brass i? as is imposed by the levers directly on the upper brass by transn.ss.on through the pin D, the latter being passed through Thole in the beam C The pressure was transmitted to both the upper and the lower brass by suitable iron blocks (shown in the cut directly above and below he brasses), representing as nearly as might be the ordinary fo"^ of the top of a journal-box. ^ ^ As thus constructed, it will be seen that the entire apparatus (when properly balanced, which is perfected by the light counLrpo se ml poised in unstable equilibrium on the axle A, and opposes no esisfance to motion in either direction, except such as arises from frict^n A v"^ heavy load maybe thrown on the bearings viz., 6000 lbs. Qc^ fbsoT ^1 ] 914 APPENDIX B. each bearing) for every 24 lbs. of load, W placed on the extremity of the compound lever, but the only weight thrown upon the lathe-centres is the dead weight of the apparatus itself, which was kept constant at 205 lbs. [Some further details are omitted here, and throughout the remainder of the paper.] When the axle A is caused to revolve, the lever C is held stationary by the platform -scale, and it is obvious that the pressure produced upon w. rt Fig. 302.— Apparatus for Te.sting Journal-Friction in a Lathe. the scale furnishes an exact and direct measure of the journal-friction It was found in practice that this pressure, varying from 10 to 140 lbs., with the proportions actually adopted, could be weighed with as much delicacy and ease as if it were a material substance resting upon the platform of the scale. Under a given load and speed of journal the friction produced, although it did not remain absolutely stationary, varied so very little and so slowly that the beam of the scale would sometimes vibrate slowly and gently between the guards (sometimes touching the upper one and again returning to the lower, but for the most .part touching neither) for 10 or 15 minutes at a time. On the other hand, when the brass was growing hot, by continuing the test for a considerable time the friction would continue to increase so that the scale-weight had to be continually moved ; but the change was never so rapid but that it could be easily followed and studied with the scale, with an absolute certainty that the friction existing for the moment was being accurately weighed. The difference in friction caused by temperature was found to be very great, but in the absence of arrangeinents for accurately determining the temperature no very close results as to its precise effect were attempted. APPENDIX B. 915 pends upon the use of the ni.^f. 1 success of this apparatus de- weighing t„e :^^ ^^^:^:::::^^z:z zT^ ■ '''"' '°^ - may be absolutely statical, no mo o o7 e bearin "Zf " T'' necessary in order to express a variation ^f f . ^ "'hatever being attempted to use sprina-scale. t„ ™ u °"- " "'^^ " ^^^^ variations of friction couwL "'^^''"l'^^ f"«i°n, with the idea that vibration which ^u dTn^^.^iirtW s t'u^ '"' r'"' '''"■ '''' sr f-r- 4-- rd'xru^t'e-rade :^-^^^ 1st. The determination of these resistanr^c o„^ . . the general laws of all friction Zl ,h! ^ °' '"vestigations of 2d. The coefficient nrl '" '"'="' '" '''^ experiments. imately, the journal-speed in feet per minutf. " ^ "PP™^" In the comparisons which follow, with vario.i, ^v„<.,- . ^ proximate formula, .?= 200C, has been used ^.T experiments the ap- efficients into pounds per ton ru!t , "'"" "'" '^'"'"^''^ <=°- of a railroad journal s^ne tenth ,h H ^ '°7'" *''"" "'^ '""'""er V4 jyjuiiid.1 IS one-tentn the diameter of thf- vvh/:»«i r •at the present time it ran^e^ from i !. ^" general, iiaving been the r^tl^ i . ZT ^^" ^ '^ ^^ '''"'^'' '^'^ ^^^^^ The apparatus heretofore described k mli^r, ^ i Cheap . the actual weights tTbe^ltdT^d Z Z' sl'JZT^t ^"' readily changed, and but little strain is produced^oH^e machri .74': 9i6 APPENDIX B. be used in any ordinary lathe and with an ordinary platform scale^ enough varieties of which can be obtained without special construction to Satisfy every requirement; it is positive in its action throughout, and no- delicate computation and construction of scales is necessary for its use;, and it admits of any desired delicacy of readings by the simple substitution, of more delicate scales. The common platform-scale of the shop where the tests were made was deemed sufficient in this instance, since the Stresses actually weighed ranged so high that the error of observation from lack of delicacy in the scales could rarely exceed a fraction of one per cent. The axle was set very slightly eccentric, so as to imitate the effect of an imperfectly centred wheel. This probably somewhat in- creased the coefficient, although very slightly at the low speed used. The effect of end play in distributing lubricants was imitated by the oc- casional use of manual force. It was found possible to do this in great degree, and it was generally found to have a slight beneficial effect upon the coefficient, but only slight; especial pains was at all times taken to« have the journal well lubricated before beginning each test. The jour- nals and brasses were fairly well polished by use up to their average con- dition in service, but no more. The tests made are shown in Table I. (omitted), and graphically in Fig. 303. Three different loads only were used in testing, corresponding as nearly as might be to the loads on bearings of a loaded car, empty car and truck alone. Each one of these it was designed to test a number of times at all the speeds which the lathe used admitted of. Whenever a bearing heated above 150° F. the tests were suspended and the bearings cooled, since no means had been provided for accurate measure of tem- perature. Each test, at any given speed and load, was contiimed for from 5 to even 30 minutes, when the bearings were cool, in order to be certain that it was a fair average. When the bearings were hot the tests were shorter, and the bearings were retained as nearly as might be at the same temperature by waiting a considerable interval between each test. During a test the resistance would generally fluctuate, slowly and gently, from 10 per cent to sometimes 20 per cent higher or lower than the average afterwards taken. This change was considered normal, and arose from no discernible cause. When the fluctuations were greater than this they were generally very much greater, and arose from heating of the bearings. APPENDIX B. 917 ^^^'^^^i^,t^~!Z2-:.r.szA-s^-s^^., \ Csq/0002) uqj.^sd-sq| - uoipuj a,xv 9i8 APPENDIX B. \ Note. — In all the diagrams below, as also in Fig. 303 giving results of the writer s tests, the Journal-speed has been reduced to its equivalent train velocity in miles per hour and the coefficient of friction to its equivalent in pounds per ton tractive resistance to the locomotive. Intensity of Load Per Sq. Inch indicated by Thickness of Lines. %M \hi.^Ytfv\. 1 1 II,- III _ 7F'"-- TT irn M \ 1 ill III .- "■ — - ■■■■■r;r.7'7:r<'//#^r}r,BBHBBBi r — — _, -' M'l. - -~ - ^^'"^ , » - "• ~ 'z ^'f. 5 iS* lj_! Z:'^ <^ .•-^*5"^" *■ .^ ■ ^r-:>-_!:; b«^--«B - ^^- lS-i--r 71- : :S3:!=S!:S:::-i-+ i::-^- — fr— ?r— ih-tH+-tf^ffi=B .Vel. Mites p«r hour. Fig. 304. , ^ .. _ = = ™«H.-'^ ' ojohrBtej^bjTBi^ : -^ ^jjjH- aujBi^siSijaa --^^^-: '^- -«;' -*_ ^ * "r "'^ •^' 2,fi_3-£_Jic: S ^ZxcssjZ;: \11\tAULC - -M, m^if It. ^ Li ^ /.c j_ ^2\'' J -_ i^ ...... s»^ V, ^ ^ s _ ^ — — y" I" ^ ^ ■" "^ /. S_i__''''._2:_ _^i ,„^mc: ■" ^ — 'i \^4!n _ "3^ — ^~ 11 ^•"tIT — '^ *""' ;*M /*"4^..-/0? . - -"^ AC '' « '/ ^^^^-^--'i , 4 ;,. .^ {' '^ i4- - ■ — Egjr = = — — -J--- --"'""■" "^~ r--*--"" " '" "T""" 1 o\iL fii M 1 lai? 1 1 1 gy 1 M g 21 2r __E___2L___£! Vel. Miles per hour Figs. 305, 306. Figs. 104-30^, Results of Mr. Beaitchamp Tower's Tests, ciriNG Effects of Higw Vklocitv, Variation of Pressure and Differences of Lubrication upon Coefficient of Friction. APPENDIX B. 919 Ve/. Miles per hour. creasing the pressure to ^ lbs. per «> in cau^d Tmri,^ • ^' "'• ""• '"' Thurston, test3 and an equally ™Led^*":rr„ Torr^testlT'''''" "' '"""'"' "" Deduction from the Tests. ( Tons of 2000 Ibs^) Initial FrMiot.-yhe. writer's observations under this head «er<. ., cepttonally complete, and the conclttsions reached were as follls " I. Fnct.on at very low journal-speeds of o + is abnormal I v great and more nearly constant than any other element of friction underf-Tv ng cond.ttons of lubrication. load, and temperature. It varies fomfs to 24 lbs. per ton (coefficient. .09 to .,2) for loads of from 30 to ^Ibs oTte:rp:::tr- ^"^'" -'- --^^^^^.o.^.^^^,,^^:^ 2. This abnormal increase of friction is due solely to the velocifv of r^olunon cont.nuing unchanged so long as the velocity is unct 1/ and returnmg to the same amount whenever the velocity is reduced to the same rate, barri,,. exceptionally slight variations, prJbab y due ^ ;^ % 920 APPENDIX B. differences of lubrication and temperature. It is not appreciably affected by the fact that the journal may be just starting into motion, or is just coming to rest, or is temporarily reduced to a velocity of o + during continuous motion. 3. At velocities higher than o +, but still very low, the same general law obtains. The coefficient falls very slowly and regularly as velocity is increased, but is constantly more and more affected by differences of lubrication, load, and temperature. 4. A very slight excess of initial friction proper (varying from \ lb. to 2 lbs.) could generally (but not always) be observed over that which continued to exist at the nearest approach to a strictly infinitesimal velocity which it was possible to obtain. This difference was, by analogy, ascribed solely to the fact that the lowest continuous velocity attainable was nt)t strictly infinitesimal, and the final conclusion was drawn that — 5. There is no such phenomenon in journal-friction as a Jrtction of rest, or a friction of quiescence, in distinction from (i.e., differing in amount from) friction of motion at slow velocities, and due to the fact of quiescence. Consequently, the use of such a term, although con- venient, is scientifically inaccurate, in that it ascribes the phenomenon to the wrong cause, and to a cause which is not necessary for its exist- ence. The fact that friction of rest, as such, appears to exist, is due solely to the fact that no journal or other solid body can be instantly set into rapid motion by any force, however great. There must be a cer- tain appreciable instant of time during which the velocity is infinitesimal and gradually increasing. This interesting fact, which is believed to have been here observed for the first time (no other apparatus being known to have been used suitable for determining it), was determined with great completeness by many tests. Very slow motion could be produced at any time by re- volving the driving pulley of the lathe by hand when geared for a slow speed. With a little experience, the weight on the scale-beam could be placed in advance at a point which would be a trifle less than the initial friction proper, and (when properly placed) it would barely lift when motion first began, and then have to be moved back a notch or two only, to weigh the friction which continued to exist indefinitely. Similarly, when a test at comparatively high speed was about to be concluded, the scale-weight would be placed to measure the same pressure, or a little less, as existed in starting, and it was always found to indicate in stop- ping substantially the same friction as in starting. The same test was made by interrupting tests at speed, so as to give a continuous motion. APPENDIX B. 921 .i)ut to suddenly reduce the speed to o +. These tests were repeated -again and again, with practically identical results. Comparing these results with others, they agree very closely indeed with the writer's conclusions from the results of his gravity tests, as will be seen below : " Initial" Journal-friction (i.e., at velocity of o +). Writer's conclusions from journal tests, above, say. . 19 to 25 lbs. per ton. Wriier s conclusions from gravity tests of rolling-stock (see Trans. Am. Soc. C. E., February, 1879), "at 'f^'" 14 to 18 •* " «' Prof. R. H. Thurston ("Friction and Lubrication," page 175). W. Va. oils .'. 22 to 28 " « « Prof. R. H. Thurston ("Friction and Lubrication." page 175). sperm ; j^ ^^ ^8 " " «« Prof. R. H. Thurston (" Friction and Lubrication " page 175). lard \^ ^^ ^^ ^2 " « •• Prof. Kimball {Am. Jour. Sci., March, 1878, or Fr. and L., page 186) ^^ ^^^^ „ ,. „ In addition, it may be noted that the writer has taken pains to observe with some care at various times that in ordinary service no railroad cars can start themselves from rest, nor can they, in general, be started without the use of much force, on a grade of .7 per cent (= 14 lbs. per ton. 36 ft. per mile), but that they will generally (but not always) start of themselves on a grade of i.i to 1.2 percent (= 22 to 24 lbs. per ton. 58 to 63 ft. per mile), in- dicating an " initial" friction of 20 to 24 " " « These results agree wonderfully well with each other, the averages running 18, 16, 25, 20, 18, 25^, and 22 lbs. per ton. the average of all bein- 18.0 to 25.0 lbs. per ton. or 20^ lbs. as the general average of all This corresponds to the accelerating force of gravity on a i per cent (52.8 ft per mile) grade, and that being also the lowest grade, by universal rail- road experience, upon which cars can be relied on to start off from a state of rest with little or no assistance, the correctness of this coefficient may be considered as well determined.* ♦ On a 0.7 per cent grade (14 lbs. per ton) the writer found it impossible in several instances for six men pushing, two with pinch-bars. to start two loaded box cars into motion. In no single instance out of over sixty did cars start "Without some assistance. \ ^\:i\ 4 Iff ] 922 APPEKDIX B. Normal Coefficient of Journal-friction at Ordinary Operating Veloci- ties. — Certain general facts seem to be clear from all the various tests here considered : The first of these is, that (i) the character and completeness of lubrication seems to be immensely more important than the kind of the oil, or even pressure and temperature, in affecting the coefficient. This is very clear from the diagrams (Figs. 303 to 307) showing the various results. Mr. Tower found that lubrication by a bath (whether barely touching the axle or almost surrounding it) was from six to ten times more effective in reducing friction than lubrication by a pad. By this method of lubrication Mr. Tower succeeded in reducing the co-^ efficient in a large number of tests to as low a point as .001, equivalent to only 0.2 lb, per ton of tractive resistance, and the general average in the bath tests, under all varieties of load and speed, is given as only .00139 or 0.278 lb. per ton, against 1.96 to 1.95 lbs. per ton with siphon- lubricator, or pad under journal. These results are very far below any heretofore reported, as will be seen from the following general average- of results; not considering now the comparatively minor variations pro- duced by ordinary working differences in temperature, load, etc. The normal journal-friction, under favorable conditions, deduced from various series of tests, may be summarized as follows for velocities- greater than 10 miles per hour, or 90 ft. per minute, journal speed : Beauchamp Tower, bath of oil . . , 278 lbs. per ton*. '* ** pad or siphon 1.9 Thurston, light loads 2.75 ** heavy loads 1.75 Wellington (gravity tests of cars in service), light loads .... 6.0 heavy " ....3.9 *• direct tests (as shown in Fig. 2) \ ^'^ ' 3-7 Thurston, inferior oils (Fr. and Lub., p. 173). \ ^' < 30 Morin, continuous lubrication 6.0 to 10.8 These discrepancies, especially as they are accompanied by many minor ones, are very instructive, as showing that the character of lubri- cation is the great cause of variation of coefficient. Resistance of Freight Trains in Starting. — It will be seen in Fig. 303 that the abnormally high coefficient of friction at starting continues during the period of getting up speed, and thus constitutes an extra tax upon tractive power for some little distance after getting under way. << «< (« <« •« APPEiVD/X B. 923 The following conclusions may, it is believed, be drawn (already sum- marized in par. 635). v ^ n Effect of Temperature on Coefficient of Friction.-So far as can be estimated, the results agree very closely with Prof. Thurston's formula that the coefficient increases as the square of the increase of heat over 90 to 100 F. at speeds under 12 miles per hour. Effect of Load per Square Inch of Bearing on Coefficient of Friction - Comparison of the results obtained by the writer, and by Messrs Thurs- ton and Tower and others, as shown in Figs. 303 to 307. develop this curious fact : that while the results differ quite widely, in fact by several hundred per cent, in what may be called the typical or average co- efficient of friction, they all agree quite closely in finding that the effect of increased load within working limits, is to very materially diminish the coefficient. Mr. Tower, in fact, goes so far as to state, as one of the results of his tests, that it almost seemed at times as if it was approxi- mately true that the absolute loss by friction was entirely independent of load, the coefficient falling almost to half when the load was doubled But It seems plain, from the diagrams given herewith, that this result is only true on account of the unprecedentedly low coefficients which he obtained by his very perfect lubrication. Inspection of the diagrams will show that the general law of variation from increase of load is not mate- rially different in the different tests, despite the wide variations in the average coefficients. ^ Effect of Velocity over Twelve Miles per Hour.~^\^^. 303 to 307 taken in connection, seem to show the following : '• w^Vu ""u'^ ""^ ^'''^^'' journal-friction is 10 to 15 miles per hour ^ 2. With bath or other very perfect lubrication there is a verv slight increase of journal-friction accompanying velocities up to 55 miles per hour (Figs. 306 and 307). ^ 3. With less perfect lubrication, as with pad or siphon, greater velocity ,s as apt to decrease as to increase the coefficient (Figs ^04 .0; and 307). The latter being more like the ordinary lubrication in railroad service, we may say. without sensible error, that the coefficient of journal- fnct^ion IS approximately constant for velocities of 15 to 50 miles per This has been the assumption which all investigators of railroad fric- tion, to date, have been compelled to make, and it is, in some respects fortunate that it proves not far from true. Higley Roller. Journal Bearings.~The direct tests of this apparatus confirmed exactly the correctness of the writer's previously stated con^ '924 APPENDIX B. elusions, that the Higley bearing was nearly as efficient as theory would indicate in reducing initial friction, but loses nearly all of this advantage under speed. [The paper was followed by a long discussion, which it is necessary .to omit, bringing out many further points of interest.] ) APPENDIX a 92S- APPENDIX C THE AMERICAN LINE FROM VERA CRUZ TO THE CITY OF MEXICO. F/A JALAPA, WITH NOTES ON THE BEST METHODS OF SURMOUNTING HIGH ELEVATIONS BY RAIL. [Read by the author at the Annual Convention of the American Society of Civil En«. neers, July 3, 1886. See Trans. Am. Soc. C. E., Nov. 1886.] The line described in this paper, and illustrated in the accompanying maps and profiles, is one located by the writer, as consulting and after- ward chief engineer, from the Port of Vera Cruz to the city of Mexico vm the city of Jalapa. being a parallel line to the existing Mexican Rail- way—the first railway built in Mexico— in the sense of connecting the same termini, although following a very different route and of a very different character. All the features of interest and of difficulty, both in the line here de- scribed and in the line of the Mexican Railway, are confined to the mountam grade by which the necessary abrupt ascent from the level of the sea to the level of the plateau. 8000 feet above the sea. is accom- plished. Once on the plateau there is no great difficulty in going almost anywhere with very light work ; many high mountains being scattered around, even on the plateau, but disconnected, with flat lands^etween The elements which appear to make the mountain grade of this line particularly worthy of description are these : J^trs/. It is believed to be by far the longest continuous grade-line ever located; 116.9 kilometres (72.64 miles) having been located on an unbroken 2 per cent grade (105.6 feet per mile), rising in that distance from elevation 600 4 feet (183 metres) to elevation 7923.3 feet above the sea (241 5 metres). The accompanying plate (Fig. 232) shows graphically the extent of the contrast in this respect with some of the other great inclines of the world. Secondly. It is believed to be on the lowest rate of grade, by about 2 per cent, ever successfully attempted for accomplishing' within a limited distance, either by a continuous grade-line or otherwise, a rise ■926 APPENDIX C. APPENDIX C. of over one half as much as was attained on this line. The grounds for this belief also are shown in the accompanying plate (Fig. 232). Thirdly. The line is believed to be, by probably one half at least, the cheapest line per mile which has ever been actually located, with equally favorable alignment, for attaining within a limited distance as much as one half the rise actually attained by this line, either by con- tinuous or broken grade-lines, on any rate of grade. As for this. Table 190, Figs. 309 and 310, and the general knowledge of engineers are the only evidence that can conveniently be appealed to, or which it is worth while to attempt to present. Finally. It appeared that the manner in which the line was obtained might have a certain instruction and encouragement to those who may be dismayed, as was the writer, by having similar problems of unusual difficulty suddenly thrust upon them, and it was also desired to give, in connection with the description of the line, certain conclusions which the observation and experience of the writer has indicated — not only on this incline, but on eight or ten others of considerable rise, which have been located or relocated in part or whole under his supervision, aggre- gating over 24,000 vertical feet — in regard to the most advantageous and economical manner of dealing with great inclines, under which may be classed anything exceeding 1200 to 1500 feet of vertical rise. It is one of the unfortunate features of the department of engineering to which this paper refers — that of laying out railway lines to the best economic advantage — that a mere description of a located line has usually little technical interest or instruction, since it is ordinarily im- possible to so carefully describe any line on paper as to enable even an intelligent impression to be formed as to the real character of the work. If the grades and work be light, it may be because the line was well laid out, or it may be simply because there were no serious natural obstacles in the way. On the other hand, if the grades and work be heavy, it may be due to bad engineering, and so discreditable ; or it may be due to the existence of gigantic difficulties, and so an evidence of skill. It is but natural, however, that the magnitude of the natural difficulties to be overcome should in general be regarded as bearing some nearly constant ratio to the magnitude of the works constructed to overcome them ; and hence, that, even when the construction of a very costly line may have been, as a matter of fact, an avoidable extravagance, due to lack of skill or foresight, the very magnitude of the works gives more instead of less reputation to the line as an engineering work. Only in the comparatively rare cases when two independent alternate 927 lines exist between the same termini, is it possible for the engineer to tind m prmted descriptions of located lines, however perfectly mapped any rational basis for intelligent judgment. The present happens to be one of the cases in which this is possible, owing to the existence of the parallel Ime before mentioned, but in order to avail of it, it becomes necessary to enter somewhat into what would otherwise be an invidious —because unnecessary-comparison with the parallel and previously constructed line. The writer feels the less embarrassed in doing this • as owing to the checkered history of the line, no one engineer can be held responsible for its character, and there were certain circumstances tending to impede entire freedom of choice and proper investigation. The whole mterior of Mexico is a vast plateau, at an elevation of 5000 to 9000 feet above the sea, bounded by an abrupt escarpment from which the descent to sea-level is almost immediate. The edge of the plateau is higher and sharper on the Atlantic than on the Pacific Coast, and at no point on either the Atlantic or Gulf Coast is it higher or sharper than directly in line between the capital of the country. Mexico, and its chief port. Vera Cruz. Here two stupendous natural obstacles, the Pico of •Orizaba on the south {i-j^Zn feet high), and the Cofre, or •• Box " of Perote (12,500 feet high), both of them described in physical geographies as volcanoes, although both are temporarily extinct, and the two con- nected by a ridge over 10,000 feet high at its lowest saddle-combine to forbid a direct line inward. Orizaba is one of the three mountains in Mexico covered with per- petual snow, the other two being Popocatepetl (17.884 feet) and Ixtac cihuatl (15.705 feet), overlooking the valley of Mexico. These however start from a plain 8000 feet high, whereas Orizaba starts practically from' sea-level on the coast side, making it in that sense by much the hi-hest mountain on the North American Continent,* and among the highest in the world. Its snow-clad peak is visible 60 miles out at sea. long before there is any other evidence of land, and with the morning sun shinin-on ■It IS a very striking sight. Its last violent eruption was in 1546 soon after the Spanish conquest, although it now occasionally throws out smoke. Only one or two men have ever ascended to its crater, the first one having been Lieutenant Reynolds. U.S.A.. in 1848. The line of the Mexican Railway passes to the south of this mountain, as shown in Ficr 308. *• \ * Mount St. Elias, in Alaska, in a possible exception, being only about 30 miles mland and its height variously given as 14.970. 