LIBRARY 
 
 OF THE 
 
 UNIVERSITY OF CALIFORNIA. 
 
ELEMENTARY TEXT-BOOK 
 
 STEAM ENGINES AND BOILERS. 
 
 FOR THE USE OF STUDENTS IN SCHOOLS 
 AND COLLEGES. 
 
 J. H. KINEALT, 
 
 Professor of Mechanical Engineering, Washington University, 
 St. Louis, Mo. 
 
 ILLUSTRATED WITH DIAGRAMS AND NUMEROUS CUTS 
 
 SHOWING AMERICAN TYPES AND DETAILS 
 
 OF ENGINES AND BOILERS, 
 
 FIFTH EDITION. 
 
 NEW YORK : 
 SPON & CHAMBERLAIN, 123 LIBERTY STREET. 
 
 LONDON : 
 E. & F. N. SPON, 57 HAYMARKET, S. W. 
 
 1905. 
 
GENERAL 
 
 COPYRIGHT, 1901, 
 
 BY 
 J. H. KINEALT. 
 
 THE BURK PRINTING HOUSE, 
 NEW YORK. 
 
PREFACE. 
 
 This book is written solely as an elementary text-book 
 for the use of beginners and students in engineering, but 
 more especially for the students in the various universities 
 and colleges in this country. 
 
 No attempt has been made to tell everything about 
 any one particular subject, but an attempt has been made 
 to give the student an idea of elementary thermodynamics, 
 of the action of the steam in the 1 cylinder of the engine, of 
 the motion of the steam valve, of the differences between 
 the various types of engines and boilers, of the genera- 
 tion of heat by combustion, and the conversion of water 
 into steam. 
 
 Care has been taken not to touch upon the design and 
 proportion of the various parts of engines and boilers for 
 strength ; as, in the opinion of the writer, that should 
 come after a general knowledge of the engine and boiler 
 has been obtained. 
 
 In the derivation of some of the formulae in thermo- 
 dynamics, it has been necessary to use the calculus, but 
 the use of all mathematics higher than algebra and 
 geometry has been avoided as much as possible. 
 
 An earnest endeavor has been made to present the 
 subject in a clear and concise manner, using as few words 
 as possible and avoiding all padding. 
 
 J. H. KINEALY. 
 
 WASHINGTON UNIVERSITY, 
 August y 1895. 
 
 (iii) 
 
 180712 
 
PREFACE TO THE FOURTH EDITION. 
 
 This edition is practically the same as the previous one. 
 The only change made has been to correct some typo* 
 graphical errors. 
 
 J. H. KlNEALY. 
 
 BOSTON, MASS., 
 August, 
 
TABLE OF CONTENTS. 
 
 CHAPTER I. 
 
 ELEMENTARY THERMODYNAMICS. 
 ARTICLES. 
 
 1. Thermodynamics 
 
 2. First Law of Thermodynamics ...... 
 
 3. Work, Power 
 
 4. Unit of Heat 
 
 5. Mechanical Equivalent 
 
 6. Application of Heat to Bodies 
 
 7. Second Law of Thermodynamics . 
 
 8. Specific Heat 
 
 9. Absolute Temperature 
 
 10. Application of Heat to a Perfect Gas . 
 
 11. Isothermal Expansion 
 
 12. Adiabatic Expansion 
 
 13. Fusion 
 
 14. Vaporization 
 
 15. Application of Heat to Water ...... 
 
 16. Superheated Steam 22 
 
 CHAPTER II. 
 
 THEORY OP THE STEAM ENGINE. 
 
 17. Theoretical Heat Engine 23 
 
 18. Cycle 
 
 19. Thermodynamic Efficiency . 
 
 20. Perfect Gas Engine 27 
 
 21. Perfect Steam Engine . 32 
 
 22. Theoretical Diagram of the Real Engine . ... 86 
 
 23. Clearance 
 
 24. Efficiency of the Actual Engine . . . . - 46 
 
Vi STEAM ENGINES AND BOILERS. 
 
 CHAPTER III. 
 
 TYPES AND DETAILS OF ENGINES. 
 
 ARTICLES. PAGE. 
 
 25. Classification of Engines , . 53 
 
 26. Plain Slide Valve Engines ....... 65 
 
 27. Automatic High Speed Engines 56 
 
 28. Corliss Engines 59 
 
 29. Cylinder and Valve Chest 61 
 
 30. Piston 63 
 
 31. Cross-head 64 
 
 32. Connecting Rod ........ 68 
 
 33. Crank . 72 
 
 34. Main Bearings 74 
 
 35. Eccentric ........ 75 
 
 36. Governors .......... 76 
 
 CHAPTER IV. 
 
 ADMISSION OF STEAM BY VALVES. 
 
 37. Opening and Closing the Ports by the Valves . , 78 
 
 38. Relative Movements of the Piston and Valve 83 
 
 39. Balanced Slide Valve 89 
 
 40. Piston Valve 90 
 
 41. Multiple Admission Valve 91 
 
 42. Meyer Valve .......... 91 
 
 43. Corliss Valve ...... . , . 92 
 
 44. Link Motion 95 
 
 CHAPTER V. 
 
