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_ Cornell University Library 
 
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 The ventilation of mines.Designed for us 
 
 3 1924 004 698 936 
 
Cornell University 
 Library 
 
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 tlie Cornell University Library. 
 
 There are no known copyright restrictions in 
 the United States on the use of the text. 
 
 http://www.archive.org/details/cu31924004698936 
 
THE 
 
 Ventilation of Mines. 
 
 DESIGNED FOR USE IN SCHOOLS AND COLLEGES; 
 
 AND FOR PRACTICAL MINING MEN IN 
 
 THEIR STUDY OF THE SUBJECT. 
 
 J. T. gEARD, C.E., E.M., 
 
 Iowa Mining Exchange^ OttuTtiwa, la. : 
 
 Secretary of the State Board of Examiners for 
 
 Mine Inspectors^ Iowa, 
 
 FIRST EDITION. 
 FIRST THOUSAND. 
 
 NEW YORK: 
 
 JOHN WILEY & SONS, 
 
 53 East Tenth Street. 
 
 1894. 
 
Copyright, 1894, 
 
 BY 
 
 J. T. BEARD. 
 
 EOBEHT DRUMMOND, ELECTEOTYPER AND PRINTER, NEW YORK. 
 
De&icateD 
 
 TO THE MINERS OF IOWA, 
 
 AMONG WHOM THE AUTHOR HAS SPENT THE PAST 
 THIRTEEN YEARS OF HIS LIFE. 
 
PREFACE. 
 
 The Ventilation of Mines is a subject to which all 
 interested, miners and operators alike, should give the 
 most earnest heed — miners^ because upon the observ- 
 ance of its laws and principles depend their life and 
 health ; operators, because a thorough knowledge of 
 the subject, followed by a faithful application of such 
 knowledge in practice, cannot but result in a large sav- 
 ing of expense, ranging from fifty to seventy-five per 
 cent. 
 
 It is a subject to which as yet American writers 
 have contributed little. This is to be accounted for 
 partly on account of the infancy, as it were, of the 
 Mining Industry in America, as compared with its de- 
 velopment in the mother country; but largely on 
 account of the inordinate haste of Americans to see 
 results. This haste is only too apparent in all of our 
 industries, but in none is it more observable than in the 
 mining; and one of its most deplorable results is to 
 hinder and in many cases render wholly impracticable 
 scientific observation. The American operator with 
 but few exceptions adopts such appliances as first come 
 to hand, or as suggest to him a saving in first cost ; 
 often not caring for, or taking the time necessary to, a 
 thorough investigation as to the comparative operating 
 
VI PREFACE. 
 
 expenses of different appliances. Very often the ma- 
 chinery, fans, and other apphances brought into use 
 have been purchased from some old mining plant and 
 remodelled and repaired with true Yankee skill and 
 ingenuity ; but the type of construction is old and 
 affords no opportunity for reliable investigation. 
 
 Such haste of Americans to see results and to make 
 a fair showing of returns upon investment is therefore 
 no help to the advancement of science ; and were it 
 not for their habits of close observation, their keen 
 perception, their practical skill and ingenuity, they 
 could not compete in the field of scientific research. 
 The methods of Americans are, however, always prac- 
 tical, and herein is their value. 
 
 The field for scientific research among English mines 
 has been larger. The mines as a rule are deeper and 
 the mining plants present a more permanent aspect. 
 English writers have contributed more to practical 
 mining literature than any others. Foremost among 
 those who have discussed the ventilation of mines are 
 Mr. J. J. Atkinson and Mr. W. Fairley. There are 
 probably many others worthy of note who have con- 
 tributed to increase our fund of knowledge in this 
 direction, but whose writings have not become so well 
 known. 
 
 The French have furnished some good physicists, 
 and their experiments and investigations of the laws 
 controlling the motion of fluids, etc., have proved in- 
 valuable. The deductions of M. Murgue, relative to 
 the " Equivalent Orifice," will be appreciated by math- 
 ematicians ; but, as M. Murgue says himself, it is a 
 mere fiction; and, we may add, does not rightly find 
 its application in the ventilation of mines. 
 
PREFACE. vii 
 
 What is needed to-day is practical reasoning, sup- 
 ported by the results of true scientific observation. 
 The investigator must possess a thorough knowledge 
 and comprehension of the laws of physics : he must be 
 a keen observer and a logical reasoner ; above all, he 
 must build his theories upon fact, never distorting the 
 fact to suit a theory. Every law of physics acts con- 
 tinuously and as though no other law existed : the 
 resultant condition is the algebraic sum of all the ex- 
 isting conditions. If any of these existing conditions 
 are neglected, a true result is not obtained. 
 
 We see reports, from time to time, made upon so- 
 called scientific investigations of results under varying 
 conditions ; giving, for example, the quantities of air 
 yielded by a straight paddle-fan, discharging into a 
 certain mine, making a certain number of revolutions 
 per minute, and giving the diameter of the fan ; but 
 stating no breadth of blade, no temperature, or barom- 
 eter, or hygrometric state of the atmosphere at the 
 time of observation. Although the simple omission of 
 the last-named item would be pardonable, as its effect 
 is small, still, in careful observation, for scientific pur- 
 poses, every affecting cause should be taken into ac- 
 count. The formulas of M. Murgue, relative to the 
 fan, make no account of the width of the fan-blade ; 
 ignore, completely the questions of temperature, ba- 
 rometer, and hygrometric state ; while it is a well- 
 known fact that a fan is less powerful in light air than 
 when working in a denser medium. 
 
 While it is the author's aim, in the following work, 
 to base all his deductions upon mathematical principles, 
 working out the same for the benefit and satisfaction 
 of the student, it is, at the same time, his desire to 
 
via PREFACE. 
 
 give to the practical miner a book of reference, the 
 careful study of which will enable him to better under- 
 stand the conditions with which he is surrounded and 
 upon which his health and happiness so largely depend. 
 As there is at present no American and probably no 
 English work that is well adapted for use in schools 
 and colleges, it is hoped that this little work may, to 
 some extent, prepare the way for more extended and 
 complete text-books upon a subject of such vast im- 
 portance to the mining engineer. 
 
 By way of encouragement, the author would say to 
 the student, where the reasonings or deductions lead- 
 ing up to certain conclusions may at times seem to be 
 difficult, the study of the subject loses much of its 
 formidable aspect if taken up one step at a time. It 
 has been the aim throughout to present the subject 
 step by step, and to so systematize the whole as to 
 maintain a constant and healthful growth, and by this 
 means to prepare the mind for a full and final concep- 
 tion of the whole. The processes of the calculus have 
 been purposely excluded ; some of the deductions en- 
 gaging the study of the author for months at a time, as 
 he has sought to disentangle them from the intricacies 
 of the higher mathematics, with which they are almost 
 inextricably associated. 
 
 To points wherein the author differs from other 
 writers he has given the most careful and patient 
 study ; and submits his honest conclusions, by no 
 means in a spirit of controversy, but with a desire to 
 establish the truth and determine the laws that under- 
 lie and form the foundation of all mine-ventilation. 
 
 The author wishes to here acknowledge the courtesy 
 and assistance of many friends, among whom may be 
 
PREFACE. IX 
 
 especially mentioned the State Mine Inspectors of 
 Iowa, who have assisted, by every means in their 
 power, to aid investigation, and whose mature judg- 
 ment has more than once afforded valuable help. 
 
 J. T. B. 
 
 Ottumwa, Iowa, December i6, 1893. 
 
INTRODUCTION. 
 
 What the author has endeavored to accomplish in 
 the following pages is to make plain and simple to 
 the practical mind the workings of the laws which ani- 
 mate and control the ventilating currents in mines. 
 These laws are at times necessarily somewhat complex, 
 because they express the relation between force and an 
 expansive, fluid medium. The mechanics which for- 
 mulates the expressions of force, as developed or trans- 
 mitted by the rigid parts of machines, is simple, compared 
 with the cubical and quadratic expressions involved in 
 the discussions of force as applied to fluids. But, 
 throughout, the endeavor has been made to express in 
 simple, practical terms the results of mathematical cal- 
 culation. While it is not expected that the general 
 reader will care to investigate the methods of deduction, 
 which require often a knowledge of algebra and the 
 higher mathematics, yet these methods have, for the 
 most part, been given in full, to demonstrate, for the 
 benefit of the student, the exactness of the conclusions 
 reached. This has seemed particularly essential, as 
 some of the results obtained are different from those 
 obtained by other writers. 
 
 It is believed some flagrant errors have crept into our 
 mining formulae, and some of the generally-accepted 
 facts are based upon wrong hypotheses. For example, 
 in relation to the action of fans, the idea seems to be 
 
XU INTRODUCTION. 
 
 quite prevalent that the air-current partakes of the pe- 
 I'ipheral velocity of the fan-blade tips, and this becomes 
 the initial velocity of the current. Although this is 
 not the expressed idea of Murgue, yet even he trans- 
 mutes the mechanical velocity of the fan-blade into an 
 expression of head-of-air-column, which leads him se- 
 ductively to the same error ; as he continues, in the 
 course of his reasoning, to treat the established veloc- 
 ity of the current as dependent alone upon the genera- 
 tive head-of-air-column ; forgetting that the same head- 
 of-air-column will produce a different velocity according 
 to the conditions under which the current is moving. In 
 other words, M. Murgue tries to assimilate the condi- 
 tions of a current moving under a resisting pressure to 
 the purely theoretical case of movement opposed by 
 no such resistance. The velocity generated by a body 
 falling through a certain height varies as the square 
 root of that height ; the velocity of the air in the mine 
 varies as the square root of the pressure, other factors 
 remaining the same ; hence it is true that the height gen- 
 erative of any given velocity represents accurately the 
 pressure animating such velocity where no resistance 
 is opposed ; but the analogy ceases when we introduce 
 a foreign resistance opposing such velocity. 
 
 In discussing the flow of a current of air through a 
 mine, we are dealing with a fluid medium moved or ani- 
 mated by a certain pressure. This pressure is created 
 and maintained by the resistance ahead of the current, 
 upon which it is directly dependent and not upon the 
 power behind it. This is a very important distinction 
 and must be borne in mind : it is merely stated here, 
 but will be elucidated further on in the growth of the 
 subject. It is aimed in this chapter to refer to certain 
 
INTRODUCTION. xiii 
 
 facts which are deduced later, in order to prepare the 
 mind for a systematic study of the subject. 
 
 In making deductions relative to the fan, the method 
 adopted in this work differs essentially from the method 
 in general use, but seems to the author to be more sim- 
 ple and practical. It is based upon the centrifugal force 
 developed by the weight of air revolved by the fan- 
 blades. When a boy ties a string to his ball and swings 
 it about his head, there is a tension, or pull upon the 
 string, which represents the centrifugal force developed. 
 Applying this principle to the fan, the air contained 
 between the blades acts as the ball ; only the ball pulls 
 upon the string, while the air presses outward toward 
 the periphery of the fan and creates a moving or ven- 
 tilating pressure in the mine. The blades are always 
 full and the air is revolved by them. We know the 
 weight of this volume of air in revolution. The cen- 
 trifugal force developed by this weight, considered as 
 concentrated at the centre of gravity of the mass, is 
 easily figured. The radial force thus determined is 
 then applied, in our formulae, to each particle of the air 
 in question (the air contained between the blades), on 
 the principle that 
 
 A force is measured by the velocity it can generate in a 
 unit of mass in a unit of time. 
 
 Thus, by combining mass of air with radial velocity, 
 we obtain an expression {mv) for the radial-mass-motion, 
 or the living force imparted to the air contained between 
 the blades. This contained air has then, by virtue of 
 its revolution in the fan, been transformed into a radi- 
 ally-moving mass, whose living force (mv) is the power 
 behind the current. If we wish to determine the pres- 
 sure the fan would create when working into a closed 
 
XIV INTRODUCTION. 
 
 space — or, as we term it, the "static" pressure — we 
 can divide the force developed {mv) by the surface 
 pressed (the circumference of the fan multiplied by the 
 width of blades). This is not, however, the most im- 
 portant determination to be made. It is more impor- 
 tant to determine the work of this centrifugal force, as 
 indicated by the expression mv', which is the force 
 {mv) multiplied into its path (v), giving the work for 
 one second of time. This will give us the work any 
 given fan can accomplish ; and taking into account the 
 coefficient of efficiency (AT), we place the effective work 
 of the fan equal to the work to be accomplished in the 
 
 mine (-t<3' )• ^^ this method we deal with no fiction, 
 
 but with plain facts ; and we believe the results obtained 
 are simple and practical. Work must always be placed 
 against work. 
 
 This brings us to another seeming error in our past 
 formulas. Mr. Fairley and others state that, " If we 
 obtain a certain quantity of air by the action of a fur- 
 nace, and another certain quantity by the action of a fan, 
 or other means, their combined effect will be accord- 
 ing to the square root of the sum of the squares of the 
 quantities obtained separately; that is, according to 
 the formula Q = ■\/q'' -\- g'. Let us consider a moment. 
 Suppose our furnace acting alone will pass a certain 
 quantity of air g, and our fan acting alone will pass 
 in the same mine, and under the same conditions, a 
 quantity of air g^. Now, the work the furnace will 
 accomphsh is denoted by the equation 
 
 ks 3 
 u = —r-q ,,..... (a) 
 
INTRODUCTION. XV 
 
 and likewise, for the work of the fan, we write 
 
 ks 
 «■ = -^q' (b) 
 
 But the combined effect must be equal to the sum of 
 these works, as, from the nature of the hypothesis, the 
 work performed by the motors in the two instances re- 
 mains unchanged ; the same power being applied to the 
 fan, and the temperature of the furnace remaining the 
 same, in each case. Hence, adding equations (a) and 
 (b), member to member, and denoting the sum of the 
 works by U, we have 
 
 u = ^{3' + g:) (c) 
 
 But we have 
 
 U=^Q. ...... (d) 
 
 a 
 
 Hence, equating the values of U as given by equa- 
 tions (c) and (d), and reducing, we have, for the value 
 
 of a 
 
 which is very essentially different from the expression 
 in general use. 
 
 It is a fallacy, in discussing the mechanics of fluids, 
 to suppose that if one motor is capable of yielding a 
 unit of pressure/, and another motor will produce a 
 unit of pressure /, , working under the same condi- 
 tions, their combined influence will yield a pressure 
 equal to the sum of these respective pressures. This 
 would be true in statics (i.e., when the airways are 
 
xvx INTRODUCTION. 
 
 closed and no movement results from the pressure); 
 but in dynamics a change in pressure results in a 
 change of velocity, and a consequent change in the re- 
 sistance of the airway, which last again affects the 
 pressure. Consequently the only basis of comparison 
 is by means of the work. Statics deals zvith pressure: 
 dynamics deals with work. It is of the utmost import- 
 ance to keep this in mind constantly, in treating the 
 subject of fluids. 
 
 The author would also draw particular attention to 
 what is termed in the following pages the Potential 
 
 factor of a mine,! -3^], and also its equivalent expres- 
 sion, l^:=i|, called the Potential factor of ventilation. 
 
 ^' ( f^)' 
 
 The one expression gives the value of the potential in 
 terms of the mine ; the other gives the same value in 
 terms of the current. The potential always shows the 
 relation existing, in a certain mine, between the quan- 
 tity of air passing and the cube root of the power neces- 
 sary to pass such quantity. Thus, denoting the po- 
 tential factor by X, we have 
 
 ft 
 X= 
 
 Vks' 
 also, 
 
 x^ Q 
 
 u 
 
 A high potential always indicates a well-ventilated 
 mine, as it shows a large quantity of air moved by a 
 small power. It is obtained by increasing the area, by 
 splitting the air-current ; also by decreasing the value 
 
INTRODUCTION. xvii 
 
 of ^ to a minimum, by cleaning up the air-courses and 
 avoiding sharp bends or angles as far as possible. 
 
 For the sake of illustration, let us compare two 
 mines, the one having a high potential factor, as mine 
 No. 4, with three spHts of the air-current (see Table 
 X) ; and mine No. 5, having but a single current of air. 
 This latter case is not represented in the tables. At 
 mine No. 4 a small twelve-foot fan, blades 30 inches wide, 
 running at a speed of 60.8 revolutions per minute, is 
 throwing 50,000 cubic feet of air, against a potential of 
 647.344. At mine No. 5, when there is but a single 
 current, the potential will be low, viz., 188.502. Against 
 this potential, a twenty-foot fan, blades 48 inches wide, 
 running at a speed of 70.7 revolutions per minute, will 
 only circulate 40,000 cubic feet of air. In this compari- 
 son we have the seeming anomaly of a twelve-foot fan, 
 making only 60.8 revolutions per minute, and yielding 
 50,000 cubic feet of air, while our twenty-foot fan, mak- 
 ing 70.7 revolutions per minute, is yielding but 40,000 
 cubic feet of air. Many casual observers would at- 
 tribute this seeming discrepancy to the fan and say, 
 "The fan is not doing its share of work." If, however, 
 we glance for a moment at the work being performed 
 in each case, we will see that the twenty-foot fan is 
 accomplishing a work of 289.546 horse-power, while the 
 twelve-foot fan is only performing a work of 13.963 
 horse-power. Hence the trouble is not in the fan, but 
 in the method of ventilation employed in the mine. 
 
 We will now split the air travelling in mine No. 5, 
 making two currents, and thereby raising the mine 
 potential to 377.004. We find now that the power 
 required is only one eighth of what it was previously, 
 and our small twelve-foot fan, running at a speed of 
 
XVIU INTRODUCTION. 
 
 79 7 revolutions per minute, will pass the same amount 
 of air as was passed before by the twenty-foot fan. 
 These results are tabulated below and serve to show 
 the importance of adopting a good method of ventila- 
 tion. The fans referred to in each case are the fans 
 described in Table X of the Appendix. 
 
 Mine No. 4. Mine No. 5. Mine No. 5. 
 Quantity passing . . . 50,000 40,000 40,000 
 Mine potential 647.344 188.502 377.004 
 
 No. of splits 
 
 Diameter of fan . . . 
 
 3 
 . 12 feet 
 
 I 
 20 feet 
 
 2 
 12 feet 
 
 Width of blade. , . 
 
 . 30 ins. 
 
 48 ins. 
 
 30 ins. 
 
 Revs, per minute. . 
 H. P. expended . . . 
 
 . 60.8 
 • 13-963 
 
 70.7 
 289.546 
 
 79-7 
 36.193 
 
 Before closing this introductory chapter, which is in- 
 tended as a preliminary sketch of the ground to be 
 gone over, the author would state that the tables found 
 in the Appendix have been carefully prepared and intro- 
 duced, for the purpose of comparison, and to show at 
 a glance results under varying conditions. It must not 
 be supposed for a moment, however, that because any 
 particular fan of the given dimensions, and working 
 seemingly under similar conditions, does not throw the 
 amount of air indicated in the table, the table is there- 
 fore wrong: there are many agencies of ventilation 
 constantly at work in the pit, and these all have their 
 influence upon the amount of air passing. To eliminate 
 these secondary influences, and obtain a simple case of 
 fan ventilation, is often a very difficult matter, requir- 
 ing patience, care, and skill. The study of such sec- 
 ondary agencies of ventilation will be taken up in 
 detail in the next chapter. 
 
INTRODUCTION. XIX 
 
 We are now prepared to enter upon a systematic and 
 thorough study of our subject, beginning at the rudi- 
 ments which the student must become a thorough 
 master of before he can expect to grasp the more in- 
 tricate problems with which the subject abounds. We 
 must not be dazed or disheartened because of the com- 
 plications which arise from the simultaneous action of 
 so many agencies ; but tlie student must bear in mind 
 that in the physical world every law continues to act 
 just as though no other law existed. Our study is 
 throughout a study of those God-given laws which 
 energize and control the universe. 
 
TABLE OF CONTENTS. 
 
 PAGE 
 
 Preface v 
 
 Introduction xi 
 
 CHAPTER 
 
 I. Conditions existing in Mines i 
 
 Ventilation. Gases, i. Gaseous and Fiery Mines — 
 " Blowers." Kinds of Gases. White Damp, 2. Black 
 Damp, 3. Fire-damp. Rhum^, 4. Agency of the Air- 
 current. Natural Agencies of Ventilation, 5. Sugges- 
 tions. Natural Ventilation, 6. Illustration, 7. 
 
 II. Force as applied to Mine- ventilation 8 
 
 Prefatory. Force, 8. Measure of Force. Static Pressure. 
 Dynamic Pressure, 9. Moving Force or Ventilating Press- 
 ure. Natural Pressure : How it obtains. Weight of Air. 
 Barometric Pressure : Variations in, 10. Expression for 
 Weight of Air, 11. Effect of Temperature, 12. Head-of-air- 
 column. Caution, 13. Air-columns as Motors, 14. Pressure 
 in Terms of Air-column, 15. Primary-columns and Sec- 
 ondary-columns, 16. Three Temperatures, 17. Pressure 
 in Terms of the Fan, 18. Other Motors. Rhum^, 20. 
 
 III. Resistance of the Mine 21 
 
 Resistance. Kinds of Resistance, 21. How Varies 
 Static Resistance. Dips and Rises, 22. Effect upon the,Cur- 
 rent, 23. Expression for Resistance. Pressure in Terms 
 of the Mine, 24. Coefficient of Resistance. Value of, 25. 
 Practical Value of k. Density as affecting Resistance, 26. 
 
 IV. Work 28 
 
 Prefatory. Definition of Work. Unit of Work. 
 Power. Unit of Power, 28. Horse-power. Work as a 
 Measure of Power. Expression for Work, 29. 
 
 V. Resultant Factors of Ventilation 31 
 
 Khumi. Prefatory. Velocity. . Expressions for Ve- 
 
 xxi 
 
XXU TABLE OF CONTENTS. 
 
 CHAPTER PAGE 
 
 locity, 31. Quantity. Expressions for Quantity, 32. Press- 
 ure. Work. Potential Factor, 33. Expression for the 
 Potential Factor. Expressions in Terms of the Potential, 
 34. Quantity due to Two Motors, 35. Expression for 
 Head-of-air-column in Terms of Temperature and Motive- 
 height. Expression for Horse-power, 36. Pressure in 
 Terms of Water-gauge. Pressure in Terms of Temperature 
 and Motive-height, 37. 
 VI. Expression for Straight-paddle Fans 38 
 
 Prefatory. Weight of Air in One Section of the Fan, 
 38. Centrifugal Force of this Weight. Measure of this 
 Centrifugal Force, 39. Work of the Centrifugal Force per 
 Second. Work of the Fan per Second, 40. Effective Work 
 of the Fan per Minute. Quantity yielded per Minute in 
 Terms of the Fan and Mine, 41. Pressure yielded by a 
 Fan. Horse-power of a Fan, 42. 
 VII. Economic Discussion of the Furnace 43 
 
 Prefatory. Economic Grate-area. How Determined, 
 43. Condition of Upcast Current, 44. Dry Shafts. Illus- 
 tration, 45. Wet Shafts, 48. Suggestions. Relative Quan- 
 tities. Suggestions, 49. Thermal Unit. French Unit. 
 American Unit. Calorics of Coals, 50. Calorific Capacity. 
 Specific Heat. Specific Heat expresses Thermal Units. 
 General Expression for Weight of Coal, 51. Gaseous Com- 
 position of Upcast Current, 52. Expression for Weight 
 of Air in Terms of Q. Expression for Weight of Ni- 
 trogen. Expression for Weight of Carbonic Acid Gas, 53. 
 Expression for Weight of Vapor of Saturation. Summary. 
 Risumi, 55. Expression for Weight of Coal to heat Air- 
 current (Dry Shaft), 56. 
 Wet Shafts 56 
 
 Prefatory. Condition of Shaft, 56. Temperature of 
 Evaporation. Absorption of Heat, 57, Expression for 
 Extra Coal (Wet Shaft), 58. Cooling Effect of Shafts. 
 Expression for Coefficient of Cooling, 59. 
 VIII. Economic Discussion of the Fan 62 
 
 Prefatory. Efficiency, 62. Coefficient of EflJciency. 
 How varies, 63. Internal Resistance of a Fan. Work of the 
 Resistance. N.B. General Expression for the Work of the 
 Fan, 64. Value of K, 65 Relative Efficiency at Differ- 
 
TABLE OF CONTENTS. xxiii 
 
 CHAPTER PAGE 
 
 ent Speeds. Limit of Speed, 66. Maximum Effective 
 Speed, 67. To determine Value of ^practically, 69. Value 
 of the Fan-constant. Effect of Humidity, 70. Risum^. 
 Outer Radius or Diameter, 72. Inner Radius or Size of 
 Eye. Number of Blades. Widtli of Blade, 73. Curvature 
 of Blades, 74. Expansion of Casing, 77. General Pro- 
 portionment of the Fan, 79. Connection with the Down- 
 cast, 85. Testing a Fan at the Shops, 86. 
 IX. Splitting the Air-current.. 89 
 
 Advantage of Splitting as shown by Table VI. Mines 
 (assumed), 8g. Quantity Increased. Power Decreased. 
 Limit to Splitting, 90. Size of Airways. Arrangement of 
 Splits. Equal Splits, 91. Unequal Splits. Natural Divi- 
 sion, 92. Regulators, 93. Present Method, 94. Objec- 
 tion. Another Method, 95. Pro and Con. Illustration, 
 96. Conclusion, 97. 
 The Theory of Splitting Air-currents 98 
 
 Dynamic Equilibrium. Theory of Splitting, 98. Cau- 
 tion. Graphic Method, 99. Style of Regulator proposed, 
 loi. Argument, 102. Illustration, 103. Objection, 104. 
 System in Ventilation. Effect of Dips and Rises, io6. 
 Example, 107. Cause for Disproportion, 108. Effect 
 tabulated, 109. 
 X. Discussion of the " Equivalent Orifice " no 
 
 Prefatory. Illustration, no. 
 XI. Compressive vs. Exhaustive Ventilation 115 
 
 Prefatory. Plenum System. Vacuum System, 115. 
 Difference. Comparative Effects, 116. Conclusion, 119. 
 XII. Care of Mine as assisting Ventilation 121 
 
 Prefatory. Conduct of the Air, 121. Keep Airways 
 Clean. Air required per Minute per Man, 122. Room- 
 stoppings. Entry-stoppings. Break-throughs, 123. Double- 
 doors. Overcasts. Undercasts, 124. Angles in Airways. 
 Stables, 125. 
 
INDEX TO TABLES. 
 
 TABLE PAGE 
 
 I. Comparison of the Fahrenheit and Centigrade Scales 128 
 
 II. Condition of the Current at the Bottom of Upcast 129 
 
 III. Tension of Aqueous Vapor 130 
 
 IV. Specific Heats of Various Gases and Vapors 131 
 
 V. Specific Gravity of Various Gases and Vapors 131 
 
 VI. Effect of splitting the Air-current 132 
 
 VII. Horse-power of Different Fans at Various Speeds 133 
 
 VIII. Effect of Atmospheric Changes upon the Yield of a Fan. 134-135 
 IX. Effect of Atmospheric Changes upon the Speed of a Fan.. 136 
 X. Speed and Horse-power of Different Fans at Different 
 
 Mines 137-139 
 
 XXV 
 
INDEX TO ILLUSTRATIONS. 
 
 PAGE 
 FIGURE. 
 
 I. Slope or Drift, ventilated by a Shaft 7 
 
 II. Illustration of a Mine (Ventilation either Natural or Arti- 
 ficial), in the Ventilation of which Three Tenaperatures 
 may be concerned 17 
 
 III. Represents one Section of a Straight-paddle Fan ; and the 
 
 Movement of the Air-current Relative thereto 38 
 
 IV. Graphic Representation of the Curves of Efficiency and of 
 
 the Initial and Effective Work of the Fan, with Respect 
 
 to its Speed 68 
 
 V. Cut showing a Conical Plate surrounding the Fan-shaft, 
 
 for the Purpose of deflecting the Intake-current Radially. 75 
 VI. Sketch showing the Arrangement of Blades in the Murphy 
 
 Fan 75 
 
 VII. Side View of a Fan in its Casing, showing the Peripheral 
 Space and its Connection with the Downcast, and the 
 
 Position of the Cut-off 78 
 
 VIII. Sketch showing the Method of testing a Fan at the Shops. 87 
 
 IX. Illustration, Tube and Water-gauge g6 
 
 X. Graphic Method, illustrating the splitting of the Air-cur- 
 rent lor 
 
 XI. Illustration showing a Form of Regulator that will propor- 
 tion the Power applied to the Mouth of any Split to the 
 
 Work to be performed in that Split 102 
 
 XII. Ideal Plan of a Mine, worked upon the Room and Pillar 
 System and ventilated in Sections, ,by Means of Over- 
 casts, avoiding Doors upon the Main Hauling Roads, 
 
 and employing the Improved Form of Regulator 105 
 
 XIII. Illustration of the " Vena Contractor,'' referred to by 
 
 Murgue in his " Equivalent Orifice " Method. no 
 
 xxvii 
 
xxviii INDEX TO ILLUSTRATIONS. 
 
 FIGURE. PAGE 
 
 XIV. Illustration showing the Fan-enclosure and Arrangement 
 
 of Doors for reversing the Air-current 119 
 
 XV. Illustration showing the Location of an Inside Stable in 
 
 the Entry-pillar and its Ventilation by an Air-leak 125 
 
 XVI. Illustration showing the Location of an Inside Stable on 
 the Side of the Entry and its Ventilation by an Air-leak 
 
 through an Overcast Box 126 
 
 XVII. Illustration showing One Section of a Fan having Blades 
 curved Backward from the Direction of Movement and 
 the Reaction of the Air against the Surface of the Blade 
 (Addenda) 168 
 
MINE-VENTILATION. 
 
 CHAPTER I. 
 
 CONDITIONS EXISTING IN MINES. 
 
 It is essential, before entering upon a discussion of 
 the methods and means of ventilation in mines, to ob- 
 tain and hold in mind a clear idea of the elements or 
 factors which enter into and form the component parts 
 of our problem. 
 
 Ventilation. — First, we understand by the term 
 " Ventilation," as applied to mines, the removing of the 
 air contaminated and laden with the poisonous gases of 
 the pit, and supplying in its place fresh air from the 
 outside. To do this requires the maintaining of a 
 constant current of air through the pit, and conduct- 
 ing such current by means of doors, stoppings, over- 
 casts, etc., around the entire pit and particularly to the 
 working faces, where it is most needed. 
 
 Gases. — The gases occurring in the pit and which 
 contaminate the air are either formed in the mine, first 
 and largely, by the slow combustion of coal in the gob 
 and by mine fires ; second, by the breathing of men and 
 aminals, explosions of powder, burning of lamps, decay 
 of timber, etc., giving rise for the most part to the 
 formation of carbonic oxide or carbonic-acid gas ; or. 
 
2 MINE-VENTILATION. 
 
 as is the case with hydrogen carbide, commonly called 
 Marsh-gas or Fire-damp, they exude from the body of 
 the coal, as a product of earlier formation. 
 
 Gaseous and Fiery Mines — " Blowers." — Mines 
 are said to be " Gaseous " when their workings emit 
 natural gases. These gases may issue as " Blowers," 
 under pressure, coming from some internal pocket, 
 cavity, or chamber, more or less remote, where they 
 have accumulated and from which they escape by some 
 crack, crevice, or feeder which the drills may have 
 pierced, or a settlement in the mine may have opened. 
 When these natural gases are combustible or explosive, 
 the mine is said to be a " Fiery" mine. In such mines 
 the question of ventilation becomes a life-issue and the 
 air-current a life-line. Upon the constant throb and 
 pulse of the fan depends the life of the miner, as surely 
 as upon the beat of his own heart. That this is not 
 true in non-fiery mines renders such mines hardly less 
 dangerous ; because the consequent partial neglect of 
 the question, or its being regarded as a purely second- 
 ary matter, renders the insidious poisoning from mine 
 gases the more certain and deadly. 
 
 Kinds of Gases. — The gases most commonly occur- 
 ring in mines are Carbonic-oxide gas (CO), Carbonic- 
 acid gas (COj), Marsh-gas (CHJ, with traces of Hydro- 
 gen sulphide (H,S) and Ammonia (NH,). 
 
 "White Damp." — Carbonic-oxide gas (CO), com- 
 monly called " White Damp," is a combustible gas, 
 burning with a pale blue flame. It is the same gas 
 which is seen burning with a lambent flame over a 
 freshly-fed anthracite fire. It is lighter than air, hav- 
 ing a specific gravity of 0.967 and hence accumulates in 
 the cavities of the roof and in the upper galleries or 
 
CONDITIONS EXISTING IN MINES. 3 
 
 headings. It is very poisonous, acting as a narcotic. 
 It is colorless and, in the mine, odorless and therefore 
 all the more dangerous, because its presence may escape 
 the notice of the miner until too late for him to avoid 
 its baneful effects. It has, however, a distinctly sweet 
 taste in the mouth, and this often leads to its detection. 
 Its effect is to cause a stupor or drowsiness, which is 
 often followed by acute pains in the head, back, and 
 limbs, accompanied with delirium. If the helpless and 
 unconscious victim is not rescued soon, death is the 
 result. The gas may be detected in the mine by its 
 effect upon the flame of a lamp, causing it to burn with 
 a small blue tip ; and when present in any considerable 
 quantity, the flame will reach upward in a long quiver- 
 ing taper. This is a warning, and the experienced 
 miner will not tarry long in that place, as he knows the 
 danger that lurks there. This gas is produced by the 
 slow combustion of coal in the gob : it also results 
 from mine fires, where the supply of air is scant ; and 
 from the decay of vegetable matter, explosion of 
 powder, etc. 
 
 " Black Damp." — Carbonic-acid gas (CO,), com- 
 monly called " Black Damp," is an incombustible gas. 
 It is heavier than air, having a specific gravity of 1.529, 
 and hence it accumulates in the swamps and the low 
 places of the mine. It is poisonous, acting as a nar- 
 cotic, but is not as dangerous a gas as the one just de- 
 scribed, because its presence is more readily detected, 
 from the dimness of the lamps, and from their complete 
 extinction when larger quantities of the gas are pres- 
 ent. It is a colorless gas, and, in the mine, has very 
 little odor, but produces a sweet taste in the mouth. 
 Its effects are similar to those of carbonic-oxide gas, 
 
4 MINE-VENTILATION. 
 
 creating also headache and nausea. It is produced by 
 active combustion, burning of lamps, breathing of men 
 and animals, decomposition and decay. 
 
 "Fire-damp." — Hydrogen Carbide, or, as it is com- 
 monly called, " Marsh-gas," is a colorless, odorless, and 
 tasteless gas. It constitutes the well-known " Fire 
 damp" of the mines, and is largely responsible for the 
 many colliery explosions constantly occurring. It 
 burns with a slightly luminous flame : it is very light, 
 having a specific gravity of only 0.559. Like hydro- 
 gen it is combustible, but will not support combustion 
 when pure or unmixed with air or oxygen. This gas 
 mixed with 3^ times its volume of air will not explode ; 
 but when the admixture of air equals 5^ times the 
 volume of the gas a light explosion is rendered possi- 
 ble ; when the gas is mixed with gj times its volume of 
 air the explosive force of the mixture is the greatest ; 
 the presence of more air than this proportion weakens 
 the explosive force of the mixture, and when the vol- 
 ume of the air equals 13 times the volume of the gas 
 the explosion is again very weak. The Davy lamp is 
 used for the detection of this gas and requires great 
 caution and watchfulness to insure safety. It may be 
 detected upon the lamp until the admixture of air has 
 reached about 50 volumes. Marsh-gas is produced by 
 the decay of vegetable matter under water, or where 
 the air has been wholly excluded. It issues from coal- 
 seams probably as a product of coal-formation, where 
 vegetable matter has undergone decomposition through 
 the agency of heat and pressure, with the entire exclu- 
 sion of air. 
 
