CORNELL 
 
 UNIVERSITY 
 
 LIBRARY 
 
 PHYSICAL SCIENCES 
 
Cornell University Library 
 QA 90.M3 
 
 Graphical methods for schools, colleges, 
 3 1924 003 979 725 
 
 ■^BSTT^irsjrr 
 
Cornell University 
 Library 
 
 The original of tiiis book is in 
 tine Cornell University Library. 
 
 There are no known copyright restrictions in 
 the United States on the use of the text. 
 
 http://www.archive.org/details/cu31924003979725 
 
GRAPHICAL METHODS 
 
"M^ Qraw-MlBock (h, 7m 
 
 PUBLISHERS OF BOOKS ,F O R_ 
 
 Coal Age ^ Electric Railway Journal 
 Electrical World -^ Engineering News-Record 
 American Machinist '=' Ingenierfa Intemadonal 
 Engineering S Mining Joumai r Pov/er 
 Chemical 6 Metallurgical^ngineering 
 Electrical Merchandising 
 
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GRAPHICAL METHODS 
 
 FOR 
 
 SCHOOLS, COLLEGES, STATISTICIANS, 
 ENGINEERS AND EXECUTIVES 
 
 BY 
 WILLIAM C. MARSHALL, M. E:, C. E. 
 
 CONSULTING ENGINEER; PORMEBLT PBOF. OF MACHINE DESIGN, SHEFFIELD SCIENTIFIC 
 
 SCHOOL OF yale; cons, enqineeh, federal sxtgar refining CO.; rese!arch 
 
 ENGINEER, REMINGTON ARMS, U. M. C; CAPT. ORD,, U. 8. A., SMALL ARMS 
 
 section; trade commissioner, u. s. bureait OF commerce; 
 
 MECHANICAL ENGINEER, NATIONAL SPUN SILK CO.; 
 MEM. A. a. M. E. and 8. &. E. 
 
 First Edition 
 Second Impression 
 
 McGRAW-HILL BOOK COMPANY, Inc. 
 NEW YORK: 370 SEVENTH AVENUE 
 
 LONDON: 6 & 8 BOUVERIE ST., E. C. 4 
 1921 
 
COPTKIGHT, 1921, BY THE 
 
 McGBAW-HiLii Book Company, Inc. 
 
 ^Y 
 
 THD MAPXtS FRX;SS TOHK FA 
 
PREFACE 
 
 Up to the year 1910 there was no book in the EngUsh language 
 treating of the art of graphical representation. 
 
 A book on the Construction of Graphical Charts appeared in 
 1910, written by Professor John B. Peddle, and one on Graphic 
 Methods for Presenting Facts by William C. Brinton. The first 
 book treated the subject from a mathematical standpoint, while 
 the second contained no mathematics at all, although written by 
 an engineer. It required the training of an engineer to under- 
 stand the first one, while the principles contained in the second 
 could be comprehended by the average man of business. 
 
 Mr. Brinton's book treated the subject of chart making and the 
 principles involved, in a very comprehensive way, and the author 
 wishes to express his indebtedness to this book for many of the 
 ideas and some of the illustrations appearing in the following 
 pages. 
 
 The author believes there is a demand for a book embracing 
 both the fields mentioned above, but not entering the field of 
 maps, orthographic projection or graphical statics. The matter 
 contained in such a book should be presented in such a way as to 
 be readily understood by anyone with a common school educa- 
 tion, and he or she ought to be able to construct or interpret the 
 charts illustrated therein. 
 
 With this thought in mind, the following pages are offered 
 in hopes that some of them will appeal to some men but not all of 
 them to all men. 
 
 W. C. Marshall. 
 
 New York, N. Y. 
 August, 1921. 
 
CONTENTS 
 
 Page 
 
 Preface v 
 
 Chapter 
 
 I. Introdttction . . 1 
 
 II. Kinds op Graphs . . . . 13 
 
 III. Making op Diagrams . . 35 
 
 IV. Applications . 61 
 
 V. Determination op Laws .117 
 
 VI. Routing and Organization . 130 
 
 VII. CAIiCtTLATIONS . . . . 142 
 
 VIII. NOMOGBAPHT . . ... . 167 
 
 IX. Mechanical Graphical Records 186 
 
 Bibliography . . . . . 221 
 
 Index ... . 249 
 
GRAPHICAL METHODS 
 
 CHAPTER I 
 INTRODUCTORY 
 
 Various methods ordinarily employed for solution of mathe- 
 matical problems are well known to all familiar with arithmetic, 
 algebra and geometry. 
 
 There is, however, a method of answering a certain class of 
 questions and representing certain results by a direct appeal to 
 the eye which is extremely simple, very effective and in some 
 cases superior to every other mode. This method involves the 
 drawing of a few hnes, straight or curved as the problem demands. 
 The use of simple graphic tables for computation is encountered 
 in antiquity and the middle ages. 
 
 The graphical solution of spherical triangles was in vogue in the 
 time of Hipparchus (B. C. 161-127) and in the 17th century by 
 W. Oughtred. 
 
 Edmund Wingate's "Construction and Use of the Line of 
 Proportion," London, 1628, described a double scale upon which 
 numbers were indicated by spaces on one side of a straight line 
 and the corresponding logarithms by spaces on the other side of 
 the line. More systematic use of this idea was made by Pouchet 
 in 1795. 
 
 In 1842 Leon Lalanne, the Parisian engineer, published his 
 "Anamorphose Logarithmique" in which he explains the first 
 principles of nomography. Advances were made along this 
 line by J. Masson of the University of Ghent, in 1884, and E. A. 
 Lallemand, in 1886. The real creator of nomography was 
 Maurice d' Ocagne of the ficole Polytechnique, Paris, whose 
 first researches appeared in 1891. His " Traite de Nomographic" 
 came out in 1899. 
 
 In 1910, Prof. John B. Peddle published a book on the con- 
 struction of graphical charts in which the subject is treated 
 
 1 
 
2 GRAPHICAL METHODS 
 
 from a mathematical standpoint. The alignment diagrams and 
 methods of Prof, d' Ocagne are treated at some length. 
 
 In 1914, Willard C. Brinton published the first book on graphic 
 methods which could be used by the average business man 
 not having had an engineering or college training. This treats 
 of statistics, organization and routing with very little concerning 
 computation. 
 
 Prof. Joseph Lipka published in 1918 a book treating of 
 graphical and mechanical computation, embodying the courses 
 given by him at the Massachusetts Institute of Technology. 
 This treats of the subject from a mathematical standpoint. 
 
 Many articles describing the use of diagrams as well as their 
 construction have appeared from time to time in engineering and 
 technical periodicals. The present extensive use of diagrams 
 for shortening the labor of solving mathematical formulas may 
 be accepted as sufficient proof of the general recognition among 
 engineers of the value of graphical methods. 
 
 Graphical methods comprise all those methods of representing 
 the relations of objects or facts by means of the relations between 
 the lines of a diagram. All devices for representing by geo- 
 metrical figures the numerical data which result from the quanti- 
 tative investigation of phenomena are included under this title. 
 Graphical methods of representing forces, motions, etc., by lines 
 have been in common use among mathematicians and engineers 
 for many years and are known by the name of graphical statics. 
 Similarly any physical quantities, such as temperatures, atmos- 
 pheric pressures or barometric heights, electrical potentials, 
 etc., may be represented by straight lines. Graphical methods 
 are employed to a large extent in physical investigations as aids 
 to calculation and for the purpose of exhibiting the nature of the 
 law of variation of various phenomena. The principal use of 
 these methods is to show the mutual variation of two quantities, 
 as evidenced by (1) the conveying of information, as when 
 parallel lines of different lengths are exhibited which are pro- 
 portional to the population of different countries or to the 
 population of one country at equal periods of time and (2) to 
 aid numerical or logical calculations as when a curve is drawn 
 through points whose coordinates represent the population of a 
 country at successive decadal intervals: and this curve is used to 
 ascertain the population at other dates. There are three classes 
 of graphical methods: (1) those which make no use of the 
 
INTRODUCTORY 3 
 
 continuity of space except to show that the extremities of lines 
 are connected (graphs), (2) those which use only the projective 
 properties of space, such as drawings and maps, and (3) those 
 which use only the metrical properties of space and produce 
 diagrams intended to be measured. To this class belong 
 graphical statics. 
 
 Any quantity susceptible of mensuration can be graphically 
 represented by a straight line, the length of the line corresponding 
 to the value of the quantity. Addition, subtraction, multipli- 
 cation and division of pure numbers are easily carried out graphi- 
 cally by means of lines. The application of this is found in the 
 slide rule used by engineers for computing. 
 
 Graphical methods have great value in the interpretation of 
 tables and solution of formulas because of the ease of drawing a 
 line, the cheapness of paper and pencils and the skillful judgment 
 of the human eye. The representation of quantities on paper is 
 a convenient way of placing them before the eye, of comparing 
 them, of handhng them. The simplest application is met with 
 in the representation of tabular data such as that met with in 
 statistics. 
 
 The graphical methods of discussing experimental data are of 
 great convenience and importance when the problem under 
 investigation is to determine the law or fundamental relation- 
 ship between two quantities. This type of problem arises 
 frequently in technical and scientific investigations. The 
 geometrical solution of arithmetical and algebraical problems is 
 usually termed graphical analysis. 
 
 Graphical methods are inferior to numerical in accuracy. 
 Ease and rapidity are essential when we want to compare many 
 sets of facts together because if the mind is long delayed in 
 taking in the facts of one set it loses count of the others. The 
 function of graphical representation is to facilitate comparison. 
 A table of statistics represents in one vertical column or row of 
 figures a series of quantities of one kind and in a parallel row or 
 column a series of quantities of another kind each horizontal or 
 vertical pair standing in some definite relation to one another. 
 These classifiied facts may also be expressed graphically, thereby 
 appealing to the eye as well as to the intellect and accomplishing 
 a twofold purpose. By tabulation we reduce facts to a logical 
 order. By graphics we add to their value. 
 
 A graph is a pictorial representation or statement of a series 
 
4 GRAPHICAL METHODS 
 
 of values all drawn to scale. It gives a mental picture of the 
 results of statistical examination in one case while in another it 
 enables calculations to be made by drawing straight lines or it 
 indicates a change in quantity together with the rate of that 
 change. A graph then is a picture representing some happen- 
 ings and so designed as to bring out aU points of significance in 
 connection with those happenings. When the curve has been 
 plotted delineating these happenings a general inspection of it 
 shows the essential character of the table or formula from which 
 it was derived. For example, if the world's production of tobacco 
 over a number of years be plotted, a poor yield is represented by 
 a depression, a rich one by a peak, a uniform one over several 
 years, by a horizontal Une and so on. 
 
 Moreover, such graphs permit a convenient comparison of two 
 or more different phenomena and render apparent at first sight 
 similarities or differences which can be made out from tables 
 only after close examination. The fuU importance and useful- 
 ness of graphs can only be appreciated after many applications 
 have been made. 
 
 Diagrams do not add anything to the meaning of statistics but 
 when drawn and studied intelligently they bring to view the 
 salient characteristics of groups and series and suggest in what 
 directions investigation is needed. They are generally illus- 
 trations of the analysis obtained by reference to tabulated 
 matter. They clarify the latter but do not displace it; in fact 
 their use supplements it and enables conclusions to be formed by 
 a superficial view of it. 
 
 Diagrammatic presentation is used in a narrower and less 
 inclusive sense than the expression "graphical methods," pri- 
 marily for the reason that graphs of various kinds may be used 
 advantageously in connection with averages and other summary 
 expressions. Graphs and pictorial illustrations are generally 
 discussed together but the latter are not only unlikely to be of 
 much use but in advertising and political propaganda are often 
 deliberately misleading though literally correct. For this reason 
 we shall omit the latter except for purposes of criticism. It may 
 be necessary oftentimes to present a pictorial illustration in order 
 to sell an inferior product by means of a highly colored diagram. 
 
 They are used many times to enable those to interpret their 
 meaning who are either too lazy to study the tabular matter or 
 not intelligent enough to abstract the matter contained in the 
 
INTRODUCTORY 5 
 
 tables. Simplicity and truthfulness should be the aim in graphi- 
 cal presentation. Find the best form of representation to use 
 and seek to fit it to the requirements of the problem as to order 
 of arrangement of details, spacing, size of figure and methods of 
 making emphatic the relations between facts. A skilful writer 
 can often devise statistical diagrams of other kinds which help 
 the visuahzation of a complex argument. The final test of a 
 diagram's value is its legibility and clearness of meaning. The 
 diagram should carry on its face a sufficient definition of the 
 facts represented. 
 
 The psychology of statistical diagrams seems to depend on 
 the difiiculty of holding in the mind at one time all the mass of 
 numerical facts contained in a series of statements, and for this 
 reason tables are used. The tables, however, compensate only in 
 part for this fault and it becomes necessary to still further 
 crystallize the facts in diagrams. 
 
 The graphical method should rarely be used except: 
 
 1. To show the relations of one part of a group to another. 
 
 2. To exhibit a series of similar estimates date by date. 
 
 3. To compare two or more groups. 
 
 4. To compare two or more series. 
 
 5. To exhibit three relations which can be geometrically united. 
 
 Monsieur Leterrier, professor in the elementary schools of 
 France, believes that the impression produced by a graphical dia- 
 gram showing historical facts will help to clear up ideas and fix 
 them in the minds of children. 
 
 Such historic facts that can be measured (figures of receipts 
 and expenditures, numbers of cannon, soldiers, ships, etc.) can 
 be made concrete rather than abstract by diagrams. 
 
 The scholar wiU understand better the importance of certain 
 details which were only confused in the midst of changes of the 
 past and which arrested his attention with difficulty. The 
 diagram may be used in reviewing and for quizzes. The teacher 
 may request the pupil to justify the rise or fall of a graph at such 
 and such a spot or period of time. As an illustration take the 
 graphs in Fig. 1 showing the increase in domain of the French 
 kings. Here the scales are in square kilometers on the F-axis 
 and 20-year periods from 987 to 1789 on the X-axis. 
 
 "Some scholars with distracted or hght minds, not able to 
 follow the teacher in the statement of facts nor draw any con- 
 clusions, have become suddenly interested by seeing drawn on 
 
6 
 
 GRAPHICAL METHODS 
 
 the board a curve which measured the relative importance of 
 each of the facts and at the same time showed the nature of their 
 
 evolution." 
 
 Business executives cannot afford to ignore the merits of 
 graphical representation which have for so long been accepted 
 by the engineer and man of science. They must look behind the 
 
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 Fig. 1. — French land acquisitions from 987 to 1768. 
 
 graphical method and study the conditions leading to the picture 
 along with the picture itseK. No business is too small to profit 
 by an examination which shall analyze and scrutinize nor too 
 large to ignore its possibiUties. Each business must adjust the 
 graphical methods to its own pecuUarities and each diagram must 
 be adjusted to the individual for whom it is prepared or the 
 individual must be educated up to the use and importance of 
 these methods of analysis 
 
INTRODUCTORY 7 
 
 The diagram prepared for an executive will be different from 
 the one designed for the pubhc at large. Graphic presentation 
 is an art and the modern executive cannot give too much atten- 
 tion to its application to his business from the scientific 
 standpoint of management if nothing else. 
 
 There has been a growth of no small amount in the past 10 
 years in the use of graphical methods for all kinds of tabular classi- 
 fication, from newspapers to higher mathematics. How has it 
 come about? In precisely the same way as twitch grass spreads 
 over a lawn underground. One man gets his cue from some 
 diagram he happens to see, tells another one who in turn passes 
 it along and the chain continues to grow. ■ The first man, how- 
 ever, begins to think about the apphcation he can make, of use in 
 clarifying his reports or simplifying his calculations, and soon has 
 evolved something better than the originator. Sometimes he 
 publishes his discoveries and the general public is benefited, but 
 more often this advance in graphical research remains hidden 
 and of use to a very small group of co-workers. 
 
 What we ought to have in every school, college and university 
 in the country is a course covering the use and construction of 
 graphical diagrams together with graphical methods. It should 
 cover all kinds of devices for enabling the eye to quickly grasp 
 the features delineated on paper or board useful in illustrating 
 past, present or future happenings. No efficient management 
 can afford to do without graphical methods in production, 
 planning, cost accounting, organization, purchasing, sales, 
 engineering or store departments. 
 
 At the present time there is a total lack of standardization in 
 the form of diagram to use for nearly all classes of representation. 
 This makes it difficult to compare reports of different investi- 
 gators on the same subject because their diagrams are not con- 
 structed alike. If one uses revolutions per minute, the other 
 feet per minute, comparison is very difficult, especially when one 
 uses it on a vertical axis while the other prefers a horizontal 
 scale. There are certain classes of data which are always 
 represented graphically in the same form of diagram. Certain 
 graphical recording instruments use charts of the same form, 
 either circular or ribbon, with records thereon made in the same 
 way. In nearly all of these charts the motion imparted to the 
 paper is obtained by clockwork, one of the units, therefore, being 
 an element of time, usually the hour. The other unit may be 
 
8 GRAPHICAL METHODS 
 
 temperature, pressure, volume or action, but time is common to 
 all and is comparable in all. 
 
 The indicator card of a steam or internal-combustion engine 
 has been made in a standard way for many years and comparisons 
 of indicator cards are very easily made on that account. We find 
 diagrams divided into three classes : 
 
 1. Those which appeal to all classes of people because they 
 illustrate things of interest to nearly everyone and are simple to 
 understand. In this class are price fluctuations of stocks, food, 
 coal, rainfall, election returns, football games, etc. 
 
 2. Those which appeal to executives and engineers, comprising 
 such charts as transportation costs and growths, costs of hght- 
 ing, wages of employees, organization charts, traction and speed 
 of locomotives, etc. 
 
 3. Those which are constructed, understood and used by 
 technically trained engineers and specialists and comprising 
 calculating diagrams. Among these are charts for solubihty of 
 CaCl in H2O, sag of steel tapes, steam boiler tests of coals, torque 
 of electric motors, moments and shear in concrete ships and 
 retaining walls, relation of cut and speed in machine tools, etc. 
 
 Engineering periodicals, technical books, newspapers, and 
 textbooks contain an endless variety of charts good and bad, 
 clear and complex, useful and useless, until the layman and 
 often the engineer wonders what they are all about. The word 
 "nomography" means nothing to the average man, I might say 
 the average engineer, but it is of very great importance in 
 graphical chart making. Every technical man should know its 
 possibilities and be able to apply its principles in his line of work. 
 The slide rule was used but little 25 years ago but today every 
 engineer knows how to use one and the principles governing its 
 construction. Engineering handbooks published within 10 
 years contain many more diagrams than previous to this period, 
 all with the aim of showing certain laws and dependence of one 
 variable on others. 
 
 We recognize the value of graphical methods but are lax in 
 teaching them in our schools and adopting them in standard form 
 in our engineering and scientific societies. 
 
 OCCUPATIONAL DIVISION 
 
 The distribution of graphical methods may in some cases be 
 extremely limited and again be so wide as to embrace all kinds of 
 
INTRODUCTORY 9 
 
 tabular analysis and be necessary for properly and quickly under- 
 standing the important deductions to be made from the tables. 
 
 Roughly speaking there are three classes of diagrams. In 
 the first class are those diagrams used by specialists in scientific 
 lines which comprise such as are given below. In this class will 
 be found nomograms which are known to engineers and mathe- 
 maticians and not to the average college or technical school 
 graduate. Most of the diagrams of the following classes are 
 simple coordinate or logarithmic diagrams and can be constructed 
 by any high school student with a knowledge of graphic algebra 
 or analytical geometry. A great number of those mentioned in 
 class (1) apply to some special line of work and would be of little 
 interest to persons outside that line. For example, "heat 
 transfer in surface condensers" would be used by power or 
 marine engineers only. A flow sheet in a copper mill would be 
 in the field of metallurgy; airplane propeller curves in the aero- 
 nautic field; costs of ploughing in the agricultural engineering 
 branch of automotive engineering; relation of cut and speed in 
 machine tools would belong to the mechanical engineer. 
 
 Class 1. — This comprises the following diagrams: solubility 
 of CaCl in HjO, study of Indian music, weighing machine hyste- 
 resis loop, curves for airplane propellers, appraisal of oil wells, 
 efficiency of boilers, accelerometer tests, sag of steel tapes, 
 retaining walls, cam curves, cargo ship calculations, carburetter 
 mixture requirements, steam boiler test of coals, comparison of 
 coal and oil fuel, gear and pinion hardness, speed and resistance 
 of ships, reinforced concrete, heat transfer in surface condensers, 
 costs of railroad ties, costs of ploughing, costs of Scotch pig 
 iron, design of stuffing box glands, draft in steam boilers, torque 
 of electrical motors, steam turbine characteristics, heat bal. tests 
 in auto engineering, gear design, flow sheet in copper mill, gas 
 velocity through poppet valves, weight of water in marine 
 boilers, hardness of babbitt, locomotive heating curves by 
 exhaust steam, relation of depth of cut and speed in machine 
 tools, moments and shear of concrete ships, well spacing in oil 
 lands, efficiency curves of centrifugal pumps, textile engineer 
 organization chart, steam flow in pipes, power plant efficiency, 
 power to swing bridges, power to crank motor, efficiency of 
 airplane propellers, skin friction and resistance of ships, heat 
 calculation charts, acceleration curves, per cent power gained by 
 vacuum. 
 
10 GRAPHICAL METHODS 
 
 Class 2. — In the second class will be found diagrams having a 
 general engineering application and comprising the following: 
 progress reports, purchase records, volume of hor-cyl. tanks, 
 accounting operations, manufacturing efficiencies, specific weight, 
 curves for air, area of segments of a circle, speed of vehicles and 
 diameter of wheels, costs of transportation by motor vehicle, costs 
 of gas and electric lighting, weight of flat steel, inches of water 
 per pound, per square inch, trend in truck design, horsepower and 
 cyl. vol. of motors, flow sheets of work in mantifactures, graphical 
 control, hardness and temperature of steel, mechanical properties 
 of steel, horsepower of conveyors, lighting distribution, terminal 
 handHng of locomotives, horsepower loss in roller bearings, 
 tension in bolts and screws, worm gear characteristics, power 
 tests of machine tools, viscosity of oils, operating data, organiza- 
 tion charts, velocity of H2O in tubes, production records, pro- 
 peller characteristics, riveted joints, routing of shop work, 
 autographic load diagrams, distribution of temperature in bear- 
 ings, time curves for steam shovels, traction and speed of loco- 
 motives, records of engineering graduates, weight of prime 
 movers, weight of electrical machinery, etc. 
 
 Class 3. — In the third class are all diagrams which interest the 
 general public either from a personal or educational standpoint. 
 They show progress or the history of those things which are of 
 financial, political or healthful importance or pertain to sports. 
 This class then comprises such diagrams as compensation of 
 employees, development of aircraft performance in war, auto- 
 mobiles stolen and recovered in Detroit, 1916-18, coal produced 
 in the United States, coal consumption for heating homes, costs 
 of living, shifting of labor, mental tests of employees, industrial 
 accidents in iron and steel industry, auto design trends, relation of 
 defective locomotives to accidents, season load curves of electrical 
 stations. Government organization charts, price fluctuations, coal 
 production, automobile production and prices, piecework rate 
 and wage calculations, roads built in the United States, freez- 
 ing temperature scales, wet and dry bulb temperature charts, 
 horse and mechanical traction, truck operation and efficiency, 
 endurance of human body, food curves and calories, water waste 
 prevention, rainfall, stock market fluctuations, election returns 
 from different states, football game charts, power boat races, etc. 
 
 Certain kinds of diagrams have been standardized and are 
 always used in the graphical representations of certain classes of 
 
INTRODUCTORY 11 
 
 information. The torque and horsepower curves of gasolene 
 motors, electric motors and steam engines are usually shown on 
 rectangular coordinate charts having the horizontal scale of revo- 
 lutions per minute and the vertical scale of pressures or horse- 
 power. Fluctuation of prices of commodities, stocks and bonds, 
 over various periods are shown on rectangular coordinate dia- 
 grams on which time intervals are measured along the horizontal 
 and price variations along the vertical. 
 
 Engineering handbooks have diagrams which graphically aid 
 calculation, their basis being formulas of design, tests of appa- 
 ratus, operation of factories, railways and machinery, efficiency 
 of machinery, organization of employment, production of goods, 
 tools, etc., handling and transportation of material. 
 
 In looking through the handbooks published for -the various 
 professions or occupations one finds diagrams pertaining to the 
 particular branch covered by the book and also general diagrams 
 which will assist in the computation of general formulas. Some 
 of the diagrams are as follows: 
 
 Civil engineering handbooks contain diagrams on consumption 
 of water, power, tractive resistance, flow of water, areas, railroad 
 operation, stresses, strength of beams and columns, railroad 
 curves, earthworks, weight of concrete construction, strength 
 of steel and concrete, evaporation, volume and per cent of 
 mixtures for roads, filtration and filter beds, sand composition 
 and water storage. 
 
 Mechanical engineering handbooks have diagrams in them 
 dealing with costs of machinery and power, efficiency of machines, 
 boilers and coal, flow of water and steam or gas, conversion 
 charts, friction, conveying machinery, heating and ventilating, 
 time and labor, production and design. 
 
 Electrical handbooks show diagrams of wiring, motor character- 
 istics, electric railway operation, costs of electrical power and 
 lighting, speed, time and distance, transformer losses, efficiency 
 of motors and generators and acceleration tests. 
 
 Mining engineering books treat of weight vs. power, power of 
 conveyors, belt efficiencies, flow of water, flow sheets of mills, 
 efficiency of pumps, electric motors, flow of steam and air, 
 condensers, ore dressing and strength of beams and walls. 
 
 Marine and naval engineering handbooks contain diagrams for 
 propeller design and performance, resistance of ships, horse- 
 power and speed, heating and ventilating, pump and condenser 
 
12 GRAPHICAL METHODS 
 
 efficiencies and powers, oil and coal burning, engine and boiler 
 tests and power curves, fuel consumption, acceleration, and costs. 
 
 Estimating handbooks give diagrams of costs of all kinds of 
 engineering and contracting work, efficiency, relative value, 
 weight and power, mechanical resistance, wire and electricity, 
 belts and machinery. 
 
 Natural gas, electrical railway, overhead lines, electric light and 
 heat, waterworks, concrete and structural steel handbooks give 
 diagrams pertaining to their special functions. 
 
 Automobile engineer's handbooks Ust in diagrams such things 
 as standard chassis lengths, speed rating, steel characteristics, 
 hardness of metals, horsepower vs. revolutions per minute of 
 gasolene motors, tractive effort and horsepower, gas consumption 
 vs. horsepower, cost of truck operation, engine detail charts for 
 design, airplane propellers, fan blade caUbration, efficiency of 
 gearing, and road resistance vs. tractive effort. 
 
 Hydraulics handbooks treat of flow of water in open channels, 
 streams and pipes, flow over weirs, and comparison of various 
 formulas. 
 
 Highway inspector's handbooks give examples of diagrams such 
 as equivalent of inches in decimal parts of a foot, volumes of 
 earthworks, length and volume of roadway, quantities of ma- 
 terial for various road sections, broken stone volumes, resistance 
 of rock to abrasion, weight and volume relations for dry sand, 
 asphalt and tar. 
 
 Fan engineering handbooks treat of heater surface and air 
 temperature, rates of heat transmission, relation of altitude to 
 air properties, specific weight of water vapor. 
 
 Handbook of machine shop management has organization, pro- 
 duction records, expense analyses, and cost accounts. 
 
 Examples for Chapter I 
 
 1. Illustrate by diagrams the three classes of diagrams mentioned in 
 this chapter. 
 
 2. Enumerate the persons or professions to whom the diagrams you use in 
 Ex. 1 would be of interest. 
 
 3. State the kinds of diagrams which have been standardized and the 
 advantage derived from standardization. 
 
 4. What class of diagrams would be found in most engineering handbooks 
 and for what reason? Illustrate. 
 
 6. What diagrams would be found only in special handbooks 7 Illustrate. 
 
CHAPTER II 
 
 KINDS OF GRAPHS 
 
 Before making a graph we must have the data necessary for 
 plotting it such as given by tables of statistics, experiments or 
 observations or indicated by a formula. With such information 
 at hand the first step is to decide what type of diagram shall be 
 used to best illustrate the problem and second to determine how 
 the diagram shall be made. These two decisions depend on 
 what class of use the diagram is to have and the size of it. The 
 classes of use are two, viz. : 
 
 Size Determined 
 
 1. Personal 
 
 Object 
 
 Reference 
 Illustration 
 Analysis 
 Research 
 Computation _ 
 
 By use on desk or in pocket or by commercial 
 sizes of plotting paper 
 
 2. PubUc... 
 
 A. Publication (Books or Bulletins) 
 
 B. Use at Lectures. 
 
 C. Use at Exhibits. 
 
 Reference 
 
 Illustration 
 
 Analysis 
 
 Research 
 
 Computation 
 
 (Reference 
 Illustration 
 Analysis 
 
 [ Reference 
 I Illustration 
 [ Analysis 
 
 Reference Graphs. — A graph, like a general table, may be 
 prepared with no other object in view than to present in graphical 
 form a given set of facts. A curve showing the value of coal 
 mined over a period of years or one showing the exports of auto- 
 mobiles is a reference graph. In general they are seldom of 
 value unless they carry a time series as the curves just mentioned. 
 They must be used with care and should be simple and clear to 
 be easily comprehended by eye-minded readers. Such curves 
 are most effectively applied to results rather than raw materials. 
 
 13 
 
14 GRAPHICAL METHODS 
 
 Never show a graph unless it helps to bring out some significant 
 relationships more clearly than text and tables. 
 
 Illustrative graphs differ from reference graphs in being inclu- 
 sive rather than selective. A bar diagram showing the number 
 of deaths from given causes is illustrative. It is useful in print 
 as well as in lectures or exhibits because it helps to fix in the mind 
 of the reader some important fact that may be the keynote of a 
 discussion. Such a graph should be very simple as it is to appeal 
 to visual memory. An illustrative diagram may be comparative- 
 ly complex and not self explanatory if used in a lecture where the 
 speaker has the opportunity of pointing out its significance. It 
 also gives the audience something to look at and helps hold their 
 attention. This advantage is lost when the lecturer has too many 
 diagrams or shows more than one at a time or spends too much 
 time in adjusting one after the other. 
 
 Analytical graphs are seldom used except in conjunction with 
 printed text or lecture. At an exhibit too much explanation 
 would be required. They may be introduced into a discussion 
 in order to show visually a relationship that the author wishes to 
 emphasize. A graph containing two curves is analytical; as one 
 curve of values, one of production. Such a graph is of distinct 
 value because the correlation is made much plainer by the 
 curves than by text and tables alone. 
 
 Research graphs are those helping to estabhsh an unknown 
 correlation as a result of plotting experiments orother data. Such 
 a graph as illustrates the relation of horsepower and gasoline 
 consumption in an internal-combustion engine is an example. 
 They are used largely in engineering. 
 
 Computation diagrams are used to lessen the tedious comput- 
 ing so often required in many branches of engineering and science. 
 They are constructed for personal use, to a large scale to obtain 
 accuracy and to a smaller scale for publication in books or 
 bulletins. Column or gearing calculations are examples of such 
 diagrams. Some mathematical knowledge is necessary to 
 enable one to construct them but they can be used by the aver- 
 age person with grammar school education, from written or oral 
 instructions. 
 
 HOW GRAPHS ARE MADE 
 
 Inasmuch as a diagram can be drawn on the back of a postage 
 stamp or enlarged to cover the side of a room, its size must be 
 
KINDS OF GRAPHS 15 
 
 determined by the conditions governing its use. As a rule 
 the page of a book is generally sufficient to show all the detail 
 that needs to be shown, especially in statistical graphics. 
 
 Nearly all diagrams depend on the location of points on the 
 plotting paper with reference to two axes at right angles which 
 are called coordinate axes. The perpendicular distances from a 
 point on the paper to the coordinate axes are the coordinates of 
 the point. The distance (F) from the point to the horizontal 
 axis (Z-axis) is the ordinate of the point and the distance (Z) 
 from the point to the vertical axis (F-axis) is the abscissa of the 
 point. Ordinates above the Z-axis are +; those below — . 
 Abscissas to the right of the F-axis are + ; those to the left — . 
 
 From the above statements it is evident that graph plotting 
 can be done in the easiest way on paper which is ruled in squares. 
 Such paper can be purchased with squares of many different 
 sizes, besides other paper having rectangles in place of squares. 
 As the greatest amount of graph plotting is done with both 
 coordinates + it is evident that the parts of the coordinate axes 
 used most will be Z to the right of F and F above Z. The 
 common point or intersection of the axes is called the origin 
 and is usually marked zero. Two lines are selected at right 
 angles for the axes as far to the left and as low down as possible 
 and still leave room for the scales to be written outside of each. 
 This brings the zero in or near the lower left-hand corner of the 
 page or sheet. 
 
 Note the range of values to be plotted and select scales so 
 that all the available space is utilized. The scales should be 
 sensible ones, if possible decimal scales. In choosing scales it is 
 permissible and usually better to have the scale of abscissas 
 different from the scale of ordinates. However, it is better to 
 choose scales so that the plotted line will be inclined at nearly 
 45° as this increases the accuracy of interpolation. In choosing 
 scales first decide which data go with the ordinates and which with 
 abscissas. 
 
 Write figures along the axes to indicate the scales adopted 
 and also indicate clearly which quantity is plotted along the 
 horizontal axis and which along the vertical axis. 
 
 The selection of plotting paper depends on the use of the 
 diagram and the degree of accuracy desired. It is better to use 
 one of the types of plotting paper which can be purchased than 
 to construct the paper oneself. There is a great variety of this 
 
16 GRAPHICAL METHODS 
 
 paper to choose from as the increasing use of graphical methods 
 has created a sufficient demand to enable a profit to be made in 
 its manufacture. In addition to the paper it will be found 
 convenient to have such tools as 60° and 45° triangles, T square 
 or straight edge 18 to 24 in. long, engineer's triangular scale and 
 architect's triangular scale, inking pen, 6-in. compasses with pen 
 attachment, small inking and pencil compasses, coarse and fine 
 writing pens and holders, black, red, blue, green, brown, yellow, 
 orange and other colored inks, 4H drawing pencil, protractor, 
 curved ruler, coarse pointed lettering pen, slide rule and table of 
 logarithms. 
 
 Paper in sheets and rolls, tracing cloth, and cards are for sale 
 in standard rulings and sizes as shown in the pages following. 
 They are carried in stock or made by Keuffel & Esser, Eugene 
 Dietzgen, and the Codex Book Co. of New York, the Edu- 
 cational Exhibition Co. of Providence, R. I., and Lefax (Inc.) of 
 Philadelphia, Pa. 
 
 In deciding on the kind of diagram to use one should have 
 clearly in mind the possibiUties of the various kinds of paper and 
 their applicability to the problem on hand. It often happens 
 that log-log or semi-log paper would be preferable to rectangular 
 ruled paper or that an alignment diagram would be more useful 
 than an intercept diagram. Training in graphical methods will 
 result in an increase in the number of diagrams adapted for the 
 proper representation of the problem at hand rather than the 
 continuation of the wrong and misleading methods so often used 
 in graphical work. 
 
 A diagram should not be too high, neither too long, and discre- 
 tion in the use of scales on both axes will produce a diagram which 
 will give a maximum of accuracy on either axis. 
 
 Codex Papers. — Codex papers have rectilinear rulings of 4, 6, 6, 8, 10, 12, 
 16 and 20 per inch both ways and in miUimeters. They come in thin and 
 thick paper in sizes 4M" X 7K", 8Ji" X 11", 11" X 17". The ruled 
 space is 6" X 9" on 8M" X 11" paper. 
 
 Poly-purpose papers.— &' X 9" plate on 8H" X 11" paper, ruled 20, 
 12 X 20 (72 div. X 180 div.), 12" X log (72 div. X 3 cycles). Fig. 2A&B. 
 Fig. 3. 
 
 Multi-purpose.— V7" X 11" (5 log cycle long way -62 div. short way) 
 spaced equal to typewriter spacing. 
 
 Other Papers.— }{2 div. long way, J^o div. short way; Ko div. long 
 way and log short way. 
 
 Daily Record. — K2 div. long way, J^o div. short way; }iQ div. long 
 way and log short way. Fig. 2B. 
 
KINDS OF GRAPHS 17 
 
 Weekly Records. — }4 "X. Ho div. 
 
 Monthly Record. — 12 X 20 div. 
 
 Log.— Both, ways 4K" X 7K" (1 cycle X 2 cycles), 8H" X 11" (2 cycles 
 X 2^i cycles), 17" X 11" (5 cycles X 3 cycles). Figs. 3 and 11. 
 
 Polar Chart.— 8H" X 11" - 360°. Fig. 6. 
 
 Isometric— 8H" X 11". 
 
 TriUnear.—8}i" X 11". Fig. 3. 
 
 Monthly Records. — 8}4" X 11" sheet, 2 rulings on same chart. Upper haU 
 60 spaces vertically X 132 spaces horizontally. Lower half 60 spaces 
 vertically X 96 spaces horizontally. 
 
 Chart Cards.— 4" X 6". charting area, 2}i" X 4H" 50 spaces at 20 per 
 inch high X 52 spaces long 12 per inch. 
 
 Computation Sheets. 8}4" X 11" with spacing Ko" approx. quadrille 
 ruling. 
 
 Profile Paper.— Yi," X Mo" in sheets 15" X 42" engraving, rolls 20" 
 and 10" wide in green and orange and on paper, mushn tracing cloth and 
 tracing paper. J4" X Mo" in sheets 13 J^" X 42" engraving and in rolls 
 with 20" and 9" engraving — green and orange, paper, muslin, tracing cloth 
 and tracing paper. }4" X J^s" paper, engraving 15" X 42". Figs. 5, 7 
 and 8. 
 
 Profile-plan Paper. — K" X Mo" engraving 10" wide which is J^ the 
 width of paper whose upper half is blank for notes, etc. Comes in green and 
 orange and 60-yd. roUs. Same yi" X J^o"> 9" wide. 
 
 Standard Cross-section Papers. — Ko" X Mo" sheets and rolls. Paper, 
 mushn and tracing cloth and paper. Green, blue and orange engraving 
 16" X 20" for sheets, 20" wide for rolls. He" X He", 17" X 22" sheets 
 and 20" rolls. Same as above. M" X H", 16M" X 21J^" sheets, green, 
 orange or blue. }-i " X H", 16" X 20" sheets, green, orange or blue. 
 K2''' X M.2", 16" X 20" sheets, green. Figs. 6 and 9. 
 
 Milhmeters, 40 X 60 cm. sheets drawing paper or tracing paper, green 
 blue or orange. In rolls 50 and 75 cm. wide, green and orange. Fig. 10. 
 
 Simplex Cross-section Paper. — }i" X }4" in orange, rolls 30" engraving 
 width, paper only. 
 
 Ruled Cross-section Paper.— }i" X M" sheets 16" X 21" blue. Ko" X 
 Ko" sheets 16" X 21" blue. H" X M" sheets 16" X 21" blue. Fig. 4. 
 
 Topog. Paper. — Sheets 16" X 21" 400 ft. to the inch ruled red and blue. 
 Fig. 4. 
 
 Constructor's Sketch Paper. — J^o X Ko 5th lines heavy printed neutral 
 tint. Engraving 5" X 7}4" tracing paper or drawing paper. 7)4" X 
 10" tracing paper or drawing paper. 10" X 15" tracing paper or drawing 
 paper. 
 
 Log Paper. — 10" X 10" neutral tint, sheets. Fig. 11. 
 
 Webb's Coordinate Paper.— Engraving 8M X llM, 11% X 17^ ruling 
 approx. H" subdivided 10 X 10. Squares 180 X 220, 240 X 350. 8" X 
 WM". 160 X 220 sqs. lOM" X 16"- 220 X 330 sqs. Fig. 10. 
 
 Isometric Cross-section Paper.— &' X 9", 9" X 12", 12" X 18" neutral 
 tint drawing paper. 
 
 Polar Coordinate Paper. — 7" X 10" drawing and tracing paper. Fig. 6. 
 
18 GRAPHICAL METHODS 
 
 Engraved paper, rectangular spaces, printed in green ink on 
 paper of good quality thin enough to blue print. Paper of 
 letter size 8}4" X H" in scales of }4", ]4o", millimeter, year hy 
 day, baragraph, 5 bars per page. Fig. 15, }4 scale in black ink, 30" 
 X 38", white paper. Arith.-log 6X9 engraving on 8^" X 11", 
 60 Ho" spaces on short edge and 3 log scales of 3" base on long 
 edge. , 
 
 Same with 5 log scales instead of 3. 
 
 Same with 4 log scales instead of 3. 
 
 Same as first with ^ the no. of Ho" lines. 
 
 Same as first with 2 log scales instead of 3. 
 
 Same as first with 1 log scale instead of 3. 
 
 Same as first with 90 Ho" spa. on long edge and 2 log scales on 
 short side. 
 
 Arith.-log paper in blue ink, 12" sq. engraving, paper 16" 
 sq., 2 log scales on vertical and 60 divisions on horizontal. 
 
 Same 18" sq. engraving with 20" X 21" paper. One log scale 
 in vertical and 360 divisions on horizontal side. 
 
 (A) Large size coordinate paper, green on white, tenths of inch. 
 16" X 20" engraving, 18" X 23" paper. 
 
 (B) Same in orange on thin tracing paper. 
 
 (C) Similar to (A) Ho" sq. engraving 20" wide in rolls 22" 
 wide 50 yds. long. 
 
 Like (C) but on tracing paper with orange ink. 
 
 (D) Twelfths of an inch green ink, engraving 16" X 20" on 
 heavy drawing paper 18" X 23". 
 
 (E) 4 X 20 to an inch, engraving 15" X 42", green on 17 X44 
 paper, every 10th Une horizontally and every 100th hne vertically 
 is heavy. 
 
 (F) Like (E) but engraving 20" wide on 22" wide drawing 
 paper in 50-yd. rolls. 
 
 (G) Millimeter paper engraving 40 X 50 cm., green ink on 
 paper 18" X 23". 
 
 (H) Like (G) on thin tracing paper in orange ink. 
 
 (/) Millimeter engraving 50 cm. wide, green, on paper 22" 
 wide in 50-yd. rolls. 
 
 (J) Same as (J) on tracing paper in orange. 
 
 (K) Log paper engraving 10" X 10", 1 log scale each way on 
 IIH" X IIH" paper. Neutral tint ink. Fig. 11. 
 
 (L) Same with 2 log scales in each direction in orange on thin 
 bond paper. 
 
KINDS OF GRAPHS 19 
 
 (M) Isometric paper 12" X 18" engraving in neutral tint 
 on thin drawing paper 13" X 19". 
 
 (N) Days in year paper engraving 7" X 12" green ink on 
 8" X 14" paper. 
 
 Curve Cards: 
 4" X 6" — ■ 7 spaces high — 12 spaces long, engraving in lower left corner. 
 4" X 6" — 10 spaces high — 12 spaces long, engraving in lower left corner. 
 
 Fig. 12. 
 4" X 6" — 7 spaces high — 31 horizontal spaces. 
 4" X 6" — 10 spaces high — 31 horizontal spaces. 
 4" X 6" — 7 spaces high — 10 horizontal spaces. 
 4" X 6" — 10 spaces high — 10 horizontal spaces. 
 4" X 12" — 7 spaces high — 52 horizontal spaces. Fig. 12. 
 4" X 12" — 10 spaces high — 62 horizontal spaces. 
 4" X 12" — 7 spaces high — 60 horizontal spaces. 
 4" X 12" — 10 spaces high — 60 horizontal spaces. Fig. 12. 
 
 In Figs. 2 to 15 following are shown the principal types of plotting and 
 cross section paper used for charting. 
 
20 
 
 GRAPHICAL METHODS 
 
 
 < ^250 spaces > 
 
 
 \ ■ ■■■■ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^' IIIIIIIIIIINIIIII'MIIIIIIIIML 1/ 
 
 -200 spaces- 
 
 MM 8J xH 20 per inch 8JX11 
 < 72 spaces > 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 20X12 
 
 
 
 
 
 
 1 
 s 
 
 
 
 
 
 
 
 — 
 
 — 
 
 
 H-" f-^ ■ — 1-..,,. . 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 k 
 
 = t 
 
 — 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i F 
 
 
 
 
 
 
 
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 - 
 
 — 
 
 
 
 
 
 
 
 
 
 
 
 
 - 
 
 E 
 
 
 
 
 
 
 
 
 
 
 
 
 = 
 
 ^ 
 
 
 
 
 . 
 
 c - 
 
 
 
 
 
 
 
 r 
 
 E 
 
 
 
 
 8^X11 
 2 log cycles short way 
 200 spaces long way 
 Semi-Log Paper 
 
KINDS OF GRAPHS 
 
 21 
 
 February 
 5 10 15 20 25 
 
 March 
 10 15 20 25 
 
 Daily Record 17)<U" 
 
 \ 
 
 z 
 
 z 
 
 — 
 
 = 
 
 - 
 
 = 
 
 r: 
 
 ^ 
 
 — 
 
 
 :: 
 
 
 
 
 
 r 
 
 — 
 
 _ 
 
 ~ 
 
 - 
 
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 = 
 
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 m 
 
 
 1 
 
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 o O 
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 ^1 
 
 s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 _ 
 
 _ 
 
 _ 
 
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 - 
 
 ~ 
 
 ~ 
 
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 — 
 
 r— 
 
 
 
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 — 
 
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 ^ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 = 
 
 
 ~ 
 
 =: 
 
 - 
 
 = 
 
 =: 
 
 i^ 
 
 zz 
 
 
 
 
 ::t^ 
 
 : -:::::::: 
 
 
 
 = 
 
 
 
 
 
 
 
 
 
 ; 
 
 
 — 
 
 :z 
 
 — 
 
 — 
 
 n 
 
 zz 
 
 ^ 
 
 
 
 
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 ---.j-| 1 II 1 1 1 1 
 
 
 
 — 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 - 
 
 
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 — 
 
 — 
 
 
 fflff 
 
 -- 5 
 
 I H r J 
 
 ■ I X 
 
 
 
 — 
 
 — 
 
 — 
 
 
 — 
 
 
 
 
 
 Semi-Log and Daily Record 
 Arith. " 
 
 Fig. 2B. — Plotting papers. 
 
22 
 
 GRAPHICAL METHODS 
 
 1 
 
 2 3 ' 
 
 1 
 
 
 
 
 9 
 8 
 7 
 6 
 
 5 
 4 
 
 
 
 ^E=|^[:;::;;|;,:: 
 
 : ^ 
 
 -^U-Jj-- 
 
 H 
 
 r= 
 
 
 
 
 
 3 
 
 2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 LliliU — [ 
 
 
 
 
 
 
 „ „ Log Paper 
 4ix7J 1 cycle & 2 cycles 
 Si'Vll" 2 <• & '2i « 
 17^11" 3 « &5 .< 
 
 TGILINEAR A CHABT 
 
 Trilinear Chart 8j"xll" 
 Fia. 3. — Plotting papers. 
 
KINDS OF GRAPHS 
 
 23 
 
 Sheets, 16 X 21 in., 5 X 5 to the inch, ruled blue. 
 
 Sheets, 16 X 21 in., 8 X 8 to the inch, ruled blue. 
 
 Sheets, 16 X 21 in. 10 X 10 to the inch, ruled blue. 
 
 Topographical paper, sheets, 16 X 21 in., 400 feet to the inch, ruled red and blue. 
 Fig. 4. — Ruled cross-section papers. 
 
24 
 
 GRAPHICAL METHODS 
 
 PROFILE PAPERS AND CLOTHS 
 In sheets and in continuous rolls 
 
 4 X 20 to the inch. 
 SHEETS 
 Green, engraving 15 X 42 in., drawing paper. 
 Orange, engraving 15 X 42 in., drawing paper. 
 
 CONTINUOUS 
 Green, engraving 20 in. wide, drawing paper. 
 Orange, engraving 20 in. wide, drawing paper. 
 Green, engraving 10 in. wide, drawing paper. 
 Orange, engraving 10 in. wide, drawing paper. 
 Green, engraving 20 in. wide, mounted on muslin. 
 Orange, engraving 20 in. wide, mounted on muslin. 
 Green, engraving 10 in. wide, mounted on muslin. 
 Orange, engraving 10 in. wide, mounted on muslin. 
 Orange, engraving 20 in. wide, tracing paper. 
 Orange, engraving 10 in. wide, tracing paper. 
 Orange, engraving 20 in. wide, tracing cloth. 
 Green, engraving 20 in. wide, Columbia cloth. 
 Orange, engraving 20 in. wide, Columbia cloth. 
 
 
 
 
 
 
 
 
 
 
 
 — 
 
 
 : 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 : 
 
 - 
 
 
 
 
 
 
 
 — 
 
 
 
 
 
 ■ 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Profile Paper 4 X 20 to the inch. 
 In sheets, engraving 13i" X 42" printed in green or orange. 
 In rolls, engraving 20 in. wide printed in green or orange. 
 In rolls, engraving 9 in. wide, printed in green or orange. 
 
 Tracing Paper and Cloth 
 In rolls, tracing paper 20 in. wide, printed in orange only. 
 In rolls, tracing paper 9 in. wide, printed in orange only. 
 In rolls, tracing cloth 9" X 20" printed in green or orange. 
 
 Fia. 5. — Profile papers and cloths. 
 
KINDS OF GRAPHS 
 
 25 
 
 CROSS-SECTION PAPERS AND CLOTHS 
 In sheets and in rolls (continuous) 
 
 10X10 to the inch 
 SHEETS 
 Green, engraving 16><20 in,, Drawing Paper 
 Orange " 16X20 " do. do. 
 
 Blue " 16X20 « do. do. 
 
 Orange " 16X20 '< Tracing Paper 
 
 CONTINUOUS 
 Green, engraving 20 in. wide. Drawing Paper 
 
 Orange 
 
 Green 
 
 Orange 
 
 Orange 
 
 Orange 
 
 Green 
 
 Orange 
 
 20 
 20 
 20 
 20 
 20 
 20 
 20 
 
 do. do. 
 mounted on muslin 
 
 do. do. 
 
 Tracing Paper 
 Tracing Cloth 
 Columbia Cloth 
 
 
 
 ^■n 
 
 
 
 
 
 
 
 
 
 
 
 
 Polar Co-ordinate Paper 61'klO^" 
 Fio. 6. — Polar plotting paper and crosa-Bection papers. 
 
26 
 
 GRAPHICAL METHODS 
 
 
 Profile Paper- Green or orange 
 Engraving 15'$<42- 5x25 to the inch 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 16X16 to the inch 
 SHEETS 
 Green, engraving 17x22 in., Drawing Paper 
 Orange << 17x22 << do. do. 
 
 Blue " 17x22 << do. do. 
 
 Orange .< 17x22 .- Tracing Paper 
 
 CONTINUOUS 
 Green, engraving 20 in. wide. Drawing Paper 
 Orange <. 20 " <« do. do. 
 
 Green " 20 " " mounted on muslin 
 
 Orange << 20 " '< do. do. 
 
 4x30 to the inch 
 Profile-Plan Papers and Cloths 
 Green, engraving 9 in. wide, Drawing Paper 
 Orange, " 9 << .< do. do. 
 
 Orange, •< 9 «• " Tracing Paper 
 
 Orange, << 9 •• <■ Tracing Cloth 
 
 Fio. 7. — Profile plotting papers. 
 
KINDS OF GRAPHS 
 
 27 
 
 PROFILE PAPERS AND CLOTHS 
 
 In sheets and in rolls (continuous) 
 
 4 X 30 to the inch. 
 
 SHEETS 
 
 Green, engraving 13J X 42 in., drawing paper. 
 Orange, engraving 13J X 42 in., drawing paper. 
 
 CONTINUOUS 
 
 Green, engraving 20 in. wide, 
 Orange, engraving 20 in. wide, 
 Green, engraving 9 in. wide, 
 Orange, engraving 9 in. wide, 
 Green, engraving 20 in. wide. 
 Orange, engraving 20 in. wide, 
 Green, engraving 9 in, wide, 
 Orange, engraving 9 in. wide, 
 Orange, engraving 20 in. wide. 
 Orange, engraving 9 in. wide. 
 Orange, engraving 20 in. wide. 
 Green, engraving 20 in, wide, 
 Orange, engraving 20 in. wide, 
 
 drawing paper, 
 drawing paper, 
 drawing paper, 
 drawing paper, 
 
 mounted on muslin, 
 mounted on muslin, 
 mounted on muslin, 
 mounted on muslin, 
 tracing paper, 
 tracing paper. 
 tracing cloth. 
 Columbia cloth, 
 Columbia cloth. 
 
 Profile paper 4 X 20 to the inch. 
 
 Rolls 20" X 10" wide printed in green, or orange. 
 
 Tracing cloth in orange only. 
 
 Tracing paper in orange only. 
 
 Paper in sheets engraving 15" X 42" printed in green or orange. 
 
 Fig. 8. — Profile papers and cloths. 
 
28 
 
 GRAPHICAL METHODS 
 
 CROSS SECTION PAPER. 
 
 5 X 5 to the half inch. 
 
 Printed in green, orange or 
 
 blue. 
 
 In sheets engraving 16" X 20". 
 
 Also tracing paper in orange 
 
 only. 
 
 CROSS SECTION PAPER. 
 8 X 8 to the inch, fifth lines 
 heavy. In sheets engraving 
 16i" X 21J". 
 
 Printed in green, orange or 
 blue. 
 Tracing paper orange only. 
 
 CROSS SECTION PAPER. 
 8 X 8 to the inch, orange, 
 continuous, engraving 30 in. 
 wide. 
 
 FiQ. 9. — Cross section papers. 
 
KINDS OF GRAPHS 
 
 29 
 
 CROSS-SECTION PAPERS AND CLOTHS 
 
 In sheets 
 
 Millimeters 
 SHEETS 
 Green, engraving 40X50 cm. wide, Drawing Paner 
 Orange " 40X50 " " do. do. 
 
 Blue " 40X50 " " do. do. 
 
 Orange " 40X50 " " Tracing Paper 
 
 CONTINUOUS 
 Green, engraving 50 cm. wide, Drawing Paper 
 Orange ' •-" •• 
 
 Green < 
 
 Orange > 
 
 Green 
 
 Orange 
 
 Green 
 
 Orange 
 
 Orange 
 
 Orange 
 
 Orange 
 
 50 
 50 
 50 
 75 
 75 
 75 
 75 
 50 
 75 
 50 
 
 do. " do. 
 mounted on muslin 
 
 do. do. 
 
 Drawing Paper 
 
 do. do. 
 
 mounted on muslin 
 
 . do. do. 
 
 Tracing Paper 
 
 do. do. 
 Tracing Cloth 
 
 WEBB'S CO-ORDINATE PAPER 
 
 
 
 
 
 
 
 _ 
 
 
 
 
 -j 
 
 "~ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Webb's Co-ordinate paper is a convenient and accurate crosa-section paper for 
 drafting rooms, technical schools, laboratories, etc. It is printed from accurate engrav- 
 ings in a neutral olive tint which can be photographed or photo-printed. The scale of the 
 rulings is between the English and French {Vk inches and centimeters) subdivided 10X10. 
 The lines are numbered in two directions for ready reference to any point on the paper 
 and the sheets are punched for portfolio binding. A table of natural tangents is printed 
 on the margin of some of the larger size sheets, for laying off angles. 
 
 Best Linen Record Paper, SfXllf in., 180X220 squares 
 
 Best thin Bond Paper, 
 
 Smooth Drawing Paper, 
 
 llfXlTf 
 
 sfxiif 
 
 llfxiTf 
 8 X10| 
 
 10^X16^ 
 8 XIOJ 
 
 240X350 
 180X220 
 240X350 
 160X220 
 220X330 
 160X220 
 
 Fig. 10. — Cross-section papers. 
 
30 
 
 GRAPHICAL METHODS 
 
 LOGARITHMIC CROSS-SECTION PAPER 
 
 3 
 2.5 
 
 1.B 
 
 
 1.5 
 
 2.5 3 
 
 8 9 10 
 
 Sheets, engraving, 10X10 in., neutral tint 
 
 On this paper the scales on each side are logarithmic instead of uni- 
 form as in other cross-section papers. The numbers and divisions marked 
 are placed at such points that their distances from the oriErin are propor- 
 tional to the logarithm of such numbers instead of to the numbers them- 
 selves. 
 
 Fig. 11. — ^Logarithmic paper. 
 
KINDS OF GRAPHS 
 
 31 
 
 
 
 
 c" 
 
 
 
 
 
 
 
 
 
 
 ^1 
 
 
 
 J 
 
 
 „„ 12 spaces 
 
 1 
 
 
 
 a 
 
 10 spaces 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 '^ 
 
 
 < 
 
 12 Card >- 
 
 
 
 
 
 
 , 60 spaces 
 
 
 =, 
 
 f 
 
 
 
 
 
 
 
 
 
 t 10 spaces 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 10 
 
 a 
 
 r-t 
 
 
 
 
 
 
 
 12"Card 
 
 
 
 
 
 
 
 
 52 spaces 
 
 
 ) 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 -1- 
 
 CQ 
 OQ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■* 
 
 
 r 
 
 Fig. 12. — Filing cards for records 4 by 6 and 4 by 12. 
 
32 
 
 GRAPHICAL METHODS 
 
 i 
 
 ft 
 
 If 
 
 < li'-^— * 
 
 - 
 
 - 
 
 
 - 
 
 
 = 
 
 = = 
 
 =F 
 
 - 
 
 -■ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 52 
 spaces 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■\l 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 36 spaces 
 
 1 
 
 fe" 
 
 
 
 < S^ ^ 
 
 / 
 
 
 
 
 
 I « " 
 
 
 
 < — i^ — > 
 
 
 
 
 
 
 
 
 
 spaces 
 
 
 1 
 
 
 
 
 60 spaces 
 
 14" 
 
 
 .• n^" 
 
 
 
 < a^ 
 
 ^ 
 
 ^-^lA 
 
 TTTTTTTTTTTTTTrnTTp 
 
 ia 10 20' 
 
 M |i| M| ri. || ii .i | . iii | i ii| |. i M| i J ii|i H i nn i | i in |. li i|i i ii| ;r- 
 
 30 40 50 60 70 80 90 100^1 
 
 1 
 
 per sheet f ^i apart in vertical direction 
 Barograph Record Paper 
 
 Fio. 13. — Special record papers. 
 
KINDS OF GRAPHS 
 
 33 
 
 9 
 8 
 7 
 6 
 5 
 4 
 
 3 
 2 
 
 1 
 9 
 8 
 7 
 6 
 5 
 4 
 
 3 
 
 ^^ * 
 
 1 
 
 
 
 
 1^ 
 
 t 
 
 1 
 
 
 1 
 
 1 
 
 1 
 
 ill 
 
 i 
 
 1 
 
 ■ 
 
 
 
 sB 
 
 
 !■ 
 
 tt 
 
 III 
 
 
 1 
 
 ^^W^ 
 
 ft 
 
 ^ 
 
 
 
 :i 
 
 EEJ 
 
 
 
 
 
 
 i= 
 
 
 eIe 
 
 M 
 
 
 
 :i 
 
 ::: 
 
 
 
 
 
 
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 i: 
 
 
 
 c 
 
 -- 
 
 
 
 
 1 
 
 
 
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 ^ 
 
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 ill 
 
 
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 = = = =3 
 
 = E 
 
 = - 
 
 
 
 zz : 
 
 
 
 
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 = E 
 
 
 
 
 1 
 
 E: 
 
 
 
 ,__ 
 
 
 
 
 IZ 
 
 
 z:: 
 
 = 1 
 
 
 
 
 1 
 
 -- 
 
 
 
 
 
 
 
 
 :: 
 
 
 ii: 
 
 :: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 60 spaces =6" 
 
 
 Fig. 14. — Arith-Log paper. 
 
34 
 
 GRAPHICAL METHODS 
 
 < 
 
 
 " 
 
 I- 
 
 ■t 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s 
 
 
 - 
 
 
 :: MM 
 
 
 ■m 
 
 1 
 
 
 
 
 ■■ 1 
 
 
 
 
 n 
 
 : 
 
 K::: : 
 
 
 
 
 
 J: :::::: : ::: :: :::: : : | 
 
 : ; 
 
 : 1 : 
 
 
 
 HIBiillllillii 
 
 
 ::::: 
 
 i; ;N :M: MIIMMi 
 
 
 20 Lines =1 Inch 
 
 T 
 
 Widths are 3}", 6J" or 9J''. Engraving is 3", 6" or 9". 
 