 VALVE DIAGRAMS. 
 
 45. Zeuner Valve Diagram . . . . . . .97 
 
 46. Valve Diagram Problems 101 
 
 47. Effect of the Obliquity of the Connecting Rod on the Point 
 
 of Cut-off .......... 110 
 
 48. Swinging Eccentrics 113 
 
CONTENTS. Vll 
 
 CHAPTER VI. 
 
 INDICATOR AND INDICATOR CARDS. 
 
 ARTICLES. PAGE. 
 
 49. Indicators .... . 118 
 
 50. Adjustments and Connections of Indicators . 120 
 
 51. Reducing Motions . 122 
 
 52. Cord for Indicator . 127 
 
 53. Taking the Indicator Card . 128 
 
 54. To Determine the Horse-power from the Indicator Card 128 
 
 55. To Find the Ratio of Clearance of the Engine from the 
 
 Indicator Card . . . 132 
 
 56. To Find the Weight of Steam used per Hour per Horse- 
 
 power ... .... 
 
 57. Interpretation of the Action of the Valves from the Ap- 
 
 pearance of the Indicator Card .... 134 
 
 CHAPTER VII. 
 
 COMPOUND ENGINES AND CONDENSERS. 
 
 58. Compound Engines 
 
 59. Tandem Compound Engines . 
 
 60. Cross- Compound Engines 
 
 61. Ratio of Cylinders of Compound Engines 
 
 62. The Horse-Power of Compound Engines . 145 
 
 63. Condensers 
 
 64. Effect of the Condenser on the Power of the Engine . 150 
 
 65. Amount of Condensing Water Required .... 153 
 
 CHAPTER VIII. 
 
 HEAT AND COMBUSTION OF FUEL. 
 
 66. Steam Making . 155 
 
 67. Steam Required per Hour . 157 
 
 68. Heat Required per Hour . .158 
 
 69. Fuel Required per Hour . 160 
 
 70. Air Required for Combustion . I 66 
 
 71. Rate of Combustion 
 
 72. The Furnace 169 
 
STEAM ENGINES AND BOILERS. 
 
 ARTICLES. p AaE 
 
 73. Firing the Furnace 171 
 
 74. Mechanical Stokers ...... 174 
 
 75. Hawley Down-Draft Furnace .... 177 
 
 CHAPTER IX. 
 
 BOILERS. 
 
 76. Types of Boilers 180 
 
 77. Old Types of Boilers 181 
 
 78. Return Fire-Tube Boilers 183 
 
 79. Water-Tube Boilers 189 
 
 80. Vertical Boilers 192 
 
 81. Marine Boilers 194 
 
 82. Rating of Boilers 194 
 
 83. Appendages to a Boiler ....... 196 
 
 84. Settings of Boilers .... 207 
 
 CHAPTER X. 
 
 CHIMNEYS. 
 
 85. Chimneys 212 
 
 86. Draft of Chimney 214 
 
 87. Velocity of the Gases Passing Through the Chimney . 217 
 
 APPENDIX. 
 
 CARE OF BOILERS. 
 
 How to Prevent Accidents 221 
 
 How to Save Fuel 224 
 
 How to Lengthen the Life of the Boiler 225 
 
 TABLES. 
 
 I. The Properties of Steam * 229 
 
 II. Hyperbolic Logarithms 234 
 
 III. Factors of Evaporation 235 
 
 IV. Heating Power of Fuels 236 
 
CHAPTER I. 
 
 ELEMENTARY THERMODYNAMICS. 
 
 I. THERMODYNAMICS. The Science which treats of the 
 laws and principles according to which work may be con- 
 verted into heat and y conversely \ heat into work is Thermo- 
 dynamics. 
 
 The whole science is based upon the present conception 
 of " heat as a mode of motion ; " and until the present 
 theory of heat was established and accepted, the science 
 was unknown. Up to about the middle of the nineteenth 
 century the usually accepted conception of heat was that 
 it was a material substance that could be made to enter 
 or leave bodies; and according as this substance was 
 present in greater or less quantities the body was more or 
 less hot. 
 
 In 1798, Count Rumford was led to assert that heat 
 was a mode of motion and not a material substance, by 
 the results of experiments made while boring cannons. 
 The results of his experiments and his conclusions as to 
 the nature of heat were given in a paper, read before the 
 Royal Society in England, entitled, "An Enquiry Con- 
 cerning the Source of the Heat which is Excited by 
 Friction," 
 
 In 1/99, Sir Humphrey Davy, by a series of experi- 
 ments upon the heating effect of rubbing two pieces of 
 ice together, supported and strengthened the conclusions 
 reached by Count Rumford. 
 
 In spite, however, of the work of Rumford, Davy, and 
 others who followed them, it was not until about 1843 
 
2 STEAM ENGINES AND BOILERS. 
 
 that the modern conception of heat as a mode of motion 
 was firmly established, and accepted by physicists. 
 