16.900, 17,850, "oyer .10,000 (U. S. Census Report), and 19 500. 928 APPEiYDIX C. The Cofre, or " Box," of Perote (so named from a cylindrical basaltic needle about 300 feet in diameter and 300 feet high which caps the mountain, like a box laid on its peak), although formerly one of the most active volcanoes in the world, and classed as still active, is perhaps per- manently extinct, its last, and probably also its greatest, eruption having been to form what looks to be, and is in fact, a frozen river of lava, shown in Fig. 309, extending to and running into the sea 50 miles distant, filling up an enormous barranca or deep gulch in the process, in a manner which was very convenient for subsequently carrying the line over it, as; may be seen in Fig. 309. The natural variations in the width of this gulch have caused lakes and frozen " water-falls" of lava, which makes it difficult to believe, as one looks up the slope upon it from some com- manding point, that the mass is not still flowing, making it a unique and impressive bit of natural scenery. Vessels have been frequently wrecked in the toe of this flow where it enters the sea. It has still hardly any deposit of sand, soil, or vegetation on it, that and other facts evidencing that the flow is geologically very recent, not antedating much the historic era. , Around the north side of this mountain, and directly over this lava flow, the line here described passes, as shown in Figs. 308 and 309, being about sixty miles north of the Mexican Railway line at its greatest diver- gence, the two beginning to come together again very soon thereafter. The summit of Perote is just below the limit of vegetation and of perpetual snow, and it is very easily ascended on horseback to the foot of the " cofre," or box, that fact alone being an evidence to the engineer of how different the topography of its slopes must be from those of its southerly companion. Evidences abound of tremendous flows of lava in. remote geologic times, which are now covered to a considerable depth with soil, and in the kind of pocket formed between the foot-hills of the two great mountains, in which lie Jalapa and Coatepec, the detritus of ages has accumulated, including probably great amounts of volcanic ash,, so that no rock exists over large areas, as was afterwards discovered, ex- cept in isolated points. Cortez followed this route on his first invasion, as did General Scott 328 years later ; but from an early date after the conquest of Cortez two leading routes have existed between the interior and Vera Cruz, follow- ing substantially the two railway lines here described, one through Jalapa, rounding Perote to the north, and the other via Orizaba, rounding the mountain of that name to the south. The northerly line was first con- structed, and over it, for 300 years (between 1521 and 1812-20) passed \ REDUCTION RATIO 16:1 > .^A b 3 3 A/ ^y^^ %,^^ # s 00 CJl 3 3 CT Q) O >> ABC cdef ^a ^71 FGHIJKLM jklmnopqr 3^:^ IJKLM nopqr CO -, J^Z OPQR uvwxy OPQ uvwx N en ^ ^ •-*— 1 M C/) Kir: »-'-4 00^ uvw 2345 OOM a>x VO ^-< O OOM <^ o •^; > ej V. 4ii> 3 3 > CD o m CD O OQ i CJl3 ^ ^ o o < X N , X -< ^^^ r»A Ul o 3 3 .« ^ '^. '^. oSi 8 3 3 ^<^ .<<^. r^pi?i?lS|5|;|- •CRISIS o 00 b Ho & 2.0 mm *eCDCFGHIJKLMNO»WSTUVW«yZ abcdpfBhtittlmnopgrstuvwiv/ 12.34 S6 7990 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 39 O o "D m -o OL,"0 X TJ ^ "CO = > O ABCDEFGHIJKLMNOPQRSTUVWXYZ ^ ^ abcdefghijklmnopqrstuvwxyz 2.5 mm 1234567890 ^ v^ ^^ 3 o 3 3 §8 |i n2 ^1 00 rx Is 11 i Ul 3 3 > o m tt) CD OQ ^ 0^3 Z --jO O 00^ no Otn ^ $ CZ X Nl '*^ ■>c m ■■< [The route shown for the Jalapa line after reaching the summit was selected (i) to reach Puebia, the second dty of Mexico ; (a) and chiefly, to nin throu^!i the heart of the pulque district between Puebia and Mexico ; M tj) 'o connect with the Mexican National system at a favorable point ; and (4) with the idea that a line might be run southwardly from Puebia at some future day. Had the purpose been merely to reach Mexico in the most direct way, as with the Mexican Railway, the dotted line marked " Natural Route to Mexico" would have been followed, or possibly one farther to the North. It was an error of judg:ment that the main line of the Mexican Railway was not carried through Puebia, as might have been done with perfect ease, with equally favorable grades and moderate sacrifice of distance, with less total line to construct.] It -I t 'a ^ ' '^' ^i - y > LJ * i U t V MlUmrit^t ftklMKi •» ZlMlLUkCAM. aTAIN ^^'l. iICO. x; iANJuMNlMkuMOl corteof lua«« t^JtA iMBiice ivco~ Oi ^^ 4s>- ^M -§ til" i 1 1 J 1 v-r"? W\rm mt »m ttm »m mm TK Jik a* a* 9« Jt> Jm iJ< M* «M ,«• Ji* m» ttm mm» m lim tu «• fJi *^» 11* SU~M M« < 5 ^- )\ « Map of Region between Vera Cruz and the City op Mkxico, showing the Line of the Mexican Raiu WAY aj?o the Jalapa Line as originally sketched. AND IN SUBSTANCE AFTERWARDS LOCATED, BELOW Pe- ROTK. SVrc,. ■"^^# ■£■ '^K^.-^t^?<»rui!9 '^'%/M|i .■!,)■ f.. >i'^ / ^y J y*c _•&•»•« *.«i.>.t.r>» *.C REDUCTION RATIO 12:1 ^^#. > ^ "5.; "<• (Jj -P^ CJl ai 5 • 3 31 > Q> CD ABC bcdef m ?Q o Q-Z! 5:m (D OqT. 3x 3 r- ^3^ a^3 z i o ^0 STUVW Z12345 RST stuv ^ c= OiX X < OOM N < X M a'' A^ ■V; a? > m o 3 3 K, > 8 3 3 t.^^ < V & fcp gp ^fp ^Sr O K3 00 o^ 00 b 10 en 1.0 mm 1.5 mm 2.0 mm ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghiiklmnopgrstuvwxyz 1 234567890 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyzl234567890 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 Aa '^. '^. '^. ^%^ ^^f^ ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 2.5 mm 1234567890 V ^ ^p fo ^fp ^c. m o o ■o m -o o ni 1 OLl"o > C CO I TJ ^ 0! 3D O m •^. yj^. en 3 3 or O >, «l •S-o ?.rn Is ■D p M > 3 X °i ?^ fvoP (T>X oorvi ;s o5 ^m^ l^, IV'' if ■y -^"^ [The route shown for the Jalapa line after reaching the summit was selected (i) to reach Puebla, the second dty of Mexico ; (2) and chiefly, to run through the heart of the pulque district between Puebla and Mexico ; (3) to connect with the Mexican National system at a favorable point ; and (4) with the idea that a line might be run southwardly from Puebla at some future day. Had the purpose been merely to reach Mexico in the most direct way, as with the Mexican Railway, the dotted line marked "Natural Route to Mexico" would have been followed, or possibly one farther to the North. It was an error of judgment that the main line of the Mexican Railway was not carried through Puebla, as might have been done with perfect ease, with equally y^ favorable grades emd moderate sacrifice of ^Tll •5v--' fJ distance, with less total line to construct.] 9^A >^ 2=1 liMllCO '^^^M ^n,m IS" «N JuM tllMiUINOt CO 1nt*r»t \W//» gEtyi«*»y> *fc ws^W'mm mm. : 5 • *• mmmmm .*- I « V ^»:^^^^:^^<^.^■^?^ * « '{{/,. I li ""''''*^^25^ An 1_4 M* //»' •«,« ll« 'cU~l«* M* •• •• 7| M •• • Jalapa line after reaching; the summit was selected (i) to reach Puebla, the second liiefly, to run through the heart of the pulque district between Puebla and Mexico ; (3) to connect with the Mexican National system at a favorable point; and (4) with the idea that a line might be run southwardly from Puebla at. some future day. Had the purpose been merely to reach Mexico in the most direct way, as with the Mexican Railway, the dotted line marked "Natural Route to Mexico" would have been followed, or possibly one farther to the North. It was an error of judgment that the main line of the Mexican Railway was not carried through Puebla, as might have been done with perfect ease, with equally favorable grades and moderate sacrifice of distance, with less total line to construct.] hilamfh^rg ZlMltykCAM. iTtiXM ^f^, for SU^fflv'W/|il? Map of Region between Vera Cruz and the City op Mexico, showing the Line of the Mexican Rail. WAY AND THE JaLAPA LINE AS ORIGINALLY SKETCHED, AND IN SUBSTANCE AFTERWARDS LOCATED, BELOW Pe. ROTE. JuMlllMlUWOt r/MV»( # SUN cy ..{r^iia^Bu'''''' ''''' 'I'..'. " ^^ •i;'."i« v->' ^f^^^o CO <^ M /•i^ .:/»i <»ilH»..»»r^#^ «•(■ APPENDIX C. 929 vj^t sums of silver and gold, practically the entire product of the Mexican mines amountmg ,n the aggregate to $3.ooo,oo still ,-oiia^ • I-.- .. ° "iguvvay ^as the leading roads are still called in republican Mexico), was suffered to fall into deL It had onginally been paved, guttered, and curbed for the entire dTsLi from Jalapa to Vera Cruz, some 73 miles, and from Jalapa upThemoun tarn a fine macadamized road, likewise curbed and guttered existed a.^d" still exists in fine order, having been recently repaired.* ™^' """ Witliin fifteen or twenty years after the abandonment of the north eriy highway, as early as ,837, the movement for a railwaj between vta" Cruz and Mexico was begun by Don Francisco Arrillaga and ve^ nat urally. but very unfortunately, the route which had byXttte become ^e^y-lfolt^al-^airra:^^^^^^^^^^^ from which the ascent was abrupt and sham to ihT . '"0"nta,ns. u.uit. for a railway line, but Ls cVu^dTT^e^'^^^^^^^^^ .unrnii^:„rrnrn,:^^ry\TeSa:i::f™\^^'' "T '^■ instrumental in pushing the project through tr.i- "'^'"''""y tat,>n l„^M „f .1, . project tnrough to completion, having then "bl^^dti:' oVe: STnt^^^^^^^^ ^ -- -- -efr r cott' atrer- "'"-- ^^ "^^ -- Cre^rrHVat cott. an American engineer, arrived with a staff of assistants ,7' , member of which now living, the writer beli:^ is Mr awrmr m" Unzaba line, that v,a Jalapa being intrusted to a Mexican engi- nl, or\f „;':7esrr:re;Vhe VS?r^ ahly Claimed to he "^Xl!^:^::'^^^ ^^^ .^^ ^"x - --on- order, and as showing .he fine quality of ,he Mexican L'h "' '" 59 930 APPENDIX C. I ^^P^ neer, Don Pascual Almazon. According to other accounts, a commis- sion of engineers examined both lines. If the first was the case, it is less surprising that " on comparing the separate surveys," as the history of the road states, that by Orizaba was finally adopted, on the grounds, first, that there was more traffic to be secured on it (which is rather more than doubtful, although the local traffic at best is an insignificant ele- ment), and secondly, that " notwithstanding it requires great and costly works, the line presents greater facilities than that by Jalapa, la/iere the larger number of ravines and the harder nature of the soil would have re- quired much heavier outlay" A greater mistake than is contained in the italicized part of the quotation could not well be. Colonel Talcott's estimate of the line was $15,000,000, but nothing more was done than to build about ten miles of surface line out of Vera Cruz, until August, 1864, when the militaiy necessities of the Emperor Maximilian led to a real beginning and prompt pushing of the work under English engineers, and by an English company, which still con- trols it. Beyond a statement that the resumption was "after rectifying the plans of Colonel Talcott," the official history contains no record of the second examination of the whole question of route, which was in fact made, although how thoroughly the writer cannot state. By 1867 the line was opened from Vera Cruz to Paso del Macho, 47^ miles, and from Mexico to Apizaco, 86|^ miles, the rails for the latter being hauled by wagons an average of 200 miles inland, at enormous cost — a hard condition imposed by the Mexican Government. A third change of engineers took place about this time, while the heavier parts of the work were still unexecuted. In 1868, the Puebla branch, 29 miles, was opened, the rails for it having been hauled in the same manner. In 1870 the line was opened to Atoyac, 54 miles from Vera Cruz ; in 187 1 to Fortin ; in 1872 to Orizaba, and on the last day of that year the entire line was opened with great ceremony. Shortly thereafter, in 1874, Don Ramon Zangronez, of Vera Cruz, succeeded in getting a branch line to Jalapa well under way, and in having it assumed by the Mexican Railway, which completed it, as shown in Fig. 308, in May, 1875. It is operated solely by animal power, being probably by far the longest horse railway in the world. Its grades are very severe (10 per cent), and its curves of ordinary horse-car radii. It is laid for a great part of its length along the old camino real, and exhibits the same trait as the main line of the Mexican Railway to the foot of the mountains — that is, it runs obliquely across the drainage lines, thus materially increasing the difficulties of both lines, but making I APPENDI X C. Q^j the lower pan of U,e o^sce^rhLtlr h^cldT^^rn'oTr^" °' ^ It seems impossible that an ascent frnn, "7°"'^^'""«ion of the route. The main line thus constructed is still one nl ,h^ costly in the world. Its cost wa, ■;,LT ^ "'°'' ""^^"'^^ *"<' First, the political cond,Uo„ o th'cou UvJir""'' '^ '"^ ^^"^^^ = that it no doubt added much to the cos7' Id "'"'.? """^ '""'*^'' quiremeut that construction, includin7trLck 1 ^ '^ "'^"''•^ ^^- both ends at once necessitatinc, Vh ^ faclc-laymg, should begin from hauling rails over ;;e a rroalsf:^^^^^^^^ expense referred to for In all some 15,000 tons of ^^1— J u T '° *^''''"° ^"-^ ^"ebla. believes, of soL S80 Per to^rorti ^to s^otf sn:,r-'''ir'A" the other hand, there was I.ffl^ a- . ^^ ^ 55i,2oo,ooo in all. On n^ost Of the sha. ^^^^tX^Z:^ 'plidTn^r""^' nommal cost of the line was as neprWac ^ u 1^ ^ ^^^ S^^oss this by one half, we shall n^;.^ aTan ; eX^frr ,^''T' abnormal causes tending to increase cL, Tf? If ^"^" °' "" Jalapa horse railway and the smTamour/ ^f"'' n '°'' '"^ '^°^' °' "^« 8iO cars), leaving $20,000,0^ to represent tjTfT""'' ^'' ^"^'"^• of n,ain line and 29 miles of branch Of ,, ."'\^""^' ~« «' ^64 miles del Macho and Boca del Monte alone som: t T"" '""""' ''''^ dimcult or costly work. The remaining rLSsTsh^h't' '" I"' T" per cent grades, which latter are quite L^^^^^^S' "°^''' """ '* nom'lnV^lt'LfolC: '"'"''"" ''' ^""^' <^°^' ^^'^ « ''a.f the 223 miles light work, at $40,000 per mile «» _6o miles very heavy work, at $.84,667 per mii;. '.'.'. [,'lTr,'°°° •* *. 000, 000 283 miles in all, at $70,670 per mile. . . ^ $20,000,0CX> out oT Ve';: %:t:Tstrz:T: ""t "^ ^-^ =^^^^^- ^-^ - -"«« are increased tH pe cent Tc find", ?^'"' """' ^''°"'>' '""-f'- is entirely unbroke^for the ^^^ 3 m Ues 0"^:° a^nd'^ T\ "'"^" '"*^^ o.,er points on the ascent. Curves as sl^s 335 " 'tTet" d "' (16 degrees 30 minutes and 17 detrree, .r, ™- » . ^' '•"" '^"^'"^ eight reversed curves of these^adfof et succeed'tTa T^'u'"" "^ °^ any tangent between them, and ^i^^o.^:^^^::^^^^^ I' 932 APPENDIX C. \ I the virtual gradient fully 6 per cent. Fairlie engines are used to operate this grade between the summit at Boca del Monte (107 miles from Vera Cruz) and Cordova. The remaming 157 miles to the city of Mexico, as well as the lower and easier part of the mountain grade (which, however^ has i\ to 3 per cent grades, mcreased by unreduced curvature), is operated by American engines. Very naturally both the freight rates and the expenses are fabulously high, receipts ranging from 10 to 12 cents per ton-mile and as high as $8 per train-mile, expenses being from 50 to 60 per cent of receipts. To show how radically the cost and revenue from the operation of this line differs from anything with which we are familiar, it was calculated in 1883 that with the Mexican rates the- New York Central would earn $27.25 and the Erie $28.50 per freight train-mile, and their total freight earnings would have been in one vear $297,025,000 and $244,300,000 respectively— $168,000,000 more than the Central's whole capital account, and $93,000,000 more than the Erie's. There are fourteen tunnels in all on the line, none of them, however^ very long, and about as many viaducts. The grading is, for miles to- gether, almost wholly rock, and the work, as a whole, can only be de- scribed as Titanic, so that it is small matter of surprise that almost every one who writes about the line describes it in much the same terms as. does Mr. George William Curtis in a late number of Harper s Magazine (February, 1886), who chances to be the last writer whose remarks in. respect to it have come to the writer's knowledge. " If it is magnificent scenery that you seek, here at hand, with no inter- vening ocean, is the railway from Vera Cruz, 260 miles, to the city of Mexico —a marvellous feat of scientific skill, crossing the mountains at a height of 8500 ft., and bearing you through every climate, amid unimaginable luxuriance and brilliancy of vegetation, changing into temperate hues of hardier growths, with awful mountain abysses between and snow-clad peaks beyond against the deep blue sky." The line located by the writer rises to almost precisely the same height of summit as the Mexican Railway, and is as nearly as may be of the same length, but in almost every other detail stands in broad con- trast with it, thus : Grade. — Continuous 2 per cent (uncompensated) against a broken 4 per cent (uncompensated) ; including the effect of curvature or of compensation there- for, 2.6 per cent against 6 per cent. Curves.— Curves of 2S9 ft. radius (19' 50 ) connected by minimum tangents of 40 metres (131 ft.), against 16° 30' to 17° 40' curves (325 to 350 ft. radius) con- nected by no tangents at all for many successive reversions. The writer con^ REDUCTION RATIO 16:1 CO J?A r??A Ss^ %* '*^. v/ CO 00 ■t^ o CJ1 CJl 3 3 3 3 3 3 > Q) CD 0) a- o >> 0) O ^o o m 00.0 =.m CD CD 5:m do'X 1? HIJKLMN nnopqrsti IJKLMN hijkimn 123456 OPQRS jvwxyz OPQR jvwxy OPQ opqr i789( N en (5^ 00 3: < -H CT>X s c oorsi a^x X < o OOM o X M A*?' A> '^s^-«, >. */ M O O I O 3 3 8 ^<^ ^ I » K 2.0 mm AaCOCFGHIJKlMNOPQRSTUVWXVZ atx detfh t{klmnopqrstuvwRy; 1 ? 3456 ^90 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghiiklmnopqrstuvwxyzl234567890 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 -cb^ 2.5 mm ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 21 ao o o TOEJJ "O Oll"0 >C w I Tl ^ m 31 O q ^1 '^ ?o ^^ & »— N> CJl 3 3 3 3 at fi 11 si h 3x |i is << :o top o^x ^-< OOM VO o '4^ CJl 3 3 > OD 0,0 o m X < N g 'V ^^' .^i JO. M i ,/^p wsm^j ■T'/r^.^Jii U^ -X 1 \^ / \ -J poCK ./^ Cv\ .^' [The degrees of curve given are for ao-metre chain (chord of 65.6 somewhat more than two thirds of the degree of the curves by the (100-foot chords). Profile of this line is shown in t ig. 310.J ft.), and are foot system fj^ fit ^■"». Tfer- '~^'' :« -^^^ W^l ^^/' r- \ "^^ i\:. r^W' ^ Sec- tion. LoCATluN OF SbCTIONS. Lr.s'gth. Increase by Develop- ment. By Air-Line from Beginninf; to End of Section. 8.5 kilos. 7.5 " 7.9 " »3 9 " .at S " By Located Line. 19. u kilos. 15.0 '• 20.5 •• 54-3 " 54.5 " 9 8 7 7-8-9 Summit to end of ra^ged-clifT work End-section to middle of third horseshoe curve luo to 324 too to 300 100 to 260 Middle of third horscsho? to middle of flat, opix>site Jalapa Air-line from summit to Jalapa loo tn 238 100 to 354 s:^ 1" ' 1 *^ 1 M ' ^ I KILOMETERS. .»Ula 14 1 MILES. \ P; If, ^ n" r-\ ). \, '^i /i> ~t \\\' ^ here fo below JSuap^ Maferiaf aepears tote sarm ro a grmat Def^ _ Wss/iea down from Mou/rta/n Skipes. V^_ « J^J 7y^'^ W \ir^ -O/ ,i Fio. 309. MEUMUmr LOCATED l/AE ^ LAS Visas SuMimr TO JAlaj¥<. Scale t-t»0OO-i>eauced from Fiela Sheats to Sca/e oFt-ioooo-aaHafeefperlncfi. AM.WaUmglon, Ctiief engineer . JalK SBIiott, atiefof/^rtf. vSa^i^ L^js(V4=AS. Section 9. Sections. Section 7. V REDUCTION RATIO 12:1 CJ1 3 3 O >> OD CD IS CD o m OQ ^ o O en X <: N ISI ^: > ''e %o- ■D 39 m o CO CO I C/) > 30 o m H O- ^^: •^^ ^ > m o 3 3 ^o V rp A^ > A^ ^^ 8 3 i 6^ .«' ^' ^^ 'fc? ^. fo fp NO o rfEi5|=|r^|-|- 00 c> s ig io |t^ a: '^: > ^^^ k^' 1.0 mm 1.5 mm 2.0 mm ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghi|klmnopqrstuw»xyz 1 234567890 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghi(klninopqrstuvwxyzl234 567890 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 2.5 mm 1234567890 4> ^* fp ^1y m H 30 O O ■o m Tj > Ceo I TJ ^ ;^Ooo "CO 5 m 30 O m '^A. ^^ ■^ ■4^ ^O H-» tS3 cn O 3 3 3 a» c a> o >> O" .c^'O 2.rn ■^o 3i 3i IJKLMN nopqrst IJKLMN nopqrst S "0 <2 |o r^c f^ C/5 **< o^x cop: cn< ■»j-< 00 Nl o o^x OOM 8 '«•, [The degrees of curve given are for 20-metre chain (chord of 65.6 ft.), and are somewhat more than two thirds of the degree of the curves by the foot system (loo-foot chords). Profile of this line is shown in Fig. 310.] Section 8. jfor ao-metre chain (chord of 65.6 ft.), and are If the degree of the curves by the foot system [ne is shown in Fig. 310.] nxm here to below JkLAPm^ Material aepearr to be £arm 10 s great Depth _ l^as/tecf down frotn Mountain SJofios. Fio. 309. ^ J'MJMIJmr LOCATED UAE SH££r N9i, LAS ViGAS Suhmtrro JAlapa.* Scale i-toOOO- Reduced From Field Sheets ta Scale oF/-ioooo>iaa*/aFeetperI/Tch . AM.Wellinaton, Chief Engineer , JOltnSa/ion^ Chief of /^rfy. ^ 5 rjiii^s □□DDL □□□at vrnKM APPENDIX 933 .he Jalapa ,i„e, shown on pTg^. 3^ nd 3.0 tLT '"^ "P"" " '''■°'""- <" be seen in Ki,. 30, .0 have V^^t L"; J^/a'Sr "^ "' '"^ ""^ ""' .anje^n:::Thr47"::.r:r::; M^L^rn::;: •"' r '^ ^-^-- upper third of the line, shown on fL 3^ aL ,!o ''/"'"' """'^''^ °" "»- ■tangent (the average tangent being 96 3 metres oI'm'" T "' '"^ ""^ '^ kilometres which have been engraved 48 per cen of the >" ""= """'^ ^* comparative degrees of curvature cannot be given " "'"^'"'- ^""^ W,: the jalapa line,'^,i.:;ra IT ;r;iiretr ""Srh'"* ■"""> '°"«" been the same, however, mereTy ,0 get to mTxLo .hifH^ '"'"''' '" "*=" been more than eliminated as will te H r ' v <''f"<^"« "ight have Marcos on Fig. 308. ^" ''''"" *= ''°"^'' ""= above San Gauge.— The Jalapa line was intended to be laid to ■x ft »= .ng to the gauge of the Mexican National Railway whereasr'M"'''"'r'" way was 4.ft. Si-in. gauge. No difference was ZL n theTodtL ho "" •""'■ account of the gauge, the road-beds having been T21T .' ""' °" r to . in cuts and ., to x in hlls. and rli f est : ed ^t sb'^: T ";' ^'""^ :r,r trroV-iVauV"- -- -^ - -'^ - ^.i^edTa:; bia„?::e;a!:dr: :-;: 'i-ti^ttfi^io^-ofr' t- -- -•'■»- Table No. 2 Is an abstract clo.in/. '^^^^^^^ of the entire mountain grade, ^e materia, on the ^:Z:^:^Zt:::^^^^^^t^ wth'eTerr: rx-ed e?'"'"^'^ t"'"^ — "p™«.:rsr eX point, any engineer can orm H ^'"^' f °™ '"= ^^"'"'"^'^ ""^"'"i" at each Table No . (omi fed to avT sna T" '"h^™'"' ''' "^ """"=' '"^ -™-'= ■" still I, ,h=, \ """*". '° ^*^<^ space) IS adequate. The writer's belief was and less than $.o'l' permile gaini: ttTr,""" ""f r"""^'"^'"' """"""^ "^ n,ou„tain-grade of the Me.r HliK.'r irthTlltfoV f ToT 7 ral'^o; .e;Le:: t^'Sir^tr unir- r- -- - 1™ •- ^^^-^ -ntrc^ir-e^r-r^ ■The general route of both l^^^^Th^^T^ibed is showT^n Fig. jos! In 934 APPENDIX C. I >Iake what allowances one will, there is a great contrast in these two- lines, and it therefore becomes of interest to consider how this latter line was obtained. In March, 1881, the writer was engaged by the Mexican National Rail- way Company to act as engineer in charge of location and surveys on the various lines for which they had concessions, extending from the city of Mexico to the United States and to the Pacific coast. On landing at Vera Cruz, with a large staff, under orders to report in Mexico, he was surprised at the receipt of a letter of instruction to the effect that a corps were engaged in examining a line from Vera Cruz to Mexico v/a Jalapa. and that he should detach another corps for service on this line, sending- forward the remaining parties by rail; that he should then make a re- connaissance " sufficient to determine the general possibilities of the route, taking such escort as might seem necessary;" set the new and old parties at work ; and not delay date of report in Mexico " more than six days." Fig. 309 IS given a reduction to one.fifth scale, or ^r^^j^ (i^ inches per mile, wiihm I per cent), of the large topographical map on a scale of y^ig^ of the upper 54 of the 117 kilometres of the mountain grade. This in turn was re- duced from the original field-sheets on the large scale of t^\j^ or 83J feet per inch, which the difficult character of the work made necessary. The topog- raphy was very accurately taken by a skilled topographer. Mr. Max Chapman M. Am. Inst. M. E. In Fig. 310 is given a photographic reduction of the original profile, which was called off, station by station, in the usual way from a paper location on the original field-sheets, and estimated, station by station, from tables, with allow- ance for surface slope, which often more than doubled the level-section quanti lies. The estimated quantities for each cut and fill are given on the profile and nature of material indicated. Retaining-walls were estimated for at every point where a fill would not catch, and are indicated by a thick line on the profile. The small amount of masonry is due to the almost entire absence of surf/ic? drainage and running water, as elsewhere noted. The line, profile, and estimate here shown were not finalities, but prepared for a special purpose. Compensation for curvature had not yet been introduced. It was fully expected to do still better at points, and in fact the location shown was greatly improved in the upper section {9) by a new line, run just before the suspension of work which threw the line back from the ragged cliff work near the summit. As maps and profiles of this improvement cannot be given, no claim in respect to it is made, but only for what had been actually secured and recorded in black and white. REDUCTION RATIO 14:1 .'V'- o 3 3 rfti ^'V/ ^A .'^Z (A) 3 '3 0) O" Q) cr o > ABC cdef CD CD ^a FGH jkIm 3? -1 : — IJKLMN nopqrst JKLMN lopqrst X VD -^-< O OOM VD ^^ 4^ 3 3 > Q) O o m CD O ^ o O cC/5 X M O O 3 3 .^i ^.^^\'^.' <^^^ ^■^^7'^ o 3 3 1^ \. ^^ ^«:. ^%i > ^< o o 3 3 o^ 00 10 b N3 00 in % ""k 2.0 mm ABCOEFGHlJKLMNOPOnSTUVWXY/ abcdrfghi|l C u X ^ 11 0(0 5 m O m /^A ■^ e "^ .^^: »v 2.5 mm ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 .^. I e^^ V .« fp ^XP 3 3 Is •< TO M CO ■*^$ cr o >> ^m Is ■o ^ ^i •^ CO a>x OOM IX) o no 3 3 > o m OQ i ^ o O < -H M < X -< A Fig. 310. FERRO CARRIL NACIONAL INTEROCEaIiICO. VCRACRU2viaJAtAPAfofheCirv OF MEXICO and »he PAc.tc COAST. ProRie oPthePREUMINARY LOCATED LINEon 1 UPPER HALF OF the MOUNTAIN GRADE From JALA PA to LAS VEGAS * Sec tions 7, Sand 9. AM. WOLINGTON.. Chief Enyine^r. John S. ELLIOTT. Chief of ft»rt>iSfc«.7-9. Iflvers «r« ary Old Datum reading about SO.ooo metres below m,^ ,,fe.T. Scare oF Original ProfUe reduced 3/5. giving the foUoviivg comparison : ORIGINAL scALcf "r:;":;*' '/^;° *"' ••'*!!