 
 
 
 
 
 
 
 
 
 
 
 , 
 
 
 
 
 ' 
 
 " 
 
 
 ~ 
 
 
 
 ~ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 % 
 
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 5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 r? 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 « 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ~ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ~ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 " 
 
 ■~ 
 
 ~ 
 
 
 
 ~ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 '" 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 Fio. 15. — Plotting paper in sheets punched for holders. 
 
CHAPTER III 
 MAKING OF DIAGRAMS 
 
 For the guidance of those about to take up graphical methods 
 it may be well to give a few universally recognized rules to govern 
 the making of diagrams. There has been no definite set of 
 standards adopted by engineers or statisticians to govern this 
 work, although a joint committee from the leading engineering 
 societies and other organizations made a preliminary recom- 
 mendation in 1915. This has not yet been followed by a final 
 report nor has the first one been adopted. 
 
 Messrs. Day, Reed and Seecrist are the authors of a set of rules 
 which was pubHshed in the Weekly Statistical News at Washing- 
 ton, D. C, Oct. 10, 1918. This contains much good advice and 
 will be quoted freely in the pages immediately following. 
 
 Standardization gives the maker and reader of diagrams com- 
 plete familiarity with the various graphic forms used. It also 
 facilitates the comparison of data displayed in different diagrams 
 and simplifies the transfer of plots from one sheet to another. 
 It also aids in developing simplicity of form which is a primary 
 requisite of the graphical method. 
 
 Readers of statistical diagrams should not be required to 
 compare magnitudes in more than one dimension. Visual com- 
 parisons of areas are particularly inaccurate and should not be 
 necessary in reading any statistical graphical diagram. 
 
 Suggestions for diagrams are as follows (abstract from Day, 
 Reed and Seecrist and committee report) : 
 
 1. General arrangement of a diagram should proceed from left to 
 right and from bottom to top. 
 
 2. Numerals for the scales of a diagram should be placed at the left 
 and at the bottom, viz., along the respective axes. 
 
 3. All numerals and lettering on a diagram should be placed so as to be 
 easUy read from the bottom or right-hand edge of the diagram as the 
 bottom. 
 
 4. Use hnear magnitude for quantities rather than areas or volumes. 
 
 5. The vertical scale should be selected to bring the zero line on the 
 
 36 
 
36 GRAPHICAL METHODS 
 
 diagram but if it will not appear normally make a horizontal break in 
 order to show it. 
 
 6. The base or zero lines of the scales, or lines which represent stand- 
 ards of attainment, should be sharply distinguished from the other 
 coordinate lines. 
 
 7. When curves are drawn on log coordinates the limiting lines of the 
 diagram should each be at some power of 10 on the log scales. 
 
 8. The curve hnes of a diagram should be sharply distinguished from 
 the ruled lines. 
 
 9. Do not show more coordinate hnes than are necessary to guide the 
 eye in reading the diagram. 
 
 10. When curves are obtained from a series of observations, it is 
 advisable to indicate clearly on the diagram aU the points representing 
 the separate observations. 
 
 11. The scale intervals on any single diagram should be exactly 
 proportional to the gradations of number, size or time represented. 
 (The log scale is an exception to this rule.) 
 
 12. Items should be grouped so as to facilitate the comparison of 
 items most significantly related. Within groups some systematic 
 order should be adopted. The most serviceable arrangements are 
 according to (a) sequence of the items in time with the earliest at the 
 left, or (6) the size of the items with the largest at the top or at the left, 
 or (c) the f avorableness of the items, the most favorable at the top or at 
 the left. 
 
 13. Data shown graphically in a diagram should be given in tabular 
 form beside or within the diagram or close by in the text. Do not, how- 
 ever, place figures so as to disturb or distort the visual impressions 
 conveyed by the chart. 
 
 14. The title of a diagram should be made as clear and complete as 
 possible. Sub-titles or descriptions should be added if necessary to insure 
 clearness. 
 
 In choosing forms for graphical presentation the following 
 suggestions from Day, Reed and Secrist are recommended. 
 
 1. For Simple Comparisons of Size. 
 
 (a) Bars are the most satisfactory. In general all the bars 
 used in the diagrams of a simple study should be of a uniform 
 width (see Fig. 16). 
 
 (&) When a large number of separate items have to be shown 
 in a single diagram lines may be employed in place of bars 
 (Fig. 17). 
 
 (c) Bars or hnes are best placed horizontally (Figs. 16 and 17). 
 
MAKING OF DIAGRAMS 
 Motor Truck Prodtjction, 1919 
 
 37 
 
 10 20 30 40 
 
 I Ton 
 
 2Ton 
 
 ^ 
 
 4Ton 
 
 Over 
 5 Tons 
 
 mmm. 
 
 : 
 
 Size of Truck 
 
 Firm 
 
 KW^ /iOTg MSMST/lr/DAFO 
 W^ZS MITH 1 X OTHFR.'i 
 
 Ford 
 
 Smith... 
 Standard 
 Others . . . 
 All 
 
 1- 
 
 2- 
 
 3- 
 
 5- 
 
 ton 
 
 ton 
 
 ton 
 
 ton 
 
 15 
 
 14 
 
 4 
 
 12 
 
 16 
 
 10 
 
 19 
 
 10 
 
 11 
 
 8 
 
 6 
 
 5 
 
 8 
 
 8 
 
 6 
 
 3 
 
 50 
 
 40 
 
 35 
 
 30 
 
 over 
 
 5- 
 
 ton 
 
 4 
 
 7 
 
 3 
 
 15 
 
 Fig. 16. 
 
 
 
 Progress Charts 
 
 
 
 
 
 S> Alcohol 
 2 Ether 
 
 Per Cent 
 3 10 M 30 40 50 60 7 
 
 D 8 
 
 9 
 
 D 10 
 
 
 
 Per cent 
 delivered to 
 
 11^^^^ 
 
 
 
 1 
 
 Sept. 14 
 
 Sept. 7 
 
 
 1 
 
 
 
 ^- 
 
 
 1 
 
 1 
 
 
 
 
 98 
 96 
 95 
 98 
 97 
 95 
 93 
 90 
 
 97 
 
 ro Mattresses 
 •£ Pillows 
 
 iS I Blankets 
 
 
 1 1 ' 
 
 
 
 ■'^~ 
 
 1 
 
 1 ~ 1 1 
 
 
 
 ^~ 
 
 96 
 
 1 
 
 1 ' 1 
 
 
 
 ^■" 
 
 94 
 
 ="f=^ 
 
 1 
 
 
 
 
 98 
 
 
 MEDICAL EQUIPMENT AND SUPPLIES 
 L EseUD f^i^uired deliveries = 100 Per oenf- 
 1 1 Percentage delivered to Sept. 7 
 
 
 96 
 94 
 92 
 90 
 
 Fig. 17. 
 
 2. For Comparison of Component Parts. 
 
 (a) Subdivided bars are most satisfactory form (Fig. 16). 
 
 (6) Cross-hatching is the best way in which to distinguish 
 the component parts (Fig. 16). 
 
 (c) Position. — Horizontal bars are to be preferred to vertical 
 except when the items are separated by intervals of time in 
 which case vertical bars should be used (Fig. 18b). 
 
 3. For Displaying Frequency Distribution. 
 
 (a) Vertical columns (histogram an alternative). In general 
 uhe vertical bar or column form is to be used. The straight line 
 histogram, however, is a satisfactory alternative. 
 
38 
 
 GRAPHICAL METHODS 
 
 (b) Position of Scales. — The scale for the variable is to be 
 placed along the horizontal axis, the scale for the frequencies 
 along the vertical axis. 
 
 4. For Showing Time Variations. 
 
 (a) Straight Line Graph.— In general the use of the straight 
 line graph between plotted points is to be recommended (see 
 Fig. 18a, c, d). 
 
 100 
 
 80 
 
 :60 
 
 20 
 
 ffome 
 
 -'Homeward '- 
 
 iWwiL __ 
 
 Porf- 
 
 oou. 
 
 ■pa- 
 
 Fmnch Pari 
 
 Oufwa 'd &m. 
 
 nd 
 
 OcF NoiT Dec Jan. Feb, Mar 
 1917 („, 1918 
 
 /. Outward dound 
 
 ■?. French Port 
 
 i. Homeward Bound 
 4.Hpme Part\ 
 
 40 
 
 30 
 
 20 
 
 Oct. Nov. Dec. Jan. Feb Man 
 
 1917 
 
 (b) 
 
 1918 
 
 50 
 40 
 30 
 EO 
 10 
 
 
 
 
 
 
 
 
 
 >5: 
 
 
 
 "^ 
 
 
 ^v^ 
 
 '.d"-/^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Ocf. Nov. Dec. Jan. Feb. Mar. 
 (C) 
 
 Oct! Nov^ Dec Joa Febl Mar 
 (d) 
 
 Month 
 
 Total 
 
 Outward 
 Bound 
 
 French 
 Port 
 
 Homeward 
 Bound 
 
 Home 
 Port 
 
 Oct. 
 
 99 
 
 ZO 
 
 27 
 
 16 
 
 36 
 
 Nov 
 
 92 
 
 18 
 
 33 
 
 14- 
 
 27 
 
 Dec. 
 
 93 
 
 Zi 
 
 32 
 
 18 
 
 21 
 
 Jan. 
 
 96 
 
 21 
 
 23 
 
 21 
 
 31 
 
 Feb. 
 
 78 
 
 le 
 
 20 
 
 14 
 
 28 
 
 Mar. 
 
 84 
 
 20 
 
 21 
 
 16 
 
 27 
 
 (e) 
 
 TIME VARIATIONS 
 TIME CONSUMED IN A TURNAROUND 
 
 Fig. 18. 
 
 (6) Positions of Scales. — Intervals of time should be scaled 
 invariably along the horizontal axis (Figs. 18a, b, c). 
 
 (c) Log Scale. — The log scale vertically is to be used when 
 rates of change or proportionate increases or decreases are to be 
 
MAKING OF DIAGRAMS 
 
 39 
 
 emphasized. When the log scale is employed, the limits of the 
 scale should be some power of 10. 
 
 5. For Showing Progress. — The most effective graphic devices 
 for showing progress are horizontal bars and simple and cumula- 
 tive time curves (Fig. 17 and Fig. 19). 
 
 Percentage Floated of Tonnage Allotted 
 Engineer Equipment 
 Tonnage Allotted 100 Per Cent 
 Floated to Sept. 14, at Port Sept. 14, 
 
 CRANES 
 
 10-Ton Locomotive 
 20 » 
 35 » V 
 
 10-Ton Gantry 
 
 5 » » 
 
 ZO 40 60 80 100 
 
 ■ ■=1 
 
 At port 
 Sept. 14 
 
 (a) 
 
 STOCKONHANOJEPT. I- 19/8 
 
 SUBSISTENCE 
 Beans 
 Coffee 
 Sugar 
 Flour 
 Meat 
 
 Oai/s stack estimafed io lasf 
 
 Sept. 1, 1918 
 
 lbs. in 
 
 thousands 
 
 250,000 
 
 25,000 
 
 150,000 
 
 275,000 
 
 15,000 
 
 Days 
 
 Aug. 1 
 Days 
 
 260 
 
 175 
 
 135 
 
 92 
 
 250 
 
 170 
 
 120 
 
 90 
 
 90 
 
 Fig. 19. 
 
 There should never be too many lines on one diagram unless 
 they can be kept apart from one another. Lines should be 
 distinguished by different kinds of hnes as solid, broken, dash 
 and dot, etc., or by different colors, although the latter is not 
 recommended especially if the diagram is to be blue-printed or 
 reproduced by photography. The meaning of the Hne should 
 be printed close to it (Fig. 25) . 
 
 Avoid cross references and separate the data, if there is much 
 detail, into two or more diagrams. An overloaded diagram 
 [I defeats the only purpose for which it is intended. 
 
40 GRAPHICAL METHODS 
 
 The ratio of vertical and horizontal scales must be chosen to 
 bring out the fluctuations or movements which are the subject 
 of study but not to exaggerate or render them inconspicuous. 
 An exaggerated vertical scale has the effect of making too con- 
 spicuous a single year in which the rise was greatest, when with 
 monthly figures the high values would be seen spread over both 
 the adjacent years. 
 
 In making graphs for comparison the scales chosen must give 
 a similar range of variation, otherwise the correspondence may 
 not be evident. For example, the scales adopted to show 
 the average consumption of tea and sugar must be ounces for the 
 former and pounds for the latter. 
 
 There are various types of curves or diagrams used to represent 
 happenings or phenomena. They may have mathematical or 
 non-mathematical bases. 
 
 If they belong to the latter class, they are usually^-expressed 
 either by data which at a single instant of time tends. jtp be 
 distributed around a central tendency and express the ;3karacter- 
 istics of a variable fact, or they express the occurrence of a 
 homogeneous fact or condition over a period of time. 
 
 In the first case the picture of a fact is viewed in cross section, 
 in the second it is viewed longitudinally. Time is important in 
 the second, degree of change being expressed in relation to time, 
 while time is of no consequence in the first. A table containing 
 variable facts and their frequency of occurrence is called a 
 frequency table and the curve illustrating the table, a frequency 
 graph. 
 
 A table describing the occurrence of a fact over a period of 
 time is a historical table and the corresponding curve a historical 
 graph or "histogram." 
 
 The distribution of measurements is of two types: (1) Those 
 which form continuous series; and (2) those which form discrete 
 series. 
 
 In the first type are those measurements which are only 
 approximate within limits set up and which differ among them- 
 selves by infinitesimally small graduations. The measurements 
 of natural objects fall in this class since neither size nor weight 
 are susceptible to accurate statement. 
 
 Frequencies in discrete series are determined by the character 
 of units in which the measurements are made. The nature 
 of the unit determines the points at which frequencies occur, 
 
MAKING OF DIAGRAMS 41 
 
 such as wages in multiples of 25 cts. or express rates at 5 cts. 
 per pound. In economic fields the latter series predominates. 
 
 To present a statistical fact two dimensions are needed. On 
 the horizontal scale are plotted the individual measurements or 
 groups and on the vertical or ordinate scale the frequency with 
 which each measurement or group occurs. Divisions are equal 
 on both axes. Equal distances on either scale should represent 
 equal facts. The ratios between the two scales is most important 
 to consider, for if the vertical scale is too large the diagram will 
 appear high and narrow, whereas the opposite ratio will produce 
 a long, low diagram. 
 
 The scales should be divided into units which are multiples of 
 the rulings of the paper used. 
 
 In plotting frequency curves the measurements are grouped 
 into classes. The smoothness of the curve depends on the class 
 divisions. In the matter of grouping there are two opposing 
 tendencies, viz., grouping into too few classes to show varia- 
 bility and grouping into too many classes to give a smooth 
 distribution. 
 
 A general rule can be laid down that the classes should be 
 only just broad enough to make the distribution fairly smooth, 
 that is, there should be no vacant classes except near the extremes 
 of the range. 
 
 When successive frequencies are added together we have 
 cumulative frequency series. Cumulative frequencies are helpful 
 in furnishing continuous summaries of distributions which, 
 reduced to a percentage basis, make it easy to determine cur- 
 rently, by inspection, how one-fourth, one-half, three-fourths of 
 the frequencies are effected. 
 
 When a cumulative frequency series is plotted, the curve may 
 extend from the lower left-hand corner to the upper right-Jiand 
 or from upper left to lower right, depending on the way the 
 cumulating is done. If it is a "less than" form it follows the 
 first, if a "more than" it follows the second. 
 
 In plotting cumulative curves, the abscissa units if they 
 represent groups are indicated as spaces but if they represent 
 single measurements they are denoted by points. Cumulative 
 curves are much employed to furnish continuous pictures of what 
 has been accomplished in the past and an indication of future 
 trend. In order to make comparisons between different series it 
 is best to reduce frequencies to a percentage basis which permits 
 
42 
 
 GRAPHICAL METHODS 
 
 of a ready means of visual judgment of the regularity of 
 distribution through the range of measures. 
 
 Elements of annual time series of economic data may be 
 conceived to be constituted of the following elements or compo- 
 nent parts: 
 
 1. Secular trend or growth elements due to increase of popula- 
 tion or development of an industry. 
 
 2. Cyclical fluctuations extending over a number of years and 
 having more or less periodicity due to alternating periods of 
 business prosperity and depression. 
 
 
 A 
 
 
 
 
 C^^-^y 
 
 
 J>-^ff JN 
 
 '^^^ ,^y 
 
 & 
 
 / / ^_^-— "^ 
 
 \^^ r^ 
 
 Si 
 
 ,-A '■fz^^ 
 
 >? 
 
 D 
 
 
 
 
 jk?C 'jo^*^^^v^ — - "^ fy^ 
 
 T 
 
 
 
 ^ 
 
 A - Economic Data 
 B - Cyclical Flucfuafion 
 C- Secular Trend 
 
 
 Time in Years 
 Fio. 20. — Historical curves. 
 
 3. Irregular fluctuations from year to year due to the influence 
 of unpredictable events such as changes in fashion, war, inven- 
 tions. Curves of this type are illustrated in Fig. 20. An 
 historical curve is used to record the changes from time to time. 
 Periods with nothing in common and units of measurement 
 which have changed during the period cannot be compared. 
 
 Great use is made of arranging on the same sheet of paper a 
 group of curves each one telling some phase of history but having 
 the same measurement of time. Such a system supplies in the 
 most convenient form one set of the factors used in every explana- 
 tion of the past and forecast of the future insofar as it is based 
 on an estimate of quantity. 
 
 They supply the rates of growth of the possible causes while 
 reason aided by theory supplies the other set of factors, OT3.,the 
 nature of the dependence of the result observed in the several 
 causes. The suggestion which an historical curve gives depends 
 
MAKING OF DIAGRAMS 
 
 43 
 
 on the scales by which it is drawn, the evil being greatest in the 
 case of things which increase very rapidly. 
 
 In Fig. 21 at every point on curve P2 there is the same propor- 
 tional rate of increase which is also true for curves Pi and P3 
 which are identical with P2. Each curve represents the growth 
 in the population of London on the supposition that starting at 
 one miUion it had increased for a century uniformly at about its 
 actual mean growth for 30 years. The only difference between 
 the curves is that the horizontal scale for P2 is five times that 
 for Pi and half that for P3. 
 
 Fig. 21. — Growth of population of London based on uniformity at its actual 
 mean growth for 30 years. 
 
 In Fig. 22 if the same scale was used for I and II it would 
 appear as if there was a much more rapid growth in sugar con- 
 sumption than tea, but if we compare pounds of sugar with 
 ounces of tea we find there is very little difference. 
 
 The plotting of historical curves is sometimes misleading as to 
 comparative rates of growth of different things. If we were 
 concerned with absolute amounts it would not be so bad but 
 we want the percentage of increase or proportional rates of 
 increase, that is, the ratio in which the increase during say a year 
 bears to the amount at the beginning of the year. It is also 
 difficult for the eye to judge without artificial aid the ratio of 
 increase at different parts of the same or different curves. One 
 method is to make the horizontal distance in Fig. 21 represent 
 the logarithm of the amounts instead of the true amounts. By 
 this method lines of equal slope denote equal rates of change and 
 the three curves of this diagram (Fig. 21) would become parallel 
 straight lines. The diagrams heretofore described have been 
 
44 
 
 GRAPHICAL METHODS 
 
 constructed on an arithmetic basis treating of absolute values 
 only and giving differences. "Very often the difference method 
 is misleading in giving absolute values based on a zero not visible 
 on the diagram and showing an increase or decrease which is not 
 in any constant ratio to the preceding quantity. 
 
 The ratio method of plotting has been described in detail by 
 Prof. Irving Fisher in a paper pubHshed by the American Statis- 
 tical Association in the June, 1917, pubhcation. 
 
 The growth and use of this method has not been as large as its 
 value warrants, but as soon as its simpHcity is realized there will 
 be no doubt of its displacing the difference method for statistical 
 plotting. 
 
 30 *0 , 50 60 70 80 
 
 FiQ. 22. — Comparative historical curves of tea and sugar consumption. 
 
 The ratio diagram has several advantages over the difference 
 diagram. A straight-line graph in a ratio plot means uniformity 
 in percentage growth, while the same uniformity in a difference 
 plot will be represented by an exponential curve. The ends of 
 such a curve are almost useless but a ratio line is of the same 
 value at all points. Another advantage is its use in forecasting. 
 In business a forecast is made by assuming a certain ratio of 
 growth. In the ratio diagram a forecast is made by simply 
 drawing a straight line or extending a Hne already drawn to 
 represent the rate experienced in the past. Equal rates of 
 growth on a ratio diagram are clearly shown by parallel lines. 
 We can move a curve bodily for comparison with another without 
 impairing its value which is not permissible on a difference 
 diagram. The best that can be said for the difference method is, 
 
MAKING OF DIAGRAMS 45 
 
 it always shows whether there is an increase or decrease. The 
 base or zero hne gives a means for comparing positive and nega- 
 tive quantities and for seeing in a simple and seK-evident com- 
 parison the vertical elevations of points in a curve above or 
 below the base line. 
 
 The features of a curve which most catch the eye are concerned 
 with comparative direction. The eye reads a ratio chart more 
 rapidly than a difference chart or a table of figures. What most 
 catches the eye is enumerated as follows : 
 
 1. If we see a curve ascending and nearly straight we know that 
 the statistical magnitude it represents is increasing at a nearly 
 uniform rate. 
 
 2. The reverse for descending. 
 
 3. If the curve bends up the rate of growth is increasing. 
 
 4. If the curve bends down the rate of growth is decreasing. 
 
 5. If the direction of the curve in one portion is the same as the 
 direction in some other portion it indicates the same percentage 
 rate of change in both. 
 
 6. Steeper in one portion than another indicates more rapid 
 rate of change. 
 
 7. Two curves parallel represent equal percentage rates of 
 change. 
 
 8. If one is steeper than another the first is changing at a faster 
 percentage than the other. 
 
 9. Imaginary straight line most nearly representing to the eye 
 the general trend of the curve is its growth axis and represents 
 the average rate of increase or decrease and deviations of the 
 curve from this hne are plainly evident without recharting. 
 The preceding relates to direction. As to elevation the eye 
 can with a little familiarity translate vertical elevation into 
 numerical ratio, for a certain elevation represents a 10 per cent 
 increase, another a 100 per cent increase. 
 
 As examples of the value of ratio diagrams, take a difference 
 plot of millions of population over a period of 70 years by tens. 
 
 Figure 23 shows both a difference scale (A) whose vertical dis- 
 tances are equally spaced and equally marked and a ratio scale (B) 
 with equal vertical spacing but with a marking corresponding 
 to a constant increase of 10 per cent. Uniformity in percentage 
 of growth is represented by a straight line. It is more convenient 
 to use a log scale whose spacing is according to a percentage 
 rate than to figure the proper marking for lines equally spaced. 
 
46 
 
 GRAPHICAL METHODS 
 
 The contrast then between the ratio and ordinary difference 
 diagram is simply one of spacing, the ratio method having the 
 numbers 1:10, 100:1,000 equally spaced. Another example of 
 the false comparison of two curves by the difference method and 
 
 200 
 o 190 
 ol80 
 
 = no 
 
 ^ 160 
 ■|l50 
 .9 WO 
 o 130 
 g_l20 
 
 S no 
 
 100 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 /' 
 
 
 m 
 lei 
 
 133 
 
 no 
 
 100 
 
 
 
 
 
 
 
 .y^ 
 
 
 
 
 
 ^ 
 
 / — 
 
 
 
 
 
 
 
 -^- 
 
 
 
 
 
 
 7^ 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 7^ 
 
 
 
 
 
 
 
 y^ 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 ^' 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 \ — 1 
 
 Years 
 (A) DIFFERENCE 
 
 Years 
 (B) RATIO 
 
 Fig. 23. — Comparison of difference and ratio plotting. 
 
 by the ratio method is shown in Fig. 24 {A) and (5). The 
 growth of $1 and of $6 when placed at compound interest for 
 40 years does not look the same in {A) although the percentage 
 increase is the same and so appears in the ratio diagram of (5) 
 
 (o) Arithmetic Chart 
 
 (6) Logarithmic Chart 
 
 Fig. 24. — Growth of 1 dollar and 6 dojiars when placed at compound interest for 
 40 years. Comparison of two kinds of charts. 
 
 as the lines of growth are parallel. Another example of false 
 comparison by the difference method is shown in Fig. 25(A). 
 Here it appears as if the sales had risen tremendously in com- 
 parison with sales costs, whereas a plot on log paper in (5) shows 
 
MAKING OF DIAGRAMS 
 
 47 
 
 the sales cost and sales had not differed at any time very greatly 
 in percentage. The table for plotting these diagrams is given 
 below them. 
 
 If the data of a reference plot cause the graph to deviate 
 continually from a straight line they may often be represented 
 
 Tofa/ Sales 
 
 Sales Cosi 
 
 Salesmen's Salaries 
 
 Salesmen's Expenses 
 
 Adyertising Expense 
 
 1,000,000 
 
 900,000 
 
 800,000 
 
 700,000 
 
 i? 600,000 
 
 o 500,000 
 
 400,000 
 
 300,000 
 
 200,000 
 
 100,000 
 
 . 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 -f 
 
 ^p^i 
 
 
 / 
 
 
 
 
 / 
 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 _. 
 
 i 
 
 — 
 
 — 
 
 — 
 
 CJ CO 
 
 Total Sales J^-. ctT 
 
 fU CO 
 
 Sales Cost co. 
 
 I.OOO.OOOi 
 
 c5 ®°'' 
 60,000 
 
 CS<i^lEU^ 
 
 Arithmetic Comparison Diagram 
 
 Logarithmic Comparison Diagram 
 
 Year 
 
 Total 
 Sales 
 
 Sales 
 Cost 
 
 Salesmen's 
 Salaries 
 
 Salesmen's 
 Expenses 
 
 Wvertm 
 Expense 
 
 Cost 
 Index 
 
 1910 
 
 5Z3,482 
 
 109,621 
 
 63,259 
 
 33,002 
 
 13,660 
 
 21 
 
 1911 
 
 5&9,ZI3 
 
 100,14-B 
 
 65,212 
 
 20,830 
 
 15,103 
 
 17 
 
 1912 
 
 692)450 
 
 103,889 
 
 66,490 
 
 21,490 
 
 16,212 
 
 IS 
 
 1913 
 
 7a3,895 
 
 86,897 
 
 57,211 
 
 18,556 
 
 11,130 
 
 12 
 
 1914- 
 
 675,003 
 
 108,361 
 
 60,576 
 
 34,S7S 
 
 13,44-5 
 
 16 
 
 1915 
 
 189,667 
 
 109,720 
 
 65,110 
 
 26,021 
 
 18,589 
 
 14- 
 
 I9ie 
 
 938,^ll 
 
 112,243 
 
 70,364 
 
 25,647 
 
 16,232 
 
 12 
 
 FlQ. 25. — Comparison plotting of difference and ratio methods. 
 
 by an exponential equation of the form y = mx" where m 
 and n are constants which may have any value. To test the 
 numerical values of m and n we may use logarithmic paper and 
 plot logs of X as abscissas and logs of y as ordinates. Writing 
 y = mx" in logarithmic form gives log y = ii log x + log m. 
 
48 GRAPHICAL METHODS 
 
 Putting x' = log X and y' = log y and 6 = log m the equation 
 becomes y' = nx' + b which is the equation of a straight line. 
 By using logarithmic paper we can locate points such as x and 
 y proportionally to their logs and obtain a straight line as 
 noted above. 
 
 The chief problems in the technique of historigram plotting 
 are those of base line scales, types of lines to use for the graphs 
 and methods of and purposes of smoothing these curves. The 
 size of page, ability of grasp by the eye, subsequent treatment of 
 the illustration, etc., are determining factors. The variable 
 factor is usually plotted from a base line along the ordinate axis. 
 Spacing and rules for scales apply as in frequency diagrams. 
 When two or more curves are shown on the same diagram it is 
 sometimes neccessary to adjust the scales to bring the curves 
 nearer or farther apart. One method of scale conversion when 
 the absolute differences are great is to equate the scales on the 
 basis of their respective averages. Another method is to plot 
 the curves of differences between the items and their averages. 
 This is more of a mathematical method which does not appeal to 
 the average business man. A more common method is to convert 
 the individual variables into percentages of a total and express 
 them in the form of index or relative numbers. Measurements 
 on successive ordinates must be made from the base line and 
 not from the tops of preceding ordinates. When related series 
 are plotted on the same sheet they should be designated by 
 similar markings. Lines should be broad enough to be easily 
 followed but not to sacrifice the accuracy of the ordinate unit. 
 
 Before plotting any data it is well to consider several points 
 with regard to that data. Statistics are collected (1) for the 
 purpose of testing the progress of a commercial undertaking, 
 (2) for testing the success of an institution, (3) for collecting data 
 for the solution of a social problem. 
 
 Some of the objects of statistical analysis are: census of popu- 
 lation, vital statistics, trade and transportation, prices, wages^ 
 production, employment, income and capital, taxes and rates. 
 
 Nine rules are suggested by Mr. Bowley to guide the hne of 
 study and criticism of statistics. These rules are here given and 
 an examination of them will show how they can be applied to 
 other data than statistics. 
 
 1. Find the exact definition of the units which go to make the 
 total. In every case the definition depends on the regulations 
 
MAKING OF DIAGRAMS 49 
 
 and methods of collection. As an example, what is meant by a 
 farmer? By a room, in the census reports? 
 
 2. How far the persons or things grouped together in a total 
 or sub-total are similar or how far the group is homogeneous. 
 Thus, persons whose occupations are grouped under textile 
 fabrics differ with respect to (1) sex, (2) age, (3) nature of material 
 worked (cotton, wool, etc.), (4) position in industry, as merchant, 
 dealer, manufacturer or employee, (5) specific occupation, (6) 
 locality. 
 
 3. Having defined and analyzed the totals, the next question is 
 what is the relation of the quantity they measure to the quantity 
 as to which we want knowledge? 
 
 4. Before trusting or even reading a statistical account it is 
 well to sit down and think quietly what statistics ought to have 
 been collected, if possible, for the purpose in hand and what 
 sources of information exist or should exist. Having got so 
 far we may consider how far the problem has been understood, 
 whether all the practicable measurements have been made and 
 whether the result gives a true index. We can thus decide as to 
 whether the information is sufficient for solving any assigned 
 problem. 
 
 5. When we have to deal with averages, rates and percentages 
 we must carry our second rule of criticism further and consider 
 not only if numerators and denominators are homogeneous in 
 themselves but whether the terms of the denominator have a 
 reasonable relation to those of the numerator. They should be 
 limited to those cases which are so. 
 
 6. When two quantities are compared we must consider 
 whether they are strictly comparable. Accurate comparisons 
 can only be made between closely similar things or over quite 
 short periods. 
 
 7. Closely related to the last is the measurement of accuracy. 
 In all statistics we must decide whether the data and methods 
 will yield results accurate enough for the arguments based on 
 them. 
 
 8. We must not depend on figures relating to single days, 
 months or years or on comparisons relating to short isolated 
 periods. Where a sufficient record cannot be obtained, judgment 
 must be suspended. 
 
 9. Having determined as far as possible the exact purport and 
 limitations of the statistics, consider to what conclusions they 
 
50 GRAPHICAL METHODS 
 
 lead or whether they are so imperfect that no conclusions can be 
 reached without further investigations. Inferences are suggested 
 and tested by the reported facts and a severely critical and 
 logical analysis is necessary before the whole investigation leads 
 on to some reasoned action. 
 
 . Examples for Chapters II and III 
 
 1. Before plotting diagrams what information must be given and in what 
 form? Illustrate by two examples. 
 
 2. Into what classes are graphs and diagrams divided? Illustrate each one. 
 
 3. Explain how to construct a diagram using two axes at right angles and 
 coordinates. 
 
 4. What is an ordinate? An abscissa? Why are plus and minus signs 
 used? 
 
 5. What are the governing factors in selecting the scales of a diagram? 
 
 6. Enumerate a few of the various kinds of ruled paper used in making 
 diagrams, and state the advantages of them. 
 
 7. How can logarithmic paper be constructed? Arith.-log paper? 
 
 8. What are the governing factors in the selection of paper for plotting a 
 diagram? 
 
 9. Where should the coordinate axes be located and how indicated? 
 
 10. How should lettering or figures be placed to facilitate reading them? 
 
 11. How should arrangement of grouping be treated as regards sequence of 
 time, size of item or favorabiUty of item? 
 
 12. What governs the form selected for graphically representing a fact? 
 
 13. When several happenings are shown on one diagram how are their 
 graphs distinguished one from another? 
 
 14. In making graphs for comparison what important points must be con- 
 sidered? 
 
 15. What is a frequency graph? Historigram? Continuous series? Dis- 
 crete series? Cumulative frequency? 
 
 16. What three elements are visualized in plotting a series of economic data? 
 
 17. Explain the "ratio" method of plotting and compare it with the 
 difference method. 
 
 18. When is log paper used in preference to coordinate paper? 
 
CHAPTER IV 
 APPLICATIONS 
 
 In the preceding pages the general subject of graphical methods 
 has been touched in the abstract although in the chapter devoted 
 to the making of diagrams, a few examples have been given of 
 the practical apphcations of the method. 
 
 The simplest Hne diagram is one drawn to show the relation 
 of two quantities such as miUimeters and inches, Fahrenheit and 
 Centigrade temperature scales, diameters and circumferences 
 
 Millime+ers 
 
 20 40 60 60 100 120 140 160 leO 200 MO 
 [l lll l | l |l ll l| llllMlMlllllNllMllllllllllllllllLlllrilllil.lllillli.ili,lJlMi l iii|lM,iliMll.|iiln,.lM.il /yj^ j 
 
 0'2 3 4^5 67 89 
 
 Inch CSS 
 
 Scale for Changing mm. +0 in. and Reverse 
 
 ° '/s 3/8 ? ^,'^8 ^{ s Distance across Flats Hex.aSq.Hd.aNut 
 I E 3 4 5 Inches diameter of Bolt 
 
 H \ 1 h 
 
 g Long diam. Hex. 
 
 (B) 
 
 30!?'-: Long. diam. Sq. 
 •t t^ <o — 
 
 Fig. 26. — Conversion scales. 
 
 of circles, etc. These relations are expressed in tables as a rule, 
 but often these tables require too much space or are not con- 
 venient to use on account of the interpolation required. 
 
 In Fig. 26 (.A) and (B) are shown two of the simplest of these 
 line diagrams. 
 
 (A) is used to convert inches to millimeters or millimeters to 
 inches. The spaces between the inch marks can be made any 
 distance, the greater they are the greater the accuracy of the 
 millimeter readings. 
 
 (B) is used to obtain the values of the distance across flats 
 of U. S. Standard bolt heads and nuts. The long diameters of 
 hexagonal and square nuts and heads are given on the lower 
 
 51 
 
52 GRAPHICAL METHODS 
 
 scale. The values of the long and short diameters of bolt heads 
 and nuts can be found in engineering handbooks and marked off 
 at the proper points of the scale opposite the corresponding bolt 
 diameters. If desired the scale can be made in the form of a 
 rule and applied directly to the drawing of bolts and nuts. 
 
 An application of the above method is found in the change 
 from arithmetical to percentage scales. If a hne such as Fig. 
 27(a) is divided into equal divisions and they are marked 10, 
 15, 20, etc., starting at one end, we will have an arithmetic 
 scale. If the lower line is marked according to a fixed percent- 
 age difference of 100 per cent between them we have a percentage 
 scale 10, 20, 40, 80, 160, etc. When intermediate numbers are 
 
 a Ari+hme-Hc Scale 
 
 10 15 ZO 30 40 50 GO 
 
 I I I \ 1 1 1 
 
 Percen+age Scale 
 10 15 to 40 80 160 320 
 
 'I I I I 1 1 
 
 Fig. 27. — Comparison of arithmetic and percentage scale. 
 
 introduced between the numbers they will be spaced equally 
 everywhere on the (a) scale but on the (6) scale the spaces will 
 be subdivided into more parts as we move to the right and 
 the points of division will be closer together on account of the 
 decreasing percentage of difference. 
 
 If we wish to locate the intermediate number 15 on the line (6) 
 we find the log of 15 and locate the point according to the relation 
 of the log of 15 to the logs of 10 and 20. When this is done the 
 point 15 will be found nearer to 20 than to 10. It is this princi- 
 ple which is at the basis of the slide rule, the divisions beingmade 
 according to the logs of the numbers marked on the rule. Paper 
 can be obtained which is ruled according to this principle and 
 called log-log paper (Fig. 11) or arith.-log paper (Fig. 26). A 
 scale for finding the length of various proportions of the circum- 
 ference of a circle when the diameter is given is shown in Fig. 28. 
 \i AB = the diameter of the circle its circumference will be equal 
 to AC. If AC is subdivided into one-eighth, one-fourth, one-half 
 and three-fourths of its length and these points joined to 0, which 
 can be taken at any convenient distance from AC, we can obtain 
 
APPLICATIONS 
 
 53 
 
 the same proportions of any circumference corresponding to the 
 diameter given on the left-hand scale AO. 
 
 This replaces a table of six columns besides affording a ready 
 means of taking off the dimension with a compass when it is 
 desired for drawing a circle or subdividing a circumference. 
 
 A further application of diagram substitution for tables is 
 found in Fig. 29. In this diagram one can find the inches of 
 mercury, feet of air, pounds per square inch and atmospheres 
 corresponding to feet of water, and vice versa, by erecting a per- 
 pendicular at the number of feet of water given, until it cuts the 
 
 graphical method of finding clkcumference 
 of circl £ when diameter is known 
 
 Fig. 28. 
 
 inclined line denoting the term required. A horizontal line 
 through this point to the vertical axis will give the number 
 corresponding to the feet of water given. This diagram replaces 
 15 tables and takes up very Uttle space. Such diagrams are 
 called conversion diagrams and their application to simple prob- 
 lems can often be made with benefit depending on the tables 
 displaced and the economy of time resulting. 
 
 There is a type of problem which can be solved by a direct 
 appeal to the eye which is extremely effective and simple. These 
 problems are those involving time and speed such as, "If a man 
 travels 5 miles in 1 hr., how far will he go in 5 hr.?" which is a 
 simple one involving multiplication. Suppose, however, we 
 have the following: 
 
 " A person walked from A to 5 at the rate of 33^ miles per 
 hour and then part of the way back from B to A ran at 7 miles 
 
54 GRAPHICAL METHODS 
 
 per hour and finished the remaining distance in 5 min. at the 
 original rate. His total time was 25 min. A second man walks 
 from J3 to A at a uniform rate and was also gone 25 mm. At 
 
 10 
 
 20 30 
 
 10 
 
 80 
 
 go 100 
 
 40 50 60 
 
 Fee+ of Waten 
 
 DIAGRAM FOR CONVERTING FEET OF WA TCR INTO ATMOSPHERES, 
 LBS. PERSa. IN./EETOFAIR INCHES OFHERCURYSt CENTmETERSOFMEKUHY 
 
 Fig. 29. 
 
 what two times will he meet the first man and how far from A 
 will the two places of meeting be?" 
 
 Here is a case where simple multiplication will not answer, 
 but by the graphical method it is nearly as simple as the first 
 
 Fig. 30. — Diagram of distance us. time. 
 
 example. The first example is solved thus: Draw a horizontal 
 line and divide it into equal parts as at 1, 2, 3, 4 in Fig. 30. Let 
 these represent hours. Through each of these points draw 
 
APPLICATIONS 
 
 55 
 
 vertical lines and on the verticals lay off equal divisions as 5, 10, 15, 
 20 to represent miles, and through these points draw lines parallel 
 to the lower horizontal. If the man travels 5 miles in 1 hr., his 
 path will be represented on the diagram by the hne from to ^. 
 If we wish to know how far he will go in 2 hr. we find B where the 
 vertical through 2 cuts the diagonal 04. A horizontal through B 
 cuts the vertical scale of miles at 10. For any other time the same 
 procedure gives the answer on the left-hand scale of miles. If a 
 second man goes twice as fast as the first his path will be shown 
 by the more steeply incHned hne from on the base line to 2 on 
 the highest hne. Taking the second example let us apply the 
 same principles. 
 
 A 
 
 5 PH 10 
 
 Minutes 
 6 IB 
 
 20 
 
 
 25 
 B 
 
 H 
 
 1 
 4 
 
 R 
 
 I 1 
 
 1 1 
 
 ^ 
 
 >ir^^ 
 
 
 
 
 
 2 
 £ 4 
 
 I 
 
 
 ^^"•~-..,^^^ 
 
 2^^^ 
 
 ^^ 
 
 r 1- 
 
 E 
 
 
 
 V 
 
 c^ 
 
 A 
 
 f 
 
 
 1 
 
 
 I 
 
 •i- 
 
 
 
 
 
 
 
 
 ~^ 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 ^ 
 
 --^ 
 
 
 ,1 
 
 
 
 
 
 
 
 
 
 
 
 ^^■^^ 
 
 Fig. 31. — Solution of problem by graphical means. 
 
 In Fig. 31 take AB = 25 min. Lay off AH = same fraction 
 of an hour that AI is of S}-^ miles. AK will then by its inclina- 
 tion represent 3^ miles per hour. Produce this diagonal in- 
 definitely toward C. Lay off BL = 5 min. on the time scale. 
 Draw the vertical LM and the diagonal BD having the same 
 slope as AC. From D draw a diagonal DS having the slope 
 corresponding to 7 miles per hour with the same scales as those 
 used for AC at 3}i miles per hour. This diagonal intersects AC 
 at C and the perpendicular distance from C to AB is the distance 
 from A to B. The distance he ran was DM. If the second 
 man starts from B and walks at a uniform rate from 5 to A and 
 back and takes 25 min., his pa;th will be represented by EG-GF. 
 He wiU meet the first man at the first time and at N the second 
 time. The distances from A wiU be the vertical distances OP 
 and QN. The times from A will be AP and AQ respectively. 
 
56 
 
 GRAPHICAL METHODS 
 
 These examples involve time and space but the same principle 
 can be applied to questions of time and work done such as labor 
 performed by men or machines, water discharged by pipes, etc. 
 Questions in alligation may also be solved by the graphical 
 method. 
 
 The appHcation of the graphical method as outHned above 
 to the adjustment of the running times of railway trains works 
 out as follows: In Fig. 32 the spacing of vertical lines are hours, 
 and horizontal Hues are stations A, B, C, etc., at distances 
 apart according to a vertical scale of miles. Suppose we wish to 
 
 
 \ 
 
 
 \ 
 
 
 
 / 
 
 
 •^ 
 
 
 
 
 / 
 
 
 \ 
 
 \ 
 
 
 / 
 
 
 
 X 
 
 
 
 / 
 
 
 
 
 \ 
 
 y 
 
 / 
 
 
 
 
 \ 
 
 ./ 
 
 / 
 
 
 
 
 / 
 
 ^ \ 
 
 
 
 
 
 /■ 
 
 N 
 
 
 
 
 
 / 
 
 \ 
 
 \ 
 
 
 
 
 / 
 
 
 
 
 
 / 
 
 / 
 
 
 \ 
 
 \ 
 
 s , 
 
 / 
 
 
 
 
 
 
 / 
 
 
 
 \ 
 
 
 y 
 
 
 
 
 
 
 / 
 
 
 
 
 \ 
 
 / 
 
 /\ 
 
 \ 
 
 ■"^ 
 
 
 
 
 / 
 
 
 
 
 
 \/ 
 
 
 
 \ 
 
 
 
 
 10 II 12 I 
 
 Hours 
 
 FiQ. 32. — Train chart. 
 
 start a train from .4 at 6 A.M. to arrive at J at 3 P.M. with 15- 
 min. stops at each station. Taking out eight stops of 15min. 
 each equals 2 hr. Therefore the train would reach J at 1 
 P.M. if there were no stops. The slope of the speed line will be 
 found by joining A at 6 A.M. with J at 1 P.M. Draw this line 
 from AtoB, then move along B for 15 min. and draw a parallel 
 to the speed line from B to C Repeat this operation until the 
 last diagonal line drawn from I cuts J, which it should do at 
 3 P.M. 
 
 If we start a train from A at 8 : 30 A.M. to reach J at 1 1 : 15 A.M. 
 without stops, its path would be a continuous straight hne from 
 A to 3 , intersecting the path of the first train at D where it would 
 meet it. Trains running in opposite directions are shown by 
 diagonals ascending from left to right. Thus a train leaving J 
 at 6 A.M. and arriving at A at noon is shown by a broken diagonal 
 meeting the 6 A.M. and 8:30 A.M. trains at D. 
 
APPLICATIONS 
 
 57 
 
 The change in slope shows that the train runs faster from D 
 to A than from J to D. If a train leaves A at noon running 
 toward J, leaving C at 2:05 and reaching E at 3:20 and another 
 train leaves J at 11:15 A.M. and G at 1 P.M. running to A as 
 by diagram without stopping, the trains will pass at 3:10 P.M. 
 between D and E at an exact point whose distance can be found 
 by the scale of miles, therefore a siding must be built. 
 
 In practice the diagram is accurately drawn to a large scale 
 and the several trains are represented by different colored elastic 
 
 Millions of Dollars 
 
 10 20 30 40 
 
 
 
 
 ania 
 
 
 
 
 
 
 
 
 
 I.PennsyK 
 
 
 
 2. Ohio 
 J.California 
 4. West Virginia 
 
 
 
 G. Oklahom 
 7. Kansas 
 B.Texas 
 
 a 
 
 
 
 Amount 
 
 39.2 
 
 ^29.6 
 
 V29.3 
 
 V28.2 
 
 H 
 
 FiQ. 33. — Comparison of lines, areas and volumes. 
 
 18.9 
 
 1^6.4 
 
 strings fastened by pins to enable schedules to be changed when 
 . necessary through accidents or delays. Grades and curves 
 may be shown on the hne A J and speeds determined more 
 readily. On a double-track road there may be a chart for each 
 track and diagonals in one direction only will appear on each 
 diagram. 
 
 Diagrams most frequently used to illustrate frequency and 
 magnitude alone are lines and bars. Some use has also been 
 made of surfaces and volumes, but this is not recommended 
 because of the difficulty of grasping more than one dimension 
 by visual inspection. Surfaces vary as the square of their sides, 
 and volumes as the cube of their edges. Figure 33 is drawn to 
 
58 
 
 GRAPHICAL METHODS 
 
 DISTRIBUTION OF HEAT tosses IN AVERAGE 
 mVER PUNT OPERA 71 NO NON CONDENSING 
 
 FiQ. 34. — ^Pie diagram. 
 
 <-3!% 
 'anbust 
 ^.HP. 
 
 ■ ii>e%- 
 
 HBA7IN OIL SUPPLIED 
 
 B.HP. 
 
 fsh^eafioMiTi 
 
 'iU^et 
 
 S.h 
 
 ■—6!%- 
 Total Heat hStsar 
 
 Losses 
 
 T'/6 
 
 Friction 
 6% 
 
 ^ 
 
 Stvch 
 
 A ±. ,i „o Heat Distribution \r\ 
 Actual B.HR the Still Enaine 
 
 (A) 
 
 lazes fl]njairresi'st,\_ 
 Friction Si vunt , . 06% 
 of front wheels ' /"/%' 
 Front tires ' ' - 
 
 Rear tirffs 
 
 Tnrnsmissiorj 
 
 Frictioninmnhir jjj^j^jjjjjjjf ^ 
 
 Muffler 
 Ettiausfpping 
 
 Exhaustgases 
 and radiation 
 
 Cooling water 
 
 ■ffrserveof 
 '•-power for 
 §i73oles, etc.S4% 
 
 ~EFf}ciencu 
 '^powerofcam.S% 
 
 -Efflcienoy 
 motor powerlOJ% 
 
 Enei^u value 
 ofgas looyi, 
 
 Energy Diagram 30 Hp. Car ftr Speed 
 0f37.3M.P.H.,(Riecller) 
 
 (B) 
 
 Fig. 35. 
 
APPLICATIONS 
 
 59 
 
 show the comparison of Unes, surfaces and volumes when dealing 
 with magnitudes. 
 
 The lines show best to the eye and give an exact relation easily 
 
 Rate of Firing Coal persq.ft.o-f Grate perhr 
 Fig. 36. — Percentage diagram. 
 
 DISTRIBUTION OF COSTS, HULLnilS 
 
 TOTAL COSTOF HULL ^TS^TS-f 
 
 Fig. 37. — Pie diagram. 
 
 understood. Often a whole may be divided into parts by a pie 
 diagram. The areas of the sectors have to be calculated and 
 
60 
 
 GRAPHICAL METHODS 
 
 the radial lines drawn to divide the circle into parts proportional 
 to the percentages desired. Such a pie diagram for showing 
 the distribution of heat losses in a power plant is shown in Fig. 
 34. The only excuse for such diagrams is the assumption that 
 
 |<-gg^->t<—-B.4— -->!<-— -»^%--->l 
 
 MATERIAL 
 
 DIRECT LABOR 
 I] 
 
 L 
 
 "[^sfvrlafinn 10% 
 
 ~iSf!tX> 
 
 Fig. 38. — Alternate to Fig. 37. 
 
 the average mind grasps more quickly the fact that a circle repre- 
 sents 100 per cent, better than any other kind of a figure. The 
 data illustrated here could be represented much better by means 
 of such diagrams as Fig. 35, A and B, or Fig. 36. The con- 
 struction is, moreover, much simpler. 
 
 100 
 90 
 
 
 
 
 
 1 1 1 1 1 1 
 M/HNJENANCE OF. WAY 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 BO 
 
 
 
 
 
 
 
 
 
 ~ 
 
 
 
 
 
 
 
 
 
 
 
 P-- 
 
 
 -^ 
 
 INT 
 
 'NAh 
 
 ICE 
 
 VEl, 
 
 1UIP 
 
 Vf// 
 
 T 
 
 
 
 
 10 
 60 
 
 4- 
 
 a 50 
 
 30 
 ZO 
 10 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 co 
 
 •^DUl 
 
 T/m 
 
 i W 
 
 'ANi 
 
 'OR 
 
 'ATIC 
 
 N 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 GE 
 
 NER 
 
 AL 
 
 ^ 
 
 \J 
 
 ■^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ~ 
 
 
 
 
 
 
 
 
 
 m 
 
 ED 
 
 CHA 
 
 9GE 
 
 r 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Ffa: 
 
 vB.v-*a 
 
 Sot. 
 
 c 
 c 
 c 
 
 3 
 
 D o; 
 
 1 I 
 
 
 5 § 
 
 1 
 
 3 C 
 
 a 
 
 n 
 
 \ \ 
 
 n c 
 D c 
 
 I \ 
 
 
 3 1 
 
 ^ C 
 
 
 1 c 
 
 3 O 
 
 Years 
 
 PlRCENTAGeDISTRIBUVONOFEXPENSESOFOPERATION CFR.R.OFU.S. 
 From Brintou'e Graphic Methods for Preaenting 
 
 Facte 
 
 Fig. 39. 
 
 Pie diagrams cannot be readily compared without being 
 superimposed. Figure 37 is a pie diagram which could have 
 been shown in the form of Fig. 35 to much better advantage. 
 Its appearance would then have been like Fig. 38. Distribution 
 form for total to be used in preference to pie diagrams. 
 
APPLICATIONS 
 
 61 
 
 _ Figure 39 is a diagram used in statistical work to show the 
 distribution of total expense cost over various departments for a 
 term of years. The objection to this is the inability to show 
 on it the actual totals without disturbing the symmetry of the 
 diagram and making the top an irregular hne to conform to the 
 variation in yearly expense which would at once destroy the 
 percentage scale hne. A pie diagram for percentages of black, 
 white, yellow, etc., of population in the United States in 1910 can 
 
 100 
 
 75 
 
 50 
 
 25 
 
 FOREIGN viy/ZZj, 
 Germane/ Ireland Canadc (£if "SH: fe 
 
 _S^SS 
 
 From BriDtOD*E Graphic Methods for Presenting 
 Facts 
 
 
 Fig. 40. — Population of U. S. in 1910. 
 
 be replaced to better advantage by a bar diagram Hke Fig. 40. 
 Magnitudes must be drawn to scale and accompanied by their 
 tabular values. 
 
 BAROGRAPHS 
 
 The vertical barograph can be used in cases where comparisons 
 of several types are needed when all types have a common part 
 and it is desired to show the relation of some characteristic of this 
 part. As an example the comparison of the mean specific opening 
 of valves on several types of automobile is shown in Fig. 41 by 
 means of vertical bars. The unshaded portions of each bar are 
 the ones to be compared. The superiority of the Benz racing 
 car over the Adler makes a strong impression on the eye. The 
 figures confirming this fact and driving the point home are 
 indicated at the base of each column. 
 
 The columns do not need to be so wide as the comparison is 
 simply one of length. The horizontal barograph is better for 
 
62 
 
 GRAPHICAL METHODS 
 
 INLET 
 Sleeve Valve Gecrr->|-s Poppet Valve Gear 
 
 Dalmier Daimler 
 
 ilO 
 
 is 
 
 > 
 
 6 
 
 ■g 4- 
 
 in 
 
 « 
 
 V Z- 
 
 T. 
 
 Adler 
 Mercedes 'teller Bern (RadngCar) Adler 
 
 IOO //30 S^/l3S 90/,40 105/130 90//is 
 
 — Wy 
 
 >, 
 
 Bern rercir^ 
 
 63 
 
 74(55) 
 
 81 
 
 IZ 
 
 100 14- 
 
 Per Cent 
 a - Throwing in carbureter ^22% 
 
 COMPARISON OF MCAN SPECIFIC OPfNING SCQTIQMS 
 
 FlQ. 41. 
 
 IBJOIZZIU* 
 lS4n l W ? 
 1950 1 \ 3III 
 IHfiO l 
 
 Figures in millions ofdollara 
 
 ISTOC 
 IBgOC 
 I890C 
 I900C 
 
 3S29 
 
 3IS0* 
 
 31647 
 
 ■PiQ. 42. — Values of exports from 1830-1900. 
 School Cosi- per Pupil 
 
 New Rochelle 
 
 Mt. Vernon 
 
 Auburn 
 
 Niagara Falls 
 
 Poughkecpsie 
 
 Kingston 
 
 Amsterdam 
 
 Jamestown 
 
 Newbuigh 
 
 Watertewn 
 
 CITIES ZS^OOO to 35,000 PEOPU 
 (Figure$ based en average daily crttendance) 
 
 From Brlnton'B Graphic Methods for Preeentlnff ^ .„ 
 
 Facto FlO. 43. 
 
 "22244 
 
 ■*61.14- 
 54.87 
 46.78 
 «.1I 
 40.27 
 39.85 
 36.18 
 3B.4I 
 34.89 
 
 50^2 
 
APPLICATIONS 63 
 
 showing values of quantities by lengths of single lines or bars. 
 The barograph is used most often for statistical representation 
 although its application in shop production methods is rapidly 
 
 D- 
 
 ■3 LABOREflS 
 
 ■ts- Tailors. 
 
 Mt. COBBIERS 
 
 1Z9 GENERAL Miners. 
 
 ITtTCAM- 
 
 _.. STER5 
 
 ? M^St:>^.:^ -^^= 1 =r OCCUPATIONAL 
 
 vn, Hofsc Hostlers- — 
 
 « Bmbcrs 
 
 I3a Sen. BoiLEB Makers 
 
 7K H0RSC6H0ER5 
 
 U RftSHOP MECHANICS 
 
 40a CATERERS- 
 
 Intelligence Siandards 
 
 u Bricklayers— m_» 
 ■Wt Cooks — 
 
 » s^Agr^i^7^r-M— - " ) v^H" OF^ Shows R^ncE OF Mime joPerCent 
 
 4ta\S£^ '' '■ " Vertical Crossbar Shows RjsiTioHOFMEOiAti 
 
 a7tr Horse TiAiMERS 
 
 13 Paikters — 
 
 Tg GEHBLACKSMrrHS 
 
 tit BfilDOECAHPCNTERS 
 
 23t Heavy Truck DRIVERS— 
 
 5g GEK. CARPENTERS 
 
 i^* Marine EJJGmCHEN 
 
 11 Butchers-. 
 
 IJU UtOMOTIVEDttlNEtlCri ^^^^ 
 
 u Lathe Hand ,-^^^^m 
 
 l« GEN MACHINISTS ^^MM 
 
 m LOCOMOTIVE riREMEN ^mmm 
 
 m K\r(o Riveters ^^._ 
 
 at BRAKEMEN ~^mmm 
 
 zit TtLtTtL Linemen .^^ 
 
 rj. RRCONDI/CTORS ,^ 
 
 Ha GEN Pipefitters ^m. 
 
 Mn Motorcyclists mm 
 
 lif Plumbers m^^ 
 
 lUTBOLtGAUCE MAKERS m 
 
 11 GUNSMltHS ■ 
 
 lu Airro CHAurrEURS bmh 
 
 l*c GCK MCCHANCS ^^^ 
 
 Mf artMo Repairmen ■«« 
 
 UrmRMMCXPEfiTS ■ 
 
 81 DTTECTlVESiRlLlCEriCN 
 
 Uf AutoCngincMcchAhics 
 
 1h AllToASSEnBLERS 
 
 tk Stock Checkers ■ 
 
 f« Ship Carpenters 
 
 U lAmtfliVETERINAIllAHS 
 
 aSU'DflCKMASTERS- 
 
 33o TtLCPHONC OPERATORS 
 
 SOt OUCRCTECmSTRUCTIDNrORmEn.- 
 
 ..- StokKeeper 
 
 31 PHOTOERAPHCfl 
 
 Bq GtnELECTfllCIAfU-. 
 41b B^tlD MuSlCIAnS— 
 
 5lt TtLEGRAPHERS -^ 
 
 WirRRClERB 
 
 3lf riLinEaEBKS 
 
 3lfl CCH CLERKS 
 
 I- MeowucalDigimeers 
 
 Army Norses 
 
 35b Bookkeepers 
 
 Oehtal otficers 
 
 lln MCCH^MICAL DRArTSMEfl— 
 SI 5TEnOGflAPHCfiSiTYPIST5-. 
 37 ACtOUMTAtlTS 
 
 as Civil CficiMEERS 
 
 YmCA Secretaries— 
 
 fiEOlCALOrnCERS 
 
 ARMY CHAPLAinS 
 
 DiGIHEER 0FriCER5__ 
 
 b- ' D ' C^ ' C ' (T* ' D I A 
 
 Fia. 44. — Occupational Intelligence Standards. Bar shows range of middle 60 
 per cent. Vertical crossbar shows position of median. Figure based on data 
 from 36,500 men. Numbers at extreme left are occupational key numbers. 
 Data taken from soldiers' qualification cards. 
 
 gaining ground. The simplest form used is for showing increas- 
 ing or decreasing phenomena over a period of time or a percent- 
 age value in a comparative way. 
 
64 
 
 GRAPHICAL METHODS 
 
 The value and growth of exports or imports over a term of 
 years may be shown as in Fig. 42, but the advantage over a table 
 is not so evident as to warrant the use of a diagram of this kind. 
 A graph would be of much more value, especially if it was plotted 
 according to a percentage scale. Fig. 43 is a barograph showing 
 the school cost in different cities arranged according to order of 
 
 Total Pop. 
 7e,303,3B7 .^ 1^;- 
 
 '^3^963, aS7 
 Native »/fe/fa«^ /4.4ss,ose 
 Native Parents wA ■''■■'■■'::■:■■ 
 
 44181 IS5 
 
 ^^,920,103 
 
 Hathe Whiteofm^. 
 Foreign Parents Xi:^ 
 
 Foreign White 
 
 Negro | 
 
 i5^e47,on 
 
 io.?i3.sn 
 
 ^^ single 
 |)S:;i] f^arried- 
 ^^ Widowed 
 ^H Divorced 
 
 8834 09-^ CONJUGAL CONDITION OF 
 
 FiQ. 45. 
 
 U.S. IN 1900 
 
 Prom Brinton'B Oraphic MethodB for Presenting Facts 
 
 Fig. 46. 
 
 expense. The value would be increased if the same diagram gave 
 population as well as cost per child in school. When the bars 
 are broken off and the middle shown instead of the whole length 
 we have a form of chart like Fig. 44. This is very unsatisfactory 
 as there is no indication of the number of men examined in each 
 class nor of the value of the standards A, B, C and D. There 
 is no base hne on the diagram which is most unsatisfactory. 
 