 Resume. — We have now considered the more im- 
 portant of the mine gases. The remaining gases play 
 
CONDITIONS EXISTING IN MINES. 5 
 
 no appreciable part in the consideration of the subject 
 of mine-ventilation. We have gone over in detail the 
 natural condition of a pit ; the vitiating influence and 
 the poisonous effect of its exuding gases ; and have re- 
 ferred to the general method in use for removing these 
 gases, viz., by maintaining a constant current of air 
 through the pit. 
 
 Agency of the Air-current. — The agency of the 
 air-current is that of a sort of common carrier, by 
 which the gases are conveyed out of the mine. This 
 is accomplished through the action of the laws of " The 
 Diffusion of Gases " ; the obnoxious and poisonous 
 gases mixing thoroughly with the air and diffusing 
 completely, so as to be lost in the current, much the 
 same as a drop of ink becomes lost in a glass of water. 
 Our part of the problem then becomes the maintaining 
 of a constant current of air into and through the entire 
 pit ; relying upon the working of natural forces for the 
 diffusion and extraction of the gases. 
 
 Natural Agencies of Ventilation. — Before taking 
 up the study of the applied forces, let us consider, for 
 a moment, what natural aids or hindrances exist in the 
 pit which become active forces, either aiding or oppos- 
 ing the circulation of the air. As previously stated, in 
 the discussion of the flow of air-currents, we are dealing 
 with an expansive, fluid medium, moved or animated 
 by the element of pressure. Pressure is always the 
 expression of some force ; or obtains when a force is 
 wholly or in part arrested. As we shall see in the next 
 chapter, in the study of applied forces, pressure obtains 
 as a ventilating force or agency whenever two columns 
 of air in equilibrium have different temperatures. 
 This will always.be the case when a mine is ventilated 
 
6 MINE-VENTILATION. 
 
 by means of two shafts, an upcast and a downcast 
 shaft ; as the air-current will naturally partake of the 
 temperature of the pit through which it passes. Hence 
 there exists, in every such pit, a natural agency of ven- 
 tilation, either aiding or opposing the applied agencies 
 in their work; and the influence of such natural agen- 
 cies must not be overlooked in careful computations. 
 This same natural force is developed in entries or air- 
 ways, running to the rise or dip. Such rising or dip- 
 ping entries act in the same manner as shafts, the 
 vertical height through which they rise or fall being 
 equivalent to the depth of the shaft. The action of 
 such rise or dip may be either to accelerate or retard 
 the circulation of the pit. 
 
 Suggestions. — On account of the above existing 
 forces or agencies, we should always, if possible, place 
 the fan, when forcing, over the shorter shaft, making 
 the deeper shaft the upcast ; for, as a rule, it will be 
 the warmer of the two. For the same reason, we 
 should always endeavor to have our intakes run to the 
 dip and return to the rise. This will not, however, 
 always be found possible or expedient. When we 
 have a strongly-pitching vein, it will be better to take 
 the air in at the lowest point and discharge it at the 
 highest. 
 
 Natural Ventilation. — As a final and resulting con- 
 dition, existing naturally in the mine, we have to con- 
 sider " Natural " ventilation. As stated above, the air- 
 current, or, more properly speaking, the ventilating 
 current, is animated or moved through the element of 
 pressure. When this animating pressure obtains in 
 the pit from natural causes, it gives rise to natural ven- 
 tilation. Natural ventilation is very unreliable and 
 
CONDITIONS EXISTING IN MINES. 
 
 7 
 
 changes, as regards the direction of the current, accord- 
 ing to the relative temperatures of the outside and 
 inside air. 
 
 Illustration. — Fig. I represents a vertical section 
 through a drift, connecting with an air-shaft. In the 
 winter season the air of the mine will be' warmer than 
 the outside air ; and the shaft will be converted into an 
 upcast shaft, the intake being through the slope. In 
 the summer season the air in the shaft becomes chilled 
 and heavier than the outside air and the course of the 
 
 Level A 
 
 ■fmummm/imm 
 
 FXG. I. 
 
 current is reversed. Comparatively very few mines 
 rely on this mode of ventilation, but all are subject to 
 its influence and the quantity of air passing in every 
 case is more or less affected by it, whatever the venti- 
 lating motor. It is important that this should be 
 borne in mind in experimental investigation. 
 
MINE-VENTILATION. 
 
 CHAPTER II. 
 FORCE AS APPLIED TO MINE-VENTILATION. 
 
 Prefatory. — Thus far we have taken a cursory view 
 of the natural condition of the pit : we have looked 
 over the ground very much as we would examine a new 
 field before beginning operations relative to opening 
 a mine, to acquaint ourselves beforehand with its exist- 
 ing conditions, the work to be done, and the natural 
 aids and hindrances to the accomplishment of such 
 work. Let us now, in like manner, continue to exam- 
 ine the material at hand ; and to this end we will take 
 up the study of force as applied to the movement of 
 the air-current. 
 
 Force. — Force is an abstract idea : we cannot see 
 force ; we can only see its results. We raise a hammer 
 and strike a blow that crushes a stone : we do not see 
 the muscular force that animated the blow ; but we see 
 its effect, which is the demonstration of its power. We 
 hold in our hand a ten-pound ball and we feel its 
 weight, or we place it in the scale-pan and see it de- 
 flect the beam : this tangible and visible effect demon- 
 strates to us the existence of a force of gravitation, but 
 we do not see the force. We see the ship flying before 
 the wind ; we feel the strength of the hurricane ; we 
 see the devastation of the tornado : all these are evi- 
 dences of a force behind the moving air which ani- 
 mates and propels. We may never answer the question, 
 "What is force?" ; but we can measure and compare 
 
FORCE AS APPLIED TO MINE-VENTILATION. 9 
 
 force with force. We have come to know the various 
 transformations of force, and to measure it according 
 to our standards. We have come to recognize pressure, 
 velocity, heat, etc., as various tangible expressions of 
 force ; and these have become our standards of measure. 
 
 Measure of Force. — Force, as applied to air, has 
 three measures, according to the conditions under 
 which that force is acting. Let us suppose that we 
 have a long conduit or air-passage, to one end of which 
 we apply a constant force by means of a fan or other 
 motor; three conditions may obtain, as follows: 
 
 1st. Closed conduit, giving pressure, but no motion 
 or velocity. 
 
 2d. Long, open conduit, giving pressure and motion 
 or velocity. 
 
 3d. Short, open conduit, giving no pressure, but ve- 
 locity only. 
 
 Static Pressure. — In the first of the three cases just 
 mentioned the force is converted wholly into pressure ; 
 and this pressure, called the " Static " pressure, is the 
 measure of the force. 
 
 Dynamic Pressure. — In the second of these cases 
 the force is converted partly into pressure, called the 
 " Dynamic " pressure, and partly into velocity, the pres- 
 sure and the velocity bearing an inverse ratio to each 
 other ; i.e., as the pressure increases, the velocity de- 
 creases and vice versa. The product of these two fac- 
 tors is the measure of the force in this case. 
 
 In the third and last case the force is wholly con- 
 verted into velocity. If this velocity could be measured, 
 it would be the measure of the force. This may, how- 
 ever, be called a theoretical case with respect to its 
 application to mine-ventilation. 
 
10 MINE-VENTILATION. 
 
 Moving Force or Ventilating Pressure. — The 
 
 second of the three cases just referred to represents 
 the condition which obtains in the mine. The moving 
 force or pressure under which the air is moving is the 
 power behind the current, and which animates the flow; 
 it is the total pressure exerted against the sectional area 
 of the airway. We term this total pressure, in this 
 work, the " Ventilating " pressure, as it is the force nec- 
 essary to move the current ; or, in other words, the 
 pressure necessary to produce ventilation. Tlie unit of 
 pressure, or the pressure upon one square foot of sec. 
 tional area, we term the " Unit " of ventilating pressure. 
 This unit of ventilating pressure is referred to by Atkin- 
 son, Fairley, and others, as the ventilating pressure, 
 although Mr. Atkinson tacitly admits that such method 
 is open to criticism. We represent the unit of venti- 
 lating pressure by the symbol p, and the ventilating 
 pressure itself by the symbol P = pa. 
 
 Natural Pressure : How it Obtains. — Let us now 
 investigate how the element of pressure obtains: first, 
 from natural causes, and, second, by the application of 
 artificial means, such as the fan or other motor; and 
 afterward find expressions for such pressure, in terms 
 of the means used. 
 
 Weight of Air. — That the air has weight, no one w ill 
 deny. It may be shown in various ways, but in none 
 more simply than by covering one end of a short tube 
 or cylinder with a flexible diaphragm, and exhausting 
 the air from the tube ; the diaphragm will be pressed in 
 by the pressure of the atmosphere upon it. 
 
 Barometric Pressure : Variations In. — The same 
 pressure is also shown in the principle of the barometer, 
 where the atmosphere supports a column of mercury 
 
FORCE AS APPLIED TO MINE-VENTILATION. II 
 
 which varies in height according to the height of the 
 observer above the level of the sea, and also accord- 
 ing to the state of the atmosphere at the time of the 
 observation. The barometer shows the pressure due 
 to the weight of the atmosphere to be subject to a 
 slight but regular diurnal variation, attaining a maxi- 
 mum about ten o'clock each morning and evening, and a 
 minimum about four o'clock. Besides this regular 
 diurnal variation, there is also shown to be a very 
 irregular fluctuation in the atmospheric pressure, accord- 
 ing to the presence of storm-centres, and according to 
 the amount of moisture in the air, or, as we say, its 
 hygrometric state ; and other causes not necessary to 
 mention here. But, disregarding these fluctuations for 
 the present purpose, the pressure of the atmosphere at 
 any level, or the barometric pressure, is produced by 
 the weight of the air above that level, which fact plays 
 a very important part in our discussion. 
 
 Expression for Weight of Air. — Our problem is to 
 find an expression for the weight of a unit of volume 
 of dry air at any temperature (/°), and under any bar- 
 ometric pressure {B"). Ganot, in his " Elements de 
 Physique," gives as the result of careful experiments 
 the weight of lOO cubic inches of dry air at the tem- 
 perature of l6° C. and a barometric pressure of 30", to 
 be 31 grains. This reduced gives, as the corresponding 
 weight of one cubic foot of dry air, at a temperature of 
 0° F. and a single inch of barometer, 0.0028885 pounds 
 avoirdupois, which agrees very closely with the results 
 given by Atkinson. It has further been ascertained by 
 careful experiment that air will expand -^^ of its vol- 
 ume for each degree of temperature of the Fahrenheit 
 scale ; and hence, taking the volume at 0° F. as one, 
 
12 MINE-VENTILATION. 
 
 t 
 the volume at any temperature, as t°, will be i -|- — ~r ; 
 
 and the weights per cubic foot being inversely propor- 
 tional to the volumes, we have 
 
 t 
 
 I : I H : : w : .002888; ; 
 
 '459 
 
 hence 
 
 or 
 
 459 X .0028885 
 
 w = ; — : , 
 
 459 + ^ 
 
 1.3258 
 
 w = 
 
 459 + t' 
 
 w being the weight of one cubic foot of dry air at 
 t° and \" barom. Now as the weights of equal vol- 
 umes are proportional to the barometric pressures, and 
 for the sake of uniformity adopting Mr. Atkinson's 
 figure, we have finally, for the weight of one cubic foot 
 of dry air at a temperature of f and under a baro- 
 metric pressure of B" , 
 
 1-3253 X B 
 
 W — r— ; — (I) 
 
 459 + ^ ^ ' 
 
 Effect of Temperature. — We come now to realize 
 that the atmosphere about us has weight, and that this 
 weight is a considerable pressure. We see from equa- 
 tion (I), that the weight of air is dependent upon the 
 temperature, and that it varies inversely as the expres- 
 sion 459 4- 1. Therefore, if two columns of air, as, for 
 example, two shafts connected by the airwaj's of a 
 mine, have different temperatures, they will not main- 
 tain a static equilibrium, but a moving pressure will b"^ 
 
FORCE AS APPLIED TO MINE-VENTILATION. 1 3 
 
 developed, incident to the two temperatures ; and this 
 surplus pressure is the moving or ventilating pressure 
 spoken of previously. 
 
 Temperature, then, is directly responsible for natural 
 pressure as it obtains in the mine. 
 
 " Head-of-air Column." — It has been found conven- 
 ient to express the unit of ventilating pressure in terms 
 of " Head-of-air Column," so called, representing the 
 pressure, from whatever source, as though animated by 
 the weight of such column of air. This head-of-air 
 column is sometimes called the " Motive Column." It 
 is an imaginary column of air of such height as to pro- 
 duce by its weight the pressure required. Denoting 
 this head-of-air column by H , its value will be ex- 
 pressed by the equation 
 
 rr_ /(459 + O /TTX 
 
 ^- 1.3253 x^ ^"^ 
 
 Caution. — In using this imaginary motive-column 
 we must not for a moment suppose that the velocity of 
 the air in the mine, due to this pressure represented, is 
 the same as the velocity generated by a body falling 
 through the height H . This is an error made by 
 many, and we cannot be too careful in its avoidance. 
 We would refer back to what has already been said in. 
 reference to this in the introductory chapter. Were 
 there no resistance ahead of the current, or, in other 
 words, were the power converted wholly into velocity, 
 this supposition would be correct ; but this is not the 
 case. We are dealing in this instance with movement 
 under pressure, or, as we say, a dynamic pressure. 
 We assume the power applied to be sufificient to give 
 
14 MINE-VENTILATION. 
 
 a certain quantity in a certain mine ; that is to say, a 
 certain velocity under a certain water-gauge or pres- 
 sure. Now it is to the power that we look for the pro- 
 duction of the velocity, whatever the opposing pressure. 
 The pressure exists by virtue of the dynamic resistance ; 
 and the resistance depends not alone upon velocity, 
 but upon another variable factor, viz., the rubbing 
 surface of the airways. It is true that the head-of-air 
 column or motive column is representative of a pres- 
 sure, but such pressure is not analogous to the dynamic 
 pressure of the air-current, for the reason that it is not 
 governed by the same laws. We may have in two dif- 
 ferent mines, whose airways have the same sectional 
 area, the same head-of-air column, as representative of 
 the same ventilating pressure, and yet yielding differ- 
 ent velocities and quantities, according as the rubbing 
 surfaces in those two mines are different. It is the re- 
 sistance that creates and maintains the dynamic pres- 
 sure. This will be more readily seen in the study of 
 the next chapter. 
 
 Head-of-air Cohimn, or pressure as applied to the 
 movement of fluids, and Generative Height, as applied 
 to falling bodies, are not correlative terms. 
 
 Air-columns as Motors. — Let us refer again to Fig. 
 I and assume two imaginary vertical columns of air, 
 having their bases at B' and B" , respectively, and ex- 
 tending upward through the atmosphere. If we assume 
 these imaginary air-columns to have each a base of one 
 square foot area, the weight of air in each column 
 above any level, as level A or level B, will be the unit 
 of pressure at such point. Multiplying this unit of 
 pressure by the sectional area of the airway, we obtain 
 the total pressure upon the air at level B due to the 
 
FORCE AS APPLIED TO MINE-VENTILATION. 1 5 
 
 weight of the air above. These two imaginary columns 
 of air, when connected below by airways, will be 
 in equilibrium — static equilibrium if their weights are 
 equal, when no current M'ill result ; and dynamic equilib- 
 rium if their weights are unequal and a current estab- 
 lished. It is evident now that the weights of the two 
 columns of air above level A will always be the same, 
 being subject to the same temperature, and therefore 
 may be ignored in ascertaining the differential pres- 
 sure. Below this level they may be very different. 
 This difference of temperature may result either from 
 natural causes, as the heat of the mine, or from the ap- 
 plication of artificial means, as the heat of a furnace. 
 In either case a difference of pressure will result, and 
 the air in the airways will be urged to move from the 
 point of greater pressure to the point where the pres- 
 sure is less, the moving force being the surplus of pres- 
 sure which we term the ventilating pressure. 
 
 Pressure in Terms of Air-column. — The vertical 
 height h between level A and level B, Fig. I, we will 
 call the "Motive Height," because it is the height 
 through which the motive force is exercised or devel- 
 oped, but this term must not be confounded with the 
 term motive column, or head-of-air column previously 
 referred to, as its significance is widely different. In 
 ascertaining the differential or moving pressure, we are 
 concerned only with the motive height. 
 
 Assume the following: 
 
 t = temperature of the outer air; 
 t^ — avg. temp, of the air in the upcast shaft ; 
 w = wt. of one cu. ft. of the outer air ; 
 w,= " " " " "" " air in the upcast shaft; 
 B = height of the barometer in inches ; 
 
l6 MINE-VENTILATION. 
 
 h = motive height ; 
 
 a = area of cross-section of the airway. 
 Then 
 
 (w— Wj) = the differential unit of weight ; 
 /i{w—w^)=: " " " " pressure; 
 
 ah{w—w^ = P = the moving or ventilating pressure. 
 Referring to equation (I), we have 
 
 1.3253 X^ 
 
 459 + ^ 
 and 
 
 1.3253 X B 
 
 w, = 
 
 Hence 
 
 459 + 1. 
 
 P=i.l2SZXahB{ ^——-- ^^V . (Ill) 
 
 ^ " US9 + ^ 459 + V ^ ' 
 
 When t^ is greater than /, the value of P will be 
 positive, which indicates an upcast current in the shaft ; 
 when t^ is less than t, the value of P becomes nega- 
 tive, and then indicates a downcast current in the 
 shaft. Equation (III) is true for all cases of mine-ven- 
 tilation where only two temperatures are concerned in 
 producing pressure. This is the case in a slope or drift- 
 mine ventilated by a shaft, either by natural draught 
 or by a furnace ; also in a mine ventilated by means of 
 two shafts, where either the downcast shaft is so shal- 
 low as to have practically the same temperature as the 
 outer air, or the mouths of the two shafts are on the 
 same level. 
 
 Primary Columns and Secondary Columns. — In 
 all cases of natural ventilation the deeper shaft will de- 
 termine the course of the current, by its relative tern- 
 
1 ORCE AS APPLIED TO MINE-VENTILATION. 
 
 17 
 
 perature ; in all cases of furnace-ventilation, the fur- 
 nace shaft will determine the course of the current, 
 being the upcast. Therefore we may call these shafts 
 the " Primary Columns " and the other shafts the 
 " Secondary Columns." The temperature of the pri- 
 mary column is always represented by one temperature, 
 while the secondary column may possess two separate 
 and distinct temperatures, which cannot be averaged 
 accurately. This gives rise to a case of mine-ventila- 
 tion where three temperatures are concerned in pro- 
 ducing the ventilating pressure. 
 
 Three Temperatures. — Fig. II illustrates a case of 
 mine-ventilation (either natural or by a furnace), where 
 three temperatures may be concerned. 
 
 Fig. II. 
 
 Assume the following : 
 
 d^ = depth of the primary or deeper shaft ; 
 d = depth of the secondary shaft ; 
 
1 8 MINE-VENTILATION. 
 
 {d^ — d) =^ height of the outer effective column ; 
 t^ = avg. temp, of the primary shaft ; 
 t, = avg. temp, of the secondary shaft ; 
 t = temp, of the outer air. 
 Then, by applying the same method used to obtain 
 equation (III), we have 
 
 P= 1.3253 X aB [^-^,+ ^— ^).(IV.) 
 
 Equations (III) and (IV) will cover all cases of natu- 
 ral and furnace ventilation that will arise, and express 
 in pounds avoirdupois the value of the elementary 
 pressure due to heated air-columns. 
 
 Pressure in Terms of the Fan. — We will now de- 
 termine the pressure due to the action of a fan. For 
 the present we will content ourselves with determining 
 the static pressure the fan is capable of yielding, i.e., 
 the pressure the fan would give if working into a closed 
 space. In all cases of compressive ventilation the pres- 
 sure is created and maintained by the resistance of the 
 mine, and its value is expressed in terms of the mine ; 
 and for this reason we delay its discussion till later. 
 The method here adopted for determining the static 
 pressure due to the action of the fan depends, as pre- 
 viously stated, upon the centrifugal force developed by 
 the mechanical revolution of the air contained between 
 the blades of the fan. This contained air possesses a 
 certain weight, and this weight of air, compelled to re- 
 volve at a certain speed by virtue of its mechanical 
 environment, will develop a certain centrifugal force or 
 outward pressure. 
 
 Assume the following: 
 
FORCE AS APPLIED TO MINE-VENTILATION. I9 
 
 R = outer radius of the fan-blades; 
 /?, = inner radius of the fan-blades ; 
 
 6 = breadth of blades ; 
 
 w, = number of blades ; 
 
 n = number of revolutions per minute; 
 R^ = rad. of the cen. of grav. of one compartment; 
 
 V, = vel. of the cen. of grav. of one compartment ; 
 
 v^ = capacity between tv;o consecutive blades ; 
 
 W= wt. of air between two consecutive blades; 
 
 F = centrif. force of air in one compartment ; 
 
 ^ — acceleration due to gravity (32.19) ; 
 
 p = unit of pressure; 
 t = temperature of the air ; 
 
 B =^ barometric pressure in inches ; 
 Now, since the unit of pressure is equal to the entire 
 centrifugal force developed in all the compartments 
 divided by the surface pressed, we write 
 
 From mechanics, we have 
 
 -5f- <^> 
 
 But as v^ is the velocity of the centre of gravity of 
 one compartment, in feet per second, to correspond to 
 the value of g, which is in feet per second, we have 
 
 27tjR,n 
 -^=^S~' (3) 
 
 and, from mechanics, we have for the value of (i?,) 
 
 2_^ + RR^±Rl 
 ^'~3 R + R, • • • W 
 
20 MINE-VENTILATION. 
 
 We have also, from equation (I), remembering that 
 
 jrjr 1-3253 X-g ,. 
 
 W= r-:—'^, (S) 
 
 Also, from geometry, we have 
 
 rr^R^-R^ 
 
 Finally, by combining these six elementary equations 
 and reducing, we have 
 
 / = 0.0001505 ^ ie ^ ^]^+"^- • • ^^ 
 
 Equation (V) is applicable to all straight paddle-fans, 
 and expresses, in pounds avoirdupois, the unit of static 
 pressure the fan is capable of producing. 
 
 Other Motors. — Other air-motors are the steam-jet, 
 waterfall, and various kinds of screw machines and 
 volumetric appliances ; but these are all unscientific, 
 and are rapidly falling into disuse. They will not be 
 discussed in this work. 
 
 Resume. — We have now referred to pressure as de- 
 veloped by and expressed in terms of some motor, or, 
 in other words, as the representative or agent of some 
 animating, energizing force. The following chapter 
 will consider opposing /r^j.yz<ri? as expressed in terms of 
 the resistance of the mine. 
 
RESISTANCE OF THE MINE. 21 
 
 CHAPTER III. 
 
 RESISTANCE OF THE MINE. 
 
 Resistance. — By Resistance, in general, is meant the 
 force opposed to the movement of a body. It is always 
 opposed to the moving force. Resistance to the move- 
 ment of a fluid always creates a pressure throughout 
 its mass, and this pressure is one of the factors by 
 which we measure the moving force applied, as we shall 
 see in the next chapter. In. the case of the flow of air 
 through the airways of a mine, the resistance (which 
 is due to the rubbing of the air-current along the sides, 
 roof, and floor of the airway) is applied all along the 
 entire length of the current. For this reason the 
 pressure arising therefrom decreases as we proceed 
 along the airway and approach the discharge, where it 
 is nil. From a consideration of this last fact we readily 
 see that the ventilating pressure in a mine can never 
 be greater than, but is always equal to, the resistance 
 offered by the mine to the passing of the current. This 
 resistance has been improperly called the "Drag "of 
 the mine. There is no drag ot pull known in the study 
 of physical laws relating to fluids. Force or power is 
 always behind the opposing resistance. 
 
 Kinds of Resistance. — It is well to notice that re- 
 sistance is of two kinds. What we will call the " Static " 
 resistance or the force to be overcome in order to cre- 
 ate a circulating current, is much greater than the 
 " Dynamic " resistance, or the force to be overcome in 
 
22 MINE-VENTILATION. 
 
 maintaining such current after it is established. What 
 will interest us the most in the study of the following 
 pages is the dynamic resistance, and, as stated above, 
 it is equal to the ventilating pressure pa. 
 
 How Varies. — The dynamic resistance varies theo- 
 retically as the extent of the rubbing surface and as the 
 square of the velocity of the current. This is what we 
 would naturally expect, because, if the velocity of the 
 air-current be doubled, each particle of air strikes, in a 
 unit of time, twice the amount of resistance, and each 
 opposing blow is of twice the force ; therefore the 
 resistance is as the square of the velocity of the current ; 
 and as the number of resisting particles increases with 
 the rubbing surface, the resistance will increase in the 
 same ratio. We say the resistance varies theoretically 
 as the extent of the rubbing surface, but, practically, 
 the physical condition of the surface rubbed, as being 
 rough or smooth, will vary the amount of the resist- 
 ance ; also, there can scarcely be a doubt but that the 
 moisture condensed upon the sides and roof of the air- 
 way will act as a lubricant, and thereby reduce the 
 resistance. Sharp bends or projecting angles in the 
 airway are a serious hindrance to the passage of the 
 air, and largely increase the resistance. But all of these 
 are physical causes, affecting the coefficient of friction 
 to be referred to hereafter ; they in no way affect the 
 working of the law by which resistance varies, and given 
 above. 
 
 Static Resistance. — Static resistance carniot be 
 formulated, as it depends upon too many arbitrary 
 conditions and influences. When resistance is spoken 
 of in this book it is dynamic resistance which is meant. 
 
 Dips and Rises. — An important factor affecting 
 
RESISTANCE OF THE MINE. 23 
 
 the flow of the air-current, and which is often alluded 
 to as a resistance (but it is not a resistance, properly 
 speaking), is the occurrence in the entries or airways 
 of dips or rises. The effect of such dips or rises, as 
 aiding or retarding the flow of the air, will be discussed 
 in this chapter ; the question of such dips and rises 
 affecting the proportionate flow at different velocities 
 will come up for discussion in the chapter upon "Split- 
 ting the Air" (Chapter IX). 
 
 Effect upon the Current. — Considerable diversity 
 of opinion has always existed among miners regarding 
 the effect of a dip or a rise in the entry. It may be 
 said with reason, however, that an intake working to 
 the dip will assist ventilation, while an intake working 
 to the rise will retard the same. This has been demon- 
 strated a number of times: it will only be found to 
 fail when the intake is warmer than the return, which 
 is seldom. The reason is obvious, and has already been 
 referred to in the discussion of " Natural Agencies of 
 Ventilation " (Chapter I). If an air-course works to 
 the dip, its return must show an equal rise in vertical 
 height. This is evidently true whether the return par- 
 allels the air-course or not, except in some special 
 cases — as, for example, a tunnel having two openings, 
 or some similar instance of one direct current and no 
 return. A mine in which the upcast shaft is locatetf at 
 a considerable distance from the downcast is an exam- 
 ple of one direct current. An intake running to the 
 dip and its return to the rise is but an illustration of 
 natural ventilation in the large majority of cases, as 
 the warmer air of the pit will naturally tend to rise, 
 while the cool outer air likewise descends to take its 
 place. On the other hand, an intake running to the 
 
24 MINE-VENTILATION. 
 
 rise and its return to the dip presents a condition of 
 things which is contrary to the natural ; and a venti- 
 lating current compelled to travel in that direction 
 will have this natural force or agency to overcome. 
 The influence of dips and rises is a very potential one ; 
 its potentiality depending upon the vertical height of 
 the dip or rise and the differential temperature of the 
 intake and the return. It is, as we have said, another 
 case of natural ventilation, in which the vertical height 
 of the rise or dip corresponds to the motive height h 
 of equation (II). The influence of dips and rises as a 
 ventilating power must always be taken into account 
 in nice calculations upon mining problems, especially 
 in figuring upon the proportionment of air in different 
 splits, and when the amount of the dip or rise is con- 
 siderable. 
 
 Expression for Resistance. — In obtaining an ex- 
 pression for the resistance offered by a certain mine to 
 its ventilating current we assume the following : 
 
 7? adynamic resistance, opposed to any ventilating 
 
 pressure P = pa ; 
 V = velocity of the air-current in feet per minute ; 
 .f = rubbing surface of the entries or airways exposed 
 
 to the current, expressed in square feet ; 
 k =^ unit of resistance, or the resistance, expressed in 
 
 pounds (avoir.), offered by i sq. ft. of rubbing 
 
 surface to air moving with a velocity of i ft. per 
 
 minute. 
 Then we may write, from what has preceded, 
 
 R = ksv' (VI) 
 
 Pressure in Terms of the Mine.— From what has 
 
RESISTANCE OF THE MINE. 25 
 
 preceded we have also seen that the ventilating pres- 
 sure P = pa is opposed and equal to the resistance R; 
 hence we may also write 
 
 R = pa (VII) 
 
 Then, by substituting this value of R in equation (VI), 
 and solving with respect to p, we have 
 
 / = — (VIII) 
 
 Coefficient of Resistance. — What we call the " Co- 
 efficient " of resistance is really the unit of resistance ; 
 it is expressed in our formulas by the symbol k. 
 Solving equation (VIII) with respect to k, we have 
 
 k=^. (IX) 
 
 Value of. — On account of the various obstructions 
 in the airways, and the varying physical conditions of 
 the mine and airways, referred to in the early part of 
 this chapter, no two mines will give exactly the same 
 value for k. The value of k, as deduced by Mr. 
 Atkinson, from a large number of experiments by 
 others, has been very generally adopted ; and we see 
 no good reason for changing it, except it may be in 
 some particular determination. For the purposes of 
 general calculation and for the sake of uniformity, it 
 should be always used. This value, as given by Mr, 
 Atkinson, is 
 
 k= 0.0000000217. 
 
 The method of mining, mode of timbering, and other 
 
26 MINE-VENTILATION. 
 
 details of working, which vary considerably according 
 to the customs habitual in the district wherein the 
 mine is located, may give upon investigation a coeffi- 
 cient more adapted to the mines in that district. Such 
 a local value of k may be determined by taking care- 
 ful observations in several typical mines of that dis- 
 trict and then averaging the results, avoiding any that 
 might seem to be unreliable on account of obstructed 
 airways, small break-throughs, or other similar defects. 
 
 Practical Value of &•■ — The practical benefit aris- 
 ing from a known local value of k would be the ascer- 
 taining therefrom the necessary ventilating pressure 
 for any proposed workings, in estimating and decid- 
 ing upon size of fans and power of engines to be em- 
 ployed. It is a good factor to know ; and after its 
 value has been established in any district or class of 
 workings, by careful observations in mines that are 
 well kept, its subsequent application to other mines in 
 that district will show the comparative condition of 
 the air-courses in such mines. 
 
 Density as affecting Resistance. — The question is 
 often asked, " Does a change in the density of the flow- 
 ing air affect in any way the resistance or the power? " 
 As far as the resistance offered by the mine to the pass- 
 ing current is concerned, the density of the flowing air 
 does not change sufficiently to produce any appreciable 
 effect. Likewise, also, the power is not appreciably 
 affected as far as the mine is concerned — that is to say, 
 the power required to pass a certain quantity of air per 
 minute through that mine. But, on the other hand, 
 the efficiency and power of the fan is very seriously 
 affected by changes in the density of the air. This 
 part of the subject, however, will be discussed later — 
 
RESISTANCE OF THE MINE. 27 
 
 Chapter VIII. The causes which give rise to a change 
 of density in the air of the pit are very numerous: 
 first, the pressure of the pit due to the resistance (this 
 pressure decreases all the way along the current, from 
 the intake to the discharge, and affects the density 
 correspondingly) ; second, the heat of the mine which 
 is more potent in its effect; third, the absorption of 
 aqueous vapor by the air in its passage through the 
 pit ; the density of the air being very slightly dimin- 
 ished by this absorption. The return current is always 
 saturated, or carrying as much moisture as the tem- 
 perature will permit, as is evidenced by its depositing 
 this moisture upon the slightest fall in temperature, 
 or what is commonly termed by the miners as the 
 "sweating" of the pit. Air saturated with moisture 
 at a temperature of 63° Fahn, which may be taken as 
 the average temperature of the pit, will weigh one per 
 cent lighter than dry air at the same temperature. 
 In gaseous mines the presence of the pit gases will 
 change the volume and the density of the air-current. 
 
28 MINE-VENTILATION. 
 
 CHAPTER IV. 
 
 WORK. 
 
 Prefatory. — Before entering further upon the subjec- 
 of " The Ventilation of Mines," let us complete the pre- 
 liminary study of forces by refreshing our memories in 
 respect to what is termed in mechanics "Work." 
 
 Definition of Work. — A force may exist in all its 
 vigor and with unchanging constancy ; and yet if that 
 force does not move, or, in other words, if it is not ex- 
 erted through a certain distance, it accomplishes no 
 work. By work we understand a force exerted through 
 a certain distance. The force and the distance through 
 which it acts together become the measure of the work 
 performed. In other words, a force multiplied by the 
 path over which it has travelled represents the work of 
 that force. 
 
 Unit of Work. — The adopted unit of work is the 
 work performed by a pound avoirdupois falling through 
 a vertical height of a foot, or that of a pound pres- 
 sure moving through a distance of a foot. This unit is 
 called in mechanics a " Foot-pound." 
 
 Power. — When we speak oi power, we mean the abil- 
 ity to accomplish a certain work in a certain time. A 
 boy may perform the work of a man if he is given time 
 enough, or a man may do the work of ten men in a 
 longer period of time. 
 
 Unit of Power. — The unit of power is a unit of work 
 performed in a unit of time. The adopted unit of power 
 
WORK. 29 
 
 is the work performed by a pressure of a pound acting 
 through a distance of a foot in precisely one minute of 
 time. A unit of power will raise one pound avoirdu- 
 pois through a vertical height of one foot in one min- 
 ute of time. 
 
 Horse-power. — A horse-power is the power that will 
 raise 33,000 pounds through a vertical height of one 
 foot in one minute of time. 
 
 Work as a Measure of Power. — Work, then, is the 
 measure of a power. The same power will always per- 
 form the same amount of work in the same time, 
 though the work may differ in its kind. If we apply 
 the same power to mines offering different resistances, 
 the work performed in each case will be the same, be- 
 cause the power is the same ; the velocities and the 
 pressures may vary, according as the relative areas and 
 lengths of the airways vary ; but even under these 
 changing conditions the same power will always accom- 
 plish the same amount of work. 
 
 Expression for Work. — Assume the following : 
 
 £/;= work performed by a ventilating current ; 
 
 p = unit of pressure of the established current ; 
 
 V = veloc. in ft. per min. of the established current ; 
 
 a = sectional area of the airways. 
 Then from the definition of work we may write 
 
 U = pav (X) 
 
 Substituting for p in equation (X) its value taken 
 from equation (VIII), and reducing, we have 
 
 U=ksv' (XI) 
 
 Again, we know that the sectional area of an airway, 
 multiplied by the velocity of the passing air (in feet per 
 
30 MINE-VENTILATION. 
 
 minute), will give the quantity Q of air passing per 
 minute, expressed in cubic feet, which gives the expres- 
 sion 
 
 Q = av (I) 
 
 Substituting in equation (X) for av its value Q, we 
 have 
 
 U=Qp (XII) 
 
 Again, referring to expression (i-XII), and solving with 
 respect to v, we have 
 
 »=e (,) 
 
 Squaring both members of this equation and substitut- 
 ing the value of v'' thus found in equation (VIII), we 
 have 
 
 ^=5^' (^) 
 
 Finally, substituting this value of / in equation (XII), 
 we have 
 
 CA=^(2^ . . . (XIII) 
 
RESULTANT FACTORS OF VENTILATION. 3 1 
 
 CHAPTER V. 
 