/^ p^^Jrw*. PftOntC o> PA'^T or FIRST MILE after reath? ng fht SUMMtT« (Une continues of tHi« general character For the entire disfanca to the CITY OF MEXICO some 160 Miles.) I 1 1 Tl 1 I I Cp|ntral| PlgrHP.aii |oF f^extct^ F3 Btainninq oTZVz iMreentGraai * 94fS.O MMrw. ai)oveTidf* "^923 ft- ElevaHon. ef Boca del MomeSummit on Mexican R.RexacHv. rSfa.U-1190. is» Pretiw.) Vertical V400 "....aai/j, Izontal V12.SOO •• i,o«« -.»„ ical 4/4,000 » SaVSi. PRESENT SCALE /"°"""^' *''^-^°° " *«o*» I Vert Pic. 310.— Profilk of Line in Fig. 309. [The fine horizontal lines are a meters (6 56 ft.) apart on this profile. The total width of the plate is 5 kilos., = 311 miles. Rock is shaded. Retaining walls indicated by heavy line and letters R W. Many of the minor culverts hare been omitted ft-om the reproduction, but the effective drainage area on the entire line was iu general very smaU] Lost by bfeatu of Grade,! n the entire distance t06 metres (4.7S percent ol Fall) of which ther« was _ On the portion shown 36 metres (3 .43 per cent) • • • n»t . TO • (ijbo • • I All Of wich ana sontefhinor more, it was expected to use u» for compensation for curvatura. REDUCTION RATIO 12:1 CJI 3 3 O >> I- CD 3 X ID ^ :^ ^ c/) cob: cn CT»X OOM VD O V. In 3 3 > o m (DO C/5 X < N X M 1^ J^ A^ ^* c> e. ^: '^e .* v en O 3 3 > -.^^ ^f^^ "^^y^ a^ o o 3 3 V < ^&> ^o ^o -i fp "is- O Pr C^ « IS N5 to 00 In 1.0 mm 1.5 mm 2.0 mm ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdetghi|klmnopqrstuvwxy;1234567890 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyzl234 567890 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 2.5 mm ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 ^fcP .X*^"' ^. ^r^ <^ :cr ^o ^fp ^^ m H O O ■oED "o OL,"D > C CO I TJ ^ Tk Ooo 0(/) ; m o m .A. 'i ** ^--^^^ 1^ •S-D Is 00 Ni S i? fp 1— • IS3 CJI o 3 3 3 3 o >> I? 8i oi< OOM s >. APPENDIX C. 935 To one landing in Mexico entirely ignorant of the language and the country; provided with no map or profile of the existing line, and know- ing nothing more of its character than the general fact that it was one of the heaviest and most costly railways in the world; unaware that its engineers had even given a thought to a route via Jalapa, or even that there was such a place, until he finally learned that the route had been examined only to be abandoned, and that the branch which had been built to Jalapa, at the foot of the mountain proper, had lo per cent grades, and was practicable only by horse-power; unaccustomed to a tropical climate and to the saddle ; provided with no map of the region better or much larger than Fig. 308 which accompanies this paper; and innocent of all knowledge as to how large an escort would insure safety, if indeed any could— these were sufficiently formidable instructions, and could never have been successfully carried out, as fortunately they were to the letter (barring two days' delay from an unseasonable rain), had recon- noitring such lines been in fact so entirely lawless a matter that there was nothing for it but to look over the whole country and then decide what to do, or at least to try for. The line which was found to be under examination is indicated by dotted lines on the general map herewith, and was at once rejected as im- practicable and absurd. It ran from the coast north-easterly to Jalapa, 4500 ft.; then descended southerly, 850 ft. in about 10 miles, to an elevation of about 3650 ft. at Coatepec ; then was expected to ascend somehow, some 7000 ft. to the " pass" between the volcanoes of Orizaba and Perote, at an unknown elevation, estimated at 10,700 ft. in an air-line distance of some 15 miles; and then to descend some 2000 or 3000 ft. on the back slope of the mountain, to the general level of the plateau. Very naturally the best grades which it was even hoped to obtain were those of the Mexican Railway, or 4 per cent uncompensated. It was at once clear that either something considerably better than this must be obtained, or the line should be reported as impracticable and the whole staff withdrawn. And it seemed equally clear to the writer that either a considerably better gradient than on the existing line must be obtained, and lighter work as well, or the project reported as unde- serving of any consideration financially. A reasonable hope for a maxi- mum grade of not over 2i per cent at most was therefore fixed upon as the highest one justifying setting parties at work on it, and hence to be considered at all ; and this, to make the project a meritorious one, re- quired that 2 per cent should be sought for. This made it indispensable to gain considerable development forthe ascent, and this in turn made it out m il n 93<5 APPENDIX C. APPENDIX C. 937 I of the question to ascend between the two volcanoes, even had the saddle between them been cleft down to the level of the main plateau, which was known not to be the case. The whole problem, therefore, turned upon the question of whether or not it would be possible to turn north- ward at Jalapa (assuming that point to have been successfully reached by the required grade, which seemed a minor question) and run parallel with the coast line and the coast range, gradually ascending with all possible development, and turn the mountain of Perote to the north. This possibility the writer was satisfied would turn, negatively at least, upon the simple question of whether or not there was some kind of an established highway ascending from Jalapa to the plateau, following in a general way the same course, and turning the mountain to the north. That is to say. the existence of a highway would not prove the line was practicable, but the absence of it would go far to prove that it was im- practicable. In respect to highways, the writer had even then learned by sad experience, and had repeated occasions in the next three years to realize still more fully, that the route of a highway is ordinarily the worst possible guide for a locating engineer, except as it may serve the negative purpose of a danger sign to warn him away. He now recalls no less than twenty-three instances on the lines in Mexico under his charge where the existence of a travelled road proved merely a snare to deceive. Some of these instances were of a very curious character and of much technical interest, but description must be forborne. But in regions of real difficulty, where the elevations to be surmounted become serious even for animal power, and even after all avoidable rise and fall has been eliminated, the case is different. The writers experi- ence and conviction is that in such cases the aggregate intelligence of the cows and the natives thereabout may safely be trusted to discover and utilize the very best route there is for surmounting the elevation with the least amount of work. Even what would be regarded in Mexico or Colorado as so simple a problem as that of making the 900 ft. rise over the Allegheny Mountains in Pennsylvania, is a case in point. The pass above Akoona and Hollidaysburg was discovered and utilized in the very earliest days of the settlement of the country, and four generations of engineers on four successive public works have been able to do no bet- ter. . The first question asked by the writer, therefore, after learnmg tne details of what was doing, was whether there was a travelled highway turning the mountain to the north, the map before him not extending far enough north to show that region distinctly at all. He was informed »at once that there was, and a very old and good one. Had the response been otherwise, he should have regarded the result of the reconnaissance as practically decided then and there. The statement was coupled with another, however, that this route had been examined by the engineers of tlie Mexican Railway, and reported far less practicable than the line afterwards adopted and built, so that the middle line described was under examination as the only hope left. Tliis was discouraging enough; but on further learning that the high- way had been for three centuries preceding the railway era the leading •one between the interior and the coast ; that there was no succeeding descent, but rather a gentle rise in it for many miles after the mountain- grade proper was surmounted ; that the summit was (this afterwards proved an error) several hundred feet lower than that of the Mexican Railway ; and some other facts which seemed hopeful,— there appeared to be a fighting chance, which was at least the only chance that the line /might be developed to give the requisite grade. . The more immediate question became then to make the ascent of 4500 ft. to Jalapa, and it was at once apparent that to have any hope of doing this on such favorable grades as were alone worthy of consideration under the circumstances, the line must be carried down to as low an elevation as possible, parallel with the coast and the mountain slope, by running south from Jalapa toward Coatepec before beginning to lose distance by turning eastward to the sea. It appeared probable that the 850 ft. of fall between these two points, as to which some definite knowledge was available, could not be made on a steeper grade than 2 per cent, and it was this fortunate fact (as it proved) which first led to conducting the reconnaissance from the beginning on the fighting chance of obtaining a 2. per cent grade. It was now determined, therefore, that the line, if there was to be any, must pass from Vera Cruz to Coatepec, and thence to Jalapa, instead of to Jalapa direct. Coatepec lies at the head of a river of considerable size, the Rio Antigua, which runs from it directly east to the coast; and the map and known elevation of the town made it at once clear that there was no physical impossibility in descending this valley directly on a 2^ per cent grade, or perhaps less, if the valley had a tolerably uniform de- scent. It needed but the most moderate knowledge of the general laws of topography, however, to make it practically certain that no even approximately uniform descent could be hoped for in a river flowing in a deep gorge, cut through what was practically only a narrow footing to xhe most tremendous mountain slope on this continent. The foot-hills ^g^ssssssz 938 APPENDIX C. APPENDIX C. 939 r of a slope which reached a height of 17.873 ft. and started practically from the level of the sea, was certain to have, like all such slopes, a de- cidedly concave profile. Nothing less than 5 per cent could be rationally hoped for in follow- ing the bed or immediate slopes of the valley, and it therefore became quite certain that the line descending from Coatepec must start from the lowest point at the head-waters of the Rio Antigua which it was possible to obtain, but speedily rise up on the higher slopes of the valley and out of the influence of the stream, until at last— and probably within a short distance— it would rise above all supporting ground. No resource would then remain but to turn across northwardly, at some favorable point on the dividing ridge, into the valley of the next river to the north, the Rio Chachalacas, with the view of gaining only such limited development as might be necessary to catch upon some high point on what were known to be the gentle slopes of the lower valley of that river, from which the line could descend eastwardly on the required grade to sea-level at a point as near to the coast as possible. The only fear in this process, be- sides the danger of heavy work, was that it might be unavoidable to make a long horseshoe development up the valley of the Chachalacas, bring- ing the foot of the grade far inland from the sea, and causing just so much unnecessary loss of distance on a level before reaching the foot of the mountain grade. The existence of these two parallel and deep-lying streams made it certain that the general scheme below Coatepec would be practicable, if not too costly ; and the immense depth of the southerly valley, which varied from 1000 to 2000 ft., together with the absence of all supporting ground to the south of it, made it certain that the line could at no point turn south between Coatepec and the coast. Thus, by a process of exclusion, the entire line was projected and sketched upon the map, with most dismal apprehensions of the charac- ter of the work which would be encountered, but with absolute confi- dence, expressed at the time to the gentlemen who accompanied the writer on reconnaissance, in the face of some opposition, that if this line was not practicable, there was nothing in the region which was suffi- ciently defensible, from an economic point of view, to make it even worth examination. The line shown on the general map (Fig. 308) which the writer now has the honor to lay before the Society, does not differ by its own width at any point in the entire ascent of nearly 8000 feet to the plateau from that which the writer thus sketched upon the map in the city of Vera Cruz, and showed to several gentlemen, on the evening of the day when he first landed in Mexico ; within two hours after first learning that there was such a place as Jalapa, or that there was, or ever had been, such a project as an ascent to the plateau through that region,. and with the elevation of only two points on the line, Jalapa and Coate- pec, approximately given. Neither does the line on Fig. 308 differ by much more than its own width at any point from the position of the line as finally surveyed, as shown on the detailed maps and profiles which are herewith laid before the Society complete, the more diflftcult upper half of the mountain grade only having been engraved on Figs. 309 and 310. The writer would not be understood to assert or imply that equal positiveness in defining in advance the limitations of reconnaissance is- often possible. On the contrary, he has never known another instance just like it, although it became his duty later to consider projects for several other lines of a similar but less exacting character. But the j>eculiar conditions, it will be seen, left no escape at any point from the chain of reasoning. Had there been no existing parallel line, one might have justifiably taken the region for better for worse, and borne with equanimity finding it a great deal worse than he took it for. As it was, the fighting chance for a low grade was the only one economically worthy of attention, and this primary fact given, the conditions left no escape at any point from the train of reasoning that it was that one route or nothing. The next morning at daybreak the reconnaissance began, and was pushed through with increasing confidence as fast as the animals could stand it, or at the rate of some 40 miles per day, the entire ex- amination of the mountain grade occupying three days — such haste being merely in fulfilment of the writer's positive instructions, and nat- urally against his inclination. Less time was required, however, be- cause the only real purpose of the reconnaissance was not to find a route, but to examine on the ground the features of what was already known to be the only route affording a rational chance of success. The first 1500 feet of rise was seen to be on slopes smooth in detail, but suflS- ciently steep for laying down a surface line on almost any grade, and were not examined critically. The dividing ridge was then followed up, to judge of what was really the only critical point of the lower descent (from the point of view of possibility and not of cost), the passage from one water-shed to the other. A long and sharp spur ridge running eastwardly from Coatepec about half way to the coast, having a crest- 5000 or 6000 feet high, and standmg at right angles to the main slope^ was found to define the point where this passage must occur pretty defi- nitely, and the material and topography was seen, with much relief, to- ,1 940 APPENDIX C. be favorable for making this passage with as much or as little develop- nient as might be necessary, with considerable latitude in elevation and easy work. The south slope of this mountain, where the line would lie, was found to be almost impracticable for passage on horseback without camp equipage and time ; but observing tlie north side to be fairly favor- able, and taking it to be very unlikely that, in a ridge of this chanicier, tlie topography would differ widely on the two slopes, it was passed bv with a confidence that the result fully justified, as well as such verv lim- ited information as was available at the time. It will be seen from the maps and profiles of this section (not engraved) that on the surveys now submitted, a few of the most costly single works on the line are here, and not on the engraved section above Jalapa, which was really the critical section. This, however, the writer is, and was then, satisfied was due chiefly to the fact that the lower section, not being a source of much anxiety, was left in less competent hands. In part it was radically im- proved almost at the conclusion of surveys, and the writer feels no doubt that it all might have been more or less, although he makes no claim in that respect. Owing to the falling away of the country to the south, before referred to, and the existence of the deep barranca, or gorge, in which the river lay, which cut down almost to sea-level, or some 3000 leet below the line, some of the most sublime views of the line were on this section; but its difficulty was not in proportion, in part because of the very fact that the line lay so high as to be above the immediate influ- ence of the barranca. The material on all this section was exceedingly favorable. The region between Coatepec and Jalapa was known to be not very rugged, and to oppose no difficulty as to elevation, so that it also was passed by with a confidence which the result justified, and the project was complete to Jalapa, as a basis for surveys, with a reasonably favor- able 2 per cent grade-line all but assured. For the critical section above, the distance by highway was found to be almost one half too short, and all hung upon the possibilities of ('C- velopment. The material and topography on the lower half was found to be favorable for this purpose, being earth to a great depth, as noted, and sufficiently broken up by ridges and hills. A long stretch at about the middle of the slope, near the village of San Marcos, was of an equally favorable character, being literally an inclined plane on a slope of about I in 10, — an old lava flow overlaid with soil, — and not much broken up in detail. The upper section was rugged, but short, with considerable opportunities for rather expensive development. APPENDIX C. 941 The whole of this region was examined on the third day of a verj- heavy rain-storm, the end of which could no longer be waited for, and the examination was necessarily restricted to salient features only. On a long grade-line of this character, how^ever, the possibilities of develop- ing on practicable ground to reach certain elevations at certain frac- tional portions of the available distance, can be judged of with some certainty, the general character of the slope being the main feature; and the writer felt no real doubt then, or at any later time, that a grade in the neighborhood of 2 to 2^ per cent was easily practicable, there being a certain considerable belt of favorable territory on which to place it, although above and below that the topography was much more forbid- ding. A leading factor in reaching this apparently hasty conclusion was the splendid and ancient highway already referred to, by far the best in Mexico, if not on this continent. It is a broad macadamized road with paved gutters, and a stone curb or masonry wall at the side,, and the writer desires to pay a tribute of admiration and respect to the unknown engineer, whoever he was, — very possibly one of the soldiers of Cortez, or one of his immediate successors,— who laid it out. From a point near Jalapa to the summit, near Las Vegas, there is not a break in the steady ascent, and there are few points on it where a fresh team of horses would not readily break into a trot. The conclusion was natural, that if a Spanish soldier in 1530 could put something like a 6 per cent highway down that mountain slope, an American engineer in 1881 ought to get a 2 per cent railroad line down it, or take off his hat to his prede- cessor. After reaching the summit, the continuation of the line to Mexico,, or any other point on the plateau, was a detail offering no difficulties and needing no immediate stud\\ The line was therefore reported on in writing to Mr. W, C. Wetherill, chief engineer, three days later (March 28), as follows : "The line under examination was too forbidding to be worth further at- tention. ... I feel no doubt that the proper place for the line is to the north of Peroie, and that something like a 2| per cent grade, or possibly a 2 per cent grade, is practicable above Jalapa. Whatever grade is there obtained can cer- tainly be continued down to sea-level and slope without excessive work. I have instructed surveys to be conducted above and below Jalapa on a 2 per cent basis for the present, and consider the prospects for a fairly favorable line good." It should be mentioned further, that the writer's examination had been merely in a consulting capacity (the line not being formally a part / •942 APPENDIX C. APPENDIX C. 943 ♦ of the Mexican National projects), and for some months later he had no permanent connection with or knowledge of the progress of the work, being absent on the Pacific slope. On being again asked to examine the line, August ist, 1881, he found that his conclusions had been re- ported on as impracticable, and that a 3 per cent compensated grade had been adopted, located in part, and was under construction.* Fortu- nately, however, a most intelligent assistant engineer, of great natural capacity for location, Mr, John S. Elliott, was in charge of the upper locating party. To his admirable conduct of surveys the success of this line was very largely due. Aided by information he had acquired, it was soon discovered that the abandonment of the 2 per cent grade had been an over-hasty conclusion, from data which in fact assured its suc- cess. The work in progress was therefore stopped by the writer's advice ; some $30,000 of completed work abandoned, chiefly in the approaches to a costly tunnel in earth ; and the writer appointed chief engineer, con- tinuing in charge until some time after the completion of the surveys now laid before the Society, when the abandonment of all furtherance of the project by the Mexican National Railway compelled his resignation, and shortly afterward led to the stoppage of all work. But for the fact that he was favored with an unusually competent assistant in immediate charge of surveys on the more difficult section, the writer fears that he should never have been able to carry through the line with the limited time at his command. Two features on the upper ascent are worthy of special note : One, the great lava flow shown in Fig. 309, and before referred to; and the other, a still grander feature, the barranca of Zimilahuacan, a vast sink-hole in the earth some 2 or 3 miles in diameter, and some 3000 feet deep by the barometer, about half of it sheer, with no transition or " ragged edge" whatever from the surrounding surface of the plateau, which was as smooth and treeless as an Illinois rolling prairie, but sloping about i m 12 or 15 in the chasm. This feature was encountered some miles beyond, where all difficulties had ceased at the summit; and so smooth was the edge that the line skirted it with a mere surface line, so near to it that a stone thrown from the car-window would fall sheer full 1000 feet before touching. On the plateau the locality was so cold and so much exposed that it was stated that wheat would hardly head, while immediately be- neath one's feet bananas, coffee, oranges, and every form of tropical vegetation could be seen growing luxuriantly. A few miles beyond was * The concession permitted of no delay in beginning construction. a large and very ancient fortress still in good repair, but unoccupied, which would cost perhaps $5,000,000 or $6,000,000 to duplicate, in which for two centuries the great bulk of the silver product of Mexico was stored pending the arrival of transports at Vera Cruz. Several of the old line of visual telegraph towers which were used to communicate between the two points are still pointed out, although out of use more than a century. From several points on the upper ascent the city of Vera Cruz. 80 miles off in an air-line and 6000 to 8000 feet below, is visible in clear weather. These and other features make the region one of the highest interest to the tourist. In view of what has preceded, the writer hopes that he may not be sus- pected of over-estimating the difficulties of securing such lines, or of per- sonal inability to cope with them, when he declares his conviction that this whole method of taking railway lines up difficult ascents by a con- tinuous succession of curves and tangents on a rising grade, over which the locomotive keeps up a steady march, is fundamentally wrong and bad, and one which might profitably be modifipd in nearly all cases when an elevation of over 1000 feet, or possibly much less, is to be surmounted. To furnish a suitable background for the expression of these conclusions, by showing that they are formed in spite of fairly successful experience in following up the more usually approved plan, is a main purpose of this paper. Three general methods for surmounting such elevations, besides the almost universal one, are more or less in use: ^ First. Rack or grip railways. Second. Inclined planes operated by stationary engines. Third. Switchbacks. The first of these was proposed in a practicable form over thirty years ago, and the two latter antedate the locomotive itself. Either one of them is probably deserving of more use than is given it, but the third (switchback) the writer deems worthy of adoption by engineers as the standard plan for surmounting considerable elevations, always provided the switchbacks be constructed and operated in quite a different manner from that usual in the few which exist, which have for the most part onlv been resorted to as a last resource. One feels a natural hesitation in expressing a conclusion which, it must be admitted at once, all the tendency of modern practice tends to discredit. The accumulated verdict of experience is rarely wrong, and it is undeniable that all