 To Dr. Jules Robert Mayer, of Heilborn, Germany, and 
 Dr. James Prescott Joule, of Manchester, England, is due 
 more than, perhaps, to any others, the honor of firmly 
 establishing the modern conception of heat. Dr. Mayer 
 published, in 1842, an essay on the subject, in which he 
 showed by clear reasoning and analysis that heat could 
 not be a material substance. This was almost immedi- 
 ately followed by the publication, in 1843, of the results 
 of the elaborate experiments made by Joule at Man- 
 chester. The results of Joule's experiments proved 
 conclusively the falsity of the materiality of heat, and 
 established the modern conception. 
 
 In February, 1850, Prof. John Macquorn Rankine 
 read, before the Royal Society of Edinburgh, a paper, 
 treating of thermodynamics, which, with a paper by Prof. 
 R. Clausius read in the same month and year, before the 
 Berlin Academy, may be considered as the beginning of 
 the work, carried on since then to the present day, upon 
 the Science of Thermodynamics. It is to be noted as a 
 curious coincidence that Rankine, in Scotland, and 
 Clausius, in Germany, each working independently of the 
 other, had reached practically the same conclusions at 
 the same time. 
 
 Before leaving this subject it may be well to call attention 
 to the fact that many of the methods of discussion used 
 in thermodynamics, in its application to the study of heat 
 engines, are due to Sadi Carnot, who, while rejecting the 
 modern conception and accepting the materiality of heat, 
 did much work that has been of value in formulating 
 methods of discussion and analysis. To him is due the 
 idea of the cycle process known as the Carnot Cycle, a 
 discussion of which will be given in the proper place. 
 
 2. FIRST LAW OF THERMODYNAMICS. Work and heat 
 
ELEMENTARY THERMODYNAMICS. 3 
 
 are mutually convertible; and whenever work is produced 
 by heat the quantity of heat consumed is exactly propor- 
 tional to the amount of work done, and, conversely, by the 
 expenditure of the same amount of work the same quantity 
 of heat may be produced. 
 
 The first part of this law was established by the 
 experiments of Rumford and Davy, but it was not until 
 the careful experiments of Joule were made that the 
 second part was assured. 
 
 / 
 
 3. WORK, POWER. Work is the overcoming of resist- 
 ance. 
 
 In order that work may be done it is necessary that 
 there should be not only a force but motion also. This 
 must be kept clearly in mind ; and it must also be 
 remembered that the element time does not enter at all. 
 A man may hold up a weight for any length of time 
 imaginable, but he does no WORK, in the mechanical sense 
 of the word, so long as the weight is held at rest. If, 
 however, he raises the weight, and in so doing overcomes 
 the resistance due to the force of gravity, he does work. 
 Again, if two men carry the same weight of goods up the 
 same stairs, each will do exactly the same amount of 
 work, even if one should carry his weight up the stairs in 
 one-tenth the time that the other does. 
 
 The unit of work is the foot-pound (ft.-lb.), which is 
 the amount of work done by a body in moving throzigh a 
 distance of one foot against a resistance of one pound. 
 
 It follows, from the definition of the unit of work, that 
 the work done by a body in overcoming any resistance is 
 equal to the product of the mean force of resistance and 
 the distance moved through. The force must be ex- 
 pressed in pounds, and the distance in feet. Since, then, 
 work is the product of two factors it may be represented 
 on a diagram as the area of a closed figure, whose mean 
 altitude represents the mean force of resistance, and whose 
 
4 STEAM ENGINES AND BOILERS. 
 
 length represents the space or distance moved through. 
 Such a figure may be termed a " Work Diagram." 
 
 To illustrate the method of forming a " Work Dia- 
 gram," let, in Fig. I, OX and OYbe two lines drawn at 
 right angles to each other, termed axes, a represents 
 the position of a body that is doing work. Its distance, 
 ad, from OX, represents the force against which it is act- 
 ing ; and its distance, ae t from Y, represents the distance 
 it has moved from its starting point or origin. Now 
 
 Fig. l. 
 
 suppose the body moves from a to b along the line ab, 
 which is so drawn that at any instant the distance of the 
 body from OX represents the force against which it is act- 
 ing at that instant, and its distance from Frepresents the 
 distance from its origin at the same instant. When the 
 body gets to b it is acting against a force represented by 
 the line be; and it has moved a distance dc from a. The 
 work done while the body moved from a to b is the mean 
 force of resistance, F m , multiplied by the distance dc t and 
 is represented by the area of the figure abed. 
 
 If the force of resistance had been uniform, while the 
 body moved from a to b, the line ab would have been 
 parallel to OX, and the work would have been equal to 
 ad X dc. 
 
ELEMENTARY THERMODYNAMICS. 5 
 
 In general, the expression for the work done is given 
 by the equation, 
 
 (1) 
 
 Where F is the force of resistance at any instant, and 
 s is the distance from the origin. In order to solve (i) 
 it is necessary to know the law of the path, ab, of the 
 body. 
 
 Power involves the element time, and is the amount of 
 work done in a unit of time. 
 