 BORN I \l ST/ITE-WilTE 
 
 Gorman 
 
 Italian 
 
 Othsn 
 
 FOREIGN WHITE 
 
 COLORED 
 
 ■> 50 
 
 Per Cent 
 population u.s.i900 
 
 Fig. 47. 
 
 15 
 
 100 
 
 A horizontal barograph which shows data clearly but is not 
 complete is the one shown in Fig. 45. Here we find the propor- 
 tionate number of people according to their conjugal condition 
 arranged in bars whose overall length varies so that comparison 
 of relative per cent of married whites and negroes is impossible. 
 If the bars were equal in length and that length equal to 100 
 
APPLICATIONS 
 
 65 
 
 per cent, the comparative proportion of each could be easily seen. 
 A diagram giving such a comparison would be like Fig. 40. This 
 also can be improved to a limited extent by making it as shown 
 in Fig. 47 which enables a comparison to be made, to the same 
 scale, of Germans, Italians and other foreigners. 
 
 3o%a 
 
 f%^yi> /s% n 
 
 % s 
 
 % 
 
 (6.^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 >«— 
 
 
 ^ 
 
 
 MM 
 
 
 
 
 — 
 
 
 
 
 
 
 
 s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ^M 
 
 
 — 
 
 
 ^^" 
 
 
 ^™ 
 
 
 ^mm 
 
 ^^^ 
 
 
 ^^ 
 
 *c% 
 
 
 
 
 
 
 ^^ 
 
 
 ^^ 
 
 tfji 
 
 
 
 
 " 
 
 
 ■= 
 
 
 
 
 
 .. 
 
 1 
 
 ^^ 
 
 
 
 
 
 ■ 
 
 
 ^^ 
 
 
 
 
 
 
 
 
 *•*%■ 
 
 
 ^ 
 
 
 ^^ 
 
 
 ^_ 
 
 
 
 
 
 
 
 = 
 
 
 
 ^ 
 
 1 
 
 ^™ 
 
 /9 09 /^OKft CYCLE J 91-^ 
 
 /6-2f 
 Z2-30 
 3I-40 
 
 ^l-60 
 6l- 70 
 7/ 3 OtV/« 
 
 On9 
 tvfO 
 
 EOur , 
 
 i',W 
 
 3^-3.99' 
 
 ■4—4A9- 
 
 S-S~S.99- 
 6- fi-J"?* 
 
 "TrAOyer 
 ST-ROICB 
 
 Vixder S'A- 
 3S~ 3.90 - 
 
 * J-- -^SiJ 
 J"- J" O " 
 
 In Bead 
 iSante side 
 Opp- Sid a 
 
 zGjv/Tiopr 
 
 Sinyie •/- S 
 Z>ou6i9 JS 
 Xmdl. J. S 
 
 7^0 rce' 
 
 PVMf 
 
 Hots r If 
 PlurufPr" 
 
 n. P.M. 
 
 S00& £.ess 
 
 SO/ - eof 
 o^cr 800 
 
 Weight * 
 200-300 
 
 300~ 399* 
 ^00-^99* 
 Soo- S99^ 
 €00- 699* 
 700 -709 * 
 600-399 * 
 900-/099# 
 //00-/191) * 
 /300-/S99if 
 /6oO-'^99'* 
 
 2000-Z499Z. 
 :lSOO- 3000* 
 
 Over - 3000' 
 
 3aVo 
 
 M 
 
 
 4/'l 
 
 '9°% 
 
 xiial 
 
 Fig. 48. — Changes in characteristics of marine motors from 1909 to 1914. 
 
 A method of using horizontal bars, which is not to be recom- 
 mended, is shown in Fig. 48. This does not facihtate comparison 
 of the bars on opposite sides of the center. If the bars were 
 placed on one side only, the effect on the eye would serve to 
 emphasize the facts, because the bars for the years would be 
 side by side. Such an arrangement is shown in Fig. 49. This 
 
66 
 
 GRAPHICAL METHODS 
 
 method of comparison can be applied to three or more types of 
 object, each one having the same component phenomena but 
 varying in degree, by using as many bars side by side as there 
 are objects compared. Each bar is cross-sectioned the same, for 
 its own object in the bars under the different headings. As 
 
 rOlTA CYCLE 
 
 ffottse ThwEff 
 
 S-3 
 
 iO-fS 
 
 lG-21 
 
 27-30 
 
 3/-40 
 
 41- SO 
 
 SI'bO 
 
 C,i-70 
 
 7f»Over 
 No of CYimDERs 
 One 
 Two 
 Three 
 Four 
 
 i.U 
 
 3 S- 3 99" 
 4^-4.43" 
 4S'f 9$" 
 S' S.fS" 
 S S'S99" 
 6- 6 3S' 
 T-aover 
 S TJROKE 
 
 Under 3/2" 
 
 ■3 - 4 ifS- 
 4 S -4 59" 
 S- S '^3'' 
 SS- SS9- 
 
 VALVES 
 
 Same 3ide 
 
 Opp ^ide 
 
 J^i£,<ie'loneovs 
 
 Diesel 
 JGN7TJON 
 SinsJe J^S 
 pou6/e -J S 
 VudI J 5 
 
 f^iscellaneoLa 
 LUB/^rCATTO/y 
 
 So /ash 
 
 Grsvty 
 T*UMP 
 
 Ppidry 
 Plunger 
 
 j-oi - eo/ 
 Oyer 8oo 
 
 Weight,^ 
 
 zoo -29SZ 
 30 -JS9^ 
 
 4-0 - ^S3 *■ 
 SOO- S99r 
 &00 - &39''' 
 700 - 755 y 
 800 - SSAJ^ 
 90O' /099* 
 //OO- /299f- 
 /300' /f55# 
 /600 - /999 * 
 ZOOO'2439* 
 2S0O - 3000*\ 
 Over- Sooo'^ 
 
 ^ pSSw wwyy 
 
 Fig. 49. — Same as Fig. 48, with all data on one side for easy comparison. 
 
 an example of this the division of motor truck costs for three 
 sizes of trucks is shown in Fig. 50. This shows how the size of 
 truck affects certain costs more than others, in a more convincing 
 way than if it was given in tabular form. 
 
 Table I gives considerable data regarding costs of operating 
 gasolene motor trucks and it will be found useful in the construc- 
 tion of various diagrams as well as for comparison with Fig. 50. 
 
APPLICATIONS 
 
 67 
 
 siB^op 'aiiiu-uo^ jad ^.soq 
 
 siB[];op *a|iui jad :jsoq 
 
 sj-Bipp 'iC-ep jad ^soo 
 
 mox 
 
 puB noT^oadBuj 
 
 jCjBlBB S,J9AUQ 
 
 ()8O0 !jsjg Bsa^) eajix 
 
 
 
 
 OOffl 
 
 »H»-lO 
 
 CONrH 
 
 MOSOO 
 
 <-«oo 
 
 00 OJ^ 
 
 ooo 
 
 oo 
 
 odo 
 
 odd 
 
 <Dd6 
 
 ddd 
 
 odd 
 
 ddd 
 
 66S 
 
 dd 
 
 COOIM 
 
 odd 
 
 OO^CO 
 t>NO 
 
 1-Hi-Hi-t 
 
 odd 
 
 moco 
 ddd 
 
 ddd 
 
 b-OOCO 
 
 ddd 
 
 to coo 
 eo<N(M 
 
 ddd 
 
 OSh- CO 
 C0OJ« 
 
 ddd 
 
 00 (N 
 
 rftCO 
 
 dd 
 
 
 coco 
 lOOb- 
 
 «oo>o 
 ^-vcoo 
 
 dodd 
 
 OMIN 
 0(Nrt 
 
 doiiN 
 
 (NCOr-l 
 OOl-H 
 
 rHiH 
 
 d-<*io6 
 
 8SS 
 
 0*0 ifS 
 
 ooco 
 
 0»0i0 
 
 T-l»OlO 
 
 OM^eo 
 
 lOOiC 
 
 cqcooo 
 
 IQOO 
 
 oot^ 
 
 lOOOt- 
 
 OiOO 
 
 OtOlO 
 OCDM 
 
 ooo 
 
 OiOCO 
 
 ot» 
 
 »o«« 
 
 QOiOTjf 
 
 t^-^I-H 
 
 00U3W 
 
 fflt-TJi 
 
 lOMOO 
 
 <NM(N 
 
 cocqM 
 
 «DiH 
 
 0»0i0 
 »OU30 
 
 OOO 
 
 Ooji> 
 
 8§§ 
 
 OSOiCO 
 
 ill 
 
 lOiOO 
 
 OOO 
 lOiOO 
 
 Mcqo 
 
 ooo 
 
 88§ 
 
 88 
 
 oo 
 
 
 .-^i-lrH 
 
 CqtNrH 
 
 WCQIN 
 
 «'«"« 
 
 ■>#■*« 
 
 IOU3 
 
 ill 
 
 ooo 
 
 MO-* 
 
 ooo 
 
 (NOCO 
 
 oooo 
 
 (NOCO 
 
 OOO 
 
 ONIN 
 
 QOOCO 
 
 11 
 
 (Nrt 
 
 CO^rt 
 
 l>.-<^« 
 
 t^-^CO 
 
 t--!t<CO 
 
 OCDCO 
 
 ON-Tfl 
 
 ot- 
 
 io»oo 
 
 CNMO 
 
 ooo 
 
 OOO 
 "*0-*< 
 
 CO 00 to 
 
 lOOCO 
 
 omio 
 
 OO-^fN 
 
 ooo 
 oooco 
 
 ooo 
 
 COMCO 
 
 oo»o 
 
 eoeob- 
 »Ot>tD 
 
 ooio 
 
 OCOh- 
 iOt»fO 
 
 o»oo 
 int-o 
 
 OiOO 
 lOh-O 
 
 oo 
 
 ^rHi-H i-ICq.-l i-ldOq (NCOM CqcOCO COTt< 
 
 o»oo 
 
 >0b-0 
 
 oo 
 
 0><N 
 
 no^iBa jad 
 
 ooo 
 
 OOCD 
 
 OOO 
 OOO 
 
 to CO CO 
 
 ooo 
 coo 
 
 lOOi w 
 
 00"0 
 i-HCOiO 
 t>(MO 
 
 ooo 
 ooo 
 
 OcDTf* 
 
 OOiO 
 
 COCOi-H 
 
 OO 
 
 oo 
 
 ON 
 
 HNcq MtNN OICOiM CO^-^ "^ »0 
 
 SuiSbj^O 
 
 OOO 
 00 .-<l^ 
 
 ■^COiH 
 
 ooo 
 
 OOl^H 
 
 CD CON 
 
 OOO 
 (Mb-iO 
 
 OiOiO 
 
 cDcqeo 
 
 OS CO CO 
 
 OOO 
 
 oooco 
 
 ^OI^BJ!^s^IIUIp■v 
 
 uoi^BToajdaQ 
 
 <^nao 
 jad g ^B ^saja^ui 
 
 ooo 
 oeoco 
 
 iCOiO 
 
 (NCOO) 
 
 H>CO 
 
 OOO 
 
 lOiOO 
 100»0 
 
 OiOiO 
 OCOCO 
 
 iHCOt* 
 
 sax-B^ pn-B asuaoTT; 
 
 omo 
 
 00 -^"5 
 CO(Mr-( 
 
 oo 
 
 <NCD 
 
 COM 
 
 sss 
 
 OiOiO 
 i-liCCO 
 
 lOOO 
 
 •ooo 
 >ot^o 
 
 lOiOiO 
 
 "OOiO 
 
 l-H|>CO 
 
 ooo 
 
 lOCON 
 lOCOCN 
 
 lOCO 
 
 
 i-HOOO 
 
 R§8 
 
 OOCOIO 
 
 oic»o 
 
 lOCON 
 
 lOOO 
 (NCOO 
 
 CDCOtH 
 
 OOO 
 
 ooo 
 
 §32 
 
 oo 
 
 8g 
 
 
 i-IWrH 
 
 (N,-HrH 
 
 (N(N(N 
 
 coeocq 
 
 Tt<Tt<CO 
 
 lOTt( 
 
 0»0i0 
 
 CO"* CO 
 
 t--00Oi 
 
 OO 
 
 O lO 
 
 oo 
 
 o>oo 
 
 ^00 00 
 
 lOO 
 <NiO 
 
 pu-B 3jg 'aou'BjnBai 
 
 ooo 
 
 "OIOO 
 OOIO CO 
 
 ooo 
 
 OiOiO 
 
 OCDCO 
 
 ooo 
 io»oo 
 
 OiOO 
 lots. CD 
 CO 00-^ 
 
 o»oo 
 
 COTt<0 
 
 t*i-HCO 
 
 aS-Ban™ I'E^OX 
 
 ooo 
 
 oom 
 
 lOiOt* 
 
 ooo 
 
 ooo 
 ooo 
 
 ooo 
 ooo 
 coo 
 
 ooo 
 ooo 
 
 0*00 
 
 ooo 
 ooo 
 
 0*00 
 
 ooo 
 ooo 
 o»oo 
 
 Bj'Ga^ 'ajT[ pa^Buiiq.sg 
 
 >ONiH 
 
 OcO"* 
 
 ^ 
 
 :« 
 
 lOO 
 00 IN 
 
 OOO 
 OOO 
 
 o»oo 
 
 OO 
 
 oo 
 
 OiO 
 
 OcO^ OC0-* OCO'^ OcO'* o«o 
 
 aSBaiTin A[ye(j 
 
 anaps'BS 
 JO noxi^S jad BaiTj\[ 
 
 :^ 
 
 jnoq jad saiT2;\[ 
 
 jaModasjoH 
 
 ejBHOp ni ^soQ 
 
 O 
 
 ^ 
 
 :^ 
 
68 
 
 GRAPHICAL METHODS 
 
 AdminishaHon 
 License and Tax. 
 Garaging 
 Insurance 
 
 OilGrease and^ 
 Wash-'- 
 
 Meresiai- 
 6PirCen-t 
 
 Tinsfless 1^ 
 CosO 
 60s at ISCerris 
 
 Inspectiorrand 
 
 Hairtknance 
 
 DepreciaHon 
 
 Drivers' Wages 
 
 Per Cen4- 
 10 15 20 25 30 35 
 
 D'^ 
 
 too lb. 
 
 Tons 
 
 STons 
 
 FiQ. 50. — Truck operating costs. Comparison of 3 sizes, 1500 lb., 2 ton and 
 
 5 ton. 
 
 Machine Numbers 
 
 12 
 
 13- 14- 
 
 IS I& 
 
 n 
 
 IS 
 
 19 
 
 20 
 
 21 
 
 22 
 
 25 
 
 24 
 
 25 
 
 2e 
 
 c 
 
 wrhea 
 
 y Travel 
 
 ler 
 
 
 
 
 
 
 v^ 
 
 7r 
 
 77.5,1: 
 
 ISITIG 
 
 
 
 
 
 
 
 
 
 fern 
 
 iCon 
 
 
 
 Tn 
 
 6er 
 
 lerc 
 
 / Jj 
 
 a';76 
 
 •yon 
 
 ' Charge 
 
 
 
 
 
 
 
 'General 
 
 •Store keep I'r^ff Charge 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 1 
 3ub 'Store 
 
 s. 
 
 
 
 
 L0CMI2/irl0NOFSTORlS-TI>AN6P0ffT FACTOR 
 
 Fig. 51. 
 
 Machine Numbers 
 
 12 
 
 B 
 
 W 
 
 15 
 
 le 
 
 n 
 
 18 
 
 19 
 
 20 
 
 21 
 
 22 
 
 2i 
 
 21- 
 
 25 
 
 26 
 
 
 
 
 
 
 
 
 
 h^ 
 
 
 
 
 
 
 
 ym"//////. 
 
 W^/////////////A. 
 
 
 
 
 
 
 
 
 
 7////////// 
 
 //// 
 
 
 
 
 
 ////>////. 
 
 
 '//)//////////////////////////// 
 
 777////////////^ 
 
 /////////. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 R 
 
 f.sa/ 
 
 ■mg 
 
 /ijc 
 
 fors 
 
 of 
 
 lacl- 
 
 777? 
 
 
 
 
 ■■ 
 
 
 
 Faf 
 
 ?S 
 
 
 
 
 
 
 
 
 
 '£--— 
 
 m 
 
 # 
 
 ^ 
 
 ^ 
 
 W 
 
 ^ 
 
 W/ 
 
 ^ 
 
 V, 
 
 
 •^ 
 
 ^ 
 
 ^^^ 
 
 APPOftTIOmeNT OFSTORES-TRANSPOR T FACTORS 
 Fig. 62. 
 
APPLICATIONS 
 
 69 
 
 A method of apportioning costs by barographs is often used in 
 showing to what machines charges are to be made. For ex- 
 ample, the cost of transportation of stores or parts in a shop must 
 be prorated among the various machines. A diagram is laid out 
 like Fig. 51, the numbers at the tops of the columns represent- 
 ing certain machines. The horizontal lines show how the costs 
 
 Lighting 
 Factor 
 
 W077^Zmm777m^^77777;^, 
 
 Heating 
 
 Supervision 
 
 Organiiatfon 
 
 'TTTZ^ , 
 
 Wrr77^^77;77>777777^;7^7^7>77777X^ 
 
 ^/^y/yy 
 
 777777>^ 
 
 ^m^7;^^'7M^^^^7^7m^^^77:V7?. 
 
 V/J///////////'////^^///^///^/^////.>/ •.'////. ■y///^>J////^ 
 
 Oil.Waste,etc 
 
 Tool Charge 
 
 ^^^^??^^^^^7^^z ^.yW/.//yy ^ 
 
 m^Z^TZ^. 
 
 '/•/////^//^^///Attt 
 
 ^77Z:'Mm7?^A 
 
 KLATIVe ABSOHPTIPN OFF/iaORS BYJHB DIFFIRCNT PUODUaiON CeHTCRS INASHOP 
 
 Fig. S3. 
 
 of certain systems of transporting parts are allocated to the 
 different machines. The total cost of transportation for each 
 machine will consist of the sum of the various items in that 
 machine column. This diagram is better illustrated by drawing 
 the width of the horizontal hues to scale as in Fig. 52, the line at 
 the bottom representing the total cost of transportation for each 
 machine, when measured by a vertical scale. 
 
 When a diagram for each item of cost has been worked out in 
 this manner they can be added together as in Fig. 53, having first 
 
70 
 
 GRAPHICAL METHODS 
 
 been drawn to scale for each item. Any excess or unequal costs 
 can be quickly detected from this diagram which a table would 
 not easily reveal. 
 
 Factors above the blank space are overhead and those below be- 
 long to each individual tool. If plotted to scale, the vertical sum of 
 horizontal hnes in each column would give total expense due to 
 each factor. 
 
 As a further illustration of the use of barographs, two figures 
 are shown of the results of tests on oil made before using it and 
 
 420 
 
 RangeofdistillafibnofGasolme 
 
 Increase above initial ^ 
 ^viscosity of oil iE 
 
 Decrease below init-o 
 vi&cosityofOil § 
 
 New 
 nOOR 
 
 Percenl-Sas infinal^,-^<<M '/ 
 CH Oilsampk(dydistiflafjop) / 
 
 -I 
 
 
 
 Variation inViscosi-hj 
 of Lubricating Oil 
 
 Initial Test 1 Z 1 4 
 
 Oas by Distillation 
 RBSUUn OFOISTILLAVON T£ST OF OIL An^R 5-HOUR 1ES7 
 
 Fig. 54. 
 
 after a 5-hr. test. If these two diagrams (Fig. 54 and Fig. 55), 
 had been combined in one, the comparison of the four oils could 
 have been more easily made than now where the eye has to 
 change from one to the other. A comparison of tabular pre- 
 sentation and graphical may be made by referring to Fig. 56 
 which is one of the simplest imaginable. There is room in this 
 case for some question as to whether or not the graphical illus- 
 tration is any clearer than the table, besides being harder to 
 make. 
 
 The principle of showing production by the horizontal baro- 
 graph is a good one as additions from day to day can be readily 
 made. For example, in Fig. 57 consider several parts A, B, C, 
 and D in process of manufacture and shipment. A report is 
 desired each week showing the per cent actually finished and 
 shipped. The solid bars show the amount finished and the 
 blank bars the amount shipped. The second week the incre- 
 ment completed is cross-hatched while the quantity shipped is 
 
APPLICATIONS 
 
 71 
 
 shown by a continuation of the blank bar with a vertical line for 
 the end. ^ The third week the bar increment of production is 
 black again. The numerals at the ends of the increments denote 
 per cent completed. If this is made on tracing cloth a print can 
 
 , 10 ^^0.6 
 
 S0.5-, 
 
 1.20 
 
 1,00 
 
 : jot 0.4] 
 
 0.80 
 
 w u. o 
 
 £ o.^5^ 0.60 
 
 "ST q c 
 
 ^ 0.2'^^ 040 
 
 0.1 a J, 0.70 
 O"^:! 
 
 TestA-l 
 
 i 
 
 TestA-2 Test A-3 
 
 Reading left to Right Ordwafcs are: 
 
 m 
 
 lest A-4- 
 
 1st PirCent Conrailion Carbon 
 2nci. " >t Waters 9 
 5rd ', •> Residue by Weighi- 
 Afti. n t> (I by Volume 
 
 results oftesrshowino varia7tofj of carbon 
 conditions in 4 samples of new oil 
 
 Fig. 55. 
 
 Dark portion ^'Unused Oil 
 Light " • Final Sample 
 In Final Sample 
 In Final Sample 
 
 be made each week which will show by comparison with the 
 previous week the quantity produced and shipped that week. 
 This method is continued until all the parts have been shipped. 
 This principle can be easily adapted to include the material and 
 operations noted in Fig. 56, by making the bars of greater width. 
 It is not advisable, however to crowd too many things into one 
 
 A-STATISTICAL 
 
 Wanted 100 
 Received 60 
 Machined 50 
 Assembled 20 
 
 %ceiveef 
 
 8-6RAPHIC 
 
 Warrheen 
 
 Machined \ 
 
 Assembledy 
 
 20 40 60 80 100 
 Number of Pieces 
 
 COMPARISONOFOIfAFHICAL aSTATlSTICAL PRESFNTATIOtl 
 
 Fig. 56. 
 
 diagram and extensions of this method must be left to the judg- 
 ment of the executive who uses them. 
 
 The bar method has been applied to diagrams illustrating the 
 movement of railway cars, lighters or towboats by assuming the 
 
72 
 
 GRAPHICAL METHODS 
 
 time element along the horizontal and cross-hatching the bar to 
 illustrate what was going on at the different periods of the day. 
 Such a diagram is shown in Fig. 58. By means of daily reports 
 
 20 40 60 80 
 
 Per Cent 
 
 Fio. 57. — Manufacturing progress report. 
 
 of this kind it is easy to note any undue delay or extraordinary 
 occurrence by a simple glance at the diagram. This can be 
 applied to the movement or operations of motor trucks, opera- 
 tives, horse trucks, freight cars, cranes, etc. 
 
 T89IOIM2ia54 56789 10 II 12 123456 
 1^ 
 
 No.5 
 
 OF£/!/l 7I0N OF FRCIGHT LIGHTERS, N. Y._ 
 
 From Brinton's Graphic Methods tor PreBentins Facts 
 
 Fia. 58. 
 
 The appHcation to operatives has been well worked out by 
 many efficiency engineers to show bonus payments and attend- 
 ance. This is shown in Fig. 59 which is taken from Mr. Gantt's 
 book on "Industrial Efficiency." 
 
APPLICATIONS 
 
 73 
 
 A similar use is made in Fig. 60 of this method in showing the 
 rating of different states from the point of view of attendance 
 and other features in schools, by varying the relative position 
 
 3> 
 O 
 
 
 1 
 
 ? 3 4 5 etc. to 51 
 
 -= 
 
 MAY 
 
 
 
 
 
 
 
 
 
 Jl 
 
 
 Wilton 
 
 
 Cooper _ 
 
 \ 
 
 AHA 
 
 
 X 
 
 XX 
 
 XX^^o 
 
 o 
 
 o 
 
 V 
 
 X^TB 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Black 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 & 
 
 
 
 V^g 
 
 
 
 
 
 
 
 
 1 
 
 ^ 
 
 
 1 
 
 . 
 
 . 
 
 ■ 
 
 ■ 
 
 ■ 
 
 ■ 
 
 ■ 
 
 . 
 
 J- 
 
 w 
 
 
 ■ ■■ 
 
 
 
 
 
 
 
 
 
 Whil^ 
 
 m 
 
 ^ 
 
 ■ 
 
 ■ 
 
 sr 
 
 ■ 
 
 ■ 
 
 ■ 
 
 ■ 
 
 ■ 
 ■ 
 
 ■ 
 
 1 
 
 ■ 
 
 
 
 ■ 
 
 1 
 
 ■ 
 
 ■ 
 
 1 
 
 I 
 
 ^ 
 
 
 Pratt 
 
 _] 
 
 _ 
 
 
 n 
 
 
 
 
 
 
 
 □ 
 
 T 
 
 
 J 
 
 III 
 
 
 
 
 
 
 
 
 -' 
 
 C 
 3 
 
 3) 
 O 
 
 C 
 
 ^ Bonus Los-f- 
 ■ Bonus Earned 
 ^DayAbsen-t 
 
 31 
 O 
 T3 
 
 C 
 3 
 
 RECORD OF WORK IN A MILL 
 
 From Brinton's Graphic Methods for PresentiDg Facte 
 
 
 Fig. 59. 
 
 
 
 of the states. The diagram is taken from W. G. Brinton's book 
 on "Graphic Methods." 
 
 A field which is adapted to the horizontal bar method but so 
 
 Children 
 
 School 
 
 ^ 
 
 ^ 
 
 STATES 
 
 I.Washington 
 
 2.H«sachusetl3 
 
 LNewYork 
 
 4.California 
 
 S.Connecticut 
 
 6.0hpo 
 
 TNew Jersey 
 
 S.IIIinois 
 
 B.Colorado 
 
 B.indiana Y^////// 
 II. Rhode Island ?//////, 
 B.Vennont v^^^^^^ 
 
 School 
 Plant 
 
 Expense 
 per 
 Child 
 
 School 
 Days 
 per 
 
 Child 
 
 V//////-'///'M 
 
 School 
 Year 
 
 ^^: 
 
 mm 
 
 V/////. 
 
 ^^: 
 
 ^^?^ 
 
 Atten 
 dance 
 
 ^^^^ 
 
 TMZ 
 
 I— i 
 
 ^^^ 
 
 Expen- 
 diture 
 and 
 Wealth 
 
 Daily 
 Cost 
 
 k*ol5"l-i= 
 
 ^^^ 
 
 ^^ 
 
 ^^; 
 
 ^ 
 
 ^?^ 
 
 white indicates State ranks in Ist 12 of 48 
 
 Light Shading » « ij «j £nd.n n ii 
 
 Dark « •; » n nJrd.n >■ •> 
 
 Black u n - Lowest 12 of 48 
 
 ftAMf OF STATES IN EACH OF 10 EDUCATIONAL FEATURES IN 1910 
 
 From Brinton's Graphic Methods for Presenting Facts 
 
 Fig. 60. 
 
 far without many examples of its value, seems to be that of show- 
 ing comparative costs and their frequency as well. The applica- 
 tion to pavement costs and variation of the cost of different 
 
74 
 
 GRAPHICAL METHODS 
 
 kinds of pavement is shown graphically in Fig. 61. The com- 
 parative cost of operating cranes of different sizes and the varia- 
 tion of this cost depending on days operated, cost of coal, etc., is 
 shown in Fig. 62 by the barograph type of diagram. 
 
 In the same class as Fig. 61, combining the bars with a fre- 
 quency diagram, is Fig. 63 showing the classification of overhead 
 
 
 n 
 
 t E g 
 
 £33 
 
 If 
 
 is 
 
 4- 
 
 if 
 
 1 — 
 
 O 
 
 f 
 
 CO 
 
 CD 
 
 £ 
 
 o 
 
 1 
 
 1.60 
 
 
 
 
 
 
 
 
 i, 
 
 340 
 
 
 
 
 
 
 
 
 d 
 
 J.20 
 
 
 
 
 
 
 
 
 
 5.00 
 
 
 
 
 
 
 
 
 - 
 
 2.80 
 
 
 
 
 
 
 
 
 J 
 
 2.60 
 
 
 
 
 
 
 
 
 
 2.40 
 
 
 
 
 
 
 
 
 
 2.10 
 
 
 I 
 
 
 
 
 
 
 
 2.00 
 
 
 I 
 
 
 
 
 
 
 1 
 
 1.80 
 
 
 b 
 
 
 
 
 
 
 ] 
 
 1.60 
 
 
 % 
 
 
 
 
 
 
 1 
 ] 
 
 1.40 
 
 
 1 
 
 
 
 
 
 
 1 
 
 i?n 
 
 
 1.00 
 0.80 
 
 P 
 
 0.60 
 
 - 
 
 ] 
 
 
 
 
 
 
 
 0.40 
 
 
 
 
 
 
 
 
 
 azo 
 
 
 
 
 
 
 
 
 
 10 20 10 10 , 5 10 ZO 5 10 
 
 Number of Localifies Reported 
 RELAml At10UN7ANDCl>5TOFPAVCHlNTC0NSTmaJ0NINI9IS 
 
 FiQ. 61. 
 
 AVIRAGC BASIC OPSRAVNB 
 COST OF STANDARD 
 lOCOMOTIVC CFtANSS 
 
 Fig. 62. 
 
 electric cranes by capacity together with their hoisting speeds 
 which divide each class into three others. The width of bar 
 allows three divisions along the X-axis to represent high, inter- 
 mediate and low-speed cranes. 
 
 An unusual type of representation is shown in Fig. 64. This 
 can be placed in the bar class although the lines showing move- 
 
APPLICATIONS 
 
 75 
 
 5 10 _ 15 20 25 30 40 50 60 75 100 
 
 Rating of Overhead Electric Crane in Tons 
 
 MAXIMUM:,MEDIUM & MINIMUM HOISTINGSPEeOS OFST/INO/IRO 
 OVBRHBAD HI6H,MEDIUM & LOW SPEED ELECTRIC CRANES 
 
 Fig. 63. 
 
 I860 
 
 N.Y. < I > 
 
 Penn. <■;.> - 
 
 1810 
 
 >- 
 
 <ZEI> 
 
 1880 
 
 <: 
 
 > 
 
 SANKOFST/ITES /N POPULATION /IT DIFFERENT CENSUS YEARS 
 
 Prom Brinton's Graphic Methoda for Presenting Facta 
 
 Fig. 64. 
 
76 
 
 GRAPHICAL METHODS 
 
 ment bring it more in the routing diagram class. It shows 
 plainly how a state changes rank from decade to decade but 
 does not denote the number of the rank after the first census 
 year indicated. By following back from later columns to the 
 first one its position number can be ascertained easily and com- 
 pared to its position in 1860 which is always carried along with 
 the progressive movement. 
 
 23 
 
 Zi 
 
 Percentage 
 
 Rated 
 AorB 
 
 ill 
 
 111 
 
 Company ABCD EFSH IK LMMJS.SUR HDQ 
 
 Percentage 
 Illiterate 
 
 or 
 Foreign '5 
 
 39 
 
 3+ 
 
 33 
 
 INEQUALITY OF COMPANIES IN AN INFANTRY RCGIMCNT 42 
 Fig. 65. 
 
 46 
 
 The bar method finds an important place in the analysis of 
 any mental tests in two examples shown in Figs. 65 and 67. In 
 Fig. 65 the diagram can be greatly improved for purposes of 
 comparing illiteracy and high mental efficiency by placing all 
 bars above or below the line of company designation and cross- 
 hatching the illiterate bars as shown in the cases of Co. A and 
 Co. E. The number examined in each company should also 
 be indicated unless it is the same and then a note should so state. 
 
APPLICATIONS 
 
 77 
 
 Figure 66 is open to the criticism that no scale is given for 
 comparing percentages nor is the percentage given for the classes. 
 The only data given is that on the diagram. 
 
 Lewis 
 
 Sheridan 
 
 Devens 
 
 Funston 
 
 Ta y I o r 
 
 Sherman 
 
 Dodge 
 
 Kearny 
 
 Meade 
 
 Gran-f- 
 
 Cus+er 
 
 Cody 
 
 Trcsvis 
 
 Bowie 
 
 Pike 
 
 Jackson 
 
 Shelby 
 
 Wheeler 
 
 mmr 
 
 iiiiiiiiiii 
 
 iiiiiiiiiiiiiii 
 
 ■II iiiiiiiiiiiiii 
 
 Below C + 
 
 C + 
 
 Aand B CD 
 
 FiQ 66.— Inequality of mental strength in eighteen officers training schools 
 (Total enrollment 9240.) The proportion of A grades in the above school varied 
 from 16.6 to 62.4 per cent. The proportion of A and B grades combined from 
 48.9 to 93.6 per cent, and the proportion below C+ from to 17.9 per cent. 
 
 FREQUENCY DIAGRAMS 
 Let us now take up the frequency and historical type of dia- 
 gram, such as those used by statisticians and engineers to denote 
 growth of population or relation of two or three variables. Such 
 
78 
 
 GRAPHICAL METHODS 
 
 diagrams as these are usually plotted on cross-section paper using 
 rectangular coordinates. Through the points thus located a 
 line is drawn which illustrates the law of change or the fluctua- 
 tions and general trend. 
 
 70 
 
 GO 
 
 i 50 
 
 Q 
 
 a 
 
 40 
 
 I'M 
 
 1/3 20 
 
 f\ 
 
 Pries < 
 
 'fWhe 
 
 ofYsc 
 
 rbyY<3Cfr 
 
 
 
 
 A 
 
 f\ 
 
 A 
 
 
 
 
 (Crrr/ 
 
 oi-hed — - 
 
 r 
 
 ' \ 
 
 /^ 
 
 -Quincj 
 
 iennici 
 
 lAvera^ 
 
 <^^ «/: 
 
 
 
 
 \ 
 
 ^ 
 
 k 
 
 Au 
 
 
 ^f 
 
 
 
 
 
 
 \ 
 
 r^ 
 
 2r^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Fluctuations 
 Tio. 67. — Variations in price of wheat in England 1864-1907, 
 
 Suppose a table gives the price of wheat annually and by 5- 
 year periods (Table II). If we plot this table in Fig. 67 we will 
 have a broken full line of the yearly changes, a dash and dot 
 line for quinquennial averages and a smoothed line showing the 
 
 -\ 
 
 ( 
 
 
 
 
 
 m 
 
 A M 
 
 Kl\ 
 
 , >* 
 
 \ 
 
 r 
 
 ' V\ 
 
 \i\ 
 
 /s/^ 
 
 I 
 
 1/ 
 
 
 
 
 f 
 
 ) c 
 
 I ' s 
 
 > 
 
 
 Differences fromMovin9 Average 
 Fig. 68. — Variations in wheat prices. 
 
 trend or consequents. The difference between the price of a 
 particular year and the average price of the 5 years of which that 
 year is the middle are caUed differences and are plotted in Fig. 
 68. 
 
APPLICATIONS 
 
 79 
 
 Table II 
 
 Average annual gazette price of 
 wheat per quarter 
 
 Quinquennial averages 
 
 Difference 
 
 1864 
 
 40.2 
 
 
 
 
 1865 
 
 41.8 
 
 
 
 
 1866 
 
 49.9 
 
 1864^1868 
 
 52.0 
 
 - 2. IS 
 
 1867 
 
 64.4 
 
 1865-1869 
 
 53.6 
 
 +10.8 
 
 1868 
 
 63.7 
 
 1866-1870 
 
 54.6 
 
 +9.1 
 
 1869 
 
 48.2 
 
 1867-1871 
 
 56.0 
 
 -7.8 
 
 1870 
 
 46.8 
 
 1868-1872 
 
 54.5 
 
 -7.7 
 
 1871 
 
 56.7 
 
 1869-1873 
 
 53.5 
 
 +3.2 
 
 1872 
 
 57.0 
 
 1870-1874 
 
 55.0 
 
 +2.0 
 
 1873 
 
 58.7 
 
 1871-1875 
 
 54.7 
 
 +4.0 
 
 1874 
 
 55.7 
 
 1872-1876 
 
 52.6 
 
 +3,1 
 
 1875 
 
 45.2 
 
 1873-1877 
 
 52.5 
 
 -7.3 
 
 1876 
 
 46.2 
 
 1874-1878 
 
 50.0 
 
 -3.8 
 
 1877 
 
 56.7 
 
 1875-1879 
 
 47.7 
 
 +9.0 
 
 1878 
 
 46.4 
 
 1876.1880 
 
 47.6 
 
 1.1 
 
 1879 
 
 43.8 
 
 1877-1881 
 
 47.3 
 
 -3.5 
 
 1880 
 
 44.3 
 
 1878-1882 
 
 45.0 
 
 -0.7 
 
 1881 
 
 45.3 
 
 1879-1883 
 
 44.0 
 
 +1.3 
 
 1882 
 
 45.1 
 
 1880-1884 
 
 42.4 
 
 +2.7 
 
 1883 
 
 41.6 
 
 1881-1885 
 
 40.1 
 
 +1.5 
 
 1884 
 
 35.7 
 
 1882-1886 
 
 37.2 
 
 -1.5 
 
 1885 
 
 32.8 
 
 1883-1887 
 
 34.7 
 
 -1.9 
 
 1886 
 
 31.0 
 
 1884^1888 
 
 32.8 
 
 -1.8 
 
 1887 
 
 32.5 
 
 1885-1889 
 
 31.6 
 
 +0.9 
 
 1888 
 
 31.8 
 
 1886-1890 
 
 31.4 
 
 +0.4 
 
 1889 
 
 29,7 
 
 1887-1891 
 
 32.6 
 
 -2.9 
 
 1890 
 
 31.9 
 
 1888-1892 
 
 32.1 
 
 -0.2 
 
 1891 
 
 37.0 
 
 1889-1893 
 
 31.0 
 
 +6.0 
 
 1892 
 
 30.2 
 
 1890-1894 
 
 29.6 
 
 +0.6 
 
 1893 
 
 26.3 
 
 1891-1895 
 
 27.9 
 
 -1.6 
 
 1894 
 
 22.8 
 
 1892-1896 
 
 25.7 
 
 -2.9 
 
 1895 
 
 23.1 
 
 1893-1897 
 
 25.7 
 
 -2.6 
 
 1896 
 
 26.2 
 
 1894-1898 
 
 27.2 
 
 -1.0 
 
 1897 
 
 30.2 
 
 1895-1899 
 
 27.8 
 
 +2.4 
 
 1898 
 
 34.0 
 
 1896-1900 
 
 28.6 
 
 +5.4 
 
 1899 
 
 25.7 
 
 1897-1901 
 
 28.7 
 
 -3.0 
 
 1900 
 
 26.9 
 
 1898-1902 
 
 28.3 
 
 -1.4 
 
 1901 
 
 26.7 
 
 1999-1903 
 
 26.8 
 
 -0.1 
 
 1902 
 
 28.1 
 
 1900-1904 
 
 27.3 
 
 +0.8 
 
 1903 
 
 26.7 
 
 1901-1905 
 
 27.9 
 
 -1.2 
 
 1904 
 
 28.3 
 
 1902-1906 
 
 28.2 
 
 +0,1 
 
 1905 
 
 29.7 
 
 1903-1907 
 
 28.7 
 
 +1.0 
 
 1906 
 
 28.2 
 
 
 
 
 1907 
 
 30.6 
 
 
 
 
80 
 
 GRAPHICAL METHODS 
 
 A study of a graph of this kind enables the statistician to 
 observe the variation of yearly price from the average over a 
 period of years. Figure 67 is useful in its assistance in the deter- 
 mination of upward or downward tendencies over a period of 
 
 IIG 
 
 [ — 1 
 
 
 
 
 
 1 — 1 
 
 
 
 
 1 — ' 
 
 
 
 1 — 
 
 
 
 1 — 
 
 1 — ' 
 
 1 — 
 
 p- 
 
 1 
 
 1 
 
 
 
 1 — 1 
 
 nr. 
 
 ■TTS 
 
 7 
 
 nr 
 
 r — 
 
 
 1 — 
 
 r— 
 
 r~ 
 
 
 p-i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 £L 
 
 'tliH-r^ -^^i-Or. of NY. - 
 
 
 
 
 
 — 
 
 
 
 
 
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 — 
 
 
 7:^ 
 
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 s 
 
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 — 
 
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 zt 
 
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 80 
 
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 ~ 
 
 
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 g 
 
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 U 
 
 
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 £ 
 
 S 
 
 
 ^ 
 
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 er_ 
 
 3t 
 
 
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 E 
 
 E 
 
 
 
 i 
 
 
 
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 1 
 
 |. 
 
 ^ 
 
 
 ^ 
 
 
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 E 
 
 E^ 
 
 ^ 
 
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 5 
 
 v 
 
 
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 g 
 
 2 
 
 ~ 
 
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 5 
 
 1 
 
 
 ~ 
 
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 zi; 
 
 i^ 
 
 
 
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 20 
 
 — 
 
 — 
 
 
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 ^ 
 
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 = 
 
 E 
 
 i 
 
 i 
 
 1 
 
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 ± 
 
 ^ 
 
 2 
 
 1 
 
 fc 
 
 
 
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 1 
 
 ~ 
 
 ~ 
 
 1 
 
 
 
 = 
 
 ^ 
 
 2i, 
 
 ao 
 
 rnj 
 
 w^ 
 
 \- 
 
 
 z^ 
 
 1 
 
 
 — 
 
 10 
 
 
 d 
 ■? 
 
 
 ■g 
 
 D 
 
 i 
 
 s 
 
 ~3 
 
 K 
 
 3- 
 
 16 
 
 1 
 
 
 
 1 
 
 s 
 
 
 1 
 
 a 
 
 i 
 
 3> 
 
 IS 
 
 3 
 
 17 
 
 < 
 
 J5 
 
 S 
 
 1 
 
 
 c 
 
 E 
 
 « 
 
 £ 
 
 1. 
 
 < 
 
 
 3 
 
 —i 
 19 
 
 f 
 
 18 
 
 
 
 >VO/l^W^ YAVERABES OF METAL Pff/CES I9I6-I3/9 
 Fig. 69. 
 
 120,000,000 
 100,000,000 
 
 la 80,000,000 
 
 
 
 = 60,000,000 
 
 o 
 
 o 
 
 40,000,000 
 
 20,000,000 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 / 
 
 
 V 
 
 
 
 s 
 
 
 \ 
 
 
 4, 
 
 f 
 
 
 \ 
 
 / 
 
 
 \ 
 
 
 -» 
 "^^ 
 
 \ 
 
 f 
 
 
 ,6 
 
 \ 
 
 ni 
 
 ('0 
 
 joi-''- 
 
 4/0_ 
 
 rzT; 
 
 
 
 f 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Years 
 SURPLUS EARNED & DIVIOENDS PAID BY U.S. STEEL CORP. 
 
 From Brinton's Graphic Methods for PreseotiDg Facts 
 
 FiQ. 70. 
 
 years even though the yearly variation presents no definite trend 
 from year to year. 
 
 A similar diagram is shown in Fig. 69 containing the fluctua- 
 tion price curves of several metals. The prices are given in such 
 
APPLICATIONS 
 
 81 
 
 a way as to bring the curves apart, yet do not prevent easy com- 
 parison of the fluctuations from month to month over a period 
 of 3 years. The trend of silver prices is seen to be upward while 
 antimony tends to dechne. 
 
 The amount of earnings applicable to dividends and the 
 dividend amount paid out by the U. S. Steel Corporation is 
 indicated clearly in Fig. 70. A curve showing the surplus divi- 
 dend fund increase could easily be added and would be illuminat- 
 ing to the average reader of such statistics. This would of 
 
 18 
 16 
 
 14- 
 
 12 
 
 +• 
 o 
 
 
 
 —t ^ 
 
 i^-^ 
 
 t t 
 
 -1 ^ 
 
 4 \ 
 
 I V 
 
 I 4 
 
 t , 
 
 t 
 
 A 
 
 
 2 r 
 
 t \ 
 
 1 ^ ^ 
 
 L ^-^ 
 
 
 20 21 24 EG 28 30 ^^ 34 36 38 4-0 42 44 
 
 Age af Marriage 
 AGE /IT M/IRR/AGE OF 4-39 MARRIED GRADUATES OF 
 MZHOLYOKE WHO GRADUATED FROM I890 TO I909 
 
 From BrintOD's Graphic Hcthode for Presenting Facts 
 
 Fig. 71. 
 
 course be a cumulative curve and not a frequency or historical 
 one. 
 
 A type of frequency curve often met with is shown in Fig. 71. 
 This brings out startUng facts which a glance at a table would 
 hardly notice, such as the large number married at 25 years and 
 the small number married after 33 years. 
 
 The occupations of engineering graduates of the University 
 of Illinois up to 1916 is shown by diagram Fig. 72 more like a 
 cumulative diagram than a frequency one. It serves rather as a 
 table with diagram attachment and is but little clearer than the 
 table alone. The arrangement followed in Fig. 71 would enable a 
 percentage determination to be made which would give a better 
 idea of the proportion in each line than shown in Fig. 72. 
 
82 
 
 GRAPHICAL METHODS 
 
 An excellent example of a graphical representation of statistical 
 facts is that in Fig. 73, which is a study of the married conditions 
 in the U. S. for the year 1900. A companion diagram for this 
 
 NAMES 
 
 MO — 
 
 214^— 
 191 ^— 
 
 let— 
 121^— 
 
 119 
 
 100^— 
 81 
 
 81 — 
 69 
 
 58^— 
 32- 
 M-^ 
 
 n^ 
 
 21 — 
 15— 
 
 8 — 
 6 — 
 5-" 
 
 5 — 
 S- 
 J- 
 
 • OCCUPATIONS ENBINEERINS GRADUAns 
 UNIVERSITY OF ILLINOIS 
 (Li&iidlin Alumni Direcfoty) 
 T0T/lLi455 
 
 Fio. 72. — Occupations of graduates to 1916, (occupation names omitted). 
 
 would be one showing the excess of married over the single and 
 widowed combined. 
 
 Figure 74 is a graphic record of the observations made in 
 running an electric power plant for one month. The delineator 
 
 CONJUGAL CONDITION OF POPULATION OF U.S. IN 1900 
 
 IN PROPORTION TO THE TOTAL No. OF EACH AGE GROUP 
 From Brinton's Graphic Methods for Pretjttuuug i-ui;ui 
 
 I'lQ. 73. 
 
 has here substituted vertical bars for coordinated points hence 
 the broken appearance of the line usually called the "curve." 
 This form is better for making comparisons from month to 
 
APPLICATIONS 
 
 83 
 
 month than the type shown in Fig. 69 and especially so if the 
 plots are made on tracing cloth or paper. Then it is possible to 
 
 35,000 
 30,000 
 
 25,000 
 20,000 
 
 30 
 
 es 
 
 550 
 530 
 510 
 4-90 
 410 
 
 -Total Kilowatt hours per day— 
 
 s 
 
 _Lbs H^OperlbCoaL 
 Av.=4.71b. 
 
 -fOD 
 
 , Lbs.CooiI per kilowatt hr.- 
 A\i- 5.89 lb 
 
 rf 
 
 ■ 
 
 _Lb5.Hj^Operkilowatt.hr . 
 Av.=2TSlb. 
 
 flr^ 
 
 g. 
 
 Vacuum inches 
 
 Av = Z7.2ftm 
 
 Flue tem|i,deg.fahr 
 
 Av 5l9.eofahrj-| IT 
 
 ffi 
 
 1 
 
 
 ^ ^. - *' Av.-Z55.1^fahr. 
 rr.n n n 
 
 
 ',":::::::::::::;ft'^^"""" 
 
 § 
 
 .<„ HjOtemp.to economiier,deg.fahr 
 
 i,\'-^ ■■ Av.= 2IU.2°roihr. 
 
 Z]Q ■■ j- 
 
 209 iST 
 
 onu n 1 ■ " 
 
 "M 
 
 
 ^ -n ^v.C02=l0.457o 
 
 
 
 q -L " " 
 
 I ■ '" 
 
 1 
 
 Boiler Load Factor^ per cent 
 Av.= 90.S8*ya 
 110 
 
 
 on " - T 
 
 
 
 
 S 
 
 Turbine Load Factor, percent 
 Av.= 70.-i7o 
 
 
 
 
 
 1 
 
 10 15 20 25 30 5 10 , 15 20 
 
 June J""2 
 
 graphic record of month !s opera tion of flectpic power plant 
 
 Fig. 74. 
 
 25 30 
 
 superimpose one month on another for purposes of compari- 
 
 son 
 
 Figure 75 is an historical graph showing the development of the 
 
84 
 
 GRAPHICAL METHODS 
 
 hydraulic turbine. This combines several curves using different 
 scales in one diagram but without any diificulty in its interpreta- 
 tion. There is no good reason for having two zero lines for the 
 scales at the bottom and the zero Kne for efficiency should be 
 indicated. 
 
 An example of the history of the financial standing of a public 
 utility over a period of 67 years is shown in Fig. 76. 
 
 1870 l»80 1890 1300 1910 
 Year 
 
 PiQ. 75. — Representation of the development of the hydraulic turbine. 
 
 The position of the three curves is on a common base line of 
 time. The base Unes for the vertical scales are separated as in 
 Fig. 74 but curves are used rather than vertical bars. 
 
 Two diagrams to illustrate rising prices for materials and 
 wages over a period of years are shown in Fig. 77. (A) represents 
 the increase on a basis of $100 in 1897 while {B) is based on a 
 per diem wage in both 1899 and 1911. The increase in both {A) 
 and (5) is shown by a straight line which is not true in either 
 case. Intermediate years should have been used which would 
 have made the cost lines appear like the lines in Figs. 75 or 69. 
 
APPLICATIONS 
 
 85 
 
 If the two years, 1897 and 1907, in (A) or 1899 and 1911 in (B) 
 were the only ones used these diagrams would have been better 
 in the form of barographs of two heights for each class of material 
 or labor 
 
 Figure 78 is a diagram to show the effect of training on the 
 earning power of boys starting at the age of 16 years. This 
 
 > 
 
 100 
 
 eo 
 
 GO 
 
 40 
 20 
 
 10 
 
 100 
 
 120 
 
 Net P/anf /nvesfmenf 
 (Unamorfiied) 
 
 Average Annual Rate 
 
 Welghfecl Average Rate 
 
 ^^""""^mdi- 
 
 Curve A -3% I860-W7S\ „„„ 
 
 ^^ I 7% 1891-1911 Electric 
 
 o°| — Curve B-8%> 1831 -19 n\ 
 
 Curve C 
 80 Curve V 
 
 Ija l89l-l9n\Electriconly 
 ejo 1831-1917) ' 
 
 Peferred Earnings (Cumulative) 
 
 I860 
 
 I8TO 1880 1890 
 
 Horse Car Period 
 
 1900 1910 igiT 
 
 Elec+ri'c Period 
 
 INVESTMENT HISTORY OF A PUBLIC UT/LlTY 
 Fig. 76. 
 
 diagram should have had a vertical scale of wages per week either 
 on the right or left hand margin also a horizontal scale denoting 
 years elapsed since training began. The diagram would not then 
 have been so covered with numerals and notes and would have 
 been just as intelhgible. 
 
 In Fig. 79 is found the application of diagram or statistical 
 
86 
 
 GRAPHICAL METHODS 
 
 QiANQES IN OJSTS OF R.H. MATERIALS AND FnEllhHTIfATES IN lOYRS. 
 
 (A) 
 
 Rising'Wage Scole per Day 
 RISING WAGESCALB 
 
 (B) 
 
 Fig. 77. 
 
 THIS LINE, APNiKENTLY, 
 
 HAS HO LMfT ANO M*Y KEEf 
 COINS UPWARD AND ONMRB. 
 
 onlyS% of this cLass rise above 
 / this une to any marf<eo oegree, 
 
 -i—THISISABWTTHEUMrTOFTHISajea. 
 
 20% LEAVe OF THEIR OWH ACCORO 
 
 40% ARE DISMISSED: IT IS FAIR70 
 ASSUME THAT THESE NEI/ERRISE 
 
 Za Z\ ?Z £3 £4 Z5 26 27 
 EACH VERTICAL LINE REPRESEtfTS ONE YEAR. 
 
 Fig. 78. — Diagram giving curves showing the comparative value of trade 
 school and shop trained boys. Curves plotted from records of two groups of 
 24 boys each. 
 
APPLICATIONS 
 
 87 
 
 plotting to a board designed to show the standing from day to 
 day of operations being performed in the shops in the process of 
 making a finished object from raw material or the hours spent 
 
 /Machines or OpsraHons, this Sca/e 
 
 GRAPHK RECORD OF PROGRESS OF OPERATIONS 
 Fia. 79. — Graphic control board. 
 
 /(noeppel 
 
 on such operations. By means of this board the engineer or 
 executive is informed of the progress of work in the shop and 
 can take steps to correct any faults as soon as they appear. 
 
 OCTOBER, I91S 
 I « S' 12 2 £=■ a < 
 
 Fig. 80.— StabUity chart m use at the works of the Chester Shipbuilding Co. 
 
 Figure 80 is a composite diagram deahng with the labor question 
 at one of the shipbuilding yards during October, 1918. Colored 
 ink was used on the original and wiU be found more effective 
 
88 
 
 GRAPHICAL METHODS 
 
 80 
 o 70 
 
 * 50 
 e> 40 
 K 30 
 
 £?o 
 to 
 
 
 
 80 
 
 5 50 
 g M- 
 u 30- 
 ^ 20- 
 10- 
 
 
 
 
 
 
 
 
 
 
 / 
 
 ^^ 
 
 
 
 
 
 
 / 
 
 
 <?"t^; 
 
 
 
 
 \ 
 
 A 
 
 
 ^;e_i 
 
 
 
 \ 
 
 
 
 
 
 
 -^ tfi^'- 
 
 -?SSf?fF-l 
 
 
 
 
 ^flSSW" 
 
 
 
 
 
 ^^n \ 
 
 
 
 1 
 
 rend 
 
 sin 
 
 Rear Axle Des 
 
 gn 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 s 
 
 B 
 
 
 
 
 / 
 
 
 
 s 
 
 
 sr 
 
 a^O- 
 
 
 / 
 
 
 
 
 
 il^ 
 
 
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 pfCi 
 
 r" 
 
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 ^•' 
 
 
 r 
 
 
 A 
 
 
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 V 
 
 
 
 -pn 
 
 Sui' 
 
 fe 
 
 "* 
 
 
 \, 
 
 T 
 
 p.ndf 
 
 inAutamo 
 
 ,ileL 
 
 ubric 
 
 atior 
 
 
 ■03 
 
 
 100 
 90 
 
 eo 
 
 « 10 
 60 
 50 
 
 S 40 
 
 t to 
 
 10 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^'' 
 
 
 
 nil"' 
 
 
 C 
 
 ii 
 
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 ^. ■ 
 
 
 
 
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 --■i 
 
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 90 
 
 0)TO 
 80 
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 10 
 
 
 
 100 
 90 
 0)80 
 g)10 
 °60 
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 =^20 
 
 
 
 
 
 
 
 
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 ^^, 
 
 
 
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 .^'=^ 
 
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 '*'"^4.i 
 
 1^= 
 
 -^ 
 
 
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 Trends in Transmission Location 
 
 
 ; 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 ^ 
 
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 pisX 
 
 
 y 
 
 
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 ----.^ 
 
 >^ 
 
 — ^ 
 
 
 
 
 
 
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 \ 
 
 
 
 
 
 
 
 
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 1910 1911 I9IZ 1913 1914 1915 1916 1917 
 Years 
 Disk and Cone ClyWi Trends 
 
 Trends inttieApplications of Ignition Systems 
 
 90 
 80 
 <» 70 
 |>60 
 ■| 50 
 o 40 
 V 30 
 
 ■Hel'csn 
 
 '5e"Jc 
 
 ' Chatp 
 
 10 
 
 °1910 1911 1912 1913 1914 I9in9i6n9irisit% 
 Trends in Dnvi'ngGeorscrfAutoinobilgAccessorim bsoo s 
 
 Avar's 
 
 80 
 o 70 
 
 eo 
 
 50 
 g 40 
 u 30 
 
 f 
 
 m. 
 
 pfg 
 
 ^ 
 
 z: 
 
 "# 
 
 S^ 
 
 X 
 
 Application of Oasolene Feeds 
 
 AveftigeCulinderSiz.es Durina 
 •ttie Past Eight Years 
 
 5000 
 
 s. 
 
 40002 
 300O g. 
 200O o 
 1000 -g 
 
 Yearly Trends of Ameriran Fbssenger 
 Car Design I n Piston Displacement and 
 Crank5liaftR.RM.perMile and 6ear Ratios 
 
 •lOOr 
 90- 
 80- 
 70- 
 
 - - - - Drive Design Showina 
 
 Popularity of Spiral Bevel Drive 
 
 1910 1911 1912 1913 1914 1915 1916 1917 1918 
 Years 
 TheTrend of Valve Construction 
 on American Passenger Care 
 
 Fig. 81. — Trends of automobile design 1910-1918. 
 
APPLICATIONS 
 
 89 
 
 than the variation in the type of line used in the reproduction. 
 The weather report at the bottom acts as a check on a factor 
 which might affect the curves of attendance in the diagram 
 above, such as extreme heat or cold or heavy snow fall. 
 
 1908 
 
 I 2 3 » S 6 7 a 9 10 II i; 
 
 1909 
 
 1910 
 
 1000 
 COOO 
 5000 
 ^4000 
 30OO 
 2000 
 
 looo 
 
 14,800 
 
 14,400 
 
 14,000 
 
 IJ,SOO 
 
 13,200 
 
 3 12,800 
 
 H 12,400 
 
 ti 12,000 
 
 ll,G00 
 
 11,200 
 
 10,800 
 
 10,400 
 
 5,000,000 
 4,000,000 
 
 4- 
 
 c. ^^000,000 • 
 
 3 
 
 O 2,000,000 ■ 
 1,000,000 ■ 
 
 
 1 2 i 4- 5 6 1 8 9 10 n 12 
 1309 
 
 5 6 T 8 9 10 II K 
 1908 
 TOML OUTPUT OF GAS POWER PLANTSfMonthly Averages) 
 
 Fig. 82. — Average load, heat consumption, plant efficiency and total output 
 
 (monthly averages). 
 
 The frequency and historical series curves as a rule are based 
 on periods of time, as a term of years, the months of a year, the 
 days of the month, the hours of a day, the minutes in an hour or 
 the seconds in a minute. There may be one curve on a diagram 
 or several to represent fluctuations of one or of several objects 
 or substances. It may be that comparisons are desired or that 
 
90 
 
 GRAPHICAL METHODS 
 
 the behavior of one thing only is to be studied. All of these 
 objects may be attained graphically in any one of several kinds 
 of diagram as illustrated in Figs. 67 to 80. 
 
 The comparison of trends which have no relation to each other 
 makes it useless to bring their graphs on the same diagram, except- 
 ing in cases where the observations are based on the same inter- 
 val of time and over equal periods. For example, all of the 11 
 diagrams showing trend of automobile design from 1910-1918 
 
 15 
 
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 Fig. 83. — Showing various slips of screw propellers. 
 
 can be collected into three or less diagrams on the same hori- 
 zontal base line of years as in Fig. 81, although the curves in each 
 separate' block are for different phenomena without relation to 
 each other. 
 
 In Fig. 82 the four diagrams illustrating the characteristics of 
 loads, efficiency output and heat consumption of a blast furnace 
 gas power plant can be condensed into three all on a monthly base 
 for 2 years. Figure 83 could just as well have been combined 
 to make one diagram and the curves drawn with different kinds 
 of lines without any detriment to the graphical representation. 
 The base in this case is divided into minute intervals and the 
 observations are clearly indicated by black circles, which make 
 a clear, readable diagram. 
 