these plans have been in many cases tried and abandoned, and have met decreasing favor. Nevertheless, causes need- -ttSSftg^--:' 944 APPENDIX C. APPENDIX a 945 less to go into, other than lack of real merit, may explain in part at least: this result, and the writer sees no escape from believing that they do so wholly. The capabilities of the inclined plane or cable plan have been greatly- extended in recent years, as applied to street and local passenger service,, and it is clearly destined in the near future to still wider use. Super- ficially, the record of its use in connection with ordinary railways is most discouraging to any hope of its future usefulness in that direction. In the early days of railways it was constantly, considered, and often used. A complete plant of the kind existed over the Allegheny summit of the Pennsylvania Railroad before that line was built, and was aban- doned in favor of locomotive traction, even to connect two lines of canals. Several complete railways operated by successive inclined planes and gravity inclines were built in Pennsylvania and elsewhere — two in North- ern Pennsylvania of considerable length, one of which is still in use and the other only recently abandoned, but not chiefly, if at all, for reasons- affecting its abstract merit. It is not generally known that the existing main line of the Pennsylvania Railroad over the Alleghenies, which was- built long after the old planes had been abandoned, was laid out with the distinct view of afterwards adding a new and enlarged system of planes for freight traffic when the volume of traffic had increased tO' justify it. This policy was favored by its distinguished chief engineer, Mr. J. Edgar Thompson, and some elaborate and interesting data in re- spect to it are given in the early reports of that road, notably in a report- by the then Superintendent, Gen. Herman Haupt, in which the ground is distinctly taken that it is a mere question of volume of traffic whether inclined planes are economical or not. That view the writer apprehends to be the true one. The fixed trac- tive plant is costly to construct, maintain, and operate, and expenses are not greatly affected by whether the tonnage moved by it be large or small. It by no means follows that, because the system was wisely abandoned in favor of locomotive power, for the thin traffic of those early days, that it is wise to continue to neglect it at points where almost a steady stream of laden cars is to be carried, first up and then down a dividing ridge, day and night, the year round, as on the Pennsylvania summit, and at many similar localities. At such points it is demonstra- ble that not only may the great amount of power used in lifting locomo- tives be saved, but that the descending and ascending cars may be bal- anced against each other, thus largely eliminating the effect of the rise; while the superior economy of stationary engines will largely reduce the: cost per horse-power, after allowmg for the friction of cables, which, on a short, steep incline is a minor element. Especially now that the making of long continuous cables is so well understood, so that as long an in- cline as the topography permits may be readily worked, it is worthy of the most serious study whether a very large economy is not readily pos- sible at such special localities, a considerable number of which may be counted up. A proper switchback system, however, seems to the writer the most generally useful and, meritorious for lines of probably thin traffic, as well as the most unquestionably practicable for use in all such localities. The germ of the proper system was contained in the first switchback laid out in America, if not in the world, — that at Mauch Chunk, — which was used for dropping empty coal-cars down into the Nesquehoning Valley, before the tunnel of that name was completed. That track was used only for cars passing in one direction (descending), and was operated as fol- lows: The cars were started from A, Fig. 311, on a down grade of about i per cent, calculated to give a considerable velocity. At B an automatic switch, whose exact mechanism the writer cannot give, was run through and the car brought to a rest by the next suc- ceeding up grade at C, from which it im- mediately started back towards I), pass- ing through the switches B and D until again stopped at E ; and so on indefinitely, the cars descending several hundred feet in all without the slightest attention, very rapidly, with very rare accidents^ and with no one on them or stationed along the track. Thus, to say the least, every advantage was gained that could have been gained by a long continuous descent, with the immense advantage that, owing to the entire liberty of choice as to the length given to each plane, the best,alignment and lightest work available on any part of the surrounding country may be chosen. But more than this was gained. Any long continuous grade which is steep enough to move cars with journals in rather bad order, must be steep enough to speedily give cars in good order a dangerous velocity. Thus it would be impossible to let cars run of themselves down a con- tinuous grade of any kind, while, on the switchback, not only was this 50 Fig. 311. 946 APPENDIX C. APPENDIX C. *i f t very readily done, but a pretty high average velocity could be safely used, from the fact that it in any case could not exceed a certain maxi- mum. Again, when necessity required, it was easy to stop cars at any point. Analogous advantages are readily obtainable, mutatis mutandis, by switchbacks operated by regular trains running in both directions, but not under the conditions of ordinary practice, which necessitates the complete loss of all the vis viva of the train at every switch. The plan shown in Figs. 312 and 313 will apparently obviate this necessity com- pletely, and introduce no new elements liable to cause difficulty, but, on the contrary, give smooth, easy, and rapid motion. The details of this plan are as follows : As Respects the Switches. — The switches should be, and are easily made, entirely automatic. Their normal position should be that in Fig. 312, in position for running up hill, and not down hill. A runaway train or car cannot then pass a switch and continue down grade. As respects a train going up grade, this arrangement presents no difficulty. It may simply run through the switch D, springing the points over to let the wheels pass. Simple devices of many different forms may be used to restrain too rapid return of the points after the passage of each single wheel, but this is not essential, as the wear and tear would be small. The mechanism here outlined acts as follows: Down Trains. — A places B and C in position to act, which are otherwise entirely inop>erative. iff, when first made op- erative by A^ opens the switch D for track C, and holds it open. C, always operative when B is, returns A^ B, and D to their original positions. A, By and C are supposed to be located with reference to having the engine always at the same end of the train. If the engine be at the other ends the switches must be oper- ated by hand. Up Trains. — If, by carelessness, the engineer of an up train should leave the switch- actuating lever down, nothing will happen except to set ^ as if for a down train, in leav- ing the switchback. This will not afiFect following trains, either down or up. Should a succeeding up train be equally careless, it will act first on C and then on A^ thus running through the switch with no effect, A train descending should be able to operate the switch, so as to con- tinue descent, by a single act of the engineer, but only by intention on 947 ^P Fig. 3x8. — Mechanism for Automatically Operating the Switches of Switchbacks. ■\ o his part. This may be accomplished by a very simple and inexpensive apparatus, such as that outlined in Fig. 312. operated by a lever or idler wheel on the locomotive controlled by the engineman, and with mechanism somewhat similar to that of the simpler forms of interlocking apparatus, which it would be super- fluous to describe in detail, as it can be designed in a few hours by any signal engineer. The general meth- od of operation is described beside Fig. 312, the whole insuring that (i) up trains shall always pass the switches freely and automatically; (2) that runaway down trains shall never pass them, but be caught ; <3) that regular down trains shall be enabled to pass the switches auto- matically by a single act of the en- gineer; (4) that careless neglect of this act shall do no other harm than to cause the train to run back again on the up track; (5) that danger signals shall be set when the switches are wrong, or any part of the appa- ratus broken; (6) that the switches can at all times be operated by hand if desired, or if the mechanism is out of order. As respects the Adjustment of the Crades.—F\g. 313 shows in detail what the writer regards as the proper adjustment of grades for a 2 percent switchback, and the principle of the adjustment for any grade. With this arrangement it is unnecessary for an up train to use brakes, or even shut off steam at all, for making the stop and then starting backwards. It will be seen that the up grade continues unbroken until it has passed the switch and then rises in a sharp vertical curve, which rises r I- 5 J u»— . 948 APPENDIX C. above the regular grade, slowly at first, and at the further end— merely as a precaution against accidents— rises very rapidly indeed. This is to- bring the train to a stop slowly and gradually, but certainly, without either shutting off steam or using brakes. The rise necessary to do this, for any given train-speed may be computed exactly, and is given in Table •. i8 of this volume. Suppose a train to be ascending the 2 per cent grade at a uniform Gpeed of 15 miles per hour. Then, by the table, a lift of 7.99 ft. above the regular grade will bring it to a stop even with the engine still using steam. If the velocity be only 10 miles per hour, a lift of 3.55 ft. only will be necessary, and this will or can readily be made to be the usual speed of approach. In that case, if the train consist of 10 cars and be 400 ft. long, it will come to rest with the steam still on, unchanged, when the rear of the train has passed a little over 100 ft. past the switch, the centre of gravity of the train being then 3.55 ft. above the tangent grade- line. The slack of the train will be taken out, under these conditions, very gradually indeed, and almost at the instant of coming to rest. If, then, without changing the throttle, the reverse lever be thrown over into back gear, or even merely into mid-gear, so as to do no work at all, the train will immediately start backward, still holding all tlie slack out of the train, which will continue out until forward motion is resumed at the next switchback. If the lever were immediately placed in the same notch of back gear in which it formerly stood in forward gear (which would be unnecessary) the speed which the train would have acquired on resuming the upper straight grade at T, Fig. 313, would be that due to the height c, which is 3.55 +(8x4)= 35.55 ft., or. as per Table 118, 31^ miles per hour, an objectionably high, but not dangerous, speed. Had the velocity of approach from below been 15 miles, this speed would have been that due to 37.99 ft. or only 32^ miles per hour, and had the velocity of approach (in case of passenger trains) been even 20 or 25 miles, this speed would have been only 36 or 39 miles per hour. Thus the switch, with grades arranged as shown, can be run through at any speed, making no more change in the brakes, steam or engine, than to throw over the reverse lever, at the moment the train comes to a stop, from full gear for- ward to full gear back. With ordinarily careful and safe working, the speed at T, Fig. 313, would be about 10 miles per hour higher than the speed of approach, a gain far more than sufficient to obviate all loss of time from the stop, and equivalent (for speeds of 10 miles per hour approaching and 10 miles leaving) to a subtraction of 10.65 vertical feet from the rise in the next APPENDIX C, 949 t?rade-a gain which will considerably increase the average speed or haul- ing capacity, or both.* Fig 313 equally well represents the conditions at the next ensuing switchback, where the train approaches rear-end to it, if we simply as- sun^e the engine to be at the other end of the train. It reaches the po- sition shown, backing up from below, with all slack out of the train In starting forward on the up grade, the rear end of the train, being on a steeper grade than the engine, will tend to crowd slightly upon it, and by setting the reverse lever in the second or third notch of forward gear the slack will be taken out in the gentlest possible way, far more gently than IS ever possible in starting on a level. Thus the ordinary and great objections to sharp hollows in grade-lines do not apply in this case. On the contrary, the action is smoother than It would be without the curved profile. Similarly, the still greater ob- jections to a stop on the grade-line do not apply at all in this case. We rather gain by it, because the whole train stops and starts again with the gentleness and economy of energy of a pendulum, for identical mechan- ical reasons. Tiiis being so,-there being no loss of time, no loss of distance, no loss of hauling capacity, and no measurable loss in smoothness of motion - we have left as a net gain two things: First. A great additional safe- guard against collisions with and derailments of runaway trains or parts of trams. Accidents resembling the terrible one on the Southern Pacific on the Tehachapi grade, some years ago, in which nearly all of a train- Ivad of people were killed or injured, are not likely to occur. Before a train can attain a velocity of 60 or 70 miles per hour it must fall 128 or 174 feet in excess of the fall required to overcome its resistance. If we •estimate its average resistance in acquiring that speed at 20 lbs. per * If the train were running: up a straight grade LOT at 15 miles per hour •., wt., *axa Asia, railways of, +43 rolling slopes in, 844 Asphalt, H. U. in, *45o Assistant engines, 585 and low grades, 590, 650 cost of, 601 ^^ and train wages, 671 how to estimate, 604 interest charge, 604 duty of, 598 -f- ^ and lighi traffic, 599 separate engs. necessary, for passenger service, 5a« example, 607 grades for, 591 .j,i ^1^ 95- INDEX. INDEX. 95S i Ass— Bac Assistant engines— C<7«//««r«/. GRADES, BALANCE OF, 593 — example, 604 + companng with uniform [grade, 604 + curve comp'n for, 598 projecting, high, 669 low, 596, 666 as aff'd by length gr., [618-9 duplicate tracks, 691 temporary grades, 766 vrhen wrong to reduce, <4d lines, introd^ on, 788 [671 CONCLUSION AS TO, 8o8 operating at yards and sta'ns, block signals for, 601 [599 cutting trains in two, 599 power of, 491 best wt., 597 tank engines as, 593 without stopping t'ns, 792 presumpt'ely always adv., 586 two or three rarely advisab., work with nature, 589 [669 & Assistants, discred'g rep's of, 836 Atchison, T. & S. F. Ry., fluct. [in stocks, ^46 jOco. performance. *439-4i . "Uncle Dick" loco., 421 miles and earnings, ♦719 sharp curves on, 279 Atkinson, E., forecast of ry. con- [struction,*4i Atlantic & Gt. W as Erie con- [nection, 730 loc'n at Springfield, O., 56 strategic disadvantage ot, 222. {See New York. P. & O.) Atlantic, M. & O. Ry., alignm't [statist., ^264 Atlanta & W. Pt. Ry., loc. per- [formance, *439 Australia, Am. Iocs, in, 423 pop'n. railways, wealth, etc., rolling slopes in, 844 [*27, *43 Austria, bridges, wt. of, 767 locos., no. and work of, *i6o pop'n, r'ys, wealth, etc., ^27, [*43. *45 rolling-s k and tiaflric, etc.. ^43 receipts per inhab't pass, and [frt., ♦105 Austrian N. W. Ry., lub'n tests. Automatic brakes, q.7>., 488 [516 couplers, q.v., 488-9 Axiom as to location, 660 Axles, accidents from, *246 car, cost and deprec'n, ^204 maint. of, *i63 w't of. ♦lej size of M.C.B., ^13 effect, on fric, 513 French, 521 loco., life of, *43o w't and cost, ♦412 -f- radiating, possible effect, 283 Axle-boxes, loc. w't and cost, [♦413 + Axle-friction, q.v., and rolling, 515 better lub'n needed, 509 -f- comp've cocflE., 512 ± Babbitt metal in loc., *4i2-4 Backing locos, q,7>., 950 Backing up in loc'n, 865-6 Bac-Bel Back pressure, locos., q.v.^ 47a Baden, cost rys., etc., ♦45 *' Bad times" and ry. const., 763 & Baggage cars, q.v.^ dimen's, etc., 1*491 Balance of grades, q.v., 593. 608 traffic, q.v.^ flucts. in, lot slide-valve, q.v.^ 532 Baldwin Loco. Wk's and Consol. catalogue, 422 [cn^M ^78 computing cap'y of Iocs., 442 Decapod loc.. det'ls, *4io loco, cost, comp. all sires,*564 narrow-gauge, *564-5 per ton, ^ii dimens., etc., •408 fast pass., 421 performance table, ♦438 test of, •461 + wt. of, incr. 13 yrs., *466 on drivers per sq. ft.. Ballast, cost of, 773 [grate, •452 various roads, ♦120 economy of, 772 imp'i in practice, 114 lining with string, 124, 277 Ballast trains, handling of, 773 Baltimore & O. rd., cars, heaviest, wheels on, 486, 513 [490 curves, sharpest, 278, 325 Y on, 279 fastest train, *529 flucts. in stock. ^46 history and causes success, inundations on, 783 [730 location, Allegheny incline, balance of grds., 618 [^699 for pushers, 585 profile, condensed, 698 temp'y lines, '700 loco, boiler pres., *4o8 cost and miles pr. y., 'isg mogul, dimens. etc., ♦408 maint'ce exps., 34 yrs., *i29 miles and earnings, *7i9 opg. exp. and trains per day, p c. opg. exp., ♦no [*i72 why low. no per train-mile, cost, ♦n6 train-load, frt. and pass, *2t7 Bankrupt lines, pass far from [towns, 68 & never from curves. 655 Bar-iron, past prices of, 763 Barranca, def., 928 Blanca, spiral, 678 Zimilahuacan. 942 Barometer, use of, 838, 847 Basaltic lava, 684 river of, 928 Bath lubrication, q.v., eff'y, 509 Bavaria, cost rys., etc., *4S fJange-fric. tests, 516 Beams, comp've strength, 742 stiffness, 740 Bearings, compass, for taking off paper loc'n, for transit work, 888 [893 use always for map'g. 886 loco., q.v.^ lire of, 420 r*i6o Belgium locos., no. and work of, popu., rys., wealth, etc., *27, l*43» *45 rolling-stock, traffic, etc.. ^43 Bell, loco., cost, ^is [♦262 Belleville & E. rd., align't statist., Bho— Bra Bhore Ghaut incline, *699 Birmingham, Eng., stat'n exp. at, Bissell truck, q.v., 430 & [828 Blackmail, r'ys built to, 14 Blast-nozzle, sfze, '409 Block-signals, interl'g, q.v.^ and [assist, engs., 6ot Blue Ridge rd., 60 ft. & 6" comb'n, ' Bogie' truck, q.v., 421 [656 Boiler, loco., q.v.^ 449 cost new, details, *i5o-s explosions, ♦247 life of, *4i9 pres.. effect increas'g, 401 repairs, details, *i46 English, *i44 . p. c. due to various [causes, *203 and minor det'ls, »i49 water in, wt., *4oo & marine, efficiency, *456-7 Bonds and stock per mile, sect'ns building on, 30 [U.S., *xo^ nature of. 29 ^ Boom' and inception of rys.,34 & and prices, 763 Boot, on Mex. ry., *699 Boreas summit, descent from, 696 Boring tools, 868, 893 Borrowed money, intox'g eff't, 34 Bosnia, cost r'ys, etc., ^s Boston — N. Y. traf., loss bydist., side track at, 823 [709 train-speed to, 650 Boston & Albany rd., alignment [statist., ♦259 curve comp'n on, 621 flucts. in stock, ^46 [•'59 locos., cost and miles i»er yr,, fast pass., wt.. etc., 421 slide-valve tests, 532 tubes in, *42o op'g exp. and trains per day, rates, fall of, ♦726 [*i72 sidings on, ^825 ton-mile rect's, etc., 'ns train-load, frt. and pass., *2i7 growth of, •100 Boston & Lowell, Iocs, cost and [miles per year, *iS9 p. c. switching-miles, *i8i Boston & Maine, locos., cost and [duty. *i5» Boston & Prov., locos., cost and washouts on, 781 [duty, *i59 Bottom lands and high water, [850 & Bound Brook line, fuel tests, 528 Box cars, q.v., dimensions, etc., 60,000 lb. st'd. ^490 [*486-7 Box culverts, q.v., wooden, 755 Brake-gear, accidents from, '246 Brakes, automatic, cost new, ♦is* effect on speed. 370 gain from, 804 & cost of, deprec'n, *204 destructive to wheels. 377 extent of do.,^3i8 efficiency of, average, 494 coefr. fric. of, 290 computing, 33^1 494 maximum, 495 on caboose, 359 waste of power by, 691 examples, 337-343 \yi}~^ when needed on grades. Bra-Bui Brakes — Continued. hand, and low speed, 268 Branches, rjr., 731, 51 av. earnings, 732 early building bad, 764 for defence, 718 pass, traff. of, 734 [732 reason for great increase of, PROJECTING, UNIV'L RULE for, SECOND, do., 734 [733 to develop territory, 735 Brasses, car, maint. of, ♦162 & locos., q.v.. wt., etc.. ♦150, [♦412 & Breckenridge, Col., loc'n at, 695 -f- Brenner, ry. profile, 698-9 British ry. dividends, ^41 operating expenses, *i78 {See Great Britain, etc.) Bridge-building, cause of prog, in. Bridges, accidents from, ♦247 [3 cost new per lb.. 905 asaff. by rolling Id., 7674- draw, weight of, 905 erecting, cost, 905 all spans but one, 68 floor of, 900, 904 heaviest car-loads, *49o maint., cost of U.S.,^i2o, *i28, prelim, esis. of, 003 [♦172-6 rerailingguard tor, 900 rolling load, 767 -|-, 490 types of. for var. spans, 904 vibration of, 447 weight of, 903 as aff. by depth, ^904 by rolling I'd, ♦767-72 by span, ♦767-71 by st'l or iron, ♦767-71 double track, 765 draw, 905 formulae for. 903 light, save little, 765 on narrow-g., 752 width of, 904 Bridge piers, prelim, ests., 898 pile, 770 Bridge spiral, q.v., 678-9, 681 Bridging, p. c cost to total. ^757 Broad St. station, Phila.,traffic, 69 ' Broken-back ' curves. 870 Brooklyn, B. & C. L. sharpest [curve, 325 Brooks, rate of fall of, 840 & Brooks Loc. Works., loc. dimen- [sions, etc., ^407-8 load on drivers per sq. ft. [grate, ^452 Brunswick & Ch. rd., alignment [statistics, ^264 Buffalo, greatest yd. in world, 822 inundations at, 783 miles of sidings in, ^821 Buffalo Creek rd., side tracks, ♦821 Buffalo, N. Y. & Phila.. alignment [statistics, ♦259 sidings, Buffalo yd., ^821 total, ^825 loco, perf'ce, ♦458 Building, const'n of, and surveys, on bonds. 30 [856 what is built well, 655 Buildings (houses), U. S ry. cost new, p. c. tototal.^757 Bul— Car Bulgaria, cost rys., etc., ^45 Bunching, curvature, q.v.., 655 grades, q.v., 587 & Burlington, la., brake tests, 496 & slack tests, 489 train-res. tests, 496 Burlington & S. W., alignment [statist., ^262-4 Burlington, C. R. &N., do., ♦262-4 Burr, J. D., paper by, 279 Burnettizing cross-ties, q.v.., 124 Cable traction, merits of, 686, 944 modern, origin of, 689 passing summits by, 689 Caboose brakes set, 359 dimensions, etc., ^486-7 Caledonian ry. locos., cost and & [*25 value. maint. various rds., •120 [♦170-6 [duty, ♦isg int'l rad'n tests, 4:72 'California: area, pop'n, sid'gs, p.c. of op'g exp.. earn'gs p. mile and head, ♦90; wealth per cap., ^26 Calumet mine bch. (8^ gr.), ^700 Camden & Atl. rd., wheel-wear [on, ♦287-8 Camp outfit for loc'n, q.v., 867 Canada, Am. Iocs in, 422 bonds and stock per m., ^107 earnings per m., ♦107 growth rys., ^424 pop'n. rys., wealth, etc., ^27 ry. subsidies by govt., ^107 Canada Southern ry., align't, and [Huds. R., 328 branches, money spent on, 764 earn'gs and length, ^719 per mile, ^107 flucts. in stock, ^46 nature of traffic, local and [through, 214 train-load growth, ♦loo {See Michigan Central.) Canadian Pac. ry., length of divs., rolling-stock per m., ^47 [169 Canals, U. S. value, ^25 [^325 Canarsie & Rock'y. sharp' t curve, Carbon, H. U. in, ^450 [dents, 254 Carelessness, as cause of acci- Cant (superelev.. q.v\ 271 Cape Government, roll'g-st'k p. [mile, ^47 Capital, floating, U. S., amt., ^25 in rys. of world, ♦27,^43 & made less by bad loc'n, 60 return on Am. rys., ^41 English rys., ♦41, ^79 Capital acct., danger of increas- [ing. 113, 654 distrib'n of, ^71 & Car-Builders' Dictionary, 491 Car, falling, ex. of grav., 342 Car-couplers, aut., and speed, 804 pass., why easily intro- [duced,489 probabilities as to frt.. 488 types, two distinct, 489 bad, impede long trains, 566 Car (^.r.) mile, fuel. P. R. R.,^i4o Carpets falling over, accidents, Carr's Rock disaster, 255 [258 Cars and rail- wear, 122 capacity of, increase, 485, ii4i effect on exp., 485 [135 on car constr. and [sp'd, 370 Car-Car Cars — Continued. capacity of. effect of narrow [gauge on. 485, 752 transition state of, 487 classes of, fr't, 486 -|- pass., 491 side-dump, 774 cost of maintenance, 160-7 as affected by additions, age, 162 [»66 M. C. B. rule, 205 curvature, 319 radius of, 641 distance, 201-4 growth of traffic, i66 high mileage, 162 local service, 162 rise and f., 377 train length, 570 average cost of, 160 per cent, details, full, frt., pass., 167 [♦161-4 bodies and trucks sepa- [rate, ^164 pass.,outsideand inside, [204 distrib'n to causes, ^203 TO VARIOUS PARTS, 167 Chicago rds., ♦174-6 sections, U. S. ,♦170-6' trunk lines, ♦172-6 34 years, 129 English, ♦mS & per car per year, ♦148 cost new, 163-4 box and stock. details,^204 flat and coal details, ^205 per mile N. Y. C, ^71 depreciation of (see above), [162, 205 varying causes for. 202 dimensions of frt., all classes. pass., ^491 [486-7 irreg'iies in, 487 European, 520 -\- and Am cross-sec, 522 elev'd ry.. 646 friction of, q.v. (& train [kes.), 501 European, ^283, ^502 invention of Am. car, 421 load of, cannot be full, 6ix E. & W.,^6o9-f how to est. prob'le, 99 mileage of. cost, all parts U. frt. cars, 161-2 [S., ♦170-6 average, 168 why low, 165 pass., 168 sleeping, 168 [^47 & number per mile, world, *43, riding of. and curves, 275 ht. cent of grav., 271 ton-miles per, U.S. sects., '97 weight of frt., 486-99 [♦49> extra large and heavy, mat'ls, separately, ♦163, pass., 451 [567 WHY GROW HEAVIER, I39 Car q.v. springs, compres'n of, 272 Car-wheels, accidents from, ^246 and rail. 307, 516 & cost and depreciation of, *204. failures on for'n rds., 166 cracks and breaks, loc'n, 319 maint. of, ^164 jl i r 956 Car-Cha Car-wheels, maint. oi— Continued. causes of failure, ♦ji; p. c. due to van causes, ^mileage life of, 319 [*203,*377 as affected by quality, *3i7 lead'g and trail'g wh Is, [*288 loco, and tend'r trucks, [*288 comparative pass, and ft., •on curves. q.7>., 282 [167 as pulleys, 302 flange wear, 308 rotation, energy of, 334 size and wt. of, *i63, av., 335 42-in., 513, 912 French, 521 U. S. standard, ^Sd eflf't on train r., 513 [335 p. c. wt. to total oftrains, skidded, fric, g.v., *29o tread, proper form, 308 errors as to, 307 •Carting, amt. of, and ry. traffic, 52 cost of, 820 ■Castings in locos., ^.w., ♦150 & prices Am. and Eng.,*4i6,*763 Cattle, accidents from, *245, ^247 Cattle-guard, plan for, 770 Caucasus ry. profile, 698 Cement, co. should furnish, 903 & Census U. S., defects in, *26i (Otherwise, the many abstracts tnot indexed.) Centre of gravity of cars, 271 of exchange traflfic, 227 of trains in sags, 357-60 of two towns, 67 [629 & Central angle and curve comp'n, Central la., align't statist., *262 Central N. J., fastest train, *529 fluct. in stock, +46 loco, perform., *44o Central-rail rys.. 404 {See Rack.) Central Vt., alignm't statist., ♦259 p. c. switching-miles, *i8i Central Pacif., alignm't statist., fluct. in stock, *^6 [*265 loco. "El Gubernador," de- [tails, ^ , '410 Mastodon loco., details, , . . . 