 In all calculations relating to engines, the power 
 involved is usually so large that the unit of power used is 
 the Horse-Power, H. P., which is 33,000 ft.-lbs. of work 
 done in one minute ', or 550 ft.-lbs. in one second. 
 
 To obtain the Horse-Power exerted by an engine, get 
 the work done per minute and divide by 33,000; or, if 
 W represents the work done per minute, the horse-power 
 is 
 
 < 2 > ** 
 
 4. UNIT OF HEAT. Rankine defines the unit of heat as 
 "the quantity of heat which corresponds to an interval of 
 one degree of Fahrenheit's scale in the temperature of 
 one pound of pure liquid water, at and near its tempera- 
 ture of greatest density (39.1 Fahrenheit)." 
 
 Other writers define it as " the amount of heat required 
 to raise the temperature of one pound of water from 32 
 to 33 F." 
 
 In this work, however, the Unit of Heat will be taken 
 as the amount of heat required to raise the temperature of 
 one pound of water from 62 to 63 Fahrenheit. 
 
 The difference between the three amounts taken as 
 
6 STEAM ENGINES AND BOILERS." 
 
 the unit, is, however, so small that in practice it may be 
 neglected. 
 
 5. MECHANICAL EQUIVALENT. The " Mechanical Equiv- 
 alent" means the number of foot-pounds of work that is 
 done when one unit of heat is consumed, and is generally 
 designated by the letter J. 
 
 The experiments made by Rumford and Davy were 
 too crude to give any accurate value for the mechanical 
 equivalent, and it was not until the time of Mayer and 
 Joule that a value could be assigned to it with any 
 degree of certainty. Mayer, from certain properties of 
 gases, deduced a theoretical value forj; but it remained 
 for Joule to determine, by a series of carefully conducted 
 experiments extending from 1842 to about 1850, the 
 value of /as 772 ft.-lbs. This value was accepted and 
 used as the correct one until Joule and others showed 
 by later, and perhaps more carefully conducted, experi- 
 ments, that 772 was probably too small. 
 
 Recently, Rowland, of Baltimore, by a series of 
 experiments, in which great care was taken to guard 
 against errors of all kinds, showed the value of the 
 Mechanical Equivalent to be 778 ft.-lbs, the unit of heat 
 being as used in this work. It is probable that 778 
 ft.-lbs. is nearer the true value of J than 772, and in this 
 work 778 will be assumed as the true value. 
 
 6. APPLICATION OF HEAT TO BODIES. Whenever heat 
 is imparted to a body, that is not on the point of chang- 
 ing its state, two effects may generally be observed : 
 
 1st. The temperature of the body rises; its "sensible 
 heat " is increased. 
 
 2nd. The body expands ; its volume is increased. 
 
 There are some exceptions to the general law that the 
 body expands when heated, but in all cases the statement 
 
ELEMENTARY THERMODYNAMICS. 7 
 
 of the law, as given, will suffice if contraction be considered 
 as a negative expansion. 
 
 When heat is supplied to a body, a part of the heat is 
 used simply to increase its temperature, and the remainder 
 is converted into work. The work done may be classed 
 under two heads, internal and external. The internal 
 work is made up of two parts: the first is the work 
 done in effecting that change of the condition of the 
 particles due simply to the increase of temperature ; the 
 second is the work done in increasing the volume of the 
 body against the resistance of molecular attraction. The 
 external work is that due to the increase in the volume 
 of the body against the resistance of the pressure of the 
 surrounding air or gases. 
 
 The general expression for the heat used in heating a 
 body may, then, be put in the form 
 
 (3) H = JQ = S + L + W. 
 
 H is the total heat used, expressed in mechanical units, 
 i. e., foot-pounds ; /is the Mechanical Equivalent of heat, 
 778 ; <2 is tne total heat used, expressed in heat units ; S 
 is the heat used in simply increasing the temperature of 
 the body ; L is the heat used in doing the internal work ; 
 W is the heat used in doing external work. S, L, and W 
 are expressed in foot-pounds. 
 
 7. SECOND LAW OF THERMODYNAMICS. Rankine gives 
 this law as follows : " If the total actual heat of a homo- 
 geneous and uniformly hot substance be conceived to be 
 divided into any number of equal parts, the effects of those 
 parts in causing work to be performed are equal" 
 
 He also says, " This law may be considered as a par- 
 ticular case of a general law applicable to every kind of 
 actual energy ; that is, capacity for performing work con- 
 stituted by a certain condition of each particle of a sub- 
 
8 STEAM ENGINES AND BOILERS. 
 
 stance, how small soever, independently of the presence 
 of other particles (such as the energy of motion) ." 
 
 Rankine's statement of the Second Law means simply 
 that a unit of heat is equivalent to a definite amount of 
 work independent of the part or the temperature of the 
 hot body from which it is taken. A unit of heat taken 
 from the inside of a body is equivalent to the same 
 amount of work as a unit of heat taken from the surface ; 
 and a unit of heat from a body whose temperature is 
 1000 is exactly the same as a unit of heat taken from a 
 body whose temperature is 60. 
 