 Figure 84 illustrates the use of graphics to represent the 
 comparative and actual number of accidents occurring in the 
 
APPLICATIONS 
 
 91 
 
 different departments of a mill for each month during a period of 
 3 years. A diagram of percentages would be of advantage here 
 to indicate the degree of risk or carelessness in each department 
 and to point out where the most attention should be paid to 
 safety appliances. 
 
 
 z^ 
 
 o 
 -9 9 
 
 Z 6 
 
 Depz e 
 
 DEPT.5 
 
 DEPT.4 
 
 DEPT.5 
 
 DEPT.2 
 
 DEPT.I 
 
 Cons+ruction 
 
 m 
 
 Section A 
 
 ^ 
 
 i rii i i m 
 
 S 
 
 1910 5 1911 E I9IZ c 19IJ 
 
 ACTUAL NO?OF ACCIDENTS OCCURING INE/ICHDEPT. 12 MONTHS AVeHAGES 
 
 Prom Brinton'B Graphic Methods for Presenting Facta 
 
 Fig. 84. 
 
 Figure 85 is a composite diagram of the operation results of a 
 power plant over a 3-year period by monthly intervals. The 
 data is weU arranged so that the influence of some factors on 
 others can be easily seen. All of the data given here can be 
 plotted on yearly record cards, filed in 4 by 6 or 4 by 12 filmg 
 cases and transferred to continuous record cards from time to 
 time. 
 
92 
 
 GRAPHICAL METHODS 
 
 The comparison of occurrences in order to determine if there 
 is any relation between them is shown in Fig. 86. Here we have 
 two cumulative production curves compared with prices of a 
 
 T815->|< 1916 w< 1S17- --jc 1918 — 
 
 j« „j0.ofawFa«jjm.wYjiiiiji)iyji)6iS£niniimofCJAiiraw!»m.Mji)EJtrAMntw 
 
 §300 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 M 100 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 6R0SS GENERATION, KW-HR. FOR 24 HR. 
 
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 IO10KJMfEaKMlllfK.MJllllE*y»ll6.SOT0a.NW,DEC.J»liraHIK/lftlW.MJllt»E5Erc0a.mi)K.« 
 1815^ 1916 ^>|, 1917 >t< 1918 — 
 
 tCOHBINED BOILER AND ECONOMIZER EFFICIENCY 
 
 (^Aiprrifzinq Stsam Deducted} 
 
 Fig. 85. — Operating characteristics of a power plant. 
 
 substance which plays an important part in the maintenance of 
 the objects produced. It is evident there is no relation between 
 these two nor can they be compared to any advantage. 
 
APPLICATIONS 
 
 93 
 
 ' pnnod J9d nuao ^ Jaqqna ^«a ?<> »>H<1 
 
94 
 
 GRAPHICAL METHODS 
 
 Cumulative curves are often used to enable a schedule pro- 
 duction graph to be estabhshed and comparisons to be made 
 between the schedule and actual production. 
 
 3600 
 3200 
 Z800 
 
 2400 
 
 01 
 
 J5 2000 
 
 E 
 
 3 leoo 
 
 1200 
 
 8000 
 
 4000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 // 
 
 
 
 
 
 
 
 
 
 
 
 
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 STB 
 1912 
 
 9 10 II 12 
 
 FACTORY SCHEDULE AND ACTU/tL OUTPUT 
 From BriDtOD' n Graphic Methods for Presenting Facts 
 
 Fig. 87. 
 
 Such a diagram is shown in Fig. 87 and illustrates by the 
 solid straight hne the expected or planned production and what 
 actually was produced as per the broken line. This type of 
 curve, a diagram and the table from which the diagram was 
 constructed are shown in Fig. 88 applied to a case where the 
 
 BY MONTHS 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 — -- -" 
 
 
 
 
 
 
 
 -'" 
 
 
 
 
 
 ^' 
 
 V - 
 
 ,--- 
 
 
 
 -gfS 
 
 ^^^. 
 
 ^^ 
 
 
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 ^~. 
 
 
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 ES 
 
 
 
 /i 
 
 '»- 
 
 
 
 
 
 
 
 y 
 
 ^ 
 
 "^rr^ 
 
 
 
 
 
 
 
 
 
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 5: 
 
 CUMULATIVE 
 
 o3 
 
 
 ^^ 
 
 (0.) 
 
 Fig. 88. 
 
 requirements called for one rate. Production was planned at a 
 certain rate, but the actual rate fell far below either of the others. 
 Two diagrams were constructed, one for monthly deliveries and 
 another for cumulative deliveries. 
 
APPLICATIONS 
 
 Requikebients, Estimated and Actual Delivbbibs 
 Manufactured Track 
 
 95 
 
 1918 
 
 
 Apr. 
 
 May 
 
 June 
 
 July 
 
 Aug. 
 
 Sept. 
 
 Oct. 
 
 Nov. 
 
 Dec. 
 
 For 
 
 Req'd. 
 
 400 
 
 500 
 
 400 
 
 600 
 
 700 
 
 500 
 
 600 
 
 500 
 
 600 
 
 the 
 
 Est. 
 
 200 
 
 350 
 
 400 
 
 500 
 
 560 
 
 625 
 
 675 
 
 860 
 
 900 
 
 month 
 
 Del. 
 
 200 
 
 330 
 
 200 
 
 150 
 
 
 
 
 
 
 Cumul. 
 through 
 
 the 
 month 
 
 Req'd. 
 
 400 
 
 900 
 
 1,300 
 
 1,900 
 
 2,600 
 
 3,100 
 
 3,700 
 
 4,200 
 
 4,800 
 
 Est. 
 
 200 
 
 550 
 
 950 
 
 1,400 
 
 1,950 
 
 2,675 
 
 3,250 
 
 4,100 
 
 5,000 
 
 Del. 
 
 200 
 
 550 
 
 750 
 
 900 
 
 
 
 
 
 
 An application of the cumulative graph is shown in an interest- 
 ing case where the amount of water in a tank must not fall below 
 the maximum requirements of several tug boats and a loco- 
 motive (Fig. 89). The maximum amount of water drawn at any 
 
 12 ' i j 4 5 G 1 8 9 lb II 12 I 2 3 4- 5 6 7 8 9 10 11 12 
 
 A.M. P-M- 
 
 Cumulative curves fo determine mmirnum s ze offanU 
 and minimum steady flow of water recfuired For a 
 group of locomotives and tug boats tahmghoiler teed 
 water from same source of supply. 
 
 From Brinton'e Graphic Methoda for Presentiog Facts 
 
 Fig. 89. 
 
 period falls just below the line denoting the minimum steady rate 
 of supply, which is a cumulative line. 
 
 The total production estimated for United States rifles 
 which was divided among three plants is shown in Fig. 90. 
 The quantity each plant was to supply is indicated by a cumu- 
 
96 
 
 GRAPHICAL METHODS 
 
 lative curve for each plant and the total of all three plants is 
 summed up by the total production schedule curve. 
 
 The progress chart of one of the plants concerned with rifle 
 production as scheduled from Fig. 90 is shown in Fig. 90A. 
 Both weekly and monthly records are shown on the same chart, 
 the latter being cumulative. Dates are given along the base 
 line, the weekly assembly scale at the right and the total assembly 
 
 1,000,000 
 
 900,000 
 
 800,000 
 
 Fia. 90. — Production schedule of rifles. 
 
 scale at the left. A chart showing the progress of manufacture 
 of component parts in a plant is often of the type of Fig. 905. 
 The three charts (Figs. 90, 90 A and 90B) complete a set showing 
 the progress of manufacture in a series of plants making the 
 same product, all under one control. The efficiency of each 
 department or plant can thus be compared to each of the others 
 and remedies suggested for increasing the efficiency of the 
 inefficient ones. 
 
APPLICATIONS 
 
 97 
 
 Vfi^t^ JScI S3liqU43SS(^ 
 
 
 
 
 
 
 
 
 
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 1 $ 
 
 
 
 
 
 
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98 
 
 GRAPHICAL METHODS 
 
APPLICATIONS 
 
 99 
 
 A diagram like Fig. 91 enables total costs of manufacturing 
 to be compared with sales income and gives at a glance the point 
 of division between profit and loss. Fixed charges, labor and 
 
 30 40 
 
 50 60 
 58 
 Percentage Output 
 
 Fig. 91. 
 
 70 80 90 100 
 
 materials when added give a cost line. The income from sales 
 increases proportionably to the quantity sold. Anything over 
 58 per cent output means profit. This shows how a shop laid 
 
 •ft 
 
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 10 ■£ 
 
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 10 
 
 '0 ;o io 30 40 50 
 
 Speed, m.p-h.-High Gear 
 ISIS Tour. Car -6 0^1. - 4^ x J^ Wgf.S0Z0lbs.6aar Ratio Di'reci-3.S 
 
 Fig. 92. — Relations of speed, power and gasoline consumption of automobiles. 
 
 out on a certain production basis of 100 per cent fails to make a 
 profit when the production falls off to a certain amount depending 
 on the relation of labor, material and overhead costs. 
 
100 
 
 GRAPHICAL METHODS 
 
 13 
 
 SB 
 
 ■3 
 
 o 
 
 M 
 
 P^lll+sip a|clmo9 j.o '4033 jsj 
 
APPLICATIONS 
 
 101 
 
 We now come to a class of diagrams which are not laid off on a 
 time basis but on some other data such as speed, revolutions 
 per minute, per cent, horsepower, diameter, temperature, etc. 
 Closely related to this variable is the variable dependent on the 
 independent variable. For example, consider Fig. 92 which shows 
 
 530 
 
 10 ZO 30 40 50 60 70 80 90 100 
 Percent Distilled 
 
 Fig. 93A. — Comparative distillation curves. 
 
 the relation between the speed in miles per hour of an automobile 
 and the drawbar pull, also the relation of speed to gasoHne con- 
 sumption. The three curves show this relation, that the faster 
 we go the less power is left for ascending grades and the fewer 
 miles we can go on a gallon of gasoline. In Figs. 93 and 93A 
 we have the relation between temperature and amount of gaso- 
 line distilled for various kinds of gasohne, shown in a simple 
 
102 
 
 GRAPHICAL METHODS 
 
 graphical way easy for the average reader to comprehend. In 
 Fig. 93(A) is drawn with a horizontal scale of percentages 
 which produces a high, narrow diagram, while 93(B) uses tem- 
 peratures on the horizontal scale which seems more logical and 
 gives a better balanced diagram, viz., long on the horizontal and 
 narrow from bottom to top. 
 
 10 20 30 40 50 
 
 (B) Speed inM.P.HrHigh6ear 
 
 Fig. 94. — -Automobile characteristics. 
 
 Figure 94(^4.) and (B) are shown the relations existing between 
 revolutions per minute, drawbar pull and horsepower and be- 
 tween speed, grade ascendable and miles per gallon of gasoline. 
 
 In Fig. 95 are shown curves of tests made on an automobile 
 motor to determine certain effects of back pressure, etc., when 
 
APPLICATIONS 
 
 103 
 
 the motor was run at assumed revolutions per minute . These are 
 plotted from the experimental determinations given in Table III. 
 The scales at the sides are of different values depending on the 
 
 200 «0 
 
 600 800 1000 1200 
 
 R.P.M. 
 
 MOTOR TEST 
 
 Fig. 95. 
 
 1400 1600 1800 
 
 magnitude of the observations. This change of scale locates the 
 curves in such a way as to prevent them from interfering with each 
 other and making them difficult to read. 
 
104 
 
 GRAPHICAL METHODS 
 
 Table III to Accompany Fig. 95 
 Curve H was Made with Throttle Wide Open; no Muffler 
 
 Run. 
 
 r.p.m. 
 
 Lb. torq. 
 1 ft. rad. 
 
 Volu- 
 metric 
 effic. 
 
 Exhaust 
 back 
 press. 
 
 sue. inlet 
 
 
 38 
 
 113 
 
 19.1 
 
 
 
 0.5 
 
 
 39 
 
 191 
 
 20.5 
 
 
 
 0.6 
 
 
 40 
 
 292 
 
 22.5 
 
 0.90 
 
 
 0.5 
 
 
 41 
 
 478 
 
 21.4 
 
 0.87 
 
 
 0.6 
 
 
 42 
 
 691 
 
 27.0 
 
 0.83 
 
 
 0.7 
 
 m 
 
 43 
 
 1,016 
 
 34.5 
 
 0.82 
 
 . 
 
 0.9 
 
 
 44 
 
 1,357 
 
 43.3 
 
 0.78 
 
 
 1.5 
 
 
 45 
 
 1,641 
 
 51.9 
 
 0.73 
 
 
 1.7 
 
 
 46 
 
 1,760 
 
 55.6 
 
 0.70 
 
 
 1.9 
 
 
 
 One-third Throttle; 'Withottt MtrrPLER 
 
 
 
 47 
 
 108 
 
 
 
 
 0.7 
 
 
 48 
 
 191 
 
 
 
 
 1.1 
 
 
 49 
 
 289 
 
 
 
 
 2.0 
 
 (/) 
 
 50 
 
 482 
 
 
 0.71 
 
 
 3.1 
 
 
 51 
 
 703 
 
 
 0. 2 
 
 
 6.9 
 
 
 62 
 
 1,015 
 
 
 0.49 
 
 
 10.2 
 
 
 53 
 
 1,344 
 
 
 0.39 
 
 
 12.3 
 
 
 54 
 
 1,660 
 
 
 0,32 
 
 
 12.9 
 
 
 
 
 Throttle Wide; With Mcffler 
 
 
 
 55 
 
 468 
 
 24.0 
 
 0.85 
 
 1.1 
 
 0.6 
 
 
 56 
 
 701 
 
 30.9 
 
 0.82 
 
 2.0 
 
 0,7 
 
 (J) 
 
 57 
 
 1,020 
 
 40.3 
 
 0.79 
 
 3.3 
 
 0.9 
 
 
 58 
 
 1,344 
 
 49.8 
 
 0.75 
 
 4.8 
 
 1.3 
 
 
 59 
 
 1,706 
 
 64.5 
 
 0.68 
 
 6.0 
 
 1.7 
 
 
 
 Inlet Mai 
 
 >JiFOLD Shut off Tight; Without 
 
 Muffler 
 
 
 60 
 
 469 
 
 
 
 
 22.1 
 
 
 61 
 
 605 
 
 
 
 
 23.4 
 
 (K) 
 
 62 
 
 1,015 
 
 
 
 
 23.8 
 
 
 63 
 
 1,355 
 
 
 
 
 22.2 
 
 
 64 
 
 1,626 
 
 
 
 
 22.2 
 
 Inlet sue. 
 
 inches mere. 
 
 
 Figure 96 shows the characteristic curves of an automobile 
 motor. In this case the vertical scale is revolutions per minute 
 and there are three horizontal scales, one for horsepower, one for 
 pounds of gasoline and one for torque. The proportions of 
 CO, CO2 and in the exhaust gas are indicated at various 
 points of the horsepower curve. This is a good example of 
 several curves on the same diagfam but without interference. 
 
APPLICATIONS 
 
 105 
 
 t-bs. per Hp. Hour. 
 0.5 0.6 0.1 0.8 0.9 
 
 llOO 
 lOOO 
 
 900 
 
 u 
 
 ■5 800 
 c 
 
 f 100 
 
 u 
 c 
 g 600 
 
 ,0 
 
 t 500 
 
 J 400 
 
 300 
 
 200 
 
 100 
 
 VALVE setTIN^ I I I I 
 Inht openi. S °befbre, doses 20.S°affer 
 
 HEWITpMOtOFf I I r 
 
 fCyh.-4i,"b(!rs-e"ifmks'3404-6cu 
 Compression space ?4^% of whole volume 
 Spark advance IS ° 
 
 ^malj Venlurl alone)i/c(X,'j3S_S£A 
 Ifiivflleparflijclosedio ^0.4- 
 
 2 4 6 S 10 12 14 16 18 20 22 24- 26 28 30 32 34- 36 38 40 
 
 Horsepower 
 
 FiQ. 96. — Motor characteristic curves. 
 
 o 
 
 o 
 
 o 
 
 GASOLINE MOTOR TESTJNG FORM No. 3 
 
 TEST CURVES OF_ 
 
 FOR DETAILS OF MOTOR AND ACCESSORIES SEE FORM 
 
 PAGE _ 
 
 TEST r 
 DATE . 
 
 NO OF FUEI_ 
 
 AVERAOE TEMPERATURE OP AIR DUC 
 AVERAGE TEMPERATURE OF JACKET- 
 TEST iHAOE BV 
 
 ASSISTED BV 
 
 lAUME. 0e0._ 
 URfNO TEST„ 
 
 . U. PER US. 
 
 BAROMETER. IN 
 
 TER DURING TEST. INLET— 
 
 DVNAMOMETER 
 CARBURETER 
 
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 REVOLUTtONS PER MINUTE. 
 Km.; F.r MsHg anKl. .nil tramr imw.r Ih. H-P.M. ..J H.F. roc, m.y to el..n a.uM. V.I1.M. 
 
 Fio. 97.— Standard motor testing form, Society of Automotive Engineers. 
 
106 
 
 GRAPHICAL METHODS 
 
 Tempering Temperature,Deq.Cent 
 14 204 315 426 538 
 
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 Fio. 98. — Effect of varying temperatures on the physical properties of a high- 
 chromium steel, oil-quenched from 2100 deg. Fahr. 
 
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 Fia. 99. — Physical properties of a nickel-chromium steel resulting from 
 proper preliminary treatment and varying drawing temperatures. 
 
APPLICATIONS 
 
 107 
 
 Diagrams of this type have been brought to a standard form 
 by the Society of Automotive Engineers. This enables graphical 
 comparisons to be made of engines tested in different laboratories 
 
 400,000 
 
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 SCALE FOn SFEEO IH KNOTS 
 
 Fio. 100. — Curves of residuary resistance for 10 vessels of dimensions and 
 displacement given in table. 
 
 as the test results are presented in the same manner. Figure 97 
 shows this standard form. 
 
 A graphical representation of the behavior of steel is shown in 
 Fig. 98. This diagram gives all the information necessary to 
 
108 
 
 ORAPHICAL METHODS 
 
 have in order to judge properly how this steel must be treated to 
 obtain certain results. The upper and lower bases are a Centi- 
 grade and Fahrenheit temperature scale and are useful as a con- 
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 various drawing temperatures on the physical properties of steels 
 is shown in Fig. 99. This form is in general use for illustrating 
 test reports as it is clear and gives all the information used in the 
 comparison of steels. 
 
 In Fig. 100 are shown comparative resistance curves of 10 
 vessels run at various speeds which are laid off along the hori- 
 zontal axis. This shows very plainly the tremendous increase 
 in resistance of most of the models when driven at high speed. 
 
 Figure 101 is a type of diagram which is instructive rather than 
 comparative as it shows what parts of an automobile require the 
 
APPLICATIONS 
 
 109 
 
 maximum attention to lubrication. The horizontal scale is based 
 on the arrangement of parts in order of importance of lubrication 
 and the vertical scale is according to the number of miles 
 traveled. 
 
 Figure 102 shows the variation in chemical analysis of a 
 number of samples of barrel steel used in the Russian military 
 rifle. The hmits of the chemical per cent of the various metals 
 are shown by horizontal lines marked maximum and minimum. 
 
 15 
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 This diagram was used to point out in a graphical manner that 
 certain samples of steel did not meet the specifications and that 
 the general trend was in the wrong direction, too high for phos- 
 phorus, too low for carbon and too high for manganese and 
 silicon. 
 
 In calculations to determine the horsepower of engines it is 
 necessary to know the average pressure of steam or gas on the 
 pi ton of the engine. This pressure is obtained by connecting 
 the interior of the cylinder with a tracing point so that the 
 pressures in the cylinder will be graphically recorded. The hne 
 thus drawn constitutes an indicator card. Figure 202, Chapter 
 
110 
 
 GRAPHICAL METHODS 
 
 IX, is an indicator card from a steam engine cylinder. A card 
 plotted from the pressures in a gasolene engine cylinder is shown 
 in Fig. 103. The dotted Hne is an enlargement of the lower part 
 of the pressure curve. If this indicator diagram should be 
 drawn on log-log paper we would have Fig. 104 which is interest- 
 ing chiefly from the standpoint of showing that the expansion 
 
 Fig. 103. 
 
 Cranh fing/e tn Degress. 
 
 Fig. 104. 
 
 Fig. 103. — Specimen indicator diagram in the usual pressure volume scaling. 
 The lower loop is reproduced magnified 20 times, in the dotted curve, to which 
 the scaling in the right-hand margin applies. 
 
 Fig. 104. — Indicator diagram of Fig. 103 redrawn on logarithmic paper. 
 
 and compression curves are exponential and appear as straight 
 lines. Both of these diagrams are plotted on the basis of pres- 
 sures and volumes. If the data is plotted on the basis of pressure- 
 time scales the diagram will appear as shown in Fig. 105. The 
 abscissa in Figs. 103 and 104 are distances passed over by the 
 piston, while in Fig. 105 they are distances passed over by the 
 crank pin. Ordinates in all cases represent pressures per square 
 inch. 
 
APPLICATIONS 
 
 111 
 
 4J(7 /«? MO /eo /oo eo 60 -^o £o o eo ^o 60 60 /oo /ed'Mo /60 /so' 
 
 CranA A/7ff/» m Oogr^as. 
 
 Fig. 105. — Specimen indicator diagram in rectangular coordinates. The 
 diagram is shown by the solid line, the corresponding pressure scale being num- 
 bered on the left margin. The portion of the diagram near the zero pressure 
 is reproduced in the dotted curve on a scale magnified 20 times, the scale being 
 noted on the right margin. 
 
 POLAR CHARTS 
 
 These are used to plot curves by polar coordinates and find an 
 application in plotting diffusion of light emanating from a single 
 source which is taken at the center of the circles or for polar 
 indicator diagrams and other similar records. This type of chart 
 has been used to show the effect of the daylight saving law on the 
 working day. Recording temperature instruments, pressure re- 
 cordersj water meters, flow meters, etc., make use of polar charts. 
 The ordinates are either straight or curved depending on the type 
 of tracing point used. The circumference is usually divided on a 
 time basis of 24 hr., the rotation of the chart being obtained from 
 a clock. Samples of records on polar coordinate paper will be 
 found in Chapter IX. 
 
 Polar indicator diagrams showing pressures vs. crankshaft or 
 camshaft angles are sometimes used in connection with internal- 
 combustion engine investigations. An illustration of this use is 
 shown in Fig. 106. Two scales are used, the larger one enabhng 
 the indistinct part of the indicator curve to be plotted more 
 clearly. 
 
112 
 
 GRAPHICAL METHODS 
 
 Fig. 106. — Specimen indicator diagram in polar coordinates, pressures vs 
 camshaft angle. The diagram is shown by the solid line, to which the right- 
 hand pressure scale applies. That part of the curve near the pole is shown in 
 the dotted curve, to which the 12H times magnified left-hand scale applies. 
 
 POi/IR COORDINATE 
 CANDLE POWER CURVE 
 
 FiQ. 107. 
 
APPLICATIONS 
 
 113 
 
 Figure 107 is a 'curve of candlepower plotted on polar cpordi- 
 nate paper. This curve is the common means of expressing the 
 intensity of candlepower of light in various directions from a 
 source. The candlepower is shown by the distance of the curve 
 from the light source. Such a curve gives at a glance a good 
 idea of the characteristics of light distribution from the source. 
 The Hght flux in various zones is proportional to the length of a 
 perpendicular line drawn from the candlepower curve at the 
 middle of the zone to the vertical axis. AB, CD and EF are such 
 perpendiculars. This is called a Rousseau diagram. Its 
 construction is described in "Illuminating Engineering Practice," 
 published by the McGraw-Hill Book Co. 
 
 TRILINEAR DIAGRAMS 
 
 Trilinear diagrams are used to show the relation of alloys 
 containing three elements, concrete mixtures containing three 
 substances, or any combinat on composed of three ingredients. 
 The diagram was first suggested by Prof. Fer^t in the Annales des 
 Ponts et Chaussees, 1892, and used for investigations on strength 
 of concrete mixtures. 
 
 (A) Density ' (B) Compressive S+rengh-1 Year 
 
 PROPERTIES OFi:SMORTARS M/IDE OF DIFFERENT MIXTURES OFSAND 
 Fig. 108. — Trilinear diagrams of mortars. 
 
 In any equilateral triangle the sum of the perpendiculars from 
 any point within to the three sides is equal to the altitude of the 
 triangle. If the altitude represents 100 per cent and a point is 
 taken within the triangle at say one-third the altitude from one 
 side, the per cent of the other two ingredients can be varied by 
 simply moving along a hne parallel to one side and measuring 
 the perpendiculars to the other two. In Fig. 108 are two dia- 
 grams showing the effect on mortars by using sand of different 
 
114 GRAPHICAL METHODS 
 
 grades of fineness. C = coarse, M = medium, F = fine. The 
 distance of a point in the triangle from the three base lines, 
 represents the proportion of each size used in the mixture. 
 Densities are given in (A) and strengths in (B). 
 
 Professor Thurston used this principle in constructing his 
 alloy chart which represented graphically the variation in strength 
 of copper-tin-zinc alloys having different proportions of each. 
 It is also used in dietetics for the proportioning of food rations. 
 The application of this chart is also found in the analysis of coals 
 to show variations in carbon, hydrogen and oxygen. This 
 method of graphical analysis can also be applied to research 
 work on fuels for internal-combustion engines where it is desired 
 to combine those with different British thermal unit values and 
 obtain a constant mixture. 
 
 Examples for Chapter IV 
 
 1. Construct a diagram to show the relation of dollars and cents to 
 pounds, shillings and pence. (1 pound sterKng = $4.87.) 
 
 2. Construct a conversion diagram for miles and kilometers. 
 
 3. What objections are there to representing quantities by areas or 
 volumes? 
 
 4. Plot Fig. 42 to a percentage scale. 
 
 5. Using Table I, draw a diagram showing the relation of costs per ton- 
 mile to miles per gallon. 
 
 6. Construct in as few diagrams as possible without sacrificing clearness, 
 Fig. 81 A-/ inclusive. 
 
 7. Plot the historigram of automobiles stolen and recovered in Detroit, 
 1916-18 {S. A. E. Jour., February, 1919). 
 
 8. Plot weight of automobiles per cyHnder displacement (Automotive 
 Industries, Aug. 30, 1917). 
 
 9. Plot diagram of comparison of steam and oil engines (Power, May 
 IS, 1917). 
 
 10. Plot fuel costs for heating and warming (Power, Nov. 12, 1918). 
 
 11. Make a conversion chart for weight of flat steel and thickness. 
 
 12. Plot a curve of electric D. C. motor torque and eiBciency (American 
 Machinist, Feb. 22, 1917). 
 
 13. Plot a curve of hardness tests of brass (American Machinist, Mar. 31, 
 1917). 
 
 14. Plot curve of viscosity of oils (Power, July 18, 1916). 
 
 15. Plot season load curves of central stations (Power, July 12, 1917). 
 
 16. Plot diagram of test runs of U. S. 110-ft. submarine chaser engines 
 (S. A. E. Jour., May, 1919). 
 
 17. Plot price fluctuations of pig-iron and cast-iron pipe (Engineering 
 and Contracting, Aug. 29, 1917). 
 
 18. Plot production record of soft coal (Eng. News-Record, July, 1918), 
 
APPLICATIONS 
 
 115 
 
 19. Plot production and consumption of gasolene (S. A. E. Jour April 
 1919). ' 
 
 20. Plot temperature-altitude curves (S. A. E. "Handbook"). 
 
 21. Plot drawbar pull and horsepower of locomotives {Railway 
 Mechanical Engineer, February, 1918). 
 
 22. Plot purchase charts ( Industrial Engineering, March, 1919). 
 
 23. Plot withdrawal tests of railroad spikes (Engineering and Contracting, 
 Nov. 19, 1919). 
 
 24. Plot vol. chart for horizontal cylindrical tanks (Eng. News-Record, 
 Vol. 81, No. 14) (Power, Aug. 20, 1918). 
 
 25. Plot compensation of engineers (Trans. Soc. C. E., Vol. 81, 1917). 
 
 26. Plot surplus dividend fund increase of Fig. 70. 
 
 27. Plot Kne showing excess of married over others as shown by Fig. 73. 
 
 28. Combine two diagrams of Kg. 74 whose comparison would be of some 
 advantage as Nos. 6 and 9 or 2 and 7. 
 
 29. Plot charts showing wages per month of railroad employees for 1917 
 and 1921 as follows: 
 
 1917 
 
 1921 
 
 Carpenters 
 
 Boiler makers. . 
 
 Watchmen 
 
 Section men .... 
 Section foremen 
 Unskilled labor . 
 
 $ 78.25 
 118.75 
 74.67 
 50.00 
 73.75 
 57.92 
 
 $168.95 
 195.11 
 154.13 
 112.52 
 168.10 
 118.14 
 
 30. Combine the two diagrams in Fig. 65 on one base. 
 
 31. Plot data in Table Ill(ff) on the standard form of the S. A. E. in 
 Fig. 97. 
 
 32. Plot for 21 knots the resistance of each model using as the other 
 variable the area of immersed midship section of Fig. 100. 
 
 33. Plot a diagram of differences from the data given in Fig. 102. 
 
 Problems for Graphical Solution 
 
 1. A syphon would empty a cistern in 48 min. while a cock would fill 
 it in 36 min. When it is empty both begin to act. How soon will the cistern 
 be mied? 
 
 2. A man mixes grain worth 30 cts. per bushel with grain at 80 cts. to 
 make 60 bushels worth 50 cts. per bushel. How much of each kind must he 
 take? 
 
 3. A and B shoot at a target. A makes seven out of 12 bulls' eyes, B 
 makes nine out of 12. They shoot 32 in all. How many shots did each 
 man lire? 
 
 4. A and B are two towns 24 miles apart on a river. A man goes from 
 A to B in 7 hr. by rowing the &st half and walking the last half distance. 
 Returning he walks the first half at three-fourths his former rate but the 
 
116 GRAPHICAL METHODS 
 
 stream being with him he rows at double his rate in coming and he does the 
 whole return journey in 6 hr. Find his rate of walking and rowing. 
 
 5. A and B start together to climb a mountain. A would reach the 
 summit K hr. before B, but loses his way, goes a mile and back needlessly 
 during which he goes at twice his former pace and reaches the top 6 min. 
 before B. C starts 20 min. after A and B and walking at the rate of 2Jf miles 
 per hour reaches the top 10 min. after B. Find rates of A and B and distance 
 to top of mountain. 
 
 6. Take a timetable of a railroad which gives the distance between 
 stations and lay out a train chart for 24 hr. 
 
CHAPTER V 
 
 DETERMINATION OF LAWS 
 
 The straight Une as the representation of an equation finds its 
 most direct and important application in the determination of 
 laws embodying the results of experiments. As an example take 
 the following case: In a test on a crane the following values 
 were found for the effort P required to raise a weight W. Find 
 the law of the crane. 
 
 W (lb.) 
 P (lb.) 
 
 10 
 
 1 
 
 20 
 1.63 
 
 30 
 2.13 
 
 40 
 2.63 
 
 50 
 3.25 
 
 60 70 
 3.75 4.25 
 
 80 
 5 
 
 90 
 55.5 
 
 100 
 6 
 
 5 
 
 u- 
 o 
 (/) -1 
 
 
 
 p 
 
 =o.a 
 
 1 
 
 i64W+0.41B 
 
 
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 ^ 
 
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 A 
 
 r^- 
 
 
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 2.S2 
 
 
 
 
 
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 c 
 
 f-t 
 
 
 •^ 
 
 
 
 
 
 
 
 
 y 
 
 
 
 
 
 
 
 
 
 
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 30 40 50 GO 
 Values of W 
 
 to 80 90 100 
 
 Fig. 109. — Test on a crane. 
 
 Figure 109 shows the points plotted on a base line using the 
 values of W as abscissas and the values of P as ordinates. The 
 equation is found to be that of a straight line P = 0.0564 TT + 
 0.418. 
 
 Another example is to find the graph of an equation of the 
 second degree. Equations of this form are y = 5x^ + 7a; — 9 
 or x = ay^ + by + c. If we assume several values for x and 
 calculate the values of y we will be able to plot the graph. For 
 example take the equation y = bx'^ + 7a; — 9. Using values 
 from a;=— 5toa; = +4 and solving for y gives us a curve 
 
 117 
 
118 
 
 GRAPHICAL METHODS 
 
 which is a form of parabola whose axis is-yertical and whose 
 vertex is at the bottom of the curve. This is 'shown in Fig. 110. 
 
 Graphs of equations of higher degree than the second such as 
 y = x^ or y = x^ — 8x^ + 3a; + 15 are plotted as in the following 
 example. 
 
 Plot a curve to show the cubes of all numbers from to 6. 
 If x represented the numbers and y the cubes then the equation 
 of the curve is y = a;', Fig. 111. The points all lie on a smooth 
 curve known as a cubic parabola. To read cubes work from the 
 
 
 
 
 
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 Y 
 
 f r 
 
 
 <r— 
 
 \ 
 
 k 
 
 . 10 
 
 V\ 
 
 
 
 — ^ 
 
 -+ 
 
 
 
 
 
 fiO 
 
 
 
 
 
 
 Fig. 110. — Parabola. 
 
 number scale up to the curve, then horizontally to the cube scale. 
 For obtaining cube roots the process is reversed. 
 
 The horsepower transmitted by a 4-in. belt M-in- thick passing 
 around a pulley and running at V ft. per second is given by the 
 equation : 
 
 V I wV\ 
 
 H = 
 
 1,100 
 
 = 350 lb. per square inch 
 0.4 lb. 
 
 T = maximum stress permissible 
 w = mass of 1 ft. length of belt, ■■ 
 g = 32.2 
 Such a plot is shown in Fig. 112. 
 
 Other curves met with most commonly are the conic sections, 
 
 x^ y^ 
 viz., the ellipse -^ + 1-2 = 1 which is the equation when the origin 
 
 is at the center of the ellipse, as in Fig. 113. As an example plot 
 a curve representing the equation Zx^ + by^ = 60. This is the 
 
DETERMINATION OF LAWS 
 
 119 
 
 3a;2 5^2 
 equation of an elliprfe and can be written -^TT + T^TT = 1. Reduc- 
 
 ing to 2Q + j^ = 1 so that a^ = 20 and ¥ = 12 from which 
 o = ±4.472 and b = ±3.464. 
 
 too 
 
 190 
 180 
 
 no 
 
 160 
 150 
 140 
 ISO 
 
 no 
 no 
 
 100 
 90 
 80 
 70 
 60 
 50 
 40 
 30 
 20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 & 
 
 = x 
 
 3 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 ; 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 y 
 
 / 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ^ 
 
 Y 
 
 
 
 
 
 
 
 
 1 t 2' , 4. 
 
 Number 
 
 Fia. 111. — Cubic parabola. 
 
 A parabola has the equation y^ = A.ax when the axis is hori- 
 zontal and the vertex is at the origin. If the axis is vertical the 
 equation is x^ = 4ay. A curve of this kind is shown in Fig. 110. 
 
 The Hyperbola. — If the center of the hyperbola is at the origin 
 
 2^ y^ 
 the equation is of the form -^ — rj = 1- 
 
 Example. — Plot the curve representing the equation 2a;2 - 
 
120 
 
 GRAPHICAL METHODS 
 
 5j/2 = 48, Fig. 114. Reduce this ^o ■^- |sp= 1 by dividing by 
 48. Then o^ = 24, h^ = 9.6 and a = ±4.9, & = ±3.1. 
 
 ?2,60O 
 
 o 22,500 
 
 2?,400, 
 
 95 97.6 100 
 
 Values of V 
 
 Ct/f!V£ OFHORSEPOWBR TI7/INSMITTED BY BELT 
 
 Fig. 112. 
 
 105 
 
 Plotting of Difficult Curve Equations. — Type y = ax". In this 
 case the necessary calculation must be made with the' aid of 
 logarithms. 
 
 CUffVe OF EQUATION TO ELLIPSE 
 Fig. 113. 
 
 As an example of this type of curve, take the expansion curve 
 for gases, pv" = c. p = pressure in pounds per square inch; 
 V = specific volume in cubic feet of 1 lb. and n and c are con- 
 
bETERMiNATION OF LAWS 
 
 121 
 
 stants, which vary with the conditions. For air expanding 
 adiabatically n = 1.41. For gas in the cylinder of a gas engine 
 n = 1.37. For isothermal expansion n = 1. 
 
 TH£ HYPERBOLA 
 Fig. 114. 
 
 10 15 M 
 
 Values of o 
 EXPANSION CURVES FOR GASES 
 FiQ. 115. 
 
 Plotting these three curves on one diagram (Fig. 115), using 
 the different values of n enables them to be easily compared. 
 
122 
 
 GRAPHICAL METHODS 
 
 The greater the value of n the steeper the curve. All these 
 curves are hyperbolas. 
 
 The sine curves appearing so often in engineering theory and 
 practice are of the form y = sin x. AU sine curves are smooth 
 and of a periodic nature, therefore a study of the simplest case 
 will serve as a basis. To plot y = sin a; select values of x between 
 
 i.o 
 as 
 
 0.G 
 OA 
 
 oz 
 
 -0.2 
 -0.4 
 
 -0.6 
 -0.8 
 
 -1.0 
 
 
 ^"" 
 
 y 
 
 
 1 
 
 
 — -y 
 
 1 1 1 
 
 N. 
 
 1 
 
 
 
 1 1 1 
 
 \ 
 
 
 
 /' 1 
 
 1 1 ' 
 1 1 1 
 
 \ 
 
 Angle 3c, degrees 
 
 
 / 1 le 
 
 31 1 i l?'o \ 
 
 80 240 
 
 3(jo J6o| 
 
 1 
 
 i 
 
 i 
 
 \ 
 
 i 5 
 
 y 
 
 
 
 
 "* 
 
 \ 
 
 
 
 i 
 
 / 
 
 
 
 
 
 \ 
 
 
 
 / 
 
 
 
 
 
 
 \ 
 
 
 
 / 
 
 
 
 
 
 
 
 V 1 . 
 
 y 
 
 
 
 SINE CURVE 
 Fig. 116. 
 
 and 90°. This will give one-fourth the whole curve, which 
 can then be folded over and inverted. Figure 116 represents the 
 complete plot for values of x from to 360°. 
 
 COMPOUND PERIODIC OSCILLATIONS 
 
 In engineering practice one often meets with curves which are 
 quite periodic but not of the sine or tangent type. An example 
 of this concerns the equation of time which is the difference 
 between the apparent and the mean time of day. The apparent 
 time is the actual time as recorded on a sun dial while the mean 
 time is calculated by the average over a year. Two causes 
 contribute to the difference between the two times, viz.: (a) The 
 earth in its journey around the sun moves in an elhpse having 
 
 , . . , .distance between foci. . , . 
 an eccentricity ( -r- 1 ) oi }j and in consequence 
 
 of the laws of gravity its speed is greater when nearer the sun 
 than when more remote. (6) The earth's orbit is incUned to the 
 plane of the equator. 
 
 The corrections due to these two causes are found separately 
 and Bre represented by the respective curves (a) and (&) in 
 Fig. 117. For (a) the period is 1 year; for (b) the period is }i 
 
DETERMINATION OF LAWS 123 
 
 year. These when combined by adding corresponding ordinates, 
 taking account of algebraic signs, give curve (c) for which the 
 period is 1 year. By the use of this curve the correction to 
 be added to or subtracted from the observed sun time can be 
 obtained. 
 
 15 
 
 10 
 
 V 5 
 
 C 
 
 'E 
 <y 
 .1-5 
 
 -10 
 
 -15 
 
 Set watch fasf met this period by 
 
 ! Set watch shw'over fhispenaol by 
 -iUarnounf^iven bijorctinafepfc 
 
 'b-Curvegivma van'atfhn 
 auefo I'ncti nation of 
 -Eclip tic to Equator — 
 
 Jan Feb. Mar. Apr. May June July Aug. Sept Oct 
 CURVE FOt? EQUATION OF TIME 
 
 Fig. 117. 
 
 GRAPHIC SOLUTION OF EQUATIONS 
 
 We can apply algebraic rules to the solution of simple or 
 quadratic equations but equations of higher degree or those not 
 entirely algebraic can best be solved by graphs. In some cases 
 no other method is possible. The general plan is first to obtain 
 an approximate idea of the expected result either by rough plot- 
 ting or calculation and then narrow the range, finally plotting 
 to a large scale the portion of the curve in the neighborhood of 
 the result. 
 
 Determination of Laws. — It is often necessary to embody the 
 results of experiments in concise form with the object of simpli- 
 fying the results for future use. We therefore wish to fit the 
 best law to correlate sets of quantities. The values of the 
 quantities obtained in experiments, except in special cases, do not 
 give straight lines when plotted directly the one against the 
 other. The general scheme then is first to reduce the results to a 
 hnear or straight Hne equation, to plot the straight hne and then 
 calculate the values of the constants. 
 
 The laws may be of the types (1) 2/ = a + r' (2) i/ = a -f hx^, 
 
 (3) 2/ = 05*^ (where e 2.718 the base of natural logs) (4) y = ax", 
 (5)y = a + bx + cx"^, and others. The law connecting volts and 
 
124 
 
 GRAPHICAL METHODS 
 
 amperes of electric arc can be determined from a series of measure- 
 ments which read as follows: 
 
 Volts 67 
 
 Amperes ... 1 . 95 
 
 63 59 58 56 53.8 52.2 52.4 
 
 2.46 3 3.44 3.96 4.99 5.96 7 
 
 Plot V against A in the Fig. 118 below. This shows V de- 
 creases as A increases or the relation of A and V is of an inverse 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 lib 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 Si 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 V 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 66 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 N 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 N 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■^ 
 
 \, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 5 
 
 
 
 
 7 
 
 Amperes-A 
 
 Fig. 118. 
 
 character. If we plot -j against V we have an equation of the 
 
 form V = b + -T and the table will be 
 
 7. ...67 
 A 
 
 63.7 59.7 
 
 58 
 
 56 
 
 53.8 52.2 
 
 51 
 
 4 
 
 0.513 0.407 0.333 0.291 0.253 0.2 0.168 0.143 
 
 This plot is a stra'ght line as in Fig. 119. Taking two sets of 
 values 
 
 V =62when-J = 0.15 
 
 A 
 
 V =64.5 when -J- = 0.45 
 
 A 
 
 inserting in the formula V = b +-^ gives C =41.7 
 
 41 7 
 b = 45.75 whence V = 45.75 + ^- 
 
DETERMINATION OF LAWS 
 
 125 
 
 66 
 
 _ 
 
 
 
 / 
 
 65 
 
 - 
 
 
 
 
 / 
 
 64 
 
 - 
 
 
 
 ~7 
 
 
 
 
 
 
 / 
 
 
 62 
 
 - 
 
 
 
 
 
 61 
 
 - 
 
 
 
 
 
 60 
 
 ^ 
 
 
 
 / 
 
 
 
 59 
 > 58 
 
 y^ 
 
 
 
 
 / 
 
 
 
 
 
 51 
 
 - 
 
 / 
 
 
 
 
 
 
 
 
 4 
 
 
 
 
 
 
 55 
 
 - 
 
 / 
 
 
 
 
 
 
 
 54 
 
 y 
 
 
 
 
 
 
 
 5? 
 
 - / 
 
 
 
 
 
 
 
 
 52 
 
 
 
 
 
 
 
 1 
 A 
 
 
 
 
 ^ 
 
 
 51 
 5( 
 
 
 11 ' 
 
 
 0. 
 
 I 03 
 
 5 
 
 0,3 0J5 04 045 0.5 
 
 Law Connecting Volts and Amperes of ElecVric Arc 
 Fig. 119. 
 
 1 ^ ~4 5~6 8 10 14 20 
 
 diadham 70 show val ues of v'-*' 
 Fig. 120. 
 
126 
 
 GRAPHICAL METHODS 
 
 PRACTICAL DIAGRAMS 
 
 Diagrams may be classified as (a) correlation diagrams or 
 graphs, (6) ordinary intercept diagrams or (c) alignment dia- 
 grams. 
 
 Correlation diagrams have been treated but adapted for 
 particular circumstances. The modification is in the substitution 
 of a straight line for a curve, as it is easiest to draw. When 
 powers occur this necessitates log plotting. The value of the 
 exponent is thus the slope of the line, hence this method can be 
 used to great advantage when the power is awkward to handle. 
 
 As an example in calculating points on an expansion curve 
 values of V ^-^^ had to be found ranging from 1 to 30. To con- 
 struct a diagram for this, draw axes OX and OF at right angles, 
 and starting from 1 at the point set off log scales on both axes, 
 the same scale of the shde rule being used throughout. Make 
 OM = 1 unit of length and MN = 1.41 units of length (actual 
 distance); join ON and produce to cover the given range. Then 
 for V = 5, 71" = 9.7. Figure 120 shows this diagram. 
 
 90 120 
 
 Values of H 
 DIAGRAM GIVING HORSEPOWER TRANSMISSION BYCJ. GEARS 
 
 Fig. 121. 
 ORDINARY INTERCEPT DIAGRAMS 
 
 A combination of two or more graphs is often of far more use 
 than the separate graphs since intercepts can then be read directly 
 and from the one diagram. 
 
 They may be arranged in various forms, one of them shown 
 in Fig. 121 as an example, being a diagram for horsepower trans- 
 
DETERMINATION OF LAWS 
 
 127 
 
 mitted by spur gears for various pitches and speeds. The 
 
 pitch varies from }-^ to 4 in. and the speed from 100 to 1,500 ft. 
 
 per minute. The formula, when all the pressure is taken by one 
 
 i PW 
 
 tooth at a time is ^ = -yr^- All the calculated values of H 
 
 produce straight lines which pass through the origin. The 
 diagram appears as follows, in Fig. 121: To use when P and 
 V are given, draw a horizontal line through V to meet the 
 inchned line of given pitch value. From the intersection drop 
 
 -1 — ' — I 1 ' — I — 'iiiiX'L'i'iilx 
 
 5 4- 3 Z I OigS°ig§ 
 
 DiamelercL, inches °„ " "^ , ^ S, S p 
 
 ■ Quanti+y 9,lbs.perTnin. 
 
 QU/INTITY OF WA T£R FLOWING THROUSH PIPES 
 
 Fig. 122. 
 
 a perpendicular line to the E scale which gives the desired answer 
 on U. A diagram to give quantity of water flowing through 
 pipes would appear as in Fig. 122. 
 Pounds per minute = 60 by 62.4 by area in square feet by 
 
 velocity in feet per second if 
 d = inches diam. of pipe. 
 Y = velocity in feet per second 
 Q = 20.4 d?Y 
 Another similar diagram is one giving volume of water in 
 cylindrical tanks for various depths and lengths as shown in 
 Fig. 123. Let the depth of water equal h (see E of Fig. 123). 
 A number of curves should be drawn in the left-hand portion, 
 one for each separate value of the diameter. For diameter = 4 
 ft. ordinates of the curve would be (^)2, viz., four times those of 
 the curve f or d = 2 as drawn. This crowds the scale so that it 
 is preferable to work from the one curve and to multiply after- 
 
128 
 
 GRAPHICAL METHODS 
 
 ward remembering that the variation will be as the squares of 
 the diameter. 
 
 There is a class of graphical work not yet touched upon which 
 belongs rightfully in a treatise on graphical methods although 
 it is usually found in books on integral calculus, viz., the plotting 
 
 U O.B 0.4- 10 20 JO ' 40 4S.6 50 
 VOiUMeS OF LIQUID IN cniNDRICAL TANKS 
 
 FlQ. 123. 
 
 Fig. 124. — Area of irregular figure. 
 
 of an integral or sum curve. The application of this is found in 
 problems where it is desired to find the area of a closed figure or 
 the volume of a solid, proceeding by increments. As an example 
 of this, reference is made to the displacement and body curves 
 of a vessel's hull. There are several ways of constructing an 
 integral curve from a given curve. The simplest is to divide 
 
DETERMINATION OF LAWS 
 
 129 
 
 the area under consideration into narrow strips as in Fig. 124. 
 Each strip is approximately a rectangle whose area equals its 
 width a times its average height b. This area is square inches; 
 therefore suppose the area of the first strip is <> Z square inches. 
 Lay off this area, to any scale assumed, on the ordinate of the 
 side of the strip farthest from the oy-axis and call it h. Find 
 the area of each of the following strips and lay off the value of 
 each one from the top of the preceding ordinate as hi, h^, etc. 
 The last ordinate H will be the sum of all the areas of the strips 
 and will equal the area of the figure between the curve and line 
 ox. If this hne is divided into halves and the middle point 
 projected back to the sum curve, an ordinate drawn through this 
 
 Fig. 125. — Integral of area bounded by curve, ordinates and base line. 
 
 point wiU divide the area of the figure into halves. We can thus 
 divide the figure into any number of equal areas by dividing 
 ordinate H into the required number of parts and projecting 
 the division points back to the sum curve. 
 
 Another method of drawing an integral curve is shown in Fig. 
 125. Divide Xo to Xs into n parts and erect ordinates. Through 
 A, Ai, Ai, etc., draw short horizontal lines. Cut the arc AAi 
 by a vertical line making the small areas bounded by this vertical, 
 the arc and the short lines through A and Ai equal. Do this 
 for the succeeding arcs. Choose a point 5 at a convenient dis- 
 tance to the left of and join S to Co, Ci, d, etc., the points in 
 which the horizontals cut Y. Then starting at So draw a line par- 
 allel to SCo until it cuts the first vertical; through this point draw 
 a line parallel to SCi until it cuts the second vertical, etc. The 
 points 5o, 5i, Bi, etc., are points on the required integral curve. 
 A smooth curve through these points will be the required curve. 
 
 The distance (Xs^s) equals the area under the whole curve. 
 If {XzBs) is measured by the vertical scale and (a) by the hori- 
 zontal scale the area under the curve will be equal to (a) X (X3B3). 
 
CHAPTER VI 
 ROUTING AND ORGANIZATION 
 
 A type of diagram of the non-mathematical kind is that used 
 for illustrating the route or path of an order from source to 
 destination or the path laid out for keeping track of an article of 
 manufacture as it passes through the shop. It may also be an 
 outline of the processes of manufacture or a flow sheet of all 
 material obtained as a by-product during the reduction of raw 
 material to a final output. As an example of the first type of 
 diagram, Fig. 126 shows how certain forms in the Ordnance 
 Department of the U. S. Army were handled after they were 
 made out. It shows the place of origin and number originally 
 made out, to what offices they were sent and where each one 
 finally arrived and was filed. 
 
 In Fig. 127 is shown the flow sheet for one unit of an iron ore 
 washing plant. This shows the outline process from reception 
 of the ore in railroad cars to the flnal location of ore in bins and 
 washing water used in pounds. A flow sheet of a copper mill is 
 shown more in detail in Fig. 128. This indicates the path of the 
 ore and the processes as regards various levels instead of a bare 
 outline of the operations. 
 
 A diagram more elaborate still is shown in Fig. 129. Here the 
 operation of refining crude petroleum and oils is followed from 
 the crude distillate tanks to the tanks storing the final product. 
 Such diagrams as the ones given above serve as a guide to the 
 manufacturing processes of many products but are not in favor 
 with many executives as they only serve to give away to the 
 layman all the information which those in the business know by 
 heart and which it is not desired to spread outside the plant. 
 
 Another application of this type of diagram is found in the 
 component and assembly records of manufacturers of machinery 
 or complicated instruments. It aims to show, first, the com- 
 ponent parts of the machine, the sub-assemblies into which these 
 parts are collected, and the progress of further assembly up to 
 the final assembly of finished product. Such a diagram is shown 
 
 130 
 
ROUTING AND ORGANIZATION 
 
 131 
 
 in Fig. 130 which is the assembly routing of the bolt action of 
 model 17 U. S. rifle. These diagrams are used mainly for a 
 first layout of the work of processing and assembling. The 
 routing, inspection and transportation diagrams are worked out 
 from this diagram as a basis. 
 
 Organization diagrams or charts, as they are usually named, 
 belong to this class of diagrams. Their function is to arrange in 
 
 FORM DISTRIBUTION 
 
 Paymen+s andShipmen+s, Oct. 17, 1917 
 
 NAME 
 
 OF 
 FORM 
 
 FORM 
 NO. 
 
 NO. 
 REOt) 
 
 URD. 
 DEFT 
 SUP. 
 DIV. 
 
 ORD. 
 
 DEFT 
 PRODSEC 
 SUHDIV. 
 
 INSP. 
 SEC. 
 GUN 
 DIV. 
 
 ORD. 
 DEPr. 
 FIN. 
 DIV. 
 
 ORD. 
 
 DEPT. 
 P.R, 
 DIV. 
 
 PLANT 
 
 irepECT 
 
 OR AND 
 [DK5I6H0I 
 
 PLANT 
 M'F'R 
 
 CARRIER 
 NiTOL 
 
 MRIER 
 FINAL 
 
 CON-' 
 ilSNEE 
 
 SETT- 
 LING. 
 
 Q. M. 
 
 REMARKS 
 
 CSffriF/CATEPf 
 
 IHSfECTION 
 
 fHDRECEIPT 
 
 mu. 
 loee 
 
 4 
 
 
 
 
 
 
 
 
 
 
 
 
 PROPERTY RETURN FOR 
 PROPERTf RECEIVED 
 
 FROM aV/UANSOURCES 
 
 
 
 
 
 — 
 
 — • 
 
 Bff»- 
 
 --0 
 •PR 
 
 
 
 
 
 '--^ 
 
 PUBLIC 
 VOUCHER 
 
 J30-A 
 
 / 
 
 
 
 9— 
 
 — .« 
 
 .... 
 
 o — 
 _o-_. 
 
 "."5 
 
 
 
 
 
 TO BE USED ON 
 FIXED PRICE 
 CONTRACTS ONLY 
 
 S 
 
 5EDE 
 1515 
 
 3 
 
 • 
 
 
 
 .... 
 
 .... 
 
 --• 
 
 
 
 
 
 
 R0Uriti6ADDED 
 
 — 
 
 
 
 -0-- 
 
 mCHERFOF 
 
 jamsfEROE 
 
 VtapROPEffTY 
 
 JHOM 
 TVBE 
 
 VO-OO 
 
 2 
 
 IN 
 VOICES 
 
 
 
 
 
 P.R 
 
 
 
 
 
 
 
 PROPERTY RETURN FOR 
 PROPERTY RECEIVED 
 FROM MILITARY 
 
 zT 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 »* 
 
 W 
 
 Z 
 ff£- 
 
 
 
 
 
 m^.. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 — o — 
 
 
 
 
 
 
 -5 
 
 »» 
 
 J» 
 
 s 
 
 mas 
 
 
 
 
 
 
 
 
 
 
 
 r"* 
 
 TO BE USED ONLY 
 WHEN SNIPPING 
 TO A FORT 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ""S- 
 
 
 
 
 
 
 
 
 
 
 
 BIlLOFUtDmS 
 ORISINAL 
 
 153 
 
 I 
 
 
 
 
 
 
 9— 
 
 
 
 
 
 — • 
 
 WIN NOTATIONS 
 OF DAMAGES 
 
 
 
 
 
 
 
 
 
 <27-- 
 
 
 MEHO. BILL 
 OFUDINS 
 
 <f».C 
 IS* 
 
 5 
 
 
 
 • — 
 
 
 
 
 
 
 
 .... 
 
 
 — • 
 
 
 
 
 
 ■oX- 
 
 
 
 
 
 
 
 
 
 2-- 
 
 
 
 
 
 
 
 
 SHIPPJNS 
 ORDER 
 
 9MC. 
 
 ise 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 KiamLEPS- 
 
 HEHTOFKCfm 
 
 OFmPERTY 
 
 g.n.c 
 
 ISB 
 
 3 
 
 •-- 
 
 
 •-- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -■o 
 
 
 
 
 
 
 
 
 
 FREIGHT 
 VOUCHER 
 
 S5-IS 
 19-16 
 
 n 
 
 18 
 
 e 
 
 
 
 
 
 
 
 
 
 0-- 
 
 
 
 
 
 
 
 
 --• 
 
 
 
 
 
 
 as. CARD 
 
 
 1 
 
 
 
 
 
 
 ■ 
 
 
 
 
 
 
 
 BILL OF 
 LADINS 
 LEDSER 
 
 
 
 
 
 
 
 
 • 
 
 
 
 
 
 
 
 PROPERTY 
 RETURN 
 
 IB 
 
 IB cm 
 B 
 
 z 
 
 
 
 
 
 Pfi-^. 
 
 --0 
 
 
 
 
 
 
 
 o'^Originahng Poirrl- — Final Resting Place 
 
 Fig. 126. — Diagram showing method of handling forms in Ordnance Depart- 
 ment, U. S. A., 1917. 
 
 a clear form, which can be quickly grasped by the executives, the 
 plan of organization of the working forces of a business or corpo- 
 ration. It shows each employee where he stands in hne of 
 responsibility, who is his superior, who must report to him and 
 his relation to the different branches of the organization. These 
 
132 
 
 GRAPHICAL METHODS 
 
 COHCEHTmns aVERSIlE 
 
 R.R.CARS 
 ■i 
 (I) eRnzuES 
 
 (S) POCKET 
 
 (3) FEEDERS 
 
 (4) BELT CONVEYOR 
 \ 
 (5) REV0LVIN6 7 ROM MEL 
 
 'RSIZE 
 
 '' UWERStZl 
 
 (6)?s'l'pS ' (7)2s'lOS 
 
 coHcamm tailings caicimkk ta'iiings 
 -< — K >'■ 1 «^ t 
 
 (dJCHIPTmmL ( 9) CHIP TROMMEL 
 
 OVER^ «Vf OVE^filZE^ ^ FliiE 
 
 ^ . \ "T t 
 
 WAkE (lO)DEWMERmTAHKs'' WASTE (llJDEWATEIflNSTAnHS 
 
 pi-v. 
 
 0Z)I8\06 (13) 18 LOG (l4)l8'L05 
 
 ■U& (I3)I810G (MJm'lOS (/Sjl3l05 
 
 'amaHfuATi \ oHCanmei' + cotmrmti ' i (mENihus' i 
 
 TAILIHGS y TAILINGS " 
 
 {l6)DEWATamTANia in)PEmmGTAm^lS)llL 
 
 •mil 
 
 TAILINGS + TAILINGS 
 
 ITCPING TANKS 
 
 (iOJTABLES (2I)tMes (ZZJTABLES ~ (ZSj/ZtBLES 
 
 ^ ^ ^ ^ ^ i. 
 
 WHcamATCs \ coKCfmcs\ caicmmm\ coNCEfifm!T\ 
 
 I TAILINGS I TAILINGS I TAILINGS \ TAILINGS 
 1 . . J . t 
 
 CONCENTRATES 
 
 Failings V " tailings 
 
 DEWATERIHS LOSS 
 
 (24) ORE BINS (25)P0NO 
 
 FLOWSHEET OF ONE LfUIT IRON ORE WASHING PLANT 
 
 Fig. 127. 
 
 ■i p,F7t L J ^i^iP"?^'' ■ IS.Pmkr-OtmfnmTaUss 30.BstrThidmer.lir3lK, 
 
 i \i!,Xl/ TypeEeedeis, f -Callow CsmjstSona ISJuttmatiiSmpler.firiSec. Jil-FKemilmTtmk . - 
 
 ■J,?«, '^'■•5 ,: " ".Ind. >• lOMaWrraanltier 3l.!1bajumnimps ^,' 
 
 4l6Com&or . I. •' ..3rd. .. 21 .("Ehiatur !i>r3Jec.33N"MutmPlimps... 
 
 ^M^mckAulomaficScak K-CallowClamingCelk i?.6ElMafar " •■ 34.VaaiumTanks ••• 
 
 b.MarcuMill a.Callmi Rixleanmg Cells ZSMnnQncentmteSm •> » 
 
 TDtiplhOorraassifhr l^.4"piaphram PumpsibriStc. 24 InlemmentSMitgTanks ~ « 
 
 15:4' Centrifuaal Pump ZS.SivrageTanlf * « 
 
 IG.Hmdinge Ball Mill 2S. Bucket Ehva-hr ■• • 
 
 n.SimpltuDorraassifwr iZOIi'ver Filters •• . 
 
 id-S-fe'Comeyors i> • 
 
 * n !S. Railnad Cars 
 
 FLOWSHCETOFONE SECTION OF HERCULES COPPERCO'S MILl 
 Fio. 128. 
 