 RESULTANT FACTORS OF VENTILATION. 
 
 VELOCITY, QUANTITY, ETC. 
 
 Resume. — We have thus far considered — 
 
 1st. The natural conditions obtaining in a pit ; 
 
 2d. Force as applied to the air-current ; 
 
 3d. The resistance of the mine opposed to such force ; 
 
 4th. Work as a measure of power. 
 
 While we have developed some important formulas 
 incidentally, yet our study has been thus far largely 
 preliminary. 
 
 Prefatory. — We will now consider, separately and in 
 order, the various factors of ventilation that result from 
 the application of force to overcome resistance, or of 
 power to produce work. 
 
 Velocity. — We have seen that movement results 
 from the application of pressure to air when such pres- 
 sure is not wholly resisted. Such movement of the air 
 in and through the airways is the velocity referred to. 
 It is uniform, and proportionate to the cube root of the 
 power and also to the square root of the ventilating 
 pressure (under like conditions of rubbing surface in 
 the airways). This is readily seen from equations (XVI) 
 and (XVII), below. 
 
 Expressions for Velocity. — We have already seen, 
 from equation (i-XIII) that 
 
 -= I (XIV) 
 
32 MINE-VENTILATION. 
 
 From equation (X) we have 
 
 ^=Ta (^V) 
 
 Again, solving equation (XI) with respect to v, we 
 have 
 
 3 I U 
 
 (XVI) 
 
 And, further solving equation (VIII) with respect to the 
 same quantity, we have 
 
 "=\/f 
 
 ,(XVII) 
 
 Quantity. — The term " Quantity," as used in refer, 
 ence to mine-ventilation, means the number of cubic 
 feet of air passing any given point in the airway per 
 minute. 
 
 Expressions for Quantity. — We have seen before 
 (eq. (I -XI I)) that 
 
 Q = av (XVIII) 
 
 Solving equation (XII) with respect to Q, we have 
 
 Q=^■ (XIX) 
 
 Solving equation (2-XIII) with respect to Q, we have 
 G = /f (XX) 
 
RESULTANT FACTORS OF VENTILATION. 33 
 
 Again, substituting in equation (XIX) for U its value 
 taken from equation (XI), we have 
 
 Q = -^ (XXI) 
 
 Finally, solving equation (XIII) with respect to Q, we 
 have 
 
 ^^iVs^'^U. . . .(XXII) 
 
 Pressure. — We have seen before (eq. (2-XIII)), that 
 
 P = -,& (XXIII) 
 
 a 
 
 Equation (VIII) represents another expression for pres- 
 sure ; it is repeated here to place these different expres- 
 sions together : 
 
 /= ~ (VIII) 
 
 Combining equations (XII) and (XXII), and solving 
 with respect to p, we have 
 
 s 
 
 /=-^'VZ7^ . . . (XXIV) 
 
 Work. — (For the expressions of work, see Chapter 
 IV.) 
 
 Potential Factor. — The term Potential Factor, as 
 used in this work, is a term of special significance. It 
 always has a value peculiar to the mine in question, and 
 which represents for that particular mine the relation 
 
34 MINE-VENTILATION. 
 
 which will subsist between the quantity of air passing 
 and the cube root of the power necessary to pass such 
 quantity. Referring again to equation (XXII), and di- 
 viding both members of the equation by the cube root 
 of U, we have 
 
 171 = ^ (XXV) 
 
 The first member of equation (XXV) expresses the 
 value of the potential in terms of the quantity and the 
 power : this expression we call the potential factor of 
 ventilation. The second member of the equation ex- 
 presses the value of the same potential in terms of the 
 mins : we call it the potential factor of the mine. 
 Expression for the Potential Factor. — Assume 
 
 X =^ potential, referred to ventilation or to the mine. 
 
 Then from the definition of the potential factor we 
 write 
 
 X=S^, .... (XXVI) 
 
 and also 
 
 X = ^=.. . . . (XXVII) 
 
 vks 
 
 Expressions in Terms of the Potential. — Substi- 
 tuting successively in equations (XIII), (XX), (XXII), 
 (XXIII), and (XXIV) the symbol X for its value, as 
 given by equation (XXVII), we obtain the following; 
 
 £/ = J3 ; . . . . (XXVIII) 
 Q = VX^- .... (XXIX) 
 
RESULTANT FACTORS OF VENTILATION. 35 
 
 , Q = X\^U; .... (XXX) 
 
 P=%' (XXXI) 
 
 P=^ (XXXII) 
 
 Quantity Due to Two Motors. — Assume the fol- 
 lowing : 
 q = the quantity due to any motor (as a fan running at 
 
 a fixed speed) working alone ; 
 ^, = the quantity due to any other motive source (as 
 
 another fan or a furnace) working alone ; 
 Q =: the quantity due to the simultaneous action of 
 
 both motors. 
 Let u, K„ and U represent the work performed in 
 passing the quantities q, q^, and Q, respectively. Then, 
 referring to equation (XIII), we write, for the work 
 performed in each of the three cases respectively, 
 
 «=^?; (i) 
 
 »^ = —r,qr, (2) 
 
 u=^iQ' (3) 
 
 Now, when both of these motors are working simulta- 
 neously, or when any number of motors are working 
 and throwing air into the same airways, each will per- 
 form its respective work, the same as when working 
 
l6 MINE-VENTILATION. 
 
 singly; for the work in each case depends solely upon 
 the power applied, which we assume remains un- 
 changed. Hence we write 
 
 U=u-\-u^ (4) 
 
 Now by substituting in this last equation the several 
 values of u, «,, and U, as given by equations (i), (2), 
 and (3), above, and dividing throughout by the common 
 
 factor ( -5), we have 
 
 G' = / + ?.'; (5) 
 
 and extracting the cube root of each member of the 
 above equation we find, for the value of Q, 
 
 Q = ^q' + q^' ■ ■ ■ (XXXIII) 
 
 Expression for Head-of-air Column in Terms 
 of Temperature and Motive Height. — Referring to 
 equation (III), we find an expression for ventilating pres- 
 sure P, in terms of the temperatures of two air-col- 
 umns, which may be the upcast and downcast shafts, 
 respectively. Let us assume 
 
 t = average temperature of the downcast shaft ; 
 
 ^, = average temperature of the upcast shaft. 
 
 Then, dividing both members of equation (III), by a 
 and substituting the value of p thus found in equation 
 (II), and reducing, we have 
 
 * ^ = '(41^)- • • ^^^^'^> 
 
 Expression for Horse-power. — As we have already 
 seen, a single horse-power is equivalent to 33,000 foot- 
 
RESULTANT FACTORS OF VENTILATION. 37 
 
 pounds, or units of work ; hence, indicating horse-power 
 by the symbol H. P., we have 
 
 H.P.= — ^. . . . (XXXV) 
 33000 '' '' 
 
 Pressure in Terms of Water-gauge. — The unit of 
 ventilating pressure, as indicated by inches of water- 
 gauge, is calculated from the weight of a cubic foot of 
 water. One cubic foot of water at a temperature of 
 62° F. weighs 62.355 pounds; and one inch of water- 
 gauge will represent a pressure per square foot of -^ of 
 this, or, say, 5.2 pounds. Assume 
 
 i = inches of water-gauge. 
 
 Then we may write 
 
 p = S.2i. .... (XXXVI) 
 
 Pressure in Terms of Temperature and Motive 
 Height. — Combining equations (II) and (XXXIV), and 
 solving with respect to p, we have 
 
 p = ^ 1-3253 X^ ^ t. -t _ (XXXVII) 
 
 ^ 459 + ^ 459 + ^. ' 
 
38 MINE-VKNTILATION. 
 
 CHAPTER VI. 
 
 EXPRESSION FOR STRAIGHT-PADDLE FANS. 
 
 Prefatory. — In Chapter II we developed an expres- 
 sion for the static pressure due to the action of a fan ; 
 we are now prepared to formulate an expression for the 
 work a straight-paddle fan is capable of performing, in 
 terms of itself. Afterward, by equating this work and 
 the work necessary to be performed in a mine in order 
 to pass a certain quantity of air (Q) per minute (eq. 
 XIII), we obtain an expression for the quantity of air 
 a fan will yield per minute in terms of itself and the 
 mine at which it is working. This is one of the most 
 important determinations in the subject of mine-ven- 
 tilation ; the general method of procedure has been 
 outlined in the introductory chapter, to which refer- 
 ence should now be made. 
 
 Weight of Air in One Section of the Fan, — Let 
 
 Fig. (Ill) represents one section of a straight-paddle fan, 
 
EXPRESSION FOR STRAIGHT-PADDLE FANS. 39 
 
 showing the space between two consecutive blades. 
 Assume as under equation (V). Combining equations 
 (S-V), and (6-V), we have, for the weight of air in one 
 section of the fan, 
 
 ^^ <R' - R.')b ^ 1-3253 X B 
 
 «, 459 + / ■ ■ ■ ^ '' 
 
 Centrifugal Force of this Weight. — We have for 
 the centrifugal force developed in one section of the 
 fan, as given by equation (2-V), 
 
 Wv'' 
 
 Measure of this Centrifugal Force. — A force is 
 measured by the velocity it can create in a unit of mass 
 in one second of time; this measure /is called the ac- 
 celeration due to the force /'"', and medins feet per sec- 
 ond. But our centrifugal force i^ acts upon a number 
 of units of mass m ; hence its measure is expressed 
 by the equation 
 
 F=fm (3) 
 
 In this equation (3) m is the mass of the weight W; 
 hence we may substitute for it its value ( — J, and we 
 have 
 
 Combining equations (2) and (4), above, and solving with 
 respect to /, we have 
 
 f=i <=' 
 
40 MINE-VENTILATION. 
 
 Then, squaring both members of equation (3-V), and 
 substituting the value of v^ thus found in equation (5), 
 above, and reducing, we have 
 
 /= 0.010966 /?, «" (6) 
 
 Work of the Centrifugal Force per Second. — 
 
 Equation (6), above, gives the value oi f, the accelera- 
 tion due to the force F, which we must remember acts 
 radially. But when the force is uniformly accelerative, 
 that is to say, when the force is constant and acts to 
 increase the velocity of the mass by a constant quantity 
 each unit of time, the space passed over during such 
 unit of time will be equal to one half of the acceleration 
 
 (4) 
 
 and, as we have seen from Chapter IV, the work 
 
 of this force F during one second of time is equal to 
 the force multiplied by this space over which it has 
 passed in one second of time. Assume the following: 
 u = the work performed in one second by one section 
 
 of the fan only; 
 C/, = the total work performed in one second by all 
 
 the sections of the fan ; 
 [/ — the total effective work performed by the fan in 
 
 one minute of time. 
 Then we have, from what has preceded, 
 
 « = ^7 (7) 
 
 Work of the Fan per Second. — For the entire 
 work of the fan per second 
 
 U,= n,FL (8) 
 
EXPRESSION FOR STRAIGHT-PADDLE FANS. 4I 
 
 Combining equations (4), (6), and (8), above, and reduc- 
 ing, we have 
 
 W o 
 
 I/, = W, 0.0000601 2i?,'«* (9) 
 
 o 
 
 Now, substituting for fFand R, their respective values, 
 as taken from equations (i), above, and (4-V), and 
 reducing, equation (9), above, becomes 
 
 U, = o.ooooosi8n'6R,(R' - R,') — ^— -. (10) 
 
 459 + ^ ^ ^ 
 
 Effective Work of the Fan per Minute. — Equa- 
 tion (10), above, gives the expended work of the fan for 
 one second of time. Multiplying this work for one 
 second by 60, to obtain the work for one minute, and 
 introducing a coefficient K of efficiency (to be ex- 
 plained in Chapter VIII. — " Economic Discussion of 
 the Fan"), we obtain for the effective work of the fan, 
 for a minute of time, the following equation : 
 
 U= o.ooosiiiKn*dR,{R'-R,') — ^p-. (XXXVIII) 
 
 Quantity yielded per Minute in Terms of the Fan 
 and Mine. — Equation (XXXVIII) gives the entire 
 effective work of the fan for one minute of time. This 
 effective work of the fan must of necessity be equal to 
 the work U performed in one minute by the ven- 
 tilating current in the pit, and which is expressed by 
 equation (XIII). Therefore, equating these values of 
 U and solving with respect to Q, we have 
 
 (2 = 0.06776 f^ Kn'bRiR'-R^) ^, (XXXIX) 
 ' 'ks 459+^- 
 
42 MINE-VENTILATION. 
 
 Equation (XXXIX) is the general equation for deter- 
 mining the yield of a straight-paddle fan, running at a 
 fixed speed, at any given mine, the temperature and 
 barometric pressure being also given. But care must 
 be taken in its application that the effect of other 
 agencies of ventilation are taken into account, such as 
 upcast shafts heated by the natural heat of the mine, 
 and dips or rises in the entries : these, as well as small 
 break-throughs, obstructed airways, etc., etc., are sour- 
 ces very often productive of error. 
 
 Pressure yielded by a Fan. — We often hear the 
 question asked, " What pressure or water-gauge will 
 the fan give? " If the fan in question is working into 
 a closed space, thereby creating a certain static pres- 
 sure, the question is a proper one. But when the fan 
 is throwing air into a certain mine, the pressure referred 
 to is created by the resistance of the mine : it depends 
 directly upon this resistance. The same fan, running 
 at the same speed, but throwing air into another mine, 
 will establish a different pressure, according to the re- 
 sistance to be overcome. In any case of mine-ventila- 
 tion, whether the motor is a fan or otherwise, the ven- 
 tilating pressure may be found by applying equation 
 (XXIII). 
 
 Horse-power of a Fan. — By combining equations 
 (XXXV) and (XXXVIII), and solving with respect to 
 H.P., we have 
 
 H.P. = o.oooooooo943/i:«^<5;?/i2=-/?/)— :^(XL) 
 
 459+'- 
 
ECONOMIC DISCUSSION OF THE FURNACE. 43 
 
 CHAPTER VII. 
 
 ECONOMIC DISCUSSION OF THE FURNACE. 
 
 Prefatory. — It does not belong to the province of 
 this work to discuss the comparative merits of differ- 
 ent ventilating-machines ; nor to remark upon their 
 construction, only as such construction may interfere 
 with the theoretical efficiency of the machine. Such 
 economic construction relative to the furnace must 
 provide — 
 
 First, a sufficient grate-area for the burning of the 
 required amount of coal to produce the ventilating 
 pressure /"in that particular mine; 
 
 Second, a sufficient flue-area or airway over and 
 around the fire, so as not to obstruct the flow of the 
 quantity Q. 
 
 There are other essential points in furnace construc- 
 tion, but these are the only ones that affect the effi- 
 ciency of the furnace. 
 
 Economic Grate-area. — By the economic grate-area 
 is meant such an area of the grate of a furnace as will 
 burn a given amount of coal in a given time and there- 
 by give to the furnace a certain heating capacity, or, 
 in other words, render the furnace capable of creating 
 a temperature t^ in a current Q of mixed air and gases 
 passing over and around itv 
 
 How Determined.— In order to determine the area 
 of grate needed to cause a given rise of temperature 
 
44 MINE-VENTILATION. 
 
 in a given current of mixed air and gases, we must as- 
 certain the following. 
 
 First, the constituents, by weight, of the gaseous 
 current and their respective specific heats, from which 
 the power of the current to absorb heat is calculated ; 
 
 Second, the heating power of a pound of coal, or, as 
 we say, the number of thermal units contained therein ; 
 
 Third, the square feet of grate-area required for the 
 combustion of a given weight of coal per hour ; 
 
 Fourth, the required rise in the temperature of the 
 upcast current. 
 
 These data form the basis of the calculation. It is 
 a practical problem in ventilation, and is by no means 
 technical or theoretical. It requires no actual analysis 
 of the gaseous current to determine its exact character 
 for our purposes. What we must base our calculations 
 upon is the worst possible state of the current with 
 respect to gases and moisture, so that the results will 
 be sufficiently large to meet any demand. Fortunately 
 this extreme condition is determinable both with re- 
 spect to gases and moisture. Having determined the 
 several constituent gases and vapors, we multiply the 
 weight of each of these by its respective specific heat, 
 and take the sum of these products ; multiply this sum 
 by the required rise of temperature ; finally, divide this 
 last product by the thermal units contained in a pound 
 of coal : the quotient thus obtained will be the weight 
 of coal to be burned. The grate-area is then propor- 
 tioned to this weight of coal, according to our experi 
 ence and established rules. 
 
 Condition of Upcast Current. — As the calculations 
 and reasonings incident to such an investigation are to 
 some extent complicated, though by no means diffi- 
 
ECONOMIC DISCUSSION OF THE FURNACE. 45 
 
 cult, and as the general reader may not care to devote 
 the time or patience necessary to a clear understanding 
 of the details, we have tabulated in concise form the 
 various factors entering the discussion, showing their 
 final combination to produce the equation referred to 
 above. This equation will be deduced in detail in the 
 latter part of this chapter. The table referred to is 
 Table II of the Appendix. 
 
 Dry Shafts. — We will now consider the practical 
 application of equation (XLIV), which applies to dry 
 shafts, and afterward explain its development in detail, 
 taking up also, in the same connection, the data refer 
 ring to wet shafts. In this equation ({> represents the 
 tension of aqueous vapor at the temperature t^, its 
 value being taken from Table III of the Appendix ; 
 t^ is the temperature of the return current just pre- 
 vious to its entering the influence of the furnace ; its 
 value may be assumed to be as low as 70° F. : if in any 
 instance it has a higher value than this, the furnace is 
 thereby aided in its work ; but we must assume such 
 probable values as to make our calculation safe, and 
 cover the case that will make the greatest demand upon 
 the furnace. The value of 4. the temperature of the 
 lower end of the upcast, will depend upon the quantity 
 of air to be furnished and the depth of the shaft. 
 
 Illustration. — To illustrate : Let us suppose we are 
 about to open a mine, to be ventilated by a furnace, 
 and we wish to provide for a capacity of, say, 500 tons 
 of coal per day. We must figure upon, say, 240 men, 
 including trappers and company men, and, say, 6 mules. 
 If we give each man loo cu. ft. of air per minute, and each 
 mule 500 cu. ft. per minute, we shall require 27,000 cu. ft. 
 per min. travelling ; but, as we must provide against 
 
46 MINE-VENTILATION. 
 
 every exigency,— gob-fires, poor stopings, obstructed 
 air-courses, etc., etc., — it will not be safe to estimate 
 upon less than 30,000 cu. ft. of air per minute in circula- 
 tion. In this problem the values assumed are taken 
 as existing, adopted, or possible limiting values of the 
 various factors of ventilation. We will suppose that 
 the inlet and discharge openings are shafts of the same 
 depth, and the seam of coal maintains a practical level 
 throughout the pit. 
 Assume the following : 
 
 h = 900 ft motive height. 
 
 a = 50 sq. ft sec. area of airway. 
 
 s = 120,000 sq. ft rubbing surf, of airway. 
 
 Q = 30,000 cu. ft at temp. t,. 
 
 t^ = 32° F avg. temp, of downcast. 
 
 ^3 = 60° F.temp. of air where quant, is taken. 
 t^ = 70° F.temp. of air before reaching furn. 
 ^5 = (?)... . temp, of air at bottom of upcast. 
 
 ^, = (?) avg. temp, of upcast. 
 
 B = 30" height of barom. 
 
 J, = 28,800 sq. ft cooling surf, of shaft. 
 
 (Size of air-shaft, 8' X 8'.) 
 
 ^, = 0.5 (relative) coef. of cooling. 
 
 (7 = (?) pounds of coal burned per h. 
 
 G = i/io C grate-area of furn. 
 
 First determination : The first step in our problem 
 is to determine the unit of ventilating pressure that will 
 circulate the given quantity of air (30,000 cu. ft.) per 
 
 ( « ] 
 minute, against the potential ^^7=/ 363.432. Referring 
 
 to (equation XXXI), and substituting therein the above 
 
ECONOMIC DISCUSSION OF THE FURNACE. 47 
 
 numerical values, which we have assumed, and reduc- 
 ing, we have 
 
 / = 18.748 lbs. 
 
 Second determination: The next step is to determine 
 the average temperature t^ of the upcast shaft which 
 will produce the above unit of pressure. By substitut- 
 ing in equation (XXXVII) the above assumed values 
 and the value of/ just found, and solving with respect 
 to ^„ remembering that t^, the temperature of the 
 downcast shaft, is the same as t, the temperature of the 
 outside air, in this case, we find, after reducing, 
 
 t^ — 202" Fahr. 
 
 Third determination : The next step is to determine 
 the necessary temperature of the bottom of the upcast 
 shaft in order to produce the average temperature 
 just determined above. By substituting in equation 
 (XLVI), hereinafter deduced, the numerical values 
 thus far assumed and determined, and reducing, we 
 find 
 
 t, = 327° Fahr. 
 
 Fourth determinatioti : The final step in our problem 
 is to determine the weight of coal that we must burn 
 per hour upon the grate in order to produce the re- 
 quired rise in the temperature of the air-current. We 
 have assumed the temperature t^ of the air just pre- 
 vious to its entering the influence of the furnace to 
 be 70° Fahr., while the required temperature after 
 
48 MINE-VENTILATION. 
 
 passing the furnace we found must be 327". This 
 requires a rise in temperature due to the heat of 
 the furnace of 257". Now, referring to equation 
 (XLIV) hereinafter deduced, and substituting therein 
 the above numerical values, assumed and determined 
 (taking the value of 0, for a temperature of 70° F., 
 from Table III of the Appendix), and reducing, we find 
 
 C = 648 lbs. 
 
 Knowing the weight of coal to be burned per hour 
 in pounds, it is usual to assume one tenth of this weight 
 as the area in square feet of the grate best adapted 
 for the economic combustion of such amount of coal. 
 Hence in this case we find 
 
 G = 65 sq. ft. 
 
 Wet Shafts. — When the shaft is wet there will be 
 an additional amount of coal necessary, beyond the 
 amount required for heating the current, to evaporate 
 the moisture of the shaft and raise the temperature of 
 the vapor thus formed to the temperature of the cur- 
 rent. Continuing the above illustration, which refers 
 only to a dry shaft, let us now assume the same shaft 
 to be making, say, four barrels of water per hour, or 
 about 1000 pounds. Assuming the average tempera- 
 ture of evaporation 4 to be 126° F., and making the 
 necessary substitutions in equation (XLV) and reducing, 
 we find, for the additional amount of coal necessary on 
 account of the wet condition of the shaft, 
 
 C = 80 lbs. (extra). 
 
ECONOMIC DISCUSSION OF THE FURNACE. 49 
 
 Adding this to the amount of coal determined pre- 
 viously in the case of the dry shaft, we obtain for the 
 total amount of coal required to be burned per hour, in 
 this case, 728 pounds, which gives for the grate-area 
 required 
 
 G = 73 sq. ft. 
 
 Suggestions. — The furnace should always be built 
 with airways or coolers above and on each side. The 
 sectional area of such airways should not be less than 
 the sectional area of the entries. 
 
 Relative Quantities. — The quantity of air Q^ will be 
 larger than the original quantity Q, owing to a rise of 
 temperature from /j to/^; the relation between these 
 volumes or quantities being expressed by the propor- 
 tion 
 
 <2: a :: 459 + ^3:459 + ^.; 
 whence we have 
 
 a=:-|$^e <^") 
 
 in which Q and Q^ are the quantities or volumes of 
 air at the temperatures t, and Z^, respectively. From 
 this equation we see that the volume of the current 
 may be increased from 30^ to 50^ by the heat of the 
 furnace. 
 
 Suggestions. — The increase of quantity referred to 
 above is usually compensated for by a corresponding 
 increase in velocity passing the furnace. Hence, if the 
 pit is free from large gas feeders, it will be sufficient to 
 provide a sectional area passing the furnace equal to 
 the area of the entries. Coal for supplying the furnace 
 
50 MINE-VENTILATION. 
 
 should be stored in cuts, in the rib made for the pur- 
 pose, and not, as is often done, deposited in the air- 
 way, in front of the furnace, or, worse still, left in the 
 car, standing in the air-course till needed. The loaded 
 car should be switched into the cut in the rib and the 
 coal used from it as needed, to save handling the coal 
 twice. 
 
 We have thus far illustrated the practical application 
 of the formulas ; the remainder of the chapter will be 
 devoted to explaining their development in detail, for 
 the benefit of the student, and may be passed over, if so 
 desired, by the general reader. 
 
 Thermal Unit. — The unit upon which all calcula- 
 tions are based, in investigations relative to the heat- 
 ing power of coal, is called the "Thermal" unit. It is 
 the amount of heat absorbed in raising one pound of 
 water one degree in temperature. 
 
 French Unit — American Unit. — The French use a 
 unit referred to the Centigrade scale, and this unit con- 
 tains more heat than our American unit, which is re- 
 ferred to the Fahrenheit scale.. The ratio betweea 
 these two units is expressed by the fraction f. 
 
 Calorics of Coals. — Different coals possess different 
 calorific powers, and hence contain a greater or less 
 number of thermal units to the pound. Experience 
 has placed the calorific value of bituminous coal, how- 
 ever, at 8000 thermal units to the pound of coal in the 
 French system, or 14,400 units in the American sys- 
 tem. In common practice bituminous coal is assumed 
 to contain 14,000 American thermal units. These units 
 are often spoken of as the calorics of the coal : they rep- 
 resent the amount of heat that coal is capable of giving 
 out when burned. 
 
ECONOMIC DISCUSSION OF THE FURNACE. 5 1 
 
 Calorific Capacity. — Different solids, such as iron, 
 copper, tin, etc., each absorb a different quantity of heat 
 for a rise of one degree in their temperature. Different 
 liquids, such as water, oil, etc., absorb likewise differ- 
 ent quantities of heat for the same rise of temperature. 
 So also different gases, including air, each absorb dif- 
 ferent quantities of heat for a rise of one degree in 
 their temperature. 
 
 Specific Heat — The amount of heat thus absorbed 
 by one pound of any solid, liquid, or gas, during a rise 
 of one degree of its temperature, as compared with the 
 amount of heat absorbed by one pound of water dur- 
 ing a like rise in temperature, is called the " Specific 
 Heat" of that solid, liquid, or gas. As the specific 
 gravity of any substance is the ratio between the weight 
 of such a substance and the weight of a like volume of 
 water at a standard temperature, so also the specific 
 heatoi any substance — solid, liquid, or gas — is the ratio 
 between the quantity of heat such substance absorbs 
 during a certain rise in its temperature, and the quan- 
 tity of heat absorbed by an equal weight of water 
 during an equal rise in temperature. 
 
 Specific Heat expresses Thermal Units. — Now 
 the amount of heat absorbed by one pound of water dur- 
 ing a rise in its temperature of one degree Fahrenheit 
 is adopted as our thermal unit. Hence it follows that 
 the specific heat of any substance, solid, liquid, or gas, 
 referred to water as unity, will express at the same 
 time the number of thermal units required to raise one 
 pound of that substance one degree Fahrenheit. 
 
 General Expression for Weight of Coal. — If, now, 
 we multiply the specific heat of the substance (which 
 we have just seen is equal to the number of thermal 
 
52 MINE-VENTILATION. 
 
 units required to raise one pound of the substance one 
 degree) by the weight W of the substance and then 
 by its rise in temperature, say t^ — t^, we shall obtain 
 the thermal units absorbed by that substance during 
 such rise in its temperature ; and, dividing this product 
 by the thermal units contained in one pound of coal, we 
 obtain the weight of coal necessary to burn, in order to 
 produce the above rise in temperature. 
 Assume the following : 
 
 C = weight of coal burned per hour, in pounds ; 
 fF= weight of air passing, expressed in terms of Q, 
 
 at a temp. 4 ; 
 IV„ ■= weight of the nitrogen in the current, expressed 
 
 in terms of Q, at a temp, t, ; 
 Wc = weight of the carbonic-acid gas in the upcast 
 
 current, in terms of Q, at a temp, t, ; 
 W^ = weight of the aqueous vapor in the saturated up- 
 cast current, in terms of Q, at a temp, t, ; 
 6 z= symbol denoting specific heat ; 
 (p = symbol denoting tension of aqueous vapor. 
 And we may write, from what has preceded, 
 
 14,000 ^ ' 
 
 Equation (XLII) is a generic equation, and in it W 
 has a general reference to the weight of any substance. 
 
 Gaseous Composition of Upcast Current. — In re- 
 gard to the gaseous composition of the upcast cur- 
 rent, it may be thought by many to be so variable as 
 to admit of no practical solution. This, however, is not 
 the case. As previously stated, we must consider such 
 a condition of the current as will make the greatest de- 
 
ECONOMIC DISCUSSION OF THE FURNACE. 53 
 
 mand upon the furnace. Such a condition will suppose 
 all the oxygen of the air to be converted into carbonic- 
 acid gas (CO,), as the result of the slow and active com- 
 bustions of the pit ; this gas being the heaviest gas that 
 could be formed by the natural chemical reactions. 
 This condition is readily determined and the weights 
 of the resulting gases easily figured. 
 
 Expression for Weight of Air in Terms of Q. — 
 We assume a certain quantity of air Q, passing along 
 the intake of a mine, at a temperature t„ and, refer- 
 ring to equation (I) and multiplying by Q, we have 
 
 W^ 1:3253:5 _ _ (XLIII) 
 
 459 + ^3 
 
 Expression for Weight of Nitrogen. — This last 
 equation gives the weight of air per minute passing 
 along the intake. Now we know from the composition 
 of the atmosphere that y^j- of this weight is the weight 
 of the nitrogen contained in that air, and which under- 
 goes no change in its passage through the mine ; hence 
 we may write for the weight of the nitrogen in the up- 
 cast current, remembering that the pressure borne is 
 the barometric pressure less the tension of the vapor at 
 the temperature of saturation tpi^, 
 
 W„ = ±^^--^Q. ... (I) 
 459 + ^3 
 
 Expression for Weight of Carboni-accid Gas. — 
 
 The oxygen of the air is the active agent in producing 
 and maintaining combustion, either slow or active ; and 
 in its passage through the pit it is converted, in greater 
 
54 MINE-VENTILATION. 
 
 or less proportion, into carbonic-acid gas by its chemi- 
 cal union with carbon, incident to gob-fires, slow com- 
 bustion of coal, burning of lamps, breathing of men 
 and animals, and, lastly, the combustion of the coals of 
 the furnace. It is readily seen that the formation of 
 carbonic-acid gas is limited by the amount of free 
 oxygen in the current and that when this oxygen is 
 exhausted combustion in any form in the pit ceases ; 
 even the furnace fire is smothered and extinguished, 
 which sometimes happens in badly managed pits. Now 
 we know from the composition of the atmosphere that 
 •^^ij^ of the weight of air is the weight of the free 
 oxygen in that air ; and, again, this free oxygen when 
 converted into carbonic-acid gas forms y\ of the weight 
 of that gas. Hence we may write 
 
 t\W^ = ^W. (2) 
 
 Substituting in this last equation for W, its value 
 taken from equation (XLIII), and reducing, we have 
 
 0.4191(^-0.0 g 
 
 Equation (3), above, presupposes that all the free oxygen 
 of the air is exhausted when the bottom of the upcast 
 is reached. This is the worst condition that can exist, 
 and will make the heaviest demand upon the furnace, 
 relative to gases. If combustible gases are present in 
 the return current, it may be assumed that such gases 
 will burn at the furnace, and that the heat of such burn- 
 ing will be sufficient to raise the temperature of the in- 
 combustible gases any probable number of degrees, 
 
ECONOMIC DISCUSSION OF THE FURNACE. 55 
 
 independent of the heat of the furnace ; such number 
 of degrees may then be deducted from the rise in tem- 
 perature expected from the furnace. In some instances, 
 in fiery mines, this combustion of gases (properly 
 aerated) at the furnace forms an essential element in 
 heating the air-current ; but it should not be relied 
 upon to any large extent, as a general rule, in calculat- 
 ing the size of a furnace. 
 
 Expression for Weight of Vapor of Saturation. 
 — We assume the air-current to be saturated with aque- 
 ous vapor from contact with the moisture of the pit, 
 which is always the case upon its return, as is evidenced 
 by the sweating of the roof and the sides of the air- 
 ways, wherever this current is chilled or its temperature 
 falls in the least. The weight of this vapor of satura- 
 tion is easily determined (its specific gravity as referred 
 to air, at the same temperature and pressure, being 
 0.6235 ; see Table V of the Appendix) by the equation 
 
 fF, = o.623si^^<2; ... (4) 
 459+ '3 
 
 or, reducing. 
 
 0M6^ (5) 
 
 459 + ''. 
 
 Summary. — Equations (i), (3), and (5), above, give the 
 greatest weight of these three constituents possible in 
 a current ; and these are the only constituents of a 
 mine-current which affect the size of the furnace. 
 
 Resume. — We have now determined the weight of 
 each of the gases and vapors passing per minute and 
 composing the upcast current. Each of these gases 
 
56 MINE-VENTILATION. 
 
 and vapors possesses a different specific heat, as previ- 
 ously stated, and this specific heat expresses the ther- 
 mal units necessary to raise one pound of each gas or 
 vapor, respectively, one degree. 
 
 Expression for Weight of Coal to Heat Air-cur- 
 rent (Dry Shaft). — Referring now to equation (XLII), 
 which is the general equation for the required weight 
 of coal, and substituting in turn for Wits values as 
 taken from equations (i), (3), and (5), respectively, and for 
 its value for each respective gas or vapor as given 
 in Table IV of the Appendix, and then adding these 
 three resulting equations together, multiplying by 60 
 to reduce to hours, and denoting the total coal required 
 by C,, we have finally, after reducing, 
 
 C, = (0.3394^ + o.o5760.)-|^X ^"j. (XLIV) 
 
 459+ '3 14000 
 
 Equation (XLIV) gives the pounds of bituminous coal 
 burned per hour in raising the temperature of the up- 
 cast current from t^ to i^ in a dry shaft. 
 
 WET SHAFTS. 
 
 Prefatory. — When we have a wet shaft to deal with, 
 we assume that the conditions are precisely the same 
 as in a dry shaft, except that we must burn an extra 
 amount of coal in order to evaporate the moisture of 
 the shaft and to raise the temperature of the vapor thus 
 formed from the temperature of evaporation to the 
 temperature of that portion of the shaft where the va- 
 por was formed. 
 
 Condition of Shaft. — In a wet shaft, evaporation is 
 
ECONOMIC DISCUSSION OF THE FURNACE. 5/ 
 
 taking place all the way up and down the shaft, below 
 the point where the moisture first makes its appearance. 
 The moisture finds its way through the curbing at or 
 somewhat below the flow, and starts to trickle down the 
 sides of the shaft : this water may or may not all find 
 its way to the bottom of the shaft, according to the 
 strength of the flow ; it may all be evaporated before 
 the bottom is reached, as the evaporation is constantly 
 going on. 
 
 Temperature of Evaporation. — The evaporation 
 from the sides of the shaft is taking place at all tem- 
 peratures, from the temperature of the percolating wa- 
 ter, which we assume to be 40° F., to the temperature 
 at which boihng takes place, 212° F. Wet boards steam- 
 ing in the cold air, or wet clothes drying in the wind, 
 are every-day examples of evaporation taking place at 
 low temperatures. 
 