1*4^0. *433 load on drivers pr. sq. ft. Mogul, 421 [grate, *452 miles and earnings, *7i9 mountain grade, *7oo Centrif. force on curves, g.z>., 269 common error as to, 301 effect on curve resist., 298 position wheels. 300 safety, 300 [eflf't, ♦273 limits of objectionable lbs. per ton var. curves, of counterwts., 446 [etc.,*27o Ceylon, long grades in, *6go rolling-stock per mile, *47 Chain, with wheels, and curve Chains, metric, 266 [res., 303 radii by, *266 -f Chairs for cross-ties, English, 125 Chances, theory of, 864 & Chanute, O., on loco, adhesion, loco, rail wear, 123 [44- train resist'ce, 518, 525 f*264 Charlotte, C. & A, align't statist.. INDEX, Cha-Chi Charlotte, C. & A —Continued. maint. wayexp., 128 Chattahoochee River fall, 841 Cheap lines, a priori preferable, 18 when to prefer, 583 Cheat River, fall, 841 ['264 Chesapeake & O., align't statist., curve comp'n on, 621 60 ft. and 6* comb'n, 656 Chicago, distances to, 240 grain rec'ts, 728 train speed to, 650 rates to and through, 218 & terminals, loc'n of, 72 relative size, 827 Chicago roads, op'g ex p. and [trains per day, *i74 train-Id. growth, *ioi rates, fall in 20 yrs, *726 Chic. & Alt'n, align't statist., *26« fluct. in stock, *^6 op'g exp. and trains per day, rates, fall of, *726 [*i74 train-Id. growth, *ior Chic. & E. 111., align't statist., ♦262 Chic. & G. T., align't statist., ♦262 Chic. & N. W. flucts. in stock, *45 furniture car, *49o miles and earnings, *7i9 op'g exp. and trains per day, chart, of, etc., 35 [+174 rates, fall of, *726 train-Id. growth, *ioi Chic, R. I. & P., fluct. in stock,*46 miles and earn'gs. ♦719 op'g exp. and trains per day, rates, fall of, *ji6 [*i74 train-Id. growth. *ioi Chic. & Spr'fd, align't statist.,*26a Chic, B. C. & W., align't statist., _^. „ [*262 Chic, B. & p., align't sutist.,*262 dining-car, *49i dynamom. tests, 501 fluct. in stock, *46 locos, cost new, det'ls, *iso-7 p. c labor and mat'ls,*i52, A- ■ * t%i6 dimensions, etc.. *407 Id. drivers, per sq. ft. [grate, ♦452 INDEX. 957 performance of, *44o wt. and cost, det'ls, ♦416 tender capacity, standard, 1*378 miles and earnings, *7i9 motive-power expenses, 157 op'g exp. and trains per day, rates, fall of, •726 [•174 traffic, growth of, 157 train and brake tests, 497 -j- water-supply on, *378 Chic, M. & St. Paul, alignment [statistics, *262-3 fluctuations in stock, *^6 miles and earnings, ♦719 op'g exp. and trains per day. rates, fall of. ♦726 t*»74 timber structures on, 770 train-load growth, loi Chief engineer should make re- [connaissance, 23, 83a & of party, duties, 867 Child, sense of distance. 844 Chili, loco, performance in, ^sS railway grade in, *699 Chu-Col Churches and schools, U. S. value Cincinnati, Erie business to, 222*^ Cine, H. & D.. align't statist'. *26i distance, value of, 2^1 curve comp'n on, 621 6i:fi Cinc.,N.O.&Tex*.P.,l^o{esS So. Ry.. pedest.iis and 'via^ [viaducts, cost, etc., got 60 ft. and e*- comb'n, 656 Cine, N O. & Tex. P. (Cine. So ). ,.l*"8f""'*"^ statistics, ♦264 Cmc, W. & Mich., align't stat.* [•261 Cities, great, to nowhere, 731 , and small, traffic of, 70 Cities often in hollows, 859 party-wall laws, 814 terminal, q.v., 655 ., 472 Clearing, illusive eflfect from, 850 p. c, cost to total, *757 Cleaning locos., g.i>., cost, *i47 Cleveland, Erie business to, 222 Cieve'd & Mar.,align't statist.*26i Clev'd &. Pitts., p. c switching- ^. ^ [miles, *i8r Clev'd. ,C., C.& I., align't statist., p. c. switching-m., *i8i [*26i rates, through and way, con- fstaiit ratio, 224-5 growth, traffic, *2i6 [♦214 p. c local traffic and thro', p. c various classes. *2i5 tons and ton-miles, E. and [W., etc., *2i6 train-load growth, •loi Clev'd,T.V. & W., align't statist., [*26l Clev'd, Mt.V.& D.,align't statist., [*26l Cluster-bent trestles. 900 Coal, cost per ton, U. S., 132 lbs. per car and eng. m., 139 & {See Fuel.) ship'ts west, economy of, 135 used at N. Y. terminals, *8i9 car, ^.7'., extra heavy, ♦490 trains, operating, *i32 &. Coatepec, line at, 937 Coasting and ry. accidents, 257 Cocks, loco., cost. 412 Col burn, Z., loc. tests, 437 Collins, C, on ditching, 773 Collisions, causes of, 245 Colorado: area, pop'n, sidings, p. c. op'g exp., earnings per mile and head, '90 ; wealth jier cap., [♦26 ditches, ocular illusions, 847 elevations, 696-8, 700 rys., cost, 682. 696 example, 694 gauge of, 694 Colo. Cenlr., align't statist., *26^ Col-Con Columbus, C. & I. C, p. c. switch- ^ . . . [ing-mile.s, ♦i8i Combustion, heal in gases, *456 loco., ^.7'.. capacity, 449 -+- Commerce, triangular course of, * Company,' nature of, 28-9 & [615 rent their line, 36 Compass lines. 863 - (of transit) graduating, 888 Compensation of curv., g.v., 620 Competition, eflfect on p. c. op'g f. . . [exp., 109 Competitive rates and non-comp., {Sie Through and Local.) [58 are from door to door, 54 on very long haul, 218 traffic, true classif'n. 212 eflfect distance on, 215 Compound interest, *8o-83, *747 eflfect of, 80 locomotives, chances for, 133 Composition of vel. ex., 287 Compression, loco., g.v.. loss and f, . [gain, 470 concentrating resistances, gain r> fby, 587 Concord & Portsm., alignment [statistics, *259 Concrete for pedestals, 903 Cond^, Hacienda del. locn at. 682 Condensing eng's, cost and eflf'y. gain by, *468 [' & Coning, eflfect on amt . slipping, path of wheels, 312 [288 probably injurious, 289 no eflfect on position of wh'ls, soon disappears, 284 [282 Connecticut: area, pop'n, sidings. p. c op'g exp., earnings per m. and head, ♦90; wealth per cap., ♦26 Connections, short, desirable, 21Q Connellsville & So. Penn., map n vj .• , [on, 888 Consolidation loco., q.v., origin [of, 278 most us*d on heavy curves, on 136 ft. radius, 279 [148, 281 rel. cost reprs., *i46 Construction, abandoning, 787 a priori basis of, 18 'cheap and nasty.' 768 cost of, and accidents, 252 [-f- and cable traction, 688 curve limit, 635 [694 indep't return tracks, switchbacks, 684, 950 — washouts, 783 bad lines cost most, 926 CONTRAST BETWEEN SHEND- [ING TOO MUCH AND TOO LITTLE. 87 economizing, safe direc [lions for, 655, 757 effect on val. of distance, [211 danger of increasing, 113 estimating, 834 by eye, 833 [849 ocular g.7'. illusions, in Colorado. 682. 696 Mexican r'y. 931 1*757 & p. c. cost various items, to S. G. a minor item, 8:53 unevenly distr'd on line. BCONOMV OF, 76a [750 Con-Cul Construction— O// ;'/««<'.. eflfect, 358 strength of, and grades, 328 three conditions for, 362 when most broken, 368 Courtesy of employes, 649 Country farmer ^nd steep hill, 656 inspecting grades, 662 Credits, scap, l(x:o., *i46-9 Crest of hill, contours of, 885 eye fixes on, 842 -f- Creusot, Corliss eng. tests at, 533 as to steam pressure, 474 Cricket and ry. accidents, 258 Crossings, grade, g.?'., accidents r • , . r^^- *246 Cross-sections plotting, 898, 897 rods ffir, 882 Cross-ties, burnettizing, 114, 125 creosoting, 320 cost of, AVERAGE, 124 putting in track, 125 cost of maint. U, S. sections. [*i28, *i7o-6 various roads, 120, 170-6 as aflfected by ballast, 774 by rad. of curves, 640 cutting. 125 economy and form of, 775 length, 780 no. 7's. wi. rails, 776 thickness, 778 life of, and curvature, 320 seasoning. 124 preserving, 114 practice as to. 777-81 size, U. S., 777 Gr. Brit, and Europe, Croton water, purity. *378 [124 Crown-bars, loco., g.v., weight r K-ii • , f^"*^ <^°s^ *4" Cuchillo, spirals on. 684 Cul-de-sacs, def'n, 851 examples, 852, 855 Culverts and floods 781 loc'g in deep fills, 851 Cul-Cur Culverts— Co»e in ui'd. prelim, esls., 898 wooden. 755 [statist.. *26a Cumberland Valley, alignment loc. performance. *438-4i Current of water, judging, 840 Curtis, G. W., on Mex. ry., 932 Curvature, 242 accidents from, 245 Adams, C. F., on, 254 danger of, real, 257 Monte Carlo disaster, 252 on elevated rys., 646 p. c. accidents due to, 249 possible pay'ts for, 250 a minor detail. 185 amount of. (See a /so Sharp.) as aflfected by care and [skill, 635 & inexperience, 654 & radius, 641-2 smooth slopes, 843 [656 time given to surveys, limits of choice, narrow. No. of, U.S., 249. 259 [188 on high line to Leadville, [697 on Rocky Ml. rys., *265 & per mile, av., 628 [*259. States & rys., U.S., full, possible change in loc'n [not great, 251 use to reduce grades, ex., and heavy engines, 278 [661 -f- loco., reprs., small eflfect on, ,. . [-^188 making lime, 268 smooth riding of cars, 275 bad practice as to, *263 English, 242 'broken back,' 870 COMPENSATION FOR, 620 as aflfected by speed, 622 by length train, 634 by radius, 633 at stopping-point's, 633 computing from cent, an- [gle, 629 CONCLUSIONS AS TO, 632 eflfect diflf. rates, *63o on pusher grades, 598 origin of, 621 proper rate not fixed, 627 EXAMPLE. 628 virtual profile given by, COST OF. 312 [621 as aflf. by radius, 323 by repairs engs , 315 by rate grades, 581 causesof. two distinct, 312 CONCLUSIONS AS TO. 321 eflfect on cross-ties. 320 p. c on loc. and car re- ( pairs, *203 per train-mile, *:!22 DEGREE OF. MEANING, 258 distinct objections to, 636 eye exaggerates, 842-!- max. and min. of limiting, max. limits for. 635 [652 disadvantages vi.-sible, 743 distribution irregular, 622 & ends of. trackmen flatten, 276 transition. ^.7'., curves, 276 entering and leaving worst, I275 958 INDEX. INDEX. 959 l| Cur— Cur Curvature— OwZ/wKf-t/. forces acting on, 281 loss of power small, 316 loco. q.v. safety on, 148, 433 loss traffic from, 375 lost time on, 648 & moral effect of, B76 prevailing error as to, 344 LIMITING, 620 TABLE OF, 652 limit of, and bankruptcy, 655 CONCLUSIONS AS TO, 653 effect on construction, 635 fixing in advance wrong, on light rys., 749 [654 60 ft. and e" comb'n, 656 TOPOGRAPHICAL LIMIT, 655 wrong mode of det'g, 244 limits of objecl'able spd.,*273 metric, degrees of, 684 Tadius of, bankruptcy never [comes from, 655 effect on compar've rail [wear, 296 curve com pens' n, 633 curve resistance, con- [cLusiONS, 305 distance, 64a speed, 645 train-load, 650 [292 flange, q z/.,press. unaff'd, in ft., ch., and m., •267 inherent cost, 638 length between same T. ,. . . „ [Ps., *644 limiting effect, 645 loss of time by, 647 cost of, 648 various modes of design- [ing, 358-66 rail wear on, ex., 293 rel. importance, ex., 395 sharp and zigzag devei'ts, 678 examples, elevated rys., [NY., 645-7 high line to Leadville, Mexican ry., 931 [697 Peruvian, 679 sharpest in regular use [U. S., ♦325 U. S. Mil. R. R., 326 flange, q.-i<., wear on, 29a gives choice more routes, [656. 698 lengthens tangts., 641 may save dist.,642 on pusher grades, 667 radii for, *266 [266-7 running with short ch., taking out on old lines, 787 on Penna. rd., 277 * train-degree ' of, 58a Curve protractor, 892 CURVB RESISTANCE, MECHANICS OF, [281 ami. due to surf. fric. only, [291 as affected by age of rails, 295 form do., 295 centrifu. force and super- [elevaiion, 298 greasing flange, 516 obliquity of traction. 301 six and four wheel [truck, 288 various types loc.,*279— I Cur-Den Curve resistance— Continued. as affected by velocity, 911 CONCLUSIONS AS TO, 304 distinction force and power, 600" = I mile dist , 315 [293 Curves, broken rails on, 356 centrif. force, q.v., on, 269 -f- functions of, det'g diffs., *644 inside and outs, rail, differ, [length, 284 loco. q.v. truck, why needed, offsets to, det'g, 872 [426 -f projecting, 892 — to fit topog'y, 668 transition curves for. 869 radii of, determ'g diffs., 644 sharp, short chords prefer- [able, 267 slipping of wheel on, cause, error as to. 287 [284-6 velocity of, 289 transition, q.v.. why needed, vertical, q.v., 869 [276 Gushing, G. W., loc. tests by, 553 Cut-off, loco., q.v., av., *463 -f- and speed, 47T theoret. gain by, •467-8 Cuts(excav., q.v.\ shallow, snow [in, 126 generally last work done, 893 Cutting of cross-ties, cause, 125 trains in two, 599 Cylinders, non-conducV theoret. loco., q.v., life of, 420 Dakota, align't statistics, ♦363; area, pop., sidings, p. c. op. exp., earnings per mile and head, ^90; wealth per capita, *26 Danville & S. W., align't statis- [tics, *263 Days per year, uken at 365, 97 Dayton & Mich., align't statistics, Dazio, spirals at, 673 [♦261 Dead weight and fuelconsump'n, freight cars, av., 610 & [139 mineral, present ratio. 614 of loco., alt grades, ♦688 pass, trains, 491 why little injurious, 139 WHY TENDS TO INCR., 567 Decapod loco., q.v., details, ^lo Defaults, railway, ^o [258 Degree of curve, q.v., measur'g, Depreciation, fr't cars, rate, *204 M. C. B. rule, ^205 Delaford, M. F., expts. as to st'm ^ , [press, 474 Delaware, area, pop'n, sidings, p. c. opg. exp., earning per mile and head, *9o; wealth per cap., [*26 Delaware, Lac. & West., align't [statistics, ♦260 loco, performance, ♦438 sidings, total, *82s p. c. switching-miles. ♦181 terminal exp., etc., N. Y., *8i9 track. Buffalo yd., ♦821 train-load, growth. ♦100 Delaware & H. C. Co., gravity [r'v, 692 Denmark, rail'ys, cost, etc., '^s Denver & Rio G., Calumet Mine [bch., *7oo Den— Dis Denver & Rio G.—Continutd. Consolid'n engs. on, 281 curve comp'n on, 6ai effect n. gauge, 753 financial status, 41 fluct. in stocks, ♦46 long grades on, 699 profile condensed, 698 Denver, So. P. & P., location map. Depots. {See Stations.) [696 Derailing switches, def., 811 Derailment accidents, q.v., 245 and caboose brakes, 359 Desdoint, M.,loco. tests, 521 Detroit grain receipts, 728 Detroit, G.H. & M., align't statis- tics, •362 [700, 932 & Development, examples of, 679 -(-, in flat country, 661 •\- RULE AS TO, 694 spiral, extreme ex., 684 wrong practice as to, 671 Diagrams lor ests. of structures, [898 geometric, exagg'n in, 387 Differences in receipts and exp. [to govern, 17, 63 of rev. make corps, rich, 50 Dining cars, competition witli, 73 dimensions, etc., *49i " Discounting" the future, 34 Dispatching, train, and improve- [ments, old lines, 791, 803 and ballast trains, 774 Disproportion of traffic, q.v., 608 effect on train-Id , 100 coal movement west, 135 Distance (Chap. VII.), 195 a minor detail, 185 and breaking tangts., 334 light railways, 756 reducing low grades, 660-}- radius of curves, 641 4- between towns, effect on [earnings, 700 compar. value, great and small [diffs., 208, 240, 709, 721 construction cost, allowing [for, 3IX contradictory law as to, 219 example of, 728 cost of, 198, 207-8 as affected by amt. of ex- [tra dist., 198 by rate grades, 581 ^ by way rects., 234 credit side to, 211 nature of, 197 [*63i developing, q.v., to gain, ex., to red. pusher grades [wrong, 671 diff. via any curve, *644 effect of, on competitive rects, [*229 on loco, and cars rep'rs, [*203 ON OPG. BXP., 198, 207-8 great diffs., 309 on receipts, on through rects,, 228 LAW AS TO, 228 do. GREAT diffs., 709 errors in values of, 211 estimating by eye, 845 across water. 845 eye foreshortens, 843 -f- Dis— Ear Distance— Cow/Z/iMt-^/, esumating by tim/^ illusions, less often exagf?., 237 [850 OE reconna*sf»i»*ce, 838 GREAT diffs. of, effect, 240, 709, increasing, discourages traffic, [238 to secure way bus., 237 rule as to, 238, 720 LAW AS to THROUGH CONNEC- example, 728 [tioks. 219 moral effect of, 239 [195 mistaken views as to, cause, passing towns to save, 58 rel. importance, ex.. 395 why made basis of rates, 196 Distributing side tracks, *82i Ditching, importance of, 773 oc. illusions as to, 847 Dividends, L. S. & M. S., *99 p. c. of rev. sections U. S., [*io8 rates of U. S. & Brit., *4i sections, U. S., *89, *92-94 Division, length of, effect on cost [grades, 573 tendency to incr., 169 Dome, loco., wt. and cost, *4i4 Dom Pedro II., ry., loco, perfce., Dorsey, E. B., paper by, 529 [*44o Double-ender loco., def., 433 Double-tracking, 764 and jfravity rys., 693 obtaining, by imp'ts grade,8o6 Drainage, mental map of, 836 Draw-bars, elev'd r'y, 646 tension on, in sags, 356 as mod. by speed, 347, 349 when most broken, 368 [*346 Drawbridges, accidents from, weight of, 905. Draw-gear, frt., cost and de- [prec'n, ♦204 repairs of, 161 p. c. due to various causes, -. [*203 Dredge, J., " Penna R.," error in, ^ . . [*4»6 Dnving-wheels, centres, life, 420 Id. on persq. ft. grate, ^452 weight {see also Loco.), 414 * Drop test ' for tr'n resist., 909 Drummers, and minor details, 192 Dubuque & S.C, align't stat., *262 Dudley, P. H., expts. on ft. speed, on train resistance, 518 [370 Dudley. P. H., fuel tests, 529 Dudley, C. B., exp'ts on rail-wear, Duluth, grain rec'ts, 738 [320 Dump-cars, 774 [222 Dunkirk, constructive mileage to. Duplicate tracks for pusher r* wv. u • • [grades, 691 Durability, buying, in rails, 739 + Durango, location at, 723 Dynamics of train move't, 331 Dynamometer tests and vel., 346, and zero temp's, 508 (349 deceptive effect of, 435 Earnings as affected by dist., 229 by dist. between towns, [709 per mile, sections U.S.,*73-8i, [*89-94. '107 Ear~Eco Earnings, per mi\&— Continued. distribution of do.. *io8 elevated r'ys, 646 Iowa, 77 L. S. & M. S., 99 Mass.. 78 per head, pass, and fr't, by [sections U. S., ♦73-81, ♦92-94 do. whole U. S., ♦73-85, Iowa, 77 [•g^ Mass., 78 per engine. Am. & English. sections U. S. *89 [♦ 159 {See Revenue, Europe, etc.) Earthwork, computing, 895 cost of, on narrow g., 753 exec'g by train, 773, 806. prismoidal form 'a, 895 [511 Eastern ry., France, journal-box, loc. tests on, 466, 533 [*i8i Eastern Rd.,p.c. switching-miles. Eastern States, fall rivers in, 841 East Kent'y. loco.perf'ce. *438 East Tenn., V. & G. loco, perfce, loco, tests on, 701 [^438 Easy country, errrors in, 584 & Eating station, and compet. traf- y> [fic. 73 isconomy in construction, q.v., [why generally safe, 87 Engravings, Index by Numbers: ' ' Edg-Eng Edgehill, sidings at, 827 Elasticity, modulus of, def., 345 Electricity as motor, possible _, [effect, 328 Electric interlocking, q.v., 811 Elevated r'ys, cost per lb., 905 curves, resist, on, 297 sharpest, ^325 speed on, 273, 325 earnings and exp., 646 growth traffic on, ^714 Eer inhab't, ♦714 andling of trains, ^559 length, stops, etc., ^559 Elevations, oc. q.v. illusions as [to, 844-f Elizabeth, L. & B. S., align't stat- ist., ^264 Elliott, T. S., & Jalapa line, 943 Ely, T. W., on Consolidation eng., Emery, C. E., paper by, *53i [*i4a Employes and break in twos, 359 and heavy engines, 360 at N. Y. terminals, ^819 courtesy in, 649 no. on XJ. S. r'ys, 249 [in, 896 End-areas, earthwork, q. v., error End platforms, frt. cars. ♦486 Energy and press., confusion as how u sed up, 333 [to, 473 Fig, Jo 1 2 3 4 5 6 7 8 9 — 33 34 35 157 189 189 230 230 230 10 20 30 230 282 292 230 283 294 230 283 293 237 284 293 242 28s 293 251 286 293 253 287 293 256 287 293 271 291 293 271 293 293 40 50 60 293 302 3" 293 303 3" 294 305 339 298 306 339 298 307 343 299 308 344 299 308 345 299 310 345 300 310 347 301 13 70 80 90 350 363 387 351 366 387 352 366 387 355 369 389 356 371 389 430 360 377 S:»0 361 38s 391 362 386 403 362 386 426 363 386 427 lUO 427 429 429 430 430 431 433 449 476 481 1 447 447 110 120 130 447 455 477 448 459 478 448 461 478 448 462 478 448 467 480 448 467 480 448 476 480 455 476 481 455 477 481 140 160 482 489 514 482 489 515 482 493 516 482 494 518 483 497 521 483 504 521 483 5»i 483 5" 536 484 5«i 537 489 511 552 170 180 190 561 621 647 561 623 647 562 624 652 562 624 660 625 661 587 629 661 588 636 664. 588 636 664 588 642 668 1 604 642-6 666 'l\ni 668 671 672 672 673 673 673 676 678 I 679 210 220 230 679 686 696 679 686 697 680 689 698 681 68q 708 682 680 708+ 684 691 710 684 693 711 684 694 711 685 695 712 685 696 723 240 250 260 727 775 802 728^ 775 803 735 783 805 735 8^5 736 791 806 739 796 807 763 799 838 767 801 843 769 801 843 770 802 844 270 280 390 845 859 882 846 862 882 846 863 883 847 869 884 848 870 88s 849 870 885 853 871 887 853 872 888 859 874 889 859 874 889 3U0I 897 902 9»4 917 918' 918 918 919 928 933 ilU| 934 945 946 947 234', P .708; ' 241', p. 734- i 960 Engravings Engravings, Inukx by Subject: Abutments, pile. 770 Alignment, possible devia'ns [small, 189 Ameca River spirals, etc., 684 Ames car coupler, 489 American line to Mexico, [maps, etc., 93a -f Arc, mental, strikinjf, 838 Areas, ft. lbs. and H. U., 455 Ball on plank, 308 Belter country than it looks. Bissell truck, 426. 429-31 [848 Boiler power, adaptingf, 403 Brakes, computing eflf'y, 494 brancli lines, examps., 734-6 Breckenridge, Col., loc^n at. Bridges, comp. wt., 767 [696 diff . rolling I'ds. 769 vibration of, 447-8 Broken-back curves, ex., 870 Burlington train-r. tests. 497 Cable system, planes for,689-93 Cars, centre grav. of. 271 Car-wheels, compression of, usual Am., 514 [562 Cattle guard, C, M. & St. P., Centre of gravity in sags, 360 of rolling-stock, 271 Chicago, M. & St. P. timber [strucs., 770 N. W. grain receipts, 728 Cine, N. O. & Tex. P. loco. ^ , , , [tests, 482 -(- Coal, lump of unbiirnt, 449 Cochituatc, L., rainfall, 783 Cone, contour map of. 874 Coning, model for testing, 311 radius of path wheels. 319 Contour lines, errors in. 884-5 maps, Hnishing, 888 nature of, 874 Counterweights, loc, 447 Couplers, automatic, 489 Couplings, forces at. 301, 303 Crossings, stops at. grades,8oa Cross-section rods. 882 Cross-ties, theory of form, 775 Curvature and accidents, 253 and tunnels, 242 [629 compensating, effect, 621, on low grades, 652 radius of, 5° and io», _ [636-40 Curves and wheel-bases, 283-!- checking speed on, 647 comp. safety locos, on, 433 offsets to, determ'g, 872 position truck on, 256, aSaJ radius of, and speed, 647 rail-wear on, 293 [646 Curves, sharp, elevated rys., may save dist., 642 variat'ns dist. via, 643 Denver, So. P, & p., map, [etc., 695-7 Development, effect, 588 examples, 668-686'& Distance and rate grade, 671 and sharp curves, 642 effect on receipts, 230 oc. illusions as to. 859 slight effect lateral dev'ns, total & rategrades,67i[237 via various curves, 642 INDEX. Engravings Engravings, I.nukx By Subject: Double track, uses of, 693-4' Eastern ry., France, jour.- Klevated ry. curves, 646-8 English tunnel, 242 Estimating, from profiles. 897 Falling bodies, paths, 339 vel.of,624 [887 Field-sheets for mapping, ex., Flange-prcs., loc., on curves, [433 resultant, 292, 294, 299 -wear, actual. 308 alleged, 307 Foot-lbs., areas and H. U.,455 Forces, triangle of. closg, s^? Forney, M. N . modd. 3I1 Friction, apparatus for test- [ing, 914 coef. of, light press., 504 experiments as to, 504, Gauge, effect of, 305 [917-19 ueometric diagrams, exagger- [aiions, 387 Georgetown spiral, 681 Grade-lines, possible devia'ns n A . [small, 189 (trades and uncomp'd curv., . , [625, 629 broken, sags and up'd, 624 forces on, 339, 536 heavy, of world, 698 long, broken vs. cont's, momentum, 344-5 & [^85 of repose iucreas'g speed, last car, 362 [369 rate of, and asst. eng., 587 St. Gothard r'y, 672-3 reduc'g by devel t. 588,668 saves no dist., 671 resistance of, 5:56 sags and summits, 623-4 switchback grades, 947 train-load on, 552 unif. and pusher, 604 virtual, ^r.?.., 348-^,703 long, 353 Grain rec'is, N. W., 728 Gravity, action on grades, 536 on diff. paths of desc't, 634 r'ys. typ. profile, 691 Great inclines of world, 698 Grooved wheel, 294 Gyration, radius of, 739 [455 Heat-units and temp.,distinc.. Hemisphere, contour map of. Hill, J. W., loc. test., 461 [S74 Hut, ocul. illusion as to, 846 Impact at ioints. 561 Inclined planes, forces on, 339 vel. down, 624 types. 689-93 Indicator diagrams, actual ex- . [amps.. 476-84 typical, simplest, 456 with expan., 467 Interlocking app's for switch- [backs. 946 Interpolating dist., effect on [reel's, 230 Iron, pnce of, past, 763 Jalapa line, maps, etc., 932 -f profile, 698 Janney car-coupler. 489 Journal-box.E. r'y,France,5ix I INDEX. g6i Engravings Engravings. Index bv Subject- Jour'l-box, usual Am., 514 [0,^ Jour'l fric, app'ius for lesiV diagrams of, 5,5, 917 + ' Lake Shore & .Vl. s. train . [resist, tests, 518 Latitudes and departures, dia- fgram for comp'g, 880 Leadville, high line to. 695-7 Lehigh Valley rail sec'n, 310 Located and prelim, line. 863 Location around ridge, 668 in fiat country, 661 Locomotives, asst. and grades profile for, 666 [587 vs. through engs., 604 use o ve r su m in i I s, 689- boiler-power of, 403 [04 Bissell truck, 426, 429-31 coal, unburnt, lump, 449 centre grav. of, 271 comp. safety on curv's,433 counterweights, 447 indicator diags., 476-84 — power of,ongrades,552. 587 resist, of, prop'nal, 521 trucks, 429 ± tests, 461-81 wheel-base diags., 426 -f- wts., 769 [test, 463 London. Br. & So. C. loco. Lubrication, effect on fric. [917-n Manhat'n elev. ry c'rves,646-7 Mapping, field-sheets for, ex., [887 good and bad ex., 888 Mexican Central, Ameca r. [spirals, 684 Tepic to coast, 676-7 spiral on, 678 National, Pacific b'ch, 723 Mexico- Vera Cruz, map, 932 Momentum grades, 344-5, [623-5. 703 Monte Carlo disaster, 253 Mounuin grade, Jalapa line, KT- .. . . r9.34 + Niagara cantilev'r brdg., wt., [etc., 902 Norihwestern gram rects., 728 Obliquity of traction, 301 Ocular illusions, 84^ -f-, 665 Offsets appear too large, 665 to curves. 872 Oroya ry. developm'ts. 679. Overlap, views of, 846-7 [684-6 Parabola, principle of, 387 Parallelogram ol forces. 302 Pass, oc. illusion as to. 845 Peruvian r'ys, profile, 698 Prelim, and located line, 863 Prices, fiuct'ns in, 763 Profile condensed, ex. of, 862 estimating from, 897 Jalapa line. 938 [853 of badly reconnoit'd line, virtual, pass., 348 -f- frt., 352 -f long grade, 355 saR''. 