ROUTING AND ORGANIZATION 
 
 133 
 
 charts are made out in various ways by using circles or rectangles 
 of different sizes to contain the names of the divisions and sub- 
 divisions of the organization and often the name of the employee 
 
 who heads each one. These circles or rectangles are arranged 
 according to the importance of the departments or positions, 
 commencing with the president or board of directors and ending 
 with the foremen or sub-foremen of the shops. The circles or 
 
134 
 
 GRAPHICAL METHODS 
 
 rectangles are joined by lines in such a way as to convey the 
 relation of one department to another. A sample of organization 
 chart for an automobile manufacturing company is shown in 
 
 
 
 Shipping 
 
 Drop Forge 
 Shops 
 
 k 
 
 Block Test 
 
 Room 
 
 Painting & 
 Trimming 
 
 Buldozer 
 Dept. 
 
 Chassis 
 Asumbly 
 
 Treating 
 
 
 
 aF^^SPv 
 
 Alummum 
 
 
 
 Molleablfl 
 
 i 
 
 Bough 
 
 Grey Iron 
 
 Process 
 
 Brass 
 
 Finished 
 Parts 
 
 Steel 
 
 Final 
 
 Pattern 
 Shops 
 
 Tool 
 
 ^ 
 
 DooKecping 
 
 ^;;^^^ 
 
 Billing 
 
 
 Invoices 
 
 1_^ 
 
 ^\!^ 
 
 'sssi:< 
 
 ^ 
 
 Pay Roll 
 
 Fig. 131. — Chart showing make-up of various branches and departments of an 
 automobile manufacturing company. 
 
 Fig. 131. This does not show necessarily the best form of organi- 
 zation as there is a difference of opinion regarding the sub- 
 ordination of certain departments to others. The organization 
 

 
 PSThSlilitli 
 
 SI 
 
 A 
 
 I liiliiiliiiiiiit-t 
 
 
 ^^ 
 
 t^ 
 
 J 5. 
 
 -5 "§5 S 
 
 §§ SsaS a ass _^*qJJ_s__ 
 
 
 
 Ri ^s 1^ 
 ll tl" tl 
 
 ft 
 
 
 
 •S'S^ 
 
 
 9 !$ £ 
 
 iillli 
 
 fnTmnT 
 
 • § 3 c » ss bS 
 
 lllllliJis- 
 
 llilillill 
 
 
 1. §■'-'• ■it ^ 
 
 liil§4iilisiatg||pl 
 PiiM illiili 
 
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ROUTING AND ORGANIZATION 
 
 135 
 
 T 
 
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136 
 
 GRAPHICAL METHODS 
 
 of the Engineering Division of the Motor Transport Corps of the 
 Army is shown in Fig. 132. 
 
 Figure 133 is a chart of organization of the personnel of inspec- 
 tion of small arms accessories and was used by the writer in the 
 control of inspection of accessories, appendages and boxes 
 
 ORGANIZATION-INSPECTION OF SHALL ARMS,ACCESS0RIES.APPENDA6ES 
 AND BOXES 
 
 5PRIN6FIELn 
 ARMORY 
 
 CHIEF JHSPECTOR, 
 
 SHAaARHS, 
 WASHINSTOH.P.C 
 
 nnKCMAisiiku 
 
 •Ser. CHIEF INSR 
 aULLARHS, 
 
 ISSr.CHIEF INSP 
 SMALL ARMS. 
 WmCH.ARIIS CO. 
 
 THOHBS. 
 JWflSOtSCS 
 
 HODS. 
 
 SCOVILL 
 
 MF6.C0., 
 
 WCTERBURY 
 
 t: 
 
 FliMIKBLUlO 
 
 U5.IHSP., 
 
 MCTERBURY 
 
 SCKEW 
 miVEKS' 
 
 B.C. ALBERT 
 ^ U5.INSR. «- 
 WkTERBURY 
 
 STANLEY 
 
 •> RULEliLEV, 
 
 HEWBBrrwN 
 
 WCWKEE, 
 
 U,S.IK6P, 
 
 W.TERBURY 
 
 OIL CANS, 
 
 sims£ ■■->■ 
 CUPS 
 
 C.COWLES, 
 NEW 
 HAVEN 
 
 
 
 
 
 
 
 
 
 
 
 RERtlH 
 KITS •■■■♦ 
 
 WINCH REP, 
 
 ARMS, 
 HEW HAVEN 
 
 
 L.B.COONEY, 
 US INSR, 
 NEW HAVEN 
 
 
 
 
 
 
 BARRACK 
 
 CLEAHIKG-f 
 
 RODS 
 
 60RHAM 
 MFS.CO., 
 PROV. R.I 
 
 . 
 
 
 
 
 
 IKSPECTOR OF 
 SHALL ARMS, 
 WIHCH. R. A. 
 
 IHSPECTORS, 
 WinCH. R.A. 
 
 RIFLE 
 
 REPAIR 
 
 KITS 
 
 EP PERRIN, 
 U.S INSP.. 
 UTOKMWHDA 
 
 RUDOLF WURLIT7ER, 
 
 N.TONAWANBA, 
 
 HEW YORK 
 
 BARRACK 
 
 CLBAR/RS 
 
 RODBOXSS 
 
 BUFFALO SLED, 
 
 N.TONAWANDA, 
 
 HEW YORK 
 
 DOCK AND MILLCO 
 
 N.TONAWANDA, 
 
 HEW YORK 
 
 .W.6. PALMER, 
 
 H.TDNAWANDA , 
 
 JEW YORK 
 
 BARREL 
 BOXES 
 
 '^RIFLS 
 ■ BOXES 
 
 P B.ByRHES 
 
 -H u.s.insp7^ 
 
 'l.Y. 
 
 RIFLETIOHS . 
 BRUSHES .-■' 
 PISTOL THONS 
 BRUSHES --' 
 
 FOREST BOX A: 
 LUMBER COj (// 
 NEW YORK CITY 
 
 HILL AND MOUNT, 
 NEWARK , N.J. 
 
 ■» CLEVELAND OSBCQ, 
 
 NEWARK, 
 
 N. J. 
 
 SPARE-PART 
 BOXES,CL. 
 ROD BOXES, 
 SCREWDRmR 
 BOXES,THOHS 
 CASE BOXES. 
 
 RJ H'HAHOKJ 
 
 UiS.IHSP.. 
 BROOKLYN 
 
 
 LOUIS BOSSERT 
 
 AND SONS, 
 BROOKLYN. NYC. 
 
 
 SPARCnRT 
 BOXES 
 
 Fia. 133. — Organization chart of small-arms accessory and box inspection. 
 Ordnance Department, U. S. A., 1917. 
 
 pertaining to them. It gives at a glance the articles to be 
 inspected, location of the shops making them, inspectors in 
 charge of inspection at each one and the routing of orders from 
 Washington and the Springfield Armory. A similar chart shown 
 in Fig. 134 shows at a glance where various accessories and 
 
ROUTING AND ORGANIZATION 
 
 137 
 
 ACCESSORIES AND 
 APPENDAGES 
 
 Cleaning Rods (Field) 
 
 » '7 (Barrack) 
 
 ■> •. (Pistol) 
 
 Cleaning Rod Knobs 
 » " Brush Sec. 
 
 Screw Drivers ( Pistol ) 
 n >. (Rifie) 
 
 Thongs 
 Thong Tips 
 
 I) Weights 
 " Brushes 
 
 » Brush Tips 
 Thong Cases {Comple-te) 
 Thong Case Bodies 
 " " Caps 
 " .< Oiler Caps 
 
 No; 
 
 of 
 Plants 
 
 Qould-Mersereau 
 Cleoping Rods 
 
 
 
 o 
 
 3. 
 
 re 
 
 Cleveland Osb 
 Thong brushes 
 PlstoTCI.Rods 
 
 
 
 Acme Die Cast 
 Aluminum Knobs 
 
 kovill Mfg Co. 
 
 Wa+erbury Mfg 
 Thong 6rusfrTips 
 Thongs a Caps 
 
 Coe-Stapleu 
 Thong Cases 
 Thonqs&Bodi' 
 
 Steele aJohnson 
 Thong Wats 
 Thong Case Oil Drop 
 
 S+an.R.aL.Co, 
 .crew Drivers 
 
 'istoU Rifle 
 
 Frank Cook 
 CI. Rods 
 tarrock 0. Rods 
 
 Accessories Mfg 
 Thong Case Bodies 
 Caps a on Droppers 
 
 S+ewart Mfg. 
 Aluminum Knobs 
 
 Milwaukee Brush 
 Thong Brushes 
 
 Kfeeler Brass Co 
 
 CI.Rods- Thong 
 CasGsaBnjsh Sec. 
 
 C.M.Smillie 
 Barrack Rods 
 
 Midi.Mot.5pec.Co, 
 Oil Dropper 
 
 Marble ArmsCO 
 ^CI.Rods 
 Screw Orivers(Rifle) 
 
 
 
 o 
 
 ~. 
 
 5' 
 
 i 
 
 o 
 -? 
 
 s 
 
 Conron MacNeal 
 
 Screw Drivisrs 
 
 (Rifle) 
 
 
 - 
 
 Pfau Mfg Co. 
 Pistol Screw Drivers 
 
 
 
 t 
 
 GorhomMfg.Co. 
 Barrack Rods 
 
 Chapman Mfg 
 
 Thong Ca&eCops 
 
 aOilers-TTiongs 
 
 Thong Tips 
 
 Fig. 134. 
 
138 
 
 GRAPHICAL METHODS 
 
 ffs 11 ^t;-^ 18,^ S»g .se 
 
 v.li||ltli1 |l fi II 
 
 111 
 
 ^11 
 
 I 
 
 ©@8 
 
 i 
 
 >& ^ 
 
 
 
 ®@© fi 
 
 *-('^) 1 ill g 
 
 III "^" 
 
 !> 
 
 Hiii I 
 
 6 6 6 6 6 6' 
 
 sdoiojuia 
 
ROUTING AND ORGANIZATION 
 
 139 
 
 COST 
 FACTORS 
 
 
 
 Im'Ha/ Cosi-of Machine 
 Cost of^ccessories 
 Ins-hallaHon 
 DepreciaHon 
 
 mVESTtf£NT 
 
 — 
 
 
 
 OPERATIONAL 
 
 Ihskeep and Repairs 
 
 Supervision 
 
 Power 
 
 Wages ofOp<?rcifor 
 
 
 
 Hourly Charge when IcHe 
 Hourly Charge whenRUnnmg 
 Mormal Prvducf ion per Hour 
 Unit Cost of Production 
 
 F /NA L 
 
 — 
 
 
 
 POINTS TO 
 CONSIDER 
 WHEN 
 CHOOSING 
 nACHINERY 
 
 DESISN 
 FACTORS 
 
 MATERIALS OF 
 CONSTRUCTION 
 
 Kind Used for Diffeivnt Parts 
 DiSfribufi'on of Metal 
 Sfrength and Slabiliiy 
 
 
 
 Is it Abundant? 
 
 Hov/Applie^? 
 
 Is Control Centralized? 
 
 Aretfeav^ Parts Power Moved ? 
 
 Is Direct Motor Mounting Provided ? 
 
 POWER 
 
 — 
 
 
 
 LU8RICA TION 
 
 fbrcedTSigfit Feeds used 
 If not; Forced Oil Holes Accessible 
 Oil and Grease Cups on Bearings 
 Gears Enclosed ?Run in Oil Baths ? 
 
 BEARINGS 
 
 Ordinarc/ 
 Ball Bearings 
 Roller Bearings 
 
 METHOD OF 
 CHUCKING WORHV 
 
 Ordinary 
 Magnetic 
 Air Controlled 
 
 SAFETY 
 
 Machine, 
 Operator 
 
 •iPEED CHANGES 
 
 Number and Ratio 
 Quickness of Change 
 
 
 
 Friction 
 
 Vibration 
 
 Ease of Feeding and Discharging 
 
 Self Helping Attachment 
 
 OPERA TION 
 
 
 
 
 REPAIRS 
 
 
 Are Wearing Parts Interchangeable ? 
 Accessible and Easily Changed 
 
 MISCELLANEOUS 
 
 racilities for Ouich Setup 
 
 Other Kinds of Work Passible 
 
 Is if Easi/y Moved ? 
 
 Rigged fbr Use of Cutting Lubricants 
 
 Elf Location Availabte 
 
 note: 
 
 keep these items fresh and apply them 
 toevery proposed pukchase op eouipment 
 
 Fig. 136A. 
 
140 
 
 GRAPHICAL METHODS 
 
 appendages for small arms were being made, the number of 
 plants making each accessory and the district in which the plant 
 was located. Such a chart is easily made and conveys much 
 information in many different ways at a glance. 
 
 Figure 135 is an elaborate chart originally made in colors and 
 used to show how the work is to be distributed in a machine shop. 
 
 INSTftUMSNTS 
 THAT HgLP 
 meMANAdER 
 WATCH AND 
 CONTROL 
 
 
 
 Watchmens C/oc/rs- 
 Fire /ilarms 
 SprinfrlerSysi^ms 
 Electric andGcis Meiers. 
 Wafer Mef^rs 
 Temperature Regulators 
 
 BUILDINGS 
 
 — 
 
 
 
 EQUIPMENT 
 
 COMMUNICATION 
 
 Machine Recorciers 
 Mechanical Counters 
 Spedometers fnc^icah'rig andf^ordir^ 
 njwme'hrs Micatiqffand Recore^ii^ 
 Oock Operated Mechanisms 
 
 
 
 Time C/Qck 
 TimeShimp& 
 Dep'arfmenf Oocki 
 Sfop Wa-h>he& 
 Mechanical t?^ce>re^ets 
 Motion Pictures 
 
 MEN 
 
 — 
 
 
 
 
 
 Automatic Coal Scales 
 Wafer^4ir;Ehctric,Gas aSfeamF/aw Meters 
 Temperature Recorders 
 Draft Gaffes 
 Engine Indicator 
 
 POWER 
 
 — 
 
 
 
 
 
 Weighing Scales 
 Counting Scales 
 Proporfioninff Scales 
 Testing Equipment 
 Measuring Devices 
 Chemical Apparatus 
 
 MA TER/ALS 
 
 — 
 
 
 
 Time-OocJtSj Gon^SjSirens 
 Cal/i -/tud'iblej Visible 
 Pneumah'c Tubes 
 Mechanical Carriers 
 Telauhtffrapha 
 
 SHOUWeHINS SUDDEN OF ROUTINE CONTROL UPON 
 MECHANIC/IL DEVICES AUTOMATICALLY OPCRATEO 
 
 Fig. 136B. 
 
 R means red, G means green and Bl black in the circles where 
 they appear. In Figs. 136 A and B and 137 will be found analysis 
 diagrams of great use to executive, engineer or purchasing agent 
 as they list in graphical form the important items to be considered 
 in certain phases of shop management. This principle can be 
 applied to other problems as they arise in the manager's office. 
 
ROUTING AND ORGANIZATION 
 
 141 
 
 CHEMICAL 
 COMPOSITION 
 
 INSTRUMENTS 
 THAT CHECK 
 ON QUALITY 
 
 PHYSICAL 
 PROPERTIES 
 
 ELECTRICAL 
 PROPERTIES 
 
 L 
 
 mUKHAHSHIP 
 
 OUALITATIVl 
 ANALYSIS 
 
 Chemical Reaffenis 
 Bunsen Ftam^ 
 Spectroscope 
 c/ectn'cal Devices 
 
 QUANTITATIVE 
 ANALYSIS 
 
 Chemical Reagents \Qualify 
 Retorts and Batancesj't^lerminaiion 
 
 SIR EN TH 
 
 Tensile I 
 Compressiv^ 
 Torsional 1 
 
 
 
 Sclerescope 
 Sc/eromerer 
 
 Fiks^acfuafed^as to femper 
 DrilJing 
 
 HARDNESS 
 
 
 
 
 DENSITY 
 
 Specific Graviiy Balances 
 Absorption, Tests 
 Hi^drostatic Pressure Rams 
 
 STRUCTURE 
 
 Microscope 
 t^icroscopic Camera 
 
 ENDURANCE 
 
 EFFECT OF 
 TEflPERATURE 
 
 ELASTICITY 
 
 VISCOSITY 
 (Oils) 
 
 effeci-of Moisture 
 Encfumrnce Tesf-Machines 
 
 
 
 
 
 Thermomefers 
 
 Pyromefisrs 
 
 P^roscopGs. 
 
 
 
 
 
 Impact tiacf7/nes 
 Extensometers 
 Spec/'crf Testing MachinQS 
 
 
 
 
 V/'scosometer 
 Fricfion-measurtn^ /r/struments 
 
 COLOR 
 
 ficftchinff with Standard Colors 
 Color uncfsr filtered li^tit 
 Special Ligtifs 
 
 FINENESS 
 
 Gr^s/ed <Sie\/es 
 Centrifugal Separators 
 
 - {CONDUCT/ VI TY\ \Currei7ta Potential Transfer merj affefers | 
 
 - \iNCANDESCENC^ \Pi/romefxirs anel Photometers] 
 
 - {MAQNETISt^ I 1 Electro'tfagnets and Galvanomefers\ 
 
 - {DIALETRIC VALUE\ 1 Special Hi^h -fens ion Trans . & Elec. Motors I 
 
 Limit Gaug&s 
 Fixture Gauges 
 Templcrtes and Jigs 
 
 DIMENSIONS 
 
 Micrometers 
 Calipers 
 Limit' Gauges 
 
 W/ITER 01? AIR 
 TIGHTNESS 
 
 AirCompressors and Pressure Gaug<?s 
 Ht/drostatic Pressure Rams and Pumps 
 
 POWER DEVELPNT. 
 (Motors ai Engines) 
 
 Absorption Dynamometer j Electrical and 
 Transmission Dj/namometer] Mechanical 
 
 technical control over properties of 
 materials a accurac y of workmanshjp 
 
 Fig. 137. 
 
CHAPTER VII 
 CALCULATIONS 
 
 In the preceding diagrams a straight Una or broken line has 
 been used to represent the law of variation, usually on a time 
 basis. That is, for a given equal interval of time there is a 
 corresponding happening of another quantity which is called a 
 variable. When the equation of a line is of the form y = ax + 6 
 the line is a straight line. For every value of "x there is a cor- 
 responding value of y. If we give values to one variable we call 
 them independent variables and the values of the other variable 
 are called dependent variables. The value of the term h gives 
 the point where the line cuts the vertical axis and the value of 
 a determines the slope of the line. If we have one point on a 
 straight line and its inclination we can draw the Kne. 
 
 In aU of the preceding pages and examples the graphs have 
 been drawn from tables or through points plotted from given 
 data. We will now take up diagrams which are used in making 
 calculations. 
 
 The two axes previously mentioned as the x- and y-axes are 
 used in plotting the curves of the diagrams, the points of which 
 are located by coordinates. 
 
 Diagrams for solving equations of a straight line such as F = 
 A + BX are very common and usually of the form shown in 
 
 —]x] therefore B = — 
 
 nl ' n 
 
 If B changes, the slope of the line changes. If A is changed the 
 line will move parallel to itself either up or down without changing 
 its slope. 
 
 Suppose the type of equation is Y = B{X+A) where A is a 
 constant. Values of B are radial lines while the tangents of the 
 angles C must be proportional to the values given to the cor- 
 responding radial lines. If A = the equation becomes Y = 
 BX and the radial lines meet at the zero point of the X and Y 
 scales. Figure 139 is a diagram of this type suitable for the 
 equation 
 
 F =B{X -A) ovX = ^ + A 
 
 142 
 
CALCULATIONS 
 
 143 
 
 
 ^ 
 
 
 - 
 
 F 
 
 -III ,'-' 1 L.I 1 
 o^peral Equation 
 
 7 
 
 'i,L 
 
 hM- 
 
 
 T 
 
 ~\ — 
 
 - 
 
 ~" 
 
 
 :j: 
 
 J- 
 
 
 ^ 
 
 
 drawn fosuifY=40-.r'x. 
 
 
 
 
 
 
 " 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -N 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -c-i-l 
 
 
 
 
 
 
 
 
 •n 
 
 
 
 
 
 
 
 
 
 
 
 
 't 1 
 
 
 
 - 7,- 
 
 -- 
 
 _ 
 
 
 
 
 V 
 
 _ 
 
 
 
 
 
 
 
 
 
 
 _ 
 
 
 
 V 
 
 
 
 ' 
 
 
 
 
 
 
 
 
 
 •s, 
 
 
 
 
 
 
 
 — 
 
 / 
 
 30 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 "s 
 
 
 
 
 
 
 
 
 ~ 
 
 I 
 
 
 1 
 
 - 
 
 - 
 
 - 
 
 ^ 
 
 
 - 
 
 - 
 
 
 - 
 
 _ 
 
 - 
 
 
 - 
 
 
 \ 
 
 -- 
 
 -- 
 
 -. 
 
 -^ 
 
 -- 
 
 -- 
 
 - 
 
 
 _L 
 
 
 - 
 
 - 
 
 
 - 
 
 
 
 
 - 
 
 - 
 
 - 
 
 - 
 
 -- 
 
 
 - 
 
 - 
 
 -r 
 
 <. 
 
 
 -- 
 
 -- 
 
 ^ 
 
 - 
 
 25 
 
 1 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 -I- General Equation Y=A -f-BoL 
 
 
 / 
 
 
 
 
 
 
 
 
 -_ 
 
 > 
 
 
 . 
 
 y 
 
 
 
 
 
 
 
 
 
 
 -i- 
 
 _ 
 
 
 . 
 
 
 
 
 
 
 V 
 
 
 
 
 
 
 
 
 
 •-.1 
 
 ■fe 
 
 <P 
 
 
 - n - 
 
 - 
 
 — 
 
 - 
 
 ■-,->- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■" 
 
 
 
 
 H 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 -n 
 
 
 
 
 
 
 
 
 
 
 
 /\ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5 
 
 -A, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - 
 
 > 
 
 
 
 
 
 
 A 
 
 
 
 ] 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - 
 
 15 
 
 
 
 
 
 
 / 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - 
 
 
 1 
 
 
 
 
 
 
 
 
 
 w 
 
 
 
 
 - B 
 
 
 
 
 
 
 
 ■ 
 
 
 
 • 
 
 
 
 
 
 
 
 
 
 
 
 ". T? 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 10 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 ' 
 
 
 ~ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■ 
 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 JL 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 J50 
 
 Values of X 
 Fia. 138. 
 
 1098 7 e S 4 
 
 300 
 
 Z50 
 
 > 200 
 
 ^ 150 
 
 100 
 
 50 
 
 Diagram suits 
 Y=B(X-S5) 
 
 ¥a 
 
 w. 
 
 f^ 
 
 II 
 
 Tij 
 
 P 
 
 -"■' 
 
 /- 
 
 ii 
 
 7- 
 
 I: 
 
 ? 
 
 I 
 
 I 
 
 l- 
 
 ^^ 
 
 f- 
 
 i^pr 
 
 W- 
 
 ■^pr 
 
 25 50 15 100 125 150 
 
 Values of X 
 General E(^uaHon X=^+A orY=B(X-A) 
 
 Fig. 139. 
 
144 
 
 GRAPHICAL METHODS 
 
 Applications of this diagram are numerous. As an example 
 
 P X D 
 
 take the formula T = — ^ h M in- for the thickness of 
 
 pipes up to 15 in. when pressures vary from 200 to 400 lb. per 
 square inch. S is assumed to be 10,000 lb. The formula can 
 be expressed as 
 
 r = n in. + I ■,f,„r.„ ) D in which A = 5 in. and B = -^, 
 
 when D 
 
 I 10000/ 
 
 15,T = \m.+f^=\ in. +^ in. 
 
 50 
 g =0 .425 in. 
 
 For each value of P equal to 225, 250, 275, 300, 350 and 400 
 there will be a line drawn through a point ^^ in. to the right of the 
 
 'j\ 10 9 8 7 6 
 
 ■5 
 
 14 
 
 13 
 
 12 
 I 
 ! II 
 
 Mo 
 
 B w Gauge Nds. 
 5 4 3 2 1 
 
 00 
 
 OOP 0000 
 
 
 
 
 
 
 1 
 
 1 
 
 / 
 
 / 
 
 ' / 
 
 / ^ 
 
 ? — 
 
 
 
 
 
 
 1 
 
 / , 
 
 ■^ , 
 
 y/ 
 
 y 
 
 
 
 
 
 
 
 ^ 
 
 '< 
 
 ^- 
 
 ^ . 
 
 -^ 
 
 ^ 
 
 ^ 
 
 ^ 
 
 
 
 
 
 1 -fl 
 
 v\ 
 
 
 >\ 
 
 / 
 
 X 
 
 
 
 
 
 
 f'A 
 
 iy\ 
 
 ^0 
 
 y 
 
 / 
 
 
 
 
 
 
 
 /?> 
 
 A 
 
 p4^ 
 
 r°/ 
 
 jO"^ 
 
 -^ 
 
 
 
 
 
 / 
 
 yy^ 
 
 y > 
 
 ^ 
 
 fie 
 
 -y 
 
 
 
 
 
 
 /^ 
 
 'Y 
 
 y\ 
 
 y" ^ 
 
 .-+■ 
 
 
 
 
 
 
 
 
 yy 
 
 yl 
 
 -^ 
 
 1 
 
 
 
 
 
 
 /'I 
 
 C'^y' 
 
 -y^ 
 
 
 
 1 
 
 
 
 
 
 1 /. 
 
 y/^ 
 
 V^'' 
 
 
 
 
 1 
 
 
 
 
 
 y/^ 
 
 ^^ 
 
 ^ >^ 
 
 
 
 
 1 
 
 
 
 
 1 yC 
 
 ^^ 
 
 ^ 
 
 
 
 1 
 
 
 1 
 
 
 
 
 ' "^ 
 
 
 
 
 
 1 
 
 
 1 
 
 
 
 
 U^^ 
 
 1 
 
 
 
 
 
 
 1 
 
 
 
 
 i i i i - 
 
 16 4 iG 8 16 2 
 
 (T) Thickness, Inches ,, 
 
 DIAGRAM FOR THICKNESS OF STEEL PIPES T=~^ +g 
 Fig. 140. 
 
 7-axis on the X-axis. The horizontal scale will be laid off from 
 the F-axis equal to thicknesses of pipe and Y, obtained from solu- 
 tions of the above formula, will be laid off from the X-axis along 
 the corresponding ordinate. One point on each of the lines 
 will determine its slope as the hues all intersect the X-axis at a 
 common point. The diagram will be like Fig. 140 when finished. 
 If the results of a set of experiments plot in a straight line, the 
 equation to suit will be of the form Y = A + BX. If certain func- 
 tions of X and y are plotted and a straight line results, the equation 
 to suit these points will be as given in the following table : 
 
CALCULATIONS 
 
 145 
 
 Functions plotted 
 
 Sin X 
 X 
 
 Equation to suit if plotted 
 points lie in a straight line. 
 
 Y = A± BsinX 
 LogY = A ± BX' 
 
 Y^=A±i 
 
 Figure 141 is a diagram based on the above principles. It is 
 for determining which cutter should be used to obtain the correct 
 shape of teeth in a spiral gear when the number of teeth and 
 
 25 30 35 "40 45 50 55 60 
 
 Spiral Angle of Gear in Degrees(A) 
 
 Fig. 141. 
 
 65 
 
 spiral angle are stated. The method adopted is to obtain the 
 number of teeth for a spur gear to which it is equivalent and to 
 use the spur gear cutter for that equivalent number of teeth. 
 
 T 
 The formula governing this is Te = g^gs^ ' 
 
 Te = equivalent number of teeth in spur gear 
 
 T = number of teeth in spiral wheel 
 
 A = spiral angle of spiral wheel 
 If the equation is written log T = log T^ + 3 log cos A it will 
 be of the form F = A + 5X and to obtain the straight line it 
 will be necessary to plot log T and log cos A. 
 
 10 
 
146 
 
 GRAPHICAL METHODS 
 
 Again, B 
 
 m 
 
 (see Fig. 138). In this case 5=3. 
 
 3 = 
 
 actual length of m X M . actual length of m 
 
 He 
 H 
 
 actual length of n X }ie 
 3X1X6 
 
 = 3X 
 
 36 
 
 = K. 
 
 actual length of n 
 We therefore mark off n on the dia- 
 
 gram twice that of m and join them to obtain the slope of the 
 lines. The sloping hnes bear the same number as their point of 
 intersection on the T-scale. 
 
 The values of the sloping lines have been selected to agree 
 with the Kmits adopted by the cutter manufacturers, viz., 
 No. 1 cutter 135 teeth and over. No. 2 cutter 55 to 79 teeth. 
 
 The chart is used thus: Given a spiral gear of 35 teeth and 
 spiral angle of 55°, what cutter is necessary? Using dotted 
 lines it is found that the point lies within the limits for a cutter 
 for 135 teeth and over. If the equivalent number of teeth was 
 required it would be necessary to draw more sloping lines parallel 
 to the others and numbered like their points of intersection with 
 the T-scale. 
 
 In order to construct the chart it is first of all necessary to know 
 between what limits the chart is to be used. In this case we will 
 take A from to 65° and T from 1 up to 100 teeth. The variation 
 on the T-scale will be log 100 — log 1=2, and by making 1 in. 
 = H unit the total length of T-scale will be 12 in. The variation 
 on the A-scale will be log cos 65° — log cos 0° = —0.374 — = 
 — 0.374. If 1 in. = Hq unit the total length of .4 -scale will be 
 — 13.46 in. By comparison with the equation Y = A + BX, 
 log T will take the Y position and log cos A will take the X 
 position. As values of log cos A are negative they will be read 
 off to the left. Draw OC and OD as axes, mark off points and 
 number them from the following tables; 
 
 T 
 
 
 Length of ordinate 
 
 A" 
 
 
 Length of abscissa 
 
 Logr 
 
 eiogT 
 
 Log 
 coaA" 
 
 36 log cos A° 
 
 1 
 12 
 40 
 90 
 
 
 1.079 
 1.602 
 1.954 
 
 
 6.475 in. 
 9^612 in. 
 11.725 in. 
 
 
 30° 
 
 45° 
 65° 
 
 
 -0.062 
 -0.151 
 -0.374 
 
 
 
 - 2.25 in. 
 
 - 5.42 in. 
 -13.46 in. 
 
CALCULATIONS 
 
 147 
 
 The sloping lines lli-i 12K, 13M . . . 134K are the straight 
 lines plotted to suit the equation log T = \og Te + Z log cos A 
 but with Te taking the values 11 J^, 123.^, 13K • - • 134M- 
 By referring to Fig. 138 it will be seen that this amounts to a 
 change of A in that diagram, the slope remaining constant. 
 Figure 142 embodies the same principles as Fig. 139. Formula is 
 , 4 _ , 4 D = diameter of sohd shaft 
 
 D3 = 
 
 di = outside diameter hollow shaft 
 di = bore of hollow shaft 
 
 Equation may be written D^ X dx = di^ — dj^- 
 Bottom scale for D' is 1 in. = 1,000 units. 
 
 General Equation :A-B 'XrV 
 
 Fig. 142. 
 
 For example, when D = 20 in. D' = 8,000 and n = 8 in. 
 Radial lines are drawn so tangents of angle with horizontal are 
 proportional to values assigned them. Commence with d^ = 20 
 line and work down. 
 
 On vertical center line of diagram values of di* have been set 
 off to a scale of 1 in. = 20,000 units. For example, for di = 19, 
 rfi^ = 130,321, m = 6.516 in. long. Values of d^ sue shown on an 
 incHned line whose angle does not matter but is preferably 45°. 
 Vertical height of ^2 is same as di and has 20,000 units per inch 
 same as di. By this means ^2^ can be subtracted from di* but 
 with some assistance from the inclined lines at the left. If A 
 represents di^ and B = d^^ then the length B must be subtracted 
 at the top end to give a reading starting at which will be com- 
 mon to the right-hand portion of the diagram. 
 
148 
 
 GRAPHICAL METHODS 
 
 To use chart: 
 
 1. Given 20-in. shaft, what diameter hole can be put through it 
 to have same strength as a 16-in. shaft? Erect perpendicular at 
 16 to meet inclined 20, move horizontally to d^ line for answer = 
 16.7. 
 
 2. What size solid shaft is equivalent in strength to a hollow 
 shaft 19-in. outside diameter, 15-in. bore? Subtract distance from 
 base to 15 from base to 19 lay the remainder off from base line 
 vertically, then horizontally to radial 19 and drop vertical to D 
 for answer = 16.1. 
 
 Thickness of Flue in inches (T) 
 1 % % \ 5/8 '/Z ?I6 Vs '/4 0. 
 
 50 
 
 IZJ45 10 12 14 16 18 20 22 M 26 28 30 32 34 36 38 40" 
 
 Length of Flue in Fee+(L) 
 STFENGTH OF BOILEf? FLUES 
 
 Fig. 143. 
 
 Another chart of type similar to Fig. 140 is used to determine 
 the thickness of boiler flues. This is shown in Fig. 143. The 
 
 90 000 r^ 
 
 formula is P = ,j , ,>.r> where P = working pressure in pounds 
 \Li -\- i.)U 
 
 per square inch, L = length of flue in feet. 
 
 Logarithmically ruled paper can be used instead of squared 
 paper when the logs of a number have to be plotted. Figure 144 
 shows this general equation y = hx" or log y = log 6 + a log x. 
 This chart is drawn for y = bx.^ 
 
 This follows the type shown in Fig. 138. It can also be used 
 as a slide-rule scale to find the value of a series of numbers which 
 are in geometrical progression. As an example find 10 numbers 
 in geometrical progression commencing at 1.3 and finishing at 6. 
 
CALCULATIONS 
 
 149 
 
 Divide the distance between these points into one less than the 
 
 number of terms required (9) and the values can be read off 
 
 directly. 
 
 Another type of chart is based on the law of similar triangles 
 
 L N 
 
 J? = jr and any equation resolved into this form can be solved 
 
 by this type of chart, as in Fig. 145. 
 
 Series in Geometrical Progression — 
 
 2 2.5 3 4. 
 
 ScalaofX 
 
 Fig. 144. 
 
 5 6 T 8 9 (0 
 
 , D2 HP. 
 
 For example, ^ = 
 
 V 
 
 0.0607 (jQo) 
 
 for finding frictional horse- 
 
 power at disc when rotating in steam. Used in steam-turbine 
 
 work. ,„ 
 
 0.06071)2 HP, 
 
 This formula can be wntten y- 
 
 ^ ^ similar to ^ =-^- 
 
 llOOV 
 
150 
 
 GRAPHICAL METHODS 
 
 HP = disc frictional horsepower 
 D = mean ring diameter in feet 
 U = mean blade speed feet per second 
 V = specific volume of steam in cubic feet. 
 
 To use chart: (1) connect values of V and D; (2) draw a 
 parallel to this from U to give horsepower. 
 
 Scale of y. 1 in. = 20 units 
 Scale of D^. 1 in. = 1 unit 
 
 / U \^ 
 Scale of 0.0607 [j^j • 1 in. = 20 units 
 
 Scale of HP. 1 in. = 1 unit 
 
 Proportional Diagram for 
 HPa-0.0S07V%^)%^ 
 
 TO USE CHART (I) Connect Values VandD 
 
 (3) Draw Ihralkl fo above fiom V to HP 
 
 Fbrrnula can be written 
 
 0.0607D i. HP 
 
 which is similar in form to 
 
 W i' 
 -M- 
 Scale -for U( Mean Blade Speed inft.persec) 
 
 FiQ. 145. 
 
 This is equivalent to expressing the equation 
 
 HP. 
 
 m 
 
 20 
 
 j from which the point marked 1,000 on the ?7-scale 
 
 0.003035 (j^)' 
 
 will be 0.003035(103) = 3,035 in. from zero point. 
 
 Another diagram of the proportional type is based onK + L = 
 M + iV. It can be applied to the plotting of logs of the 
 variables as log if + log L = log M ■\- log iV or KL = M'M. 
 If the equation of Fig. 145 is written in this manner log HP. + 
 log 7 = 2 log Z) + (3 log C/ - (6 - log 0.0607)). This must be 
 
CALCULATIONS 
 
 151 
 
 multiplied by 2 to make the diagram easier to read, from which 
 we have 2 log HP. + 2 log F = 4 log Z) + (6 log U - 14.43). 
 
 This has been plotted in Fig. 146, .ffP. = 0.0607D^(~Yx-- 
 Formula may be written log HP. + log F = 2 log D + (3 log U + 
 8.7831). To use chart join values of U and D and draw parallel to 
 above from F to give HP. 
 
 K+L 'M-tK 
 
 PROPORTIONAL CHART FOR FINDING FRICTIONAL 
 HORSEPOWER A T DISC WHEN ROTA TINS IN STC/IM R 
 
 «Pa-.0607D^^-^ftif 
 
 ,5 
 -20 
 ■li 
 3.25 
 
 1-1 
 
 iO B 
 
 20 
 25 
 30 
 
 Fig. 146. 
 This table gives a few of the values marked off: 
 
 HP. 
 
 2 log HP. 
 
 F 
 
 2 log 7 
 
 Z) 
 
 4 log D 
 
 V 
 
 6 log V 
 -14.43 
 
 1 
 
 0.5 
 
 20 
 
 
 
 1.40 
 
 2.60 
 
 10 
 200 
 340 
 
 2 
 
 4.60 
 
 5.063 
 
 0.3 
 1.5 
 
 2.5 
 
 r 
 
 3.91 
 0.70 
 1.59 
 
 500 
 1,000 
 1,600 
 
 1.76 
 3.57 
 4.62 
 
 Minus characteristics and mantissa may be laid off on opposite 
 sides of the zero mark. 
 
 Still another chart of proportional type can be used for pro- 
 
 90 OOOy 
 portioning boiler flues (Fig. 147). The formula is P = /r ' \^\T\ 
 
 which is written 4 log P + 4 log D = (8 log T + 4 log 90,000) - 
 
152 
 
 GRAPHICAL METHODS 
 
 4 log (L + 1). P should read to 200 lb. pressure and log 200 = 
 2.301. We can make 1 in. = }-i unit or multiply equation by 4. 
 This is the same formula as used for Fig. 143 but the diagram is 
 easier to construct although not so easy to use. 
 
 t3 X- 
 
 Va- \ 12 
 
 140= 
 
 p/5- 
 
 
 ^ 
 
 M 
 
 1 ■'^ 
 
 VLi. 
 
 /f+i 'M+N 
 
 ^\ Before usina chart, adct 
 \\ one to length of pipe 
 
 L-N 
 
 STRENTH OF BOILER FLUES 
 Fig. 147. 
 
 A similar chart can be constructed when there are three vari- 
 ables instead of four as in the f orniula for collapsing pressure for 
 
 Bessemer steel tubes (see Fig. 148). P = 50,210,000 i~j ^ when 
 
 P is less than 580 lb. per square inch and length of tube is over 
 6 times the diameter. The equation rewritten is 3 log D + log 
 P = log 50,210,000 + 3 log t. In the chart the third scale 
 becomes a common point for all values as the third variable is 
 now a fixed quantity log 50,210,000. To use chart connect D 
 with P. Draw parallel from to find t 
 Z diagrams are used for a different form of equation from those 
 
CALCULATIONS 
 
 153 
 
 preceding. These forms are A + 5 = ^ and the diagram (Fig. 
 149) shows how the formula is applied. 
 
 K ^L 
 
 D C ■ 
 
 
 ii:+L=^+L = ^(i) + C)=^(D + C) 
 
 M 
 K -\- L = ^ (length of diagonal) 
 
 V 
 
 general equation A + B = ^ 
 
 XFi'xed 
 
 Prvporfional Char-f-for 
 Collapsing Pressure for 
 Bessemer Steel Tubes 
 
 P=5O,2iqO00(-^fwhenP<58Oltis.perspn. 
 
 and length is over Gx diam. S 
 
 Hach'meiy>landboohp.3S3 
 
 Fig. 148 
 
 Where K represents A, L represents B. 
 
 M represents X, N represents Y. 
 Scales : 1 in. on scale A represents R units, 
 then 1 in. on scale B represents R units. 
 Let 1 in. on scale X represent S units. 
 Let 1 in. on scale Y represent T units. 
 
154 GRAPHICAL METHODS 
 
 then K = rf-, L = r-, M = -^, N = -ff,> 
 K ti o J 
 
 A Ti JC T 
 
 ■ ■ R'^R^^^Y (*^^S*^ °^ diagonal) 
 
 A+B X/T 
 
 R 
 
 X / i \ 
 = Y\~^) (l^^S*^ of diagonal) 
 
 1 T 
 
 -^ = -^ (length of diagonal) 
 K o 
 
 Length of diagonal = 
 
 RXT 
 
 Slope of diagonal is best at about 45° but its length is impor- 
 tant. 
 
 
 k- -^---M- A 
 
 FiQ. 149. 
 
 1.24D2 
 Such a formula as P = — ^ h -D can be used on the Z 
 
 diagram for finding the pitch of units in double-riveted lap 
 joints (plate at 56,000 lb. and rivets 18,000 lb. per square inch., 
 Kent, p. 358). 
 
 D = diameter of rivets 
 
 T = thickness of plate 
 
 PT 
 This formula may be written 1.24D + ^ = ^- In Fig- 150 
 
 place 1.24Z) values on top line, values of T on upper side of lower 
 line of Z, values of D on the diagonal; then values of P X T will 
 be on lower side of lower bar of Z. As values of P are required, 
 different scales are given for different values of T. 
 Scales of chart: 
 
 1 in. on 1.24 D scale = K unit 
 
 1 in. on T scale = ^ unit 
 
 1 in. on D scale = Y^ unit 
 
 1 in. on P X r scale = J^ unit 
 
CALCULATIONS 
 
 155 
 
 H 
 
 M 
 
 Length of diagonal necessary = , , ~ , . = ~- = s in. 
 
 >4 X >4 Me 
 
 Distance to 3^-in. division on top line oi Z = 1.24 X .5 X 4 
 
 = 2.48 in. 
 
 Diam of RwetCDJ 
 iji iVs I % \ % '/!^ 94gr 
 
 \ ThicknesSS!fPlatcfT) 
 
 ';;■ Plate 
 
 ^1 
 
 ■ 3 ■■ ■ 4. ■ 5 
 
 , F . 1 . 1 , 1 . . . .1 . 
 
 .^ . , .1 . , .? 
 
 W; " 
 
 
 ^ .,.?,,, 1 , 
 
 , , t , , . ^ , , 
 
 V ■' 
 
 
 2 3 
 1 ... 1 . 1 
 
 4 5 
 
 78 " 
 
 
 ^ . , . ^ 
 
 4 
 
 1" - 
 
 
 ^ , , . 
 
 ^ , , , t 
 
 I'/e" » 
 
 
 ^ , 
 
 , . ? , , 
 
 IV .. 
 
 
 } 
 
 , =^ , 1 , 
 
 PITCH OF RIVns FOR OOUBLE HIVFTTeO LAP JOINTS 
 
 FiQ. 150. 
 
 r--- --->j 
 
 Scale of A ;, I 
 
 / Scale oFX-" 7~ 
 
 FlO. 151. 
 
 Draw a line from D on top line to T on upper side of lower line. 
 From D on diagonal draw parallel to meet lower line of Z. Drop 
 vertical to scale for size plate used (for 28 tons in plate and 24 
 tons in rivets, Kent, p. 358). 
 
156 
 
 GRAPHICAL METHODS 
 
 Another type of Z diagram is used when the type of equation 
 is A — B = ^- Theory of diagram shown in Fig. 151 
 
 K 
 D 
 
 L 
 C 
 
 K-^^ 
 
 ^--c 
 
 General equation A — B — y^ 
 
 M 
 
 M 
 . K — L = ^ (length of diagonal; 
 
 X 
 
 % 
 
 Scale of D finches) 
 
 J_ 
 
 V4- 
 
 _L 
 
 S'/2 
 
 I 
 
 ^ o-^ \ Scale of d. (indies) y 
 
 t 
 
 I 
 
 s<? 
 
 \ // 
 
 \ // 
 
 \ // 
 
 'V ^o^' 'K \?<:aleofd.(inpjJ^s) ..■ 0.3927Sd.^ 
 
 / SAFF LOAD ON SPRIN6S 
 
 
 OF ROUND STEEL WIRE 
 
 .^ 
 
 When K represents A, L represents B. 
 M represents X, N represents Y. 
 
 Scales: Let 1 in. on scale A — R units 
 then 1 in. on scale B must = R units 
 
 Let 1 in. on scale X represent S units 
 
 Let 1 in. on scale Y represent T units 
 
 c 
 
 then length of diagonal 
 
 0.3927»Sd' 
 
 RXT 
 Using above principle lay out Z diagram for W = ry _ ^ 
 
 23,562d' 
 
 S taken as 60,000 before charting, then D — d = 
 Safe load on springs of round steel wire (Fig. 152). 
 
 W 
 
CALCULATIONS 
 
 157 
 
 120 
 
 110 — 
 
 fllOO 
 
 «.— 
 
 : 80 — 
 
 ■ 
 
 70 
 
 
 ) 
 
 p 
 
 
 
 f 
 
 
 ^ 
 
 
 
 
 
 i 
 
 \ 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 r 
 
 \ 
 
 
 
 \ 
 
 
 
 
 
 \ 
 
 
 
 
 
 V 
 
 
 
 \ 
 
 
 
 
 CO 
 
 \ 
 
 
 
 
 
 N 
 
 
 
 \ 
 
 
 
 
 
 \ 
 
 
 
 
 
 ^ 
 
 
 
 X 
 
 
 
 
 
 ; \ 
 
 
 r 
 
 \o- 
 
 
 
 N — 
 
 
 
 X — 
 
 
 
 ll 
 
 \ 
 
 \ 
 
 A— 
 
 — ^■ 
 
 
 
 ^^ 
 
 
 
 ^v 
 
 
 
 
 \ 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 \ 
 
 \ 
 
 \ 
 
 
 
 
 
 \ 
 
 
 
 \ 
 
 
 
 ^T- 
 
 -\- 
 
 ^ 
 
 % '■ 
 
 V- 
 
 
 
 — ^ 
 
 
 
 ^ 
 
 
 
 * 40 
 
 ^ 
 
 ^V 
 
 
 V- 
 
 ^ 
 
 
 
 
 ^^ 
 
 
 
 ^v. 
 
 
 \ 
 
 
 
 V 
 
 
 \ 
 
 
 
 
 
 
 
 
 \ 
 
 
 V« 
 
 N 
 
 
 ■-^ 
 
 
 
 
 ■"■^ 
 
 
 
 
 \ 
 
 
 x%> 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 vt' 
 
 
 \ 
 
 
 ^^ 
 
 
 
 
 ■^ 
 
 
 
 
 \ 
 
 "^ 
 
 
 ^ 
 
 
 ■^ 
 
 
 
 
 ■'"-^ 
 
 
 
 
 \ 
 
 
 
 
 
 
 •^^ 
 
 
 
 
 
 
 ^ 
 
 X.? 
 
 
 V 
 
 
 ■-V. 
 
 
 "-^^ 
 
 
 
 
 -V 
 
 
 \ 
 
 X'6 
 
 
 •^ 
 
 
 ^~- 
 
 
 
 *~-^ 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 ■^ 
 
 
 
 
 
 
 
 
 
 
 
 N 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^_ 
 
 
 "■~~-^ 
 
 
 
 
 ~- — 
 
 ^^^ 
 
 
 
 ^^^ 
 
 
 ^T( 
 
 ^ 
 
 ^^ 
 
 
 ■ — 
 
 
 
 =— 
 
 — ^ 
 
 
 
 =- 
 
 
 s 
 
 
 
 
 
 
 
 
 i:: 
 
 J! 
 
 
 =^ 
 
 
 
 ot—"* 
 
 gSH:: 
 
 
 =— 
 
 
 ^— 
 
 
 . 10 — 
 
 ^ 
 
 ^ 
 
 
 ^^^ 
 
 ^^^ZT 
 
 
 
 = 
 
 
 
 . 
 
 — = 
 
 
 :„ — =: 
 
 '^' 
 
 
 
 
 
 
 
 
 
 
 
 
 ;7-^^^ 
 
 ^^^ 
 
 ^^^ 
 
 — ^^^ 
 
 
 
 
 
 
 
 
 
 
 ^. 
 
 3yr ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 y y 
 
 ^5*i^ 
 
 ^'' 
 
 
 
 
 
 
 
 
 
 
 
 •- X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / / 
 
 *S^ 
 
 
 
 
 
 
 
 
 
 
 
 
 / / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 / / 
 
 A,y 
 
 
 
 
 
 
 
 
 
 
 
 / / 
 
 'i>y 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 ^> 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 / 
 
 / 
 
 
 
 
 y 
 
 
 
 
 
 
 
 
 / 
 
 / 
 
 
 
 y 
 
 
 
 
 
 
 
 
 
 f 
 
 / 
 
 
 
 y 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 y 
 
 
 
 
 
 
 
 
 
 
 — ^ 
 
 
 
 .-y^ 
 
 
 
 
 
 
 
 
 
 
 — -f— 
 
 
 
 V — 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 f 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 /.. 
 
 
 
 
 
 
 
 
 
 
 
158 
 
 GRAPHICAL METHODS 
 
 Diameter ot Ftpe 
 
 200 
 
 " .^M 
 
 
 >; n 
 
 
 
 S 9 
 
 10 11 
 
 12 13 
 
 14 
 
 IS 
 
 
 ■iii 
 
 ■■ ■ '■ 
 
 ^^ t-Wn 
 
 1 m '^'^^^ 
 
 
 
 
 
 ■■ ^ff'nf'' 
 
 
 1 
 
 1 
 
 190 
 
 ^^^n^ 
 
 ::: '|- : 
 
 
 3 
 3 
 
 160 : 
 170 ■ 
 
 
 
 
 ■ 
 
 
 ™ 
 
 WfMMw 
 
 
 
 1 
 
 5 
 S 
 
 7- 
 
 
 
 
 :; 
 
 1 
 
 ;:: 
 
 ,: :; ; 
 
 
 160 
 
 II 
 
 
 
 
 
 S 
 
 
 ^M 
 
 - 
 
 ;: 
 
 : 
 
 
 
 
 ^ 
 
 9 
 
 ISO 
 
 
 
 
 
 i i 
 
 
 
 to 
 
 
 
 : : 
 
 
 :: 
 
 h 
 
 
 
 
 II 
 
 140 
 
 
 ; 
 
 
 S 
 
 12 
 
 
 
 
 !;; 
 
 ■ 1 
 
 ;!:: ::;j: :i: : 
 
 
 1 fI ■ 
 
 13 
 
 130 ' 
 
 
 ; 
 
 
 
 ; 
 
 
 f 
 
 : : :: 
 
 i 
 
 ; ;i ;j 
 
 1 
 
 U 
 
 120 ' ' ' 
 
 
 
 
 
 \ !:; 
 
 :; :M: 
 
 
 
 
 15 
 IS 
 
 •s 
 
 
 : 
 
 
 
 ::: 
 
 
 1 ^^^ 
 
 ; ■[':[: 
 
 II II II 
 
 
 17 
 
 
 1 ::::::: 
 
 ■■li ; 
 
 |: ! 
 
 
 L8 
 
 1 
 
 
 
 
 :: 
 
 mmM 
 
 
 
 |l 
 
 
 19 
 
 |100 
 
 
 
 !j :i ;:: 
 
 
 !0 
 
 K 00 
 
 :::::::; 
 
 ; 
 
 HB 
 
 
 :: 
 
 |!i 
 
 iHi 
 
 1 ■■ 
 
 21 
 22 
 
 80 
 
 i 
 
 
 
 ; ! 
 
 
 - 
 
 
 : ! :: : 
 
 
 1 
 
 I 
 
 
 ;:i' 
 
 :H 
 
 
 :;::; '. 
 
 70 
 
 II 
 
 iiilli 
 
 p' 
 
 
 
 1 
 
 i 
 
 
 
 
 
 1 
 
 2S 
 
 60 : 
 
 
 1 
 
 
 
 
 
 
 
 SO ' 
 
 
 
 
 
 j! 
 
 
 ;l 
 
 29 
 30 
 
 40 
 
 
 
 
 
 
 
 
 
 31 
 32 
 
 30 ■ 
 
 
 : : ! 
 
 II IIJJP 1 1 1 llMolli H lilfflilillllilllllw 
 
 ::: i 
 
 
 33 
 
 34 
 
 SO 
 
 1 III 
 
 ;i! :: 
 
 
 ■■— 
 
 
 I 
 
 35 
 3S 
 
 
 
 ffi 
 
 
 ; i 
 
 37 
 
 10 
 
 ■ 1 '■ ■ '■ WW 
 
 
 MlMtimpHMtti 
 
 
 1 
 
 
 |M|; liiHil 
 
 ::;; J :|: 
 
 mm wmmm w^\ 
 
 38 
 
 : 
 
 
 ro 
 
 ■|'H H : ttfflftl1"t1 1 [ 1 1 1 1-| WW\ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i 1 ] 1 1 1 111111111111 1 1 ! 1 1 1 1 1 1 1 Iffl 
 
 
 
 
 
 m 
 
 ■|-l-l-i4l-ii-l-l-H-t4 H-l 1 H-ititrl 1 1 1 1 1 1 1 1 l4UIUti4|w44l|l444Hm 11 1 II 1 1 1 1 11 1 11 ITPJI^ 
 
 
 2 
 
 4» 
 
 Diameter of Pipe 
 
 12 13 14 IS 
 
 Fio. 164. — Diagram for the proportioning of piping systems. 
 
CALCULATIONS 
 
 159 
 
 si-S^aA-A----""- — I":—-" 
 
 \_ V \^^\ ^^ . 
 
 Xaa^-X-^ Z 
 
 -A_AA^-^-A i-Mi: I-I 
 
 \ \-^A^ \ V--- - I 
 
 _^.__!^A\\A_\ : 
 
 _\__\^\\\j : 
 
 \ s Vvvv V 
 
 ._ _^^ _\A^vvVV ~ 
 
 -__\-\-\$v^-^ " 
 
 \ ^ \^V\-v « 
 
 i. f mMi : 
 
 \ \\\\\ \ : 
 
 j\ \ ^^Xa t z 
 
 5^^ ^^^O^^A Z 
 
 M ^v-^^xVv- I 
 
 '% ^AVvv\ 1 
 
 % \\^\\ - I 
 
 " i"^^S\^ I 
 
 
 v^wX ^ 
 
 ^^\^S^I 
 
 " " " -^v\^^\^^ -— ^ 
 
 -S^^S— - 
 
 \^^sv _ r 
 
 -^^1^- - « 
 
 i - -^1^ — 
 
 5^1 
 
 
 ^^^ 009 
 
 ^m— "0* 
 
 ^U- 001 
 
 3 
 
 J3 
 
 W 
 
 i| 
 
 s S 
 o o 
 
 d o 
 
 
 ■eaiipuj ui jpq jo ja^dra-eKl 
 
160 
 
 GRAPHICAL METHODS 
 
 ^ *^ "5 "^ •^ 
 
 V 1— o o o_o o 
 
 ^ 3 & S ^ 3 3 
 
 satioai biBnbg nj ;no jo 'eajy 
 
 831IDUI u] aiJOAV JO aa^era-Bia 
 
CALCULATIONS 161 
 
 Scales adopted: 1 in. = }4 unit on D scale and lower d scale 
 
 1 in. = 2,000 units on upper d scale 
 1 in. = 500 units on W scale 
 
 T^- , 2,000 2,000 
 
 Diagonal = -—- — —- = ' = 8 in 
 M X 500 250 
 
 To use, join D to lower d and from upper d draw a parallel to 
 this line to meet W in required value. 
 
 In order to present forms of calculating diagrams used by- 
 engineers the author has selected a few which have been taken 
 from the current periodicals and cover a diversified range of 
 application. 
 
 Figure 153 is used to obtain the friction and radiation losses 
 per thousand feet of pipe. The friction loss is calculated from 
 
 the formula H^ = f ,^j where 
 
 d = diameter of pipe in feet. 
 
 L = length of pipe in feet (including equivalent length for ells 
 and globe valves). 
 
 V = velocity in feet per second. 
 W = pounds of steam flowing per hour. 
 
 The diagram was constructed from the British thermal unit 
 
 (Q A\ TT7" 2 
 (1 + ~y-)-i\ 
 
 di = diameter of pipe in inches. 
 Wi = pounds of steam flowing per minute. 
 
 DIRECTIONS FOR USING FIG. 156 
 
 (o) To find cutting speed: From intersection of horizontal line corre- 
 sponding to diameter and vertical line corresponding to spindle speed, 
 foUow nearest curve and use value found in oblique line of figures marked 
 cutting speed. 
 
 (6) To find area of cut: From intersection of horizontal line correspond- 
 ing to depth of cut and vertical hne corresponding to feed, follow nearest 
 curve and use value found in oblique line of figures marked area of cut. 
 
 (c) To find cubic inches of metal removed per minute: From intersec- 
 tion of horizontal line corresponding to area of cut and vertical line cor- 
 responding to cutting speed follow nearest curve and use value found in 
 oblique line of figures marked cubic inches of metal removed per minute. 
 
 To use curve, knowing diameter of work, spindle speed, depth of cut 
 and feed, find cutting speed from (a) area of cut from (6) and cubic inches 
 of metal removed per minute from (c). 
 11 
 
162 
 
 GRAPHICAL METHODS 
 
 S S T 
 
 ^ S3 J ■ 
 
 o S 5v ' 
 
 ^ %^\ 
 
 3 ?V 
 
 c J- .r\ , 
 
 - & Iv V ' 
 
 - ^ . -'5 ^, 
 
 S -3 "S - ?^ ^ " 
 
 •S S S -^5 ^ . 
 
 S " '3 7V X 5" 
 
 >- g .r\ N "<, 
 
 »i -a " ?!v ^ S " 
 
 S ^ ■" « a.' \ ^ \. 
 
 «">•§)& K ^ S ^'' 
 
 i rq-S^tt ■ i' ^ ^ \ s 
 
 g --c^ - A ^ S ^Z 
 
 § nl ° ^ ^'^^ ^ \^^' 
 
 B .N^ ^ X "%% \ I \t 
 
 ^ c rt « ,-^ ^r\ ^ . /^ ^ 
 
 s^^gK <2^xS J v" 
 
 rt 3 M .r\ ^ \7s ^. 
 
 o " = II '"Jx X S 2 V " 
 
 1 ?i i i^^ V y^S ^ o 
 
 S 'S fe ^» ^ S *^\ S" 
 
 •S g "> ^'^ ^r- K S ^v^- 
 
 ^ " > "Jx \ s^^^ ^, ^,- 
 
 S!-g,.& ^f\ ^ 7^ ^ ^. S. 
 
 fc M \ ^l^^ \ ^^^ 
 
 S 2 c "'^ \A ^ \ ^"t 
 
 ■~ -M *3^ s S5^^ :^ \ S 
 
 •o ^^ ^^^ V/X ^ \^^^-. 
 
 c.s^ °5^ ^ 5^ X vC ^^" 
 
 E "c £ "'^ \-Zx S isi^^v ^^ 
 
 ° ^ 7t ^ ^^ V S^i^^ ^^ 
 
 o. " ^r\ ^ /\ \ i?"^. ^. . 
 
 <-A ^ ^ \ ^2 \ \ 
 
 ^^^^7 \ \^^ N i^^. 
 
 "2!^ SvS V S*- N i. ^ 
 
 ~7^N Z: S, ^AS s ^s -. 
 
 "IT S,/.^ K^^^ ^^ \ ^^' 
 
 -r\ ^t ^ $Z ^ ^ ^, - 
 
 ^M \^'^ \ ^^ ^v "^N ^ 
 
 ^A 1i. ^ ^e '^. ■^. ^^ ^v„ 
 
 c Jvo 5*A ^^ V ^ :^. ^■.°" 
 
 ^r\ ;?. x^?^ ^v, ^s --^ "^x. 
 
 ^ /X y ^^z^ ^ :^ ^^ ^^ "■ 
 
 «/A^5^v ^' \ \^ -^^ ^^ ^^. 
 
 IK K ^i^ ^ ^^ ^^ i. ^^^« 
 
 ^7^^/\^^^ ^^ ^s, ^x^ ■=^^^><s.. 
 