 Clausius agrees with Rankine in his statement of the 
 first law, but as his method of reasoning is different from 
 that of Rankine, his statement of the Second Law, or 
 Second Main Principle as he calls it, is different. It is : 
 " Heat cannot, of itself, pass from a colder to a hotter body" 
 
 8. SPECIFIC HEAT. There are two specific heats to 
 every body ; they may be termed the apparent specific 
 heat, and the real specific heat. 
 
 The apparent specific heat is the amount of heat required 
 to raise the temperature of one pound of a substance one 
 degree Fahrenheit. 
 
 The apparent specific heat is usually spoken of as 
 simply the " specific heat. " It includes not only the 
 amount of heat required to change the temperature of the 
 body one degree, but, also, that heat used in doing such 
 internal and external work as may accompany the change 
 of temperature. It is further subdivided into specific heat 
 at constant volume, CM, and specific heat at constant pres- 
 sure, p . 
 
 Specific heat at constant volume is the amount of heat 
 required to change the temperature of one pound of a 
 substance one degree when the volume is kept constant. It 
 includes only such heat as is required for the change of 
 temperature and that part of the internal work due to this 
 change, and excludes all heat required to do work on 
 account of change of volume. 
 
ELEMENTARY THERMODYNAMICS. 9 
 
 Specific heat at constant pressure is the amount of heat 
 required to change the temperature of one pound of a sub- 
 stance one degree when the pressure is kept constant. It in- 
 cludes all the heat required to do the internal and external 
 work due to change of volume, and is, therefore, greater 
 than the specific heat at constant volume. 
 
 The real specific heat of a body is the amount of 
 heat required simply to change the temperature of one 
 pound of a substance one degree, excluding all heat used 
 for internal and external work. 
 
 In the case of perfect gases the internal work done 
 during a change of temperature is zero, and the specific 
 heat at constant volume is actually equal to the real 
 specific heat. In the cases of solids and liquids, the amount 
 of heat used for internal work when the temperature is 
 changed at constant volume is so small as compared with 
 that required only for change of temperature, that it is usual 
 to consider the specific heat at constant volume as equal 
 to the real specific heat. 
 
 Let -v represent the specific heat at constant volume, 
 expressed in foot-pounds ; K^ the specific heat at constant 
 pressure, in foot-pounds ; then, for a perfect gas, 
 
 (4) Jp, = ,7cp = 7 * =14Morair _ 
 
 Ay J C V 
 
 9. ABSOLUTE TEMPERATURE. Gay-Lussac made a series 
 of experiments to determine the change in volume of a 
 gas when heated under constant pressure, and, as a result 
 of his experiments, found that the volume, Ft, of a gas at 
 a given temperature, /, on the Fahrenheit scale, was always 
 given in terms of its volume, V Q , at o, and its temperature 
 /, by the equation 
 
 (5) F t = F (l + aO, 
 
 where a is a constant factor, equal to ^ , termed the co- 
 efficient of expansion of perfect gases. 
 
 * This symbol is the Greek letter Gamma. It is used by all writers to repre- 
 sent the ratio of Jf p to K^. 
 
10 STEAM ENGINES AND BOILERS. 
 
 If the temperature, /, of the gas is below zero, or nega- 
 tive, then the plus sign in (5) becomes minus. 
 
 If a gas is cooled below o its volume will be less than 
 Vo\ if the cooling is continued, and the gas should always 
 contract in the manner indicated by Gay-Lussac, it is 
 apparent that finally a temperature will be reached where 
 the volume of the gas will become zero. To determine 
 this temperature put, in (5), for V^ its supposed value, and 
 get, 
 
 O = F (l+aO. Whence t = -- -=461. 
 
 ct 
 
 This point y 461, is the absolute zero, on the Fahrenheit 
 scale, and temperatures counted from it as the starting point 
 are absolute temperatures, and are usually designated by T. 
 
 Since the absolute zero is 461 Fahrenheit degrees below 
 the Fahrenheit zero, any temperature, /, on the Fahrenheit 
 scale may be converted into a temperature, T, on the 
 absolute scale by adding 461 to it. T = 461 + t. 
 
 Equation (5) may be written in the form 
 
 
 
 To is the absolute temperature for o F., and is equal to 
 461; T is the absolute temperature for f F., equal to 
 461 +t. 
 
 Equation (6) may be changed to 
 
 (7) I r = ^ = a constant. 
 
 10. APPLICATION OF HEAT TO A PERFECT GAS. If a 
 pound of gas be put into a cylinder, closed at one end, 
 in which works, without friction, a piston, the gas will 
 expand and force out the piston until the pressure of the 
 gas inside the cylinder is equal to that of the air on the 
 outside. If now, while the temperature is kept constant, 
 
x> "7"* 
 
 f o" THE 
 
 (UNIVERSITY 
 
 V^ o? 
 