 Absorption of Heat. — Evaporation at any temper- 
 ature is always accompanied by an absorption of heat, 
 which becomes latent in the vapor. This absorption of 
 heat by the vapor cools the upcast current. Accord- 
 ing to the experiments of Regnault upon the absorp- 
 tion of heat by vapors, and which are more conclusive 
 than the experiments of Watt upon the same subject, 
 this absorption of sensible heat varies as the tempera- 
 ture of evaporation varies. The absorption will there- 
 fore be much greater in the lower part of the shaft 
 where the temperature often reaches the boiling-point. 
 The effect of this absorption is to assimilate the tem- 
 peratures of the upper and lower parts of the shaft, 
 bringing them nearer to the average temperature : the 
 vapor acts as a carrier of the heat from the lower to 
 the upper part of the shaft, absorbing it in the lower and 
 
58 MINE-VENTILATION. 
 
 condensing and giving it up again in the upper cooler 
 portions. This heat of vaporization or latent heat is 
 expressed by the empirical formula of Regnault ; as is 
 also the heat absorbed in raising the temperature of 
 the vapor, after it is formed, to the temperature of that 
 part of the shaft. 
 
 Expression for Extra Coal (Wet Shaft). — These 
 formulas of Regnault are empirical, but none the less 
 valuable, as the experiments were carefully made and 
 the experimenter himself reliable. 
 
 Assume the following : 
 
 w = wt. of water (approx) shaft makes per hour, in 
 
 pounds ; 
 /, = average temp, of upcast shaft; 
 4 = average temp, of vaporization ; 
 fj = extra coal burned per hr. on account of wet 
 
 shaft ; 
 
 10S2 \ 
 
 / = constants determined by Regnault's experi- 
 
 „ ^^^ ( ment ; 
 0.305 } 
 
 0.4805 = sp. heat of aq. vapor (see Table IV, App.). 
 Then we have Regnault's expressions for 
 
 Heat of vaporization .... zw(io82 -f- 0.305/^) 
 Heat absorbed by vapor o.48o5(/, — 4) 
 
 These two expressions represent the total heat ren- 
 dered latent by the formation of the vapor and the 
 raising of the temperature of that vapor to the tem- 
 perature of the shaft. Adding these together and 
 dividing by the thermal units in a pound of coal, we 
 
ECONOMIC DISCUSSION OF THE FURNACE. 59 
 
 find an expression for the extra coal required per hour, 
 on account of the wet condition of the shaft : 
 
 C = M1082 + 0-3054) + o.48o5(^. - fy) (XLV) 
 ' 14000 • • \ ) 
 
 The total coal required in wet shafts is the sum of 
 equations (XLIV) and (XLV). 
 
 Cooling Effect of Shafts. — Referring again to the 
 " third determination " in the practical problem in the 
 fore part of this chapter, we observe that it is there re- 
 quired to ascertain the temperature of the bottom of 
 the upcast current when we know the average tem- 
 perature of the shaft ; or, in other words, when we 
 know what the average temperature of our upcast shaft 
 must be, in order to produce a certain ventilating cur- 
 rent, we are hereby enabled to establish therefrom the 
 necessary temperature at the furnace. This determina- 
 tion depends upon a certain empirical coefficient of 
 cooling k^, based upon the principle that one square 
 foot of the inner surface of the shaft possesses a certain 
 cooling power or conductivity of the heat of the cur- 
 rent, by which a definite number of units of heat are 
 carried off per minute from the volume of air passing. 
 
 Expression for Coefficient of Cooling. — It is ob- 
 vious that the loss of heat, or fall in the temperature of 
 the upcast current, in different shafts is proportionate 
 to the exposed cooling surfaces of the respective shafts, 
 and inversely proportionate to the weight of air pass- 
 ing; hence assume the following: 
 
 = perimeter of the shaft ; 
 d = depth of the shaft ; 
 
6o MINE-VENTILATION. 
 
 Q = quant, of air passing per min., at any temp, (/). 
 W = weight of air passing per minute. 
 L = loss of heat or fall in temp, of the current in pass- 
 ing from the bottom to the top of the shaft ; 
 k^ = relative coefificient of cooling. 
 
 And from what has preceded we have the following 
 compound proportion, remembering that the cooling 
 surface of the shaft is indicated by (do), and represent- 
 ing the like quantities in another shaft by the same 
 symbols primed : 
 
 L-L^-WW, ' (') 
 
 But, referring to equation (XLIII), we may write the 
 proportion 
 
 '"459 + ^ ■459+^." * ^^ 
 Combining these two proportions, we have 
 
 From this last proportion, (3), we may write the equa- 
 tion 
 
 e,5,4 QBL 
 
 ^.''■(459 + o ^^(459 + ^y 
 
 (4) 
 
 Now, as we are in search of an empirical formula, 
 the first member of equation (4) (containing all the 
 quantities referring to one shaft) is determined by ex- 
 periment, and its value denoted by ^,. Experiments 
 should be performed upon several shafts, and the re- 
 
ECONOMIC DISCUSSION OF THE FURNACE. 6l 
 
 suits averaged, to obtain a reliable value for this co- 
 efficient of cooling. Substituting k^ for the first mem- 
 ber of equation (4), above, we have 
 
 ^•=^^(459 + ^^^ 
 
 Again, solving with respect to L, and replacing t by t^, 
 our assumed temperature relative to the quantity Q, 
 we have 
 
 _ Kdo{A^9 + Q if-s, 
 
 ^~ QB ^^> 
 
 But it is obvious at once that 
 
 z = 2(^,-0; (;) 
 
 hence, combining these last two equations, (6) and (7), 
 and solving with respect to t^, we have, finally, 
 
 : = '. + '''°^tQ^'^ . ■ ■ (XLV.) 
 
 This coefficient {k^ is relative, having, as we have 
 said, an empirical value which represents in degrees the 
 amount of cooling of one cubic foot of the upcast cur- 
 rent due to one square foot of the inner or cooling sur- 
 face of the shaft. No reliable determination of its 
 value has as yet been made. We assumed previously, 
 in our practical problem in the fore part of the chapter, 
 that this coefficient had a value of 0.5 degree, which 
 is more or less approximate. 
 
62 MINE-VENTILATION. 
 
 CHAPTER VIII. 
 
 ECONOMIC DISCUSSION OF THE FAN. 
 
 Prefatory. — As remarked in the previous chapter in 
 regard to the furnace, this discussion will treat of the 
 construction of the fan only as such construction 
 affects its efficiency as a ventilating-machine. We will 
 take up in their order the essential or vital points re- 
 lating to fans and fan construction, a thorough under- 
 standing of which is necessary before perfect designing 
 and constructing can be attained. 
 
 Efficiency. — We will begin with efficiency. Much 
 depends upon the efficiency of a fan. Some fans work 
 better than others, on account of the details of their 
 construction being more perfect : they have been better 
 made ; better mechanics have worked upon them. 
 Some types of fans work better than others on account 
 of better designing: they have been constructed upon 
 a better principle. ^ The term " Efficiency," as applied 
 to a fan, is a termin dicating the ratio existing or 
 inherent in that faiTbetween the theoretical and the 
 practical work such fan is capable of performing. Thus 
 if we say a certain fan has an efficiency of 90^, we 
 mean that on account of internal friction or defective 
 construction, or some other cause, known or unknown, 
 that particular fan will only perform 90^ of its theoreti-' 
 cal work ; we do not mean that the fan will only supply 
 90^ of the theoretical quantity of air, nor do we mean 
 that it will only yield 90^ of the theoretical depression 
 
ECONOMIC DISCUSSION OF THE FAN. 63 
 
 or water-gauge, but its practical or effective work, de- 
 noted by U, will be 90^ of its theoretical work, U^. 
 
 Coefficient of Efficiency. — Denoting this coefficient 
 of efficiency by K, as in Chapter VI, we write 
 
 u=K(u:), ....... (I) 
 
 or 
 
 ^=1 (^) 
 
 How Varies. — We see then, from what precedes, that 
 the simple passage of a current of air through a fan re- 
 quires a certain amount of work, owing to the resistance 
 offered by the fan to the flowing air. This work is prac- 
 tically lost or absorbed in the fan ; the balance of the 
 work, which is applied to the movement of the air-cur- 
 rent through the mine, is called the Effective work. 
 It is obvious, then, that the efficiency of a fan depends 
 upon the amount of work thus absorbed by the fan 
 and lost. Let us now investigate a step further, and 
 ascertain upon what the coefficient of efficiency de- 
 pends, and whether or not it is a constant for the same 
 fan running at all speeds. We observe at once — 
 
 First, the work of the fan lost within itself is due 
 wholly to the resistance encountered by the air in its 
 passage through the fan, whether such resistance is 
 owing to defective construction or other cause whatso- 
 ever. 
 
 Second, that this resistance varies as the inner rub- 
 bing-surface of the fan and the square of the accelera- 
 tive * velocity, and material obstructions common to 
 
 * The accelerative velocity is taken as creative of the internal resist- 
 ance, for the reason that the accelerative velocity is the measure of 
 
64 MINE-VENTILATION. 
 
 fan-construction ; but for any one fan in question the 
 rubbing-surface of the fan and other material obstruc- 
 tions are constant, and the internal resistance of that 
 fan will vary as the square of the accelerative velocity 
 only. 
 
 Internal Resistance of a Fan. — We may therefore 
 represent the internal resistance of a fan by the ex- 
 pression k^f^, k^ being a constant factor expressive 
 of the resistance of that particular fan to an air-current 
 having a unit of accelerative velocity. 
 
 Work of the Resistance. — The work of this resist- 
 ance is clearly the work lost in the fan, its expression 
 being k^f^, in which k^ is a new constant. Assume 
 u = the effective work of the fan for a unit of time ; 
 «j= the expended work of the fan for a unit of time ; 
 u^=- the work lost or absorbed in the fan in a unit of 
 time. 
 
 Now, referring to equation (6-XXXVIII) we see that 
 f varies as n^ ; hence from what precedes we may 
 write, for the work lost or absorbed in the fan, 
 
 «» = k,n^ (3) 
 
 The coefficients k^,k,, ,^, are merely general coefficients. 
 
 N.B. — We must note here, that the work lost in the 
 fan is dependent alone upon the acceleration f due 
 to the mechanical velocity of the fan, and is in no way 
 affected by changes in temperature or barometric pres- 
 sure, as is the effective work of the fan. 
 
 General Expression for the Work of the Fan. — 
 
 the force created within the motor where the resistance is developed ; 
 and it is this active, energizing force within the motor that is produc- 
 tive of the resistance to the passage of the current through that motor. 
 
ECONOMIC DISCUSSION OF THE FAN. 65 
 
 Referring now to equation (lO-XXXVIII), which ex- 
 presses the total expended work for one second of time, 
 we see that for any one fan the total expended or theo- 
 retical work of that fan is dependent upon three vari- 
 ables, viz., speed of fan, temperature, and barometer. 
 We may therefore write for that equation the general 
 equation 
 
 ^' = '("'^5^^) ^^^ 
 
 in which t is a constant for any one fan. But as the 
 effective work is always equal to the total expended 
 work, minus the work lost, we have 
 
 u — u,—u^ (5) 
 
 Substituting for «, and u^ , in equation (5), above, their 
 respective values as taken from equations (3) and (4), 
 above, we have for the general equation for the effective 
 work 
 
 B 
 
 : cn 
 
 459 + ^ 
 
 -ky (6) 
 
 Value of K. — But the value of K, (see equation (2), 
 above) is found by dividing the effective work by the 
 total expended work ; hence, dividing equation (6) by 
 equation (4), above, member, by member and reducing, 
 substituting IC for its value, we have, finally, 
 
 K=i-cy^^^, . . (XLVII) 
 
 13 
 
 in which c, is a new constant, which we term the fan 
 constant, as explained later. Thus we see that the 
 
66 MINE-VENTILATION. 
 
 coefficient of efficiency K is not a constant, but varies 
 with the speed and with the temperature and baromet- 
 ric pressure, but not in the same proportion. 
 
 Relative Efficiency at Different Speeds. — Let us 
 investigate further, and ascertain what effect the speed 
 of the fan will have with reference to a maximum and 
 a minimum yield. It is interesting to note in this con- 
 nection, that if a fan has an efficiency of 95^ at a speed 
 of 50 revolutions per minute the efficiency of the same 
 fan, at a speed of 100 revolutions per minute will only 
 be 80^, the temperature and barometric pressure re- 
 maining the same. If the efficiency is 90^ at a speed 
 of 50 revolutions per minute, the same fan working 
 under the same conditions of temperature and baromet- 
 ric pressure will only present an efficiency of 60% at a 
 speed of 100 revolutions per minute. We note also, 
 from an inspection of equation (XLVII), that for the 
 same speed the efficiency of a fan will vary as the ex- 
 pression 4594-^ varies, and inversely as the baromet- 
 ric pressure, but not in the same proportion. 
 
 Limit of Speed. — We see, from a further inspection 
 of equation (XLVII), that the value of K will become 
 zero when 
 
 3 459 + ^ 
 \-c^n^ "'^^^ =0, 
 
 or when 
 
 V 
 
 n=- ^ 
 
 f=(4S9 + 
 
 (XLVIII) 
 
 This last equation gives the limit of speed for the fan 
 in question, or the speed at which that particular fan 
 will cease to deliver any air. We must remember, 
 
ECONOMIC DISCUSSION OF THE FAN. (i^ 
 
 however, that the quantity c, has a particular value 
 for every fan, according as the fan is more or less effi- 
 cient in its work. This will be explained later. 
 
 Maximum Effective Speed. — Let us now deter- 
 mine the maximum effective speed, or the speed at 
 which any particular fan will throw its maximum of 
 air at a certain temperature and barometric pressure. 
 Referring to equation (XXXIX), and substituting for 
 K its value as taken from equation (XLVII), we ob- 
 serve that Q will have a maximum value for any par- 
 ticular fan forcing air into any particular mine, when 
 the expression 
 
 «'(i-.yll9±l) .... (I) 
 
 is a maximum ; or, as this expression may be written, 
 
 [n^-c^r,^^) (2) 
 
 In expression (2), n represents any possible velocity or 
 speed of the fan. Now, denoting the next consecutive 
 velocity or speed by n-\-\, we have for the corre- 
 sponding expression, relative to the speed «+ i, 
 
 («+iy_4«+i)«45Hi^_ . . (3) 
 
 Let us analyze these three expressions carefully. From 
 expression (i), we see that the quantity yielded by any 
 fan depends upon two variable factors, relative to the 
 speed of the fan : the first a direct factor, increasing as 
 the speed increases ; the second an inverse factor, de- 
 creasing as the speed increases (not, however, in the 
 
68 
 
 MINE-VENTILATION. 
 
 same proportion). The first of these two factors repre- 
 sents simply the speed of the fan ; while the second, as 
 we have seen from equation (XLVII), represents the 
 efficiency, which continues to decrease as the speed in- 
 creases. 
 
 Origin 
 
 Fig. IV. 
 
 Fig. IV represents graphically the relation existing 
 between the power, speed, and efficiency of a fan. 
 
 Expressions (2)and (3) are expressions relative to quan- 
 tity for any two consecutive states of speed of the fan. 
 Examining expression (2), we see that its value increases 
 as n increases, but not in the same proportion, the 
 rate of increase being less and less as the velocity is 
 higher. For this reason, as we increase the speed by 
 one, the resulting increase of quantity for each consec- 
 utive state will be less and less, till finally there ceases 
 to be any increase of quantity for an increase of speed. 
 Previous to this juncture the value of expression (3) has 
 been greater than the value of expression (2), but it 
 now becomes equal to it ; and if the speed be in- 
 creased beyond this point the value of expression (3) 
 will become less than that of expression (2) : that is to 
 
ECONOMIC DISCUSSION OF THE FAN. 69 
 
 say, the quantity of air will diminish from this point 
 until it fails altogether, as shown by equation (XLVIII). 
 Hence it is obvious that to determine that value for 
 n which will give the maximum quantity of air, we 
 must equate expressions (2) and (3), which will give, 
 after reducing, 
 
 This is the simplest form of this equation obtainable : 
 it means that the difference between the fourth powers 
 of two consecutive speeds of the fan, at the point of 
 its maximum yield, divided by the difference between 
 the sixth powers of the same speeds, will be equal to 
 the expression given in the second member of the 
 equation. These are important formulas, and reveal the 
 true action of the fan ; they should be understood by 
 all who are interested in the question of scientific fan- 
 construction. They show that it is of no avail to speed 
 a fan beyond its maximum effective speed ; and it is, 
 moreover, a profligate waste of power, the power being 
 proportionate to the fourth power of the speed (see 
 eq. (lO-XXXVIII) ; and for this expenditure of 
 power we obtain less air than at a lower speed. 
 
 To determine Value of K, practically — This de- 
 termination should be made in the shop for each type 
 of fan made. The best method is to set the fan up, as 
 will be described later in this chapter under " Testing 
 a Fan " ; and having carefully noted the quantity and 
 pressure at a speed of, say, 50 revolutions per minute, 
 increase this speed to 75 revolutions per minute, and 
 note the quantity and pressure again ; repeat the same 
 
70 MINE-VENTII.ATION. 
 
 at a speed of loo revolutions per minute. Now by 
 referring to equation (XII) we see that the product of 
 these two factors will give the work — in this case the 
 effective work (the observations being taken at the 
 point of application) ; hence, substituting these several 
 products successively for U, in equation (XXXVIII) 
 and solving with respect to K, we obtain the value of 
 K for each of these speeds, respectively. The tem- 
 perature and barometric pressure must be noted in 
 these observations, and substituted in the equation at 
 the same time. This will give the value of K for 
 certain speeds of the fan and under certain atmospheric 
 conditions. 
 
 Value of the Fan Constant. — Referring to equation 
 (XLVII), and substituting therein successively the sev- 
 eral values found for K and the corresponding values of 
 n, together with the noted temperature and baromet- 
 ric pressure, and solving with respect to f„ we ob- 
 tain the value of this constant, which we call the " Fan 
 Constant, " because it has a constant value, peculiar to 
 any one fan in question. Knowing the value of this 
 constant, the efficiency of the fan at any speed of the 
 fan may be determined by substitution in equation 
 (XLVII). 
 
 Effect of Humidity. — There is one other factor which 
 affects not only the efficiency of a fan, but also its ini- 
 tial work, as expressed by equation (XXXVIII). This 
 factor is the humidity of the atmosphere, or, as we 
 say, its " hygrometric state." Its effect is small, and 
 for all practical purposes may be ignored ; nevertheless, 
 as a matter of information, it is well to refer to it. The 
 quantity of air a fan will yield, as expressed by equa- 
 
ECONOMIC DISCUSSION OF THE FAN. Jl 
 
 tion (XXXIX) varies with the cube root of the expres- 
 sion 
 
 (i^) <■) 
 
 H59 + t 
 
 The coefficient of efficiency K depends for its value 
 upon the reciprocal of the same expression. This ex- 
 pression is taken from equation (I), and relates to the 
 weight of dry air. Now if we write equation (I) so as 
 to express exactly the weight of a cubic foot of air sat- 
 urated with aqueous vapor, we should have 
 
 ^ _ 1.3253 (-g- 0-37650) n\ 
 
 459 + ^ ' • • • V ; 
 
 in which is the tension of the vapor of saturation' 
 at the temperature ^ (see Table III of the Appendix), 
 the specific gravity of aqueous vapor, referred to air of 
 the same temperature, being 0.6235 (see Table V of the 
 Appendix). Since this effect is so small, we do not bur- 
 den our equations with its expression ; but, for the 
 matter of information, we have prepared Tables VIII 
 and IX of the Appendix, showing the effect atmos- 
 pheric changes have upon the quantity of air delivered 
 by a fan, the speed being maintained constant (Table 
 VIII), and the effect of the same upon the speed when 
 the power applied remains constant (Table IX). We 
 see from Table VIII that the effect of complete satu- 
 ration at a temperature of 60° F. amounts to about 
 0.25^ of the yield, while at 90° F. it amounts to about 
 0.55^. That is to say, if a fan is throwing 100,000 
 cubic feet of dry ait at 90° F., it would throw at the 
 same speed and temperature 99,450 cubic feet of air 
 
72 MINE-VENTILATION. 
 
 fully saturated with aqueous vapor, against the same 
 mine-potential. 
 
 Resume. — We have thus far discussed the efificienc}'' 
 of a fan, showing upon what it depends, how it varies, 
 and how it is affected by atmospheric conditions ; refer- 
 ring incidentally to the effect of the same upon the in- 
 itial work of the fan. Let us now take a step further 
 and consider some factors or elements in the construc- 
 tion of the fan, as bearing upon its yield. 
 
 Outer Radius or Diameter. — The distinctive di- 
 mension of a fan is its diameter. We speak of a fan 
 in terms of its diameter — as, for example, a lo-foot fan 
 or a 20-foot fan ; and this is proper, as the radius or 
 diameter more than any other dimension symbolizes 
 the power and determines the comparative importance 
 of the fan as a ventilating motor. As different styles of 
 fans are adapted to different kinds of work, so the vari- 
 ous dimensions of a fan have each their respective 
 functions and adaptability to certain portions of the 
 work. We may have a small volume of air to pass 
 through a long or contracted airway ; or we may have 
 a large volume of air to circulate through short, ex- 
 panded airways : in each of these cases the necessary 
 power may be the same, but the kind of work and the 
 style of motor best adapted to perform the work in 
 each case are very different. Referring to equation 
 (XXVIII), we may call it the elemental equation of power; 
 because it represents the two elementary factors of 
 ventilation which absorb the power. These two ele- 
 mentary factors of ventilation, quantity of air passing, 
 and mine-potential against which it is passing, have their 
 representative adjuncts in the several dimensions of the 
 fan. The. diameter of the fan is the counterpart or repre^ 
 
ECONOMIC DISCUSSION OF THE FAN. 73 
 
 sentative of the mine-potential; and the fan whose diame- 
 ter is thus proportioned to this factor of its work is best 
 adapted to do its work, and will yield the best results. 
 This will be explained fully under General Proportion- 
 ment of the Fan. 
 
 Inner Radius or Size of Eye. — This dimension of 
 the fan is most important, as determining the area of 
 the eye or the size of the inlet of the fan ; and as such it 
 is the representative of the quantity of air passing. It 
 should, beyond a doubt, be proportioned to this factor. 
 The size of this opening should be such as to accom- 
 modate the quantity of air the fan will be required to 
 throw, at a velocity not greater than from 16 to 20 feet 
 per second. In figuring upon this area it must be re- 
 membered that the unobstructed area of the two eyes 
 is referred to as the inlet area. 
 
 Number of Blades. — The number of fan-blades is 
 somewhat dependent upon the size of the fan. There 
 should be as few blades as is consistent with keeping 
 the contained air pressed forward. For all ordinary 
 sizes eight blades make a good number, but when the 
 distance between the blade tips exceeds ten or twelve 
 feet we should begin to increase the number of the 
 blades. In order to reap the best results, the air at 
 the circumference should not be left unsupported. A 
 good plan is to introduce small or secondary blades at 
 the circumference of the fan, running inward only half 
 as far as the other blades ; the air is thus supported at 
 the circumference and the friction at the inlet is not 
 materially augmented. 
 
 Width of Blade. — This is a most important dimen- 
 sion of the fan, although one which has been ignored 
 by writers. Why this is so is hard to understand. 
 
74 MINE-VENTILATION. 
 
 It is possible that this omission occurs from the failure 
 to distinguish between static and dynamic pressure, as 
 in static pressure the width of the fan-blade divides 
 out (see Chapter II.). This dimension of the fan is the 
 representative of the quantity, as the diameter is the 
 representative of the mine-potential : it should be pro- 
 portioned to the quantity of air the fan is expected to 
 pass per minute. As we have previously stated in the 
 introductory chapter, a high mine-potential always indi- 
 cates a large quantity of air moving at a comparatively 
 small expenditure of power; and this condition always 
 obtains when several splits are made in the air-current. 
 The typical fan, under such conditions, should have 
 short, broad blades. In fact, however, it is possible, 
 by the adoption of a judicious system of ventilation, 
 and by splitting the air from time to time as the mine 
 becomes more extended, to maintain the elemental 
 equation of power referred to above (eq. XXVIII) at 
 about a constant value. This should be done, and 
 a fan employed having a less diameter and broader 
 blades. This type of construction will be seen to pos- 
 sess a mechanical advantage also, by giving better op- 
 portunity for sway-bracing, and will make a stronger 
 fan. Such a fan, under the conditions stated, will be 
 adapted to its work, 
 
 Curvature of Blades. — Another point with reference 
 to the blades of the fan is the. form of blade that will 
 yield the greatest efficiency, or transmit the greatest 
 percent of the power applied. This is a question which 
 has from time to time given rise to considerable differ- 
 ence of opinion, some maintaining that the blades when 
 curved backward from the direction of the motion was 
 best adapted to propel the air. We believe there is 
 
ECONOMIC DISCUSSION OF THE FAN. 
 
 75 
 
 but one solution to the question : we give our ver- 
 dict in favor of the straight-paddle blade, except as the 
 inner edge of each blade should be curved forward in 
 the direction of the motion ; the idea of the forward 
 curvature of the inner edge of each blade being to con- 
 vert the radial motion of the incoming air into the 
 enforced rotary motion of the fan-blades, with as lit- 
 tle shock as possible. There is always absorp- 
 tion of power in lost motion or shock ; and any de- 
 vice by which this is avoided, by deflecting the 
 course of the current into its proper channels without 
 shock, is an assistance : it will show in the increased 
 
 Fig. V. 
 
 Fig. VI. 
 
 efificiency of the fan. A conical arrangement about the 
 shaft, whereby the incoming current would be deflected 
 radially, as shown in Fig. V, would be beneficial in 
 cases where the fan is crowded, or where the intake is 
 at a high velocity ; in general, however, this arrange- 
 ment is unnecessary, as the intake-chamber of the fan 
 should be large, and the velocity at this point thereby 
 reduced to a minimum. Before leaving the discussion 
 of blades, let us look for a moment at the " Murphy" 
 fan, represented in Fig. VI. The characteristic of this 
 
^^ MINE-VENTILATION. 
 
 fan is the curved blade : the fan gives fair results, and 
 has many advocates; but we believe that this type of 
 construction will consume a greater amount of power, 
 in proportion to the yield, than the straight-paddle fan. 
 The main point of difference between these two types, 
 with reference to their working, is the speed : working 
 under the same conditions and delivering the same 
 amount of air, the speed of the Murphy fan is much 
 the greater of the two. The Murphy fan is in some 
 sense a screw-motor, and as such differs essentially 
 from the straight-paddle fan in its working principle. 
 Certain it is that some of the air is carried around by 
 the revolving blades and expelled by virtue of the cen- 
 trifugal force thus developed : the amount of air thus 
 contributing to a centrifugal pressure will vary accord- 
 ing to the greater or less inclination of the blades ; the 
 blades could be so wreathed into a spiral as to convert 
 the fan wholly into a screw-machine, when its action 
 would cease to be anything other than mechanical ; and 
 its necessary speed would have to be enormous in order 
 to compete as an air-motor. The reasoning that would 
 lead some to adopt a curved blade is to establish as lit- 
 tle friction as possible between the radial passage of 
 the air through the fan and the rotary motion of the 
 blades ; but we must remember that whatever tends to 
 decrease the rotary motion of the air in the fan will 
 decrease in the same proportion the efficiency or 
 transmitting power of the fan, because the less the air 
 is revolved the less will be the centrifugal force devel- 
 oped. The equations developed in Chapter VI giving 
 the work, yield, and horse-power of straight paddle fans, 
 do not apply to fans having curved or inclined blades. 
 (See Addenda.) 
 
ECONOMIC DISCUSSION OF THE FAN. TJ 
 
 Expansion of Casing. — The peripheral expansion 
 of the fan casing is another important point in the eco- 
 nomic construction of the fan. The reason for such 
 expansion is simple and obvious. Each section of the 
 fan is supplying its quota of air to the conduit or shaft 
 leading to the mine ; and the effective power of the 
 fan depends upon the continual and free passage of the 
 air through these several compartments or sections and 
 thence to the mine, the moving force behind the cur- 
 rent, being the combined pressure from all of these com- 
 partments. Now if the connection of these compart- 
 ments with the airways of the mine is cut off during a 
 portion of their revolution by a tight casing, their ac- 
 tion ceases for such time, and the power of the fan is 
 diminished. On the other hand, if the peripheral cas- 
 ing be regularly expanded from a point near the cut- 
 off, around the entire circumference of the fan, to the 
 cut-off again, there will be provided thereby a gradual 
 increase of the sectional area of the peripheral space, 
 equal to the augmentation of the flow from each com- 
 partment; consequently there will be established a 
 peripheral flow of air about the fan and past the cut-off, 
 having a constant velocity. That is to say, the veloc- 
 ity of this peripheral flow will be the same at any point 
 of the circumference of the fan, and may be determined 
 by dividing the area of the cut-off by the entire flow. 
 The amount of this expansion e (see Fig. VII), mul- 
 tiplied by the width of the fan-blades b, will give the 
 area of expansion. This area of expansion should be 
 large enough to accommodate the flow of the air-cur- 
 rent at a velocity proportionate to the peripheral veloc- 
 ity of the fan. We say that the velocity of the current 
 in the peripheral space should be proportionate to the 
 
78 
 
 MINE-VENTILATION. 
 
 velocity of the blade tips, for the reason that better 
 results will be obtained if the air travels with the fan 
 through this space. If necessary, however, the air will 
 travel ahead of the fan. For like reasons as the above, 
 this expansion of the casing should not be too large, 
 and the air left to travel behind the fan. It is better 
 that the expansion be less and the air urged to travel 
 ahead of the fan rather than behind it, as in the lat- 
 
 FiG. VII. 
 
 ter case there is an opportunity given to baffle. Now, 
 having explained the office of the peripheral space 
 formed by the expansion of the fan casing, let us ascer- 
 tain carefully the relation and proportion this expansion 
 must sustain to the other dimensions of the fan. It 
 will be seen more clearly later that this expansion e is 
 the representative and the counterpart of the mine- 
 potential in the elemental equation (XXVIII), and 
 
ECONOMIC DISCUSSION OF THE FAN. 79 
 
 must be proportioned to this factor of the work. This 
 will be seen readily from a practical problem. For ex- 
 ample, from Table X of the Appendix we see that a 
 twelve-foot fan, in order to circulate 25,000 cubic feet 
 of air per minute against a mine-potential of 685.064, 
 must have a speed of 33.7 revolutions per minute; 
 while to circulate the same current against a potential 
 of 342.532, the same fan, working under the same at- 
 mospheric conditions, must have a speed of 58.0 revo- 
 lutions per minute. In each of these cases the same 
 amount of air is passing through the area of expansion 
 at the cut-off. Now, to go back a little, we see that 
 the velocity of the peripheral flow should be maintained 
 as nearly as possible at the velocity of the blade tips, 
 which has changed very materially in the two cases ; 
 hence, the same amount of air passing in each case, if 
 we would vary its velocity as the velocity of the blade 
 tips vary, we must vary the area ot expansion through 
 which the current flows ; but we have ahead)- propor- 
 tioned one factor of this area b to the quantity of air 
 passing, and the other factor e must therefore be pro- 
 portioned to the potential. 
 
 General Proportionment of the Fan. — The three 
 distinctive dimensions of the fan are then, as we have 
 seen, the Outer Radius, Breadth of Blade, and Expan- 
 sion of Casing. In referring to these elements of the 
 motor we have stated in a general way the elements of 
 the work to which each corresponds and with reference 
 to which it must be proportioned. It must not be sup- 
 posed, however, that this proportionment of the ele- 
 ments of the motor to the elements of the work is a 
 simple proportioning of element to element. It will be 
 readily seen that these elements so relate to each other 
 
80 MINE-VENTILATION. 
 
 that a change of one necessitates a change of all. For 
 example, a change in the radius of a fan not only results 
 in a change of power, but also in a change of quantity ; 
 and the change in quantity necessitates a change in the 
 breadth of blade, which again affects the power. The 
 expansion of the casing is likewise affected by the 
 change of the radius. We propose now, for the benefit 
 of the mechanic interested in the construction of fans, 
 as well as for the mine operator who must decide upon 
 the size of fan that he will need for the ventilation of 
 any proposed workings, to formulate these elements 
 of the motor, expressing the value of each in terms of 
 the work. 
 
 Let us have then and retain in our minds a clear idea 
 of power as applied to the accomplishment of a certain 
 work. The power thus applied finds expression in 
 \.t.r^cvi%, factors or elements of the work. We have re- 
 ferred to equation (XXVIII) as the elemental equation 
 of power. 
 
 U=^,. . . . (XXVIII) 
 
 The second member of this equation designates the 
 elements of the work — a quantity of air Q to be circu- 
 lated against a mine-potential X. This is the work to 
 be accomplished, and these are the elements of such 
 work. As we have seen, these elements of the work 
 have their counterparts or representatives in the motor; 
 and as one or the other of these elements is increased 
 or diminished, its representative part in the motor must 
 be varied, that the motor may be adapted to its work. 
 We must note here that while this proportionment of 
 parts will adapt a certain motor to a certain work, 
 there is yet another factor of the working oi the motor, 
 
ECONOMIC DISCUSSION OF THE FAN. 8l 
 
 viz., its speed, that will enable it to perform a different 
 work, to which it will be alike adapted. 
 