 A.s 3r ^. ^^ ^N^ '^^^i'^^ •= 
 
 _y^7 v^^. ^^ ^s, ~=-.^-<<^ -^, 
 
 l\/^&^\ X --.^ S5?^^^ -^•■ 
 
 ">7^X ^ ^ ~^ ^^^^=. ^-^ ^, 
 
 A^^^^^ \^ ^^>^---^ "=-^ --=. 
 
 i^X^^^ ^-^ %|i^ -^ -- ^-I ", 
 
 ,^^(^^ ^-^ %5^ --= "-^, ^^--- 
 
 ^/7</ -N ^x,>?'=~.^ ^-^^ ^-~, _:: = -- , 
 
 M/^-^ ^^-'^^^ ^^^ ;3=E- 
 
 -53; ^N^C<^-^ "-~-,-s=-^ 
 
 7^^ %^ ■"-- ^ = --T-"' 
 
 
 ^^^>"'''^ 
 
 ^:i>--' HEIGHT tfJ FEET 
 
 ■© 
 
 a 
 
 J3 
 ft 
 
 a 
 
 ■3 
 
 O 
 
 M 
 
 PR 
 
 *X3£Iji NI LH9IHH 
 
CALCULATIONS 
 
 163 
 
 Friction Load on Scale Pounds 
 30 40 GO 60 
 
 a 
 
 Ah 
 
 
164 
 
 GRAPHICAL METHODS 
 
 The loss by radiation (B.t.u.) per pound transmitted = -^ — 
 
 dn outside diameter of pipe in inches. 
 TFi = pounds steam flowing per minute. 
 
 Radiation losses per hour in B.t.u.'s are expressed hy U = 
 irduLc{Tg — To) where dn = outside diameter of pipe in inches, 
 c = constant, 
 
 Ts = temperature of steam 
 To = temperature of room 
 
 MILES 
 40 
 
 PER HOUR. 
 60 60 70 80 90 100 
 
 4-5 
 
 » 
 
 3 3-6 4 
 
 TOP GEAR PATIO. 
 
 Fig. 159. — Curves from which, when the details of any three are known, either 
 the engine speed, speed of the car in miles per hour, wheel diameter, or gear ratio 
 may be obtained. 
 
 In Fig. 154, a ready means is given of finding the number of 
 pipes equivalent to a pipe of given size. It may be used to find 
 the size of pipe equal to any other two or more sizes and is used 
 in the proportioning of pipe lines. The basis of construction is 
 the formula for volume in cubic feet of water delivered by a 
 
 iz 
 
 2ghd^ 
 
 pipe, .i..,g= 0.7854^ ^_g^_^^^ 
 
 In Fig. 155 is shown a diagram used in finding the diameter of 
 shafts when the torsional moments and Unit stresses are known. 
 
CALCULATIONS 
 
 165 
 
 S i 
 
 «! 1 
 
 Vpmj I* pjoog 
 
 S i I .1 I I I 1IJ=I - 
 
 S I 1 ■! t ■? 5 !|i«* 
 
 I ; I ^ J I I » -= li'^ I'Ji'i' , 
 
 e^ ill f i- 4 4 ^llJur/s I z — i — 3 — 5 — I — r 
 
 I i "J i I b ! =4^s5l't V '^ i ' i - .i - i - i - t =■ 
 
 ^ ^ " * e •§ e el'^^EE-' -'•■IDUpaii.jpint.tJuojipuinitidugji 
 
 "" '' ° I *! « •* ^ iliilk AiT-r- .p."...-. 
 
 P n I, 1, a<3-^*c<Eci" w ^ 
 
 '^ § S a « 1 ""■! 'I " ■ ".^/ r— 
 
 s s *' '^ « 
 
 
 ; XX X|i 
 
 i " i " i 
 
 tlti'll /o'l/lSiajig /a aSotutM^ 
 
166 GRAPHICAL METHODS 
 
 The horizontal scale is logarithmic and the vertical scale arith- 
 metic otherwise the diagonal hnes would be curved as those of 
 Fig. 154. 
 
 Figure 156 is a diagram for making various calculations in 
 connection with the removal of metal by different kinds of ma- 
 chine tools. Directions for use are given below it. 
 
 Figure 157 is a diagram used to compute the number of steps 
 in a flight of stairs when the total horizontal and vertical lengths 
 of the stairway are known. The product of rise and tread 
 equals 72. 
 
 Figure 158 is a diagram used to find the horsepower from the 
 revolutions per minute, friction load and length of brake arm 
 of a Prony brake. By means of this diagram the horsepower 
 for any length of brake arm can be reduced. to the 3-ft. arm or it 
 can be used to find the horsepower for any length of brake arm 
 by drawing a line on the diagram for that particular arm. Horse- 
 2tRNW 
 
 R = length of brake arm. 
 
 H = revolutions per minute, t = 3.1416 
 
 W = friction load on scale pan. 
 
 Figure 159 is a diagram for finding the engine speed per minute 
 when the road speed is known. It is necessary to know the wheel 
 diameter and gear ratio on direct drive. Gear ratios are given 
 along the bottom scale and miles per hour on the top scale. To 
 find revolutions per minute when gear ratio, wheel diameter and 
 miles per hour given, find number on top line corresponding 
 to miles per hour and drop vertically to cut the Une of wheel dia- 
 meter. Then move along horizontally to meet the vertical line 
 through the given gear ratio. The nearest curved line to the 
 point of intersection of these vertical and horizontal fines will 
 be the revolutions per minute. A conversion table for millimeters 
 and inches in the diameter of wheels is also given. 
 
 Figure 160 is a diagram for calculating rivetted joints, for 
 different kinds of joints, rivets and plates. The rules from which 
 the diagrams were drawn are in use by Lloyds and the English 
 Board of Trade. Directions for using the diagrams are given 
 with each one. 
 
CHAPTER VIII 
 NOMOGRAPHY 
 
 The reader of engineering periodicals is struck by the variety 
 of diagrams used by the authors of the articles therein. Some 
 are simple and others so comphcated as to preclude their careful 
 scrutiny. The rectangular coordinate diagram is one of those 
 most employed and often is a mass of squares most of them of no 
 value whatever whereas the ahgnment diagram based on nomo- 
 graphy has no lines on it except the ones marked with the scales. 
 
 It is true that a coordinate diagram often has several lines 
 plotted on it referred to different scales on its borders while an 
 alignment diagram represents but one formula and can be used 
 for the solution of but one. 
 
 As an example of the simphcity of the ahgnment diagram over 
 the rectangular diagram take the formula for weight of rails 
 
 W = ny/{L + O.OQQILV^Y 
 
 L = greatest load on one driving wheel in tons. 
 
 V = maximum velocity, miles per hour. 
 
 W = weight of rails, pounds per yard. 
 
 The rectilinear diagram is shown in Fig. 161 and requires much 
 interpolation unless the V curves are many which makes the 
 diagram hard to use. Compare this with the alignment diagram 
 for solving the same formula which is shown in Fig. 162. Here 
 three Mnes are drawn and divided into parts. The values of W 
 for any values of L and U are found by placing a straight edge 
 to connect the L and U assumed values and finding the point 
 where the edge intersects the W line. 
 
 The basis of ahgnment diagrams is the book of Prof. Maurice 
 d'Ocagne "Traite' de Nomographie" published in 1899. This 
 work has been followed by those of other writers among them 
 being the books of Prof. John B. Peddle and Prof. Joseph Lipka. 
 These books cover the subject from a mathematical standpoint 
 and should be read by those who wish to get an extended 
 knowledge of the subject. 
 
 167 
 
168 
 
 GRAPHICAL METHODS 
 
 lU 
 
 ?' 
 
 <u 7 
 a I 
 
 JC 
 > 
 
 X 
 
 '^ s 
 
 c 
 O 
 
 T5 
 
 ^3 
 
 VD 
 
 
 
 
 
 
 / 
 
 y 
 
 / 
 
 
 
 
 
 
 // 
 
 '/ 
 
 / 
 
 
 
 
 
 /^ 
 
 </ 
 
 / 
 / 
 
 / 
 
 
 
 
 (i 
 
 >!7> 
 
 
 / 
 
 
 
 
 
 ^ 
 
 
 ^ 
 
 
 
 
 
 ^ 
 
 5> 
 
 ;x 
 
 
 
 
 
 t^ 
 
 ^ 
 
 r 
 
 
 
 
 
 
 ^ 
 
 •X 
 
 
 
 
 
 
 
 /^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 20 30 40 50 60 70 80 
 Pounds per YardW 
 
 90 
 
 100 
 
 Fig. 161. — -Diagram for finding the weight of rails per yard. 
 
 (L) 
 
 rlO Tons 
 
 Pio. 162. — Alignment diagram for finding the weight of rails per yard. 
 
NOMOGRAPHY 169 
 
 A nomograph of a formula is a graph or diagram composed of 
 lines scaled relatively and placed in such relative positions that 
 the values of the variables are found on a hne crossing the scales. 
 The object is to substitute for the labor of computation a simple 
 mechanical operation such as the one previously described. It 
 is easy to read a nomogram with precision because of the few 
 lines. It provides a tabulation of all possible values, enables 
 solutions to be made irrespective of what quantity in the formula 
 is unknown and also enables one to observe instantly the effect 
 of a change, either small or great, in any one of the variables. 
 The principles of such diagrams may be given in a general way 
 and simple nomograms be constructed, but equations with many 
 unknown quantities cannot be solved graphically without higher 
 mathematics. There are in general three types of nomograms; 
 A, B and C. 
 
 A is a nomogram with three parallel rectilinear scales which 
 can be constructed whenever the formula can be written a + 6 + 
 c = 0. 
 
 If the formula is in this form already we can use regular ordi- 
 nary scales, but if it is in the form a X 6 = c it will be necessary 
 to use logarithmic scales as this can then be written log a + log 
 h — log c = 0. 
 
 B. This type has two parallel rectilinear scales and one inclined 
 to these two. If the formula is written in the form a -\-hc 
 = this type can be constructed for by taking logarithms this 
 type can generally be converted into type A. 
 
 C. In this type we have two parallel rectiUnear scales and 
 one curviUnear scale. This type is constructed when the formula 
 can be written aci ± 6c2 + c = where Ci, d and c are functions 
 of the third variable c. 
 
 ALIGNMENT DIAGRAMS 
 
 Plotting generally is connected in most minds inseparably with 
 two axes at right angles. This is the easiest arrangement 
 when two variables only are concerned. Suppose three to nine 
 variables occur. Then this method fails and vertical axes only 
 can be used to advantage. 
 
 Let us take the simplest case, viz.; X-\-Y = CoxU + V = C 
 as U- and F-axes are to be vertical (Fig. 163). Draw two verti- 
 cals AE and BF any convenient distance apart and let AE be the 
 
170 
 
 GRAPHICAL METHODS 
 
 axis of U and BF the axis of V. Draw the horizontal AB which 
 is the line on which the zeros of the scales of U and V lie. As- 
 sume values for C and calculate values of U and V for two cases. 
 Set off along AE these values of C/ to a scale h units per inch and 
 along BF the values of F to a scale of h units per inch. Let AH 
 represent the value of U corresponding to the value of V repre- 
 sented by BK and AM on U corresponding to BN on V. Join 
 HK and MN. They intersect at G through which a vertical 
 line GC is drawn called the mid-vertical. 
 
 AH represents the first value of U called Ui. 
 BK represents the first value of V called Vi. 
 
 1 
 
 V 
 
 F 
 L 
 
 N 
 K 
 
 
 
 B 
 
 C 
 
 
 Fig. 163. 
 
 Similarly AM and BN represent U2 and V2 respectively and 
 since U + V = C we have 
 
 U, + Vi=C and U2 + V2 =C (A) 
 AH, AM, BK and BN are actual distances on the paper hence 
 hXAH = Ui, hXAM = Ui, kXBK = Fi and ia X 5iV = F2. 
 Substituting in 
 
 Eq. A above (h X AH) + {U X BK) = C (1) 
 
 and (Zi X AM) + (^2 X BN) = C (2) 
 
 From Fig. 163 AH = AM -f MH (3) 
 
 BK =BN - NK (4) 
 
 Multiply (3) by li and (4) by ^2 gives 
 
 hAH = {AM X k) + {MH X ii) 
 kBK = (SA^ X ^2) - {NK X ^2) 
 
 By similar triangles 
 
 MH AC 
 
 or NK = 
 
 MH X CB 
 
 (5) 
 (6) 
 
 (7) 
 
 NK CB AC 
 
 Add Eqs. (5) and (6) and substitute for NK its value found in (7). 
 
NOMOGRAPHY 171 
 
 We then have (AH X h) + (BK X ^2) = (AM X k) + (MH X h) 
 
 -LrRArv7^ (MHXCB \ 
 
 + Ktsjs X k) - ^^ 2^ X Zaj . Substitute from (1) and (2) 
 
 we ha.veC= C +Mff (Z, - g X Z.) . HenceM^(z, - ^ X Z.) 
 must equal zero, which means that MH = or ?x - — X Z2 = 
 Accordingly, as MH is not zero, h =^h (8). If the lengths 
 AB, AC and 5C are represented by mmi and ma respectively 
 
 the Eq. 8 becomes Zi = — Z,. 
 
 mi 
 
 Also Zi + z^ = ^^ + Z, = (^^ + ^1) 7 = ^ 
 
 »^i mi mi 
 
 Whence ^ = J- and ^ = .A- 
 
 m Zi + Z2 m Zi + Za 
 
 As the values of U and 7 were any values whatever and the 
 
 constant C remains the same, the ratio — will always hold and 
 
 there can only be one mid-vertical. Also G will be a fixed spot 
 vertically over C and any one cross line satisfying the equation 
 U +V = C will locate it on the mid-vertical. GC is then fixed. 
 Let it represent the constant C to some scale say h units per inch. 
 GC X I3 = C. Substituting in (1) and (2) gives 
 
 (Zi X AH) + (h X BK) =kXGC 
 (h X AM) + (h X BN) =kXGC 
 
 Calculate the value of V when U = and plot BL to represent 
 this value. Join AL which will pass through G. 
 
 When U = 0, V = C and BL actually represents C or BL X k 
 = C but GC X k also = C. .'. BL X h = GC X k. By simi- 
 lar triangles -7^ X BL X h = ^ X BL X h or Z2 =— X Zs- 
 
 "m " h + h ■'■ ^ I +1 ■^ '^^ °^ ^3 = Zi -1- k that is the 
 mid-vertical scale is the sum of the scales along the outside axes. 
 Let us take the general case when the equation is au + bv = c. 
 Use the same diagram as shown in Fig. 163. The scales must be 
 changed, that of U being opened out a times and that of V opened 
 
 c 
 h times. BL which represented C now represents j- since it shows 
 
 the value of V when U = zero. 
 
l'2 = 
 
 172 GRAPHICAL METHODS 
 
 If I'l and l\ are the new scales along AE and BF, I'l = - and 
 
 h 
 
 h 
 hence the scale along GC = ?i + ?2 
 
 = ah' + 6Z2' 
 
 and — = T = ~^u" i'l and Z'2 would be the actual scales used, 
 ma h at 1 
 
 For a general statement we can regard these as Zi and I2 and 
 the GC scale k. k = ah + bh or — = ^- where Zi, h and k are 
 
 the actual scales used . 
 
 Summarizing. — If au + bv = c is the general equation. The 
 scale along the midvertical = a times the scale of m + b" times 
 
 CR 
 
 the scale of V and the division of AB at C is such that -7-^ = 
 
 a times the "f7" scale 
 b times the "F" scale 
 
 Most of the formulas found in practice contain products, and 
 often powers and roots besides. By taking logs the multiplica- 
 tions are converted to additions which enables the methods above 
 described to be applied with modifications. 
 
 Taking a simple case of horsepower supplied to an electric 
 motor: amperes vary from 2 to 12, volts from 110-240. 
 
 watts = amperes X volts or 746H = AV 
 
 Taking logs throughout gives log 746 + log H = log A + log V. 
 
 Let log 746 + log F = C. A = log A and F = log V. 
 
 Then the equation becomes A ,+ F = C as in the simple equation 
 
 U + V = C. We can use Z3 = Zi + Z2 and — = rr = r • 
 
 mi bh k 
 
 Instead of actual scales we must now use log scales along the 
 vertical axes. Slide rule scales are convenient for small diagrams. 
 If the B scale is used, 9.86 in. would represent two units while 
 9.86 in. on the C scale would represent one unit. Questions 
 involving more complicated formulas can be dealt with by a com- 
 bination of charts. When three axes are employed, three vari- 
 ables may be correlated or one axis for each variable. Whatever 
 number of variables occur they may be connected together in 
 threes by merely extending the graphical work of three axes. 
 The plotting of these diagrams can be done as follows: 
 
NOMOGRAPHY 
 
 173 
 
 Settle the range it is desired to indicate on each scale, draw two 
 parallel lines about 6 in. apart and mark on them a few points 
 of the scale suggested. Do this by using log paper where a log 
 scale is to be used or an ordinary paper in the case of a regular 
 scale. Assume values of the variables scaled on the outer lines 
 and obtain by calculation a value for the third variable. With 
 this value and a second value for the first variable obtain a 
 second value of the second variable. To fulfill the conditions of 
 the diagram these values lie on two straight lines joining points 
 on the two outer parallel lines and crossing at the common value 
 on the central line. One point on the central line determines it. 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 \ 
 
 N 
 
 N 
 
 
 
 
 
 
 
 
 N 
 
 \ 
 
 ^ 
 
 
 
 s 
 
 
 
 
 
 \ 
 
 
 N 
 
 C' 
 
 s\ 
 
 
 
 
 
 
 \ 
 
 \. 
 
 
 s 
 
 \^ 
 
 
 
 
 
 
 ^^ 
 
 
 \ 
 
 ^ 
 
 \ 
 
 ^ 
 
 ^ 
 
 \ 
 
 
 
 
 
 --- 
 
 -^ 
 
 
 \ 
 
 ^ 
 
 ^ 
 
 ^ 
 
 
 
 
 ■"- 
 
 ■— 
 
 
 
 ~\ 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 Fig. 164. 
 
 I0 98T6643J I 
 0, 
 
 Fig. 165. 
 
 Repeat this process at the other end of the diagram and the 
 result will be that two points will be determined giving the 
 position and scale of the central line. Figure 164 shows the three 
 lines, (a) for first variable, (b) for second, both outer scales. 
 As a rule it is necessary to use log scales. To facilitate laying 
 out these scales a scale with modulus 10 should be laid off with a 
 slide rule on paper. Figure 165 line 0] 10 will represent such a 
 scale. To find the scale corresponding to any other modulus, 
 take any point to the right of Oi and divide OOi into equal 
 parts. Find the point on this line corresponding to the required 
 modulus and erect a perpendicular, say 5B. Join with each 
 of the scale divisions on Oi 10. The points where these fines cut 
 5B will be the points of division of the new scale required. 
 
 The term modulus is used to designate the length on a scale 
 proportional to a unit difference of logarithms. For example, 
 a scale has a modulus of 2 in. because the distance on the scale 
 
174 
 
 GRAPHICAL METHODS 
 
 from the point representing 1 to the point representing 10 is 2 in. 
 The log of 1 = 0.000 and that of 10 = 1.000, the difference be- 
 tween them being unity. 
 
 When the moduli of the outer scales are not equal the modulus 
 of the middle scale is determined by the following formula in 
 which Mi = modulus of middle scale, Mi = modulus of right scale 
 and Mi = modulus of left scale 
 
 Ms = (MiM2)/(Mi + Mj) (See Fig. 166) 
 
 At the same time the middle scale must be shifted towards that 
 outer scale which has the smaller modulus. The position of the 
 middle scale is determined by the following equation in which 
 Ml and M2 have the same values as before. Di = distance 
 from middle to right and D^ = distance from middle to left. 
 
 Di _Mi 
 
 Di ~ M2 
 
 The length of any scale may be determined by the following 
 formula: L = M (log Ft — log F2) where L = length of scale, 
 M = its modulus and Fi and F^ = maximum and minimum 
 values of the variable to be represented on the scale. 
 
 NOMOGRAMS 
 
 Professor Lipka has classified nomograms and formulas in 
 such a way as to enable the engineer to determine to what class 
 of nomogram the formulas belong. This classification is pre- 
 sented here in condensed form and with explanatory notes to 
 assist the delineator or diagram constructor in deciding how he 
 shall construct the nomogram after rewriting the equation in 
 proper form for plotting. A key is given for the kind of diagrams 
 
NOMOGRAPHY 
 
 175 
 
 to be used for equations of given form. The fifteen examples 
 given at the end of the chapter have been worked out and dia- 
 grams drawn in Prof. Lipka's book. 
 
 At the end of the examples a list of nomograms is given, the 
 formula from which they were constructed and where the nomo- 
 gram can be found. This may prove of assistance to those who 
 wish to construct and use nomograms although the Hst is not at 
 all complete. 
 
 Class 
 I. FyiU) + F^iV) 
 FiiU) 
 
 NOMOGRAM FORMULAS 
 
 Formula Type of diagram 
 
 Samples. U-V = W 
 \/TFV* = W 
 P71-41 = C 
 
 V = 0.785D2ff 
 
 V = 0.524D3 
 
 Q = g.sd^Vh 
 
 W = 0.0165APi"" 
 
 FsiW) or Three parallel scales. 
 FiiV) = FsiW) (This can be brought 
 to first by taking 
 logs of both sides.) 
 or log U + log V = log W 
 or log f/ -|- 4 log 7 = 5 log W 
 or log P + 1.41 log 7 = log C 
 or 2 log I> H- log H =logV - 
 log 0.785 
 or log D -I- 2 log D = log 7 - 
 log 0.524 
 or 2 log D + }i log H = log 
 Q - log 6.3 
 or 2 log D 4- 0.97 log Pi = log 
 W - log 0.01296 
 
 W = 0.01296D2Pi°-" 
 
 ^ g-o.oi745Pa Log Ta - log Ti = -0.01745i^alog e 
 
 HP = ^^33~ooo^'^ Log (^1 - T,) -f- log S = log HP + log 
 ' 33,000 
 
 1 four 
 
 
 or more 
 
 U. F^iU)+F2(V)+FsiW)+. . . =Fi{t) 
 
 or Fi{U) • FiiV) ■ FsiW) . . . = F^) | paraUel scales 
 
 Extension of I and same method used. 
 Samples, v = cVrs or H log s +^logr + log c = 
 log V. Introduce q = }i log s + }i log r and g -f- 
 log c = log y and construct diagram for each equation. 
 
 V = CR''-^^S''-^*(0.001)-''-°*. Replace (O.Ol)-"-"* by 1.318 
 and expressing R in inches. 
 
 7 = 0.2755CR°-^^8'>-^* or 
 
176 
 
 GRAPHICAL METHODS 
 
 0.63 log R + 0.54 log *S + log C + log 0.2755 = log V which is 
 
 of form II. 
 PLAN irPLDW 
 
 HP = 
 
 = 0.000001983PLDW 
 
 33,000 (33,000) (4) (12) 
 
 This is charted in three parts: (1) PL = q; (2) DW = t; 
 (3) HP = 0.000001983 qt. 
 
 PL = q is written log P + log L = log q (form I). DW = t 
 is written 2 log D + log N = log t (form I) and (3) is written 
 log g + log t = (log HP - log 0.000001983) (form I). 
 
 III. Fi(m) = F2(f) • Fi{w) or Fi(m) = F^ivf'^^ Z chart. 
 
 Second form brought to first by taking logs. First form same as 
 second form of class I but using three natural scales two parallel 
 and one oblique instead of three parallel log scales. 
 
 D = 1.24 
 
 w, 
 
 + 0.088. Write in form 
 
 IV. 
 
 L 
 
 F, 
 
 (D - 0.088)2 
 
 (1.24)2 
 
 (form III) 
 
 Fsiw) 
 
 F2(v) Fi(q) 
 
 Two intersecting index lines. 
 
 This is included in second form of II but there log scales, here 
 natural scales. 
 
 HP = 
 
 A = 
 
 A = 
 
 Ns = 
 
 2tLNW 
 33,000 
 
 WLn, 728 
 192EI 
 
 WLn, 728 
 192aEI 
 
 nVhp 
 
 mi 
 
 or 
 
 or 
 
 or 
 
 or 
 
 HP ^ W 
 
 N 5,260/L 
 
 A, ^ W 
 L' 3,333.000/ 
 
 A = TF 
 
 L' 3,333,000a7 
 
 N^ _ VHP 
 N H^* 
 
 Two or more intersecting 
 
 V. F^(u) =F2{v) F,(w)-F,(t). 
 index lines. 
 
 Similar to second form of II but use natural scales in place of 
 log scales. 
 
 M = 0.196PDS or 
 M :D^ =F -.5.1 
 B'L 
 
NOMOGRAPHY 
 
 177 
 
 F = 
 
 OWL 
 
 „ F W ,Q m 
 2eq.^ = ^and^=^ 
 
 w 
 
 ^ 1,728WL' Q ^ 
 
 192EIP "^^^'L' 3,333,0007 
 
 VI. Fxiu):F2{v) = F,{w) : F,{q) 
 Parallel or perpendicular index lines. 
 
 and Q = AP 
 
 W = 
 
 or 
 
 576 V 
 W-.d"" = v :183.5F 
 Ri _ 234.5 + h 
 Ri 
 
 d^ 
 
 234.5 + h 
 F +P 
 
 F -P 
 
 VII. Fi{u) - F^iv) = Fsiw) - Fi{q) or 
 Fi{u) -.Fiiv) =Fz{w) :Fi{q) Parallel or 
 
 perpendicular index lines. 
 
 Second form can be transferred to 
 
 first by taking logs of both sides. 
 
 Second form same as VI only we here 
 
 use log scales. 
 
 (6) 
 
 i 
 
 (d) 
 
 Flv'' 268.337? v"" 
 
 (log H + log 268.33) 
 
 VIII. Fx{u) + FsW 
 
 W 
 / = g {Zr^ + h^) or 
 
 R = (^p - D)tFt or 
 jg/ 55,000 
 t 
 1 
 
 and 
 
 a 
 
 log Z = 2 log V 
 
 id) 
 
 log d 
 
 (6) 
 
 Fzjw) 
 F.iq) ' 
 
 Parallell or perpendicular 
 index lines. 
 
 p-D = 
 11 
 
 (&) 
 
 IX. 
 
 + 
 
 or 
 
 Fiiu) ' Fiiv) Fz{w) 
 Three or more concurrent scales 
 1.1.1 
 
 Fi(w) 
 
 + 
 
 Fiip) 
 + 
 
 + 
 
 F,{w) 
 
 F.{q) 
 
 12 
 
178 GRAPHICAL METHODS 
 
 X. Fiiu) + F^iv) ■ Fsiw) = Fi(w) 
 
 q + Nq^ = P or 
 
 P - Nq^ = q 
 
 Q = 3.33(B - 0.2H)H^ 
 w^ + pw + q = 
 w^ + pw -\- q =0 
 w^ = nw^ + pw + q = 
 
 XI. Additional forms; combined methods. 
 
 Straight and curved scales. 
 
 (a) 
 
 1 
 
 + 
 
 F,{w) 
 
 Fiiu) F,{v) Fsiw) 
 
 (b) Fr(u) +F2(v)-Fs{w) = F,{q) 
 
 (c) Fx{u) ■ F,{q)+F2(.v) F^iw) = 1 
 F,{q) ^ 1 _ 1 
 
 id) 
 ie) 
 
 Fi(.u) 
 FM) 
 
 F,{v) 
 Fi(w) 
 
 Fsiw) 
 = 1 
 
 Fi{u) F,{v) 
 
 if) F,{u) -FM + Fs(v)-F,{w) 
 
 = F,(w) 
 (g) F^{u) F,{q) + F,{v) ■ F,{w) 
 
 = F,{q) +F,{w). 
 
 \^ 
 
 "A 
 
 
 i-- 
 
 ■f 
 
 1. </u-Y' = 
 
 TOi = 10 
 
 Nomogram Examples 
 
 W in McMath run off formula. 
 10 
 
 ma = 
 
 mi = 2 mi '.mi 
 
 4:1 
 
 2. F =0.524Z)' Volume of a sphere. 
 
 mi = 10 ma = 5 1713= m.x'.m.i = 2:1 
 
 3. HP = = Horsepower of belting 
 
 33,000 
 
 mi = 5 ma = 5 m,z = mi : mi = 1 : 1 
 
 4. F = C-\/rs Chezy formula for velocity of flow of water in open channels 
 mi = 10 ma = 10 ms = mt = 5 ms = 
 
 5. HP. = 0.000001983 PLD'N indicated horsepower of steam engine, 
 mi = 10 ma = 10 ma = mi : ma = 1 : 1 
 mt = 5 ms = 10 me = m4 : ms = 1 : 2 
 
 mj : me = 5 : 3 . 33 
 
NOMOGRAPHY 
 
 179 
 
 L=F, 
 
 (D -'0.088)2 
 
 7. HP. 
 
 (1.24)2 
 mi = 0.0001 
 2wLNW 
 33,000 
 
 Tension on bolts with U. S. standard threads. 
 m-i = 0.0001 
 
 = Prony brake or electric dynamometer. 
 
 Scale Limits Modulus 
 
 HP 0-80 TO ' = . 15 
 
 N - 5,000 rrn = 0.00225 
 
 W 0-400 TOs = 0.03 
 
 L 0.5-5 mi = 0.00045 
 
 8. M = . 196 FW = Twisting moment in a cylindrical shaft. 
 
 Scale Limits Modulus 
 
 M Up to 190,000 TOi = 0.00005 
 
 D 1 in. to 4 in. m2 = . 1 
 
 F Up to 16,000 TO3 = 0.0005 
 
 9. F = 
 
 BH^' 
 
 Distributed load on a wooden beam. 
 
 F 
 
 First equation y 
 
 Second — 
 
 Scale 
 F 
 L 
 W 
 
 Second equation 
 
 Q 
 B 
 H 
 
 W 
 
 Q" 
 
 Limits 
 
 Up to 2,000 
 Up to 40 
 
 Up to 15,000 
 
 Up to 10 
 Up to 12 
 
 9 
 
 Modulus 
 mi =0.003 
 
 TO2 =0.3 
 
 TO3 = 0.0008 
 
 m2m3 
 
 m^ 
 
 TOs 
 TO6 
 
 my 
 
 TOs 
 
 0.08 
 
 TOi 
 
 = 0.08 
 = 1 
 
 = 0.08 
 = 1 
 
 10. W = 
 
 Scale 
 
 W 
 
 d 
 
 V 
 
 V 
 
 irdH 
 
 5767 
 
 Weight of gas flowing through an orifice. 
 
 Limits 
 to 0.4 
 0.2 to 2 
 
 to 3,000 
 to 200 
 
 Modulus 
 TOi = 10 
 
 TO2 = 1 
 
 TOs = 0.00135 
 rrn = 0.000135 
 
 11. 
 
 £)2 F -\-P 
 
 ¥ ^ F - P 
 internal pressure. 
 Scale 
 d 
 D 
 
 F -P 
 F +P 
 
 Lame formula for thick hollow cylinders subjected to 
 
 Limits 
 2 to 16 
 
 2 to 20 
 
 Oto 10,000 
 to 20,000 
 
 Modulus 
 TOi = 0.03 
 TO2 = 0.02 
 ma = 0.00075 
 TO4 = 0.0005 
 
180 
 
 GRAPHICAL METHODS 
 
 12. H = 
 
 Scale 
 
 H 
 
 I 
 
 V 
 
 d 
 
 2dg 
 
 Friction loss in flow of water. 
 
 Limits 
 0.5 to 20 
 20 to 1,000 
 2 to 10 
 1 to 24 
 
 Modulus 
 
 TOl = 5 
 
 mi = 5 
 mi = 5 
 mi = 5 
 
 13. 
 
 W. 
 
 I = — (3r2 + h^) Moment of inertia of cylinder. 
 
 Scale Limits 
 
 r to 25 
 
 h to 40 
 
 / to 6,000,000 
 
 W Oto 25,000 
 
 14. Q = 3.33(J5 -0.2£r)H'^ Francis formula for 
 B varies to 5 
 H varies to 8 
 Q varies to 33 
 
 15. K = 3^6c sin A. Area of triangle K with sides 6(0 to 10) and c 
 (1 to 10) and included angle A (0° to 90°). 
 
 Modulus 
 mi = 0.008 
 mi = 0.008 
 TOa = 0.000,0002 
 mi = 0.000,375 
 
 a contracted weir. 
 TOi = 0.3 
 m2 = 0.6 
 K =\2 
 
 R = 
 
 Formula 
 
 3.34F2 
 
 NOMOGRAMS 
 What it is for 
 
 D 
 
 d = ^'i(^V 
 
 Q = 95{H + 0.7)?* Weir (metric units) 
 
 V 
 irh 
 l2 
 
 Author, nomo- 
 gram shown 
 
 Hezlet book 
 
 Hezlet book 
 
 Strachan Trans. 
 A.S.C.E., Feb- 
 ruary, 1915 
 
 (D^ + Dd + d^) Volume conical frustum Strachan Trans. 
 
 A.S.C.E., Feb- 
 ruary, 1915 
 
 Speed of perforation of Strachan Trans. 
 
 ,0.75 
 
 pO.6 
 
 P = 
 
 1 + 
 
 nr" 
 
 projectile 
 
 Gordon formula for col- 
 umns (metric units) 
 
 A.S.C.E., Feb- 
 ruary, 1915 
 
 Strachan Trans. 
 A.S.C.E., Feb- 
 ruary, 1915 
 
NOMOGBAPHY 181 
 
 ^ ^ \ R — P ~ ^ Thickness of hollow Strachan Trans. 
 cylinders A.S.C.E., Feb- 
 
 ruary, 1915 
 N = 18,293(1 + 0.002837 cos 2X) Strachan Trans. 
 
 fi + ^±J)li„ K A.S.C.E., • Feb- 
 L "^ 1,000 V°^ h ruary, 1915 
 Barometric formula for determining heights. 
 5'pZ* 
 / = 384gJ deflection of uniformly loaded beam De Mussan 
 
 Pl^ - j?I T> 1Q nort^^'^^ Hollow cast-iron col- t^ T,;r 
 
 ~c ^v' " ~ l^>"OU-^r-— /XT J , • , s De Mussan 
 
 8 V iyi' umns (Hodgkmson s) 
 
 p ^ Srd^ ^^^ . ^ 64JPRn Reuleaux formula for De Mussan 
 
 UR •' Gd* springs 
 
 L2 
 
 -(third case) 
 
 F = — jT^— (fourth case) 
 
 Euler's formulas De Mussan 
 
 L2 
 
 Moment of inertia and resistance of four angles, De Mussan 
 
 equal legs 
 
 Weight and moments of four angles, unequal legs De Mussan 
 
 Weight per linear meter of steel bars and plates De Mussan 
 
 DA 
 M = 0.098 FD' = F~ Pin moments Strachan 
 
 P = ~ — v^— Gordon columns Strachan 
 
 1+ ^ 
 
 ^ 8,000 r-2 
 
 S = 125 - 
 
 3'^-\/2,000 L —L^ Impact for bridges Strachan 
 
 Public Service Commission First District of New York 
 
 Concrete (reinforced) beam formulas Strachan 
 
 V = Cr^-^^o-^^O-OOl)-"-"* Williams-Hazen Strachan 
 
 rj 6L + md J /^^ Rivets supporting _,. , 
 
 U = and n = VKu f . , ? Ehot 
 
 mp an eccentric load 
 
 Stresses in Fink Truss. Trans. A.S. 
 
 C.E. Eliot 
 
 Reinforced-concrete beams (resistance moment 
 
 Reinforced-concrete beams (resistance moment un- 
 equal) 
 
182 
 
 GRAPHICAL METHODS 
 
 Rectangular beams (yellow pine) 
 
 7?/? 
 p = -^ Flange rivets in plate girder 
 
 V 
 
 Deflection of steel beams 
 
 384i?/ 
 
 q + iVg^ = P Buerger run-off 
 
 D = (100[(p + RY-\- q^]^) - 100 Drop in 
 
 alternating-current wiring, single phase, 
 
 Two-phase, four-wire low-potential systems 
 
 Ernest W. Tipple (Line Charts) 
 2a; H- 32/ = C 
 
 P = SS.SOOD"-^ X r°-^ 
 
 Yb 
 
 Eliot 
 Eliot 
 
 Eliot 
 Eliot 
 
 Eliot 
 
 C =BY - AXovC = 
 
 x" 
 
 ^=62(|^e)andD= 48.5(1^) 
 
 L^ 
 
 72,ooor^ 
 
 HP = 0.0607D2 (~) ' 
 
 X 
 
 /fP = 0.458DQ 
 
 X 
 
 V 
 
 F = 
 
 SN'L'D 
 
 28,000i!:2 """ 54,667X2 
 
 and 
 
 General formula. 
 Thrust on drills. 
 Subtraction or divi- 
 sion. 
 For finding ideal diam- 
 eter of screw propel- 
 lers (three variables). 
 Strength of unstayed 
 flat circular plates 
 (three variables). 
 Frictional horsepower 
 loss at disc rotating 
 in steam (four varia- 
 bles). 
 Frictional horsepower 
 loss at vanes of tur- 
 bines (five variables). 
 Bending stresses in 
 locomotive coupling 
 and connecting rods 
 (six variables). 
 
 Inst. Aut. Engr's., 1917-18 (Transactions) 
 a; = a" Powers and roots of numbers. 
 
 V = at Velocity, acceleration and time. 
 
 V^ = 2aS Velocity, acceleration and space. 
 
 „ aP 
 
 F = 
 
 KE 
 
 Wa 
 9 
 
 29 
 
 Acceleration, time and space. 
 Force, weight and acceleration. 
 Kinetic energy. 
 
CF = 0.000343T^r-iV2 
 
 R 
 
 Tm = 
 
 V2 _ 62 
 
 63,025gP 
 
 N 
 
 W = — 
 D 
 
 E = 71)2 
 
 L = MP 
 
 7. =^D2S 
 
 Q = FeJ 
 
 396,000 
 
 F - Q^ 
 " ISOirDi^ 
 
 " 360A 
 
 N0M06RAPHY 183 
 
 Centrifugal force. 
 Compression ratio and pressure. 
 
 Twisting moment of solid shafts. 
 
 Hollow and solid shafts compared. 
 
 Twisting moment from horsepower. 
 
 Helical spring diagram. 
 
 Cylinder and working volume. 
 
 Horsepower from mean effective 
 pressure. 
 
 Pipe sizes for engines. 
 Valve area. 
 
 ^~ 144 
 
 John B. Peddle (Graphical Charts) 
 Chart for areas. 
 
 P = 50,210,000 (1^) ' 
 M = O.imDW 
 
 P = 0.196 -/ 
 
 r 
 
 W = l,6006/i2 
 
 
 Stewart's formula for collapsing pres- 
 sures of Bessemer-steel tubing. 
 
 Chart for twisting moment in cylindri- 
 cal shafts. 
 
 Space passed over by falling body. 
 
 Load supported by helical spring. 
 
 Load on rectangular beams. 
 Proportional Charts 
 
 Lame formula for strength of thick 
 hollow cylinders subject to internal 
 pressure. 
 
184 
 
 ORAPHICAL METHODS 
 
 P 
 
 h 
 
 w 
 
 W 
 
 /I — sin 4>\ 
 \1 + sin <i>} 
 
 gr 
 
 d = 0.013 VDlp or 
 
 d^ ^ Z_ 
 
 D 5,917 
 P 
 
 W 
 I = g(B2 + L^) 
 
 1 + 
 
 800Z)2 
 
 Resistance of earth "to compression. 
 Centrifugal force [C]. 
 
 Piston rod diameter. 
 
 Polar moment of inertia of a flat 
 rectangular plate. 
 
 Intensity of chimney draft. 
 
 Safe load on hollow round cast-iron 
 columns with flat ends. 
 
 Q = 3.33 (L - 0.2H)H^ Francis' Weir Formula. 
 
 2 ,-H,^-H^^^ 
 ^ - 3V2g jj^ _ jj^ 
 
 M = 
 E = 
 
 V = 
 
 T = 
 
 11 
 2E 
 
 W 
 
 2g __ 
 
 issV^ 
 
 (Vi^ 
 
 V\) 
 
 N 
 
 pj^QO-oorepa 
 
 Flow of water through rectangular 
 orifices. 
 
 Modulus of resilience. 
 Energy of a moving mass. 
 
 Bazin formula for flow of water in open 
 channels. 
 
 Chart for brake bands. 
 
 200.0076^11 
 
 Joseph Lipka Graphical & Mech. Computation 
 
 U XV -= W Multiplication chart. 
 
 U XV = W 
 
 ■^uv^ = w 
 
 P71.41 = C 
 
 V = 0.785DW 
 
 V = 0.524Z)W 
 Q = 6.3DWH J 
 W = O.OieSAP."-" 
 
 Combination chart. 
 
 Grashof's formula. 
 
NOMOGRAPHY 185 
 
 W. N. Rose (Math, for Engineers) 
 t — 0.7d + .0051) Thickness of edge of pulley rim. 
 
 {d ranges from 0.1 to. 5 in. 
 andD from 3 to 10 in.). 
 
 Q = -j^ X ^ d'^ = 0.34^*2; Flow of water through circu- 
 lar pipes. 
 (Pipe diameters 1 to 9 in., 
 velocity of flow 1 to 10 ft. 
 per second.) 
 
 7Q1H 
 
 T = j^r 3 Number of teeth necessary for 
 
 strength in cast-iron gearing. 
 t = 0.7 d + 0.005 D Thickness of edge of pulley rim. 
 
 jj _ -^_L Horsepower in volts and am- 
 
 746 peres. 
 
 Q = j^x|d2F = O.MdW Quantity of water flowing 
 
 through circular pipes. 
 
 T = -j^ — Number of teeth in cast-iron 
 
 gearing to transmit horse- 
 power. 
 
 Capt. R. K. Hezlet (Nomography) 
 
 C^ = a^ + 62, R = 3.34^' Molesworth, p. 251. 
 
 Q = 4,000 D^Vp Molesworth, p. 483. 
 
 W = 17\^{L + O.OOOILV^y Molesworth, p. 223. Weight 
 
 of rails. 
 t = 0.000125Pd + 0.15-s/d Thickness of cast-iron pipes. 
 
 Molesworth, p. 311. 
 
 Molesworth, p. 389. Hollow 
 shafts. 
 
 Discharge of gas in pipes. 
 Molesworth, p. 360. 
 M = PR " Compound interest formula. 
 
 P = Principal, n = Number of years. M = Amount. 
 
 R = 1 + -^, R = Amount of 1£ for 1 year at r per cent per annum. 
 
 R ■■ 
 
 ^4^ 
 
 b' 
 
 
 Q- 
 
 = 1,350I>5 
 
 -rt 
 
CHAPTER IX 
 MECHANICAL GRAPHICAL RECORDS 
 
 RECORDING INSTRUMENTS 
 
 The preceding pages have touched on graphical methods of 
 drawing diagrams but in all cases these diagrams have been 
 drawn by hand using tables on formulas as a basis. Engineers 
 have found that it is very necessary in the keeping of records of 
 many operations, or processes or conditions, to have these records 
 made by graphical recording instruments. These instruments 
 make records which show on paper the occurrences taking place 
 over some period of time. These periods may be from minute 
 to minute, hour to hour or day to day but in nearly all cases 
 the element of time enters in, which necessitates the use of a 
 clock as the driving mechanism either to rotate a circular disc 
 or move a ribbon of paper on which a marking point leaves a 
 record of its movement. This marking point is usually connec- 
 ted to an operating device controlled by the mechanism or con- 
 dition which is to be recorded- Thus a recording thermometer 
 marks the temperatures on a disc or ribbon moved by a clock. 
 A CO2 recorder shows the percentage of CO2 in the. flue gas of a 
 boiler from hour to hour by the movement of a pen actuated by 
 a gas-analysis apparatus. 
 
 A tensile-testing machine on the other hand does not depend 
 on a clock for moving the paper as the operation of the machine 
 rotates a drum on which the paper is wrapped. The same is 
 true of the paper on a steam-engine indicator and on a recording 
 dynamometer for testing the drawbar pull of a tractor. Such 
 instruments serve an important purpose in making a record which 
 can be inspected at any time, one which can easily be compared 
 to another, besides acting as a check on operations which involve 
 the personal element. It is proposed to show in the following 
 pages graphical records made by recording instruments. Where 
 possible these will be reproductions of actual records made by 
 these instruments themselves. 
 
 186 
 
MECHANICAL GRAPHICAL RECORDS 187 
 
 The first examples and the most common ones are on circular 
 discs. These have various types of ordinates as shown in Fig. 
 167 a, b and c. 
 
 a has radial ordinates with uniform scale from center to periphery. 
 b has circular ordinates, uniform scale, 
 c has circular ordinates, non-uniform scale. 
 
 Besides the disc records there are those made on a ribbon or 
 rectangular sheet of paper. These are of the types shown in 
 Fig. 167 d, e, f, and g. 
 
 d has rectangular ordinates of imiform scale 
 e has rectangular ordinates of non-uniform scale 
 / has circular ordinates of uniform scale 
 g has circular ordinates of non-uniform scale 
 
 ^s 
 
 ce; 
 
 eg) 
 
 Besides these there are circular time recorders which are not 
 divided to scale radially but have the circumference divided into 
 hours and minutes as in Figs. 170 and 178. There are pressure 
 records whose ordinates must be calibrated according to the 
 various springs or diaphragms used in them. Under this head 
 come the indicator diagrams from steam and oil engines. 
 
 In the class denoted by 167a will be found the record in Fig. 
 168 from a Venturi water-meter covering a period of 24 hr. and 
 giving the flow of water to a boiler in pounds per hour. 
 
 Figure 169 is a record from a Uehling CO2 analyzer which 
 shows the variation in CO2 found by chemical analysis of the 
 gas taken from the flue of a steam boiler. The radial distances 
 represent percentages of CO2 while the divisions around the cir- 
 cumference are time intervals. 
 
188 
 
 GRAPHICAL METHODS 
 
 To obtain an average of such a diagram it is necessary to 
 measure the diagram with a polar averaging instrument which is 
 made especially for this work. A record for the same purpose 
 but made in a different way and increasing from periphery in- 
 wards, is the polar diagram from the automatic CO2 combustion 
 
 Fia. 168. — Venturl meter records showing improvement in feed water regulation. 
 
 Chart A Chart B 
 
 Fig. 169. — Records from Uehling analyser. A shows av. 8.45 per cent COs 
 B shows av. 13.2 per cent CO2. 
 
 recorder of the Precision Instrument Co. shown in Fig. 170. 
 The blacker the chart the better the performance of the furnace 
 and fireman. 
 
 On the other hand the diagram of the Hays Automatic CO2 and 
 Draft Recorder increases from center outwards and the less of 
 
MECHANICAL GRAPHICAL RECORDS 
 
 189 
 
 Fig. 170. — Automatic CO2 recorder chart. 
 
 Fig. 171.— Combined draft recorder and C0= automatic recorder. 
 
190 
 
 GRAPHICAL METHODS 
 
 black the better the performance. This diagram (Fig. 171) also 
 has on it another scale with a record nearer the center showing 
 draft in the furnace, the scale increasing towards the center from 
 the zero circle which is half way from center to periphery. By 
 having two record lines on the same chart it is easy to compare 
 the bearing the draft has on CO2. 
 
 In Fig. 172 a diagram from a Brown Instrument Co. recording 
 thermometer is shown. This belongs in the class shown in Fig. 
 1676 and has curved ordinates with uniform scale. It is adapted 
 
 
 
 
 
 FiQ. 172. — Chart from recording thermometer. 
 
 to temperatures above 100°F. and makes a 24-hr. record. An- 
 other type of multi-recording instrument is the Bailey Boiler 
 Meter which makes the diagram shown in Fig. 173, 
 
 The inner portion of the chart contains records of steam tem- 
 perature in red and flue-gas temperature in blue. Distances 
 between concentric circles represent degrees of temperature 
 according to the scales for the respective curves. 
 
 The outer portion of the chart is divided into circles denoting 
 rate of flow of air or steam. The records are in blue for air and 
 red for steam. Comparisons can be easily made between the 
 
MECHANICAL GRAPHICAL RECORDS 
 
 191 
 
 four curves when they are located on the same sheet which is 
 rotated by clockwork. These charts are 12 in. in diameter. 
 
 We find in type 167c the records made by a G. E. flow meter 
 which records steam flow in pounds per hour, gallons of water 
 per minute or boiler horsepower (using 30 lb. per hour as a unit) . 
 This is shown in Fig. 174. The readings increase from the center 
 outwards and the divisions are unequal. 
 
 Fig. 173. 
 
 A type of chart containing a time record as well as a pressure 
 record is shown in Fig. 175. The outer part of the disc is divided 
 into 10 sections of 6 sec. each by concentric circles over which 
 a pen travels which records the distance travelled. The dis- 
 tance between the ordinates represents 100 ft. The chart is 
 made to rotate by an odometer wheel which rolls on the ground 
 
192 
 
 GRAPHICAL . METHODS 
 
 and transmits motion to the chart by a flexible shaft and gearing. 
 The drawbar pull is shown by the irregular marking between the 
 curved ordinates. The pen marking in the annular space at 
 the margin of the chart indicates the elapsed time. A clock 
 trips the pen at one minute intervals. This dynamometer is 
 used for recording the horsepower deUvered at the drawbar by 
 tractors and was devised by the Hyatt Roller Bearing Co. As 
 stated above it gives drawbar pull, time and distance from which 
 the drawbar horsepower can be computed. 
 
 Fig. 174. — Chart from General Electric flow meter. 
 
 In Fig. 176 is shown a chart belonging to the time recorder 
 class in which the disc is turned by clockwork, and the record 
 made whenever motion or operation takes place. This chart 
 indicates when a motor truck is in operation by making a broad 
 black mark. The narrow line shows the truck is standing still. 
 The margin is divided into 24 hr. which are subdivided into 10- 
 min. intervals. 
 
 A type of chart embracing more records than one is shown by 
 the Bristol Time Recorder in Fig. 179. This type of chart may 
 have from 1 to 12 records on it of operations which may or may 
 
MECHANICAL GRAPHICAL RECORDS 
 
 193 
 
 not have any relation to each other. In the chart shown, the 
 outer circle registers feed-water consumption, the next, coal 
 going to stokers, third switchboard breaker openings, fourth 
 drop of pressure in hydraulic elevator line and fifth operation of 
 
 HVdTT ROUEII flMRINO CO. ,_,- ,_ ,/,,-«, 
 
 CHicMM 4 OHf ' <iu~ir am IK. IU03 
 
 •.Mr TBI Mrf. 0. Cub Junior':— v/flLus T^Rcfon Co. t™ok 
 
 SrlLHS. 71x713. |>«|[« a-14' J.IXBSE "Ifexns STECIHLjBHEBHEnBorftMa PlHi 
 
 ,,«w«.llUT^Le7QWEl'0F««:itkenfn&oBiuBdMixcD.OLnY^NiiBi.iic«&o)L, ViTioiMSon. HogWiiiw 
 • nnHOta SQOor-r. toui nmuu. tui> 2.e.ff nina. <b/i. 1^41 e.iS" 
 
 thrrb Dnii tutt-in. Drw ■« 
 
 plHtt <■««« r<»x>.i«. ^^'^ run BBM.'P 
 
 ElTKr. 14.7.5- 
 
 MiiM Ts* leuLss ie.e3 2.15* esao 14.75* 
 ■MM. as-- I6ZS - IZ.ZE r.B 32 so is.s 
 
 MMIUO.a.P. 
 
 ILCkW. 
 
 L»rt. ^ow, rw ac««,«io, gS?«» |^^;i"=^?H?3;.'¥!f.;a"R!iS?? 
 
 Diuitw 74-17 nun. 
 
 TWWCTQB flWP WOroR DftTH _ _ fixl Uii4 &ll«OUNE hms Ttil 
 
 MbW KliK WnuHCSHTI B<fl ^yi BtnkaS'/a Cytlndin 4 Cy^i 4 OtwIuiriMBI SI 
 
 Hsnul SnK 90O IL r. M_ HHnna.H.P. ZS TtnM Sots' rnM (il. TrMV WiUM 300O 
 
 RfwOMii 48''au.N l£- riftUveflw.C-aH'nin'CbHStHiiiu.rnariHbMi 3Q' ou.N fi' pki e HYNTrs 
 TRANSM(SSION 5VSTEM Tm SeLECTWC SLIOINeGenlt eiirKtiii SZ-IE. Tg t <Mo 
 
 HoteuraUMitnaT^ITt CM YES ciir None btHaua COnFLEtfeLYOPu HOHE 
 
 suftao. TMri No. fMv 13 H'^R'TTS Bill KTHIfUS-r puu None 
 
 Fig. 175. — Record of dynamometer test on tractor. 
 
 an ash conveyor. The instant of operation is shown by the break 
 in the continuous line. The chart is rotated by clockwork and 
 covers a 24-hr. period. Circular recording instruments are 
 limited from the fact that the record usually has to be changed 
 
 13 
 
194 
 
 GRAPHICAL METHODS 
 
 every 24 hr. whereas with the continuous tape the record may- 
 run continuously for weeks or months. It can also be made to 
 travel a high speed for short periods thus enabling a better graphic 
 record to be made of rapidly occurring operations. 
 
 Hea^y mark showsv/hen 
 ' truck iimmotitm: Narrow 
 '' line showsiruck is 
 ^fanding^fill 
 
 .Fig. 176. 
 
 Fig. 177. — Record from Bristol time recorder. 
 
 Figure 167d record is made by a pen moving on a strip of 
 paper driven along by clockwork. Figure 178 is a record of 
 this type made on a " Recordograf " and shows the movement 
 
MECHANICAL GRAPHICAL RECORDS 
 
 195 
 
 and stoppage of a truck. The tape in this case is 36 hrs. long. 
 The squares represent 5 min. each along the tape and }^i mile 
 each across the tape. It can be readily seen that horizontal 
 
 m 
 
 I 
 
 t 
 
 m 
 
 ffi 
 
 5 
 
 ft 
 
 &-;: 
 
 Awsncetn TeiximetepQ<3. 
 
 Fig. 178. 
 
 lines or abscissas represent stoppages and inclined lines move- 
 ments, the steeper the Une the faster the movement. 
 
 In Fig. 179 is shown a graphic record of the electric current 
 used in operating a shear scarfer. The movement of the paper is 
 
 le 
 
 tt 
 
 ffii 
 
 I 
 
 iLnn'''j»^"T!T'n:M 
 
 P 
 
 m:'WM'rM''M 
 
 s 
 
 Fio. 179. — ^Reoord from shear scarfer. 
 
 accomphshed by clockwork, the speed in this case being 24 in. 
 per hour. The peak load varies, as shown by the irregular line, 
 from 10 to 13 kw. 
 
 A record made by the pulsations of the human heart is called a 
 cardiograph. Such a record is shown in Fig. 180. This is 
 
 iiiiinniiiiiiiiniiiiiiuiiiiiiiffliiiiJiiiiiiiiiiiiiiifiiiiiiiii 
 
 Tio. 180. — Cardiograph of electro-currents developed in the human heart. 
 
 made by the electric currents developed in the heart at each of 
 the contractions of that organ. These currents deflect a galvano- 
 meter filament which in turn throws a shadow on a sensitive film 
 
196 
 
 GRAPHICAL METHODS 
 
 which is moved at a constant speed of 1 space per Ks sec. The 
 10 vertical spaces equal 1 cm. and measure 1 miUivolt of current. 
 The study of the direction, time relations and magnitude of the 
 currents developed by the heart contractions constitute modern 
 electro-cardiography. Figure 181 shows the pressure curve of 
 the heart pulsations direct taken by a sphygmograph fastened 
 to the wrist or throat of the patient. The record is made on 
 
 A— 'fyp^i||-A..,-v^ 
 
 Carotid Pulse Jugular Pulse 
 
 no.3 aortic insufficiency 
 
 Fig. 181. 
 
 smoked paper which is afterwards fixed to prevent obliteration. 
 The paper moves at a uniform rate which is regulated by the 
 operator and the humps in the curve depend on the frequency 
 of the heart pulsations. 
 
 Another graphical record of a similar kind is that made by a 
 strainograph on the concrete ship "faith" and shown in Fig. 182. 
 The notches in the top line indicate the speed of the paper as they 
 are 15 sec. apart. Ordinates represent tension and compression 
 to the scale indicated on the left-hand margin. 
 
 200 
 ISO 
 o 160 
 a 140 
 e 120 
 I" 100 
 Q 80 
 o 60 
 g 40 
 
 e eo 
 
 ,2 
 
 
 
 
 Time in 
 
 /Ssec 
 
 mter\/ah 
 
 
 
 
 
 
 
 
 
 
 
 7-49-45- 
 
 May 24- 
 
 
 
 
 
 
 
 
 '-49-30 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 V J 
 
 \ > 
 
 \ 
 
 / \ 
 
 / \ 
 
 f \ 
 
 / \ 
 
 ' \ i 
 
 V, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 STRESS IN DECK BEAM BETWEEN HATCHES 
 CONCRETE SHIP "FAITH " 
 Fig. 182. 
 
 . A similar record is shown in Fig. 183 which was made on a 
 Westinghouse totalizing wattmeter. The ordinates are watts 
 of electric current and abscissa time intervals of 10 min. each. 
 
 Records of the same kind but having a vertical scale of volts 
 or amperes are made on graphic voltmeters and ammeters. 
 
 A record of pressure of gas is shown on the chart of Fig. 184 
 which was taken from a gas pressure recording meter. This 
 
MECHANICAL GRAPHICAL RECORDS 
 
 197 
 
 measures the actual pressures of gas passing. Below the zero 
 line vacuum indications are recorded. 
 
 A recording instrument of especial value in railway work or in 
 fact any line of transportation is the Wimperis accelerometer 
 
 O 
 
 O 
 
 c 
 
 |w^|ffi|lli 
 
 o 
 
 c 
 
 o 
 
 10AM 9AM 
 
 Fig. 183. — Westinghouse graphic meter record. 
 
 and equilibristat. It gives two kinds of charts, (1) one showing 
 starting acceleration, braking and coasting as indicated in Fig. 
 185. This is a record made on a recording accelerometer during 
 the time a train was stopping at a station and starting from the 
 same station. Ordinates denote accelerations in feet per second 
 
 « 
 4 
 
 '. 3 4 .. 5 6 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 
 
 
 
 
 
 
 
 
 
 
 ir""' 
 
 1 W. fl. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 "<v 
 
 
 
 
 
 
 \ 
 
 
 
 10 
 
 
 
 \ 
 
 
 
 
 
 
 x^ 
 
 X 
 
 
 
 
 
 
 \ 
 
 
 -y 
 
 \ 
 
 
 
 ^^ 
 
 
 ^^ 
 
 \ 
 
 
 
 
 -* — . ■ 
 
 
 \ 
 
 
 
 
 
 
 v 
 
 
 
 
 
 
 > 
 
 .^^-^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 10 
 
 
 
 Fig. 184. — Gas pressure recording chart. 
 
 per second and abscissas are time intervals. Motion of the paper 
 is produced by clockwork. (2) When used as an equihbristat the 
 needle points in the direction of motion of the train or vehicle and 
 moves according to influences tending to throw the vehicle out 
 
198 
 
 GRAPHICAL METHODS 
 
 of level towards either side (centrifugal force on curves, or eleva- 
 tion of either rail). 
 
 On straight sections of track this will be indicated on the graph- 
 ical record. This is shown by Fig. 186 which is a partial equilib- 
 
 .]■ ^ 
 
 
 S 2 
 
 
 f-m,,^^"'^'!^.,^. 
 
 a. 
 
 — QU££N6 ffOADzz:^ 
 
 =iu — 
 
 
 v..^^^^ 
 
 ^-Ul U KtNl HUAI) 1 
 
 o ? 
 
 -\ 
 
 
 \ i 
 
 t^ 4- 
 
 <. 
 
 
 X, , i 
 
 
 
 
 
 1 
 20 
 
 4-0 
 Seconds 
 
 NJ 1 
 
 60 80 
 
 ACCELERATION CURVE FOR L.B.&S.C.RY. 
 A.C.ELECTRIC TRAIN 
 Fig. 185. 
 
 ristat diagram taken from an express train of the London and 
 South Western Railway. The upper hne gives the speed in 
 miles per hour. The line just below the arrow is mileage. The 
 oscillation curve is given by the needle. The lowest line gives 
 the layout of the railway, the figures being radii of curvature 
 
 
 47 
 
 '/2 M.P.H. 
 
 
 
 16 
 
 - 
 
 
 
 "' 
 
 
 
 n 
 
 1 
 fi 
 
 4 
 
 
 T^ 
 
 6 
 
 K 
 
 
 ? 
 