 ^^JJ^-'^ 
 
 ELEMENTARY THERMODYNAMICS. 11 
 
 the volume of the gas is decreased by pushing in the 
 piston, the pressure exerted by the gas on the piston will 
 be increased ; if the volume occupied by the gas is 
 increased, the pressure exerted by it on the piston will be 
 decreased. The pressure exerted by the gas, while its 
 temperature remains constant, will increase or decrease, 
 as the volume is decreased or increased, according to 
 " Boyle's Law," which is: the pressure exerted by a gas, 
 whose temperature remains constant^ is inversely as its 
 volume. 
 
 In other words, if V\ and P represent respectively the 
 initial volume and pressure of a gas, at a constant tem- 
 perature, and V-2 and P 2 its final volume and pressure, the 
 relation existing between V\, Pi, Vi, and Pi, is 
 
 (8) ZL = 4X or p 2 F 2 = Pi Fi = a constant. 
 
 Fl /2 
 
 From equation (7), representing the relation between 
 the volume and absolute temperature of a perfect gas 
 under a constant pressure, and equation (8), representing 
 the relation between the volume and pressure of a per- 
 fect gas under a constant temperature, is obtained the 
 relation that must always, under all circumstances, exist 
 between the volume, pressure and absolute temperature 
 of a perfect gas. It is given by the equation 
 
 (9) ^p = ~p = R, a constant. ' 
 
 When the pressures are expressed in pounds per square 
 foot and the volumes in cubic feet, the value of R for one 
 pound of air is 53.15. For w pounds of a gas the con- 
 stant is w R. 
 
 Let it be supposed that the air in the cylinder, spoken 
 of before, is heated, while the pressure is kept constant 
 at PI Ibs. per square foot, until the absolute temperature 
 is increased from 7i to 7a . By definition, the amount 
 
12 STEAM ENGINES AND BOILERS. 
 
 of heat supplied to the pound of the gas is, in mechan- 
 ical units, the change in temperature, T 2 71, multiplied 
 by the specific heat at constant pressure, K P) or 
 
 (10) H = K(T 2 Ti). 
 But from (3) it is evident that 
 
 (11) H=S + L + W. 
 
 Where S, the heat required to change only the temper- 
 ature, is, fora perfect gas, K v (T* 71), since the real 
 specific heat is equal to the specific heat at constant volume; 
 L, the internal work, is, for a perfect gas, equal to zero ; 
 and W, the external work, must be the total force exerted 
 on the piston multiplied by the distance it has moved. 
 The total force exerted on the piston is the pressure per 
 square foot, Pi, multiplied by the area, A, of the piston ; 
 and if the initial distance of the piston from the bottom 
 of the cylinder is d\, and the final distanc e is d^, the dis- 
 tance moved is di d\. The external work is, then, 
 
 W=PiA (d 2 di) =Pi (Ad 2 Adi). 
 
 But Adi is equal to V 2 , the final volume occupied by 
 the gas ; and Adi is equal to V\ t the initial volume of the 
 gas. The expression for Wis, therefore, 
 
 Tr=Pi(F 2 Fi). 
 If for 5, L, and W\ are put their values, (n) becomes, 
 
 (12) H=K v (T, Ti) + Pi(F 2 Fi) 
 
 = K V (T 2 Ti) + P, F 2 Pi Fi. 
 
 Since the relation between the initial, and the final 
 
ELEMENTARY THERMODYNAMICS. 13 
 
 pressure, volume, and absolute temperature must satisfy 
 
 P Vi PI V\ 
 
 equation (9), we have \.. R, and = R. 
 
 Whence, P 1 Vz= R T^ and PI Fi = /2 TI 
 
 Substituting these values of /\ J^ and /^ f^l in (12), 
 and putting for .// its value, as given by (10), there is 
 obtained, 
 
 (13) #p (T 2 TO = /r v <!T 2 - TO + R (T 2 7\). 
 
 From which, 
 
 For a perfect gas, /^* specific heat at constant pressure 
 is equal to the specific heat at constant volume plus R % 
 
 ii. ISOTHERMAL EXPANSION. A body expands or 
 contracts Isothermally, when its volume is increased or 
 decreased in such a way that the temperature remains 
 constant. 
 
 Since the temperature remains constant during 
 isothermal expansion, the term S, representing the heat 
 required to effect a change of temperature of the body, in 
 (3) becomes zero ; and the expression for the heat used 
 by the body during isothermal expansion is 
 
 H = L + W. 
 
 That is, all the heat given to the body is transformed 
 into work, part of which is internal and part external. 
 
 Since, for a perfect gas, the term Z, representing the 
 internal work, becomes zero, as has been stated, the 
 expression for heat becomes, 
 
 11= W. 
 From the general law of a perfect gas, expressed by 
 
14 
 
 STEAM ENGINES AND BOILERS. 
 
 (9), it is evident that if the temperature is constant we 
 have, 
 
 (15) 
 
 p, 2 V? = 
 
 TiR=a, constant. 
 
 \ 
 
 Fig. 2. 
 
 Equation (15) represents the law of the change of 
 pressure and volume during isothermal expansion ; and 
 the curve represented by the equation, on the work 
 diagram, is called the Isothermal curve, which for a 
 perfect gas is the equilateral hyperbola. 
 