 In deciding upon what size and type of fan will be 
 needed for the ventilation of any proposed workings, 
 we must first know the elements of the work ; or, in 
 other words, we must decide upon the quantity of air 
 we wish to put in circulation, and against what poten- 
 tial (size and length of airways, giving the resisting 
 power of the proposed workings). This will determine, 
 according to the above elemental equation, the power 
 we must employ in terms of the work. Let us now 
 find an elemental equation showing the relation be- 
 tween the elements of the work and the elements of 
 the motor. Referring to equation (XXXIX) and assum- 
 ing a value for the inner radius R, equal to ^R, which 
 gives an approximate value for R^ equal to ^R, and the 
 value of the expression R^ — 7?/ becomes approximately 
 ^R' : these factors all then reducing to the expression 
 cR*, in which ^ is a constant; and substituting JCior its 
 value and assuming constant values for B, say 30 inches, 
 and for t, say, 60° F., we may write 
 
 ^, = c{KdR'n') (LI) 
 
 This is the general equation for the yield of a straight 
 paddle-fan under fixed atmospheric conditions, as as- 
 sumed. By referring now to Table VII of the Appen- 
 dix, which gives the horse-powers developed by certain 
 fans at certain speeds and under the same atmospheric 
 conditions as those which we have assumed, we may 
 ascertain the value of the coefficient c, which gives 
 
 %-^ = o.ooooii944{Kl>R'n'). . . (LII) 
 
82 MINE-VENTILATION. 
 
 By combining equations (XXVIII), (XXXV), and (LII), 
 and solving with respect to H.P., we have 
 
 H.P. = o.oooooooooz62{KbR'n'). (LIII) 
 
 Equations (LII) and (LIII) are general equations, giv- 
 ing the work and the horse-power of a fan in terms of 
 itself, and may be used in estimating upon the size of 
 fan needed for the development of any assumed horse- 
 power, or to circulate any desired quantity of air per 
 minute against any assumed mine-potential. Equation 
 (LII) is the desired elemental equation expressing the 
 relation that should exist between the elements of the 
 work and the elements of the motor, including the 
 speed of the same. But we have said that the fan 
 should be so proportioned that the velocity of the pe- 
 ripheral flow shall not much exceed that of the blade 
 tips. This imposes a new condition upon the propor- 
 tioning of the parts, which is expressed by the equation 
 
 Q = 2-n:R)i X be, (i) 
 
 in which e is the expansion of the casing at the cut-off. 
 (See Fig. VII.) We assume a value for e equal to ^R, 
 as we have shown that R and e are both functions of 
 the same element of the work; and equation (i) above 
 then becomes 
 
 Q^i.i^i6{bR'n) (LIV) 
 
 Combining equations (LII) and (LIV) so as to elimi- 
 nate b, and solving with respect to R, we have, after re- 
 ducing, 
 
 R= 512.8S4 „ ^, . (LV) 
 
ECONOMIC DISCUSSION OF THE FAN. 83 
 
 From the same equations we have in like manner, for 
 the value of b, 
 
 ^ = 0.00000121 — Y) — - • • (LVI) 
 
 We have also, as previously assumed, for the expansion 
 of the casing, 
 
 e = o.t,R (LVII) 
 
 Now as equations (LV) and (LVI) express the values 
 of R and b in terms of a work performed at a speed n, 
 the values of these elements are indeterminate until 
 we have decided upon what grade of fan to employ; or, 
 in other words, at what speed of the fan the work is to 
 be accomplished. There are different grades of fans 
 capable of performing the same work at different 
 speeds. We may therefore assume such a value for n 
 as will make b equal to f of R. This will make b and 
 R sustain such a relation to each other as will be best 
 adapted to the passage of the current through the fan. 
 Under this supposition, combining equations (LV) and 
 (LVI) and solving with respect to n, eliminating R, we 
 have 
 
 « = 268.67 /j/^^,. . . (LVIII) 
 
 In using equation (LVIII) we must first approximate 
 a value for K, which will then give an approximate 
 value for n. From this value of n, however, the true 
 value of K is found and substituted' in the equation, 
 which will then give the true value of n. We see from 
 equation (LVIII) that to maintain the best proportion 
 between the outer radius of a fan and the breadth of 
 
84 MINE-VENTILATION. 
 
 the fan blades necessitates a certain speed of the fan 
 for the accomplishment of a certain work. From equa- 
 tions (LV) and (LVI) we see that as we increase this 
 speed for any one work we obtain a smaller radius and a 
 greater breadth of blade ; and vice versa. It is there- 
 fore possible to obtain a narrow fan of large diameter 
 or a broad fan of small diameter which will be alike 
 adapted to the same work. But when the breadth of 
 blade is taken at about three fourths of the outer ra- 
 dius, the air will pas'^ through the fan with less shock 
 and less internal resistance. These last four equations 
 are important in fan construction, and should be in com- 
 mon use in the shop and at the mine. As we have seen, 
 they have been deduced from the more complicated 
 formula (XXXIX) by approximation, and are only in- 
 tended to be used in estimating upon the size of fan 
 needed for proposed workings, and in the construction 
 of the same. It is not intended to convey the idea 
 that a difTerent-sized fan should be figured for every 
 mine, but to show the necessity for the proper propor- 
 tioning of parts, and the adaptation of fans of different 
 sizes and proportions to different workings. It is sel- 
 dom advisable, where the fan is working fairly well and 
 yielding the necessary amount of air, to make changes, 
 although such changes would be for the betterment of 
 the fan and result in a saving of power ; but where 
 there is a scarcity of air, changes may often be made 
 and must be made to increase the supply. In con- 
 structing a new fan, however, it will be of great pecu- 
 niary advantage to have the new fan adapted to its 
 work. Again, if we cannot build a new fan, we can 
 often, by changing the system of ventilation below, by 
 splitting, or otherwise, so adapt the work to the fan in 
 
ECONOMIC DISCUSSION OF THE FAN. 85 
 
 use that the required results uill be attained. We 
 often see a fan that is expected to throw 100,000 cubic 
 feet of air per minute, when its size and proportions 
 would barely permit the passage of 50,000 cubic feet 
 per minute; and yet the operator has a vague, indefi- 
 nite idea that, by speeding this fan up, it can be made 
 to throw all the air he will need for future develop- 
 ment : and perhaps it will supply all the air he will 
 tieed, if he knows as much about the rest of the mining 
 business as he does about fans. 
 
 Connection with the Downcast. — The connection 
 of the fan with the downcast shaft requires as much 
 care as the construction of the fan itself. We have de- 
 termined, in the last paragraph, what the area of expan- 
 sion, or the area at the cut-off, should be : from this 
 point the area of the air-conduit should increase uni- 
 formly till the top of the downcast is reached, care 
 being taken to avoid sharp angles. The cut-off itself 
 should be a sharp, well-defined line, made with a sheet 
 of boiler-plate iron bent back upon itself, and forming, 
 for a short distance on either side of the cut-off, a lin- 
 ing to the fan casing and to the air-conduit, as shown 
 in Fig. VII. The expansion of the air-conduit from 
 beyond the cut-off should not be too slow, as a great 
 deal depends upon getting the air quickly away from 
 where it would hamper the free action of the fan ; but 
 its expansion must be regular, and changes in direction 
 be made with curved surfaces, as the occurrence of 
 angles or sudden changes in the sectional area of the 
 conduit gives rise to bafffes and eddies. The periphe- 
 ral casing should be continued tangentially to the outer 
 curve. The expansion of the air-conduit should con- 
 tinue till its sectional area is equal to the sectional area 
 
86 MINE-VENTILATION. 
 
 of the downcast shaft. This downcast area should be, 
 properly, twice the sectional area of the main airways 
 below, and the air-course leading from the foot of the 
 downcast should have the same double area, until the 
 point of the first split is reached. It is a good plan to 
 set the fan as far over the mouth of the downcast shaft 
 as the foundation of the fan will permit. Fig. VII 
 shows the general arrangement of the connection with 
 the downcast shaft. 
 
 Testing a Fan at the Shops. — The proper test to 
 apply to a fan at the shop is to place it under condi- 
 tions as nearly similar to those under which it will be 
 compelled to work at the mine, as it is possible to make 
 them ; in other words, to cause it to deliver a certain 
 quantity of air while working under a certain pressure, 
 and then making all the observations and noting them 
 down carefully, as described earlier in this chapter ; and 
 from these observations determining the value of the 
 efificiency and of the fan constant, as there described. 
 To conduct this test, which when once done will answer 
 for all fans of that type and need not be repeated for 
 each particular fan, the motor is set up and cased in, 
 the discharge being conducted away by a conduit or 
 box long enough to prevent any bafifling of the air, and 
 to insure the taking of accurate observations. A par- 
 tition is inserted in the conduit, at a distance of, say, 
 fifty feet from the fan, provided with a movable shutter 
 by which the discharge or flow of air may be regulated 
 from the outside ; the conduit is extended beyond this 
 point (having a uniform sectional area) far enough to 
 give a regular and established velocity to the discharged 
 current, the object being to provide a means of measur- 
 ing the current of air produced by the fan : the object 
 
ECONOMIC DISCUSSION OF THE FAN. 
 
 87 
 
 of the partition or regulator is to establish a certain 
 pressure or water-gauge under which the fan will work, 
 and which will represent accurately the dynamic pres- 
 sure of the mine, due to the resistance encountered by 
 the current in its passage through the airways. A 
 
 1 
 
 Water- 
 gauge 
 
 Anemometer 
 
 Fig. VIII. 
 
 water-gauge is inserted in the side of the conduit, half 
 way between the fan and the regulator, as shown in 
 Fig. VIII, and an anemometer is also placed, as shown, 
 some distance from the open end where the velocity of 
 the current will be uniform. The reading of the ane- 
 mometer may be taken with an instrument or glass, if 
 convenient, to avoid obstructing the free discharge of 
 the air. The fan is now started and regulated to an 
 exact speed of, say, 50 revolutions per minute ; and giv- 
 ing a few moments for the current to establish itself, 
 the shutter is moved in the regulator until a certain 
 fixed water-gauge is obtained, which is noted : as is also 
 the reading of the anemometer, from which the quan- 
 tity of the current is figured ; the temperature and 
 height of barometer being likewise noted and recorded. 
 The experiment is repeated for a speed of, say, 75 revo- 
 lutions per minute, and like observations recorded ; and 
 
88 MINE-VENTILATION. 
 
 again for a speed of loo revolutions per minute. Now 
 by substituting these recorded results and the known 
 dimensions of the fan in equation (XXXVIII), as 
 previously explained in this chapter, we ascertain the 
 value of K for each speed of the fan experimented 
 upon ; and likewise, by substituting in equation 
 (XLVII), as explained, the value of the fan constant 
 for this type of fan may be obtained. The fan con- 
 tant is the same for any particular type of fan, at all 
 speeds of such fan. The subject of the fan as a motor 
 is one of the most important subjects relating to mine- 
 ventilation, and should be carefully considered in all its 
 bearings, with reference to details of construction, by 
 makers as well as by all others who are in any way con- 
 nected with the operation of the fan. 
 
SPLITTING THE AIR-CURRENT. 89 
 
 CHAPTER IX. 
 
 SPLITTING THE AIR-CURRENT. 
 
 Advantage of Splitting, as shown by Table VI.— 
 
 The advantages of splitting the air-current are not duly 
 appreciated. The gain from this source is so enor- 
 mous as to be, in many cases, disbelieved by practical 
 miners and mine-operators before they have thoroughly 
 investigated the subject. In order to make apparent 
 at a glance the effects of splitting the current one or 
 more times, we have carefully prepared Table VI, 
 showing the respective amounts of work and horse- 
 power necessary to circulate different quantities of air 
 through different mines, and also through the same 
 mine, but using one, two, three, etc., splits successively. 
 The table also shows the unit of ventilating pressure/, 
 water-gauge i in inches, and velocity v in feet per min- 
 ute at which the current travels. 
 
 Mines (assumed). — The table assumes all entries or 
 airways to be 6 X 8|^ feet, giving a sectional area to 
 each individual split of 50 square feet. The lengths of 
 the several air-currents, including the returns, are as 
 follows : 
 
 Mine No. 
 
 I. 
 
 Total length of 
 
 airway, 
 
 1,000 
 
 feet 
 
 H ti 
 
 2. 
 
 it ti (t 
 
 it 
 
 5,000 
 
 il 
 
 ti 1< 
 
 3- 
 
 t( ct a 
 
 11 
 
 10,000 
 
 l( 
 
 H it 
 
 4- 
 
 ti ti a 
 
 a 
 
 20,000 
 
 H 
 
 11 11 
 
 S- 
 
 a (( it 
 
 it 
 
 30,000 
 
 (t 
 
go MINE-VENTILATION. 
 
 Mine No. 6. Total length of airway, 40,000 feet. 
 " " 7. " " " " 50,000 " 
 
 " 8. " " " " 60,000 " 
 
 Quantity Increased. — By inspecting the table, we 
 see that with tlie same power we can increase the quan- 
 tity of air any given number of times, by employing a 
 like number of splits. For example, it requires an 
 application of 70.690 horse-power to circulate 25,000 
 cubic feet of air per minute, in one current, through 
 mine No. 5 ; but by splitting into two currents we can 
 circulate 50,000 cubic feet per minute in that mine 
 with the same power ; and if we split the air into four 
 currents we can circulate 100,000 cubic feet per min- 
 ute by the application of the same power. 
 
 Power Decreased. — Again, we see that it requires 
 the application of 141.379 horse-power to circulate 
 100,000 cubic feet of air per nriinute through mine No. 
 8, employing four splits of the air-current ; but if one 
 more split is made, making five in all, the power nec- 
 essary to drive the same air is only a little more than 
 one half, viz., 72.386 horse-power. These examples serve 
 to illustrate the great importance, from an economic 
 standpoint, which attaches to splitting the air into sev- 
 eral distinct currents, to say nothing of the avoidance 
 of danger and delay in case of local accident, when 
 one or more sections of the mine can be immediately 
 and completely isolated. 
 
 Limit to Splitting. — A limit to the indefinite split- 
 ting of the air-current arises from the consequent re- 
 duction of the velocity, which should not be too low, 
 as a sluggish current will not remove the damps or 
 gases which hang in the recesses of the roof and sides, 
 
SPLITTING THE AIR-CURRENT. 9 1 
 
 and in the mouths of old rooms, etc. Again, a high 
 velocity becomes dangerous, especially in fiery mines, 
 where the gases may become ignited by the flame be- 
 ing blown through or against the gauze of the lamp. 
 The limiting velocities of the current may vary some 
 under varying conditions, but practice has shown that 
 the air should not travel less than four nor more than 
 twenty feet per second. At the working face a veloc- 
 ity of five or six feet per second gives good results. 
 
 Size of Airways. — There should be a regular size of 
 airway established in the mine, according to the vol- 
 ume of air we expect to circulate, that the velocity 
 of the current may be normal. In the working of 
 low coal it may be necessary to make the airways 
 very wide, where the roof is not taken down, in 
 order to provide a sufficient sectional area. As stated 
 in the foregoing chapter, the air should be brought 
 down the shaft and through an airway having a sec- 
 tional area double that of the main airways, as far as to 
 the point where the first split is made. 
 
 Arrangement of Splits. — As far as possible, all the 
 main splits should be made as near as practicable to the 
 foot of the downcast, and their several returns join the 
 main current likewise near the foot of the upcast. 
 This will reduce the resistance of the pit to a minimum 
 by reducing the distance the current is forced to travel 
 at a high velocity. 
 
 Equal Splits. — The word split, as used in reference 
 to mine-ventilation, relates to the division of the air- 
 current : as used in this book, a single split means a sin- 
 gle undivided current ; two splits signifies that the cur-, 
 rent is divided, and is travelling in two separate and 
 distinct currents ; equal splits refers to an equal divi- 
 
92 MINE-VENTILATION. 
 
 sion of the air passing. It is possible without the use 
 of regulators to have an equal division of the air-cur- 
 rent between two airways which differ from each other 
 in every respect. 
 
 Unequal Splits. — Where the division of the air be- 
 tween two airways is not equal, they are referred to as 
 unequal splits. This is the case in the large majority 
 of instances where the ventilating current is divided 
 either by the use of regulators or naturally. 
 
 Natural Division. — Now, let us ask, upon what prin- 
 ciple or in obedience to what law does the division of 
 air between two or more airways take place? We will 
 state here in answer to this question, what will be ex- 
 plained later in the chapter, that the division of the 
 air-current is, in obedience to the law, that action and 
 reaction are always equal. Let us consider for a mo- 
 ment two airways open alike to the free passage of the 
 ventilating current. It is by means of these airways 
 that the current is to find egress from the mine ; behind 
 it is the power of the motor urging it forward against 
 the resistance of the airways : it is the resistance that 
 produces and maintains the ventilating pressure; the 
 power behind compels this pressure to move at a cer- 
 tain velocity until, exhausted, it reaches its limit, and 
 the avp of the airways is the work ^ applied to the 
 current. Now, between the works being performed in 
 these two airways, counterbalanced and held intact by 
 the power of the intake current, there exists a dynamic 
 equilibrium : here is the reaction of moving forces ; the 
 reaction is square foot against square foot of sectional 
 area. We see now clearly that the ujtits of work, or 
 the work transmitted by one square foot of sectional 
 area, must be the same for each split. The expression 
 
SPLITTING THE AIR-CURRENT. 93 
 
 for this unit of work, in terms of the airways and their 
 respective currents, is 
 
 i(ksQ\ kloQ 
 
 -1 — =^) or f^, (l) 
 
 in which / is the length of the spHt, the perimeter of 
 the airway, etc., etc. Hence we may write 
 
 !^'J^^, (.) 
 
 a a^ 
 
 from which we may write the proportion applicable to 
 all cases of splitting where the division is natural ; that 
 is to say, where no regulators are used. 
 
 Q 
 
 ^a^^t^i/i ("^' 
 
 If the splits in question have the same cross-section, 
 but their lengths vary, we have 
 
 Q■.Q.■.■.'^rl,•■Vl. (LX) 
 
 If they vary in their length, and their perimeters are 
 different while their sectional areas are the same, we 
 have 
 
 Q:Q,:: Vl^: V7o (LXI) 
 
 Regulators. — Regulators are devices by which the 
 division of the air is controlled and regulated at will. 
 There are two ways or methods by which proportion- 
 ate division may be accomplished ; and though seem- 
 ingly similar to the casual observer, they are based 
 
94 MINE-VENTILATION. 
 
 upon essentially different principles and accomplish 
 very different results. 
 
 Present Method. — The method in general use at 
 the present time is to place a resistance upon the re- 
 turn of those splits which will naturally take more air 
 than the desired amount ; the resistance thus intro- 
 duced being created by means of an obstruction, as a 
 curtain or door having a movable shutter, placed in 
 the entry so as to retard the flow of the air. The work 
 of the box-regulator is discussed and shown in the Ad- 
 denda ; but we will say here, that the immediate prac- 
 tical effect is to increase the ventilating pressure of that 
 
 split, so that the unit of work (— ) will be the same for 
 
 all the splits in question. We readily see that the 
 unit of ventilating pressure in any split will be inversely 
 
 proportionate to f :lj, or to the velocity v in that split, 
 
 and that by enlarging or contracting the opening in the 
 regulator any desired proportionment of the current 
 may be secured. From what we have shown thus far, 
 it is readily seen that in this method of splitting by 
 the use of box-regulators the work performed in each 
 split is exactly proportional to the sectional area of 
 that split, regardless of the quantity of air passing in 
 that split ; for the reason that the unit of work at the 
 point of split is the same for each, and the full area of 
 each is left exposed at its mouth, and each split conse- 
 quently absorbs an amount of work avp proportionate 
 to its area a. It follows, further, that the work per- 
 formed in that split in which there is no regulator, as 
 
 indicated by the expression ( — =^1 is the measure of 
 
SPLITTING THE AIR-CURRENT. 95 
 
 the work performed in each spht, starting from the 
 same point ; and the total work of these sphts will be 
 found by multiplying the work in this free split by the 
 number of splits. 
 
 Objection. — The objection to this method is a se- 
 rious one; viz., it requires the introduction of a large 
 amount of foreign resistance into the airways, and the 
 consequent absorption of power, for which the operator 
 receives no return. This absorption of power is large, 
 as will be shown later. 
 
 Another Method. — Another method, and one which 
 has the advantage of not introducing any foreign resist- 
 ance into the airways, is to divide the intake air ap- 
 proaching the mouths of two or more splits so as to 
 apportion the applied power, the avp of the main cur- 
 rent, to the works of the several splits, a{i\p^ and a^^p^ , 
 respectively. This is accomplished by the use of a 
 form of regulator to be described later, by which the 
 exposed area A^, A^, etc., of each split, respective!}', is 
 made proportional to the above respective works of 
 those splits, according to the proportion 
 
 A,: A,:: a^i\p^ :«,«'= A ; 
 and by substitution and reduction we have 
 
 ^ :^ ::^^/'^ (LXII) 
 
 From this proportion the exposed areas of the various 
 splits may be determined, and the moving forces /y4j 
 = /,«j and/^,=A^2 proportioned to their respective 
 works. (See Fig. XI.) 
 
96 MINE-VENTILATION. 
 
 Pro and Con. — It has been said by some, though 
 not with much apparent forethought, that if such divi- 
 sion of the air were to be made at the mouth of the 
 split it would not have the effect to change the moving 
 force /« ; arguing that, as the sectional area of the air- 
 way again enlarges to the regular size immediately be- 
 hind the point of split, the same moving force would be 
 again established: forgetting that there is nothing there 
 to re-establish the unit of ventilating pressure/, and that 
 in the expansion of sectional area immediately behind 
 the point of split, the unit of pressure has fallen from p 
 to p^ , which latter pressure, p, , is maintained by the re- 
 sistance inherent in this particular split. We stated in 
 the introductory chapter that the dynamic pressure 
 which animates the current is created and maintained 
 by the resistance ahead of the current, upon which it is 
 directly dependent, and not upon the power behind it. 
 Were it not for this resistance there would be no pres- 
 sure ; we would have an illustration of the third case 
 cited under " Measure of Force," in Chapter II. 
 
 Illustration. — This can be proved in a very simple 
 and conclusive way, by taking a short tube connected 
 near one end with a water-gauge, as shown in Fig. IX, 
 by which the pressure in the tube will be indicated any 
 
 Fig. IX. 
 
 moment. If we blow into the end marked a, the other 
 end being open, there will be no appreciable pressure 
 
SPLITTING THE AIR-CURRENT. 97 
 
 indicated by the water-gauge ; but if we now lengthen 
 the tube by the successive additions of lengths of tubing 
 to the end marked b, blowing as before into the tube at 
 a, we will observe a continual rise of pressure for each 
 additional length : such pressure, as in the mine, being 
 created and maintained by the resistance offered by the 
 tubing to the flow of air. 
 
 Conclusion. — It is then a most important point to be 
 borne in mind, viz., that the unit of ventilating pressure 
 p is created and maintained directly by the resistance 
 ahead of the current, the power behind the current giv- 
 ing motion or velocity ; thus these terms become correla- 
 tive, but each has its particular source or derivative. It 
 is as the spring between the bumpers of a railroad train 
 being pushed up a grade — the steeper the grade, the 
 greater the resistance and the consequent pressure upon 
 the spring : the power of the engine imparts the motion 
 or velocity to the train ; but it is perfectly evident that 
 the resistance regulates the pressure upon the spring: 
 this is analogous to the condition which exists in the 
 mine with reference to the ventilating pressure. Rea- 
 soning further, we see that as each split has its own 
 particular resistance, it should have its own unit of ven- 
 tilating pressure, denoted by p^, p^, etc., respectively. 
 Each split will have its own particular velocity, denoted 
 by v^,v,, etc., respectively, dependent upon the quantity 
 of air required and the sectional area of the split or air- 
 way. Hence, as an evident consequence, the work to 
 be accomplished in each split and the power applied at 
 the mouth of each split, and consequently the exposed 
 areas A^, A^, etc., at the mouth of each respective split 
 should be proportional to these factors, p^v^,p^v^, etc., 
 respectively. Let us now summarize 
 
98 MINE-VENTILATION. 
 
 THE THEORY OF SPLITTING AIR-CURRENTS. 
 
 Dynamic Equilibrium. — We all understand what is 
 meant when we speak of static equilibrium or the equi- 
 librium of pressures ; but we may not so clearly com- 
 prehend the meaning of the term dynamic equilibrium. 
 When a force is exerted to produce motion against 
 resistance, as alluded to in Chapter II, there is devel- 
 oped a dynamic or moving pressure, which in connec- 
 tion with the velocity becomes the measure of the force ; 
 this measure (see Chapter IV) we call work. In the 
 illustration previously referred to, where the engine is 
 pushing a railroad train, the dynamic pressure there 
 developed is represented by the compression of the 
 spring between the bumpers. This dynamic pressure, 
 as we have seen, is a factor of the resistance under 
 which the moving force is acting, and is always present 
 as an active agent; in no way promoting or retarding 
 the movement of the body, only as it acts as a medium 
 between the resistance and such portion of the moving 
 force as is neutralized by that resistance, thereby estab- 
 lishing a dynamic equilibrium between these two com- 
 ponents. This affords us a clear comprehension of the 
 forces at work and concerned in the movement of a 
 fluid mass. As stated above, the measure of the ap- 
 plied or moving force is this dynamic pressure taken in 
 connection with the velocity of the movement ; in other 
 words, the product of these two factors/?', which is, as 
 we have said, the work of the force. 
 
 Theory of Splitting. — Now for the theory of split- 
 ting ; and by this we mean simply the action of the 
 laws concerned in the splitting or dividing of currents 
 
SPLITTING THE AIR-CURRENT. 99 
 
 of air. When a split is established in an air-current, and 
 the air is passing in proper proportions through the 
 respective splits, there is established at the point of 
 split a dynamic equilibrium of the moving forces; in 
 other words, these forces react against each other. Unit 
 of pressure (pressure upon a unit of surface) reacts 
 against unit of pressure ; and since action and reaction 
 are always equal, the units of work (the measure of such 
 reaction) will be equal. Hence we may write 
 
 pv = p,v, (LXIII) 
 
 Caution. — Equation LXIII is always true at the point 
 of reaction; but we must not mistake the units of work 
 at this point for the units of work back in the entry 
 where the sectional area is enlarged to the regular size. 
 The areas at both of these points are transmitting the 
 same work obviously : it could not be otherwise. Now 
 if the work to be performed in the respective splits is 
 different, and the units of work at the point of split are 
 equal, our problem is simply to proportion the exposed 
 area at the mouth of each split to the work to be ac- 
 complished in that split. The unit of work as here 
 spoken of is the work transmitted by one square foot of 
 sectional area. This is the whole theory of the splitting 
 of air-currents. 
 
 At the point of reaction or the point of split the units 
 of work (work transmitted by one square foot of sectional 
 area) are equal; and the exposed areas at the mouths of 
 the several splits must be proportioned to the work to be 
 performed in each respective split. 
 
 Graphic Method. — There is still another method of 
 demonstrating this important law ; and in order to 
 
100 MINE-VENTILATION. 
 
 make more plain the action of the law, as well as to aid 
 the practical mind to retain the points gone over, we 
 will resort now to an every-day illustration. If a cer- 
 tain blow will drive a certain nail one inch into a block 
 of oak, the same blow will drive the same nail two 
 inches into a block of pine: applying this principle to the 
 movement of air in mines, let us suppose we have a 
 current of 100,000 cubic feet of air per minute coming 
 down the intake A, animated by a certain unit of ven- 
 tilating pressure/. Arriving at a, there are two entries 
 or splits open to its passage or egress : the one, B, 10,000 
 feet long; the other, C, 5000 feet long. Each of 
 these splits has its respective resistance or back pressure, 
 analogous to the respective densities of the oak and 
 pine blocks referred to above. Now the force applied, 
 corresponding to the blow upon the nail, is the unit of 
 ventilating pressure multiplied into the sectional area 
 of the entry, or pa, the moving pressure. This force is 
 applied alike to each of the splits B and C, and, follow- 
 ing out the analogy, will drive the air further in one 
 minute of time in the short split C than in the longer 
 split B. In other words, the resulting velocity, and con- 
 sequently the quantity, will be greater in the short split 
 than in the longer one ; but the work accomplished in 
 each split will be the same, because the same moving 
 force pa is applied to each split under the same condi- 
 tions, and must perform the same amount of work in the 
 same time. The hatched portions of each entry (Fig. 
 X) represent the respective quantities or velocities in 
 the two splits. Now in performing their work the mov- 
 ing forces applied to the splits B and C react against 
 each other and against the moving force in the main 
 entry A ; this is evident. The reaction is unit of area 
 
SPLITTING THE AIR-CURRENT. 
 
 lOI 
 
 against unit of area, square foot against square foot ; 
 hence it is evident that the units of work or the work 
 transmitted by a unit of sectional area at the point of 
 split will be the same. It is important to notice that the 
 units of ventilating pressure may be unequal although 
 reacting against each other, the rebound from such re- 
 
 FiG. X. 
 
 action being through different spaces, or, in other words, 
 the resulting velocities being different. The unit of 
 ventilating pressure in the direction of either split can- 
 not be greater than the resistance of that split will 
 support; as we have previously seen, it is the resistance 
 ahead of the current in each split that maintains the 
 pressure for that split. 
 
 Style of Regulator proposed. — The style of regu- 
 lator proposed by the author to accomplish the propor- 
 tionate division of the intake area, and give to the mouth 
 of each split an exposed area proportioned to the work 
 to be accomplished in that split, is shown in Fig. XI. In 
 this figure be is a door hinged at c and provided with a 
 set-lock at b, by which the door may be fixed and held 
 firmly in any desired position. The current of air com- 
 
I02 
 
 MINE- VENTILATION. 
 
 ing down the intake A strikes the edge of this door b and 
 divides. It is evident that any proportionate division 
 of the air may be made, as the door may be set so as 
 
 lyiHoT«rPi' 
 
 Fig. XI. 
 
 to almost entirely shut off the current from passing into 
 the shorter split, by which it seeks to find egress from 
 the mine, and cause it to almost wholly pass through 
 the longer split. 
 
 Argument. — The question has frequently been asked 
 by intelligent men, "Wherein does this form of regu- 
 lator differ from the one already in use, and upon what 
 different principle is its action based ? " It may be as- 
 serted by some, after a cursory investigation, that there 
 can be no essential difference, claiming that it obstructs 
 the entry in the same manner and to the same degree 
 as does the shutter-regulator. Such claims are based 
 upon no fact. The difference lies in the fact that the 
 splits having a small resisting power are, by the use of 
 this method, ventilated under a low pressure, and not, 
 as in the other method, under a pressure in correspond- 
 ence with the resistance of the entire pit. This results 
 at once in an enormous saving of power. The mouths 
 of the several splits being left open, in the one method 
 
SPLITTING THE AIR-CURFENT. 103 
 
 they are all subjected to the same moving force pa\ and, 
 as a result, in those splits where a less quantity of air is 
 desired, or where the resistance is small, a foreign re- 
 sistance must necessarily be introduced to take up 
 and neutralize this excess of power, or it would apply 
 itself to the movement of more air than is desired in 
 that split. In other words, we introduce into all the 
 lesser splits an amount of dead work to absorb the 
 surplus of power applied to each, making the work to be 
 performed in each of these splits equal to the work of 
 the greatest split in the pit. In the use of the other 
 method the power applied to each split is proportionate 
 to the work of the split. 
 
 Illustration. — Let us now assume a practical case. 
 We will suppose mine No. 8 to be passing 100,000 
 cubic feet of air per minute in four splits, as follows: 
 
 Split a, 5,000 ft. long 20,000 cu. ft. 
 
 " b, 15,000 " " 30,000 " " 
 
 " c, 20,000 " " 30,000 " " 
 
 it <i 
 
 " d, 20,000 " " 20,000 
 
 Total, 60,000 " " 100,000" " 
 
 If there were no regulators used in any of these four 
 splits, the air would divide itself as follows: 
 
 Split a 33.898 cu. ft. 
 
 " b 23,390 " " 
 
 " c 21,356 " " 
 
 " d 21,356 " " 
 
 Now it is evident that to obtain the desired quantities 
 of air in the various splits some artificial means must 
 
104 MINE-VENTILATION. 
 
 be resorted to that will decrease the flow into sections 
 a and d, and cause a corresponding increase in b and c. 
 As we have seen, the means adopted and in use at the 
 present time is to place an obstruction — a so-called 
 " Regulator " — upon the return of those splits which 
 naturally take more air than the desired amount, 
 thereby driving more air into the other splits which 
 are deficient. We have had this method under discus- 
 sion in the preceding pages, and we believe it has been 
 proven to result in a profligate waste of power ; never- 
 theless, to make this more plain, we have tabulated 
 below a comparison of the horse-powers consumed in 
 the two methods alluded to, which should not fail to 
 convince any who still remain skeptical. 
 
 
 Length, 
 ft. 
 
 Nat. Div., 
 cu. ft. 
 
 ReqM Div., 
 cu. ft. 
 
 H. Power, 
 Old Way. 
 
 H. Power", 
 New Way. 
 
 Split a , . 
 
 . . 5,000 
 
 33.898 
 
 20,000 
 
 81.439 
 
 6.030 
 
 " b.. 
 
 .15,000 
 
 23,390 
 
 30,000 
 
 81.439 
 
 61.079 
 
 " c. 
 
 . 20,000 
 
 21,356 
 
 30,000 
 
 81.439 
 
 81.439 
 
 " d.. 
 
 .20,000 
 
 21,356 
 
 20,000 
 
 81.439 
 
 24.121 
 
 Total ... 60,000 100,000 100,000 325.756 172.669 
 
 From this table we see that the same results are ob- 
 tained in both cases with the expenditure of but little 
 more than 50^ of the power in the new method than is 
 required in the old. 
 
 Objection. — It has been further objected that the 
 placing of a door or any form of regulator at the 
 points indicated would block the main roads and seri- 
 ously interfere with the working of the mine. But 
 this is not true if the mine is properly planned and a 
 systematic mode of ventilation adopted, as will readily 
 be seen by referring to Fig. XII. 
 
SPLITTING THE AIR-CURRENT. 
 
 105 
 
 Mim 
 
 1^,000 er/TU 
 
 T 
 
 I 
 
 [T 
 
 r> 
 
 Lb 
 
 ^n 
 
 Lb 
 
 Li. 
 
 
 >CIS53| 
 
 ~?V7 
 
 Reference. 
 — Door 
 =i Stopping 
 X Overcast 
 
 i^Regulator 
 
 ft^r^n 
 
 ir 
 
 isfio S^ffT^ H— ^ - 
 
 IJ l g?MWc./t 
 
 i^ 
 
 ^t:U 
 
 cCJdJ^t^. 
 
 i 
 
 _, < ■■■■ O lio 6G,000Z^3raL.=2d»8M 
 
 Tatt-iTope Engine 
 
 to be located jKro 
 
 TlcU block of coal to 
 be worked out later 
 
I06 MINE-VENTILATION. 
 
 System in Ventilation. — System in the ventilation 
 of a mine is everytliing. One of the first points to 
 be considered is the disposition of the main haulage 
 roads with respect to the ventilating currents. A 
 good general rule, though not without exception, is to 
 make the return air-courses the main haulage roads. 
 This plan has many points in its favor : as, the avoid- 
 ance of doors upon the haulage roads ; the freedom of 
 the air-ceurses from the dust of travel, thereby insur- 
 ing a pure current of fresh air to the men ; the main- 
 taining of a warmer temperature in the hoisting shaft 
 in the winter by means of the heat of the upcast 
 current, thereby preventing the formation of ice, which 
 otherwise often incapacitates the hoistways ; the mov- 
 ing of the loaded cars through the entries in the same 
 direction with, and not opposed to, the circulating cur- 
 rent, thereby offering no resistance to the ventilation 
 of the mine. (The resistance to the ventilating current 
 arising from this cause, when the output is moving 
 against the air, is often very considerable and almost 
 as often overlooked by the one in charge, the sluggish 
 circulation being attributed to some other cause.) 
 This paragraph may seem a digression from the sub- 
 ject-matter of the chapter, but it bears directly upon 
 it, inasmuch as it refers to that system of ventilation 
 which will permit of the arrangement of regulators at 
 the mouths of the several splits without interfering 
 with the working of the mine. 
 
 Effect of Dips and Rises. — There is one more 
 topic that demands our attention before leaving this 
 branch of the subject. It is the effect upon the circu- 
 lating current produced by a rise or a dip in the air- 
 way. We have seen in Chapter III, in the discussion 
 
SPLITTING THE AIR-CURRENT. I07 
 
 of " Dips and Rises," that a dip or a rise in an airway 
 becomes a natural factor of ventilation. Its effect 
 upon the proportionate splitting of the air-current is 
 sometimes misleading, because unlooked for. We 
 often hear the question asked, "Will an entry going to 
 the rise or to the dip receive its proportion of air, if 
 from any cause the total quantity of air furnished to 
 the pit is increased or decreased, no change being 
 made in the regulator?" We answer, undoubtedly 
 the proportion will change for every change in the 
 total quantity of air passing. 
 
 Example. — To illustrate : Let us suppose that we 
 have 100,000 cubic feet of air passing into our pit per 
 minute; and we have divided this air so that one split 
 running level is receiving 50,000 cubic feet of this air, 
 and another split running to the rise is likewise receiv- 
 ing the same amount. If now a fall occurs on the main 
 air-course, so that the total supply of air to the mine 
 is thereby reduced from 100,000 cubic feet to 80,000 
 cubic feet per minute, we will then find that the split 
 running to the rise is receiving less than its former pro- 
 portion of the entire circulation ; i.e., less than 40,000 
 cubic feet of air per minute. If, on the other hanci, 
 the circulation of the pit is increased to, say, 120,000 
 cubic feet of air per minute, this split running to the 
 rise will receive more than its former proportion of the 
 air ; i.e., more than 60,000 cubic feet per minute. In 
 the case of a split running to the dip, the dip-split will 
 take more than its proper proportion when the circula- 
 tion of the mine is decreased, and less than its proper 
 proportion when the circulation is increased. These 
 results may be tabulated as follows: 
 
Io8 MINE-VENTILATION. 
 
 Rises. Dips. 
 
 Circulation increased More. Less. 
 
 " diminished Less. More. 
 