356 -f- Pulley and rope, 302 Radiation, effect on cyls., 476 Rails, alleged corner wear, 307 and wheels, positions, [292-4 Engravings Engravings, Index bv Subject- Kails, bending of, 493, 775 compression of, 516, 562 price of, past, 763 section, L. V., 310 sections, worn, 293 strength of, 739 yielding of, 493 . at joints, 561 Kainlall, past 20 yrs., 78^ Rates, dec. in U.S., 727 ^^-c Reconnaissance, ex. of' bad, I853 manner of making, 838 Resultant, flange press., 292 Ridge, low. loc'g over, 661-4 Rise and fall, on grades and [level, 366 worstclassof, 37,, 377 Rolling-load, comp. effect, 767 diags. of, 769 bags and summits, 363, 623-4 centre ot grav. in, 360 motion through, 356 -(- filling up, 806 erceptib1e slip exp'ts, no. and work of, ^160 repr. details, *i45 963 Fra— Fue France — Continued. loco.drivers, tests of, 521,533 -|- railway manage't in, ^575 safety in, 258 system, growth of, 44 rec'ts per inhabt. pass, and [frt., ♦los rolling-stock, traffic, etc., 43 details, 521 train-loads in, and Am., 575 train-resist, tests, 521, 528 Francis. Chas., diagram by, 889 Free omnibuses and errors of [location, 54 Freight and pass, locos., q.v., [tire reps. *i49 Freight cars a.v. per mile, sects. [U. S. *89 world, 43 earnings, ^.7/., thro' and local, [sect'ns U. S., ♦231 per head, do., 92-4 tons of, world, ^43 [U.S., ♦181 traffic, f.T., p. c. of, sections, trains, q.v., no., load and haul, [U. S. sections, ^97 growth of load, 98-100 Fremont pass., ♦700 Freshets and structures, 781 Freycinet, est. by, loco, rail-wear, [122 Friction and heat, journals, 314 app's for test'g in lathe, 914 as affected bv area, 295 by lub'n, 509, 917-9 by press., 504-5, 917-9 by temp're, ^505 by coei. fric, time, ^290 by velocity. 289, 913 bath lub'n, 509, 918 brakes, y.7'., av., 494 brake-shoes and wheels, ♦290 car-wheels. 289 driving-wheels, 435 loco.. O.V., *529 -j- & Morin s exp'ts, 503 of rest, 920 rotative, wheel on rail, 291 skidded wheels, ^290 slide-valve. 532 starting, y v., 919 stationary eng.. ♦ssi Friction-grip r'y, origin, etc., 691 Frogs, accidents from, ^246 and switches, cost, various [roads. *i2o Frost and broken rails, 256 [♦409 Fry, Howard, and W. S. enRines, on English coal consump., 133 Fuel, consumption of, 132 as affected by comp d [eng., 133 train-length, *i36 due to head resist., 53° — English and Am... ^^^^ ^ [diff., 134 per mile, ♦sig cost of, 132 as affected by curv., 3*3 distance, 199 radius of curve, 639 rise and fall, 375 temperature, 3'4 wt. of engine. 563 wt. trains, 568 work done by eng., 376 Fue-Gra Fuel, cost ol— Continued. causes of variation, 158 C, B. & Q., tendency on, per ton-mile, ^147 [157 Chicago rds., *i74-6 sections, U. S., *i7o-6 trunk lines, ♦172-6 ejected from smoke-stack, 449 heat units in, ^450 high and low speeds, 529 per car-mile, P. R. R.. *i4o H. P., actual, ^460 stationary engines, 531 theoretical, ^460 train-mile P. R. R. lbs., cost, ^140 [♦ho rate of combustion, 449 terminal wastage of, 2cx) wastage of, by blast, 449 wood as, 139 amt. burned P. & R., ♦200 furniture, U. S. value, ^25 Furniture car, C. & N. W., ^490 Future growth, f.v., of traffic, [est'g, 24 not to be est'd far ahead,79 ■fl, value of, 332 ■Gallon, D.. exp'ts on brakes, 290, •Gauge, def'n. 284 [434-5, 495 and curve resist, 305 [751 narrow, q.7'., pros and cons, tight, effeci,on wheels, 283 'General and sia'n expenses, 118, [178 as affected by distance, 206 considerable diff 's, 210 no. trains, 568 of car repairs, j6o of loc. repairs, ♦145-7 Oeneral officers and clerks, cost, [Chicago r'ds, ♦174-C sections, U. S., ♦170-6 trunk lines, ^172-6 [lence, 832 Geometric and commerc'l excel- diagrams, exagg'd, 387 ■Georgetown, spiral at, 680 -[- ■Georgia, align't statist., ^264; area, pop'n, sidings, p.c. opg. exp., earnings per mile and head, ♦go; wealth per cap, ^26 Georgia r'y, align't statist., ^264 miles and earnings, ^719 pile-driver car, ^490 Germany, align't statist., ^265 axle-boxes in, 515 coal consumption per m., 135 growth r'y system, 44 locos., life of, *4ig no. and work of, ♦160 high steam-press., ^519 popul'n r'ys, wealth, etc., ^27, '43. *45 rolling-stock, traffic, etc., ^43 Giovi r'y grade, ^699 Gondola cars, dimens., etc., ♦486-7 ■* Good times ' and r'y constr., [763 & Gothard r'y, condensed profile, [698-9 Governing points for grade-lines, [675 Grading, p. c. cost to total, ♦757, filling by train, 773, 806 [^833 cost of, vs. rail-sections, 749 790. (809 Grades Grade-contour, def., 874 examples, 678, 684, 888 horiz'l approx. to, error, . . [877 use in projecting, 890 Grade crossings and curve limits, [655 AND INTERLOCKING, old lines, 802-3 laws as to, 812 Grades, accidents on, 949 and ductuating vel., 346 and rise and f., distinct., 327-9 asst. eng., g.v., laying out, [596, 600 bad not always cheapest, 583 balance of, for assi. engs., 591 for unequal traffic, 608 diff. for each class traff., example, 617 [617 errors in computing, 61 1 practical consid'ns, 611 table for all con- [ditions, 612 breaks of, measure cost rise [and f., 384 bunched, 585 -|-. 618 {See As&t. Engines.) changes in, comp. effect with [diff. locos., 555 choice of, 659 GENERAL RULE FOR, 66o comparison of pusher and [uniform, 604 -j- cost of, 560 asaff'd by Tgth division. 573 cheap pass, traffic, 580 conclusions as to, 573 diff. for through and pusher [gr., ex., 674- due to work not done, 589 interest charge on new Iocs , [570 per daily train and ton-m., [compar'n, ^574 French est., ^576 German est., 576 VALUE OF AVOIDING IN- [CREASE, 574 de facto, def'n, 543. 515 descending, when brakes [needed, 371 disadvantages not visible, 242 effect on loc. and car repairs, [♦203 on net train-Id., diag., . , , ^552 on train-load, 536 estimating by eye, 844 -|- fixing rates of, 893 and inundations, 783 high, causes favoring, 671 expedients for red'g, 675 great inclines of world, [♦698-9, ♦700 handling trains on, diff'y, p. c. wt. eng. on, 669 rel. train-l'ds on, ♦669 speed on, 369 how expressed, 537 in England, 538 humps in, dangerous, 367 hydraulic grade line, 625 improving, and more traffic, [comp. value, 112 double track, 806 Grades Grades — Com in u ed. improving, loco. q.v. design [an obstacle, 478 — on old lines, 788 inherent objections to, 328 irregular, effect on pass, ir'ns, length of, effect on virt. pro- [file, 704 per sta., boriz. and along , , u ^, • [slope. *34i level, hardly exist, 551 limit'g eff't, and rail-wear, 379 locating, field-work for, 865 -f- selecting rate, 675 long, errors as to, 329 longest in the world, 925 switchbacks for, 943 loss of wt. on, 539 low, adapting to topog'y, 665 compens'g for curves, 620, projecting, 660 [652 reducing, 665 wrong use of, 671 moinenlum, def. and ex., 344 motion of trains on. 342 -f objections to. two distinct, 327 of repose, def., 341 table, ^358 French, ^522 pass., all speeds, ^579 last car in sags, 362 one p.c, effect, changes in. on [loco, mileage, ^557 pass, locos, aff'd little, 479 PER CENT CHANGE NET LOAD [due TO CHANGES, 554-7 projecting, 890 descent ag'st valley slope, [682 GENERAL RULE FOR, 66o lifting bodily, 892 long g's dangerous, 893 ovtr streams. 893 selecting rate, 675 shallow cuts bad, 126, 893 prop'n traffic affected by, 576 rale of, as aff'd by care, 659 and light rys., 758 effect on cost, minor de- [lails, 581 fitting to ground, ex., 670 improving old lines, 785 order of importance, 768 projecting, 893 p. c wt. eng. to train, all [grades, 66g PER MILE AND P. C, small imp ce with [pushers, ^587 REDUCING, BY LOWER PASS. [speed, 579 by more care, ex., 667 & relative imp'ce, ex., 395 net load on, ^574 train-load for all, ^669 resistance of, 536-40 effect on gross load, 540 on net load, 541 formulae for, 540 gain by concentrat'g, ^587 how determined, 339 rolling frict. adds to, 34^ rising above and below, diff.. [367 I 964 INDEX, INDEX. 965 Grades Grades — Continued. ruling, AND LIMITS OP cunvA- [tuke, 652 eflfect on pass, trains, 577 devices lor reducing, 659 NATUKE OF EXPENSK FROM, u ,1587 + pusher vs. throuf^h, 667 rule for reducing, 665 60 ft. and 6° comb'n. 656 speqd, slow, effect, 622 stations on, 788 -|- starting, TO ELiM. f.xtra fric, station, ^.7'., 788-4- [512 and pass, trains, 4Q1 statistics of, U. S., Stales, etc., stops, q.v., on, ♦512 importance of (elev. rys.), switchback, 947 -f- TRAIN-LOAU ON ALL, FOR ALL [logs.. *543 -f (small table), •593 undulating, q. v., and im- [proving old roads, 799 eliminated by speed, 348 error as to, 329 little eff't on pass, I'ns, 592 on light railways, 755 safe limits, 356 uniform, hard to secute, 586 & virtual, q.v.^ and actual, diflf., length makes no diff., 799 starting, ex. of compu- [tation, *S59 Grading, abandoning old, cost, 787 Grain, bushels of, per mile r'y, +90 Northwest receipts, 728 Grand Central sta., N. Y.,cost, 70 Grand Trunk, capM and earnings. L*io7 competitive disadv's, 240 Grate area, loco.,y.7/., act'l,*407-io H. P. p. sq. ft., expt., 484 limits for, 451-3 wt. on drivers, p. sq. ft., 452 Gravity, acceleration of, 333 action on incl'd planes, 339, 536 railways, nature of, and ex., rail-wear on, 122 [691 tests of train res., 497 [124 Great Britain, cross-tie practice, curves, mode of design'g, 266 curves not compens'd, 621 fastest trains, and Am., *529 fuel g.v. consump. in, and lU. S., 131-3 cause of dm., 134 expenses per mile road, 116 grades, modes of expr'g, 538 growth traffic, q.z'., 131-2 locos., f.v.f comp. safety on [curves, 434 duty of, comp. with Am., life of parts, *4i9 [*i59 & maint. per year per eng., [and Am., ♦159 p. c. labor and mater'l. [*I52 & no. and work of, ♦159-60 scrap value, ^20 type of wheel-base, 428 wt. and cost, and Am., error as to, *4i6 [*4ii-i- Gre-Hau Great Britain— r<)«//««^a'. no grade crossings, 8ro op'g exp.. cts. and p. c, ♦178 pass, speed, why higher, ♦530 p. c. op'g exn., *iio, *i78 recent tendency, 116 [*io5 rects. p. inhab. pass, and fgt., switching-mileage prop'n, 135 terminals, y.r.,and term, exp , [827 & train-mile cost, etc., *ii6 Vignoleson, 187 wages in and Am., *isi Great Eastern r'y. locos., cost and [miles per yr., ♦159 traffic and fuel consump.. ♦131 Great inclines of world. *698-9 Great North, ry., fastest trains, 1*529 locos., cost and miles per yr, repr. details, *i45 [•iso Great So. & W. ry. ^ locos., cost new details, 155 per ton. details, ^ii repairs in detail, •144-5 and renewals, 146 many small details. 149 p.c. labor and mat'ls, *i52 wt. and cost in det'l, *4i6 motive-power exp., ♦133 details. *i47 wages in shop, *isi Great system of r'y. U. S., *7i9 Great VVestern r'y, fastest trains, [*5*9 locos., cost and miles per yr.. _, „ [*»55, *iS9 p. ton, det Is, *i55, *4ii repr. details, ♦145 motive -power exp..' details, trarncand fuel consump., *i3i Green river, fall, 841 [533 Grossman. J., on lubrication, 516, Growth of r'y system, world, *43 traffic, q.v., irregular, 85 how to estimate, 87 ratio to rate interest, 85 TO BK CONSIDERED ONLY [for 3 to 5 VRs., 80, 85 in no. engs., Engl., *i45 of train-load, q.v., •97-101 Guadalajara. Mex. Nat. loc'n to. Guessing, effect of, 658 & [723 Gulf States : area, pop'n, earn gs, [p. m. and head, etc., *9i fall rivers in. 8ti gen. r'y statistics. ♦88 pass, and frt. haul and tratO' [I'd, etc., V (Sfe South.) Gyration, radius q.v. of, 739 Hachures, use, 873 Hackmen profit by bad location. Hammer blow, 447 [60. 6a, 68 Hand-level, use of. 838, 847 [*26< Hannibal & St, J. align't statist, Harlan & Hoi. Co. pass. car. *49i Haul, extra, not a burden on [traffic. 61 pass, and freight C, C, C. & [I., 12 yrs., 224-5 U. S. and States, *97, ♦us, ['217 & L. S. St. M. S. do., ♦9a Hau-lll Haupt, H., on asst. engines, 585 on inclined planes, 944 Head resistance table, 522 eflfect on fuel, 530 — Headway of trains, det. and elev. [r'ys, 646 Heat from journal-fric.,y.7'.. 314 Heating surface, various locos., „ _, [*407-io Heat-units and temperature dis- in fuels, *45o [tinction,*454 in steam, various press., *454 Heavy construct'n, g.v., error in, [20 & Highways, errors resulting from, [835, 850 examples, 667, 853, 936 grades of, illusions, 844 old Mexican road, 941 Higley roller journals, 923 Hill, A. F.. loco, test by, 445 Hills, propinq'ty of, oc. illu'n. 846 Holland, align't statist., *a6s [*^^ pop'n, r'ys, wealth, etc., ♦27, Hopper cars, dimens., etc., *486-7 Horizon, best line lies beyond, 837 Horse-cars benefit by bad loco., [60, 62, 6a traffic of N. Y., ♦714 per inhab't, •714 Horse-power, cost of, stationary- definition, 338, 403 [eng., •531 effective and indic'd.464 increases as 7'*, *522 lbs. steam per, loco.. 456 -j- stat'n'y eng., *53t theoret'l, all press., *46» min., fuel per, 469 persq. ft. grate, 451, 484 to utilize full adhesion. ♦45, Horse r'y. longest in world, ojo Houses, U. S., value, 25 and r'y accidents, 258 [6«4 Huayacan, Cuchillode, spirals at, Hudson, C. H., loco, teste by, 701 Hudson river, fall, 841 ocular illus*n on, 848 water of, purity, ^378 Huds. R. Rd., alignoient statist., level grades of. 327 [*259> (See New York C. & H. R.) Hut. ocular illus'n as to, 847 Hydraulic grade-line and sags. q. Hyperbola, locus of, 404 [v., 625 Ice and snow, cost due to, 126 Idaho r area, popu., sidings, p. c. opg. exp., earnings per mile and head, '90 ; wealth per cap., *26 Illegitimate r'y enterprises, 14 Illinois : alignment statist., ^262 ; area, popu., sidings, p. c. opg. exp., earnings per mile and bead, *go interlocking law, 814 water in, quality, *378 wealth per cap., 26 Illinois Cent., align't statist, *262 flucts. in stock, '46 loco, old, wt. in det'l, *4i4 maint. way exp. by items, ♦120 miles and earn'gs, *7i9 opg. exp. and trains per day, rates on, fall of, *726 [*«7* train-Id. growth, *ioi Illusions, ocular, q.v., 84^ Imp-Jac Impacts, law of. 561 Imperceptible shp. q.7>.. 445 [785 Improvement of old lines, q.v., Inception of r'y projects (ch. i.), 13 Inclined plane, theory of. 536 lifting car up by vel.. 343 Inclined planes, gravity on, 339 law of motion on, 339 passing summits by, 689 pros and cons, 686 [*378 Incrustation, loco., q.v., aval, daily. Indeterminate problems, bad so- [lutions of, 7 India: locos., no. and work of,*i59; p. c. of operating exp's, *iio; railway equipt.. etc., ^43 ; roll- ing-stock p)er mile. *47 Indiana : alignment statist. in,*26i area, popu., sidings, p. c. opg. exp., earnings per mile and bead, *9o interlocking law, 813 wealth, per cap., 26 [*26i Indian., D. & S., align't statist.. Indicator diags., exs., all cond'ns. T .,• .,*''f°''yo/' 459.467 +[*476 Individuals, each a traffic unit, 715 Intiernillos. location at. 685 Ingenio river, location in, 675 Initial friction, q.v., 919 & Inspection of steel rails, q.v., neg- [lected. 119 Insurance cost. Chicago r'ds, sections, U. S., *i7o-6 [*i74-6 trunk lines, ♦172-6 Interchange of frt. cars, rates and [conditions, 164 Intercolonial, rolling-stock per m.. Interest charge, nature of, 106 [^47 compound, tables, *8o-83 how .iffects location, 17 on add'l locos., 570, 604 on bonds, p. c. of rev., sections [U. S., ♦108 Interlocking, amt. used, England and asst. eng , 601 [& U. S., 809 easy curves, 655 grade-crossings, 790, 802, switchbacks, 946 [809 cabins for, size, 809 cost of, 810-11 Inundations of r'y lines, 783 Invention and engineering, i Iowa: align't statistics, ♦262;area, population, etc., 90 fall rivers in, 841 growth r'ys, popu., earnings, u ,[etc.,*77 r'y earnings per head, etc.,^77, [*9o sidings, p. c. opg. exp., etc., 90 wealth per cap.. ^26 Iquique r'y, Peru, Fairlieloc.,^4io Irrigating ditches, oc. illus'ns as [to, 847 Italy, adhesion in, assumed. 443 locos., no. and work of, ♦160 popu., r'ys, wealth, etc., ^27, [*43i *45 rolling-Stock, traffic, etc.,^43 p. c. opg. exp.. ♦110 rects. per inh'abt.pass.and frt., Ixtaccihuatl, mt*n, 927 [♦los Jackson, L. & S., align't statistics, [♦262 Jal-Lak Jalapa, highway via, 928 horse r'y to, 930 line, description, 932 low grades needed for, 670 map, 928 Mexican rep't on, 930 profile, condensed, 698, 701 zigzag devel't on, 678 Janney car-coupler, 489 Jeans. J. S., table from, *i59-6o Jervis, J. B., invented loco, truck, [421 Journal, effect, size of, 51^, 012 M. C. B. st'd, 499 max. I'ds on, 513 [tion, ^204 bearing, cost, and deprecia- roller, 912,923 weight of, ^163 box, defects of ord'y, 510 -{■ improved, 511 friction, 509, 913 as affected by I'd, 503, 611 expts. as to, 913 app'sfor, 914 normal am't, ^509 starting, 512 [24* 'Judgment." danger of trusting, Junction points for fr't cars, 166 Justifiable expend, for future $1, to save $1 per y'r, ^83 [*82 Jura r'y, profile, 698 Kansas: area.popu., sidings, p.c. opg, exp., earnings per mile and head, *9o; wealth per cap., ^26 Kansas Pac. loco, perf'ce, *439 Kentucky, align't statist., ^264; area, popu., sidings, p. c. opg. exp., earnings per mile and head, ^90; wealth per cap, ^26 Kentucky river bridge, wt., 901 Kindling fires. Ph. & R. cost, *2oo Kingwood tunnel, temp'y line, [♦700 Labor, wages, q.v., Amer. and [Eng.,*4i7 and mat 1. cars, q.v., *i6i-4 locos., y.7/. , details,*i33, Eng., ^133 [*i4S,*i5i French. ^147 [19 Laborer, useless work no gain to, Lagging: loco., <7. 7/., eflfect of, 508 wt. and cost, ^413 -j- Lake Erie & W., align't .stat.,^26i Lake Shore & M.S. .align't statist., ditching on, 773 [*26i chart of financial record, 33 exp'ts on frt. speed, 370 flucts. in stock, *46 freight car, reprs. on, 162 renewals separately,^i6s fuel tests, 529 loco, boiler, life, *4i9 water supply, +420 miles and earn'gs, *7i9 motive-power, exp. det'ls,*i47 radiation tests, 313 rates, through and way, E. & [W. b'd, 226, 115 fall in, *726 sidings, total, etc., ^825 statistics frt. trafl[., *98 pass, traff., ♦gS ton-mile rects.. etc.. ♦iis track Buflfalo yd , *82i train-resist, tests of, 518, 909 Lan-Loc Lancashire & Y. loco, repr. det'ls. Landscape gardening and maint. [way, 124 Landslides, accidents from, *247 Lap, def'n of, 470 [122 Launhardt, est. by, loc. rail wear, Latimer rerailing guard, 900 Latitudes and departures, use of. 886 [comput'g. 889 Latrobe, B. H., cxpts. on adh's'n, [temp'y iines by, 445. 7(x> Lava, basaltic, character, 684 [443 river of, 928-32 La Veta Pass, *698-9 Lead, loco., 470 of freight, etc. {See Haul.) Leadville, high line to, 695 4- Legal exp's, various rds. and sec- [tions U. S., ♦170-6 Lehigh & Susq. loc. perform., *44o sharpest curve, ♦325 Lehigh Valley align't statist., ^260 Consolidation loc. invented [on. 278, 423 loc. performance, ♦438-40 Mastodon, details, ^410 Id. on drivers per sq. ft. [grate, ^452 pass, car, st'd, ^491 rail-sect'n and wh'l tread, 310 track Buflfalo y'd, ♦82- Level, hand, use of. 838. 847 line, guessing at. 838 party, organiz'n, 8t>i,867 slope, 882 Levelling on preliminar's, 861, 865 Lewisbg& Tyrone align't statist., 1*260 Lighters, no., N.Y. term'ls, *8i9 Light lines in difficult c'try, 20 & Light rails, q.v., and I't r'ys, 737 Light railways, 737 and curvature, 749 and dist. (choosing route), 722 and value low grades, 576, 758 CONCLUSIONS AS TO, 761 expedient economies, 748 rel. value of more traflf. 10,^713 total cost, 758 & why do not multiply, 737 Lignite, H. U. in, ^450 [on. 679-f- Lima & Oroya ry., developments profile, 698-9 Limiting curvature, q.v., 620 grades, q.v., 536 Line, always easy to get a, 832, 840 best, lies beyond horizon, 837 may survey a, but no^ recon., no. of, to survey, ^.7'., 834 [835 worst errors in wrong selec'n, [832 (See Route, Location, Topogra- , phy.) Line cars, def n, i68 mileage of, 168 relative cost reprs., ^161 Link, coupling, q.v., forces act- [ing at, 303 Link-motion, invention, etc., 458 Liverpool, sidings at, 827 station exp. at. 828 Live-stock, U. S. value, ^25 Local freight, sidings for, ^821 + Local rates, q.7'., constant ratio [to through, 224-6 mmm 966 Loca— Loco Local traffic, i^.7/., true classifi., an effect distance on, 213 Locating engineer, g.v., altitude [of mind, 21, 831 +, 840, 855 & end of, 2 {(q.v.), 684 Location and transition curves, aptitude for, and topog'y, 880 art of, lies in choice of route, av. practice in, 4, 583 [840 bad, reasons for, 4 -|- care in, and amt. curv., 656 & CHOICB OF ROUTE WHEN CLOSE, [583 freer with sharp curves. CONDUCT OF, 831 [656 correct'g by trans'n curv.. 870 curve limit and topog'y, 655 difficulty of good prac. in. _ [2 4-, 926 effect on rev., 48 errors in, & cont'r maps. 876 how originate, 658 worst in recon'sance,832 GENERAL RULES FOR, 66o, 694 LINE ALWAYS EXISTS, 832, 840 marvellous feat sci. skill, qt2 office chair ioc'n, 880 — [787 old lines, common errors in, over prairie ridge, 66i 4- paper, q.v., 868 + party for, 867 [328 possibl« effect of electricity, project's (y.t'.) and mapping, [886, 890 RULE FOR, IN MODERATE [COUNTRV, 694 running in the, 867 [698 sharp curves give new routes. Western States, errors in, 6. . [21, ^263, 330, 588, 660 Loch Katrine water, purity, *378 Locomotive engine, 399 adhesion of, 434 AMT. OF, 435 -I- computing from I'ds, 444 defic'y, how shown, 405 effec»^ of changes in, *44o exp'ts as to, 434 -|- extreme resorts to incr., maximum, 440 [424 per sq. ft. grate, *45a RATIOS OF, 437 Am. and for'n, 443 resistances which tax, 49a safe limits for, 441 sand, effect, 437 slipping, q.7i., drivers, flaws, 435 St. imperceptible, 445 speed does not affect, 435 winter and summer, 443 American, advantages of, 422 decreasing use, 114 dimensions, etc., 407 invention of, 421 [*407-|- wt. various parts, •400, and curvature, f.r-., 278 & stationary q.71. engs.,493 assistant, q.v., 585 boiler-power, 449 and tractive p., ♦453 blast-nozzle, sizes, '409 combust'n and evap'n,45o max. rate, 449 deficiency in power, how [shown, 405 INDEX. Locomotive Locomotive — Continued. Doiler power, diagram of dimensions of b., 407-11 various parts, changes, efficiency high, 457 [*409 energy stored in, *454 evap'g boilerful, time [for, 456 evap n, average rate, 449 explosions, *:?47 JNDEX. 96; Iire-l>ox, life, *4i9 as aff. by water, *42o fractures, * size, *407- grate area 420 410 and load on [drivers, *45a H. P. per sq. ft. grate, 484 incrustation, amt. daily, V. ■ t*378 incrusting solids in water, [♦378 lbs. coal per h. p., *46i life of boiler, ^ig loss of heat in, a v., *456 low water, gain by, 455 pass, and fr"t service [same b., 403 p. c. efficiency, 457 [402 power measured in ft. lbs., radiation, q.v., winter and [sum., 508 shell, thickness, *42o steam, lbs. per h.p. pressure, ♦409-10 av., U51 boiler and cffec, ♦479 cutting down, efi't, [405 higher, effect, 408, 468 high, Ger. and Swiss, *5»9 reserve of, 453-4 steam-chest and b. [press., 473 tendency to incr'se b., 408 tubes, life of, *42o no. and size, *409-to wt. and cost *4ia-|- washing out, *42o water supply.quality, ♦378 weight of, ♦407-1 1. ^is-e w'ts, q.v., all parts and [maps, ♦400, *4i2 -f- to incr'se boiler power [id p. c, 400 water and steam, '407- 1 u ., •, L"' '♦54 coal burned per mile, ^129 English, *i3i-2 I Penn. R. pass., ♦134 compound, chances, 133 Consolidation I., q.T>., def'n [and origin, 423 cyl. q.v. tract, power, 553 change in, Penna. R.,%09 increased use of, 114 most used on heavy [curves, 281 wts. of diff. sizes, 701, 769 various parts, '400 ['564 cost new, all types and wts.. Am. and Eng. per ton, [det'ls, ^ii as affected by wt., etc., [•4", ♦564 Locomotive Locomotive — Continued. cost, builders' approx. rules, details, 150-1-2-4-5 narrow-gauge, *564 disadvantages. 565 per ton, all types, ♦564 cost of operating, 121 -f- as aff'd by wt. eng., 560 as pushers, 6:1 -f- ^cost of double no. for [same train, ♦568, *57i double wt. for same train, [*567 ^ain by fully Ioading,*587 intermitteni service, eff t, [603 mat'l and labor. Am. and [foreign, ^u & per year, *i48 & shop and gen'l exp., *4ii,. [*4i7 standing still, cost, 602 cylinder power, 457 all cyls. and drivers, •479. and slipping drivers, 406 back pressure, ami.. 472 compared with adhes., [diag., 552 cut-on, no tendency to [early, ♦467^ denciency, how shown, * 11 • u . f<°5^ falls with speed, 457 expansion, theoret., gain . , , [by, 467 practical losses. 470 indicator diags., *476 -\- limits of, ex., 703 losses of eff 'y, chief, 470 of frt. eng. and speed, 474 often too little, 406 ratio to wt. on drivers. reciproc g parts, loss by, speed, effect of reduc g, varied easily, 400 wt. to increase cyl. p. lo- [p. c, 401 why should be in excess, cyliDders, cold or hot, eff't. [476- clearance space, eff't, 472 common error of design [iOi 474 disadvan. of too large, 40a- entrained water in, 470 large cyls. disadvanta- [geous, 406- lead and lap., def., 470 loss of press, in, *4io radiation, external, 315, [377, 471 internal, nature, 315, 471 locos., 376 size of, why used to de [scribe engines, 40a steam cap'y of, *459 design of, 402-4- fimits for same boiler, 40% logical order, 402 narrow-gauge. 7^1 [*«4« p. c. standard, P. R. R.^ Locomotive Locomotive— C(7«//««(» + frt. Iocs., op'g conditions, 478 friction resist., q.v., of, 530 fuel q.v. consump. light, 315 future improv'ts, possible [efltect, 328 handling locos., breaking in [two, 359 cut-off, usual, 469 drawing fires, fuel lost, first in first out, 141 [199 heavy engines and break- [ages, 360 running backward, 950 starting of, how dune, 797 switching Iocs., use as [pushers, 79a using heavier vs. more, u . u . [560 height cent, of grav., 371 horse-power in practice, computing do., 338 interest charge on, due to [grades, 570, 604 hmitations of, 399 -f- and grades, 327 and boiler, 406 limits to work of, 399 mileage of. Am. and Europ'n, „ [*i43. ♦159-60 as affected by age, ^418 C, B. & Q., 20 years, 157 exaggerations in statist., life, q.v.. ^143 [103, 142 Pass. max. N. Y. C, ^143 enna.R.R. pass, and fr't. [t886, ♦51-84, ♦mo, ♦418 U. S. sections, ^97 run in general office, 142 special performances. ^419 switching, q.v., prop'n 1/ * * « [mileage, 135 hfe of, ♦143, ♦418-9. ^438 various parts, ^419 machinery, breakages of, ^247 cost new, ^41 2 4- essential elements of, 457 link-motion, 458 repairs, ^143 slide-valve, fric. of, 532 valve-gear, 458 weights of, ^400, ^412 & Mastodon loco., 423 [553 cyl. and adh. tract, power, dimensions, etc., ^410 increased use of, 114 Mogul loco., def'n, 422 dimensions, etc., ♦408 Locomotive Locomotive— C<;«^z««^^. Mogul loco., max. w't, 769 motive-power record, Penn. [R.R., 1851-84, ♦mo number of, various countries, [*i6o English, ^148 per mile all countries.^43, [♦47, ♦mS, ♦160 sections U. S., ♦Bg No. of separate pieces in, ♦415 passenger l.,coal consumption [light, 132 grades affect little, 479 need much tract pV, 407 power limited by boiler, performance of American [Iocs, (long table), ^438 Mastodon loco., ^410 rail- wear, q.v., due to, 122 & repairs, cost of, 139 as affected by align't, ^188 class of engine, ♦146-8 curvature, 315 radius of, 641 distance, 201 grade-crossings, 202 length of trains, 570 rise and fall, 377 w't of engine, 144, 563 av. Chicago r'ds, ♦174-6 sections U. S., ♦170-6 trunk lines, ♦172-6 cleaning, 147 details by items, ♦143-9 deterioration, causes for [and rates, 202-3 distribution to causes,^203 to loco, part?, 153 effect growth q.v. traffic [on. 153 & English, ^133 and American, 42a details, ^144 fittings, ♦mj [153 gen'I exp. often notinc'd, KSee Motive Power.) gen. rep'rs, freq'cy, 420 labor and mal'al. Amer. [and foreign, ♦143-5 & Mass., etc., 142 minor details (many),^i4g painting, ^143 pass, and fr't, ♦148 past history of, C. B. & [Q-. 