 't 
 
 / 
 
 20 
 
 •^■^'"TiJ^ 
 
 '\~^.^^-\^^^.^ 
 
 
 
 no 
 
 Fig. 186. — Equilibristat diagram. 
 
 in chains. Ordinates in this case represent inches out of level. 
 In Fig. 187 is a record of acceleration of a 15-hp. touring automo- 
 bile made on the Brooklands track by a recording accelerometer 
 made especially for automobiles. The ordinates show accelera- 
 tions in feet per second per second. 
 
MECHANICAL GRAPHICAL RECORDS 
 
 199 
 
 The Yarway blowoff meter prepares a graphic record as shown 
 in Fig. 188 on which appear two separate records, one of which is 
 made with a short pen (line A) and which is magnified 10 times. 
 The range of the short pen is to 33,000 lb. per hour and the 
 long pen from to 300,000 lb. per hour as shown by the scale 
 on chart. Different colored inks are used on the two pens and 
 they are spaced 2 hr. apart to prevent colliding. There are two 
 
 o<u. 6 
 0) oj * 
 < 
 
 ISHP.nURINGCAR 
 BROOKLANDS TRACK 
 
 " 10 y ZO 30 
 
 10 y zo 
 
 Seconds 
 
 Fig. 187. — Acceleration diagram. Wimperis acoelerometer. 
 
 sets of figures at the bottom, upper in black, lower in red, indi- 
 cated by roman and italics respectively. Corresponding chart 
 lines are shown at '5 and 4. The motion of the chart is obtained 
 from a clock. The movement of the pen is obtained from a float 
 actuated by the water passing through the floatchamber. 
 
 Besides this type of chart there is one of a similar kind which 
 shows two records of different kinds of conditions as shown in 
 
 300,000 
 Z50,000 
 200,000 
 150,000 
 100,000 
 
 50^000 
 
 Scah of chart. 
 lsq.in.=ZI7j8?0lb. 
 
 This area represents 
 
 ,/OjOOOIb. 
 
 
 
 
 —~ 
 
 ~ 
 
 — 
 
 r^ 
 
 P" 
 
 -n. 
 
 — 
 
 — 
 
 
 
 
 1 I 
 
 
 m 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ; 
 
 t 
 
 ' I 
 
 
 
 
 
 
 1 
 
 n 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ( 
 
 i; 
 
 I/I 
 
 / 
 
 / 
 
 
 
 
 1 
 
 
 
 i 
 
 
 
 
 Lt 
 
 AK 
 
 
 
 
 
 
 
 
 / 
 
 
 / 
 
 / 
 
 / 
 
 
 
 
 
 
 rl'i 
 
 
 ^ 
 
 
 / 
 
 s 
 
 
 V 
 
 
 \ 
 
 
 
 
 /A 
 
 ^/ 
 
 1 
 
 / 
 
 
 
 
 
 / 
 
 
 vi 
 
 
 
 
 
 
 
 
 
 
 
 — . 
 
 .^ 
 
 ^> 
 
 
 
 y 
 
 G 
 
 ._ 
 
 -. 
 
 
 
 / 
 
 
 
 1 \ \ 
 
 
 
 
 -^ 
 
 
 
 
 ightll 
 
 10 9 8 7 6 
 P.M. 
 
 5 4 
 
 3 2 1 IZ II 
 Noon 
 
 10 9 
 
 8 1 6 5 4 3 Z 1 
 A.M. 
 
 12 
 
 9 
 
 6 16 5 4 
 
 3 1 
 
 1 12 II 10 9 
 Noon 
 
 3 7 
 
 6 5 4 3 2 1 12 1 
 A.M Night 
 
 10 
 P.M 
 
 CHART MADE BY YARWAY BLOW OFF M^TER 
 Fig. 188. 
 
 Fig. 189. The upper chart ordinates represent rate of flow of 
 water in pounds per hour while the ordinates of the lower record 
 indicate temperatures in degrees Fahrenheit. Such a record is 
 advantageous from the fact that comparisons are readily made 
 by inspection and show conditions at the same hourly periods. 
 This chart was made on a Lea V-notch recording meter. 
 
200 
 
 GRAPHICAL METHODS 
 
 2P.M. 1P.M. 12N00N tlA.M. 10A.M. 9A.H. 
 TEMPERATURE RECORD DEGREES FAHRENHEIT 
 
 Fig. 189. — Chart from Yarway-Lea recording meter. 
 
 TRANS FOR MA T/ON CC/RVFS 
 Ordipa-tes = Temperatures 
 
 /thsissaa = Temperature differences between samp/e 
 and non-recalescing bod^ 
 
 Fig. 190. — Leeds and Northrup transformation recorder curves. 
 
MECHANICAL GRAPHICAL RECORDS 
 
 201 
 
 Figure 190 is taken from a Leeds and Northrup recorder 
 designed to show the transformation curves obtained when steel 
 is heated above its critical temperature and allowed to cool. 
 The curves are drawn by a pen whose position is controlled by 
 
 N0.4-JUDSON S//4/0P 
 
 Port 
 
 OAR LOCK PRESSURE D/AGR/IM 
 Fig. 191. 
 
 an operator who follows the movement of two spots of Hght which 
 show on a ground glass screen. Their movement comes from 
 two reflecting galvanometers connected to a potentiometer 
 which in turn is connected with a sample of the steel under test 
 and to a non-recalescing body. The ordinates are temperatures 
 
 ONE INCH DRAUGHT 
 
 FCUE DRAUl 
 
 1^^ 
 
 Boikf.— 
 
 
 Sloket-SlM, 
 
 p,tna><U 
 
 
 Z)ate 
 
 12 
 
 ^ ^ 
 
 3 4 
 
 3 6 
 
 '-'' -r- 
 
 5 
 
 
 Wlilliili 
 
 Mi 
 
 ^ 
 
 Pig. 192. — Precision combustion and draft recorder. 
 
 and the abscissas are temperature differences between the steel 
 and the non-recalescing body. 
 
 In Fig. 191 is shown a form of recorder similar to the one shown 
 in Fig. 180. It was designed and used by the author to record 
 the pressure exerted by an oarsman on the oarlock of an eight-oar 
 
202 
 
 GRAPHICAL METHODS 
 
 Fig. 193. — American trainagraph records of air pressures. 
 
 
 
 
 
 
 
 
 =-p.M. - 
 
 • 
 
 
 - 
 
 " P.M z 
 
 
 - 
 
 - 
 
 - 
 
 D z 
 
 
 - 
 
 - 
 
 - 
 
 
 
 3 X 
 
 - : 
 
 
 4 
 
 
 
 3x 
 
 - = 
 
 
 - i - 
 
 
 
 -|x _ 
 
 _ ^ 
 
 
 - d - 
 
 
 
 - 5 
 
 1 - 
 
 - E 
 
 
 " 3 " 
 
 
 
 - = 
 
 h - 
 
 - ^ - 
 
 -i 
 
 
 
 ^ 
 
 1 
 
 z 
 
 - E - 
 
 - 3 n 
 
 9 ~ 
 
 
 -: 
 
 1 
 
 - = - 
 
 - J - 
 
 
 - 1 
 
 -^ 
 
 I - 
 
 3 
 4 
 
 
 ^ 1 = 
 
 
 - 
 
 
 - 
 
 
 
 - 
 
 - 
 
 - 
 
 
 
 -4i - 
 
 -X 
 
 3 
 
 - 1 - 
 
 
 "11= 
 
 -3' - 
 
 - i - 
 
 - z| - 
 
 
 
 Pi 
 
 oduc 
 
 togr 
 
 FlQ. 
 
 aph 
 194 
 
 Record 
 
 
MECHANICAL GRAPHICAL RECORDS 
 
 203 
 
 racing shell for every stroke taken during a 4-mile row. The 
 abscissas represent successively lengths of power stroke and 
 recovery. Ordinates represent pressures on the oarlock at each 
 point of the puUing stroke. The movement of the paper is 
 obtained from the angular movement of the oarlock about a 
 pivot. 
 
 In some cases it is advantageous to have two or more records 
 in parallel on the same strip of paper. A sample of this kind is 
 shown in Fig. 192, a record made by a Precision CO2 recorder 
 and a draft gage. The abscissas are periods of time, the ordinates 
 
 
 
 
 
 
 100 TON 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 r 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Fia. 195. — Graphic wheel press record chart for the American hydraulagraph. 
 
 representing pressures in the upper and percentages in the lower 
 chart. Comparison can easily be made and the influence of 
 draft on CO2 noted. 
 
 Figure 193 shows a record of the air pressures on a train made 
 by the American Trainagraph. Here there are three pens record- 
 ing pressures in air reservoir, brake pipe and brake cyhnder, 
 ordinates representing pounds per square inch. A comparison of 
 operations can be made by these three curves as they are drawn 
 at the same time and from closely connected pipes. 
 
 In Fig. 194 the record from a Productograph is shown. This 
 has four records but as many as 20 pens are used in a single record- 
 ing instrument. This records motions or operations of machines, 
 the paper moving by clockwork and the pens by electrical current. 
 
 In Fig. 195 is a diagram from an American Hydraulagraph. 
 This is a simple succession of diagrams whose ordinates denote 
 
204 
 
 GRAPHICAL METHODS 
 
 tons pressure, the abscissas representing any distances whatever 
 but long enough to move one diagram away from the space to be 
 occupied by the one to follow. 
 
 Figure 196 is a record of the pressure in a steel furnace made on 
 
 Fig. 196. — Bacharach blast furnace pressure record. 
 
 a Bacharach pressure recorder. The ordinates give pressures 
 in millimeters of water. The advance of the paper ribbon is by 
 means of clockwork. 
 
 A graphic record of draft in furnaces is shown in Fig. 197. 
 The records here are from a hydro-differential draft gage and 
 
 0.4 
 02 
 
 ttM.i_j — I 
 
 6189I0III2IZ345GT89I0 1II2I'J3456 
 Noon Midnight 
 
 /ICru/ll DRAWING FROM A DIFFERENTIAL DRAFT-DRAFT RECORDER 
 Fig. 197. 
 
 from a combustion chamber gage and represent tenths of inches 
 of mercury. Movement of the paper is obtained from a clock. 
 There are several types of machines which draw a record on 
 paper having rectilinear coordinates the record being used to 
 
MECHANICAL GRAPHICAL RECORDS 
 
 205 
 
 check the observations of the operator. A tensile-testing ma- 
 chine is an example of this. 
 A diagram from a Riehle testing machine is shown in Fig. 198. 
 
 UO.DOO 
 
 M 0.2 0-3 ■ 0.4 0.5 0.6 
 FiQ. 198. — Strain diagram from a Riehle testing machine. 
 
 The record shows the elongation of the test specimen by abscissas 
 while ordinates represent the load applied. This is used for test- 
 ing metals. The strain is magnified 50 times. Other diagrams m 
 which revolutions are used for abscissas and also torque are shown 
 
206 
 
 GRAPHICAL METHODS 
 
MECHANICAL GRAPHICAL RECORDS 207 
 
 in Fig. 199. All of these diagrams are actual curves made by the 
 Olsen Universal Efficiency Testing Machine under working con- 
 ditions. The scales used are indicated on the axis. A description 
 of each diagram follows. 
 
 No. 1. Curve No. 1 is that of one side of a file tested. 
 
 In this test a standard tool-steel test bar is used and the rela- 
 tion between material filed and number of revolutions recorded 
 with the file under definite standard pressure and operating under 
 standard cutting speed. 
 
 No. 2. Curve No. 2 is that of a hack-saw blade test. 
 
 In this test, as in the file test, a standard steel bar is used, 
 showing relation between depth of cut and revolutions recorded 
 under standard pressure and cutting speed. 
 
 No. 3. Curve No. 3 represents the test on a M-in. high-speed 
 driM. 
 
 In this test 0.30 carbon steel shafting is used as standard ma- 
 terial, with a drill speed of 360 r.p.m. and feed of 0.01 in. per 
 revolution. The pressure at the point of the drill was noted at 
 1,100 lb. 
 
 No. 4. Curve No. 4 represents the test on a %-in. carbon steel 
 drill. 
 
 The conditions of the test, excepting for the speed, was the 
 same as in the case of the high-speed drill. The speed in this 
 case being only 90 r.p.m., while the pressure at point of drill 
 was 1,350 lb. 
 
 Comparing No. 3 and 4. From the curves and data reported 
 it can readily be seen that the high-speed drill operates under 
 less pressure and less torque than the carbon drill, and at the 
 same time doing four times the amount of work. The power 
 factor is thus many times less using the high-speed drill and the 
 strain on the machine correspondingly less. 
 
 No. 5. Curve No. 5 is of a machine die and in this test a rod 
 is run through the die under standard conditions and relation 
 between torque and penetration recorded. 
 
 No. 6. Curve No. 6 is the test of a 2%4-in. carbon drill 
 drilling standard material at a speed of 370 r.p.m. and under a 
 gravity of 200 lb. 
 
 The relation between torque and penetration is recorded, and 
 we wish to call special attention to the heavy torque required for 
 drill to penetrate the material. This added torque often breaks 
 drills and proper grinding will largely remove the trouble. 
 
208 
 
 GRAPHICAL METHODS 
 
 No. 7. Curve No. 7 is the test of a >^-in. nut tap in tapping 
 hole bored as shown by curve No. 6, running at speed of 90 r.p.m. 
 The relation between torque and penetration is recorded and the 
 area of diagram represents the work of tapping. 
 
 Fig. 200. 
 
 end 
 
 mnincf 
 
 Average Pull 42 Lbs. 
 Fig. 200A. 
 
 In Fig. 200 are shown the curves made on a textile testing 
 machine recording attachment while four different strands of 
 yarn were being broken. Ordinates represent stretch of the 
 yarn and abscissas represent the pull which produces the stretch. 
 
MECHANICAL GRAPHICAL RECORDS 
 
 209 
 
 Dynamometer Tests of Tractors and Plows 
 Remarks: 8-16 Int'l Tractor, at Hinsdale farm. 
 
 10" Wheels — extension angle lugs — right hand wheel in furrow. 
 To determine d.b.hp. — and d.b.p. as follows: 
 
 Sheet No. 2 A 
 Test No. 22~ 
 
 Section 
 Number 
 
 "A" 
 Draw- 
 bar area 
 
 "B" 
 Length 
 
 "C" 
 Velocity 
 M.p.h. 
 
 "D" 
 D.b.p. 
 
 "E" 
 Db.hp. 
 
 Average 
 
 Depth 
 
 area 
 
 "G" 
 
 Plowing 
 
 depth 
 
 "H" 
 Dbp in 
 depth 
 
 20 
 21 
 22 
 23 
 
 4. SO 
 3.38 
 1.72 
 2.38 
 
 3. 03" 
 1.99 
 1.13 
 1.64 
 
 1.72 
 1.13 
 0.64 
 0.93 
 
 1485 
 1699 
 1522 
 1451 
 
 6.82 
 9.02 
 2.61 
 3.61 
 
 10.75 
 7.66 
 3.76 
 5.45 
 
 9.10 
 9.70 
 3.66 
 
 8.64 
 
 163. 
 175. 
 176. 
 168. 
 
 'A" Draw bar area: Measured by hand with a planimeter for each 30 sec. division. 
 'B'* Length: Distance of paper travel in 30 sec. scaled. 
 
 'C" Velocity in m.p.h. = length time 25 divided by 44. 
 
 'D'* Draw bar pull (d.b.p.) = "A" -^ "B" X 1000(50# spring gives 1000# per inch) 
 ■E" Draw bar h.p. (d.b.hp.) = "C" X"D" -h 375. 
 *F" Average depth area = (DB + DR) divided by 2. 
 
 'G" Plowing depth — ("F" -i- "B") X2 +2(.depth readings are reduced in the ratio 
 of 2 to 1. Plows set 2" deep when pencils record zero on chart. 
 'H" Draw bar pull per inch depth = "D" -r "G." 
 
 AH results obtained by comptometer, tables or logarithmic charts, except "A" and "B" 
 
 Dynamometer Tests of Tractors and Plows 
 Remarks: 8-16 Int'l Tractor at Hinsdale farm. Wheat Sheet No. 2B 
 
 Stubble — -dry — new standard extension on lug on 10" wheel 40" diameter. Test No. 22 
 
 
 Furrow wheel 
 
 Land wheel 
 
 Section 
 
 "J" 
 
 
 
 "M" 
 
 
 
 Number 
 
 Revolu- 
 
 "K" 
 
 "L" 
 
 Revolu- 
 
 "N" 
 
 "P" 
 
 
 tions and 
 
 Ground 
 
 Per cent 
 
 tions and 
 
 Ground 
 
 Per cent 
 
 
 paper 
 
 travel 
 
 Blip 
 
 paper 
 
 travel 
 
 slip 
 
 
 travel 
 
 
 
 travel 
 
 
 
 20 
 
 10-2. 95" 
 
 73. 75' 
 
 29.6 
 
 8-2. 85" 
 
 71.25' 
 
 14.9 
 
 21 
 
 9-2. 13" 
 
 53. 25' 
 
 43.6 
 
 7-2. 18" 
 
 54. 50' 
 
 25.6 
 
 22 
 
 7-1.07" 
 
 26. 75' 
 
 63.5 
 
 4- .99" 
 
 24. 74' 
 
 40.9 
 
 23 
 
 12-1.72" 
 
 43. 00' 
 
 65.8 
 
 7-1.75" 
 
 43. 75' 
 
 40.3 
 
 24 
 
 10-1.55" 
 
 38. 75' 
 
 63.0 
 
 7-1. 56" 
 
 39.00' 
 
 46.8 
 
 25 
 
 8-1.21" 
 
 30. 25' 
 
 63.9 
 
 5-1.31" 
 
 32. 75' 
 
 37.4 
 
 26 
 
 7-1.81" 
 
 45. 25' 
 
 38.3 
 
 7-2. 03" 
 
 50. 75' 
 
 30.8 
 
 "J" Number of revolutions made in approximate 3 sec. 
 
 measured for the number of revolutions made. 
 "K" Paper travel measured times 25. 
 "L" 100{K divided by peripheral travel of drive wheel). 
 "M" — "N" — ."P" corresponding valves for land wheel. 
 
 Exact distance of paper travel 
 
 70^ 
 
 Vord Every Revolution ^ f 
 
 Time Record Evert^SOsec. 
 
 Mmunng Wheel X?" 
 
 II«M Every Revoluhorf aghmndPlo>» 
 
 „. . CDb)- 
 
 < D'^'^io^of LeffHmdPlow 
 
 Paper Travel (Dr)- 
 
 'iiotPaperTravel Drawbar Pull 
 all 25 ft. of 
 
 und Travel HOTE'.SOIIiSl ., 
 on Pressure Ihdicalor 
 
 Left Wheel - 
 RightWheelln Furrow 
 
 Zero or Base li'ne -^ 
 
 Fig. 201. 
 
 U 
 
210 GRAPHICAL METHODS 
 
 Figure 200A is a dynamometer record of drawbar pull necessary 
 to move an automobile on a level floor. The pencil is actuated 
 by a Tabor gas engine indicator and the paper is moved by a 
 clock. Ordinates represent pounds pull. A record of drawbar 
 pull on a much more comprehensive scale is shown in Fig. 201. 
 This is a record of drawbar pull of tractor pulling two plows 
 and the pull exerted on each of the plows as well. A description 
 of the various phenomena and conditions of the test will be 
 found in the tables which accompany the record. 
 
 One of the most common recording instruments is the steam 
 engine indicator. This draws a diagram which shows the pres- 
 sure in the cylinder of a steam engine at every point in the stroke 
 
 Scale 30 
 Fig. 202. — Steam engine indicator diagram. 
 
 of the piston. A sample of the diagram drawn is shown in Fig. 
 202. Abscissas denote positions of the piston along the stroke 
 and ordinates represent pressures in the cyhnder at each of these 
 positions. The paper is held on the surface of a cylinder which 
 is oscillated by being connected with the moving piston. A 
 pencil point actuated by the pressure of steam in the engine 
 cylinder is pressed against the paper and draws the indicator 
 card. The scale to be used in mesisuring ordinates depends on 
 the spring used in the indicator. It is usually denoted on the 
 card as "Scale 30" "Scale 50" etc. in Fig. 202. 
 
 A similar diagram can be made from the cylinder of an internal 
 combustion engine but the line of pressures is traced by a beam 
 of Hght instead of a pencil point and the paper is sensitized instead 
 of plain. 
 
 There are two types of diagrams taken from an internal com- 
 bustion engine and shown in Fig. 203. The pressure volume card 
 is similar to the steam engine card of Fig. 202. The pressure- 
 time card is useful in studying fuel characteristics. The beam 
 of light which describes the pressure curve has a compound 
 movement and the paper does not move as on steam engine 
 indicators. 
 
MECHANICAL GRAPHICAL RECORDS 
 
 211 
 
 In the class of graphic records illustrated in Fig. 167e is found 
 the record of Fig. 204 made by a recording pyrometer of the 
 Taylor Instrument Co. The ordinates are of a non-uniform 
 scale and represent temperatures from to 2,500°F. The curve 
 is composed of a series of dots. The paper is moved by clock- 
 
 Iqn'ifion/^ 
 
 ■ rXW 
 
 Scavenging 
 
 Exhausf- 
 Valvs 
 ^^ Opening 
 
 Intake 
 
 Valve 
 
 Opens 
 
 PRESSURE-TIME 
 
 Intal^e 
 
 PRESSURE-VOLUME 
 Fig. 203. — Internal combustion engine diagrams. 
 
 OOOO oooooo 
 TwflorlnstnmentCompames Rochester, N.Y. 
 
 _2t 8 
 
 
 \ 
 
 c 
 
 Ri 
 
 m 
 
 CO 
 CO 
 
 ± 
 
 to 
 
 r- 
 ts> 
 
 o 
 
 
 
 
 \^^ 
 
 
 = 
 
 
 
 
 m 
 
 
 1 
 
 
 
 
 
 m 
 
 
 i 
 
 
 
 
 
 ^ 
 
 
 3 
 
 
 
 
 
 ^ 
 
 
 s 
 
 
 ■ J 
 
 
 ^ 
 
 ^ 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 s 
 
 2AM 
 
 o -o 
 
 12 M 
 
 o o 
 
 lOPM 
 
 COO 
 
 8PM 
 
 o o 
 
 Fig. 204. — Taylor recording pyrometer record. 
 
 work. Figure 205 is a sample chart made on a Bacharach volume 
 recorder for measuring volume of gas or air by the Pitot tube 
 principle. This ribbon is 8 in. wide and the divisions are log- 
 arithmic. The motion of paper is obtained from clockwork, the 
 time divisions being uniform. 
 
212 
 
 GRAPHICAL METHODS 
 
 The ribbon graphical records so far mentioned have been made 
 on paper having straight hne ordinates. There are many dia- 
 grams which are made with a pen which moves in a circular arc 
 and records on paper having circular ordinates. These diagrams 
 
 „ THOUSANDS OF CU FT PEH * 
 
 ^^g^^^i 
 
 V30!6_ 
 Fig. 205. — Baoharach volume recorder for gas or air. 
 
 Pig. 206. — Brown recording pyrometer record. 
 
 belong in the class shown in Fig. 167/ and g. A record of this 
 type is shown in Fig. 206. 
 
 This is a recording pyrometer record made by a series of dots 
 on a paper ribbon moved by clockwork. The ordinates represent 
 
MECHANICAL GRAPHICAL RECORDS 
 
 213 
 
 degrees Fahrenheit. Records from recording barometers are 
 shown in Figs. 207 and 208. These charts are made to record 
 for a week without change of paper. Ordinates are inches of 
 
 Fio- 207. Pig. 208. 
 
 Recording barometer records. 
 
 Pig. 209. — Recording barometer and thermometer records combined. 
 
 mercury and abscissa are time intervals. Measurements of 
 ordinates can be more accurately made on 207 than on 208 but 
 the record is equally good on both. 
 
214 
 
 GRAPHICAL METHODS 
 
 Fig. 210. — Double record from duplex pyrometer. 
 
 O 
 O 
 O 
 O 
 O 
 O 
 O 
 O 
 
 I -. - 
 
 ^r~ ,.-.,.-.----.---- 
 
 : '• i 
 
 :. I..,.^:^..! 
 
 ^' 'i \ 
 
 ..{ :] 
 
 ,.: ^..- 
 
 ^° ... ..,::: , 
 
 \ac^:.f Jin.'i' \ lwomi'I 
 
 ,fj. : 
 
 V .'• ? 
 
 ...::.:: [. 
 
 Q i :■.., 
 
 y r *■;, ^1 
 
 "E) . \ ■^ i^K J ft: 18 A V 
 
 ::::: \::::::::::::::y\ 
 
 •\ ■ I 
 
 o 
 o 
 o 
 o 
 o 
 o 
 o 
 o 
 
 Fig. 211. — Englehard multiple pjrrometer record. 
 
 ■/:■■■ 
 
 
 .' 
 
 1 > £ '-■ 
 
 
 > 
 
 ; 
 
 . 
 
 
 . 
 
 ; - 
 
 : , Mi i 15 1-- 
 
 ; 
 
 f '■ 
 
 
 Fig. 212. — A four-record chart from a Thwing recorder. 
 
MECHANICAL GRAPHICAL RECORDS 
 
 215 
 
 Fig. 213. — Critical temperature chart. 
 
 Fig. 2X4.— Esterline graphic recording power factor metar chart. 
 
216 
 
 GRAPHICAL METHODS 
 
 Figure 209 is a chart used for two records one of temperatures, 
 one of barometer heights. There are two scales for ordinates, 
 the time element remaining the same. This is from the Stormo- 
 graph of the Taylor Instrument Co. 
 
 DART 
 
 M/O/4. 
 
 
 
 4-: 
 
 0|PE 
 
 
 
 LtS. PCR HOUR. 
 
 
 
 
 
 
 
 CI 
 
 = 
 
 
 = 
 
 ^ 
 
 
 
 ^ 
 
 
 
 
 ^ 
 
 
 ^ 
 
 
 h 
 
 
 E 
 
 
 ta^ 
 
 ^ 
 
 
 s;fc 
 
 
 
 
 P 
 
 
 <(3 
 
 t^rV 
 
 
 W 
 
 
 
 
 
 fe 
 
 ta 
 
 ^ 
 
 FROM 
 
 ^ 
 
 ^ 
 
 
 s 
 
 
 
 FiQ. 215. — Curnon meter record of steam delivered. 
 
 A record from a duplex pyrometer is shown in Fig. 210. One 
 line gives tank temperatures the other those in a furnace. There 
 are two separate ordinate scales, although it is possible to run 
 several records on one ribbon with one scale only. The lines in 
 that case would be made in diiferent colors. These are made on 
 thin paper from which blue prints can easily be made. 
 
 ooooooooooooooooo 
 
 FiQ. 216. — Chart from Westinghouse graphic recording voltmeter. 
 
 A recording pyrometer record made on a recorder with four 
 pens is shown in Fig. 211. There are four colors of ink which 
 prevents confusion if the lines happen to cross. Temperatures 
 run from to 2,100°. The paper travels by clock mechanism, 
 the holes in the edges of the paper fitting over teeth in a driving 
 
MECHANICAL GRAPHICAL RECORDS 
 
 217 
 
 drum which eliminates any chance of slipping while passing 
 through the instrument. This is made on an Englehard recorder 
 which can be arranged to trace 12 different records if required. 
 A similar pyrometer record is made by the Thwing recorder, 
 the principal difference being that the lines of Fig. 211 are 
 colored to distinguish them while the lines themselves of the 
 Thwing record are composed of different kinds of dots and spacings. 
 
 o o o o o 
 
 Fig. 217. — Chart from Esterline graphic time recorder. 
 
 A four-record chart is shown in Fig. 212. As many as 12 records 
 can be made on a single chart. The paper is moved by clockwork 
 and is long enough to last 24 hr. without change. 
 
 Figure 213 is a graphical record of the behavior of steel when 
 heated above its critical temperature and allowed to cool. The 
 two Hues represent the temperature of the steel specimen and the 
 recalescent standard. This record can be compared with the 
 one shown in Fig. 190 made with straight hne ordmates. 
 
 In Fig. 214 is shown a graphical record of the type of chart 
 noted in Fig. 167g, having curved non -uniform ordmates. This 
 
218 
 
 GRAPHICAL METHODS 
 
 was made on an Esterline graphic recording power-factor meter. 
 The ruled portion is 43^^ in. wide. The speed of the paper 
 through the meter can be varied from ^ to 12 in; per hour, 
 although rapid fluctuations can be provided for by minute 
 chart speeds varying from % to 6 in. per minute. The standard 
 speed is 3 in. per hour. 
 
 Fia. 218. — Chart from Precision Instrument Co.gravitometer. 
 
 A similar type of chart is one from a Curnon steam meter, the 
 steam measurement being based on the Pitot tube method. 
 Ordinates represent pounds of steam per hour. This is shown in 
 Fig. 215. The ordinates are non-uniform scale. 
 
 Fia. 219. — Colorograph chart of B.t.u. content in gas. 
 
 A type of chart having curved ordinates and unequal spacing 
 on the vertical scale is shown in Fig. 216. This was made on a 
 Westinghouse graphic recording voltmeter. The time intervals 
 are 15 min. each and motion of the chart is obtained from 
 clock-work. 
 
MECHANICAL GRAPHICAL RECORDS 
 
 219 
 
 o 
 2 o 
 
 '^^^^^illlljiui 
 
 i^^ 
 
 -? 
 
 
 ■D 
 
 c 
 a 
 
 Si 
 
 J 
 
 o 
 u 
 
 q: 
 
 x: 
 
 £ 
 
 D 
 
 ca 
 
220 GRAPHICAL METHODS 
 
 A chart showing amperes instead of volts but differing in no 
 other respect is the product of an ammeter. 
 
 In Fig. 217 is shown a diagram made by an Esterhne graphic 
 time recorder. This indicates only when certain machinery is 
 put in motion. Five different machines are indicated here, the 
 upper line being continuous which shows no movement of that 
 machine. These records have a time value only as ordinates 
 and are of no value for measuring quantities. The paper can be 
 moved through the recording instrument at a speed suitable for 
 the records desired. 
 
 In Fig. 218 is a chart showing the density of Newark Public 
 Service Gas referred to air as unity, made on a Precision Instru- 
 ment Co. Gravitometer. In Fig. 219 is shown a chart from a 
 Colorgraph of the same gas. This gives the B.t.u. content in 
 Newark Public Service Gas. Ordinates are curved in both these 
 diagrams but the divisions of the vertical scale are equal. 
 
 The speed of airplanes is obtained by an airspeed recorder. 
 The one at present used in government work is the Toussaint- 
 Le Pere. It works on the Pitot-Venturi system and the pen 
 records on a continuous paper strip. The speed record is usually 
 accompanied by a barograph record. 
 
 Figure 220 is a record made with a Toussaint-Le Pere air speed 
 recorder. The paper is moved by clockwork, the horizontal 
 scale reading to minutes. 
 
BIBLIOGRAPHY 
 
 Books and Pamphlets 
 
 "Mathematics for Engineers," W. N. Rose. 
 
 "Graphic Methods," Joint Committee on Standards for Graphic Pre- 
 sentation. 
 
 "Industrial Management," A. H. Chubch. 
 
 "Production Factors in Cost Accounting and Works Management," A. H. 
 Church. 
 
 "Graphic Production Control," C. E. Knoeppel. 
 
 "Resistance des Materiaux," Ch. DbMttssan. 
 
 "Nomography," Capt. R. K. Hezlet. 
 
 "The Ratio Chart for Plotting Statistics," Irving Fisher. 
 
 "Graphic Algebra," Arthur Schultze. 
 
 "Business Statistics," M. T. Copeland. 
 
 "An Introduction to Statistical Methods," Horace Secrist. 
 
 "Statistics in Business," Horace Secrist. 
 
 "Graphs," R. J. Alby. 
 
 "Line Charts," E. W. Tipple. 
 
 "Graphical Methods," C. D. T. Runge. 
 
 "Treatise on Graphs," Geo. A. Gibson. 
 
 "Book on Curve Tracing," Perceval Frost. 
 
 "The Elements of Statistical Method," Willpord I. King. 
 
 "Elements of Statistics," Arthur L. Bowlby. 
 
 "An Introduction to Theory of Statistics," G. Udny Yule. 
 
 "Graphic Methods for Presenting Facts," Willabd C. Brinton. 
 
 "Graphic Chart for the Business Man," Stephen Gilman. 
 
 "Graphical and Mechanical Computation," Joseph Lipka. 
 
 "How to Make and Use Graphic Charts," Allan C. Haskell. 
 
 "The Construction of Graphical Charts," John B. Peddle. 
 
 "Graphic Method of Statistics," Prof. Alfred Marshall. 
 
 "Rules for Graphical Presentation of Statistical Data," Day, Rebd and 
 Secrist. 
 
 "Straight Line Engineering Diagrams," Manifold and Poolb. 
 
 "Elementary Machine Drawing and Design." William C. Marshall. 
 
 Bibliography op Magazine Articles with Diagrams 
 
 Accounting. 
 
 Accounting operations, Harrison, Industrial Engineering, January, 
 1919. 
 
 Costs, planning and control, Harrison, Industrial Engineering, Jan- 
 uary, 1919. 
 
 Sales, costs, manufacturing efficiencies, Harrison, Industrial Engineer- 
 ing, March, 1919. 
 
 Use of specifications, costs, profits, Harrison, Industrial Engineer- 
 ing, May, 1919. 
 
 221 
 
222 GRAPHICAL METHODS 
 
 Air. 
 
 Fans, horsepower curves, Hdbbabd, Engineering Magazine, December, 
 1914. 
 
 Velocity of air, Reuter, American Machinist, February 1, 1917. 
 
 Calibration of fan blades, Society of Automotive Engineers Handbook. 
 
 Specific weight and temperature curves for air. Society of Automotive 
 Engineers Handbook. 
 
 Explosive pressure air and gas, Wimperis. 
 
 Compressed air calculation, Crispell, American Institute of Mining 
 Engineers, Vol. 58, 1918. 
 
 Excess air on combustion, Power, Nov. 11, 1916. 
 
 Aerographic charts, McAdie, Scientific American Supplement, June 2, 
 1917. 
 
 Fan horsepower and volumes, Society of Automotive Engineers Trans- 
 actions, July, 1917. 
 
 Cooling fans automobiles. Society of Automotive Engineers, May, 1919. 
 
 Flow through poppet valves, Engineering, Jan. 10, 1919. 
 
 Synthetic air chart, American Society of Heating & Ventilating Engi- 
 neers, Vol. 23, 1917. 
 
 Air duct design (nomographical chart), American Society of Heating & 
 Ventilating Engineers, Vol. 25, 1919. 
 
 Radiator cooling fans performance curves, Hoyt, Automotive Indus- 
 tries, Mar. 30, 1919. 
 Airplanes. 
 
 Engine, plane and propeller speeds, Upton, Society of Automotive 
 Engineers, October, 1918. 
 
 Curves for propellers, Caldwell, Society of Automotive Engineers, 
 August, 1918. 
 
 Radiator curves. Black, Society of Automotive Engineers, June, 1919. 
 
 Carburetor condition of engines. Society of Automotive Engineers, 
 January, 1919. 
 
 Airplane Engines, Squier, Society of Automotive Engineers, December, 
 1919. 
 
 Air mileage of airplanes, Coales, Engineering, May, 8, 9, 1919. 
 
 Development of aircraft performance in war, Wibr, Engineering, 
 July 25, 1919. 
 
 Accelerometer tests on aircraft, Wier, Engineering, July 11, 1919. 
 
 Diagrams of airplane speed records, Le Genie Civil, Oct. 23, 1920. 
 
 Screw standards. Automotive Industries, Nov. 8, 1917. 
 Ammunition. 
 
 Ammunition (alignment) charts, Bkayton, American Machinist, Apr. 
 10, 1919. 
 Appraisal. 
 
 Machine tools. Industrial Management, August, 1919. 
 
 Service value machine tools, American Machinist, Aug. 21, 1919. 
 
 Curves of oil wells, American Institute of Mining Engineers, Vol. 59 1918. 
 Area. 
 
 Boiler head segments. Power, May 20, 1919. 
 
 Boiler head segments, Berry, Power, Apr. 29, 1919. 
 
 Bumped heads, Berry, Power, June 17, 1919. 
 
BIBLIOGRAPHY 223 
 
 Automobiles. 
 
 Stolen and recovered in Detroit, 1916-18, Sodety of Automotive 
 
 Engineers, February 1919. 
 Engine mixtures, gas and air, Berry, Society of Automotive Engineers, 
 
 November, 1919. 
 Weight per cylinder displacement, Hulst, Automotive Industries Aug 
 
 30, 1917. 
 Steering wheel curves, Howabth, Automotive Industries, Aug. 23, 1917. 
 Tests by accelerometer, Skinner, Automotive Industries, Apr. 25, 1918. 
 Performance, Elmendorf, Automotive Industries, Jan. 2, 1919. 
 Shipments, prewar, 40 countries, Sinsheimer, Automotive Industries, 
 
 June 12, 1919. 
 
 B 
 
 Beets, yield of, Sugar, October 1917. 
 Boilers. 
 
 Efficiency and calculation charts, Lbefax. 
 Seventy-eight steam boiler tests, Lefax. 
 
 Bolts, machine tool practice. Force fits, Knobppel, Industrial Engi' 
 neering, January, 1919. 
 
 C 
 Cables, carrying capacity, American Society of Naval Engineers, 1919. 
 Calculating. 
 
 Bonus in wood working. Industrial Engineering, September, 1919. 
 
 Bonus curves, Emer and Bigelow, Industrial Engineering, November, 
 1919. 
 
 Bonus record, Polakor, Industrial Engineering, July, 1918. 
 
 Railroad curves. Engineering News-Record, Vol. 83, No. 11. 
 
 Steel tape sag connections, Engineering New-Record, Vol. 83, No. 9. 
 
 Storm sewer (alignment and coordinates). Engineering News-Record, 
 Vol. 83, No. 19. 
 
 Timber columns, Wolfe, Engineer and Contractor, Nov. 28, 1917. 
 
 Retaining walls, Engineer and Contractor, July 23, 1919. 
 
 Disc brakes and clutches, Jacob, American Machinist, June 21, 1917. 
 
 Cam curves, Furman, American Machinist, Apr. 10, 1919. 
 
 Safety valve formulae, Power, Oct. 24, 1916. 
 
 Proportion of fuel economy, Clark, Power, Apr. 22, 1919. 
 
 Stress in shafts for bending, Bailey, Engineering, July 13, 1917. 
 
 Stress in flate plate, Bailey, Engineering, July 13, 1917. 
 
 Tension on steel cables, Le Oenie Civil, July 21, 1917. 
 
 Abaque for wire helical springs, Le Genie Civil, May 25, 1918. 
 
 Draftsmens' time, Hunger, Industrial Engineering, May, 1919. 
 
 Maximum efiBciency belt pull, Wilson, American Institute of Chemical 
 Industries, Vol. 11, 1917, pp. 237 
 
 Calculations and tests of four coil spring. Railway Mechanical Engineer, 
 October 1917. 
 
 Driving axle, crosshead crankpins. Railway Mechanical Engineer, 
 
 April, 1916. 
 
224 GRAPHICAL METHODS 
 
 Air weight and volume, Automotive Industries, June, 12, 1919. 
 
 Air propeller charts, Caldwell, Society of Automotive Engineers, 
 
 August, 1918 
 Economical Cargo Ship Calculations, Robertson, Society of Naval 
 
 Architects and Marine Engineers, Vol. 27, 1919. 
 Pressure. Altitude, Society of Automotive Engineers, Handbook. 
 Pressure and volume, Gunn, Motor Cars. 
 
 Carburetors. 
 
 Mixture requirements, automobile engines, Behey, Society of Automo- 
 tive Engineers, November, 1919. 
 
 Performance curves of carburetors, Berry, Society of Automotive Engi- 
 neers, February, 1917. 
 Cloth. 
 
 Cloth sales for knit cloth and yarn sizes, Tompkins, The Textile World 
 Journal, Jan. 20, 1917. 
 
 Elongation and contraction in ply yarns. The Textile World Journal, 
 July 14, 1917. 
 
 Coal. 
 
 Coal tar products. Engineering, June 20, 1919. 
 
 Extraction chart of products, Engineering, Aug. 21, 1920. 
 
 Products of U. S. 1846/1816, American Institute of Mining Engineers, 
 Vol. 69, 1918. 
 
 Consumption for heating homes, American Society of Heating & Ventila- 
 ting Engineers, Vol. 24, 1919. 
 
 Production in various states, 1915, American Society of Heating & 
 Ventilating Engineers, Vol. 24, 1919. 
 
 Consumed in steam heated buildings, American Society of Heating & 
 Ventilating Engineers, Vol. 24, 1919. 
 
 Radiator requirements in buildings American Society of Heating & Ven- 
 tilating Engineers, Vol. 29, 1919. 
 
 Comparison of coefficient of friction. Society of Automotive Engineers 
 Handbook. 
 
 Combustion value required for coals. Power, Apr. 23, 1918. 
 
 Seventy-eight boiler tests of coals, Lepax. 
 
 Coal loss, Beaman, Power, July 8, 1919. 
 
 Fuel consumption. Berry, Power, Oct. 8, 1918. 
 
 Waste in ash and coal, Shoudy, Power, Nov. 5, 1918. 
 
 Lignites, Krbisingbr, Power, Apr. 30, 1918. 
 
 Chimney design, Brayton, Power, Sept. 3, 1918. 
 Coefficient of Friction. 
 
 Variation of coefficient of friction and load, Le Genie Civil, May 29, 1920. 
 
 Lubrication friction and load tests, American Society of Naval Engineers, 
 November, 1917, p. 708. 
 Concrete. 
 
 Concrete mixtures. Engineering News-Record, Vol. 81, No. 7. 
 
 Asphalt paving, Kennedy, Engineer and Contractor, Mar. 7, 1917. 
 
 Paving, Engineer and Contractor, Feb. 7, 1917. 
 
 Reinforced concrete. Ward, Engineer and Contractor, Jan. 24, 1917. 
 
BIBLIOGRAPHY 225 
 
 Depression in wood, Engineer and Contractor, Jan. 24, 1917. 
 Block pavement. Engineer and Contractor, Feb. 5, 1919. 
 Effect of water on strength, Engineer and Contractor, Mar. 26, 1919. 
 Commercial. 
 
 Commercial vehicles. 
 
 Frame lengths. Society of Automotive Engineers Handbook. 
 Speed rating. Society of Automotive Engineers Handbook. 
 Body weight, Society of Automotive Engineers Handbook. 
 Comparisons. 
 
 Street flushing equipment (N. Y.), Engineer and Contractor, Jan. 3, 1917. 
 
 Steam and oil engines, Morrison, Power, May 15, 1917. 
 
 Coal and oil fuel. Power, Mar. 13, 1917. 
 
 Uniflow engines and others, Rozbnswbig, Power, July 17, 1917. 
 
 Gas and oil engine tests, Engineer, Jan. 12, 1917. 
 
 Naturally and mechanically ventilated rooms, American Society of 
 
 Heating & Ventilating Engineers, Vol. 25, 1919. 
 Direct drive and gear turbine and reciprocating engines, American 
 
 Society of Naval Architects, 1917, p. 428. 
 Liberty and other airplane engines. Automotive Industries, June, 13 1918. 
 Petroleum products. Automotive Industries, Jan. 15, 1920. 
 Gas and kerosene engine performances, Clark, Society of Automotive 
 
 Engineers, August 1917. 
 Gear and pinion hardness, Logub, Gear Book. 
 Speed and pressure in gears, Alford. 
 Speed and resistance of ships, Atwood, Naval Architect. 
 Speed of vehicles and diameters of wheels, Tatler, Motor Vehicles. 
 Speed of vehicle to traction, Tayler, Motor Vehicles. 
 Compensation of engineers. Transactions Society of Civil Engineers, Vol. 
 
 81, 1917. 
 Condensers. 
 
 Assistance in selection of, Macintire, Power, Sept. 5, 1916. 
 
 Surface in shell and tubes. Power, Aug. 29, 1916. 
 
 Performance, Power, Apr. 10, 1917. 
 
 Efficiencies, Morgan, Power, Jan. 16, 1917. 
 
 Heat transfer in surface condensers, Porter, Engineering, Jan. 24, 1919. 
 
 Chart for surface condensers, Lefax. 
 
 Consumption. 
 
 Steam and coal, Polakov, Industrial Engineering, July, 1918. 
 
 Steam, Polakof, Industrial Engineering, September, 1918. 
 
 Water, Engineer and Contractor, Jan. 8, 1919. 
 
 Fuel efficiencies furnaces, Sklorsky, American Machinist, Sept. 11, 
 
 1919. 
 Consumption and production of coal, American Institute of Mining 
 
 Engineers, Vol. 59, 1919. 
 Consumption of fuel on Ford, Dickinson, Society of Automotive 
 
 Engineers, April, 1919. 
 Consumption of gasoline, also production. Automotive Industries, Oct. 
 
 25, 1917. 
 15 
 
226 GRAPHICAL METHODS 
 
 Three different fuels and horsepower, Automotive Industries, Nov. 14, 
 14, 1918. 
 
 Gasoline and brake horsepower and exhaust gas analysis, Wimpekis. 
 Conversion charts. 
 
 Pressure-attitude, Society of Automotive Engineers Handbook. 
 
 Temperature-altitude, Society of Automotive Engineers Handbook. 
 
 Metal gauge. Society of Automotive Engineers Handbook. 
 
 Weight of flat steel. Society of Automotive Engineers Handbook. 
 
 Inches water to pounds per square inch. Society of Automotive Engineers 
 Handbook. 
 Costs. 
 
 Transportation by motor vehicle, Durbn, Engineer and Contractor, 
 May 7, 1919. 
 
 Annual cost per mile of road, Duhbn, Engineer and Contractor, May 7, 
 1919. 
 
 Gas-electric arc welding, Power, Nov. 28, 1916. 
 
 Boiler room, Morgan, Power, July 4, 1916. 
 
 Central station costs, Moses, Power, June 12, 1917. 
 
 Fuel for heat and power, Rosbnceantz, Power, Nov. 12, 1918. 
 
 Fuel costs and plant efficiency, Foster, Power, Mar. 4, 1919. 
 
 Fuel and lubricating costs, Waas, Engineering, Oct. 26, 1917. 
 
 Scotch pig iron, Engineering, Aug. 29, 1919. 
 
 Horse and mechanical traction, underground, Le Genie Civil, Jan. 17, 
 1920. 
 
 Gas and electric lighting, American Gas Engineers Journal, Apr. 6, 1918. 
 
 Oilfield pipe drilling, American Institute of Mining Engineers, Vol. 59, 
 1918. 
 
 Costs of plowing, Goldbergbb, Automotive Industries, Dec. 6, 1917. 
 
 Concrete hull construction. Wig, Society of Naval Architects & Marine 
 Engineers, Vol. 29, 1917. 
 
 Gas motor truck operation, Society of Automotive Engineers Handbook. 
 
 Steam shovel work, Dana, Handbook Steam Shovel Work. 
 
 Cost per yard material handled, Dana, Handbook Steam Shovel Work. 
 
 Evaporation of water with different coals, Lbpax 
 
 Costs and production of looms per weaver, Otis, Industrial Engineer- 
 ing, December, 1919. 
 
 Material size. Starker. Industrial Engineering, August, 1919. 
 
 Living, Hudson, Industrial Engineering, September, 1918. 
 
 Systematic, machinery, Harrison, Industrial Engineering, October, 
 1918. 
 
 Power stations, Polakov, Industrial Engineering, November, 1918. 
 
 Standard, Harrison, Industrial Engineering, November, 1918. 
 
 Central plant, Polakov, Industrial Engineering, November, 1918. 
 
 Service, Polakov, Industrial Engineering, November, 1918. 
 
 Building materials. Engineering News-Record, Vol. 83, No. 19. 
 
 Public utility. Engineering News-Record, Vol. 83, No. 20. 
 
 Elevator equipment (conveyors and elevators). Engineering News- 
 Record, Industrial Engineering, November, 1916. 
 
 Railroad ties, Engineering Magazine, March, 1915. 
 
BIBLIOGRAPHY 227 
 
 One kilowatt-hour, Polakov, Engineering Magazine, May, 1915. 
 Steam power, Trautschold, Engineering Magazine, March, 1916. 
 Belt conveyors, Tbatjtschold, Engineering Magazine, August, 1916. 
 Cranes, Trautschold, Engineering Magazine, June, 1916. 
 Belt slip. Engineering and Mining Journal, Aug. 24, 1918. 
 Traffic ton mile, Engineer and Contractor, May. 7, 1919. 
 Cranes. 
 
 Cranes Qifting capacity) Trautschold, Engineering Magazine, July, 
 
 1916. 
 Speeds, TRAUTSCHOiiD, Engineering Magazine, July, 1916. 
 
 D 
 
 Design charts. 
 
 Machine tool handles, Colvin, Draining Room Kinks. 
 
 Stuffing box glands, W. C. Marshall, Machine Design. 
 
 Cast-iron pipe fittings, W. C. Marshall, Machine Design. 
 
 Eivet hole diameter, W. C. Marshall, Machine Design. 
 Draft. 
 
 Steam boilers, Morgan, Power, Mar. 20, 1917. 
 
 In boiler practice, Lawrence, Power, Sept. 18, 1917. 
 
 Gas passage areas in boilers. Stripe, Power, July 31, 1917. 
 
 Tests Sturtevant forced draft blower, American Society of Naval Engi- 
 neers, 1918, p. 470. 
 
 Drill bit tests, Forbes and Barton, American Institute of Mining 
 Engineers, Vol. 58, 1918. 
 
 E 
 
 Electric motors. 
 
 Torque, Popcke, American Machinist, Feb. 1, 1917. 
 
 Efficiency, D. C, Popcke, American Machinist, Feb. 22, 1917 
 
 Efficiency, squirrel cage, Popcke, American Machinist, Feb. 1, 1917. 
 
 Efficiency induction, Popcke, American Machinist, Feb. 1, 1917. 
 Employment. 
 
 Employees, hiring, etc., Sawyer, Industrial Engineering, January, 1919. 
 
 Overtime, Von Htjhn, Industrial Engineering, January, 1919 
 
 Labor replacement, Talbot, Industrial Engineering, January, 1919. 
 
 Employees, rate of hiring, Richards, Industrial Engineering, March, 
 1919. 
 
 Functioning of employees, manufacturing department, Nelly, Indus- 
 trial Engineering, June, 1919. 
 
 Idle time, Knoeppbl, Industrial Engineering, November, 1918. 
 
 JEmployment, Goldberger, Industrial Engineering, November, 1918. 
 
 Shifting of labor. Engineer and Contractor, Aug. 27, 1919. 
 
 Working days, full and overtime, machine tool industry, American 
 Machinist, June 19, 1919. 
 
 Mental tests (bar coordinate), Yerkes, American Institute of Mining 
 Engineers, Vol. 60, 1919. 
 
 Industrial accidents in iron and steel. Engineering, Feb. 7, 1919. 
 
228 GRAPHICAL METHODS 
 
 Engines. 
 
 Engine characteristics, Automotive Industries, Feb. 14, 1918. 
 
 Svid engine, Automotive Industries, June 20, 1918. 
 
 Steam turbines, Bhblspord, Power, June 18, 1918. 
 
 Kerosene burning engines, Clabk, Society of Automotive Engineers, 
 August, 1917. 
 
 Average Liberty engine, Vincent, Society of Automotive Engineers, 
 May, 1919. 
 
 High speed gas engines. White, Society of Automotive Engineers, May, 
 1919. 
 
 Tractor engines. Automotive Industries, Nov. 21, 1918. 
 
 With water jacket and exhaust inlet, American Industries, Feb. 14, 1918. 
 
 Variable speed engine curves, Prof. Roesch, S'^cieiy of Automotive 
 Engineers, January, 1917. 
 
 Twelve cylinder Liberty engine performance, Vincent, Society of Auto- 
 motive Engineers, May, 1919. 
 
 Ford, thermal and construction tests, Dickinson, Society of Automotive 
 Engineers, April, 1919. 
 
 Brake horsepower of four and eight cylinder engines, White, 
 Society of Automotive Engineers, May, 1919. 
 
 Equivalent radius of automobile engines, Institute of Automobile 
 Engineers, Vol. 11, 1916-1917. 
 
 Automotive trends. Automotive Industries, Jan. 3, 1918. 
 
 1918 — and eight years. Automotive Industries, Jan. 3, 1918. 
 
 Automotive design trends, Schippeh, Society of Automotive Engineers, 
 April, 1918. 
 
 Automotive engineering tendencies. Automotive Industries, Jan. 16, 1919. 
 
 Automotive trends, American, 10 years. Automotive Industries, Jan. 16, 
 1919. 
 
 1920 trend in truck design, Schippbr, Automotive Industries, Jan. 15, 
 1920. 
 
 Passenger car design trend, 11 years, Heldt, Automotive Industries, 
 Jan. 15, 1920. 
 
 Heat balance tests in automobile engine, Fishleigh, Society of Auto- 
 motive Engineers, December, 1916. 
 
 Tests on 16/20 horsepower Daimler engine, Wimperis, Internal Com- 
 bustion Engines. 
 
 R. A. C. rating for horsepower gasoline engines, Wimperis, Internal 
 Combustion Engines. 
 
 Characteristic motor curves, Heirman, L' Automobile. 
 
 Horsepower and cylinder volume, Heirman, L' Automobile. 
 
 Fatigue and output, Polakov, Industrial Engineering, December, 1919. 
 Flow sheet. 
 
 Copper mUl, Engineering and Mining Journal, June 28, 1919. 
 
 Mixture of phenol, Pbtbbkin, American Institute Chemical Journal. 
 
 Refining crude petroleum, Stratford, Society of Automotive Engineers, 
 Vol. 11, 1917, p. 149, July, 1918. 
 
BIBLIOGRAPHY 229 
 
 G 
 
 Gases, action, of, on hot copper, Pilling, American Institute of Minina 
 
 Engineers, Vol. 60, 1919. 
 Gases, action, electro-zinc, Hansen, American Institute of Mining 
 
 Engineers, Vol. 60, 1919. 
 Gas engine — details. 
 
 Gas velocity through poppet valves, Automotive Industries, Dec 19 
 
 1918. ■ ' 
 
 Piston speeds and cubic feet of cars, Automotive Industries, June 5, 1919. 
 
 Small inlet valves, charts of, tests Pomebot, Automobile Industries 
 
 Feb. 20, 1919. 
 Carburetor required, typical gas engine, Tice, Automotive Industries 
 
 June 24, 1920. 
 Piston ring grooves and piston diameter, Society of Automotive Engi- 
 neers, Handbook. 
 Compression, space and cylinder volume, Gunn, Motor Car. 
 Diameter cylinder and valves, Gunn, Motor Car. 
 Piston area and speed for one horsepower, Gunn, Motor Car. 
 Gears. 
 
 Relation of gear and pinion hardness, Logtje, Gear Book. 
 Multiplier for number of teeth in spur gears, Logue, Gear Book. 
 Relation of circular pitch to K. for weight of spur blanks, Logue, Gear 
 
 Book. 
 Proportion of gear arms and diametral pitch, Logue, Gear Book. 
 Relaton thread angle and efficiency, Logue, Gear Book. 
 Relation thread and efficiency and speed, Logue, Gear Book. 
 Relation temperature pressure and velocity, Logue, Gear Book. 
 Cutters for spiral gears, Logue, Gear Book. 
 Graphic. 
 
 Graphic charts and use of logarithm scale, Wenzel, Scientific American 
 
 Supplement, Apr. 14, 1917. 
 Graphic charts that mislead, Wenzel, Scientific American Supplement, 
 
 June 16, 1917. 
 Nomography in engine design, Mahtineau, Society of Automotive 
 
 Engineers, September, 1918. 
 Nomography, Martineau, Institute of Automobile Engineers, Vol. 12, 
 
 1918. 
 Graphic control, Knoeppel, Industrial Engineering, November, 1918. 
 Pieces purchasing and assembling, Knoeppel, Industrial Engineering, 
 
 December, 1919. 
 Efficiency principles, Knoeppel, Engineering Magazine, November, 
 
 1914. 
 Metallurgical, Engineer and Contractor, Dec. 10, 1919. 
 Operation control, Wadsworth, American Machinist, Sept. 4, 1919. 
 Graphical control, Gilbbeth, Scientific American Supplement, Mar. 24, 
 
 1917. 
 Drill shop control board, Railway Mechanical Engineer, September, 
 1918. 
 
230 GRAPHICAL METHODS 
 
 H 
 Hardness. 
 
 Hardness scale (nomography), Barth, Industrial Engineering, Novem- 
 ber, 1919. 
 
 Hardness of steels, various methods, American Society of Naval Engi- 
 neers, pp. 81, 1917. 
 
 Hardness tests of brass, Shepard, American Machinist, May 31, 1917. 
 
 Indent of steel balls, American Machinist, July 19, 1917. 
 
 Effect of tempering on hardness of metals, American Institute of 
 Mining Engineers, Vol. 69, 1919. 
 
 Hardness and tempering of steel, Edwards, Engineering, Mar. 8, 1918. 
 
 Stress-strain curves of steel, Van den Brock, Engineering, July 26, 
 1918. 
 
 Dynamic hardness tests Batson, Engineering, Oct. 25, 1918. 
 
 Cooling of steel ingots, Fletcher, Engineering, Sept. 27, Oct. 4, 1918. 
 
 Heat treatment of steel, Denis, Le Genie Civil, Feb. 23, 1918. 
 
 Mechanical properties of steel, Hatfield, Engineering, May 16. 1919. 
 
 Hardness of babbitt, American Institute of Mining Engineers, Vol. 60, 
 1919. 
 
 Tempering temperature and Brinell hardness, Society of Automotive 
 Engineers Handbook 
 
 Scaling of high chromium steel, Society of Automotive Engineers Hand- 
 book. 
 Heating. 
 
 Heating required, Ehrlich, Power, Mar. 5, 1918. 
 
 Amount required in radiation, Ehrlich, Power, Feb. 12, 1918. 
 Horsepower. 
 
 Scraper conveyors 
 
 Screw conveyors Lefax 
 
 Belt conveyors 
 
 Bucket conveyors and carriers 
 Hydraulics. 
 
 Hydraulics, method applies, Herschel, American Society of Civil 
 Engineers, Vol. 82, 1918. 
 
 K. W. from flow of water, Meares, Engineering, Aug. 15, 1919. 
 
 Velocity of water in evaporator tubes, American Institute of Chemical 
 Engineers, Vol. 10, 1919. 
 
 Weight of water in marine boilers, Meyer, Society of Naval Architects & 
 Marine Engineers, Vol. 27, 1919. 
 
 Indian music, study of, Densmore, Scientific American Supplement, Apr. 20, 
 1918. 
 
 L 
 
 Lighting. 
 
 Distribution, Clewell, American Machinist, May 23, 1918. 
 Schedule chart, Bailey, Power, June 5, 1916. 
 
 Per cent of absorption and reflection 1 Lijpien, The Textile World 
 in colored cotton goods mill. J Journal, Nov. 3, 1917. 
 
BIBLIOGRAPHY 231 
 
 Locomotive. 
 
 Terminal handling, Railway Mechanical Engineer, May, 1918. 
 
 Time, distance an,d velocity, acceleration, Railway Mechanical Engineer, 
 
 September, 1918. 
 Tonnage, rating, weight diagrams. Railway Mechanical Engineer, 
 
 November, 1918. 
 Heating curves by exhaust steam, Railway Mechanical Engineer, 
 
 December, 1918. 
 Relation of defective locomotives to accidents. Railway Mechanical 
 
 Engineer, December, 1917. 
 Money saved by locomotive furnished with water heaters. Railway 
 
 Mechanical Engineer, June, 1917. 
 Rail pressure from counterbalance. Railway Mechanical Engineer, April, 
 
 1917. 
 Smoke emitted by locomotive on test, Railway Mechanical Engineer, 
 
 January, 1916. 
 Head and hand in firing locomotive. Railway Mechanical Engineer, 
 
 October, 1917. 
 
 Loss. 
 
 Heat in flue, Htjtzel, Power, Dec. 12, 1916. 
 
 Coal through grates, Htjbbaed, Power, Feb. 27, 1917. 
 
 Coal unpreventable in grates, O'Neill, Power, Apr. 9, 1919. 
 
 Carbon in furnace (alignment), Berby, Power, Sept. 23, 1919. 
 
 By friction in turbin thrust bearing, Alford, Bearings. 
 