 Cause for Disproportion. — The cause for such 
 disproportionate splitting is simple and obvious. There 
 exists in every dip-split, as explained in Chapter III, 
 an independent factor of ventilation or a ventilating 
 power which is generally positive, rarely ever negative. 
 In the illustration cited above, where 100,000 cubic 
 feet of air are passing per minute, this ventilating 
 power in the dip-split is responsible for, say, 10,000 
 cubic feet of this circulation within the limits of the 
 split; i.e., this factor of ventilation, existing in this 
 split by virtue of its dip, is potent to draw upon the 
 main current at the point of split for 10,000 cubic feet 
 of air per minute, and to circulate this amount through 
 the split. The balance of the circulation in the split 
 and throughout the pit is dependent upon the ventilat- 
 ing motor. Now, the occurrence of a fall in the main 
 entry outside of the split in question, reducing the flow 
 of air in the main entry at the split to 80,000 cubic feet 
 of air per minute, does not affect the potency of the 
 ventilating power existing in the split ; and the split 
 still continues to draw from the main current, inde- 
 pendent of the motor, the 10,000 cubic feet per minute, 
 which is the capacity of its own inherent power. This 
 draught upon the main current will continue as long 
 as there is sufificient air passing in the entry to supply 
 the demand ; and we further venture the assertion that 
 should the fall so choke the main entry as to reduce 
 the total supply of air to 10,000 cubic feet per minute, 
 all of this air, upon reaching the point of split, would 
 
SPLITTING THE AIR-CURRENT. 109 
 
 pass down the dip-split, and none would find its way 
 into the other airway. 
 
 Effect Tabulated.— Now, to make plain the fore- 
 going, we may tabulate the effect of this independent 
 factor of ventilation existing in the dip-split upon the 
 proportionate division of the air-current as follows: 
 
 Before the fall : 
 
 Main airway 100,000 cu. ft. per min. 
 
 Level or rising split, $0%. . 50,000 " " due to motor. 
 
 Dip-split, so^ HO,ooo " " " " motor. 
 
 \ 10,000 " " " " dip. 
 
 After the fall : 
 
 Main airway 80,000 cu. ft. per min. 
 
 Level or rising split, 48.6^, 38,889 " " due to motor. 
 
 T-»- 1-^ ^, .V ( 3i>iii " " " " motor. 
 
 Dip-split, 5 i.4J^ J •^ ' 
 
 I 10,000 " " " " dip. 
 
 Thus, by a reduction of 20J^ in the total quantity of air 
 passing, the dip-split in this mine takes somewhat more 
 than 1000 cubic feet per minute beyond its propor- 
 tion at the expense of the other split. Analogous 
 reasoning will show the effect of increasing the circula- 
 tion, and apply likewise to rise-splits. The above is 
 figured directly from the principle of equation (LIX). 
 
no 
 
 MINE-VENTILATION. 
 
 CHAPTER X. 
 
 DISCUSSION OF THE "EQUIVALENT ORIFICE." 
 
 Prefatory. — Since the application of the method of 
 the " Equivalent Orifice " to the solution of problems re- 
 lating tofans is coming somewhat into use, a discussion of 
 its merits or demerits will be of value, and perhaps save 
 us from error. The author of this method, M. Murgue, 
 deserves credit for his mathematical deductions ; but 
 after all the whole method is, as its author himself says, 
 simply a " fiction." It is a generalization, wherein the 
 passing of a certain current of air through a mine is 
 compared to the passing of the same current through 
 an aperture in a thin plate. 
 
 Illustration. — To simplify this and make it plain to 
 
 
 
 Fig. XIII. 
 
 the mind's eye, let us suppose we have a tank of water, 
 as shown in the accompanying figure. One of the sides 
 
DISCUSSION OF THE "EQUIVALENT ORIEICE." Ill 
 
 of this tank is pierced near the bottom with a round 
 hole. The tank is made of thin boiler-plate. A con- 
 stant stream of water flowing into the tank above, 
 maintains the level of the water in the tank at a given 
 height h above the orifice. As a result the water issues 
 from the orifice at a constant velocity v, determined by 
 the equation for falling bodies, 
 
 V = ^'Zgh, (i) 
 
 from which we have 
 
 k = — (2) 
 
 Now, knowing the area of the orifice a and the velocity 
 of the fluid as it issues v, the quantity of the flow Q 
 will be expressed by the equation 
 
 or 
 
 Q = a^^h (3) 
 
 But the water in the tank is pressing from all directions 
 toward the orifice, giving rise to a baffling and a con- 
 sequent loss of velocity at the orifice, which is only re- 
 stored by a contraction of the area the flow just beyond 
 the orifice. This contraction of area, called in Physics 
 the " Vena contracta," is dependent for its amount upon 
 the style of the orifice ; but, for a round hole in a thin 
 plate it has been determined as 0.65 of the original 
 area a. Hence we have 
 
 Q =■ o.ei^a V2gk. .... (4) 
 
 Now as the laws governing the flow of all fluids under 
 like conditions are the same, and as air is a fluid, it is 
 
112 MINE-VENTILATION, 
 
 suggested by Murgue to assimilate our formulas expres- 
 sive of the flow of air through mines to the above, 
 letting Q represent the quantity of air passing in cubic 
 feet per second, h the head-of-air column in feet, and a 
 the equivalent orifice of the mine. Reducing this to 
 cubic feet per minute and inches of water-gauge i, we 
 have finally for the value of the equivalent orifice, 
 
 « = 0.000383 -^r. . . . (LXIV) 
 
 Equation (LXIV) gives the value of the area of the 
 imaginary equivalent orifice a in terms of the quantity 
 of air passing, and the pressure which animates such cur- 
 rent. This is true enough, and so far the analogy drawn 
 is correct, the flow of a fluid through an aperture in 
 a thin plate being correspondent to the flow of air 
 through a mine. Murgue then proceeds to show the 
 practical utility of this imaginary orifice by supposing 
 a fan to be revolving at a uniform speed, discharging 
 its air through two orifices in thin plates successively : 
 one of these orifices he uses to represent the fan and 
 the other to represent the mine. Now, as he says, he 
 has in effect replaced the resistance offered by the fan 
 to the passage of the air through itself, by the first 
 plate, and the resistance of the mine by the second 
 plate. From this point, however, Murgue fails in the 
 application, because he assumes that the effective de- 
 pression is equal to the initial depression minus the 
 depression caused by the passage of the air through the 
 fan. Let us look carefully at this matter of depressions 
 and first form a clear idea of the significance of the term. 
 It relates primarily to the depression of the water in one 
 
DISCUSSION OF THE "EQUIVALENT ORIFICE." II 3 
 
 arm of the water-gauge. It is synonymous with " Unit 
 of pressure." Murgue's assumption, then, makes the 
 unit of pressure due to the resistance of the mine plus 
 the unit of pressure due to the passage through the fan, 
 equal to the initial unit of pressure. This is undoubt- 
 edly true of the respective works of these pressures, but 
 is not true of the pressure themselves, as was stated in 
 the introductory chapter. No one will deny for an in- 
 stant that the work lost in the passage of the fan plus 
 the work performed by the current in the mine repre- 
 sents the total work of the fan, or the initial work ; but 
 if the sum of the two works is the initial work, the sum 
 of the two pressures cannot give the initial pressure, 
 except and only when the velocities with which these 
 pressures move are equal. In the consideration of falling 
 bodies, the height through which the body falls is gen- 
 erative of the velocity. The method of the Equivalent 
 Orifice treats of pressure in the same manner as genera- 
 tive of, or at least correspondent to, the established veloc- 
 ity. This can only be true for the same equivalent orifice; 
 when the equivalent orifice remains unchanged, the 
 'same pressure will always indicate the same velocity. 
 Therefore the fallacy of this ingenious method lies in 
 adding together the pressure due to the passage of the 
 air through the equivalent orifice of the fan (called by 
 its author the " Orifice of passage") and the pressure 
 due to the passage of the same current through the 
 equivalent orifice of the mine, and calling their sum the 
 initial pressure of the fan. 
 
 It is important to remember that, while in statics we 
 equcLte pressures, in dynamics work must always form 
 the basis of comparison. 
 
 Further, we should always study to avoid vague and 
 
114 MINE-VENTILATION. 
 
 imaginative reasonings as far as possible, never dealing 
 in fiction where the case will admit of absolute demon- 
 stration. It is due to the failure to reduce his compari- 
 sons to a basis of work that Mr. Murgue finds no 
 expression in his formulas for the width of the fan-blade, 
 which is a most serious omission ; as, also, the tem- 
 perature of the air and the height of the barometer 
 should appear there. These are all factors which 
 increase or diminish the yield of a fan very materially. 
 What the author has said in this chapter, or elsewhere 
 in the book, must not be understood in the light of criti- 
 cism, but rather as striving to interpret more truly 
 Nature's laws, and in this we must all be only learners. 
 
COMPRESSIVE VS. EXHAUSTIVE VENTILATION. I15 
 
 CHAPTER XI. 
 
 COMPRESSIVE vs. EXHAUSTIVE VENTILATION. 
 
 Prefatory. — The subject of the ventilation of mines 
 would not be complete without a reference to the rela- 
 tive merits of these two systems. Very little can be 
 said that has not been already said in regard to either 
 of them, and still we find strong advocates of each. 
 As a rule, however, the men who are apparently the 
 strongest advocates of either systemcannot giveany ade- 
 quate reason for their preference that will stand the test 
 of criticism. The fact is that both of these systems are 
 valuable, and alike find their particular adaptation to the 
 Varied conditions of mine-ventilation. The one or the 
 other should be adopted for any proposed workings 
 only after a thorough consideration and study of the 
 conditions to be encountered in such workings; and 
 not for the reason given by one mining man, much to 
 the amusement of his friends : laying a rope upon the 
 ground, he explained his preference by saying, "You 
 see, gentlemen, I can pull that rope, but I cannot push 
 it." 
 
 Plenum System. — Compressive ventilation is repre- 
 sentative of what is known as the " Plenum " system. 
 It is ventilation by means of the force-fan or some 
 other motor, by which the air is forced into the mine 
 and through the airways under a pressure greater than 
 that of the atmosphere. 
 
 Vacuum System. — Exhaustive ventilation is the 
 
Il6 MINE-VENTILATION. 
 
 representative of what is known as the " Vacuum " sys- 
 tem. It Is ventilation by means of the exhaust-fan, 
 furnace, or some other motor by which the pressure in 
 the upcast shaft is reduced and falls below that of the 
 atmosphere. 
 
 Difference. — The essential difference between these 
 two systems lies in the fact that the one is a high-pres- 
 sure system and the other a low-pressure system. The 
 moving or ventilating pressure pa is the same in both ; 
 at least there is no appreciable difference. The water- 
 gauge, showing the difference between the pressures of 
 the intake and the return, will give very approximately 
 the same reading for the same mine under like con- 
 ditions, when the air is forced by the motor, as when it 
 is exhausted. The same volume of air must be passing 
 in the same direction, under absolutely the same con- 
 ditions of temperature, barometer, and hygrometric 
 state. It will not answer to observe the water-gauge 
 when the fan is forcing, and then to reverse its action 
 and take the same observation. This would not be an 
 adequate test, although the same quantity of air might 
 be passing at the time of taking the two observations : 
 the obstacles met with and the resistance to be over- 
 come by the current in the mine would not necessarily 
 be the same ; and this is a point about which we have to 
 be assured before making the test. In the one system 
 the motor acts to establish a pressure in the mine as 
 much above the atmospheric pressure as it is below it 
 in the other system. 
 
 Comparative Effects. — Now, what are the compara- 
 tive effects of ventilating by these two systems ? The 
 system by compression establishes an actual pressure 
 in the pit which is always greater than the atmospheric 
 
COMPRESSIVE VS. EXHAUSTIVE VENTILATION. II7 
 
 pressure, inflating the pit as we would a balloon. As a 
 natural result, the air of the pit seeks vent by every 
 fissure or crevice open to its egress. This may seem a 
 trivial circumstance but in the vicissitudes of mining 
 it has often proved a very important one. The fissures 
 and crevices formed in the roof of the mine by the gen- 
 eral sinking of the overlying strata often extend to the 
 surface, frequently opening up seams from which ob- 
 noxious and dangerous gases issue. If the air of the 
 pit is under compression these gases will be driven from 
 the pit, in place of being drawn into it, as would be the 
 case were the ventilation exhaustive. This finds even 
 more practical application in the case of the near ap- 
 proach to old workings, in which dangerous gases are 
 very apt to have accumulated. Such accumulations 
 of gases find easy access to a pit under exhaustion ; in 
 fact, without warning they may and often are thrown 
 out upon the miner in great volume. The writer re- 
 members at one time tearing out a brattice shutting 
 off some old workings where there had been an exten- 
 sive fire, and gas had in all probability accumulated in 
 considerable quantity ; when the first small opening was 
 made, the sound was like the rushing of a mighty wind, 
 as the air under compression in the pit found vent into 
 the old works, where the air was dead. There was no 
 fear of this possible accumulation of gas coming out, 
 although for the time some of the miners were fright- 
 ened. Giving the space time to ventilate, the hole was 
 then made larger and the workings entered with im- 
 punity. 
 
 Again, it is argued in favor of the exhaustive method 
 of ventilation, that accumulations of gases in old rooms, 
 in crevices, etc., do not increase as fast as when they are 
 
1 1 8 MINE-VENTILATION. 
 
 driven back by the compression of the air, and are not 
 as great a menance to the safety of the pit. The claim 
 is that these gases are held back in their crevices and 
 corners by the extra pressure of the compressive 
 method ; and if at any time this pressure is relieved, by 
 the stoppage of the fan or by a fall in the airway, the 
 pent up gases will then issue in a larger volume and 
 prove more dangerous. In regard to this, we all know 
 that the pressure under which a pit is ventilated, even 
 in the compressive method, falls far short of the pres- 
 sure necessary to restrain a gas from expanding, or the 
 pressure arising from the tension of such gas. Again, 
 the natural tendency of a body of gas (by the law of 
 diffusion) is to slowly diffuse itself and mingle with the 
 surrounding air, and this tendency is as great under the 
 pressure due to compressive ventilation as it is under 
 the more reduced pressure of the exhaustive method. 
 Were the gas more of a cohesive body, as a fog or other 
 vapor, this argument would be more tenable. It is true 
 that when the fan stops and circulation ceases the air- 
 ways seem to be at once filled with the issuing gases ; 
 but the gases were not pent up by the pressure due to 
 the circulation, nor do they issue now in any greater 
 volume than before the circulation ceased. They are 
 not now, however, brushed away by the passing current, 
 but accumulate where they issue. 
 
 An argument uncontrovertibly in favor of the ex- 
 haustive method of ventilation arises from the fact that, 
 in the short-sighted economy of the average coal opera- 
 tor, the fan is established at the dump or in close prox- 
 imity thereto; and it not infrequently happens that the 
 air forced down the shaft to furnish the breath of life to 
 the hundred or so men compelled to breathe it is 
 
COMPRESSIVE VS. EXHAUSTIVE VENTILATION. II9 
 
 partially vitiated before it starts upon its journey, 
 laden as it is with the odors of the gob-pile or the fur- 
 nace-stack. In this respect the exhaust-fan possesses an 
 unquestionable advantage, as it admits of the downcast 
 shaft being placed entirely away from the other outside 
 works, and thereby insures a supply of the purest air. 
 
 Conclusion. — It is better, in order to provide against 
 possible contingencies that may at any time arise, to 
 arrange the fan so that it may be converted immediate- 
 ly from a force-fan into an exhaust, or the reverse of 
 this. This is usually arranged in a very simple manner 
 by constructing an air-tight enclosure in such a way as 
 to cover the eyes of the fan and connect them with the 
 
 Side View 
 
 Fig. XIV. 
 
 top of the shaft. The enclosure should have a sectional 
 area somewhat greater than the area of the shaft, and 
 must be provided with a pair of doors upon each side of 
 the fan and opposite the eyes, as shown in the side-view 
 and marked d, d. These doors may have a half-circle 
 cut from each of them, if necessarj^ so that when shut 
 they enclose the shaft of the fan ; when open and the 
 
120 MINE-VENTILATION. 
 
 fan is forcing, they afford unobstructed access of the air 
 to the eyes of the fan. When the fan is forcing, all the 
 doors are closed except the ones d, d, just mentioned; 
 these are thrown wide open to afford free access for the 
 intake air. The fan is then working in its normal con- 
 dition. When it is desired to exhaust, the intake doors 
 d, d are closed, the doors in the side-casing 21 c c are 
 swung back till they meet in the centre of the shaft, 
 thereby cutting off the connection of the mine with the 
 circumference of the fan and at the same time establish- 
 ing its connection with the eyes ; an opening is then 
 made in the face casing of the fan by throwing back 
 the door a and raising slightly the door b, thus giving 
 free exit to the discharge from the fan. In this position 
 of the doors the fan is an exhaust-fan. All of the doors 
 should be made to fit as tightly in the casing as possible ; 
 they may be provided with canvas flaps at the edges, 
 if necessary. 
 
CARE OF MINE, AS ASSISTING VENTILATION. 121 
 
 CHAPTER XII. 
 
 CARE OF MINE, AS ASSISTING VENTILATION. 
 
 Prefatory. — Having gone over the ground, as 
 viewed from a theoretical standpoint, let us now look 
 at a few essential practical points with which every 
 mine manager, every pit foreman, indeed every miner 
 or day-hand employed in the pit should be familiar. 
 
 Conduct of the Air. — The distribution and conduct 
 of the air-current through the pit and to the face of 
 the workings should receive the constant and most 
 careful attention of the pit foreman, approved by the 
 mine manager. It is a question of vital importance, 
 both as a source of revenue to the company and 
 health and safety to the men. The carrying of a large 
 quantity of air through an ordinary-sized airway for 
 any considerable distance should only be tolerated 
 when there is no alternative ; it is expensive, as the 
 velocity is high and the power correspondingly large ; it 
 will also require a constant watching and timbering of 
 the air-course to prevent a fall shutting off the entire 
 section. When possible, the system of ventilation 
 should be such as to distribute the air from the foot of 
 the downcast evenly over the entire pit, without pro- 
 ducing a high velocity of the current at any point, and 
 to isolate the different sections of the mine, giving to 
 each its own independent circulation. The velocity of 
 the current in the main airways of the several splits 
 should preferably not exceed lo or 12 feet per second ; 
 
122 MINE-VENTILATION. 
 
 though this velocity may be increased for short dis- 
 tances to 20 feet per second. We find it sometimes 
 higher than this, but always at a large expenditure of 
 power. 
 
 Keep Airways Clean. — The airways leading to the 
 workings of a mine should, of all places in the pit, 
 be kept clean and pure. Mules should not be allowed 
 in them at all ; and miners, for their own sake, should 
 abstain from any nuisance in them. This should be an 
 imperative rule of every pit, and its enforcement should 
 be insisted upon. 
 
 Air Required per Minute per Man. — The fixing of 
 the amount of air which it is necessary to furnish per 
 minute for each man and for each mule is in many 
 respects wholly arbitrary, because the conditions are 
 different in almost every pit, and because the amount 
 of air actually vitiated by the breathing of the men and 
 animals is small in comparison with the amount ren- 
 dered obnoxious from other causes. Nevertheless, 
 experience has demonstrated and the mining laws of 
 most states and countries now provide for the mainte- 
 nance of a definite amount of air, which most authori- 
 ties agree should not fall short of 100 cubic feet per 
 minute for each man and 500 or 600 cubic feet per minute 
 for each mule. But even this law must be modified in 
 mining practice ; as, for example, in the working of a 
 thick, fiery seam of coal the above amounts would not 
 be sufificient in the large airways to carry off the accu- 
 mulating gases; while, on the other hand, in many 
 thin seams, and also in small, non-fiery mines, the above 
 amounts prove much too large. In fiery mines espe- 
 cially, the velocity of the air-current is an essential 
 factor, and hence the required amount of air should be 
 
CARE OF MINE, AS ASSISTING VENTILATION. 123 
 
 taken in connection with the size of the airways in all 
 such cases, to insure the necessary velocity. 
 
 Room-stoppings. — Another important point is the 
 stopping up of old or abandoned rooms. This should 
 always be done when the gob has a tendency to fire ; 
 as is the case when the coal slack has been mixed with 
 the refuse. If the stoppings are built at all they should 
 be well built ; for their object is to prevent the air 
 from drawing through such works and maintaining 
 slow combustion in them ; this can only be done by 
 making such stoppings practically air-tight. A poor 
 stopping is, in many instances, worse than no stopping 
 at all. 
 
 Entry-stoppings. — Entry-stoppings are even more 
 important than room-stoppings; because upon their 
 perfect construction depends the circulation of the 
 entire pit ; their leaking permits a constant loss of air 
 into the return, so that the full amount never reaches 
 the face of the workings where it is needed. These 
 stoppings should be built double ; i.e., two walls should 
 be built a foot or so apart and the space between them 
 filled with sand or fine dust from the roads. This is 
 work which should not be slighted ; it should be left in 
 the hands of men that can be trusted. 
 
 Break-throughs. — Small or contracted break- 
 throughs exert an untold influence upon the circulation 
 of a mine. The area of any break-through between 
 entries should not be less than the area of either of the 
 entries. It will often be necessary for a pit boss to see 
 that his orders in this respect are carried out, and com- 
 pel entry-men to widen all narrow openings. It is a 
 common practice in most mines for entry-men to store 
 their tools in the last break-through, where the air- 
 
124 MINE-VENTILATION. 
 
 current is passing and where every inch of area should 
 be available, instead of carrying them back to the next 
 break-through, which has been stopped, but still affords 
 ample room for the storage of tools. This practice 
 should be prohibited, as it is an imposition upon all the 
 men located upon that air, and an absolute loss to the 
 company, making them furnish more power to obtain 
 the same amount of air. 
 
 Double Doors. — When doors are in use upon the 
 main roadway and the roadway at any point taps or 
 opens into the main air-course, such point should 
 always be protected by the use of double doors ; i.e., 
 two doors far enough apart that they will not be both 
 open at the same time. This will prevent the tempo- 
 rary stoppage of the circulation of the pit, and is very 
 essential in many instances. 
 
 Overcasts. ^ — Every good pit foreman will put in 
 overcasts on the main roadways wherever the develop- 
 rhent of the cross-entries warrants so doing. They may 
 seem to be expensive, but this initial expense is more 
 than repaid by the saving in current expenses for trap- 
 pers, to say nothing of the avoidance of delays to 
 drivers, if trappers are not employed. The overcast 
 will always yield a more steady current and avoid the 
 annoyance to the miners of having their air cut off by 
 some careless or indifferent man setting the door open 
 and leaving it so. Did mine managers realize for a 
 moment how much of valuable time is lost to the com- 
 pany from this source, they would permit nothing 
 other than an overcast at these main points. Men 
 cannot and do not work when their supply of air is cut 
 off. 
 
 Undercasts. — In some rare instances we find under- 
 
CARE OF MINE, AS ASSISTING VENTILATION. 1 25 
 
 casts preferred to overcasts ; but we believe that expe- 
 rience advocates the adoption of the overcast. The 
 author has seen the airway coming from an undercast 
 so filled with fine dust as to be decidedly unpleasant 
 and hurtful to the lungs; the dust arising largely from 
 the roadway passing over the framing, making it practi- 
 cally impossible also to prevent leaking and loss of air. 
 
 Angles in Airways. — It will be necessary to draw 
 but a passing attention to the avoidance of all sharp 
 angles in airways generally, but especially in the main 
 air-courses, where such material obstructions add largely 
 to the resistance of the pit. 
 
 Stables. — The arrangement of the mine stables is an 
 important point with respect to good ventilation, as 
 too often they are located upon the air-course in such 
 a manner as to taint the air passing into the pit. This 
 is not good judgment, nor is it good policy to place 
 the stables upon the return of the air, without giving 
 to the mules a fresh supply of air. The mule needs 
 pure air and plenty of it for his wholesome, as well as 
 man ; treat him well, if you expect him to work well. 
 It is advisable to have the mule stabled as near to his 
 
 Hauling Rood 
 
 Inside Stable 
 Fig. XV. 
 
 work as possible ; it is also advisable to have his stable 
 located at no great di.stance from the bottom of a shaft, 
 where he may be rescued in case of accident, and 
 
126 
 
 MINE-VENTILATKJN. 
 
 by means of which his fodder may be sent down and 
 the refuse of the stables hoisted. As far as possible, 
 let these requisites be taken into consideration in the 
 location of the stable; but, in any event, let the egress 
 from the stable be upon the return of the air, and ven- 
 tilate by means of a small split direct from the air. 
 We would suggest a location similar to that in the 
 accompanying figure. The entry-pillar may be widened 
 at any point where it is advisable to place the stable ; 
 or it may be located on the other side of the entry, as 
 shown in Fig. XVI. In this latter arrangement the 
 
 
 
 Air Course 
 
 Air-lealc 
 
 >. 
 
 
 
 -y ^ 
 
 H 
 
 H 
 
 H H 
 
 ] 
 
 i N 
 
 
 
 
 
 
 
 
 Bauling Road 
 
 
 tl 1 
 
 ~ Curtain 
 
 
 1 1 1 1 1 lS\Ua]b]He\ 
 
 1 l1 
 
 Air-box, 
 overcast 
 
 
 Fig. XVI. 
 
 
 
 ventilation of the stable should be secured by means 
 of a small split, carried from the air-course by an over- 
 cast box. By this means the mules will not be com- 
 pelled to breathe the outgoing powder-smoke and gas 
 from the workings ; they will work better and live 
 longer. On no account should the stable be allowed 
 upon the air-course. The main stable located at the 
 shaft-bottom maybe arranged as shown in Fig. XII. 
 
APPENDIX. 
 
 TABLES AND PROBLEMS. 
 
128 
 
 APPENDIX. 
 
 TABLE I. 
 
 COMPARISON OF THE FAHRENHEIT AND CENTIGRADE 
 SCALES. 
 
 Fahr. 
 
 Cent. 
 
 Fahr. 
 
 Cent. 
 
 Fahr. 
 
 Cent. 
 
 Fahr. 
 
 Cent. 
 
 -30 
 
 -34.4 
 
 70 
 
 21. 1 
 
 180 
 
 82.2 
 
 280 
 
 137-8 
 
 — 20 
 
 -28.8 
 
 80 
 
 26.6 
 
 I go 
 
 87.8 
 
 290 
 
 143-3 
 
 — 10 
 
 -23.3 
 
 90 
 
 32.2 
 
 200 
 
 93-3 
 
 300 
 
 148.9 
 
 
 
 -17-7 
 
 100 
 
 37.7 
 
 210 
 
 98.9 
 
 310 
 
 154-4 
 
 10 
 
 — 12.2 
 
 no 
 
 43-3 
 
 212 
 
 lOO.O 
 
 320 
 
 160.0 
 
 20 
 
 -6.6 
 
 120 
 
 48.9 
 
 220 
 
 104.4 
 
 330 
 
 165.5 
 
 30 
 
 — I.I 
 
 130 
 
 54-4 
 
 230 
 
 IIO.O 
 
 340 
 
 171.1 
 
 32 
 
 0.0 
 
 140 
 
 60.0 
 
 240 
 
 II5-5 
 
 350 
 
 176.7 
 
 40 
 
 44 
 
 150 
 
 65.5 
 
 250 
 
 121. 1 
 
 360 
 
 182.2 
 
 50 
 
 lO.O 
 
 160 
 
 71. 1 
 
 260 
 
 126.7 
 
 
 
 60 
 
 15-5 
 
 170 
 
 76.6 
 
 270 
 
 132.2 
 
 
 
TABLES AND PROBLEMS. 
 
 129 
 
 < 
 
 H 
 
 < 
 U 
 
 cu 
 
 b 
 O 
 
 O 
 
 H 
 O 
 
 oa 
 
 Id 
 H 
 
 < 
 
 Z 
 
 w 
 oi 
 Pi 
 
 U 
 
 u 
 H 
 O 
 
 z 
 
 o 
 
 p 
 
 Q 
 
 z 
 o 
 u 
 
 Pounds of Bit. 
 Coal burned 
 
 5j 
 
 (0.33945 + 
 
 0.05760(4) 
 
 60 Q 
 
 h-tt 
 
 per hour. 
 
 
 
 
 459 + '3 14,000 
 
 
 
 OJ 
 
 0)_ 
 
 
 1 
 
 
 1 
 
 + 
 
 1 
 
 + 
 
 
 
 
 
 o^ 
 
 
 c^ 
 
 
 ^ 
 
 
 
 
 •*.i 
 
 in 
 
 
 wt 
 
 < 
 
 
 
 •* 
 
 
 ^ 
 
 
 ■** 
 
 
 
 
 
 ^ 
 
 
 'a 
 
 1 
 
 1 
 
 1 
 
 1 
 
 lO 
 
 + 
 a- 
 
 "ri 
 
 
 05 
 
 2. 
 
 
 a 
 
 
 So- 
 
 v5' 
 
 •^ 
 
 V 
 
 
 00 
 
 
 
 r^ 
 
 JS 
 
 
 ■* 
 
 a^ 
 
 
 
 H 
 
 
 w 
 
 
 
 CO 
 
 
 
 d 
 
 6 
 
 6 
 
 
 
 00 
 
 m 
 
 m 
 
 Sp. Heat or 
 
 « 
 
 en 
 
 vO 
 
 
 00 
 
 Thermal Units. 
 
 
 C4 
 
 M 
 
 T 
 
 
 
 6 
 
 6 
 
 d 
 
 
 
 o* 
 
 O) 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 hS 
 
 
 ^ 
 
 
 
 ^r^ 
 
 
 ■0- 
 1 
 
 ^ 
 
 1 
 
 "t? 
 
 O) 
 
 cS 
 
 ^ 
 
 1 
 
 + 
 
 1 
 
 + 
 
 
 „ 
 
 
 
 S 
 
 
 
 N 
 
 
 M 
 
 
 
 IT) 
 
 0- 
 
 d 
 
 
 
 in 
 
 w 
 
 CO 
 
 d 
 
 + 
 
 in 
 
 •* 
 
 Symbols. 
 
 
 z 
 
 d 
 
 
 
 Constituents. 
 
 
 
 c5'5 
 
 ■2 »-■ 
 
 &> 1 
 
 
 
 z 
 
 
 u 
 
 CO 
 
 < 
 
 1 
 
130 
 
 APPENDIX. 
 
 TABLE III. 
 
 TENSION OF AQUEOUS VAPOR, 
 
 AT VARIOUS TEMPERATURES, EXPRESSED IN INCHES OF BAROMETER. 
 
 Deg. 
 
 Tension, 
 
 Deg. 
 
 Tension, 
 
 Deg. 
 
 Tension, 
 
 Deg. 
 
 Tension, 
 
 Fahr. 
 
 inches. 
 
 Fahr. 
 
 inches. 
 
 Fahr. 
 
 inches. 
 
 Fahr. 
 
 inches. 
 
 -30 
 
 O.OIO 
 
 45 
 
 0.316 
 
 65 
 
 0.616 
 
 105 
 
 2.18 
 
 — 20 
 
 0.016 
 
 46 
 
 0.328 
 
 66 
 
 0.635 
 
 110 
 
 2.53 
 
 — 10 
 
 0.026 
 
 47 
 
 0.339 
 
 67 
 
 665 
 
 115 
 
 2.92 
 
 
 
 0.042 
 
 48 
 
 0.351 
 
 68 
 
 0.676 
 
 120 
 
 3-33 
 
 10 
 
 0.070 
 
 49 
 
 0.363 
 
 69 
 
 0.698 
 
 125 
 
 3-75 
 
 20 
 
 O.IIO 
 
 50 
 
 0.375 
 
 70 
 
 0.721 
 
 130 
 
 4-34 
 
 30 
 
 0. 180 
 
 51 
 
 0.388 
 
 71 
 
 0.745 
 
 135 
 
 5.00 
 
 32 
 
 0.200 
 
 52 
 
 0.401 
 
 72 
 
 0.770 
 
 140 
 
 5-74 
 
 33 
 
 0.207 
 
 53 
 
 0.415 
 
 73 
 
 0.796 
 
 145 
 
 6.53 
 
 34 
 
 0.214 
 
 54 
 
 0.429 
 
 74 
 
 0.823 
 
 150 
 
 7.42 
 
 35 
 
 0.221 
 
 55 
 
 0.443 
 
 75 
 
 0.851 
 
 160 
 
 9.46 
 
 36 
 
 0.229 
 
 56 
 
 0.458 
 
 76 
 
 U.880 
 
 170 
 
 12.13 
 
 37 
 
 0.237 
 
 57 
 
 0.474 
 
 77 
 
 0.910 
 
 180 
 
 15-15 
 
 38 
 
 0.245 
 
 58 
 
 0.490 
 
 78 
 
 0.940 
 
 190 
 
 19.00 
 
 39 
 
 0.254 
 
 59 
 
 0.507 
 
 79 
 
 0.971 
 
 200 
 
 23.64 
 
 40 
 
 0.263 
 
 60 
 
 0.524 
 
 80 
 
 1. 000 
 
 210 
 
 28.84 
 
 41 
 
 U.273 
 
 61 
 
 0.542 
 
 85 
 
 1. 1 70 
 
 212 
 
 30.00 
 
 42 
 
 0.283 
 
 62 
 
 0.560 
 
 90 
 
 1.36 
 
 
 
 43 
 
 0.294 
 
 63 
 
 0.578 
 
 95 
 
 X.58 
 
 
 
 44 
 
 0.305 
 
 64 
 
 0.597 
 
 100 
 
 1.86 
 
 
 
TABLES AND PROBLEMS. 13I 
 
 TABLE IV. 
 SPECIFIC HEATS OF VARIOUS GASES AND VAPORS, 
 
 REFERRED TO WATER AS UNITY. 
 Gas or Vapor. Specific Heat. 
 
 Air. 0.2374 
 
 Oxygen 0.2175 
 
 N itrogen o. 2438 
 
 Hydrogen 3.4090 
 
 Carbon ic-oxide gas o. 2450 
 
 Carbonic-acid gas 0.2163 
 
 Ammonia gas 0.5083 
 
 Aqueous vapor 0.4805 
 
 TABLE V. 
 SPECIFIC GRAVITIES OF VARIOUS GASES AND VAPORS, 
 
 REFERRED TO AIR AS UNITY. 
 Gas or Vapor. Specific Gravity. 
 
 Air 1. 0000 
 
 Oxygen 1.1057 
 
 Nitrogen 0.9713 
 
 Hydrogen 0.0693 
 
 Carbonic-oxide gas 0.9670 
 
 Carbonic-acid gas 1.5291 
 
 Ammonia gas 0.5367 
 
 Marsii gas o. 5 590 
 
 Sulphuretted hydrogen I.igi2 
 
 Aqueous vapor 0.6235 
 
132 
 
 APPENDIX. 
 
 TABLE VI. 
 
 EFFECT OF SPLITTING THE AIR-CURRENT. 
 
 Note. — Size of all airways is 6 X 8J ; making the perimeter 28 
 feet, and the area of each individual split 50 square feet. 
 
 Pi 2; 
 
 
 1 
 
 cnt^mi-HO r^u^i-i-c C»yD wco cno W 00 en m w eo cmo « oo co 
 
 
 
 oON-l-coON'-l-coO'OOOcoOO'OooOOinNcoO'OcoO 
 
 r-r^mi-* r-r^ini-i i>cni^cnomr^cnOincnij-)0 r^r^cnOMn 
 
 r^ocTrCinoico r^incio N o"r^inofcrr^in'^w~Ooo"w''o'r^in 
 
 r^oo r^incnoo r^u-)cnM cnwcovo cnMooo Oo^cT-oo cnwcoio 
 
 cn^^u^cntD^^u^cOM cnwoovO cni-icoio ►"< mo^cocnwoovo 
 
 Mcf M'wcn«cncn^fcicocnrfwMH*MN<T)cnr? 
 