 In Fig. 2 let OX and Y represent the two axes ; the 
 co-ordinates of a, PI, V\ t the initial pressure and volume 
 of the gas ; and the co-ordinates of b t P%, Vz, the final 
 pressure and volume of the gas. Also, let the curve ab 
 be an isothermal curve, or equilateral hyperbola. The 
 work done by the gas in expanding isothermally from V\ 
 to Fz, is represented by the area of the diagram abed; 
 and since the heat used is equal to the work done, 
 
 (16) H = W = area abed = \PdV=Pi Fi K 
 
 r 
 
 l 
 
 ^ Vi 
 
 = PI Fi hyp. log. ^r 
 
 * Hyp. log. ifi the usual contraction for " hyperbolic logarithm." Table II is a 
 table of hyperbolic logarithms. 
 
ELEMENTARY THERMODYNAMICS. 15 
 
 12. ADIABATIC EXPANSION. Bodies expand adiabati- 
 cally when during the expansion, they neither emit nor 
 receive any heat. This is expressed by making H in 
 equation (3) equal to zero, and the equation then be- 
 comes, 
 
 (17) = 8 + L + W. 
 From which 
 
 (18) L + W = 8. 
 
 For one pound of the body 5 is equal to the specific 
 heat at constant volume, assumed as equal to the real 
 specific heat, multiplied by the difference between the 
 final and initial absolute temperatures, and (18) becomes, 
 
 (19) L + W= S = K V (T 2 7\) =/f v (!Fi T 2 ). 
 
 This equation shows that during adiabatic expansion 
 the temperature of the body falls and that the heat freed 
 by the fall in temperature is converted into work. Dur- 
 ing adiabatic compression, the work done on the body is 
 converted into heat which increases the temperature of 
 the body. 
 
 For a perfect gas the internal work, Z, done during 
 expansion is equal to zero, so that for a perfect gas (19) 
 becomes, 
 
 (20) 
 
 In order to obtain an expression for the relation that 
 exists between P and V during adiabatic expansion, 
 assume, in Fig. 3, that the curve ab t termed an adiabatic 
 
16 
 
 STEAM ENGINES AND BOILERS. 
 
 curve, represents the changes of volume and pressure 
 during expansion of one pound of gas; and that the 
 
 Y 
 
 d c 
 
 Fig. 3. 
 
 area abed represents the work done during adiabatic ex- 
 pansion. Assume the law of the relation of P to V to 
 be represented by the equation 
 
 P F n = P 2 F 2 n = Pi Fi n = a constant. 
 
 Where n is an exponent whose value remains to be 
 determined. The work done during expansion is repre- 
 sented by the area abed ; and by calculus, 
 
 (21) areaa&cd:= W = 
 
 l-n 
 
 c & 
 
 *-/ T-T *S TT1 
 
 Fi ~ F 1 
 
 Pi Fi P 2 F 2 
 n-1 
 
 It is already known, from (20), that the work done 
 during adiabatic expansion is 
 
 (22) 
 
ELEMENTARY THERMODYNAMICS. 
 
 From (9) it is known that 71 T 2 = PI Vl ~ 
 
 17 
 
 R 
 
 Putting this value of 71 T-i in (22), we get from (21) 
 and (22), 
 
 (23) W 
 
 From this, 
 
 (Pi Fi P 2 F 2 
 
 R 
 
 Pi P 2 F 2 
 
 71-1 
 
 From (14) we have A" p = ^ + A" v ; and from (4) we have 
 
 ^P T-I r ^P 
 
 pr = 7. Therefore, ^ = -77- = 7. 
 
 Ay Ay 
 
 The relation, then, between P and F during adiabetic 
 expansion is, since n is equal to 7, 
 
 (24) PF 7 = P 2 F 2 7 = Pi Fi 7 = a constant. 
 
 Fig. 4. 
 
18 STEAM ENGINES AND BOILERS. 
 
 A comparison of the equation of the isothermal curve 
 (15), with that of the adiabatic curve (24), makes it 
 apparent that the latter is the steeper curve. 
 
 A F 2 Pi Vi 
 From (9) ^ ^ , and, therefore, 
 
 /j ~ ' T7" '^ T 7 * 
 2 Kl -*2 
 
 Therefore, 
 VFij 
 
 ^i / ^2\ ' 
 
 But -^ 1 = = ( -y \ > 
 
 T7" /\ /7i 5 or 
 
 Kl ^2 
 
 (25) ^ 
 
 In Fig. 4, let #^ and <:</ represent the isothermal curves 
 of a perfect gas corresponding to the absolute temperatures 
 71 and 7a respectively. Also, let # and ^ represent 
 adiabatic curves intersecting the isothermal curves. If 
 now a gas expands so that the relation between P and V 
 is shown by the adiabatic curve ac, from 71 to 7a, the 
 work done will be, from (20), K^ (71 7" 2 ), and will be 
 represented by the area #/". Also, if the gas expands 
 according to the adiabatic curve bd, from 71 to 7" 2 , the 
 work done will be Kv (71 7i), and will be represented 
 by the area bdnm. 
 