158 Penna. R., 35 y>rs, 140 p. c. m shop, P. R. R., [*i40 p. c. renewals, ♦146-7,^563 p. c. round-house rep'rs, [♦145-6, ^149 per year per engine. Am. [and Eng., ^159 running gear, ^143 shop, tools, and general {q.v. exp., 153 tenders, q.v.. ♦143-6-7 trucks, q.v., ^143 [*i29 trunk-line exp., 34 y'rs, resistance of, av'ge, ^465, ^530 experim'ts, q.v., as to, 279 accurate, diffic't, 533 coupled drivers, extra [for, 534-5 Locomotive Locomotive — Continued. resistance of, in practice, [*463-h head, at high speed, ^522 error by neglecting, 533 internal, no tax on ad- [hesion, 532 machY separately, 534-5 probable amt., 531 4- slide-valve fric, 532 true test for determining, running gear, 421 [49a Am., distinctive peculi- [arities, 421-5 comparative safety on [curves, diag., 433 coupled drivers, extra A- V , '^['■'*^' 434-5 driving-wheel base, rota- [tion of, 427 foreign, hard on track, 425 hammer-blow, 447 H. P. transmissible, 452 journals, sizes, ^409 load on driv. per sq. ft. ... . [g'ate, ♦45? slipping drivers, 285, 406, [797 tires, cost q.v. maint., 316 truck, mechanics of, 426 • u. ^ L+' 433 weight and cost, ♦413 -{-, ♦400 wheel-base lengths, [♦407-10 wheel- wear, C. & A. r'y, [♦288 runs, tendency to incr'se, 169 starting q.v. power of, 352 & slack, effect of, 490 [424 switching, a.v., def. and use, no N. Y. terminals, ♦819 per cent of, sect'ns U. S., [♦i8i tank Iocs, as asst. engs., 592 why advantag's, 551, 554 ten-wheel, def'n, ^423 dimensions, etc.,^4o8 theoretical defect, most sen- three forces of, 399 [ous, 329 deficiency, how shown, -^ t4oS tractive power, q.v., 434 average between stations, .532 compared with single [tests, 551 all cyls. and drivers, ^479 as modified by speed, 346 by type of eng., 280 causes of fluct'ns in. ^440 comparative, cylinder and [adh., 55a compared with boiler [power, 452-3 with weight, all grades, [♦688 deficiency, how shown, [405 economy of fully em- [ploying, 587 effect low boiler press., [405 French practice as to, head resistance, ♦520-21 968 IXDEX, INDEX. 969 Loc— Los Locoinoti \ti— Continued. tractive power, high speed, horse-power, *5i9 *i\() imperceptible slip, 445 increases faster than fuel [burned, 133 loss at speed, nature of, [473 ON AI.L GRADES IN DAILY [service, *544 -j- fass. and freijjht Iocs., [diflf., 478 pass., needs much, 407 P.O. CHANGE, FROM CHANGE [in any GRADE, 554-7 p. c. wl. train to wt. eng., [all grades, 669 ratio to total wt. loc., ♦542 weight train, all grades, [— *544 4-. *593 [ f speed reduces, 474 starting needs most, 474 tank locos.. 551 testing by fiuct'ns of vel., I- . » ^792 why great in Am., 422 wire-draw'g reduces, 474 wt., to increase lo p. c, trimmings, wt. of, *4oo [401 TVPKs OF, defs., 422 change in most used. 114 compar. cost, new, *565 effect grades on, 55';-7 weight of, all parts and m'^t'ls. [*4oo, *4i2 -f, ^le ALL TYPES. *407-424, *279 as affected by low grades. [566 by steel rails, 561 by volume traffic, 597 & boiler, water and steam, , . .,. [*^54 cost of doublmg to haul [same train. *567 details (full), *4i2-4-6 effect on cost, new, *565 on operat'g exp., *56o empty and in service, [*407-8 fast pass., wt., etc., 421 French practice, ♦576 increase in recent years, [♦407-10, *466 P. R. R. since 1852, *i4i explanation of. 408 of parts, constancy in [ratio, *4oo on drivers compared with [cyl. p., *4o8 p. c. to train-load, all [grades, *669, *688 p. c various materials, [Am. and Eng.. ♦416 ratio to trac. power, *542 various engs.,*279,*407-24 extra heavy eng., *42i parts of eng., 400 roads, ♦438 Long chords, diffs. length, det'g. Long tangents, q.v., bad practice [as to, 324 Long Isl. r'y. loco, perf'ce, ^439 Loop, 679 {See Spiral.) Loss and damage, cost, r'ds and [sections, U. S., ♦170-6 Los— Mai Loss of time by reduc'g speed, [^.7/., *594-s Low grades, q.v.^ and asst. eng., London terminals, cost, 827 [659 expenses at, 827-8 location of, 72 [*529 London, B. & S. C, fastest train, kindling tires, exp'ce, *2oo locos., cost & ms. per yr., ♦159 tests, ^462 traffic and fuel consump, ♦131 London, Chat. & D., fastest train, [♦529 London & N. W., ara't sid'gs, 827 fastest trains, *529 Mai— Mas Maintenance of ^a\— Continued. exps., ratio to maint. cars, etc.! [*i3i ratios of ,to each other, [♦127-31 why constant pr. train- [mile, 127. 569 Manchester, stat n exp. at, 828 Manhattan (elev'd, q.v.) ry., [length, stops, etc., ♦559 operating details, speed, etc., f*559 stations on, and power used, [*aoi Iocs., cost and miles per yr, rep'r details. ^145 interlocking app's on, 809 terminals, cost, 827 Louisiana: area, pop'n, sidings, p. c. op*g exp., earnings per mile and head, *9o; wealth per cap., *26 Louisville, fall at, 841 Louisville & N.. align't stat,, ♦264 fluct. in stock, *46 maint. way exp. by items, *iao miles and earn'gs, ^719 op'g exp. and tr ns pr day,*i72 train-l'd. growth, ♦101 Louisville, C. & L., miles and [earn'gs, ^719 Lubricat'n as affect'd by temp.,506 bath, eff'y, 509, 918 minute diffs., effect, 509 Luchmanier pass, grades at, ^700 Lunch counters and curvat., 649 Luxemburg locos., no. and work [of, ♦160 Luxury in cars, why tends to [incr., 139, 567 McAIpine, C. L., on sharp curve. [326 Machinery, loco., q.v., cost new, [details, ♦150-5 reprs. p. c. due various [causes, ^203 minor detailsof,smaIl, shop, maint. of. 154 (♦149 Macon «& Br., align't statist., ^264 loco, perform., +4^8 \q.v., 732 Mahoning bch., N. V. P., & O., handling trains on. 791 Making time and curvature, 268 & Malicious obstructions, derailm'ts from, 245 Maine: area, popu.. sidings, p. c. op'g ex., earnings per mile and head, ^90; wealth per cap., *26 [miles, ♦181 Maine Central, p. c, switching- Main (trunk, ^.7'.), lines and bchs.. .^ t707 + ex. of error in, 978 & Maintenance of way, tiS anomalies in. 127 as affected by distance, 199 gauge, 753 minor details, 191 no. of trains, 127, 569 pushing eng,, 602 exps., details, U. S. sec- [tions, etc., ♦128. ♦170-^ general tendency, 117 iron rail era, items, ♦120 trunk lines,34 years,^ia9 . ^ speed on curves, 273 [*i59 I Mann sleeping-cars, ^491 Manufacture of rails, 121 of transportation. 48, 106 Manufacturing regions, burden [traffic into, 618 heavy traffic of, 63 Mapping and project'g loc'n, 886 contours (^.t'.), pro and con [874 -f GOOD AND BAD, CX,. 888 large scales, best, 884 loose sheets always best, 886 Maps, making mental, 835, 849 ex. of need for, 85a ocular illusion, q.v.^ on, 665 right use of, 836-7 small scale, making, 889 need for. 665 use in reconnais. ex., 934 Mari^, G., loco, tests. 464, 470 Marine engines,comp'd, and loco., coal per H. P.. ^460 [133 utmost economy of, 469 Marriotte's law, 467 [♦ada Marquette H. & 0.,align't statist., Marsh, Sylvester, invented rack Marshall pass., ♦egS-g [r'y, 690 Marvellous feat, sci, skill. 932 Maryland: area, popu., sidings, p. c, op'g exp.. earnings per mile and head, ♦90; wealth per cap,, [♦26 Mason loco.. Am., dimens,, etc., [*407 Id. on drivers persq. ft. [grate, ^458 Masonry and floods, 781 cost of, 752 dry. bad, 898 estimating, 898 Mexican, 929 p, c. cost to total, ^757, ^833 Massachusetts: align't statist., 259; area, popu., sidings, p, c. op'g exp., earnings, per mile and [head, *9o classification of through and [local traffic, 211 cost per year per eng. and fuel, cost of, 136 [car, ♦148 interlocking law. 812 loco, reprs., cost, 142 maint, way exp. by items, ♦120 motive-power exp., det'Is,^i47 ry. earnings per head, etc., ^78 wealth per cap.. 26 Master Car-B'dersAss'n. assumed [action on rail-heads, 307 Comm, rep't on heavy eng,, [279 on interchange rules, 166 rule for deprec'n cars, ♦aos Mas-Mid Master Car-B'ders Ass'n— 0«'eeds from, 648-50 New York State, align't statistics, ♦259; area, popu., sidings, p.c. op'g exp., earnings per mile and head, *9o curvature in, 259 interlocking law, 813 [♦120 maint. way, exp. by items, switching engines in, 156 wealth per cap., 26 New York & Harlem, alignment [statist., *2S9 N. Y. & New Eng . alignment [statist., ^259 New York Cent. & H. R., align't [statist., *259 INDEX. New York New York Cent & H. R.—Cond. an ex. oi long line prospering, [240 asst. engs. on Hudson R.. 591 construction acct., items, *7i cars, box, wt. of, det'ls, *i63 distance and through traffic [of, 240 negative val. on, 234 fastest trains, *S29 loss by Slops to, 595 flucts. in stock, *46 formation unforeseen, 707 [724 HISTORY AND SUCCESS OF, 707, level grades on, H. R., 327 Iocs, cost and miles per yr.. reprs. by items, *i43 [*i59 p.c. labor and mat l,*i5a maint. way and roll, stock [exp. comp. 34 yrs., ♦129 miles and earnings, *7i9 [♦172 op'g exp. and trains per day, p. c. of, why high, no. and rates. 220 [725 op'g pushers, H. R. div., 79a pass, trains, longest, 596 rail section, 307 rail-wear on. pass, and frt., 561 rates on. fall of, ^726 and Mex. r'y. 923 [230 effect on p. c. op'g exp., sharpest curve on, 326 sidings, total. ^825 Buffalo y'd, 821 terminal exp., etc., N. Y.,*8i9 train-Id., frt. and pass.,*2i7 growth of. ♦100 train-mile cost, ♦116 train-resist, tests, 518 New York. Chic. & St. L., sidings, Buflfalo yard, ♦821 elsewhere. 825 New York, L. Erie & W., align't [sutist., ♦259 Carr's Rock disaster, 255 connections, relations with, [221,729 curve com pens n on, 621 distance, value of, to, 221 dynamom. tests, 501 financial status, 41, 739 flucts in stock, *46 freight time-table on. loa grades, balance of, 618 60 ft. and 6* comb'n, 656 inundations on, 783 location of heavy grades. 585 locos, cost and miles per yr., tests of (Z. C). ♦437 [♦159 loss traffic from curves, 275 maint. way and rolling-stock [exp. 34 y'rs, ♦lag miles and earnings. *7iq op'g exp. and trafhc detTs,*i7a p. c. of, comparison, no pass, pushers on, 595 rates, fall of, ♦726 rates on and Mex. r'y, 01% and N. Y., P. & O., 221 sharp curves on, 278. 326 sidings, total, etc.. *825 term'l exp., etc.,^. Y., 'Sig tires, cost m'nt'g. 316 ton-mile rec'ts, etc., *ii5 track. Buffalo y'd. •821 train-load, la, and pass., *2i7 INDEX. 971 New-Nor New York, L. Erie & Vf.—Cen'd, train-load, growth of, *ioo train-mile, cost, *ii6 wheel-wear, statistics, •317 why has poor connect'ns, 730 New York, U. H. & H., fastest ' [train, *529 flucts. in stock. ^46 locos, cost and duly, *i59 sharpest curve, *325 [•217 train-load, frt. and pass . New York, Ont. & W., term'l 1.T ,r . f«*P»etc., N. Y.. *8i9 New York, Penna. & O., align't [statist., *26i bad location of, 223 bridge vibration tests, 447 handling trains on, 791 locat'n at Springf'd,0., 56 Mahoning B'ch, 732 op'g exp. and trains per [dav, *i72 p. c. switching miles, •181 rail-wear tests on, 294 strategic disadvantage of,. . , [222 train-load, frt. and pass., [•217 why a bad property. 223 New York-Phila., etc., traffic,. XT 1 , L*"*^ '?.'.'^' *39. 709 -I- New Zealand, rolling-stock per XT- [m\]c. *47 Niagara cantil. bridge, w't, etc.,. ».T- [90^ Niagara river, discharge, 841 fall, 841 [695-6- Nigger-hill, develop't around. Non-competitive traffic and good [facilities, 58 and restaurants, 74 comparative rates, 58 effect distance on, 213 true classifications of. 212 Norfolk & Wn.,Consoi. loco, tests, XT L ^ [«t<-'-. 431 North British r'y, locos., cost and XT L ^ [miles per yr., *i59 North Carolina: align't statists.,^ ♦263 ; area, popu., sidings, p. c. op'g exp., earnings per mile and head,*9o; wealth per cap., *26 North Central States: alignment statist., ^262; area, popu., earn- ings per mile and head, etc., ♦91 [*259 curve and grade statist., fall rivers in, 841 freight earn., thro' and [lucal, *23i ,en. r'y statist.. 88, 91 laul and train-1'd, etc., *qT no. pass, trains, 96 op'g exp. and traffic det'ls, [*i70-6 p. c. pass, and frt. traffic, [♦181 switching-mileage, •181 ton-mile rec'ts and haul, [*i«S train-load and haul, frt. [and pass., *2i7 North-Eastern r'y, Iocds. cost and [miles per y'r, *i^9 Northern Pacitic r'y, flucts. in [stock, '46 Nor— Ope Northern Pacific r'y— Continued. heavy cars on. 485 loco, dimens., etc., 553, 407 tests on, 552 -. ^ Jong grades, *7oo Northern r'y (France), impercept. . [slip tests, 445 Northwestern gram receipts, 728 Northwestern States: area, pop- ulation, earnings per mile and head, etc., *9i; general r'y stat- ist., *88 [*,28 maint. way exp. details, pass, and frt., haul and [train-load, etc., *97 {See Western.) Norway, align't statist., *265 locos, no. and work of, *i6o performance of, *439 popu., r'ys. wealth, etc., ♦27, Notch, loco., g.v., def'n, 797 = %n 9A 872 Obelisk, ex. of natural, 684 Obliquity of traction and curve . . [resist., 301 -f- Obstructions, accidents from,*247 Ocular illusions, 842 as to quantities, 849 broken back curves, 871 chief danger from, 852 distance on maps. 665, 859 examples of, 680, 846 & grades in flat country, 661 sharp ridges, 668 steep slopes, ex., 684 Odometer, use of, 838 Office location, evils of, 880 — Offsets, eye exaggerates, 842 -f for transition g.v. curves. r.u ,- ■ 869+. 684 Ohio: alignment statist, in, ♦261; area, popu.. sidings, p. c. op'g exp., earnings per mile and head, *<)o interlocking law, 813 ' rough country' of, 840 wealth per cap., 26 Ohio & M., align't statist., ♦261 -f- train-ld.. growth. ♦loi Ohio river, & tribs., fall, 841 Oil and waste, cost, *i47, ♦170-9 Oil excitement and rys., 30 Old Colony, locos., cost and miles [per year, ♦isg p. c. switching-miles, ♦181 washouts on, 782 Old lines and oper'g rules, 791 improvement of, 785 CONXLUSIONS AS TO, 8o8 gaining double track, [806 possibilities as to, 787 pushers on, 788 sags, taking out, 806 virtual profile, 798 usual errors in, 787 origin of, 789 Open road (the part between stations), improving grades on, ^803 Operating ballast trains. 77^ Operating Expen.ses (Ch. v.), 106 and bad bridge eng., 3 as affected by curvature, 313 Ope— Pap Operating Expenses— Continued. as affected by distance, ♦207-8 no trains, 568 radius of curves, 638 rise and fall, 375 train-Id., 560 average amt., 108 -+- ESTIMA TKn AVERAGE, l8o — grand divisions in, 117 great change in, 107 p. c. Chicago roads, ♦174-6 English, ^70, •188 [♦88 sees., U. S.,»io8-io,^i7o-6, trunk lines, ♦172-6 p. c. to exp., no criterion of [management, 109 trunk lines, g.v., cause [incr., 725 per mile road, English. ^79 U. S., ♦170-9, *99 & per ton-mile, ♦us & per train-mile, English, U „ ^ [*79,*i78 U.S., ♦170-9 Operating heavy grades, g.v., r, . , [d iff 'y, 596 + Operating rules and ballast trains, [773 and impr't old lines. 791. 803 Operation, lines in. See Old Lines. Optimism proper in loc'n, 832 Oregon- area, popu., siding.s, p. c. op'g exp , earnings per mile and head, ^90; wealth per cap., ^26 Orizaba, peak of. 927 Oroya r'y. developments, 6794- sharpest curve, ^325 profile, 698-9 train, g.v., 911 Oscillatory train g.v. resist, 517, Overlaps, 848, 836 [91 1 ex. of, 852, 854 Overloading cars, accidents from, [♦246 Pacific States: area, pop'n, earn- [ings p. m. and head, etc., ^91 bonds and stock p. m., ^107 earnings per mile, ^107 distribution of, ♦loS fuel, cost of, 136 frt. earnings, thro' and local, general r'y statis., 88-90 1*231 growth r'y system, ^44 aul and train Id., etc., pass, [and frt.. ^97, ♦217 main results, op'n. ^94 maint. way exp., details, ^128 op'g exp. and traffic details, [♦170-6 p. c. pass, and frt. traffic. ♦181 switching mileage, ♦181 rolling slopes in, 844 rolling-stock per mile, ^47 sidings, ♦gi train-I'd and haul, freight and [pass., ^97, ^217 ton-mile rects. and haul, ♦115 wealth per cap., ^26 Painting, car, ♦162-4, ^204 locos., ♦Me, ♦Mg-SS, *4i3 English, 144-6 Palace-car. inspection from, 2 Pan Handle, tunnel on, 240 (.S-<'^Pittsb.,C.&St.L.) Paper location, 890 Pap-Pen Paper location— Continued. best hard to secure, 880 deficiencies of, 877 from office chair, 878-81 take off by bearings, 892 use of, 868 Parabola, cubic, 869 law of, 387 not suitable for r'y curves, 276 properties of, 390 Parallelogram of forces, 302 Parallel rules, best, 887 [♦iss, ♦4i6. Paris & Orl., cost locos., details, per ton, details, ♦411 repairs, details, ♦145-7 p. c. labor and mat'ls,^ [*i5^ wt. and cost in detail. Pans, Lyons & M. r'y locos., repr., [details, ♦145, tests, 464 Parlor-cars, dimens., etc., 491 why so freely used, 567 Party-wall laws, 814 Pass, lowest usually best, 858 ocular illusions as to, 846 & Passaic, sharp curve at, 326 Passenger and freight locos., g.v.^ [tire reprs., ♦149, cars, g.v., no. perm., world. , • * [*'t? per train, g.v., ♦134& -mile rates, g.v.. Am. and [Eng., ♦159, revenue, g.v., per head, U. S., [sections, ♦92-4, 103 & traffic, g.7'., pushers, ex., 607,. and speed, 645 [616 irregular eff. of grades,577 LOW SPEED REDUCES- [grades. 578 -j- luxury in, why increas'g,. ,. f567& no. 01 pass., world, 43 on branches, 734 p. c. of, sects., U. S., ♦181 third class, likely to in- [crease, 580 tram-load, U. S., sects., ^97 trains and grades, 576, 616 — gain on grades by speed, [593 length for diff. speeds, 592 longest, 592, 596 manufacture pass, trips, 50 no. load and haul, U. S., [sects., ^97, ♦lyo-g, probable no. of, est'g, 95 trip, av. U. S. sections, ♦97 Passes, travel on, 249 Payments per head to r'ys, U. S,,. "■92-4, *io3 & l*q'. for, Pedestals, concrete lor, 903 design and est'g, 901 Peekskill, ocular illusion at, 848 Pegram, G. H., bridge formulae,, trestle formula, 901 [766, 903 Pennsylvania, align't statist., ♦259. area, pop'n, sid'gs, p. c. op'g, exp., earn'gs p.m. & h'd, ^90 curves on coal roads, 278 gravity r'ys in, 692 wealth per capita, ^26 Penna. & N. Y. Canal rd., align't [statist., ♦260 972 Pennsylvania Penna. Coal Co., gravity r'y, 692 Penna. Co., freight car, dimens., [etc., once and now, *486 Pennsylvania Rd., align't statist., bal. of traffic on, *6o9 [*26o capital account, items, *-ji stock of control, lines, *7i cars, frt., dimens., etc., once [and now, *486 pass, dimens., etc., ♦491 load, average, *6io changes in, 485 movement of Id, *6o9 condensed profile, 698 curvature, taking out, on, 277 distances. N.Y. to Piitsb.,*6c9 dynamometer tests, 501 expt. as to curve slipping, 285 fastest trains, *529 fiucis. in stock, *46 frt. move't, thro, and local. fuel burned, freight, *i35 pass., 134 good condition, value of, 276 grades, balance of, 618 location for pushers. 585 Tyr. & CI. branch, *7oo hist, and cause of success, 725 inundations on, 783 local traffic, large prop'n, 235 locos., breakages in starting, /- It t*4i9 Consorn, experience, *i48 cost, new, details.* 15 1-2-4 per ton, details, *4it fast pass., weight, etc., 421 loads hauled, Tyr. br'h, mileage of, 140 L*44o all ages, *4i8 running, tirst in first [out, *i4o, *4i9 repairs, cost of, 140 & per year per eng., *i59 by divs., *i88 general repairs on, [frequency, 420 p. c. labor and mate- Trials, ♦isz ■Statists, loco, op n, 185 1-84, [*i40 wt. and cost, det'ls, *4i2-6 Consol. eng., *409 various parts, *4oo tank, wi., etc., 421 wt. on drivers per sq. ft. [grate, *452 maint. way exp. on, 123, 128, [130 and roll. -stock, ^4 yrs., ... . 1*129-30 by Items, •120 policy as to, 123 & miles and earnings, ^719 motive-power exp., details, . . [*i47 statistics, 1851-84, *i4o -op'g exp., and trains per day, [*i7a p. c. of, why low, 110, 725 why increasing, 725 planes on old line, 944 pres't line plan'd for, 944 pass, pushers on, 595 rail- wear tests, 119, 295, 320, [380, 562 INDEX. Pen-Pit Pennsylvania Vi^.— Continued. rates and p. c. opg. exp., 220 & fall in, 726 ton-mile rects., etc., *ii5 sharpest curves on, *325-6 term'l exp. etc., N. Y., *8i9 tires, cost m'nt'g, 316 track, best in world. 277 -f traffic, disprop'n E. & W., [etc., *6o9 tram-Id., frt. and pass.. *2i7 growth of, 100 -f- pass., no. cars and fuel, [*i34. *595-6 INDEX. train-mile cost, •116 wages on, loc. shops. *isi wheel-record and brakes, 377 why many branches, 729 Peoria grain rec'ts, 728 Per-diem rate for frt. cars, 165 Perkiomen r'y, align't statist.,*a6o Perote, Cofre de, ht., etc., 927 Perspective, mental, i Peruvian ry"s, profiles of, 698-94 Petersburg, sharp curve at, 326 Petroleum, H. U. in, ♦450 Philadelphia-N. Y. traff.. loss by [dist., 709 terminals, loc'n, etc.. of, 68 train-speed to, 648-50 Phila. & Atl. City, align't r,u-, » „ . [statist., *26o Pnila. & Erie, align't statist., ♦260 expts. as to loc. resist., +279 loco, performance, *44o rep'rs by divs., *i88 trains and fuel consump., ♦138 Phila. & Rdg. coal car, heavy, „ , 1*490 coal consump. pass., 134 fastest train, *529 fuel tests, var. speeds, 528 kindling fires on.*2oo locos., cost new, *i52 fast pass., wt., etc., *42x fr't, heavy. *42i rep'r details, *i45 and renewals, *i45 tests of fast, 473 maint. way and roll. -stock ,_ . [exp., 34yrs., *i29 by Items, *i2o pushing serv., cost, 601 Piedmont, yard at., 618 Piers, area, etc., N.Y. term's, *8i9 bridge, estimating, 898 Pig-iron, past prices of, 763 Pile-driver car, Ga.C, detis, *49o Piles, driving by vel. of car, ex.. Pile structures, 770 [473 Piston, loco., q.v., loss energy by, Pittsburg & Conn., align't statist., „ [*26o Pittsburg, C. & St. L., align't . , [statist., ♦261 train-Id. growth, *ioo tunnel on, saving dist.. 240 Pittsburg & Ft. W., flucts. in [stock, *46 opg. exp. and trains per day, . [♦172 .sharpest curve, ♦325 ton-mile rates, etc., ♦115 fall in, on. *726 train-Id., growth, ♦100 975 Pla-Pru Planimeter, use of, 897 Plateau of Mexico, descr., 616 Platte Cafion, 697 Plotting cross-sections, 868. 897 mapping, q.-v., proper [methods, 886 Plates. {See Engravings.) Political economy of cheap con- [struction, 18, 27 of distance, 197 Pony truck, g v., mechanics of, [431 Poor, H. v., table by, *726 S Popocatepetl, mtn., 927 Population, sections growth of la.. '77 Mass., *78 U. S. *88-9o does not help large and small. [*92"- . 73-81, [227 poor lines, traffic per [head. '713 LAW OF ADDITIUM Ti> TRAF- [PIC, 708 per mile road, la., ♦77 Mass., *78 sections U. S., ♦88-90 world, ♦43 law as to. 720 per sq. m. & m. r'y, U. S., ♦SB pay'ts per head to r'ys, ^92 . . [*»04 & r'y capital per head U. S.. *fc8 Portable engines, cost & eflf 'y, *53i Port Jervis, grades at, 619 [+27, *4g Portugal, pop'n, r'ys, wealth, etc.. Postal-cars, dimens., etc., *49i Power, static, and dyn., 292 &. Practice does not make loc'g T, . [^-'^Ji''", 22 & Prairie ridges, loc'g over, 661 -f Prairie States, bad loc'n in, 6, 21 & Preliminary line, q.v , 861-2 and contour maps. 876 Prepossessions, abandon'g, 835 & Present worth of future $1. *82 of future $1 per year, *83 Pressure, loco., q.v., steam, q.v., [efTec. cyl. in pract., *46i -f- Pnsmoidal form'a, use and abuse. Probabilities, theory of, 864, 896 Profile, balancing quantities of, . , . [89s errors in laying grades on, 329 estimates from, 895 paper and actual, 868, 880 putting grades on, 893 small scale, 861-2 need for, 665 Profit from r'ys, conditions for, 14-16 Profit traffic, importance of. 62 Progress of r'y cons., q.v.. world, . .y-s.,;44 [V-3 Projectiles and air resist., 517 Projecting asst. eng. grades, low, 666 [high, 669 grade-lines, 675 location, q.v.^ 890 Propellers, no. N. Y. term'ls, *8x9 Protractor, best, 886 Providence &Worc'er, p.c. switch- [ing-mijes, *i8i Provision cars, dimens., etc.,*487 Prussia, cost r'ys. etc., *45 loco. repr. details, ♦145 p. c. op g exp., •110 Pul-Rai Pulley, transmiss. of power ar'd. Pusher (asst. q.v. engine) grades, [projecting, 666 Pucbla, error in line to, 928 Puente Nacional, 929 Pulque district, Mexico, 928 Pusterhal r'y profile, 698 Pyramid, of traffic, 712, 731 Quantities, balance of. not exact, estimating {q.v.). 895 [895 Quarries, U. b., value, *25 Queensland, roll'g-st'k perm., *47 Quincy, Mass., double-truck car [at, 421 Rack r'ys, history, etc., 690, 943 reason for, 404 Radiation and fr't speed, 370 external, 313, 456,471, 508 boiler and cylin., comp. in yards, 315 [imp'ce, 471 winter and summer, 508 internal, 315, 471 Radius of curv., q.v., cost, etc., designation, 258-66 [635 gyration of car-wheels, 334 rails, 739 Radius-bar, loco., def'n, etc., 426 Rail joints, accidents from, *246 best form of. 123 wear of rail from, 123 yielding at, 561 Rails, and cro.ss-iies, 7754- foreign locos., 425 speed, 268, 274 track labor, 758 average life, 119 [256 broken, accidents from, 246, condition in winter and sum- [mer, 315 cost of, best IS cheapest, 748 durability, *745 stiffness, *74j strength, *742 elastic reaction of, 516 form of ,307-8, 738 and flange wear, 317, 639 hard and soft, 121 inspection of. 121 [*i2o iron, cost of. various roads, formerly, 119, 763 vs. steel. 110, 268, 561 light, and I't ry's, 737 past prices of, 763 renewals of, cost, U. S. sec- [tions. etc., ♦128, ♦170-9 spread, acc'd'ts from, ^246 steel, effect on op'g exp., ♦130 revolutionized mt. of way. whv better, 119 [118 wear of, as affected by age of [rails, 296 curvature. 297-319 radius of, 639 grades, 380 quality, 320 rise and fall, 379 sand, 380 speed. 561 front and back wheels, 287 loco, and car, 122, 561-2 nature of wear, 308 of pa.ss and frt. trains, 562 on curves, q.v., 293, 319 Rai— Rec Rails — Continued. wear, as aff. by age and form. CONCLUSJONS, 304 [296 diff. European & Am. [exp.. 283 wt. of, and grading, 749 [744 comp. durability, est'g, buying, strength, etc., 739 choice of wt., 738 [*747 interest charge on, extra. vs. cross ties, 776 [13 & Railway projects, inception of. Railways, acres in crops per mile, all legitimate enterpr., 14 [*9o capital, p. c. to total, ^27 of world, ^27 construction, est. of future,^4i past progress of, ^44 -f- cost, *27, ^43, *45 of world, progress, ^42 value, ^25, ♦27. ^45 cost per head, world, ♦27 total, world, *45 per mile English, *^o , U.S., etc, *25-7,>43-5 earnings, q.v., per mile, ^77, [*78«& financial errors in projects. 707 foreclosures, ^40 [186 good lines for, popular error, indirect wealth from, ^27 light, 737 miles of. sections U. S., ^92-4 world, ♦25,27. ^43-45 per head, world, ^43 per sq. mile, ^43 must go to traffic, 53 profit on, conditions for, x6 Rainfall, amt. of, 783 fluct'ns in, 783 and floods, 784 [759 Raising and surfacing track, q.v., Rankine,Prof., on steam exp'n,469 Rates, fixing of. 195 -|- & as affected by diffs. dist., 709 cartage, 820 distance, 194 -f-, 723 -f- strategic advantages, competitive, 212 [218, 723 -|- sum of two, 218 division of, 217 fractional per cents, 227 E.&W.-boundC.,C.,C.&I., L. S. & M. S., 226 [225 how fixed on through traffic, Mex. r'y and N.Y. C, 932 [217 on regular and occas'l traffic, {q.v., diff., 235 per pass.mile. Am. & Eng., [♦^59 per ton-mile, q.v.. Am. & [Eng. ^159 recent fall of. 726 ± through, division of, 219 LAW AS TO DISTANCE RK- [SULTING FROM, 219 and local, q.v., constant [ratio of, 224-6 why based on distance, 196 Receipts per head by sections, [♦103-5, ♦lis & Reconnaissance, art of, 831, 21 conditions of success, 22 maps, ose of, 836-7, 934 rule for choosing grades, 675 descend 'g into valleys,682 Rec- R is Reconnaissance — Continued. to be of line, not area, 835 worst errors orig'te in, 832 Refrigerator cars, dimens., etc.,. 