 
 0000 
 0000 
 m <ri m in ■^ m 
 
 6| 
 
 s §;^^ s ?n §?- s^?^^ s;^^^ ? s g> ?<? s g; §.^^ 
 
 Owinnr^M M ^cowmr-o^'-' ■^tmr^oD « cncn-^w cotj-ui 
 
 4-> U 
 
 so- 
 
 SS2S?>'S.S2g5 2qi^SS2ggSS3^<?SRS.2 
 
 "^S?,S g'^^^^S ^^^5 5??>^^K ^2^S>^g ^?, 
 
 il 
 
 a a 
 
 0. 
 
 aH^HH8HH5=Hsl^aH?ssgs 
 
 €s&5§sS?sHSHH^sll'HH>pi 
 
 ^ bo 
 a 
 
 |888888§§8888888|88||8|8|8 
 
 Quantity, No. of 
 eft. p. m.jSplits. 
 
 M « cn ■* m 
 
 8 i i i § 8 
 
 S> g K 8 8 9; 
 
 "is 
 
 M « .^ * u,o .-.CO c^ M « CO 2- u,o r^co o^ - « cj ^ jno 
 
TABLES AND PROBLEMS. 
 
 133 
 
 TABLE VII. 
 
 HORSE-POWER OF DIFFERENT FANS AT VARIOUS 
 SPEEDS. 
 
 Note. — Dry air; temperature 60° F. Barometer, 30". Efficiency, 
 90^ at 50 revolutions per minute. 
 
 
 
 
 
 
 Horse-power 
 
 
 Diam. 
 
 Inner 
 Rad. 
 
 Width of 
 Blade. 
 
 Area of 
 Eyes. 
 
 
 
 
 £t. 
 
 
 
 
 
 
 
 
 50 rev. 
 
 100 rev. 
 
 i2g.i rev. 
 
 10 
 
 2' 6" 
 
 2'o" 
 
 30 sq. ft. 
 
 2.608 
 
 27.814 
 
 42.919 
 
 
 
 2 6 
 
 
 3- 259 
 
 34.768 
 
 53.649 
 
 
 
 3 
 
 
 3-9II 
 
 41.721 
 
 64-379 
 
 
 
 3 6 
 
 
 4563 
 
 48.675 
 
 75-109 
 
 
 
 4 
 
 
 5.215 
 
 55.629 
 
 85.839 
 
 12 
 
 3 
 
 2 6 
 
 50 sq. ft. 
 
 6.759 
 
 72.094 
 
 111.247 
 
 
 
 3 
 
 
 8. Ill 
 
 86.513 
 
 133.496 
 
 
 
 3 6 
 
 
 9.462 
 
 100.932 
 
 155.746 
 
 
 
 4 
 
 
 10.814 
 
 115.351 
 
 177-995 
 
 14 
 
 4 
 
 3 
 
 50 sq. ft. 
 
 14.461 
 
 154.247 
 
 238.014 
 
 
 
 3 6 
 
 
 16.871 
 
 179-954 
 
 277.683 
 
 
 
 4 
 
 
 19.281 
 
 205.662 
 
 317.353 
 
 
 
 4 6 
 
 
 2l.6gi 
 
 231.370 
 
 357.023 
 
 16 
 
 4 6 
 
 3 
 
 125 sq. ft. 
 
 24.821 
 
 264.758 
 
 408.542 
 
 
 
 3 6 
 
 
 28.958 
 
 30B.885 
 
 476.633 
 
 
 
 4 
 
 
 33095 
 
 353-011 
 
 544.724 
 
 
 
 4 6 
 
 
 37.232 
 
 397.138 
 
 612.814 
 
 
 
 5 
 
 
 41.369 
 
 441.263 
 
 680.905 
 
 18 
 
 5 
 
 3 6 
 
 125 sq. ft. 
 
 46.594 
 
 497.000 
 
 766.907 
 
 
 
 4 
 
 
 53-250 
 
 568.000 
 
 876.466 
 
 
 
 4 6 
 
 
 59906 
 
 639.000 
 
 986.250 
 
 
 
 5 
 
 
 66.562 
 
 710.000 
 
 1095.584 
 
 20 
 
 5 6 
 
 4 
 
 175 sq. ft. 
 
 81.438 
 
 868.674 
 
 1340.432 
 
 
 
 5 
 
 
 101.798 
 
 1085.843 
 
 1675.541 
 
 
 
 6 
 
 
 122.157 
 
 1303.012 
 
 2010.648 
 
134 
 
 APPENDIX. 
 
 TABLE 
 
 CHANGE IN TEMPERATURE, BAROM- 
 
 SHOWING THE EFFECT UPON THE YIELD OF A FAN RUNNING AT 
 
 Note. — The conditions are assumed to be such as to yield 80,000 
 
 
 V 
 
 Temperature (Fahr.). 
 
 
 Ka 
 
 
 
 
 
 
 
 
 PQ 
 
 -30 
 
 —20 
 
 —10 
 
 
 
 10 
 
 20 
 
 
 
 
 (cubic 
 
 feet 
 
 per mi 
 
 Dute.) 
 
 
 
 29" 
 
 80902 
 
 80284 
 
 79684 
 
 79IOI 
 
 78534 
 
 77984 
 
 Dry. 
 
 30" 
 
 81822 
 
 81197 
 
 80590 
 
 80000 
 
 79427 
 
 78870 
 
 
 31" 
 
 82721 
 
 82089 
 
 81476 
 
 80879 
 
 80300 
 
 79737 
 
 
 29' 
 
 80900 
 
 8028 r 
 
 79679 
 
 79093 
 
 78521 
 
 77965 
 
 50^ Saturation. 
 
 30" 
 
 81820 
 
 81194 
 
 80585 
 
 79993 
 
 79415 
 
 78852 
 
 
 31" 
 
 82719 
 
 82086 
 
 81471 
 
 80873 
 
 80289 
 
 79720 
 
 
 29" 
 
 80899 
 
 80279 
 
 79675 
 
 79086 
 
 78509 
 
 77946 
 
 100^ Saturation. 
 
 30" 
 
 81819 
 
 81192 
 
 80581 
 
 79986 
 
 79404 
 
 78834 
 
 
 31" 
 
 82718 
 
 82083 
 
 81467 
 
 80867 
 
 80279 
 
 79703 
 
TABLES AND PROBLEMS. 
 
 135 
 
 No. VIII. 
 
 ETER. AND HYGROMETRIC STATE. 
 
 A CONSTANT SPEED AND DISCHARGING INTO THE SAME MINE. 
 
 cubic feet of dry air at a temperature of 0° F. and a barometer of 30". 
 
 Temperature (Fahr.) 
 
 i. 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 an 
 
 a 
 
 
 
 (cubic 
 
 feet per 
 
 minute.) 
 
 
 
 
 77449 
 
 76928 
 
 76421 
 
 75927 
 
 75445 
 
 74976 
 
 74518 
 
 29" 
 
 7S329 
 
 77803 
 
 77290 
 
 76790 
 
 76303 
 
 75828 
 
 75365 
 
 30" 
 
 79190 
 
 78658 
 
 78139 
 
 77634 
 
 77142 
 
 76661 
 
 76193 
 
 31" 
 
 77419 
 
 76883 
 
 76358 
 
 75840 
 
 75328 
 
 74816 
 
 74303 
 
 29' 
 
 78300 
 
 77760 
 
 77230 
 
 76706 
 
 76189 
 
 75672 
 
 75155 
 
 30" 
 
 79162 
 
 78617 
 
 78081 
 
 77552 
 
 77031 
 
 76509 
 
 75987 
 
 31" 
 
 77389 
 
 76839 
 
 76296 
 
 75755 
 
 75214 
 
 74661 
 
 74096 
 
 29- 
 
 78271 
 
 77718 
 
 77170 
 
 76624 
 
 76078 
 
 75520 
 
 74953 
 
 30" 
 
 79134 
 
 78577 
 
 78023 
 
 77472 
 
 76923 
 
 76361 
 
 75789 
 
 31" 
 
136 
 
 APPENDIX. 
 
 TABLE IX. 
 
 CHANGE IN TEMPERATURE, BAROMETER, AND. 
 HYGROMETRIC STATE. 
 
 SHOWING THE EFFECT UPON THE SPEED OF A FAN. 
 
 Note. — The power applied remaining the same, any change in 
 atmospheric conditions will produce a corresponding change in the 
 speed of the fan, and the quantity of air produced will remain practi- 
 cally unchanged. 
 
 The following table is figured from a base of 100 revolutions 
 per minute, at a temperature of 60° F. and a barometer of 30", the 
 air being dry. The fan is a 12-foot fan, 30" wide, giving an effi- 
 ciency of goi? at a speed of 50 revolutions per minute, being the same 
 fan as the i2-foot fan mentioned in Table X; it is also found recorded 
 in Table VII. 
 
 Temperature, 
 Fahr. 
 
 Barometer, 
 inches. 
 
 Hygrometric 
 State. 
 
 Revolutions 
 per minute. 
 
 Horse-power. 
 
 -30° 
 
 28 
 30 
 30 
 
 Dry. 
 Saturated. 
 
 95-7 
 93-4 
 93-4 
 
 72.094 
 
 60° 
 
 28 
 30 
 30 
 31 
 
 Dry. 
 Saturated. 
 
 102.7 
 
 100. 
 
 100.3 
 
 99 -o 
 
 
 1 00° 
 
 28 
 3" 
 30 
 
 Dry. 
 Saturated. 
 
 105.8 
 102.9 
 103.8 
 
 
TABLES AND PROBLEMS. 
 
 137 
 
 TABLE X. 
 
 SPEED AND HORSE-POWER OF DIFFERENT 
 DIFFERENT MINES. 
 
 FANS AT 
 
 Note. — Mine : Size of all airways, 6 X 8J. 
 
 Motor : 12-ft. fan, 30 in. wide, 6-ft.eye; area of the two eyes, 
 
 50 sq. ft. ; efficiency, 90^ at 50 revs, per min. ; max. 
 
 effect, speed, 129.1 revs, per min. ; limit of power, 
 
 111.247 h.p. 
 Conditions : Temp. 60° F., barom., 30 in., air dry. 
 
 Mine 
 No. 
 
 Quantity, 
 cu. ft. p. m. 
 
 No. of 
 Splits. 
 
 Length, 
 Ft. 
 
 Mine- 
 Potential. 
 
 Revolu- 
 tions p. m. 
 
 Horse- 
 power. 
 
 2 
 
 25,000 
 
 1 
 2 
 
 5,000 
 
 342.532 
 685.064 
 
 58.0 
 33.7 
 
 11.782 
 1.473 
 
 
 50,000 
 
 1 
 2 
 
 '•' 
 
 342.532 
 685.064 
 
 IIZ.O 
 
 58.0 
 
 94-253 
 11.782 
 
 3 
 
 25,000 
 
 1 
 2 
 
 10,000 
 
 271.867 
 543-734 
 
 70.3 
 
 40.2 
 
 23-563 
 2.945 
 
 50,000 
 
 1 
 
 2 
 
 it 
 
 271.867 
 543-734 
 
 70.3 
 
 188.507 
 23-563 
 
 
 25,000 
 
 1 
 2 
 
 20,000 
 
 Z15-781 
 431-563 
 
 86.5 
 
 48.2 
 
 47.127 
 5.891 
 
 4 
 
 50,000 
 
 1 
 2 
 3 
 
 
 215.781 
 431.563 
 647.344 
 
 60.8 
 
 377.014 
 47.127 
 13.963 
 
138 
 
 APPENDIX. 
 
 TABLE X. {Continued^) 
 
 SPEED AND HORSE-POWER OF DIFFERENT FANS AT 
 DIFFERENT MINES. 
 
 Note. — Mine : Same as before. 
 
 Motor : i6-ft. fan, 36 in. wide, g-ft. eye; area of the two eyes, 
 
 125 sq. ft. ; efficiency, 90^ at 50 revs, per min. ; max. 
 
 effect, speed, 129.1 revs, per min. ; limit of power, 
 
 408.54 h.p. 
 Conditions : Same as before. 
 
 Mine 
 No. 
 
 Quantity, 
 cu. ft. p.m. 
 
 No. of 
 Splits. 
 
 Length, 
 
 Mine- 
 Potential. 
 
 Revolu- 
 tions p. m. 
 
 Horse- 
 power. 
 
 s 
 
 50,000 
 100,000 
 
 150,000 
 
 2 
 3 
 
 2 
 
 3 
 
 4 
 
 4 
 5 
 6 
 
 30,000 
 
 it 
 ti 
 
 tt 
 
 377-004 
 565-507 
 
 377.004 
 565 . 507 
 754.009 
 
 754.009 
 
 942.511 
 
 I131.013 
 
 66.4 
 47-8 
 
 "85.6 
 66.4 
 
 96-3 
 77-7 
 66.4 
 
 70.690 
 20.945 
 
 565.521 
 
 167.562 
 
 70.690 
 
 238.575 
 
 122.152 
 
 70.690 
 
 6 
 
 75,000 
 
 100,000 
 150,000 
 
 2 
 3 
 4 
 5 
 
 2 
 
 4 
 6 
 
 4 
 6 
 8 
 
 40,000 
 tt 
 
 11 
 
 342.532 
 513-798 
 685.064 
 856.330 
 
 342.532 
 
 685.064 
 
 1027.595 
 
 685.064 
 1027.595 
 1370.128 
 
 107.7 
 72.0 
 56.7 
 47-5 
 
 72.0 
 51.6 
 
 107.7 
 72.0 
 56.7 
 
 318.100 
 94.253 
 39.762 
 20.359 
 
 754.021 
 94.253 
 27.927 
 
 318.100 
 94-253 
 39.762 
 
TABLES AND PROBLEMS. 
 
 139 
 
 TABLE X. {Concluded) 
 
 SPEED AND HORSE-POWER OF DIFFERENT FANS AT 
 DIFFERENT MINES. 
 
 Note. — Mine : Same as before- 
 Motor : 20-ft. fan, 48 in- wide, ii-ft. eye; area of the two eyes, 
 
 (net), 125 sq. ft. ; efficiency, 90^ at 50 revs, per min. ; 
 
 max. effect, speed, 129.1 revs, per min. ; limit of power, 
 
 1340.432 h.p. 
 Conditions : Same as before. 
 
 Mine 
 No. 
 
 Quantity, 
 cu. ft. p. m. 
 
 No. of 
 Splits. 
 
 Length, 
 Ft. 
 
 Mine- 
 Potential. 
 
 Revolu- 
 tions p. m. 
 
 Horse- 
 power. 
 
 7 
 
 100,000 
 it 
 
 150,000 
 200,000 
 
 2 
 
 4 
 6 
 
 4 
 6 
 8 
 
 4 
 6 
 8 
 
 50,000 
 
 317-978 
 
 ■ 635.956 
 
 953-934 
 
 635-956 
 
 953-934 
 
 1271.912 
 
 635-956 
 
 953-934 
 
 1271-912 
 
 103.2 
 55-2 
 40 -1 
 
 77-6 
 55-2 
 43-9 
 
 103.2 
 70.0 
 55.2 
 
 942.530 
 
 117.817 
 
 34-909 
 
 397-629 
 
 117. 817 
 
 49.704 
 
 942.530 
 279.268 
 117.817 
 
 8 
 
 100,000 
 
 150,000 
 
 200,000 
 It 
 
 2 
 
 4 
 6 
 
 4 
 6 
 8 
 
 4 
 6 
 
 8 
 
 60,000 
 
 299.229 
 598.458 
 897.687 
 
 598-458 
 
 897-687 
 
 1196.916 
 
 598-458 
 
 897-687 
 
 1196.916 
 
 III. 8 
 58.0 
 42.0 
 
 81.9 
 58.0 
 46.1 
 
 III. 8 
 73-8 
 58-0 
 
 1131.029 
 
 141.379 
 41.890 
 
 477-152 
 
 141.379 
 
 59.644 
 
 1131.029 
 335.120 
 141-379 
 
NOTES 
 
 EXPLANATORY OF THE TABLES. 
 
 Tables I, III, IV and V need no explanation. Table II is 
 fully explained in Chapter VII. 
 
 Table VI. — From an inspection of Table VI we see that by 
 the application of the same power the quantity of air in cir- 
 culation is increased in the same proportion as we multiply the 
 number of splits. Thus, compare lines 5, 9, 11, 15 and 23; 
 these all represent Mine No. 5, referred to in the early part of 
 Chapter IX; but employing successively one, two, three, etc., 
 splits. (The term " one s;plit," as hereused, refers to a single 
 undivided current.) We observe the power in each instance is 
 70.690 h.p., while the quantities in circulation hold the same 
 proportion to each other as do the number of splits employed. 
 
 Again, for the production of the same quantity of air per min- 
 ute in the same mine, the powers required are inversely pro- 
 portionate to the cubes of the number of splits employed. 
 Thus, compare lines 15 and 19, or lines 16 and 20, etc., of the 
 same table. 
 
 By further inspection of the table we see that the application 
 of the same power to different mines, or to the same mine em- 
 ploying a different number of splits (which is practically a dif- 
 ferent mine, as far as the circulation is concerned), gives a dif- 
 ferent water-gauge, according to the quantities of air yielded 
 in each respective case. Thus in the table, line 5 represents a 
 power of 70.690 h.p. applied to Mine No. 5, producing a single 
 current of 25,000 cubic feet of air per minute, moving under a 
 water-gauge of 17.94 inches : in this case, the power is applied 
 to a current compelled to move against a mine-potential of 
 188.502. Referring now to line 23, we find that by dividing the 
 circulating current into six separate splits, thereby increasing 
 the mine-potential to 1 131. 013, the same power applied will 
 yield a current of 1 50,000 cubic feet of air per minute and a 
 
 140 
 
NOTES EXPLANATORY OF THE TABLES. I4I 
 
 water-gauge of only 2.99 inches. Hence, we see the fallacy of 
 taking the yield alone, or the dynamic pressure (water-gauge) 
 alone, as expressive of the power of a fan. To say that a fan 
 will yield a certain quantity of air per minute, running at a cer- 
 tain fixed speed, is not significant ; nor yet to say that it will 
 produce a certain water-gauge, running at such speed. We 
 must know the power developed by the fan at that speed, 
 which can only be expressed by the union of both these fac- 
 tors. The power of a fan, or the work it is capable of perform- 
 ing, indicates its value as a motor. 
 
 Again, we see from the table that the same power applied 
 will produce, under the same atmospheric conditions, quanti- 
 ties proportionate to the respective mine-potentials, or, the 
 mine-potential remaining the same, the quantities will be pro- 
 portionate to the cube roots of the respective powers. 
 
 Table VIL — This table shows the horse-power developed 
 by the fan running at three different speeds, the last being the 
 maximum effective speed ; and consequently the powers given 
 in that column will be the limit of power of such fan. In all 
 of the tables relative to fans, we have assumed a temperature of 
 60° F., a barometer of 30 inches, and a dry state of the atmos- 
 phere ; we have also assumed all of the fans to show an efficiency 
 of 90^ at a speed of 50 revolutions per minute, which efficiency 
 would give a maximum effective speed of 129. i revolutions per 
 minute. Any one particular fan may have a greater or less 
 efficiency than this; and as a consequence, its maximum effect- 
 ive speed may be above or below this, as the case may be, as 
 also its limit of power. 
 
 An important showing of Table VII is the effect of the 
 change of the width of the fan-blade upon the power of the 
 fan — the power varying in the same proportion as the width of 
 blade varies. But, the proportionment of the fan and the 
 adaptability of the different dimensions of the same to work of 
 different kinds have been carefully considered, under the proper 
 heads, in Chapter VIII and will not be repeated here. 
 
 Table VIII. — Table VIII is the counterpart of the last preced- 
 ing table, and shows what would be the effect upon the quan- 
 tity of air produced, due to change of temperature, barometer, 
 or hygrometric state, were the speed of the fan to be maintained 
 
142 APPENDIX. 
 
 at a uniform rate. The table presupposes that the power ap- 
 plied is changed in such a manner as to maintain a constant 
 speed of the fan ; and is useful for showing the relative yields 
 of a fan under varying atmospheric conditions. For example, 
 if our fan is yielding a current of, say, 80,000 cubic feet of air per 
 mmute, at a temperature of 0° F., and a barometric pressure of 
 30 inches, the air being dry, the same speed of that fan, when 
 the temperature has risen to 90° F. and the barometer stands 
 at 29 inches, the air having become saturated with moisture, 
 will only yield a current of 74,096 cubic feet per minute. 
 
 It will be seen from the table also that tlie effect of satura- 
 tion upon the yield is very much greater at the higher temper- 
 atures than at the lower, amounting at go° F. to 0.55^ of the 
 entire yield, while at 0° F., it is but 0.02^. 
 
 The effect of a change of, say, ten degrees in temperature, on 
 the other hand, is less at the higher temperatures than at the 
 lower, being only 0.61^ of the yield, in rising from 80° F. to 
 90° F. ; while in rising from 0° F. to 10° F. the effect is 0.725^ 
 of the yield. This effect of a rise in temperature, at any point 
 of the scale, is the same whether the air is dry or saturated 
 with moisture. 
 
 The effect of a rise or fall of, say, one inch of barometric 
 height upon the yield of a fan is constant, between the same 
 points of the barometric scale, for all temperatures and whether 
 the air is dry or saturated with moisture. This effect is 1.082^ 
 of the entire yield when the barometer falls from 31 to 30 
 inches, and 1.127^ when the fall of the barometer is from 30 to 
 29 inches." The percentage increases slightly as we drop in the 
 scale. 
 
 We see from these two last tables that a meteorological 
 change will not produce any appreciable change in the power 
 necessary to circulate a given quantity of air, but will simply 
 vary the speed of the fan. It will take more power to produce 
 a certain speed of the fan in a heavy atmosphere than in alight 
 one. The lesser speed in the heavy atmosphere will produce 
 the same quantity of air per minute and will perform the same 
 work that a greater speed will accomplish in a light atmos- 
 phere, so that we conclude that a heavy atmosphere is a bene- 
 fit to the working of the fan, providing it is not murky or 
 
NOTES EXPLANATORY OF THE TABLES. I43 
 
 f°ggy> so as to largely increase the resistance of passage. On 
 the other hand, the heavy atmosphere may, as we have previ- 
 ously stated, increase to some extent the resistance of the pit, 
 and is a very decided hindrance to the working of the furnace, 
 as the absorption of heat for the same rise of temperature is 
 greatly augmented. 
 
 Table IX. — The effect is here shown of a change in tem- 
 perature, barometric pressure, or hygrometric state upon the 
 speed of a fan operated by the same cylinder pressure or power 
 applied. Our table assumes that the application of a constant 
 power (72.094 h.p.) maintains a uniform speed of fan (100 rev- 
 olutions per minute) when the temperature of the atmosphere 
 is 60° F., barometric pressure 30 inches, and the air dry; and 
 shows that if the temperature were now to rise to 100° F., the 
 barometer at the same time falling to 28 inches, the air still re- 
 maining dry, the speed of the fan, under the same cylinder 
 pressure, would increase to 105.8 revolutions per minute. The 
 saturation of the atmosphere likewise increases the speed of 
 the fan, other conditions remaining unchanged. The power 
 applied remaining the same, the table shows that atmospheric 
 changes produce a corresponding change in the speed of the 
 fan. Atmospheric changes produce a greater effect upon the 
 yield of a furnace than they do upon the yield of a fan, be- 
 cause, in the former case, they affect directly the power of the 
 furnace, which is the power applied to the current ; in the 
 latter case they do not affect the power applied, which is the 
 cylinder pressure of the engine, and is assumed to remain un- 
 changed. If this power applied to the current remains un- 
 changed, the quantity passing will also remain unchanged, 
 although there is an almost inappreciable change in the resist- 
 ance of the mine, which would affect to a small extent the quan- 
 tity of air passing. This effect is so small, however, as not to 
 be represented in our formulas. 
 
 Table X. — This table is for the purpose of showing the com- 
 parative work of three different fans, with respect to their 
 adaptability to different grades of work. The atmospheric 
 conditions are assumed to be the same as those used in former 
 tables. Where the fan is incapable of performing the work of 
 any given mine, dashes have been inserted. We do not mean 
 
144 APPENDIX. 
 
 to intimate for a moment that any one of the fans mentioned 
 is well adapted to all ot the work of which it is here shown to 
 be capable; for example, the 12 ft. fan is evidently not well 
 adapted to circulate a current of 50,000 cubic feet of air per 
 minute through Mine No. 2, in a single split; although it is 
 capable of doing so, if required. It is crowding its speed a lit- 
 tle and the area of its eyes is none too large. The size of fan 
 more suitable for this work would be 42 inches wide and have 
 a 7-foot eye, the outer diameter remaining the same. It is very 
 important that the internal capacity of a fan be proportionate 
 to the quantity of air it is expected to pass, in order that its 
 efficiency may be high. The proportionment of the fan has 
 been thoroughly discussed in Chapter VIII, and a careful 
 study of Table X will serve to illustrate the principles there 
 referred to. Too much attention cannot be given to this part 
 of the subject. A fan not proportioned to its work is like a 
 man staggering under a burden that is too heavy for him ; or 
 like a youth compelled to grapple with a problem that is be- 
 yond him. The result is dissatisfaction, if not complete fail- 
 ure ; and the thumping of the engine, the racking of the frame, 
 and the straining, wearing, and breaking of various parts is evi- 
 dence of the want of adaptation of the machine to the work it 
 is compelled to perform. 
 
 It is worthy of note that the same number of revolutions per 
 minute of any fan, under the same atmospheric conditions, will 
 always develop the same power. 
 
 Conclusion. — The study of the tables should prove of great 
 benefit to the practical mind. We do not doubt that many 
 will be skeptical in regard to some of the results ; but, as these 
 are in accordance with the known and accepted laws of the 
 mechanics of fluids, they should be received or disproven. 
 Many are the difficulties attending the thorough investigation 
 of this subject; and many are the slight occurrences, some- 
 times known, but more often unknown to the investigator, 
 which destroy, or at least impair, the results of the most care- 
 ful observations: a door stands open in the entry; one or 
 more break-throughs are so contracted as not to allow the free 
 passage of the current ; loaded coal-cars standing in the entries ; 
 dips and rises not taken into account ; the temperature of the 
 
NOTES EXPLANATORY OF THE TABLES. I4S 
 
 upcast not observed; failure to observe and record the temper- 
 ature and anemometer readings at various points in the pit, so 
 as to obtain the true resistance to the circulating current ; leak- 
 ing of stoppings; escape of exhaust steam from pumps or in- 
 spirators into the upcast; influence of steam-pipes extending 
 along the entry ; upcast or downcast shafts obstructed b> stair- 
 ways, coverings, tight cages, etc. These and many other affect- 
 ing causes must render us cautious in our judgment and criti- 
 cism. Before making investigations, we should always follow 
 the current around the entire pit, carefully noting any condi- 
 tions which might influence the flow. We may often simplify 
 our task, by setting open one of the main doors and thereby 
 shortening the course of the current. In all investigations cf 
 this class, we should carefully avoid being too minute and thus 
 obtaining coefficients which are applicable only to surfaces of 
 exact measurement. Practically, we are dealing with mines in 
 respect to xhe. general extent and size of their air-ways ; an it is 
 of little moment to us, whether or not we know the precise co- 
 efficient of friction for air rubbing against one square foot of 
 the sides of those air-ways. The actual resistance offered by 
 the air-ways of a mine to the circulating current consists 
 mainly of mechanical obstructions, such as entry-timbers, jut- 
 tings of the ribs, sharp bends or angles in the air-courses, etc., 
 whereby the momentum of the current is broken. What we 
 need and should strive to ascertain is sucii a coefficient as will 
 express this resistance for the entire mine, reduced to one 
 square foot of rubbing surface and a velocity of one foot per 
 minute. We mention this in closing, because some experi- 
 ments which have been recently made confine themselves too 
 elosely to minute details, which are more valuable as a scientific 
 experiment than applicable to the solution of practical mining 
 problems. 
 
PRACTICAL PROBLEMS. 
 
 1. Find the weight of one cubic foot of dry air at a tem- 
 perature of 30° F. and a barometric pressure of 30 inches? 
 
 Ans. 0.0926783 lb. 
 
 2. What will be the weight of the same at a temperature of 
 60° F. and a barometric pressure of 28 inches? 
 
 Ans. 0.0715 lb. 
 
 3. What will be the weight of one cubic foot of air saturated 
 with aqueous vapor at a temperature of 60° F. and a baromet- 
 ric pressure of 28 inches ? 
 
 Ans. 0.070996 lb. 
 
 Solution.— VHhtn air is saturated with any vapor whatever, 
 that vapor supports a part of the barometric pressure equal to 
 the tension of the vapor at the existing temperature; for ex- 
 ample, in the case mentioned in problem 3, the vapor of satu- 
 ration supports 0.524 inch of the 28 inches barometric pressure, 
 and the air supports the remaining 27.476 inches (Table III). 
 
 We first find the weight of one cubic foot of dry air at the 
 given temperature (60° F.) and a barometric pressure of 27.476 
 inches, which gives 0.0701617 lb. 
 
 We then find the weight of one cubic foot of dry air at the 
 given temperature and a barometric pressure of 0.524 inch 
 (the pressure borne by the vapor), and multiply this result by 
 0.6235 (the specific gravity of the vapor, Table V). This last 
 product will be the weight of the vapor saturating one cubic 
 foot of air, which we find to be 0.0008343 lb. 
 
 Finally, adding this weight of vapor of saturation to the 
 weight of dry air found above, we obtain for the weight of one 
 
 146 
 
PRACTICAL PROBLEMS. 147 
 
 cubic foot of saturated air at the given temperature and press- 
 ure 0.070996 lb. 
 
 4. What will be the weight of one cubic foot of vitiated air, 
 at the foot of the upcast, assuming that the air is here com- 
 pletely saturated with moisture ; temperature 70° F., barometer 
 30 inches, and the oxygen of the air wholly converted into car- 
 bonic acid gas (COa) ? 
 
 Ans. 0.080805 lb. 
 
 Solution. — This is the worst case which can occur, as far as 
 the gaseous composition of the current is concerned ; for the 
 presence of carbonic oxide gas, or of fiery gases in the current, 
 would aid ventilation; but it is here assumed that the oxygen 
 of the air is wholly converted into carbonic acid gas. 
 
 We find the weight of nitrogen and carbonic acid gas which 
 one cubic foot of air would yield, by substituting the given 
 numerical values for their respective quantities in equations 
 i-XLIV and 3-XLIV ; remembering that these gases support 
 orily 29.279 inches of the 30 inches barometric pressure, the 
 vapor of saturation supporting the remaining 0.721 inch., be- 
 ing its tension at 70° F. (Table III). The weight of the vapor 
 of saturation is then found, by substitution, in equation 5-XLIV. 
 
 As a result, we obtain the following : 
 
 Nitrogen 0.0564824 lb. 
 
 Carbonic acid gas . . 0.0231964 " 
 Aq. vapor o.ooi 1262 " 
 
 0.0808050 lb. 
 
 5. Referring again to problem 4, and assuming that the 
 average temperature of the upcast is 70° F., while that of the 
 downcast is 60° F., and the depths of both the upcast and the 
 downcast shafts are each 200 feet, what amount of back press- 
 ure per square foot of sectional area will be entailed upon the 
 fan, due to such vitiated condition of the upcast ? 
 
 Ans. 0.83958 lb. 
 
 Solution. — We find the weight of dry air at a temperature of 
 60° F. and a barometric pressure of 30 inches to be 0.0766071 
 
148 APPENDIX. 
 
 lb. Deducting this from the weight found in problem 4, we 
 have for the difference of pressure due to one foot of vertical 
 height, 0.0041979. Multiplying this by 200, the depth of shaft, 
 we obtain 0.83958 lb. as the back pressure per square foot, or 
 the unit of back pressure. 
 
 Note. — This is an item which is frequently overlooked in investigations, and it 
 may at times exert a powerful influence over the circulation. 
 
 6. Express the unit of pressure found in the last problem, 
 in terms of head-of-air column. (See equation II.) 
 
 Ans. 10.96 ft. 
 
 7. Express the same in inches of water-gauge. (See equation 
 XXXVI.) 
 
 Ans. 0.16 in. 
 
 8. What will be the reading of a water-gauge inserted between 
 the intake and the return of an air-split 10,000 feet long; size 
 of air-way (6x8-^) feet; when 50,000 cubic feet of air are passing 
 per minute, in this split.? 
 
 Ans. 2.99 ins. 
 
 9. Find the horse-power of the air-split mentioned in the 
 last problem. 
 
 Ans. 23.563 h.p. 
 
 10. What quantity of air is passing per minute through an 
 air-course whose size is (6x10) feet, when the velocity of the 
 current is 10 feet per second ? 
 
 Ans. 36,000 cu. ft. 
 
 11. In a certain mine, 100,000 cubic feet of air is passing per 
 minute, in four splits or currents, as follows : 
 
 "A" split, (6x8f) 1000 ft. long, 15,000 cu. ft. 
 
 " B " " " 8000 " " 20,000 " " 
 
 " C " " " 6000 " " 35,000 " " 
 
 " D " " " 4000 " " 30,000 " 
 
 u << 
 
PRACTICAL PROBLEMS. I49 
 
 The division is accomplished by the use of box-regulators. 
 What is the horse-power of this pit ? 
 
 Ans. 155.177 h.p. 
 
 Note. — The box-regulators, which are necessary in splits "A," " B, ' and " D," 
 make the work performed in those splits equal to the work in split " C." This is 
 the great disadvantage of the use of this form of regulator. In the use of the 
 other form of regulator, each split has its own separate work, peculiar to itself, as 
 given in the following problem. 
 
 12. What would be the horse-power of the pit mentioned in 
 the last problem, if the division of the air were accomplished by 
 the use of the improved regulator ? 
 
 Am: 
 
 A" 
 
 ' split 0.509 h.p. 
 
 B" 
 
 ' " 9.651 " 
 
 C" 
 
 " 38.794 " 
 
 D- 
 
 • " 16.287 " 
 
 Total .. 65.241 " 
 
 13. What quantity of air per minute will 100 horse-power 
 produce, under a three-inch water-gauge ? 
 
 Ans. 21,154 cu. ft. 
 
 14. What will be the unit of ventilating pressure, developed 
 by a furnace capable of maintaining an average temperature of 
 300° F., in an upcast shaft 500 feet deep; the depth of the 
 downcast being the same and its average temperature 60° F. ; 
 barometer 30 inches ; ignoring the vitiated condition of the up- 
 cast air ? 
 
 Ans. 1 2. 1 1 lbs. 
 
 15. If we have 10,000 cubic feet of air passing down the in- 
 take of a mine per minute, having a temperature of 60° F. ; and, 
 if we introduce a water-gauge communicating between the first 
 of the air and the last of the return, which gives a reading of 
 1.5 inches ; what will be the volume of air passing per minute 
 upon the return at ttie point of observation, the temperature 
 here having increased to 70° F. and the barometric pressure at 
 the same point being 30 inches ; supposing no augmentation 
 of the volume of the current by gases from the mine ? 
 
 Ans. 10,230 cu. ft. 
 
ISO APPENDIX. 
 
 Solution. — The weight of air passing per minute through the 
 mine is obviously tlie same at all points of the air-course, 
 supposing there to be no leaks through doors or stoppings ; it 
 is unquestionably the same at the two points of observation. 
 Hence, by referring to equation XLIII, we see that the vol- 
 umes passing these two points are inversely proportional to 
 the pressures and proportional to the expression (459 + /) ; and 
 we may write the proportion, 
 
 459 + /i ■ 459 + ^ 
 
 But Bi, the barometric pressure at the point of observation 
 upon the first of the air, may be determined by reducing the 
 inches of water gauge to inches of barometer and adding this 
 to the barometric pressure given upon the return, according to 
 the equation. 
 
 -5i = — !— -\rB....7.. 
 13-596 
 
 Substituting given numerical values for their respective quan- 
 tities in equation 2 above, and reducing, we find, 
 
 Bi = 30.1103 inches. 
 