 Horsepower loss in roller bearing, Alford, Bearings. 
 
 M 
 Machine tools. 
 
 Relations of feed. 
 
 Depth of cut and speed, Barth, Industrial Engineering, September, 
 1919. 
 
 Depth of cut and speed (log), Barth, Industrial Engineering, Novem- 
 ber, 1919. 
 
 Cutting of hack saws, American Machinist, April 5, 1917. 
 
 Cutting speeds and feeds. Peddle, American Machinist, Mar. 15, 1917. 
 
 Reaming charts, American Machinist, Nov. 22, 1917. 
 
 Pulley sizes, American Machinist, Sept. 27, 1917. 
 
 Milling cutters, Jenkins, American Machinist, July 19, 1917. 
 
 Cutting metals, Jenkins, American Machinist, Apr. 11, 1918. 
 
 Cutting metals, Herberts, American Machinist Mar. 28, 1918. 
 
 Feeds, speeds and power, lathe tools, American Machinist, Mar. 14, 
 
 1918. 
 Planing machine time, lathe tools, American Machinist, Oct. 24, 1918. 
 Metal removed, turning and grinding, American Machinist, May 15, 
 
 1919. 
 Screw threads, depth and root (alignment), Brayton. American 
 
 Machinist, January 23, 1919. 
 Gear teeth strength, Berard, American Machinist, Dec. 4, 1919. 
 
232 GRAPHICAL METHODS 
 
 Tension bolts and screws, Bratton (alignment), American Machinist, 
 Nov. 13, 20, 1919. 
 
 Tooth pressure (alignment), Cronk, American Machinist, Oct. 9, 1919. 
 
 Cutting speed steel (alignment), Brayton, American Machinist, Oct. 9, 
 1919. 
 
 Spur gear diagram, Stjndberg, American Machinist, September 18, 
 1919. 
 
 Rating value centrifugal machinery. Reed, Power, October, 1916. 
 
 Standard screw thread pitch, Society of Automotive Engineers, Novem- 
 ber, 1918. 
 
 Worm gear characteristics, Bostock, Engineering, Nov. 2, 1917. 
 
 Rake angles of lathe tools, Burlby, Engineering, Dec. 26, 1917. 
 
 Moment and shear 1 
 
 Oil. 
 
 _, . , . r Engineering News-Record, Vol. 81, No. 4. 
 
 Concrete ship j f » 
 
 Concrete ship strain, Engineering News-Records, Vol. 83, No. 12. 
 
 Bending moment beams. Engineering News-Record, Vol. 83, No. 20. 
 
 Loads and stresses railroad bridges, American Society of Civil Engineers, 
 
 Nov. 13, 1917. 
 Significance of load graphs, Cropt, Power, Oct. 2, 1917. 
 Material, receipt, machining and assembling, Knobppel, Industrial 
 
 Engineering, November, 1918. 
 Molding, foundry, Marston, Industrial Engineering, March, 1919. 
 Brake horsepower gas, Society of Automotive Engineers Handbook. 
 
 O 
 
 Oil lands, well spacing and drilling time, American Institute of Mining 
 Engineers, Vol. 59, 1918. 
 
 Viscosity of oils, O'Neill, Power, July 18, 1917. 
 
 Viscosity and coefficient of oils, Macintrie, Power, June 27, 1917. 
 
 Flow of oil. Power, July 11, 1916. 
 
 Petroleum bore hole, Sington, Engineering, Sept. 5, 1919. 
 
 Oil field pipe and diagram drill costs, American Institute of Mining 
 Engineers, Vol. 59, 1918, p. 536. 
 
 Oil cooler performance, American Society of Naval Engineers, p. 301, 
 1917. 
 
 Oil tests of bearings, marine engines, American Society of Naval Engi- 
 neers, p. 48, 1917. 
 
 Operating. 
 
 Belt conveyors, Morgan, Power, Oct. 3, 1916. 
 
 Waterloo plant. Power, Aug. 22, 1916. 
 
 Central station operation, Rogers, Power, July 4, 1916. 
 
 Load curves, season. 
 
 Typical season load curves, Moses and Morgan, Power, July 12, 1917. 
 
 Diversity in load curves, Schallen, Power, Feb. 6, 1917. 
 
 Power and lighting loads. Power, Feb. 6, 1917. 
 
 Charts for boilers, O'Neill, Power, Apr. 2, 1918. 
 
 Load and equipment. Power, Dec. 16, 23, 30, 1919. 
 
. BIBLIOGRAPHY 233 
 
 Central power stations, Power, Oct. 7, 1919. 
 
 Load curves and steam engines, Diesel, Power, May, 13 1919. 
 
 Factor of evaporation and boiler efficiency, Power, June 24, 1919. 
 
 Torque and horsepower water wheel, Bboadbbnt, Engineering, Feb. 7, 
 1919. 
 
 Operations on gas meter through shop, American Gas Engineers Journal, 
 Nov. 15, 1919. 
 
 Capitalization steam, Von Fabeicb, Power, Dec. 26, 1916. 
 
 Daily train movements, Jersey City, Railway Mechanical Engineer, 
 May, 1916. 
 
 Efficiency curves, circulation pumps, American Society of Naval Engi- 
 neers, p. 23, 1918. 
 
 Operation water evaporators, American Society of Naval Engineers, 
 p. 63, 1919. 
 
 Results of strikes. Automotive Industries, Jan. 15, 1920. 
 
 Acceleration tests, automobile speedway. Society of Automotive Engi- 
 neers, May, 1917. 
 
 Test runs, U. S. 110-foot submarine chaser engine, Crouds, Society of 
 Automotive Engineers, May, 1919. 
 
 Ford engine thermal and speed curves, Dickinson, Society of Automotive 
 Engineers, April, 1919. 
 
 Torque and horsepower, Pelton wheel. The Engineer. (London) Feb. 
 7, 1919. 
 Organization. 
 
 Inspection division Ordnance, American Machinist, Jan. 30, 1919. 
 
 Function organization chart for care of injured, American Machinist, 
 Jan. 16, 1919. 
 
 Amer. Rolling Mill Co., American Institute of Mining Engineers, 
 Vol. 59, 1918. 
 
 Commonwealth Edison, Power, July 30, 1918. 
 
 Power station, Edison 111. Co., Bhlyn, Power, July 23, 1918. 
 
 Buffalo Gen. Elec. Co., Power, July 16, 1918. 
 
 Works organization charts. Reeves, Society of Automotive Engineers 
 Journal, July, 1917. 
 
 Industrial organization chart, McMullbr, Society of Automotive Engi- 
 neers Journal, Jan., 1918. 
 
 Engineering division Motor Truck Corps, Society of Automotive Engi- 
 neers Journal, January, 1919. 
 
 Engineering standards committee. Engineering, May 4, 1917. 
 
 C. M. & St. P. superintendent motive power. Railway Mechanical 
 Engineer, November, 1918. 
 
 Organization for service tests, Railway Mechanical Engineer, July 1916. 
 
 Forest products laboratory. Industrial Management, August, 1919. 
 
 Planning department, Industrial Engineering, September, 1919. 
 
 Organization charts, Estes, Industrial Engineering, April, 1919. 
 
 Organization charts, Rogers and Scott, Industrial Engineering, April, 
 
 1919. 
 
 Organization class table (Franklin Co.), Industrial Engineering, Decem- 
 ber, 1916. 
 
234 GRAPHICAL METHODS 
 
 Organization charts, Engineering News-Record, Vol. 81, No. 7. 
 Navy Department, Engineering Magazine, November, 1916. 
 Factory eiEciency, Mason, Engineering Magazine, June, 1916. 
 Federal Trade Commission, Engineering Magazine, June, 1916. 
 British airplane inspection, Automotive Industries, Jan, 10, 1919. 
 U. 8. Army, American Machinist, Jan. 24, 1918. 
 U. S. Ordnance Department, American Machinist, Nov. 14, 1918. 
 Drafting room, Conway, American Machinist, Sept. 26, 1918. 
 Procurement division Ordnance, American Machinist, July 25, 1918. 
 Factory organization. White Motors Co., American Machinist, July 25, 
 
 1918. 
 Production division Ordnance, American Machinist, July 25, 1918. 
 Organization chart, large engine house, American Machinist, March, 
 
 1916. 
 Organization chart Council National Defense, Automotive Industries, 
 
 Nov. 22, 1917. 
 Packard Motor Car Co., Automotive Industries, Mar. 21, 1918. 
 Quartermaster Corps, U. S. A., Automotive Industries, July 25, 1918. 
 U. S. Aviation, Automotive Industries, Nov. 13, 1919. 
 Motor Transport Corps, Automotive Industries, Jan. 9, 1919. 
 Chart for production engineers. Reeves, Society of Automotive Engi- 
 neers, July, 1917. 
 Chart for sales engineers, Reeves, Society of Automotive Engineers, 
 
 July, 1917. 
 Shipyard and premium systems, Roberts, Society of Naval Architects & 
 
 Marine Engineers, Vol. 25, 1917. 
 Organization and route chart schedule 1 Reeves, Institute of Auto- 
 Department and plant organization \ mobile Engineers, Vol. 11, 
 
 chart J 1916-17. 
 
 Modern engineering works. Institute of Automobile Engineers, Vol. 13, 
 
 1919. 
 Textile engineer, Perkins, The Textile World Journal, Mar. 3, 1917. 
 
 Performance twenty inch dredge. Engineering News-Record, Vol. 81, 
 
 No. 24. 
 Pipes. 
 
 Carrying capacity steam lines, Power, Dec. 18, 1917. 
 
 Heat losses, Bagley, Power, Dec. 24, 1918. 
 
 Steam flow. Shearer, Power, Oct. 15, 1918. 
 
 Velocity of water in tubes, American Institute of Chemical Engineers, 
 
 Vol. 10, 1917. 
 Oil field pipe cost, American Institute of Mining Engineers, Vol. 59, p. 
 
 536, 1918. 
 Steam pipe sizes saturated and superheated steam, American Society of 
 
 Naval Engineers, p. 418, 1918. 
 Steam trap ratings and capacity, American Society of Naval Engineers, 
 
 p. 432, 1919. 
 
BIBLIOGRAPHY 235 
 
 Power. 
 
 Distribution Steam Plant, Engineering Magazine, September, 1915. 
 
 Loads, Clbwell, American Machinist Mar. 20, 1919. 
 
 Tests Hardinge mill, Taggert, American Institute of Mining Engineers, 
 
 Vol. 58, 1918, log. 
 Plant efficiency, Azbe, Power, Dec. 26, 1916. 
 Plant design and operation, Pigott, Power, Jan. 9, 1917. 
 Power to turn gasoline engine. Getting, Society o} Automotive Engineers, 
 
 February, 1918. 
 Power to swing bridges. The Engineer. (London) Feb. 16, 1917. 
 Power to crank 3%6 X 4% in motor, Society of Automotive Engineers. 
 
 Price. 
 
 Price fluctuations. 
 
 Price lead. Engineering and Mining Journal, Jan. 11, 1919. 
 
 Price base metals, Engineering and Mining Journal, Jan. 11, 1919 
 
 Average of monthly prices. Engineering and Mining Journal, Jan. 11, 
 
 1919. 
 Pig iron and cast-iron pipe. Engineer and Contractor, Aug. 29. 1917. 
 Price fixing machine tools, American Machinist, Aug. 21, 1919. 
 Price pig iron and production. Automotive Industries, Nov. 14, 1918. 
 
 Production. 
 
 Production record, Bundbsman, Industrial Engineering, November, 
 1919. 
 
 Progress, Knoeppel, Industrial Engineering, November, 1918. 
 
 Soft coal. Engineering News-Record, July, 1918 
 
 Rand mining. Key, Engineering and Mining Journal, Apr. 19, 1919. 
 
 Progress five story building. Engineer and Contractor, June 27, 1917. 
 
 Asphalt paving plan, Engineer and Contractor, Dec. 4, 1918. 
 
 Government work, Schuyler, American Machinist, Feb. 21, 1918. 
 
 Shop production. Rich., American Machinist, Mar. 27, 1919. 
 
 Future production oil wells, American Institute Engineers, Vol. 59, 
 1918. 
 
 Coal production, American Institute of Mining Engineers, Vol. 69, 1918. 
 
 Petroleum production, Stratford, Society of Automotive Engineers, 
 July, 1918. 
 
 Production and consumption of gas, PoGUE, Society of Automotive 
 Engineers, April, 1919. 
 
 Coking industry growth. Gas Engineers Journal, Mar. 10, 1917. 
 
 Load curves, gas output, Gas Engineers Journal, June 28, 1918. 
 
 Freight, passenger and locomotive orders. Railway Mechanical Engi- 
 neer, January, 1918. 
 
 Pig iron. Automotive Industries, Nov. 14, 1918. 
 
 Production and price of automobiles, 1915-19, Automotive Industries, 
 June 12, 1919. 
 
 Production crude petroleum, Stratford, Society of Automotive Engi- 
 neers, July, 1918. 
 
 Production shipyards, Bakenhus, Society of Naval Architects & Marine 
 Engineers, Vol. 27, 1919. 
 
236 GRAPHICAL METHODS 
 
 ■ Chart for production engineers, Reeves, Institute of Automobile 
 
 Engineers, Vol. 11, 1916-17. 
 Progress, Knobppel, Industrial Engineering, November, 1918, Septem- 
 ber, 1919. 
 Progress, Johnson, Industrial Management August, 1919. 
 Progress, boiler house. Engineering Magazine, September, 1915. 
 Progress, man. Industrial Management August, 1919. 
 Propellers. 
 
 Cavitation curves, Holst, Scientific American Supplement, May 12, 
 
 1917. 
 Model screw propeller experiments, Engineering, June 8, 1917. 
 Curves for propeller design, American Society of Naval Engineers, p. 538, 
 
 1918. 
 Economy of propulsion, engine and propeller, American Society of Naval 
 
 Engineers, p. 556, 1919. 
 Efficiency of airplane propellers. Automotive Industries, Caldwell, July 
 
 18, 1918. 
 Air propeller calculation charts, Caldwell, Society of Automotive ' 
 
 Engineers, August, 1918. 
 Propeller characteristics, thrust and torque, McEnteb, Society of Naval 
 
 Architects & Marine Engineers^ Vol. 26, 1918. 
 Purchase charts, Sutton, Industrial Engineering, March, 1919. 
 
 R 
 Radiation. 
 
 Radiation walls, Toensfeldt, Power, Nov. 27, 1917. 
 
 Radiation required in buildings, American Society of Heating & Ventilatr 
 
 ing Engineers, Vol. 25, p. 196, 1919. 
 Radiators (airplane) performance. Society of Automotive Engineers, 3nne, 
 
 1919. 
 Rails, transverse fissure, American Institute of Mining Engineers, Vol. 
 58, 1918. 
 Rates. 
 
 Piece work. 
 
 Charts, Burkhakdt, American Machinist, Aug. 29, 1918. 
 Wages calculated by various formulae, Le Genie Civil, Nov. 30, 1918. 
 Readability of radio telegraph messages, Le Genie Civil, Aug. 3, 1918. 
 Record. 
 
 Machine and idleness. Industrial Management, August, 1919, Engineer- 
 ing News-Record, Vol. 81, No. 10. 
 Refrigerating. 
 
 Power plants, Azbb, Power, Mar. 19, 1918. 
 
 Charts of refrigerating car temperatures. Railway Mechanical Engineer, 
 November, 1916. 
 Riveted joints. 
 
 Riveted joints. Power, May 22, 1917. 
 Safe working pressure on, Power, Mar. 27, 1917. 
 
 Strength and efficiency boiler seams, Parks, Railway Mechanical 
 Engineer, March, 1918. 
 
BIBLIOGRAPHY 237 
 
 Roads. 
 
 Miles improved in twelve states, Automotive Industries, Sept. 6, 1917. 
 Routing. 
 
 Wood working, Bigblow, Industrial Engineering, September, 1919. 
 Supplies of drafting department, Hamilton, Industrial Engineering, 
 
 October, 1918. 
 Customers order, Harrison, Industrial Engineering, December, 1919. 
 Routine chart for purchasing and allied departments, Reeves, Institute 
 
 of Automobile Engineers, Vol. 11, 1916-19. 
 
 S 
 Ships. 
 
 Skin friction resistance, Baker, Scientific American Supplement, Nov. 
 
 17, 1917. 
 Launching calculations. Engineering, Apr. 13, 1917. 
 Weights displacement and cargo of concrete vessels, Pollock, Engineer- 
 ing, Apr. 11, 1917. 
 Sizes and speeds cargo vessels, Anderson, Engineering, Mar. 22, 1918. 
 .Lost through enemy action. Engineering, Dec. 13, 1918. 
 Loss during war, Le Genie Civil, Mar. 23, 1918. 
 Alignment chart distance travelled, U. S. S. Wyoming, American Society 
 
 of Naval Engineers, p. 662, November, 1917. 
 Pressure on rudder and variation., American Society of Naval Engineers, 
 
 p. 695, 1918. 
 Economy cargo ship calculation, Robertson, Society of Naval Architects 
 
 & Marine Engineers, Vol. 27, 1919. 
 
 Shipyard factors and output, Bakenhus, Vol. 27, 1919. 
 S, miscellaneous. 
 
 Soap film stress, GRirriTH, Engineering, Dec. 21, 1917, 28, 1917. 
 Solubility of calcium chloride in water. Power, Aug. 19, 1919. 
 Shovelling, study of, Harlby, American Institute of Mining Engineers, 
 
 Vol. 61, 1919. 
 Spikes, withdrawal tests, Engineer and Contractor, Nov. 19, 1919. 
 Soots and soot blowers. Power, June 11, 1919. 
 Steam. 
 
 Saturation and superheat, Pearce, Power, Aug. 5, 1919. 
 
 Strength. 
 
 Strength curves, C. I., Power, July 23, 1918. 
 
 Load extensometer diagrams (autographic). Engineering, May 18, 1917. 
 Alternative stress experimental charts, Engineering, Feb. 23, 1917. 
 Stresses in discs with hole. Knight, Engineering, Aug. 3, 1917. 
 Physical characteristics, S. A. E. steels (ten charts). Society of Automo- 
 tive Engineers Handbook. 
 
 Temperature. . ir r> j 
 
 Temperature frozen and unfrozen subsoils Engineering News-Record, 
 
 Vol. 83, No. 3. ,, . T 1 101R 
 
 Temperature wet and dry bulb charts. Engineering Magazine, July, 191b. 
 
238 GRAPHICAL METHODS 
 
 Temperature curves in guns, AmericMV, Machinist, May 23, 1918. 
 Temperature effects on grain size and on mechanical properties of 
 
 metals, Jefpeies, American Institute of Mining Engineers, Vol. 60, 
 
 1919. 
 Heat insulating material, Power, May 1, 1916. 
 Heat transfer per hour Allan, Power, Oct. 16, 1916. 
 Heat balance charts, U. S. nitrate, May 27, 1919. 
 Metals at high temperatures, Williams, Power, July 1, 1919. 
 Forecasting changes in, Febgusson, Scientific American Supplement, 
 
 Mar. 31, 1917. 
 Freezing temperature scales. Society of Automotive Engineers Handbook. 
 Temperature altitude curves. Society of Automotive Engineers Handbook. 
 Distribution of temprature in bearings, Alpobd, Bearings. 
 Relation of speed and temperature use in bearings, Alpord, Bearings. 
 Expansion of material with heat, Le Genie Civil, Oct. 30, 1920. 
 Melting temp. Copper-Zinc alloys, American Gas Journal, Mar. 2, 1918. 
 Heating up curve, gas range oven, American Gas Journal, Jan. 6, 1918. 
 Boiling water in vacuum, American Institute of Chemical Engineers, 
 
 Vol. 10, 1917. 
 Effect of temperature on metal hardness, American Institute of Mining 
 
 Engineers, Vol. 60, 1919. 
 Temperature humidity and air motion, American Society of Heating & 
 
 Ventilating Engineers, Vol. 25 
 Temperature rise in different bearings, Society of Automotive Engineers 
 
 Handbook. 
 Temperature rise and speed in bearings, Alpobd, Bearings. 
 Time. 
 
 Time curves for shovels, Dana, Handbook Steam Shovel Work. 
 Time (idle) for shovels, Dana, Handbook Steam Shovel Work. 
 Time (working) for shovels, Dana, Handbook Steam Shovel Work. 
 Tonnage handled by train ferries, Engineering, Jan. 24, 1919. 
 Tolerance chart. Motor Transportation Corps, Society of Automotive 
 
 Engineers, February, 1919. 
 Tractor. 
 
 Tractor engine tests, Dasey, Automotive Industries, Nov. 21, 1918. 
 Tractor gear ratios. Automotive Industries, Aug. 29, 1918. 
 Accelerometer curves (Wimperis), Heldt, Automotive Industries, 
 
 June 10, 1920. 
 Accelerometer data, Speedway test, Society of Automotive Engineers, 
 
 May, 1917. 
 Tractive effort and brake horsepower, Society of Automotive Engineers 
 
 Handbook. 
 Tractive effort and road resistance. Society of Automotive Engineers 
 
 Handbook. 
 Traction effort and farm tractor, Society of Automotive Engineers Hand- 
 book. 
 Resistance of automobiles and effect on speed, Wimperis. 
 Resistance of wheels to rolling, Hiehman. 
 Resistance of automobiles to starting, Hbibman. 
 
BIBLIOGRAPHY 239 
 
 Tractive resistance on pavements, Baenett, Engineer and Contractor 
 Nov. 6, 1918. ' 
 
 Traction and gas consumption, Engineer and Contractor, May 7, 1919. 
 
 Wind resistance of train, Marshall, Engineer and Contractor July 30 
 1919. ' 
 
 Grades and traEer loads, Marshall, Engineer and Contractor Dec 3 
 1919. ' ■ ' 
 
 Wind resistance and railway speeds, Marshall, Scientific American 
 
 Supplement, Aug. 16, 1919. 
 Road resistance and adhesion, Chorlton, Society of Automotive Engi- 
 neers, 1918. 
 Traction and speed and horsepower of locomotives. The Engineer. 
 
 (London) Apr. 26, 1918. 
 Acceleration and retardation. May 3, 1918. 
 Road resistance and adhesion, Chorlton, The Engineer. (London) 
 
 Jan. 4, 1918. 
 Energy consumption of electric vehicles. The Engineer. (London) Dec 
 
 5, 1919. 
 Noise and mechanical traction, Le Genie Civil, Jan. 17, 1920. 
 Drawbar pull and horsepower of locomotive. Railway Mechanical 
 
 Engineer, February, 1918. 
 Speed, time, resistance and traction of locomotives. Railway Mechanical 
 
 Engineer, October, 1917. 
 Speed pull curves and traction of locomotives, Railway Mechanical 
 
 Engineer, July, 1916. 
 Critical point wheel sliding, Railway Mechanical Engineer, June, 1917. 
 Trucks. 
 
 Truck impact tests. Engineering News-Record, Vol. 83, No. 12. 
 Truck efficiency, Davis, Automotive Industries, Jan. 3, 1918. 
 Truck operation, Davis, Society of Automotive Engineers, October, 1919. 
 Distribution of motor truck weights, Heldt, Automotive Industries, 
 
 July., 11, 1918. 
 Truck load capacity and yearly production. Automotive Industries, Jan. 
 
 1919. 
 Truck design tendencies, 1920, Schipper, Automotive Industries, Jan. 15, 
 
 1920. 
 
 V 
 Vacuum. 
 
 Vacuum for steam plants. Baker, Power, Dec. 4, 1917. 
 Vital Statistics. 
 
 Vital statistics, Goldberger, Industrial Engineering, November, 1918. 
 
 Engineering News-Record, Vol. 83, No. 2. 
 Mine accidents, Charlton, Engineering and Mining Journal, Nov. 30, 
 
 1918. 
 Engineering graduates University of Illinois, Engineer and Contractor, 
 
 May 28, 1919. 
 Visualizing accidents, American Machinist, May 17, 1917. 
 Endurance of human body, Elmendorp, Scientific American Supple- 
 ment, Aug. 11, 1917. 
 
240 GRAPHICAL METHODS 
 
 Food curves and calories, Horning, Society of Automotive Engineers, 
 July, 1917. 
 Volume. 
 
 Volume of tanks, horizontal cylindrical, Szabo, Engineering News- 
 Record, Vol. 81, No. 14; Society of Automotive Engineers Handbook, 
 Power, Aug. 20, 1918. 
 
 W 
 
 Water. 
 
 Reservoirs, regulating. Engineering News-Record, Vol. 81, No. 10. 
 
 Irrigation, Engineering News-Record, Vol. 83, No. 12. 
 
 Rainfall, Engineer and Contractor, Oct. 9, 1918. 
 
 Maximum rainfall, American Society of Civil Engineers, Vol. 81, De- 
 cember, 1917. 
 
 Flood records at Yuma, American Society of Civil Engineers, Vol. 82, 
 1918. 
 
 Rainfall, Engineer and Contractor, Dec. 4, 1918. 
 
 Softening water, Stein, Engineer and Contractor, Apr. 7, 1919. 
 
 Waste prevention, Lanham, Engineer and Contractor, Dec. 10, 1919. 
 
 For crops, American Society of Civil Engineers, February, 1918. 
 
 Reservoirs, flood control, American Society of Civil Engineers, May, 1918. 
 
 Mine flooding, Rood and Hobton, American Institute of Mining 
 Engineers, Vol. 61, 1919. 
 
 Bacteria resistance to filtration. Engineering. (London) Feb. 9, 1917. 
 
 Altitude and boiling point of water. Society of Automotive Engineers 
 Handbook. 
 
 Water meters loss of head, Engineering News-Record, Vol. 81, No. 24. 
 Weight. 
 
 Flat steel, Society of Automotive Engineers Handbook. 
 
 Spur gear blanks, Logue, Gear Book. 
 
 Prime movers and electric apparatus, Lepax. 
 
 Weighing machine hysteresis loop, Schlink, Engineering, Feb. 14, 1919. 
 
BIBLIOGRAPHY 
 
 Handbooks 
 
 In addition to the list of books, pamphlets and magazine articles dealing 
 with methods of graphical presentation, there is also presented here a list of 
 the diagrams which were noted in the handbooks of various branches of 
 engineering. 
 
 Handbook of Mechanical and Electrical Cost Data, Gillette and Dana. 
 
 Diagrams. Curve of steam consumption with superheat. 
 
 Twenty diagrams cost per brake horsepower, running various hours per 
 
 day with coal of different prices and B.t.u. 
 Effect of air on furnace efficiency. 
 Relation between furnace efficiency and CO loss. 
 Relation between furnace efficiency and excess air. 
 Comparative efficiency, first cost and annual charges of coal, oil and gas 
 
 plants. 
 Per cent of ash in dry coal and horsepower. 
 Per cent of ash in dry coal and value of coal. 
 Relative value of anthracite and semi-bituminous coal. 
 Heating value of coal and proximate analysis. 
 Weight of prime movers (log. scale.) 
 
 Cost of direct connected engine driven D.C. and A.C. generators. 
 Power required to push gases through boiler and furnace. 
 Approximate yearly cost of steam power 150 days at 10 hour per day. 
 Power of efficiencies, producer gas (bar chart). 
 Power efficiencies, oil (bar chart). 
 Power efficiencies, water (bar chart). 
 
 Comparative efficiencies of various sources of power (bar chart). 
 Cost of complete electric power plants. 
 Boiler efficiency chart. 
 
 Steam power cost of fuel per horsepower hour. - 
 Producer gas cost of fuel per horsepower hour. 
 Oil, cost of fuel per horsepower hour. 
 Cost of labor, steam, gas and oil electric plants. 
 Effect of coal cost on power cost. 
 
 Comparison of Diesel and 600 kilowatt steam turbine plants. 
 Comparison of costs per brake horsepower of steam, electricity, gas, and 
 
 gasoline in small powers. 
 Curves of lighting loads for different hours in day. 
 Floor space required for gas engines. 
 Cost of operating oil engines. 
 Weight of wood poles of varying height. 
 Cost of iron poles and load in pounds. 
 Comparative costs of transmission lines. 
 Cost of underground telephone cable. 
 16 . 241 
 
242 GRAPHICAL METHODS 
 
 Average candle-power ranges of old and new lamps. 
 
 Curves of average wages relation to lighting costs. 
 
 Costs of pulley drives. 
 
 Economical belt sizes. 
 
 Chart for coal required per season for steam and hot water heating. 
 
 Costs, capacities, depreciation, horsepower of conveyors, hoists cranes, 
 etc. 
 
 Charts of insulation of pipes. 
 
 Cost of ice per ton. 
 Electric Railway Handbook, Richey. 
 
 Curve of energy saved by use of grades in station stops. 
 
 General energy output charts. 
 
 Power required per ton weight of train. 
 
 General straight line speed-time curves. 
 
 Typical speed and distance curves. 
 
 Typical coasting, braking and distance curves. 
 
 Chart of acceleration coefficient. 
 
 Method of joining retardation and acceleration curves. 
 
 Typical run curves. 
 
 Effect of temperature on power station load. 
 
 Freight train resistance. 
 
 Train resistance locomotive and train (Armstrong formula). 
 
 Train resistance five-car train (Armstrong formula). 
 
 Train resistance three-car train (Armstrong formula). 
 
 Train resistance two-car train and one-car (Armstrong formula). 
 
 Movement of passengers boarding cars. 
 
 Typical performance curves of car with different gear ratios. 
 
 Motor characteristic curves. 
 
 Sag and pull of double track span wires. 
 
 Current and resistance, lead, and lead alloy cable sheath and pipe. 
 
 Chart for calculating feeder drop and capacity. 
 
 Comparative costs copper and aluminum conductor. 
 Handbook Overhead Line Construction. 
 
 Insulator test curves. 
 
 Conductor and wire curves. 
 
 Transformer iron loss. 
 
 Relation between length and sag per foor of space. 
 Handbook of Hydraulics, King. 
 
 Diagram for solution of Manning's Formula, Flow of water in open 
 channels. 
 
 V = — r^s^ n = coeflBcient of roughness. 
 
 r = hydraulic radius, feet. S = slope. 
 
 Y = velocity feet per second. 
 Also discharge, mean velocity and area curves for discharge of streams. 
 The ordinary discharge curve when plotted on log paper becomes a 
 straight line. 
 
 Hydrographs are used, which are graphical representations of records of 
 discharge, the ordinates expressing discharges and the abscissas time. 
 
BIBLIOGRAPHY 243 
 
 Comparison diagram of Fteley and Stearns experimental values of 
 discharge over suppressed weirs. Also comparison of Bazin, Francis 
 King, Fteley and Stearns formula for discharges. 
 
 Chart showing discrepancies of above theoretical and experimental 
 formulae. 
 
 Civil Engineers' Handbook, Merriman. 
 
 Area of culverts by various formulae compared by graphical chart 
 
 (seven curves). 
 Chart to locate spacing of turnouts or passing points. Vertical scale 
 
 minutes (zero at top). Horizontal scale miles. 
 Stress-elongation diagram. 
 
 Properties of mortars made of different mixtures of sand. 
 Effect of consistency on amount of water and variation of tensile 
 
 strength with age. 
 Variation of compressive strength with age. 
 Charts of mechanical analysis of two sizes of aggregate and combining 
 
 two sizes of aggregate. 
 Effect of mica on tensile strength of mortar. 
 Diagram showing size of steam plant to supplement deficiency of flow 
 
 in watershed. 
 
 Civil Engineers' Handbook, Trautwine. 
 
 Ultimate stresses in reinforced beam chart. 
 Working stresses in reinforced beam chart. 
 Scales for strength of concrete. 
 
 Diagram showing values of - = \t~aL jp) (columns) for medium 
 
 and nickel steel and wrought iron. 
 Diagram for maximum sharpness of curves for various speeds of railroad 
 
 trains. 
 Charts of resistances of trains. 
 Values of friction factor F. for iron pipe. 
 Discharges, velocities and head losses in pipes and conduits by Williams- 
 
 Hazen formula. V = CHy''.«3-S».»^0.001-»." complicated log and 
 
 curve diagrams. 
 
 Mechanical Engineers' Handbook, Marks. 
 
 Kennison's open channel flow diagram for the Kutter formula. 
 Discharge coefficient for square ring nozzles (rectangular). 
 Coefficient for sharp edge orifices (J^ log.) 
 Plain scale showing on one side depth of bottom of plane below water 
 
 surface. On other side total hours pressure in pounds on planes 
 
 extending from water surface to depths indicated on upper half of 
 
 scale. 
 Conversion head for water. Head in feet to pressure in pounds per 
 
 square inch. 
 Diagram of influence of bearing temperatures on the coefficient of 
 
 journal friction. 
 Chart for determining factors of evaporatiori. 
 Heat carried away by chimney gases in B.t.u. 
 
244 GRAPHICAL METHODS 
 
 Ratio of air supplied per pound of combustible to that theoretically 
 required. 
 
 Diagram for designing worm gearing of maximum efficiency. 
 
 Efficiency of worm gearing. 
 
 Diagrams for determining diameters of shafts subjected to torsion and 
 bending. 
 
 Chart for loss of pressure in forced ventilation. 
 
 Chart for loss of pressure ia heating and ventilating by gravity. 
 
 Chart for loss of pressure in steam one pound per square inch mean 
 gauge pressure. 
 
 Chart for loss of head in forced hot water heating. 
 
 Charts for locomotive performance. 
 
 Costs of hauling by horse teams, trucks and tractors. 
 
 Costs of loading and hauling gravel. 
 
 Refrigeration produced by brine. 
 
 Properties of calcium chloride solutions. 
 
 Relations between temperature pressure and concentration of aqua 
 ammonia. 
 
 Relation between temperature specific gravity and concentration of 
 aqua ammonia. 
 
 Costs of electric motors, wires and cables. 
 
 Determination of economic cross-section of copper and aluminum con- 
 ductors. 
 
 Torque curves of induction and direct current motors. 
 
 Characteristics of different kinds of fans. 
 
 Characteristics curves of centrifugal compressors. 
 
 Chart of work done in one, two, and three stage air compression. 
 
 Efficiencies in centrifugal pumps. 
 Pocket Book Electric Lighting and Heating, Walker. 
 
 Curves for incandescent lights run above and below normal pressure. 
 
 Curves of demand indicators. 
 
 Callender's curves for three-phase transmission. 
 
 Callender's curves for two-wire feeders. 
 
 Efficiency and regulation curves of transformers. 
 
 EflBciency and regulation loss curves of alternators and generators. 
 
 Eddy current losses in sheet iron. 
 
 Magnetization curves of steel and iron. 
 Milling Engineers' Handbook, Peele. 
 
 Compressive strength of concretes. 
 
 Average strength of mortars. 
 
 American rope drives, horsepower per part of rope. 
 
 English hemp rope drives. 
 
 Belt speeds and horsepower. 
 
 Centrifugal pump curves. 
 
 Speed and efficiency of reciprocating pumps. 
 
 Chart for flow of steam or air in pipes (log.). 
 
 Condenser water ratio chart. 
 
 Mollier entropy diagram. 
 
 Horsepower for various stage air compressors. 
 
BIBLIOGRAPHY 245 
 
 Hydrograph of stream flow. 
 Diagram for solving Hazen- Williams formula. 
 Diagram for solving Kutter formula. 
 Scheme for smelting lead-silver ores. 
 Scheme for treating copper ores. 
 CarryiQg capacity belt conveyors. 
 Weight of belt conveyors. 
 Diagram for weight of flywheel. 
 Rail bond resistance chart. 
 
 Pressure voltage and efficiency curves of turbo-blower. 
 Bending stresses in hoisting ropes. 
 Engineer's Field Manual. 
 
 U. S. Corps of Engineers. 
 
 Graphical scale for running time of trains and construction of time 
 tables. 
 Handbook of Natural Gas, Wescott. 
 
 Monthly fluctuations in average daily rate of production and consump- 
 tion and in stocks of domestic crude petroleum, 1918-1919. 
 Chart of comparative value of sales of natural gas and gasoline, 1918- 
 
 1919. 
 Chart for calculation of flue gas analysis from analysis of natural gas. 
 Chart of home wastes of natural gas (bar charts). 
 Chart of decrease in price and increase in B.t.u., Los Angeles, Cal. 
 Full costs of meals (bar chart). 
 Chart of line loss when meters are read continuously throughout the 
 
 year. 
 Hourly and monthly peak load. 
 
 Per cent of open flow of gas well capacity available for domestic use. 
 The Naval Constructor, Simpson. 
 Oil fuel consumption chart. 
 Chart for ventilation pipes. 
 
 Diagrams of ordered lengths of rivets, countersunk points. 
 Wrought iron rings, safe working load. 
 Ordered lengths of rivets. 
 Ship resistance curves. 
 Stability curves. 
 Railroad Curves and Earthwork, Allen. 
 
 Standard diagram giving minimum lengths of casement curves for 
 
 various speeds and degrees of curve. 
 Diagrams for earthwork calculation, prismoidal corrections, and 
 
 triangular prisms. 
 Mass diagrams for earthwork calculations. 
 Highway Inspectors' Handbook, Hubbard. 
 
 Equivalent of inches in decimal parts of a foot. 
 
 Diagrams for calculating contents of cylindrical tanks. 
 
 Volumes per linear feet represented by various end section areas. 
 
 Area of 100 linear feet of road. 
 
 Length of road represented by 100 square yards. 
 
 Length of road represented by one square yard. 
 
246 GRAPHICAL METHODS 
 
 Crown section areas. 
 
 Quantities of material required for filling joints in brick pavements. 
 
 Quantities of material required for different parts of road sections. 
 
 Fine aggregate and cement required for concrete construction. 
 
 Length of road which may be treated with 100 gallons bituminous water. 
 
 Quantities of broken stone required for macadam. 
 
 Quantites of broken slag required for macadam. 
 
 Bushels of clean oyster shells required for shell roads. 
 
 Cubic yards of gravel and tons of gravel for gravel roads. 
 
 Quantities of material required for sand clay construction. 
 
 Equivalent of Fahrenheit and Centigrade scale. 
 
 Resistance of rock to abrasion and wear. 
 
 Toughness of rock. 
 
 Relation of hardness and toughness. 
 
 Weight and volume of broken stone. 
 
 Weight and volume relations for dry quartz sand. 
 
 Weight and volume relations for bituminous materials. 
 
 Weight of bitumen per gallon of bituminous water. 
 
 Volume of bitumen per ton of asphalt. 
 
 Volume of bitumen per ton of tar. 
 
 Volumes at elevated temperatures equivalent to 100 gallons at normal 
 temperature and reverse. 
 Waterworks Handbook, Fliim, Weston and Bogart. 
 
 Economical dimensions of filter beds. 
 
 Effective size of sand. 
 
 Loss of head in filters. 
 
 Expansions of normal sands at optimum velocity of wash water. 
 
 Discharges through circular orifices. 
 
 Time of settling of particles in water. 
 
 Discharge through circular sluice gates. 
 
 Diagram of economic size of pipe for high pressure. Waterpower 
 installations. 
 
 Friction head diagrams (log) (Prof. I. P. Church) for pipes. 
 
 Values of Chezy's C. for new and tuberculated cast-iron pipes and 
 rivetted. 
 
 Flow from six, eight and twelve inch cast-iron pipe. Box's formula. 
 
 Equivalents of parallel pipes. 
 
 Flow in cast iron pipes, Box's formula (Nomography chart). 
 
 Wooden tanks, stress in hoops and spacing of hoops. 
 
 Discharge diagram for venturi meters. 
 
 Nomographic chart of costs of cast-iron water pipe. 
 
 Impounding reservoirs, relation of run-off, rise, waste and overflow. 
 
 Discharge of waste weirs of various lengths. 
 
 Quantity collected, or run off from watershed in 24 hrs. 
 
 Storage capacity one square mile of drainage area. 
 
 Relation of capillary rise to effective size. 
 
 Average daily yield of one square mile of drainage area. 
 
 Type of diagram showng relation of precipitation, run-off and tempera- 
 ture (bar type). 
 
BIBLIOGRAPHY 247 
 
 Stream flow diagram. 
 
 Transpiration curve. 
 
 Evaporation curves — water, snow, ice and shallow water. . 
 
 Evaporation from land for various temperatures and rainfall rates. 
 
 Relation between intensity and duration of rainfall. 
 
 Marine Engineers' Handbook, Sterling. 
 
 Classiiication of blast furnace products. 
 
 Comparison of full costs for oil and coal (Harrison Safety Boiler Works). 
 
 Absolute viscosity conversion curves. 
 
 Pressure, capacity curves. Bureau Steam Engineering Typo Standard. 
 
 Pressure atomizer. 
 
 Pressure atomizer, Peabody Press atomizer. 
 
 Pressure atomizer, Schutte-Koerting atomizer. 
 
 Temperature viscosity curves light and heavy oils. 
 
 Oil burned per square foot of water heating surface. 
 
 Alignment chart. Specific volume of superheated or wet steam. 
 
 Relation between turbine efficiency and speed ratio. 
 
 Performance curves. Westinghouse and gears. 
 
 Performance curves, Poole, U. S. Eagle boats. 
 
 Relation effective horsepower to speed. 
 
 Proportion steel and of cast-iron piston (design). 
 
 Changes in valve functions for open and closed rods. 
 
 Condenser insulating water temperature. 
 
 Ship resistance forms. 
 
 Speed horsepower and length charts. 
 
 Cavitation chart. 
 
 Centrifugal pump efficiency charts. 
 
 Fan discharge curves. 
 
 Insulation for pipes, efficiency charts. 
 
 Concrete Engineers' Handbook, Hool and Johnson. 
 
 Chimneys flexure and dead load. 
 
 Concrete walls for wheat bins. 
 
 Box culverts. 
 
 Arches, stresses and values of coefficient, thrusts, moments. 
 
 Thickness of arch crown. 
 
 Retaining walls, reinforcement. 
 
 Retaining walls, proportions. 
 
 Column footings. 
 
 Moments in columns. 
 
 Bending and direct stress. 
 
 Rectangular beam and slab chart. 
 
 Approximate weight of rectangular beams. 
 
 Moment diagrams for beams. 
 
 Spacing of stirrups. 
 
 Rise in temperature of mass concrete in setting and hardenmg. 
 
 Stress, steam curves for concretes. 
 
 Comparison of strength with age. 
 
 Effect of lime on strength. 
 
248 GRAPHICAL METHODS 
 
 Effect of salts on strength. 
 Effect of mixing time on strength. 
 Effect of composition on strength. 
 Effect of size of sand on strength. 
 Proper consistency of concrete for road work. 
 Structural Engineers' Handbook, Ketchum. 
 
 Normal wind load on roof according to different snow load on roofs. 
 Quantities of masonry in abutments, N. Y. C. & H. R. R. R. 
 Quantities of masonry in abutments, lU. Central R. R. 
 Weight of steel viaducts and single track, through deck and plates girder 
 
 bridges, etc. 
 Bending moments in floor beams. 
 
 Safe working stresses in crucible steel round hoisting rope. 
 Stresses in square plates. 
 Stresses in eye bars due to weight. 
 
 Fan Engineering (Buffalo Forge Co.) 
 
 Relation between heater surface and temperature of air with steam 
 
 pressure from to 100 pounds. 
 Maxmium economic velocity of air through heater. 
 Velocity of water and heat transmission. 
 
 B.t.u. per square foot per hour per degree difference in temperature. 
 Rate of heat transmission for indirect or pipe coil heater. 
 Performance of pressure blowers. 
 Performance of exhausters. 
 Equalizing friction for piping. 
 Efficiency of diverging nozzles. 
 
 Psychrometric chart for wet and dry bulb thermometers. 
 Effect of temperature on air velocity. 
 Relation of altitude to air properties. 
 Specific weight of water vapor. 
 
 Handbook of Machine Shop Management, Van Deventer. 
 
 Organization chart. 
 
 Drafting room organizations.. 
 
 Production order system. 
 
 Production charts. 
 
 Graphical analysis of defects. 
 
 Analysis of expense with production factors. 
 
 Handbook for Heating and Ventilating Engineers, Hoffman. 
 Pipe diameters and friction heads. 
 
 B.t.u. transfer through one square foot of surface per hour. 
 Hygrometric chart. 
 
 Mechanical Engineers' Pocket-book, Kent. 
 
 Per cent of power gained by vacuum. 
 
 Pounds of water evaporated per square foot heating surface. 
 
INDEX 
 
 Accelerometer records, 198 
 Accidents, Fig. 84 
 Alignment diagrams, 169 
 chart classes, 176-178 
 
 construction. Figs. 163-165 
 moduli, Fig. 166 
 Amperes and volts. Figs. 118, 119 
 Analysis diagrams, 106, 108, 109, 
 
 139-141 
 Analytical, graphs, 14 
 Apportioning diagrams, 69 
 
 of costs. Figs. 51-63 
 Area diagrams, 129 
 
 irregular figures. Figs. 124, 125 
 Arith-log paper, 21, 23 
 Army mental tests, Figs. 65, 66 
 Arrangement of graphs, 35, 36 
 Assembly diagrams, 130 
 of rifles. Fig. 90A 
 Bolt action, Fig. 130 
 Automobile Co. organization chart. 
 
 Fig. 131 
 Automobile design trends, 88, Fig. 
 81 
 characteristics. Fig. 94 
 
 B 
 
 Bacharach blast furnace record. Fig. 
 196 
 gas volume record, Fig. 205 
 Bailey boiler meter chart, Fig. 173 
 Barograph paper, 32 
 record, Fig. 220 
 Barographs, 37-39, 61-67 
 Barometer record. Figs. 207, 208 
 and thermometer record, Fig. 
 209 
 Belt horsepower. Fig. 112 
 Bibliography, 221-248 
 Boiler Flues, strength charts. Figs. 
 143, 147, 148 
 
 Bolt action assembly. Fig. 130 
 Books, 221 
 
 Brake (prony) record. Fig. 158 
 Bristol Time record. Fig. 177 
 Brown thermometer record. Fig. 173 
 recording pyrometer record, 
 Fig. 206 
 
 Calculation diagrams, 14, 142-166 
 Candlepower polar diagram, Fig. 
 
 107 
 Cardiograph record, Fig. 180 
 Cards for filing, 12 
 Caution about diagrams, 39 
 Census of States, Fig. 64 
 Chart cards, 31 
 Charts (mechanical), 186-220 
 Chemical steel analysis. Fig. 102 
 Civil engineers' handbook, 243 
 Classes of alignment charts, 176, 178 
 
 of nomograms, 175 
 Classification diagrams, 74 
 Colorograph chart. Fig. 219 
 Comparison valve inlets, Fig. 27 
 differentials and ratio. Fig. 23 
 interest by ratio. Fig. 24 
 sales and costs by ratio, Fig-. 26 
 Concrete engineers' handbook, 247 
 Conic sections, 117-126 
 Conjugal condition U. S., Figs. 45, 73 
 Conversion diagrams, 51, 62, 63 
 
 scales. Fig. 26 
 Coordinate paper, 20 
 Copper mill flow sheet. Fig. 128 
 Cost diagrams, 69, 74 
 
 railroad rates, Fig. 77A 
 distribution railroad operatives, 
 
 Fig. 39 
 motor truck operation, Fig. 60 
 of apportioning, Figs. 51-63 
 of pavements. Fig. 61 
 Costs vs sales, Fig. 91 
 
 249 
 
250 
 
 INDEX 
 
 Cranes, operating costs, Fig. 62 
 
 speed rating, Fig. 63 
 
 test curves. Fig. 109 
 Critical temperature curves, Fig. 213 
 Cross-section paper, 23, 25, 28, 29, 
 
 32, Figs. 9, 10 
 Cubic parabola, Fig. Ill 
 Cumulative charts, 39, 41, 94, 95 
 Curnon steam meter. Fig. 215 
 Curve plotting, 120 
 Cutters, spiral gears. Fig. 141 
 
 D 
 
 Daily record paper, 21 
 Deciding on diagrams, 16 
 Diagrams, 106, 108, 109, 139-141 
 
 analysis, 14 
 
 area, 129 
 
 assembly, 130 
 
 calculation, 14, 142-166 
 
 classification, 37, 83, 90-92, 99 
 
 computation, 14 
 
 conversion, 51, 52, 53 
 
 cost, 69, 74 
 Differential draft record. Fig. 197 
 Disc records, 188-194 
 Distance vs time. Figs. 30, 31 
 Distillation tests. Fig. 54 
 Dividends, U. S. Steel, Fig, 70 
 Drawbar tractor record. Figs. 200A, 
 201 
 
 E 
 
 Education rank, Fig. 60 
 Efficiency machine (Olsen), Fig. 199 
 Electric current record. Fig. 179 
 cost data handbook, 241 
 light heat handbook, 244 
 railway handbook, 242 
 Ellipse, Fig. 113 
 Energy diagram of automobiles, Fig. 
 
 35 
 Engine, car and gear ratio. Fig. 159 
 Engineering journals, 221-248 
 Engineers' field handbook, 245 
 Equation curves, 117-125 
 
 Equilibristat (Wimperis), Fig. 186 
 Esterline power and time records, 
 
 Figs. 214, 217 
 Examples (general), 12, 50, 114, 115 
 
 (nomography), 178 
 Expansion of gases. Fig. 115 
 Experiment laws, 117-123 
 Export values. Fig. 42 
 
 Factory schedule. Figs. 87, 88 
 Fan engineering handbook, 248 
 Feed water records, Fig. 168 
 Filing cards. Fig. 12 
 Flow sheet (iron ore), Fig. 127 
 (copper ore). Fig. 128 
 (petroleum), Fig. 129 
 Form distribution, U. S. Ordnance 
 
 Department, Fig. 126 
 French land acquisitions, 6 
 Frequency graphs, 37, 40, 57, 77, 81 
 Friction losses, pipe. Fig. 153 
 
 G 
 
 Gasoline distillation curves. Fig. 93 
 Gas engine cards. Figs. 103-105 
 expansion. Fig. 115 
 pressure record, Fig. 184 
 power plant operation costs. 
 Fig. 82 
 Gear cutters for spiral gears, Fig. 141 
 Gear horse power. Fig. 121 
 Gear ratio, car and engine speeds. 
 
 Fig. 159 
 General equation. Fig. 139 
 G. E. flow meter record. Fig. 174 
 Graph and statistics, Fig. 56 
 Graphical record types. Fig. 167 
 
 records, 186 
 Growth of population (London), 
 Fig. 21 
 
 H 
 
 Handbooks (charts in), 241-248 
 Hays CO 2 recorder. Fig. 171 
 Heat distribution (Still engine). Fig. 
 35 
 
INDEX 
 
 251 
 
 Heat and ventilation handbook 
 
 248 
 Horse power of discs revolving m 
 
 steam, Figs. 145, 146 
 Belts, Fig. 112 
 gears, Fig. 121 
 Highway inspectors handbook, 245 
 Historical diagrams, 43 
 curves, Figs. 20, 22 
 Historigrams, 40, 42, 48, 83 
 Hyatt dynamometer. Fig. 175 
 Hydraulagraph, Fig. 195 
 Hydraulic turbine development. Fig. 
 
 5 
 Hydraulics, handbook, 242 
 Hyperbola, Fig. 114 
 
 Illustrative graphs, 14 
 Indicator cards, 110, 210, 211 
 Instrument control, Fig. 136B 
 
 for quality, Fig. 137 
 Integral diagrams, 128, 129 
 
 curves, Fig. 125 
 Intercept diagrams, 126 
 Internal-combustion engine cards, 
 
 Fig. 203 
 Investment history, public utility, 
 
 Fig. 76 
 Iron ore flow sheet, Fig. 127 
 
 K 
 
 M 
 
 Kinds of graphs, 13 
 paper, 21-34 
 
 Machine tool calculating. Fig. 156 
 shop management handbook, 
 248 
 Machinery, cost,- design, Pig. 136A 
 Magazine articles (bibliography), 
 
 221-240 
 Magnitude of graphs, 57 
 Makers of paper for graphs, 16 
 Making graphs, 15, 36, 48 
 Managers instrument control. Fig. 
 
 136B 
 Marine engineers' handbook, 245, 
 
 247 
 Marine motor changes. Figs. 48, 49 
 Marriage age, Mt. Holyoke, Fig. 71 
 Marshall recording oarlock, Fig. 191 
 Mechanical charts, 186-220 
 
 chart classes, 187 
 Mechanical and electrical cost hand- 
 book, 241 
 Mechanical engineers' handbook, 243 
 Mental tests, U. S. A., 76, Figs. 65, 66 
 Metal price variation, Fig. 69 
 Meter disc charts, 188, 191, 192 
 Millimeter paper, 20, 32 
 Mill work record, Fig. 69 
 Mining engineers' handbook, 244 
 Moduli of alignment charts. Fig. 166 
 Motor test curves, Figs. 95, 96 
 
 form S. A. E., Fig. 97 
 Motor truck production. Fig.. 16 
 
 disc records. Fig. 176 
 Multiple pyrometer record. Fig. 211 
 
 N 
 
 Labor chart ship building. Fig. 80 
 Laws of experiments, 117, 123 
 Lettering of graphs, 35, 36 
 Lines, areas, volumes. Fig. 33 
 Location arms accessory manu- 
 facturers. Fig. 134 
 Log chart, Fig'. 144 
 
 paper, 22, 30, Fig. 11 
 Lubricating oil tests. Fig. 55 
 
 frequency. Fig. 101 
 
 Natural gas handbook, 245 
 Naval construction handbook, 245 
 Nomograms, 169, 174, 180 
 
 classes, 175 
 
 examples, 178 
 Nomograph, 169 
 Nomography, 167-185 
 
 O 
 
 Oarlock pressure chart, Fig. 191 
 Occupation charts, 81 
 
252 
 
 INDEX 
 
 Occupations, University of lUionois 
 graduates, Fig. 72 
 U. S. Army, Fig. 44 
 Oil distillation tests. Fig. 44 
 lubricating tests, Fig. 55 
 Olsen eflBciency machine records, 
 
 Fig. 199 
 Operation charts, 72, 82, 87, 89, 99 
 of lighters. Fig. 58 
 
 electrical plant, Fig. 74 
 power plant. Fig. 85 
 Organization charts, 130, 131, 134, 
 136 
 automobile plant. Fig. 131 
 machine shop. Fig. 135 
 small arms accessory inspection, 
 
 Fig. 133 
 U. S. Motor Transportation 
 Corps, Fig. 132 
 Overhead line handbook, 242 
 
 Paper makers, 16 
 Papers, 21-34 
 
 for graphs, 16-34 
 Parabola, 118, 118, Fig. 110 
 Parts accepted, (rifles), Fig. 90B 
 Percentage chart. Fig. 36 
 Periodic curves. Fig. 117 
 Pie diagram, 60, Figs. 34, 37 
 Pipe thickness calculation. Fig. 140 
 Pitch of rivets. Fig. 160 
 Plots of straight line, 142 
 Plotting paper, 15, 34, Figs. 2A, 2B, 
 
 3 
 Polar paper, 25, Fig. 6 
 
 charts. 111 
 Population, U. S., 1910, Fig. 40 
 
 1900, Fig. 47 
 Power plant operation. Fig. 82 
 
 diagrams. Fig. 34 
 Practical diagrams, 126 
 Precision CO2 record, Fig. 170 
 
 and draft record. Fig. 192 
 
 gravitometer. Fig. 218 
 Price variation, 78-81, 84 
 Production of motor trucks, Fig. 16 
 
 of rifles. Fig. 90 
 Productograph, Fig. 194 
 
 Proffle paper, 24, 26, 27, Figs. 5, 7 
 Progress charts, 39, 96, Figs. 17, 19 
 
 report. Fig. 57 
 
 of operations. Fig. 79 
 Prony brake curves. Fig. 158 
 Proportion in pipe system. Fig. 154 
 Pyrometer record. Figs. 204, 206, 
 210, 211, 212 
 
 Q 
 
 Quantity of water. Fig. 122 
 
 R 
 
 Railroad cost distribution. Fig. 39 
 curves and earthwork, hand- 
 book, 245 
 train charts, 66 
 wage changes. Fig. 77B 
 Rails, weight of. Figs. 161, 162 
 Ratio charts, 44r-46 
 Recording oarlock record. Fig. 191 
 Recordograph, Fig. 178 
 Reference graphs, 13 
 Research graphs, 14, 103, 104, 108 
 Resistance of ships. Fig. 100 
 Revolver parts accepted. Fig. 90B 
 Riehl6 testing machine. Fig. 198 
 Rifle assembly totals, Fig. 90A 
 bolt assembly. Fig. 130 
 production. Fig. 90 
 Rivet pitch, Fig. 150 
 Riveted joints trength, Fig. 160 
 Routing diagrams. Fig. 130 
 Rubber and automobile production. 
 
 Fig. 86 
 Ruled cross section, paper. Fig. 4 
 Rules for charting, 35, 36 
 
 S 
 
 S. A. E. standard test. Fig. 97 
 Sample graphs, 37, 38, 39, 42 
 Scale, diameter and circumference. 
 
 Fig. 28 
 Scales for graphs, 36, 38, 40 
 Schedule and factory output. Figs. 
 
 87, 88 
 
INDEX 
 
 253 
 
 School cost per pupil, Fig. 43 
 Semi-log paper, 20, 21 
 Shaft calculating chart. Fig. 142 
 Ship resistance curves, Fig. 100 
 
 stress. Fig. 182 
 Shop and trade training, Fig. 78 
 Sine curves, 122, Fig. 116 
 Slsetch paper, 32 
 Slip of screw propeller. Fig. 83 
 Solution of equations, 123 
 Special record paper. Fig. 13 
 Speed and time graphs, 53-57 
 
 power and gas ratio, Fig. 92 
 Sphygmograph record. Fig. 181 
 Spiral springs, load, Fig. 152 
 Springs (spiral), load. Fig. 152 
 Stair diagram. Fig. 157 
 Statistical graphs, 48, 49 
 Steam engine indicator card. Fig. 
 
 202 
 Steel, chemical analysis. Fig. 102 
 
 characteristics. Fig. 98 
 
 physical properties. Fig. 99 
 Straight line equation. Fig. 138 
 
 graphs, 38, 142 
 Stress in ship, Fig. 182 
 Structural handbook, 248 
 
 Truck operation costs, Fig. 50 
 Turbine (Hydraulic), Fig. 75 
 
 U 
 
 Uehling COj disc record. Fig. 169 
 
 IT. S. conjugal chart 1900, Fig. 73 
 Motor Transportation organiza- 
 tion, Fig. 132 
 occupational record. Fig. 44 
 
 U. S. A. Ordnance Department form 
 distribution. Fig. 126 
 
 U. S. population, 1900, Fig. 47 
 1910, Fig. 40 
 
 U. S. A. small arms accessory inspec- 
 tion organization. Fig. 70 
 
 U. S. Steel dividends, Fig. 70 
 
 Valve inlet areas, Fig. 41 
 
 Volts and amperes. Figs. 118, 119 
 
 V1-" curves. Fig. 120 
 
 Volume of liquid in tanks, Fig. 123 
 
 W 
 
 Tank input and draft. Fig. 89 
 
 Test of crane. Fig. 109 
 
 Testing machine (Riehle), Fig. 198 
 
 (Olsen), Fig. 199 
 Textile testing machine. Fig. 200 
 Time variation charts, 38 
 paper. Fig. 18 
 
 and speed, 53-57 
 Torsional strength (shafts), Fig. 155 
 Toussaint-LePere air speed record. 
 
 Fig. 220 
 Trade and shop training. Fig. 78 
 Train air pressures, Fig. 193 
 
 and time, 56 
 
 chart. Fig. 186 
 Transformation curves, Fig. 190 
 Trends of automobile design. Fig. 81 
 Trilinear charts, 113 
 
 paper, 22 
 
 diagram of mortars, Fig. 108 
 
 Wage change on railroad. Fig. 77B 
 Water flow in pipes. Fig. 122 
 Water, inches, lbs., etc., scale. Fig. 
 
 29 
 Waterwork's handbook, 246 
 Webb's coordinate paper, 29 
 Weekly record paper, 21 
 Weight of rails, Figs. 161, 162 
 Westinghouse meter chart. Fig. 183 
 
 volt meter chart, Fig. 216 
 Wheat prices (England), Figs. 67, 68 
 Wimperis accelerometer. Fig. 185 
 
 equilibristat, Fig. 186 
 
 Yarway blow-off meter. Fig. 188 
 -Lee recording meter. Fig. 189 
 
 Z diagrams, 152-161, Fig. 151