1*487 Renewals, p.c. of, etc., frt. cars, \q.v., *\t^Si. loco., q.v., ^145-7 & [•255 Rensselaer & Sarat., align't stat.. Rental, pd. by fixed charges, 106 Repose, grade q.v. of, def'n, [341 & Rest, friction q v. of, 920 Restaurant and compet. traffic, 73 Retaining walls, Colorado, 697 and improving old lines, [8o» indic'g on profile 934 Return grades, q.v., for Tt t tains, [612 -f Return tracks, indep't, 693-4 Reventon tunnel, etc., 668 Revenue and minor details, rel. [imp'ce, 397 effect of location on, 48 [*64 moving stations on, more dist. on, *229 from through traffic, q.v.,di- [vision of, 218 increase of, effect on profits [in& more important than [low exp.. Ill pass, and frt., sections, U. S., [etc., *92-94 per head by States, ♦go. *io4 sections, U. S., etc., *89. law as to, 716-7 per mile road, sec s U. S., ^89 States, U. S., *9o small p.c. decisive to proper- [ty, 62, 7» THEORY OF GROWTH OF, 708 Revenue train mile, av. cost, ♦179. difficulty of est'g, 103 Revere disaster, 254 [*4i4 Reverse-lever, loco., q. v., wt.,. Reynolds, Lieut., ascent to Ori- r,. . [zaba, 927 Rhigi r'y and Mt. Wash., 690 Rhode Island: area, popu., sid- ings, p c. opg. exp., earnings per mile and head, ♦go; wealth per cap., ^26 Rhode Island Loco. Works, incr. o- u ., [wt. eng. i5yrs., ^466 Richardson bal. slide-valve, 532 Richelieu River disaster, 254 Richmond & Danville, align't „. [statist., *264 Richmond, F.& P., align'tstafist., [♦264 Ricour, M., est. value reducing [grades, ^576 tram-resist, tests, 527 Ridge and valley lines, 836 & low, loc'g over, ex., 66i -{■ Ridge line, eye fixes on, 842 -f- Right of way, folly of economiz- [ing, 16, 53 cost, N.Y.C and Penna. rds.. Rip-rap, natural, 850 [^71 Rise and Fall (Chap. IX.), 327 a minor detail, 185 and ruling grades, distinct.^ 1 327 ^m 'm9,im'*iwys 974 RIs-Rol Kise and F&U—CoMiiaued. as modi tied by speed, 347 amount of, est'jf, 366, 374 limits of choice narrow, {188 measured by no. breaks, [384 rys and States, U. S., [•259 -f classes of. defs., 330, 374 cost of, 375 [injur's, 385 concentrated r. and f. less CONCHrsiONS, 382-3 as aff'd by rate grades, 581 iron and steel rails, 380 loco, reprs., small effect [on, ♦188 foot of. defined, 374 limits of classes, 366, 356 class A, 365 -f class B, 363 class C, 369 [grade, 375-7 incl's whole rgth under various- conditions, *372 I most imp't to frt., 354 -|- relative importance, 185. 395-}- I sags and summits, different [effect, 363* speed in, #367 •train-foot ' of, 582 what constitutes, 366 [of, 682 "Rivers, descending into valleys est'g fall of, 840 grade-lines over, 893 Road and equipt., cost, U. S..*io7 Road-bed and track, cost, U. S. [sections, *i28, *7i cost as aff'd by rad. of curves, rise and fall, 381 [639 proper width of, 772 rel. cost, 833 Robinson, S. W., expts. on bridge [vibration, 44/ Rochester & Pitts'g, sidings, total, Buffalo yd., 821 [*82s Rochester & St. L., align't statist.. Rock, estimating, 897 [*259 indic'g on profile, 934 testing for, 893 Rock cuts, needless, 867, 868 shallow, 881 on contour maps, 877 Rocky Mountains & rough coun- align't in, 2, 265 (try, 840 Rocky points, decept. effect, 836, „ , [842 +, 848 Rod, extended by vel. of car, ex., [345 Rogers Loco. W'ks, catalogue, [422 Roller jour, bearings, value, 012, Kolling country, illusions as to, r, „. locating in, 661 [849-50 -Kolhng-friction, ^.v., def'n, 493, as affected by coupled [wheels, 534-5 computing trom I'ds [hauled, 444 constit. elements, 505 effect like a grade, 343 on pusher grades, 597 — higher in winter, 314 (Srg Train Resistance.) INDEX. Rol-Sax Rolling-load, diags. of, 769 effect on wt. bridges, 767 Rolling-stock, 485 {See Car, Loco.) per mile U. S., •47 foreign, +43 rel. cost, 833. 71 trunk line, maint. exp. 34 [years, *i29 Rome, W. & Ogd. align't statist.. Roof, car, cost, etc., ♦163, *2o4 Rough country and grade con- . [tours, 877 a relative term, 840 errors in, 843 & [849-54 for foot-travel, illusions, two prelims, in, 865 Roumania, locos., no. and work Round-house reprs. p. c, * 145-6, Route, choice of, favored by sharp [curves, 656 ONE GBNRRAL RULE FOR, [660 & easier with sharp curves, [698 to be studied as a whole, 665 Ruling grades, q.v.^ and minor . . [det'ls, 185 Running at grades, 804 & {See Virtual Profile.) Running-gear, cars, rel. cost of, [*i6i-4 p. c. due var's caus., *203 loco., q,v.^ cost new, details. INDEX. 975 Sca-Slo Scales of maps should be large, 884 small scales, use of, 665 & Scenery, ex. of imp't'ce, 678 & Schools and churches, U. S.,value, Science and Art. 831 [♦25 Scientific skill, marvellous feat of^ Scott, Gen., route of, in Mex., 928 Scrap credits, loc. amt. of, *i46 9, cars, details. *2C4 [♦412 value of rails, allow'g for, 122 Searles, W. H., train-r, formula, [517 Section hands, limit to reduc'n, 199 Sections, length of, 126 as affected by curvat're, 321 Selling price of commodities, how Selling transp'n. 48 -f [fixed, 196 and whims of buyer, 52 Semmering ry. profile, 698 Sharpsville ry., loco, perf 'ce, *438 Shinn. W. P.. paper by, •7,9 Shipping, U. S., value, *25 [* I 50-1-2-4-5 repairs, ♦144-9 p. c. due various causes, Russia, locos., no. & work of, * 160 pop'n, r'ys, wealth, etc., •27, rolling-stock, traffic, etc.', *43 Safety, as affec. by centrif. force, ,r> ^ [etc., 300 {See Curvature, Grades.) Safety-guard for bridges, 900 Sags and hydr, grade-line, 625 and summits, diff., 367 vert, curves on, 363 extreme example of, 625 increase speed. 366-7, 623 on grades and levels, 366 safe, limits of, 356 taking out on old lines, 806 TO OBVIATE ALL DANGER FROM, why admissible, 623 [363 example, 623 (See Rise and Fall.) St. Gothard r'y. location of, 671 and prairie lines, est'g betw'n, St. Louis grain rec'ts, 728 [858 terminals at, 70 train speed to, 6«;o [*264 St. Louis & S. E. align't statist,, St. Louis & S.F., loco, perform 'ce, [*438 St. Paul, Minn. & Man., financial Q. A e* . ^. t^l'S^'y* *37-38 band, effect on adhesion, g.v., 437 use of, and rail-wear, 380 Saving per year, aggregating $1 [at given dates, *82 Saxony, cost r'ys, etc., '45 " Shoo-fly" line, 860 Shop and gen'l charges, loco. q.v. [maint., *i45, *i54 English, 133 Short-haul traffic, ^.r., and conve- [nient depots, 57 Short line, moral effect of, 239 trunk line, value of, 728 law as to, 219 {See Distance.) Side-hills, illusions as to, 850 & Side-hill lines, culverts on, 851 prelim, ests. of, 897 Sidings, amt. at Boston, *823 Buffalo, *82i New York. *8i9 and trunk lines, law as to, 825 classes of, *82i for pusher grades, 599 p. c. of, sections U. S., *88 Side-track, taking, and imp't old c- , u. . . [lines, 791 bignal cabins, interlocking, q.v., c, . ,, [sizes, 809 Silver, in world, etc., 929 Silver Plume, spiral at. 680 -f Sixth Ave. Elev. ry. curves, 646 Skill, marvellous feat of, 932 [359 Slack in couplings, q.v.^ amt. of, Burlington tests of, 490 effect of, 359 import 'ce of eliminat'g, 487 & Sleeping-cars, dimens., etc., ^gi English, ^gi whyr so freely used, 567 sections in. ♦491 Slide-valve, balanced, 532 description of, 457 friction of, 532 life of, 420 \q.v.. 284-6 Slipping of car-wheels on curves, amt. due to flange press., error as to, 287 [294 vel. of, on curves, ^289 of drivers, 446, 797 and skill of eng'r, 406 coeffs. of fric, 435 if begun, continues, 285 must not be too easy, 406 no fault in fgt. eng., 406 •* Slope-level, use of, 882 [842 & Slopes, rate of, eye exaggerates, smooth, meaning of, 843 Smi-Spa Smith, C. A , loc. expts. by, 445 tables from. 468 Smithville-N. Y. traffic, 718, 729 -Jonesburg, etc., 729 Snow and ice, accid'is irom, *247 cost due to, 126 storms, as cause of accid't, 255 Soft-steel rails, q.v.^ error as to, e -I ti2i Soil, layer of, and rough country, [840 South America, Am. Iocs, in, 422 rollin<; slopes in, 844 South Australia, rolling-stock per . y, [mile, *47 South Carolina, alignm't statist., ♦263; area, popu., sidings, p.c. of op'g exp., earnings per mile and head, ^90; wealth per cap., ♦26 Southern Pacific, accident on, 949 align't statist., ♦265 long grade on, *7oo miles and earnings, •719 :Southern States, align't statist., [*263 area, popu., sidings, p.c, opg. exp., earnings per mile and head, etc., *9i bonds and stock per mile,*io7 curvature, etc., in, 263 earnings per mile, etc., *io7-8 fall rivers in, 841 fr't. earn., thro. & local, *23i gen'l ry. statistics, *89-9o growth ry. system, *44 haul and train-load, etc., , ^ [*97i 217 mam results op'n, *93 maint. way exp., details, *i28 mineral devel't, effect, 616 opg. exp. and traffic details, [*89-93. * 1 70-6 p. c. pass, and Ir't. traffic, [*i8i switching-mileage, *i8i rects. per inht., pass, and fr't, [* 104-5 rolling-stock per mile, *47 ton-mile rects. and haul, ♦us train-Id. and haul, fr't and [pass , *97. *2i7 triangular course of traffic,6i5 wealth per cap., *26 South-western States: area, popu., sidings, earnings per mile and bead, etc., *9i freight earnings, through and [local, *23i general r'y statist., 88 haul and train-Id., etc., *97, main results op'n,*93 [*2i7 maint. way exp., details, *r28 op'g; exp. and traffic det'ls, [♦170-6 p. c. pass, and fr't traffic, ♦181 switching-mileage, ♦181 rects. per inhabt., pass, and [fr't, ♦104-5 ton-mile rects. and haul, ♦115 train-Id. and haul, fr't and - . , [pass. ^97, *ai7 ^pain, p. c. op'g expenses, ♦no popu., r'ys, wealth, etc., ^27, [*43» *45 rolling-stock, traflSc, etc., ^43 Spa-Sta Spalding, E. C, on car rep'rs, [161 Specie U. S., value, *25 Speculative interest, nature of, 29 Speed and adhesion, 435 and centr'f force. ^270 and curvature, 268 diff. much or little,648 very sharp, 326 and curve resist,, 305 and fr't loc. cyls., 474 and heavy grades, 169 and pass, traffic, 645 corresp'g to time over 293', [♦795 elevated r'y sp., 648 effect on locos., ^476 -^ [579 TO REDUCE PASS. GRADES, to reduce grades, limit, [592 extreme examp. of, 625 fluctuations of, in practice, [*46i testing locos, by, 792 freight, and improving old xt r u * [lines, 804-7 English, ^132 maximum, 368 safe assump'sas to, 371 tendency to high, 369, 488, I.- .. [804 high, economy of, 488 has caused large boilers, highest, Engl. & Am.,i529 tendency to use higher, [488, 804 increased by sags, q.v., 366-7 limits of objectionable, *27i-3 lowest, at summits, 353 loss of, from stop, 274 on max. grades slow, 622 pass, and fr't (also above), 268 vel. -head due to, ^335 why higher in Engl'd, *53o Speed-gauge, injurious effects of Sphere, rolling of, and flange- c. ■ , , [wear, 308 Spirals, classes of, 679 def., and advantages, 681 examples of, 682-4-6 St. Gothard r'y, 671 series of. 684 typical, 679 Split stringers, etc., 900 Sprague, F. J., tests on elev. r'y, Springfield, O., loc'n N. Y., K& c . [O- at, 56 bprings, car, compression of, 272 by vel. of car, ex.. 345 loco. wt. and cost, ♦413 -f Stable equilibrium on truck, 282 Stage-coach measures necessary [fav., 52 Starting, effect slack on, 490 effect to cut down trains, 44a fric, q.v., journal, 512 grades for, needed, 512 greatest trac'n req'd for, 474 locos., how done, 797 loco, breakages from, ^419 on elevated r'y, +559 on switchback, 947 pass, trains, 406 Sta-Sti Starti ng — Conthi ued. resist, of, 910. {See Stations, Stop, Virtual Pro. file.) State r'ys, projecting, 20 Station (100 ft.), length on slopes, Q. »• L*34i Stationary engines, comp. econo- [my for planes, 688 cost and eff'y. ♦531 loco, an equiv't for, 492 Stationery and printing, cost, U. [S. r'ds and sects., *i7o-9 Station, etc., expenses, abstract of. as affected by dist.. 206 [118 no. trains, 568 English, 828 Stations, area, etc., N. Y., ♦819 asst. engs. at, 599 correcting grades at, 790.801-3 cost, N. Y. C. & H. R., ^71 curve compens'n at, 633 diffic'ties in moving, 786 elevated r'y, ^559 effect on grade resist., 347 est'd effect removing from grades at, 512 [towns, ^64 and loco, design, 475 and pass, tr'ns, 491 growth of towns to, 71 large, switch-eng. as pushers neatness of, 649 [at, 792 on grades, moving, 803 on summits, and virt'l prof., [80s, 807 RULE FOR LOCATING, 63, 791 -}- virtual grades at, 704 791 -j- Station supplies, cost, ids. and [sects., U. S., ♦170-9 Stay-bolts, wt., etc., in boilers, [*4" Steam, expansive energy only [used, 457 lbs. per H. P., av. loc, 451 theoretical, ^460 [^454 wt. and heat, various press, wt. in loco. q.v. boiler, ^454 Steam-boats, full stroke eng. for, o ^ [*46o Steam-chest and boiler press, 473 Steam-engines,cost and eff'cy,^53i lead and lap, defin.,470 Kerfect, eff'cy of, ^460 liss'pi river, ^460 [457 uses expansive energy only, working full stroke, *458 {See Stationary, Loco.) Steam-pipe, loco., size, *409 wt. and cost, ^412 4- Steam-ports, losses by, 470 -f- Steam-press, boiler and effective. English, ^132 [*479 H. U. due to various, ^450 little effect on economy, 473 theoret. gain by higher, *468 Steam-shovel, working with, cost, [etc., 773 Steel-rail, q.v., per cent of. sec- _ ^ [tionsU. S.,^88 Stephenson, G., and link-motion, Steubenville, O., tunnel at, 240 Stevens, A. J., inv. Mastodon o .« l°c., 423 Stiffness, cost of and wt. rails, [7391 *74i wSt 976 INDEX. INDEX. reps. 203 Sto-Sur Stock and bonds p. mile, sections. , . . [U.S., ♦107 nuct nations in price, ^e nature of, 29 per mile r'y and head, U. S., watering:, nature of, 32 [*88 Stock cars, dimens.. etc., *486-7 Stopping and starting, i^.7/.,acci- [dents from, *246 at grade-crossings, ^.z/., 810 & loss by, 810-12 effcft on car and eng, fuel burned for, 200 Stops, cost of, 810 heavy trains, 600 effect on grade resist., 346 virtual profile. q.7>., 350-2 no. of, Mich. C. R. R., 136 & on max. grades, effect, 623 on pusher grades, 596 power lost by, 200, ♦335 time lost by, 201, 274, 595 Stop-watch and loco, tests, 794 cost, etc., 796 Storage sidings, q.v., ♦821 Stores, loco., 7.7'., cost, *i47 & Storms and structures, 781 great ones, local, 782 Strategic advantages, effect on -,. , , [rates, 218, 241 «& Streams, est'g fall of, 840 grade lines over, 893 mental map of, 836 «& Street accidents and r'y, 257 Street r'ys, cable, 690 traffic of, N. Y., ♦714 per inhab't, ♦714 [*739-42 strength, cost of and wt. rails, Stroudley, Wm., loc. tests by, 451, _ [460 Success, conditions of, i, 8, 840 — Summits, false, 836 gravity r'y seeks, 692 high, ascending to, 925, 943 may cost little, 590 often wise to go to, 590 lowest safe speed at, 353 normal types, 689 leading, of world. *698"9 of Colorado, 696 -}- not always control grades, [675 - not always governing point, [670 passmg. by cable tract'n, 889 RULE lOR PASSING, 66o Store power in train, 692 station, q.v.^ on, and virtual [profile, g v., 805, 807 Sun, why larger on horizon, 845 Sundays disappearing from r'y [serv., 97 tram-work on, 169 Superelevation, 298 -f common error as to, 301 effect of, 271 on curve resist., 298 on position wheels, 300 on safety, ^00 lateral force from, 298 on tang., possible effect, 911 Surfacing. {SeeTr^cV.) [4-5 Surplus, fluctuations in, etc., 33- Surveys, care q.v. in, and amt. [curv., q.v., 656* compass lines, 863 Sur-Tax Surveys— Ct>«//««tf«//««s of Rails. SIEEL BLOOMS. FORGINGS. and MERCHANT BARS of Open Hearth or Bessemer Steel. Capacity over 400,000 Gross Tons of Steel per Annum. STEEL RAIL FROGS Of all the Standard Patterns, with various improvements of importance suited to all conditions of service ' SPIIT SWITCHES AND IMPROVED SAFETY SWITCHES, OF MANY IMPROVED PATTERNS. SWITCH STANDS AND FIXTURES. OF ALL KINDS. This Company has the createst capacity in the United States for the pro- duction of FROGS SWTTrwp'c *, j • • . ^ nualifv All 1 ,^^^^^"E^' &c., and invites attention to prices and quality. All work made interchangeable, and true to standards. AD VER TJSEMENTS. lU Established 1831. m Mill L Annual Capacity, 600. i\ m ii± \) i I lEIS, E BUENHAM, PAREY, WILLIAMS & CO., T^roprietfyrSf Broad and Narrow Gauge Locomotives, Mine Locomotives, Plantation Locomotives, Compressed Air Locomotives, Logging" Locomotives, Tramway Motors and Steam Cars. ALL IMPORTANT PARTS MADE TO STANDARD GAUGES AND TEMPLATES. Me B^rts of different Enlnes of saie clas^ perfectly interrli?npalile. f, AD VER TISEMENTS. IV j. - • - - - --wsi \ 253'--. F. ANDERSON. THE ATCHAFALAYA BRIOOf. C. C. BARR^ ANDERSON & BARR, Engineers and Contractors. Address S40 Kleventli Street, JTerse.r City^ mfiYrir^r^irrfy[i-tTVi'irrf|iir-' :^-::^-'l :■.'•'/ ".> ^•.•vV*ivv»>': ^-HuoaoM Rivera tunneu'-.^*"^ TUNNELLING THROUGH •ILT. Pneumatic Work, Deep Foundations, and Tunneling in Soft Materials. Con- trol the Patents for the Automatic Dredge and the Anderson System of Tunneling. The following Works, among others, have been executed by the present firm of Anderson & Barr, and will show the wide range of their experience. Atcha/alaya Bridge. Pneumatic Cylinders and Dredges. Little Rock, Ark., Bridge. Pneumatic Caissons. Seekonk River Bridge, Providence, R. I. Cylinders sunk by Dredges. Fourteen-Foot Light House, Delaware Bay. Pneumatic Caissons, 53 feet below water, ao miles from nearest land. Chestnut Street Bridge, Philadelphia, Pa. Oblique Pneumatic Cylinders. Main Sewers, Brooklyn, N. Y. 4,000 feet of i2-ft. tunnels through sand. Ha7vkeii>ury Bridge, Australia. Open Caissons, sunk 170 feet below water^ by Dredges. Harlem Riv^r Bridge, New York City, PnetMnatic Caisson, 54x104 ft. AD VER TISEMENTS. EDGE MOOR IRON CO., —DESIGN AND MANUFACTURE- RAILWAY BRIDGES, VIADUCTS, AND ROOFS, IN STEEL AND IRON. Tension Members Forged without the addition of extraneous Metal, and without Welds, Piles or Buckles. Compression Members manufactured by Processes which insure an entire absence of constructional strains. WROUGHT-IRON TURN-TABLES, With Centres of Conical Steel Rollers and Steel Plates. GALLO^WAY BOILERS Giving Greatest Safety, Economy and Durability. Main Office, Edgemoor, on Delaware River. POST-OFFICE, WILMINGTON, DEL. Philadelphia Office, 1600 Hamilton St WM. SELLERS, Presideni. GEO. H. SELLERS, Gen. Supt. JOHN SELLERS, Jr., Vice-Pre»idenf. WM. F. SELLERS, Secretary. WM. H. CONNELL, Treasurer. VI ADVERTISEMENTS. SAMUEL M. DODD. Pretidenf. JOHN B. GRAY, Vice-President. E. L. AOREON, Sec'y end Treei^ GEO. H. POOR, 8upt. American Brake Company, NEW YORK OFFICE, 160 BROADWAY. JOHN B. GRAY, Vice-President. MANUFACTURERS OF AUTOMATIC FREIGHT CAR BRAKES AND STEAM DRIVER AND TENDER BRAKES, ST. LOUIS, MO. We offer to Railway Companies the only Exclusively Independent Self-Actin^ Freigh 1 ram Brake which has yet been adopted by any Railway in the work? •Our Steam priver and Tender Brake is acknowledged to be^the Che^oest RaTroads"^ '''^''^ "^^'^ ^"'^ "°" ''' "^^- ^^ ^^ ^^^ by 250 diffeS THE NEW^ "IRON CLAD" FIBRE TRACK WASHERS. Perfected ly Ten Years' Experience. Surpassing all other Lock-Nut devices in I>nrabiIUy. Eflectivene»8 and Cheapness. Strengthened and protected from the weather, cannot be crushed, or burst, will not lose their elasticity, nor rot. Adapted for both plain and angle-bars. Price, only S18.00 per Thousand. They also absolutely protect the threads on the bolts from becoming; chafed, and permit old bolts to be utilized upon ivhlch the threads have become battered. NEW YORK OFFICE : ISTo. 15 Dey Street. mmm fibre CO, WjIniiDgtoD, Dei AD VER TISEMENTS. ▼u THE CLARK FISHER "BRIDGE" JOINT OF WROUGHT IRON AND STEEL. AU Parts Warranted against Breakage, J ', '•i:.:;<;!i;r:"!' >-m~ <:-ll ^^ 1-7 Full size. This is not a " suspiinsion" joint. It is a ^'supported'''' joint, with double the amount of support given by any other through the arched bearer, bringing the load upon two ties acting together as one directly under thi rail ends. Combined support of two ties, acting as one, for each joint, and rail ends carried directly by the arched beam and screwed DOWN to it with a force of I t;,ooo pounds— making practically a continuous rail. No holes in web of rail — whole surface of base for support and wear. No breakage of rails or joints. No "low joints." No "creeping."' No loose nuts. Cost of keeping up track reduced to one half of that with angle- bars, and giving smoother surface. For further information, address, FISHER RAIL-JOINT AND ANVIL WORKS TRENTON, N. J. > THE BUSH INTERLOCKING BOLTS, SAFETY By Preyentingr Spreading of Rails, and Derailment of Trains from Broken Rails. ECONOMY By Reducing the Cost of Maintenance of Way, and Prolonging Life of Ties. SPREADING OF RAILS ABSOI-UTEI.Y PREVENTED. T«?sted for more than FOUR YEARS, and approved by some of the most eminent railroact officials in the United States. In use on FIFTEEN first-class r^ads. with the most satis- factory results. References, with price-list and full descriptive circulars, sent on application ta THE BUSH INTERLOCKBNC BOLT CO., 267 South Fourth Street, PHILADEIiPHIA. v:ii A D VER TJ SEMEN TS. ESTABLISHED 1848. W. & 1. E. GUELEY, TROY, N. Y., U. S. A., Manufacturers of CIVIL ENGINEERS' ant SURVEYORS' INSTRDHENTS. All Instruments sent to the purchaser ad- justed and ready for immediate use. Send for full Illustrated Price-List and Circular. THACHER'S CALCULATING INSTRUMENT. This instrument overcomes the drudgery of calculation, itnd accomplishes rapidly by mechanical means otherwise tedious arith- metical solutions. Examples in multiplication, division, prc- portion, powers and roots, involvine not more than three quantities are solved by one operation, and any number of values of a single variable are found by one setting It is designed for the use of engineers, architects, actuaries, scientists, accountants, rae- cbanics, and business men generally. Its useful applications are as general as the fundamental rules of arithmetic. It IS quickly learned, is easily operated, and worth double its price. Send for testimonials. Price, in Mahogany Box, $30.00. For further information, address EDWIN THACHER, 503 Penn Ave., Pittsburgh, Pa. WORKS ^ ^r.r«T.«- Fred. C. Weir's m k Improved STtaRAiLFROGS.CROs SINGS fiTi Com piETE System Switch Bars^ ' "^-^^^^^^^switch Fixtures *- Alu PARTS MADt BV MACHINERY IN DIES g. PfWtCTLV^ INTERCHANtABU.' '='MQTOGfiAf»M 4 ESilMAIES 5URSji':.M!^ ON APPl tr AT , Qn . «r*».T. ■» Frcd.C.Weir. PRES, AD VER TISEMEIVTS. IX OSGOOD DREDGE CO., ALBANY, N. Y., U. S. A. —MANUFACTURERS OF— BOOl MEDGES and EXCAVATOES, DITCHING MACHINES, CRANES, &c. No. 1 EXCAVATOR. No. 2 EXCAVATOR. Weight ' 40 Tons. 30 Tons Main Engine 10x12 Dbl. Cyl. 8^x10 Dbl. Cyl. Crowding Engine 6J4^xS " " 6^x8 " " Dipper 2 cubic yards. i>^ cubic yards. Average Capacity, 10 hours 2,500 cubic yards. 1,800 cubic yards. Boom and A-Frame lowered to go under bridges. Will run in any freight train. No. I Excavator dug 450,000 yards in 9 months. 1886. No. I '^ *• 52.000 " in May, 1886. 10 hours a day. No 2 " averaged i,Soo yards a day for whole season, 1886. No. 2 " was taken down, run 50 miles, and set up ready to go to work, in one day. AD VERTISEMENTS. TRAUTWINE'S POCKET-BOOK. 27th T hoggand (1887) Now Ready. » » » J'^'"- ^- *'<"'..u,'^ull^l^^^:i-Zt,,^t'^^^,l^^^- ■"■">"<- and so well affected by them and ■^^^ro..,^r'^LT^:^,i:';itZ\7Xt:iZ'^ £*^Lr* " " '' ""^ ''"' """ «"8'"«''^ pocket-book in existence. "-^^,„v^„ -• ♦ • TRAUTWINE'S RAILROAD CURVES gg'^;:^:.-:v:ffiiX's-i^.'^^^^ ■ ♦- TRAUTWINE'S EXCAVATIONS AND EMBANKMENTS. 9th Edition (1887) Now Beady. f John Wiley & Sons. New York. E. & F. N. Spon, London. THE BEST AND MOST PRACTICAL WORK ON EARTHWORK COMPUTATION. COMPDTATION OF EARTHWORTfROM DIAGRAMS. By A. M. Wellington. M. Am. Soc. C. E. Tol. I.— Text, SI. 50 ) Vol. II.— Plates, 3.50 j IN TWO VOLUMES. . 85.00 Sold Separately op Together. Gives quantities on inspection to the nearest cubic yard for both regular and irregular sections, direct from ordinary field-notes. Saves all muhiplica^on and dmsion Very simple in use. Contains a discussion on the theory of he Pr^ ^^Hnf w K^ applied to earthwork solids, which is by much the most complete in pnm, being based on the actual results of various methods of computation on some thousands of actual solids and showing that the simplest met3 of apply- ing the formula, involving hardly any additional labor, is also the most accurate tkif! tedious part of the computation of earthwork is saved by the methods or this volume, with substantial increase of accuracy. For sale by « ENGINEERING NEWS," Tribune Buildlne. New York. A D VER TI SEME AT TS. 3a GUSTAV LINDENTHAL, CIVIL ENGINEER, Pittsburg, Pa. SPECIALTIES— Diflacult Foundations, Long-Span Bridges, and all Jron and Steel Constructions. LEWIS M. HAUPT, A. M., C. E., Professor of Civil Engineering, University of Pennsylvania, Philadelphia. AUTHOR OF "ENGINEERING, SPECIFICATIONS AND CONTRACTS," "THE TOPOGRAPHER: HIS INSTRUMENTS AND METHODS," "THE AMERICAN ENGINEERING REGISTER" (1886), Orders received by the A uthor. $3.00 4.00 2.00 Consulting Engineer and Ezpert in Patent Causes. HARBOR AND RIVER IMPROVEMENTS A SPECIAI.TY. rr itaraloFf of Waslington lliiiversilj. Icstinj Cor. 17th St. and Washington Ave., St. Louis, Mo. All kinds of Physical and Chemical Tests made on short notice, and certificates furnished. Facilities unequalled in the West. Tests of the strength of Wood, Stone, Brick, Iron and Steel, in Tension, Compression and Cross- Breaking up to 100,000 pounds. Cement also tested in various ways. Specimens can be shaped at the Laboratory at shop prices. Chemical composition determined when desired. Re- sults copied and kept confidential. Send for Descriptive Circular. Also Strain-Sheets examined and checked, and consultation given on the drawing of Specifi- cations and the Dimensioning of Structures in accordance with the latest practice and the most reliable tests of materiak. Address, J. B. JOHNSON, Prof, Civil Engineering and Director of Laboratory. A. M. WELLINGTON, CONSULTING ENGINEER ON THE LOCATION AND IMPROVEMENT OF RAILWAYS. Room 97 TRIBUNE BUILDING, NEW YORK CITY. k Xll AD VEK TI SEMEN TS. Fngineering News D. McN, StAUFFER, \ r j;.„,^ A. M. Wellington. \ ^^'*°'^'- George H. Frost. Business Manager. Engineering News is a weekly record of all important engineering works projected and in progress. It discusses fully and carefully all problems con- nected with such works as they arise. It is especially full in relation to matters connected with Surface, Cable and Elevated Railways, Water Works and Hydraulic Engineering. Its regular and occasional contributors include a large proportion of the more eminent and capable engineers of the country. 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