 Finally, substituting numerical values for their respective quan- 
 tities in equation i above and reducing, we obtain for Q the 
 answer given above, 10,230 cubic feet. 
 
 16. Suppose a mine having two shafts, each 200 feet deep, 
 to be ventilated by a furnace. Assume the outside temperature 
 to be 60° F., barometer 30 inches, average temperature of the 
 upcast 200° F. ; and also assume the worst condition of the 
 vitiated air possible, as in problem 4, the oxygen of the air 
 having been wholly converted into carbonic acid gas ; and the 
 return air being saturated at a temperature of 70° F. ; what 
 unit of ventilating pressure will result.' 
 
 Ans. 2.348 lbs. 
 
 17. What unit of ventilating pressure would result in the 
 
PRACTICAL PROBLEMS. 151 
 
 above case if the return current was comparatively free from 
 carbonic acid gas, the other conditions remaining the same ? 
 
 Ans. 3.364 lbs. 
 
 18. What unit of ventilating pressure would result in prob- 
 lem 17, were we to ignore the fact that the return air is satu- 
 rated with moisture just before entering the influence of ilie 
 furnace ; i.e., were we to figure this problem by the method in 
 general use in our text-books ? 
 
 Ans. 3.255 lbs. 
 
 Note. — Air saturated with moisture is always lighter, bulk for bulk, than dry 
 air under the same conditions. 
 
 19. In a certain mine ventilated by a furnace, 10,000 cubic feet 
 of air are passing per minute, the upcast shaft being 100 feet 
 deep ; to what extent would this circulation be increased by 
 building a chimney over the shaft 16 feet high, other con- 
 ditions remaining the same .'' 
 
 Ans. 10,770 cu. ft. 
 
 20. What quantity of air would pass per minute, under the 
 unit of ventilating pressure (3.364 pounds) found in problem 
 17, supposing the total length of airway to be 10,000 feet, the 
 sectional area of the same 50 square feet, and the perimeter 28^ 
 feet, the air travelling in one undivided current, using Atkin- 
 son's coefficient and ignoring the resistance of the shaft.'' 
 
 Ans. 8,222 cu. ft. 
 
 21. What quantity of air would pass per minute in the last 
 problem were we to split the current once, the other conditions 
 remaining the same ? 
 
 Ans. 23,255 cu. ft. 
 
 22. What will be the mine-potential in the two cases respec- 
 tively ? 
 
 Ans. I St case, 271.868 ; 2d case, 543.736, 
 
 23. What horse-power is expended in these two cases re- 
 spectively } 
 
 Ans. ist case, 0.838 h.p. ; 2d case, 2.371 h.p. 
 
1 52 APPENDIX. 
 
 Note. — In problems 14 and 16 we assume that the power applied is changed so 
 as to maintain the same unit of pressure in the airways after the current is split; 
 we have in these two cases a different power and a different quantity of air pass- 
 ings per minute. 
 
 24. If we have 100,000 cubic feet of air passing per minute by 
 tlie expenditure of 70.69 horse-power, the air travelling in a 
 single current, what quantity of air per minuie would the same 
 power yield were this current to be divided into two equal 
 splits? 
 
 Ans. 200,000 cu. ft. 
 
 25. In the last problem, what power would be required to cir- 
 culate the 100,000 cubic feet of air per minute in two equal 
 currents ? 
 
 Ans. 8.836 h.p. 
 
 26. What water-gauge will be developed in the case just 
 cited, where 100,000 cubic feet of air are passing per minute, at 
 an expenditure of 70.69 horse-power. 
 
 Ans. 4.48 ins. 
 
 27. What is the unit of ventilating pressure indicated by this 
 water-gauge ? Ans. 23.33 lbs. 
 
 28. The entire length of airways being 30,000 feet, and the 
 sectional dimensions 6 x 8| feet, what is the mine-potential for 
 a single, undivided current? 
 
 Ans. 188.502. 
 
 29. What will be the potential for the above mine when the 
 current is divided and travelling in two splits? Ans. 377.004. 
 
 30. What power would be required to circulate 100 000 cubic 
 feet of air per minute against this potential? 
 
 Ans. 565.520 h.p. 
 
 Note.— This is toi great a power to be transmitted, practically, through a sec- 
 tional area of 100 square feet (2 splits) ; we should use in this case from 4 to 5 
 splits. 
 
 31. Employing 4 equal splits, in problem 30, what would be 
 
PRACTICAL PROBLEMS. I S3 
 
 the required power; and what velocity of the current and water- 
 gauge would result ? 
 
 Ans. 70.69 h.p. ; 500 ft. per min. ; 4.48 ins. 
 
 32. Reduce 600 feet of air-column to inches of water-gauge. 
 
 Ans. 8.83 ins. 
 
 Note. — One cubic foot of air will weigh sJe of the weight of one cubic foot of 
 water at temperature of 60° F. and a pressure of one atmosphere (14.7 pounds), 
 its specific gravity being 0.00123, referred to water as unity. 
 
 Note. — One or two problems will be here introduced, for the purpose of show- 
 ing the actual effect of the vitiated condition of the upcast column ; or, in other 
 words, the back-pressure resulting therefrom. These problems are useful in cases 
 of careful investigation, and should then always be taken into account. For prac- 
 tical purposes, however, the condition of the upcast and downcast columns may 
 be considered as identical. (See Addenda.) 
 
 33. Suppose a mine to be ventilated by means of a force-fan, 
 the upcast and downcast shafts being each 200 feet deep, size 
 of airways 6x8^ and 30,000 feet long; what horse-power will 
 be required to pass 100,000 cubic feet of air per minute through 
 the mine in four splits; not assuming any differential tempera- 
 ture of the upcast and downcast columns, or the vitiated con- 
 dition of the upcast, but figuring in the usual approximate 
 manner for practical purposes .'' 
 
 Ans. 70.69 h.p. 
 
 34. Assume the same conditions as given in problem 33, and 
 now suppose the average temperature of the downcast (/a) to 
 be 60° F., that of the upcast (/i) 70° F., barometric pressure 
 (B) 30 inches, and a vitiated condition of the upcast current ; 
 and determine the weights of one cubic foot of the upcast and 
 downcast columns respectively. 
 
 Ans. Upcast ( J^i) 0.080805 lb. ; downcast ( IV2) 0.077267 lb. 
 
 35. What unit of back-pressure will result from problem 34, 
 the upcast and downcast shafts being each 200 feet deep; and 
 what horse-power will now be required to pass the same qunntity 
 of air per minute (100,000 cubic feet) ? 
 
 Ans. Unit of back-pressure, 0.7076 lb. ; actual horse-power, 
 72.841 h.p. 
 
154 APPENDIX. 
 
 36. Under the conditions of problem 34, what quantity of air 
 per minute would pass were the horse-power applied 70.69, as 
 figured in problem 33? 
 
 Ans. 97,048 cu. ft. per min. 
 
 Note. — The actual unit of ventilating pressure, as indicated by the water- 
 B^auge, should correspond under all conditions of temperature anj barometric 
 pressure to the theoretical unit of pressure, as derived from equation XXIII ; 
 but in order to this, and for careful determination for purposes of investigation, 
 the varying functions of temperature and barometric pressure must be taken into 
 consideration, as in the above problems. 
 
 FAN FUNCTIONS. 
 
 37. What is the efficiency of a twenty-foot fan at 50 revolu- 
 tions per minute (width of blade 48 inches, inner radius 66 
 inches), which is yielding a current of 172,270 cubic feet per 
 minute, under a three-inch water-gauge; temperature at the 
 time of observation being 60° F., barometer 30 inches, and the 
 air dry ? 
 
 Ans. 90^. 
 
 38. If we now speed the same fan up to 100 revolutions per 
 minute, under the same atmospheric conditions, what efficiency 
 should it show? 
 
 Ans. 60^. 
 
 Solution. — Referring to equation XLVII., and assuming the 
 temperature and barometric pressure constant, we see that 
 
 n'' varies as (i — K), 
 
 which gives the above result. 
 
 39. Assuming that the fan is working against the same 
 potential in problem 38 as in problem 37, what will be the re- 
 sulting quantity and unit of pressure ; and what horse-power 
 will be developed ? 
 
 Ans. 379,220 cu. ft. per m. ; 75.6 lbs. per sq. ft. ; 868.674 h-P- 
 
 Note. — The mine-potential in problem 39 is not large enough for the increased 
 power of the fan at 100 revolutions per minute ; as is shown by the resulting unit 
 of pressure and the velocity of the current, which would be almost 32 feet per 
 second. The potential should be increased, in this case, by splitting the air-cur- 
 rent, until a normal water-gauge and a moderate velocity is obtained. 
 
PRACTICAL PROBLEMS. 1 55 
 
 40. What is the value of the fan-constant (c^) in problems 37 
 and 38? (See equation XLVII.) 
 
 Ans. 0.000002312. 
 
 41. What is the value of the fan-constant when the yield and 
 water-gauge indicate an efficiency of 85 per cent at 50 revolu- 
 tions, or 40 per cent at 100 revolutions per minute, tempera- 
 ture being 60° F. and the barometer 30 inches ? 
 
 Ans. 0.000003468. 
 
 42. Give the value of the fan-constant under the same condi- 
 tions, when the efficiency is 95 per cent at 50 revolutions, or 
 80 per cent at 100 revolutions per minute .' 
 
 Ans. 0.000001156. 
 
 43. Find the maximum effective speed, under the conditions 
 of problem 42; i.e., when the fan-constant is 0.000001156, the 
 temperature being 60° F. and the barometer 30 inches; or, in 
 other words, at what speed will the fan yield the greatest quan- 
 tity of air per minute ? 
 
 Ans. 182.6 rev's per m. 
 
 44. Find the limit of speed of the same fan, under the same 
 conditions; i.e., at what speed will this particular fan cease to 
 throw any air under the atmospheric conditions mentioned? 
 
 A?ts. 223.6 rev's per m. 
 
 45. Find the maximum effective speed and the limit of speed 
 for the fan mentioned in problem 40, under the same atmos- 
 pheric conditions? 
 
 Ans. Max. effect, speed, 129.1 rev's perm.; limit of speed, 
 
 1 58.1 rev's per m. 
 
 Note. — A fan will rarely ever give as fow aa efficiency as that mentioned in 
 problem 41. The efficiency will frequently exceed that given in problem 42. The 
 Murphy type of fans may present a higher efficiency than that afforded by the 
 straight-paddle fan; but their yield is not represented by equations XXXVIII- 
 XL. The backward curvature of the blades, resulting in a loss of rotary motion 
 to the air, weakens the pressure incident to speed. This type of fan therefore 
 requires a higher speed for the same yield. (See Addenda.) 
 
 46. We are opening a mine to be ventilated by a force-fan, 
 straight-paddle; and we wish to provide for the circulation of 
 
156 APPENDIX. 
 
 100,000 cubic feet of air per minute, in four equal, separate 
 splits ; size of airwa\'s (6 x 8) and 50,000 feet long. What size of 
 fan should we adopt ? 
 
 Ans. Diam. of fan, 18.9 ft.; width of blade, 7.1 ft.; exp. of 
 casing, 4.7 ft. 
 
 47. In the last problem, what will be the speed of the fan at 
 which it will throw the 100,000 cubic feet of air per minute, 
 under the conditions mentioned, temp. 60° F., barom., 30" } 
 
 Ans. 50.3 rev's per m. 
 
 48. Assuming that the value of the fan-constant of this fan 
 is 0.000002312, what quantity of air per minute will it circulate 
 in the mine mentioned, in four equal splits, when running at a 
 speed of 100 revolutions per minute, the temperature being 
 60° F. and the barometer 30 inches.? 
 
 Ans. 215,745 cu. ft. 
 
 49. What would be the velocity of the intake of the fan in the 
 last problem ? 
 
 Ans. About 19 ft. per sec. 
 
 50. What is the velocity of the blade-tips and the peripheral 
 flow, respectively, in each of the cases mentioned in problems 
 46 and 48? 
 
 Ans. First case: Blade-tips 49.8 ft. per sec, per flow 50.0 ft. 
 per sec. ; second case : Blade-tips 99 ft. per sec, periph. flow 
 108 ft. per sec. 
 
 51. What will be the horse-power of this same fan running at 
 a speed of 60 revolutions per minute, assuming the fan-constant 
 to be 0.0000023 1 2, temperature o" F., and the barometer 30 inches ; 
 and what will be its efficiency } 
 
 Ans. 252.231 h.p. ; efficiency, 87.27^. 
 
 52. What will be the horse-power of the same fan, running at 
 the same speed, when the temperature is 90° F. and the bar- 
 ometer 28 inches, and what the efficiency.'' 
 
 Ans. 188.727 h.p. ; efficiency, 83.68^. 
 
PRACTICAL PROBLEMS. 157 
 
 53. At what speed will it be necessary to run the fan under 
 the conditions prevailing in problem 52, in order to maintain 
 the power developed in problem 51 ? 
 
 Ans. 65.1 revs, per min. 
 
 54. What is the horse-power of a 12-foot Murphy fan, blades 
 3x3 ft., inclination of blade to the radial at the centre of 
 gravity 30 degrees, fan-constant 0.000001156, at a speed of 100 
 revolutions per minute, when the atmospheric temperature is 
 60° F. and the barometric pressure 29 inches ? 
 
 Ans. 102.314 h.p. 
 
 55. What would be the horse-power of a straight- paddle fan 
 of the same dimensions and having the same fan-constant, at 
 the same speed and under the same atmospheric conditions.' 
 
 A?is. 111.538 h.p. 
 
 56. What is the horse-power of a 16-foot straight-paddle fan, 
 blades 5 feet wide and 42 inches deep, running at a speed of 50 
 revolutions per minute, and showing an efficiency of go% at this 
 speed ; temperature being 60° F. and the barometric pressure 
 30 inches ? 
 
 Ans. 41.369 h.p. 
 
 57. What will be the horse-power of the same fan under the 
 same atmospheric conditions, at a speed of 100 revolutions per 
 minute ; and what will be its efficiency at this speed ? 
 
 Ans. 441.263 h.p.; efficiency 60^. 
 
 58. If a i2-foot fan, blades 3x3 feet, running at a uniform 
 speed of 50 revolutions per minute under a 2-inch water-gauge, 
 yields 24,048 cubic feet of air per minute at a temperature of 
 60° F. and a barometric pressure of 29 inches, what is its 
 efficiency and what is the fan-constant? 
 
 Ans. Efficiency, 87^ ; fan-constant, 0.0000029. 
 
 59. Suppose we wish to arrange for the circulation of a cur- 
 rent of 100,000 cubic feet of air per minute, travelling in four 
 separate splits, through an airway (6 x 8^ feet) 60,000 feet long; 
 
IS8 APPENDIX. 
 
 what size of straight-paddle fan should we adopt, and at what 
 general speed should the fan be run to accomplish this work? 
 
 Ans. Diam. of fan, 18.35 ^^- '• width of blade, 6.88 ft. ; exp. of 
 casing, 4.6 ft. ; diam. of eye, 10 ft. ; net intake area, two eyes, 
 no sq. ft. ; speed of fan, 54.9 revs, per min. 
 
 SPLITTING THE AIR. 
 
 60. Suppose two airways having the same sectional dimen- 
 sions, and whose lengths are respectively 1600 and 5400 feet long_ 
 to be open to the free passage of the circulating current; how 
 will an intake current of 10,000 cubic feet of air per minute 
 divide itself between these two entries.? 
 
 Ans. 6,000 cu. ft. ; 4,000 cu. ft. 
 
 61. What is the horse-power of a current of 100,000 cubic 
 feet per minute, circulating in four equal splits; size of airways 
 (6 X 8^) feet; total length 25,000 feet.? 
 
 Ans. 58.908 h.p. 
 
 62. Find the total horse-power of the following splits when 
 box-regulators are used : 
 
 Split A. 6 X 8-J^ ft., 5,000 ft. long, 10,000 cu. ft. 
 " B. " " 6,000 " " 15,000 " " 
 
 " C. " " 8,000 " " 20,000 " " 
 
 " D. " " 10,000 " " 18,000 " " 
 
 Ans. 38.6 h.p. 
 
 63. Find the total horse-power of the same splits, using the 
 o.her form of regulator. 
 
 Ans. 22.253 h.p. 
 
 64. What will be the sizes of the openings in the box-regula- 
 tors in problem 62 ? (See Addenda.) 
 
 Ans. Split A, 247 sq. in.; split B, 480 sq. in.; split D, 1491 
 sq. in. 
 
 65. Taking the width of the airway (8-J feet) as 100 inches, 
 
PRACTICAL PROBLEMS. I 59 
 
 wliat will be the respective widths of the openings at the mouths 
 of the several splits, in problem 63 ? 
 
 Alls. Split A," 3. 38 in. ; split B, 13.75 in. ; split C, 43.37 in. ; 
 split D, 39.50 in. 
 
 66. Suppose a vein dipping at an angle of 30 degrees to be 
 ventilated in two main splits. The headings or levels are 400 
 feet apart, measured upon the slope ; the size of the dip-split is 
 6x8^ feet and 10,000 feet long ; temperature of the intake 
 50° F. and of the return 70° F., barometer 30 inches. The regu- 
 lators are arranged so that the dip-split takes 20,000 cubic feet 
 of air per minute, while the level-split takes 30,000 cubic feet. 
 How much air per minute will each split take when the total 
 quantity of air furnished per minute to the mine has been re- 
 duced to 40,000 cubic feet, supposing that no change is made in 
 the regulators ? 
 
 Ans. Level-split, 23,555 cu. ft. ; dip-split, 16,445 cu. ft. 
 
 67. In the last problem, what quantities of air per minute 
 would each split take were the circulation to be increased from 
 50,000 to 60,000 cubic feet per minute ? 
 
 Ans. Level-split, 36,444 cu. ft. ; dip-split, 23,556 cu. ft. 
 
 GENERAL PROBLEMS. 
 
 68. Suppose we have a current of 50,000 cubic feet of air per 
 minute travelling in two splits; size of airways 6 x 8 J feet and 
 the entire length 30,000 feet ; if a fall occur upon the main air- 
 way before the split is reached, so as to reduce the sectional area 
 of the same from 50 to 25 square feet, the power of the motor 
 remaining the same, what quantity of air per minute will pass 
 over the fall and through the mine, assuming a temperature of 
 60° F. and a barometer of 30 inches ? 
 
 Ans. 49,437 cu. ft. 
 
 69. In a certain mine a current of 50,000 cubic feet per minute 
 is passing in two splits of the following size : 
 
 Split A. 6 X 8i ft., 10,000 ft. long. 
 " B. 6 X 10 " 40,000 " " 
 
l6o APPENDIX. 
 
 It we now introduce a box-regulator having an opening of 60.56 
 square inches, into split A, what quantity of air will then pass 
 in each split per minute, assuming that the power is increased 
 to maintain the flow of 50,000 cubic feet in the main intake, 
 temperature 60° F., and barometer 30 inches? 
 
 Ans. Split A, 10,000 cu. ft. ; split B, 40,000 cu. ft. 
 
 70. In the last problem, what per cent of the power is lost in 
 the regulator ; give also the horse-power of the circulation in 
 the two methods ? 
 
 Ans. 49.66^; old method, 446.828 h.p. ; new method, 224.922 
 h.p. 
 
 71. If a certain motor is capable of circulating a current of 
 20,000 cubic feet per minute through a certain mine, and another 
 motor 30,000 cubic feet per minute in the same mine, each 
 working alone but under like conditions, what quantity of air 
 per minute will result from their combined action under the 
 same conditions? (See equation XXXIII.) 
 
 Ans. 32,711 cu. ft. 
 
 72. If the motor first mentioned above, in performing its work 
 of circulating 20,000 cubic feet of air per minute through a cer- 
 tain mine, yields a water-gauge of 2 inches, the water-gauge 
 yielded by the second motor in the circulation of the 30,000 
 cubic feet of air per minute will be4-i- inches; what will be the 
 water-gauge vjhen the two motors are working together under 
 the same conditions? 
 
 Ans. 5.35 ins. 
 
ADDENDA. 
 
 We will consider here such other conditions prevailing in the 
 pit as affect to a greater or less degree the ventilation of the 
 same, but which are ignored in our ordinary calculations. 
 These are interesting, however, as matters of information, and 
 are quite essential in all cases of careful investigation. We 
 refer now to the change in the weight of the downcast column, 
 due to the pressure of the pit, in compressive ventilation ; and 
 to the variation in the weight of the upcast column, arising 
 from the saturation of the return current. Also such other 
 cases will be here introduced and other formulas developed as 
 require to some extent a knowledge of the higher mathematics. 
 These have been eliminated from the main body of the book, 
 because they are not essential to a practical knowledge of the 
 subject; but the work would not be complete without refer- 
 ence to them. 
 
 Condition of Current due to Pressure and Saturation. — There 
 are three conditions of the air in the pit, and the weight of this 
 air is therefore represented by three different expressions, as 
 follows : 
 
 Exhaustive downcast : 
 
 1.32535 , , 
 
 Wj = ^ ^^ (i) 
 
 459+A 
 
 Compressive downcast : 
 
 TV, = 
 
 Upcast (2 cases) : 
 
 g3.7B+p+/i(w^ -vr,) 
 
 iv, ■=■ — \^) 
 
 70.7(459 + /,) 
 
 1.4396(5 — (pt^ + 0.826302', 
 
 Wi = —. • 
 
 459 + ^> 
 
 (3) 
 
 i6i 
 
1 62 ADDENDA. 
 
 In the case of the upcast column two conditions may arise. 
 First, as in the case of a dry furnace-shaft, the temperature it, 
 at which the air was saturated, is lower than the temperature 
 /i, the average temperature of the upcast. Second, as in the 
 case of a wet furnace-shaft, or any case of fan-ventilation or 
 otherwise, where the upcast column is not heated, the tempera- 
 ture (A) at which the air is saturated will be equal to the tem- 
 perature of the shaft, the excess of moisture being deposited 
 all the way up the shaft, as the current is cooled in its ascent. 
 The average temperature of saturation will then be identical 
 with the average temperature of the shaft. The temperature of 
 saturation can never be greater than the temperature of the 
 shaft, as the moisture would then be at once deposited. 
 
 The above three expressions are developed as follows : 
 Expression (i) is a simple case, and gives the weight of one 
 €ubic foot of dry downcast air under the barometric pressure 
 S, and the average temperature of the downcast shaft ti ; it 
 is derived from equation (I). This expression is applicable only 
 to the exhaustive system, where natural draft, furnace, or ex- 
 haust-fan is in use. 
 
 Expression (2) applies to the compressive system of ventila- 
 tion, and gives the weight of one cubic foot of dry, downcast 
 air, subject to the barometric pressure B and the theoretical 
 unit of ventilating pressure p, due to the resistance of the 
 rubbing surface of the airways, and expressed by equation 
 (XXIII), and a further back-pressure, arising from the vitiated 
 condition of the upcast current. This unit of back-pressure, 
 due to the heaviness of the upcast current, is readily found by 
 deducting the weight of one cubic foot of air, as given by ex- 
 pression (i), from the weight of one cubic foot of air derived 
 from expression (3) ; and multiplying the excess or difference 
 thus found by the motive height k, which will give the unit of 
 back-pressure from this cause very approximately. Now, equa- 
 tion (i) gives the weight of one cubic foot of air under the 
 barometric pressure B, which pressure is expressed in inches 
 of mercury ; hence, in the present instance, we must reduce the 
 unit of ventilating-pressure p, and the unit of back-pressure 
 /^(Wl — wa) to inches of mercury, and add these results to the 
 B of equation (i). We see by referring to equation (XXXVI) 
 
ADDENDA. 1 63 
 
 that one inch of water-gauge represents a unit of pressure of 
 5.2 pounds; and since the specific gravity of mercury is 13.596, 
 it follows that one inch of mercury represents a unit of pressure 
 of 70.7 pounds. Hence, dividing these units of pressure by 70.7, 
 and adding the results to B, and substituting for B. in equation 
 (i), and reducing, we obtain expression (2). 
 
 Expression (3) gives the weight of one cubic foot of the viti- 
 ated upcast current, and is obtained by adding together the 
 following expressions (see equations (i), (3), (5), (XLIV)) : 
 
 (Nitrogen, i cu. ft. upcast). ^'°^°^^ — ~ '\ . (4) 
 
 459+^1 
 
 (Carb. acid, I cu. ft. upcast). "'^'^K^ - 0^)^ _ ^^^ 
 
 459+^' 
 
 0.82630^. 
 
 (Aq. vapor, i cu. ft. upcast). . . . (6) 
 
 459 + A 
 
 Box-regulators. — There has always been experienced some 
 difficulty in estimating exactly the influence which these regu- 
 lators exert upon the current of air, and in figuring the size of 
 opening in such a regulator which will give the required 
 amount of air in each of the splits in question. As a matter 
 of fact in practice, we set up the regulator and move the shutter 
 to and fro, until the desired proportion of air is obtained ; and 
 this practice is correct, as the varying conditions of the air- 
 courses are constantly introducing factors which modify the 
 results. Nevertheless, it is interesting to investigate the prin- 
 ciples which control the flow of the air-current through the 
 opening. 
 
 To begin with, we recognize that this form of regulator is 
 introduced into that one of two splits which is taking more air 
 than the desired proportion, in order to obstruct the flow in 
 that split. The obstruction thus introduced creates an increase 
 of pressure behind the regulator, which increase is due to the 
 regulator alone, as distinct from the mine-pressure at this point, 
 or the pressure incident to the flow of the current ahead of the 
 regulator. We note that the pressure due to the regulator is 
 unbalanced by anything on the other side ; it is, in other 
 
164 ADDENDA. 
 
 words, the pressure which animates the flow through the open- 
 ing of the regulator, or it is the pressure which will talce the 
 current through this opening. It will not do any more ; it does 
 not contribute to the movement of this current ahead of the 
 regulator; the mine-pressure does that; it simply overcomes 
 the regulator, and places the current ahead of the regulator 
 under the same conditions as would exist were the regulator 
 not there. We will first find what this pressure due to the 
 regulator is, in terms of the quantity of air passing through the 
 opening and the size of the opening (we are speaking now of the 
 pressure per square foot, or the -unit of pressure). Having 
 found this unit of pressure (/) due to the regulator, we will 
 multiply it by the sectional area of the airway to obtain the 
 total pressure due to the regulator, and then again multiply this 
 result by the velocity of the current, which will give the work 
 absorbed or lost in the passage of the regulator; or, we may 
 multiply at once by the quantity of air passing per minute, and 
 obtain the same result. 
 
 Pressure due to Box-regulator. — The flow of a current of air 
 through the opening in a box-regulator is identical with the 
 flow of any fluid through an orifice in a thin plate ; and, as we 
 have seen in Chapter X, the velocity of the flow is represented 
 by the equation, 
 
 V = 4/^ (i) 
 
 from which we have, 
 
 A=^ (2) 
 
 in which 7/ is the velocity of the flow through the orifice in feet 
 per second. Hence we have for the quantity of the flow per 
 minute Q, through the orifice or opening «„, 
 
 Q = 6oa„v, (3) 
 
 from which we may write. 
 
 3600a,,' 
 
 (4) 
 
 But in all cases of the flow of a fluid through an opening in a 
 thin plate there results a contraction of the area of the flow 
 
ADDENDA. 165 
 
 just outside of the orifice, which reduces the quantity of the 
 flow. This contraction of area is known in physics as the vena 
 contractu, and varies according to the form of the orifice, and 
 in our case, where the orifice or opening is within an airway, 
 and bears a considerable relation to the sectional area of such 
 airway, the contraction of area will vary according to the size 
 of the opening, relative to the sectional area of the airway ; thus 
 the contraction will diminish as the area of the opening ap- 
 proaches that of the airway, and vice versa. The coefficient of 
 this contraction may, therefore, be represented very approxi- 
 mately for our purpose by the seventh root of the ratio ex- 
 pressed by dividing the area of the opening by the area o.f the 
 airway, or by the expression 
 
 '/ — 
 
 (5) 
 
 Hence, the true area of the flow will be represented by the ex- 
 pression, 
 
 l/^a„ or i/^ (6) 
 
 y a fa 
 
 Squaring this expression, and substituting itfora,," in equation 
 (4), we have. 
 
 3600 V a, • 
 
 7/' = -^i/JL- (7) 
 
 Now h in equation {2) is the generative height ; it is the height 
 of the surface of the fluid above the orifice (see Fig. XIIL), it 
 is the head of air-column. Hence, referring to equation H., 
 and substituting this value for h in equation (2) above, and sub- 
 stituting for V in the same equation its value as taken from 
 equation (7) above, solving with respect to/, and reducing, we 
 have for the unit of pressure due to the regulator, 
 
 * = 0.00000572 |/-2.^Q'. . . . (LXV) 
 
 Work due to Box-regulator. — To find the work absorbed or 
 lost in the passage of this form of regulator, we multiply the 
 
1 66 
 
 ADDENDA. 
 
 above unit of pressure (/) due to the regulator by the quantity 
 of air (0 passing per minute and we have 
 
 ^.^=o,ooooo572^-|/^^2=. . . (LXVI) 
 
 Illustration. — Suppose now that we have in a certain mine a 
 current of 10,000 cubic feet per minute travelling in two splits 
 as follows : 
 
 Split A. 6 X Z\, 5000 ft. long. 
 " B. " 8000 " " 
 
 If no regulator is introduced the natural division of the air 
 would send 5391 cubic feet into split A and 4609 cubic feet into 
 split B. Now suppose we desire to throw 6000 cubic feet of this 
 current into split B, what size of opening in a box-regulator 
 introduced into split A will accomplish this result ? We have 
 seen in Chapter IX that the unit of work pv at the point of 
 split or the work transmitted by one square foot of sectional 
 area to each of the several splits is the same, reacting against 
 each other, and as the exposed areas of the two splits in this 
 case are the same, the total work performed in each must be the 
 same. Now we ascertain from equation (XIII) the work that 
 will be consumed in circulating 6000 cubic feet of air per minute 
 through split B, and this work (8600 foot-pounds) will be also 
 the work applied to split A, that is to say, the work that is re- 
 sponsible for the circulation of 4000 cubic feet of air in this split 
 per minute plus the work lost in the passage of the regulator. 
 Finding from equation (XIII) the work absorbed in this split 
 by the circulation of the 4000 cubic feet of air (i 592 foot-pounds) 
 and deducting this from the total work applied (8600 foot- 
 pounds) we obtain 7008 foot-pounds as the work absorbed by 
 the regulator. Finally, substituting this value for u in equa- 
 tion (LXVI), and assuming a temperature of 60° F. and a bar- 
 ometric pressure of 30 inches, giving to a and g their numerical 
 values and reducing, we obtain for the value of a,, , 
 
 a, I = 380 sq. ins., 
 
 or an opening of ig^- inches square. This problem, as well as 
 many others of this nature, is very easily worked by the aid of 
 
ADDENDA. 167 
 
 logarithms, but on account of the high powers of some of the 
 quantities can only be approximated by the methods of arith- 
 metic. We would recommend the use of logarithms in the 
 solution of all problems in mine ventilation. 
 
 Quantity of Air passing a Box-regulator. — We may write for 
 the work performed in each split as follows : 
 
 Work in split A. (0.00000572 4/ -^ + —JO'. 
 
 As 
 Work in split B. —!,Q,\ 
 a,' 
 
 Then, equating these works and solving with respect to Q, 
 the quantity of air passing the reguhitor per minute, and 
 writing the potential X for its value (see equation (XXVIIj), 
 we have, 
 
 Q = — 3 , ^' _ = (LXVII) 
 
 ^y 0.00000572^^^^/ ^. + 3^ 
 
 Effect of Fall upon Main Air-course. — When a fall occurs 
 upon the main air-course so as to seriously obstruct the flow of 
 the air-current the amount of the flow after the fall may be 
 figured from equation (LXVII), by Q, represent the quantity of 
 air passing in the airway before the fall occurred, and «,, , the 
 reduced sectional area of the airway at the fall ; in this case X, 
 will be equal to X. 
 
 Effect of Inclination or Curvature of Blade of a Fan. — In all 
 fans having inclined or curved blades, the reaction of the air 
 against the blade being normal to the blade is no longer 
 tangential to the rotary motion of the fan, and as a consequence 
 there results a loss in the accelerative velocity imparted to the 
 air by virtue of its revolution in the fan. 
 
 Let us for a moment suppose the air contained in one section 
 of a fan to be concentrated at the point a upon the path of its 
 centre of gravity. Now, the point a is impelled or moved 
 forward by the motion of the blade in the direction ad 
 tangential to the rotary path of the blade, and the force which 
 
i68 
 
 ADDENDA, 
 
 impels it is the velocity with which the blade is moving, but 
 the direction of this motion or of the impelling force ab not 
 being normal to the surface of the blade at this point, there 
 results a sliding [ac) of the point along the surface of the blade, 
 and the resultant of these two motions is ad; consequently the 
 point a has been moved outward in a radial direction, or nor- 
 mal to the tangent ab, a distance (ed). Now, inasmuch as the 
 power of the fan is derived from the centrifugal force incident 
 to the revolution of the weight of air which we have considered 
 as concentrated at its centre of gravity a, and inasmuch as this 
 
 Fig. XVII. 
 
 centrifugal force is dependent for its development upon the 
 retention of the point a in the rotary path, any movement or 
 yielding in a radial direction, due to mechanical influence, will 
 result directly in a loss to the centrifugal force, as expressed by 
 the equation (3-XXXVIII) ; it will be readily noted that while 
 this movement in a radial direction reduces the acceleration 
 due to the centrifugal force and therefore the measure of this 
 force (//«), it does not reduce the distance through which this 
 force acts ; it only makes a part of such distance due to the 
 mechanical influence of the inclined blade. 
 
 Now, referring again to Fig. (XVII), we see that for any 
 infinitesimal period of time the tangent ab will correspond to 
 and form a part of the circle described by the point a, and will 
 therefore represent the space passed over by this point in such 
 
ADDENDA. 169 
 
 infinitesimal time. Denoting this space by v, we may write 
 from the figure 
 
 ed=iV sin a cos a, (i) 
 
 ed representing, as we have seen, the loss to the accelerative 
 velocity for an infinitesimal period of time. 
 
 Referring to equation (6-XXXVIII), and dividing by two, to 
 obtain the space passed over by the air considered as concen- 
 trated at the point a under the accelerative influence in one 
 second of time, we have the expression 
 
 o.oo5483i?«' (2) 
 
 and for the infinitesimal period of time referred to above we 
 have, 
 
 2S^(°-°°5483^«'). (3) 
 
 or, reducing, we have, 
 
 o.oS2359w« (4) 
 
 This last expression represents the space passed over by the air 
 considered as concentrated at the point a under the accelera- 
 tive influence of a straight-paddle blade in the same infinitesimal 
 period of time. 
 
 Then, finally, by dividing expression (i) by expression (4) we 
 obtain the ratio expressing the loss to the accelerative velocity 
 and consequently to the centrifugal force. 
 
 sin cc cos a 
 I9-I (LXVIII) 
 
 This expression (LXVIII) represents the ratio by which the cen- 
 trifugal force of the revolved air is weakened, and by which also 
 the power of the fan is impoverished. Any particle of air, as 
 a, for example, in its passage through the fan moves under the 
 influence of two forces; one of these forces (the mechanical 
 revolution of the fan) impels it in a direction normal to the 
 surface of the blade ; the other (the-centrifugal force) is a radial 
 
I/O ADDENDA. 
 
 force; as a result of the combined action of these two forces, 
 the particle moves in a spiral path, revolving with the fan-blades, 
 but ever approaching the outer circumference, where it is 
 thrown off. The radius of curvature of this spiral will be 
 greater, and consequently the centrifugal force developed by 
 fne revolution will be less, as the fan-blade is more inclined. 
 
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