 Therefore, the area acgfis equal to the area bdnm. 
 
 By inspection of the figure it is seen that, area abdc + 
 area cdng + area acgf = area abmf + area bdnm. 
 
 From which, as area acgf = area bdnm, we get area 
 ai& = area abmf area cdng. 
 
 If the expansion were carried so far that 7a became zero, 
 the area cdng would also become zero, and we should 
 have area abdc = area abmf. When T% is zero, the lines 
 
ELEMENTARY THERMODYNAMICS. 19 
 
 eg and dn will be at infinity and each equal to zero. 
 Hence we have, since acgf is always equal to bdnm, that 
 the work done during adiabatic expansion from Pi and T\ 
 to zero temperature is equal to that done during adiabatic 
 expansion from P\ and 71 to zero temperature. 
 
 13. FUSION. When a solid body changes to a liquid 
 it is said to fuse or melt. 
 
 The temperature at which fusion takes place, under 
 standard atmospheric pressure of 14.7 Ibs. per square inch 
 or 2 1 1 6. 8 Ibs. per square foot, is termed the fusing point of 
 the body. During fusion the temperature of the solid 
 and liquid remains constant at the fusing point, so that in 
 the general expression, H= S + L + W, for heat used by 
 a body, the term .S becomes zero. The expression for the 
 heat to fuse one pound of a body, is, then, H= L -f- W. 
 
 The heat required to fuse one pound of a solid, under stand- 
 ard atmospheric pressure, is the latent heat of fusion. 
 
 As the change of volume on fusing is small, for most 
 solids, the value of W, the external work, is small ; and 
 the greater part of the latent heat of fusion is used in 
 doing internal work. In the case of bodies, such as ice, 
 that decrease in volume on fusing, W becomes negative. 
 
 14. VAPORIZATION. Vaporization is the conversion of 
 a liquid into a vapor. 
 
 The temperature at which vaporization takes place 
 depends not only upon the liquid to be vaporized, but, also, 
 upon the pressure to which it is subjected. During the 
 vaporization the temperature remains constant, if the 
 pressure does not vary. 
 
 The temperature at which, under a given pressure, a 
 liquid is converted into a vapor is termed the " boiling 
 point " for the given pressure. 
 
 The heat required to vaporize one pound of liquid under 
 a given pressure is the latent heat of evaporation for the 
 given pressure. 
 
20 STEAM ENGINES AND BOILERS. 
 
 Since, during vaporization, the temperature of the 
 liquid remains constant, the expression for latent heat of 
 evaporation is 
 
 H = l = L+ W. 
 
 As most liquids expand considerably upon being con- 
 verted into vapor, the value of W t the external work, may 
 be quite large. 
 
 15. APPLICATION OF HEAT TO WATER. When heat 
 is applied to water its temperature rises gradually, and as 
 the specific heat of water increases slightly as the tem- 
 perature rises, the heat required to raise one pound of 
 water from ti to fa is somewhat greater than fa 1\. For 
 ordinary work, however, it is sufficiently accurate to assume 
 that the specific heat of water is constant, and, therefore, 
 that the heat, in heat units, required to change the tem- 
 perature of one pound of water from t\ to fa is fa 1\. In 
 mechanical units it is J (fa ti). If the heating is con- 
 tinued long enough the temperature of the water will be 
 raised to the boiling point, and the water will be converted 
 into steam. 
 
 The latent heat of evaporation, in heat units, of steam 
 is usually denoted by /, and may be approximately 
 calculated by the equation, given by Rankine, 
 
 (26) I = 1114. 4 Q.7t. 
 
 t is the temperature, in Fahrenheit degrees, at which 
 the steam is formed. 
 
 If (26) is multiplied by J 9 equal to 778, there will be 
 obtained, l lt the latent heat of steam expressed in 
 mechanical units : 
 
 (27) l l= =Jl = 867000 544.6*. 
 
ELEMENTARY THERMODYNAMICS. 21 
 
 The heat, h, in heat units, required to raise the 
 temperature of one pound of water from h to t\ and 
 convert it into steam at t\ is 
 
 (28) h=l + t l 1- 2 . 
 
 Multiply (28) by J and we shall have, h\ t the heat in 
 mechanical units required to raise the temperature of one 
 pound of water from / 2 to t\ and convert it into steam 
 at /i. 
 
 (29) hi =Jh=J[l + t 1 fe]. 
 
 The latent heat is used in doing the internal work L, 
 and the external work W. The external work is the 
 product of the pressure per square foot, under which the 
 steam is formed, and the difference between F w , the 
 volume of one pound of the water and F s , the volume of 
 one pound of the steam. Assuming that F w is so small 
 as compared to F s that it may be considered as zero, and 
 that the pressure per square inch under which the steam 
 is formed is p, the external work is, approximately, 
 
 (30) TT=144#F 8 . 
 
 In practical problems relating to the steam engine we 
 usually know the values of/ and A; but the value of F 3 
 must be obtained from a table made from the results of 
 actual experiments. 
 
 Pressure gauges, used to indicate the pressure of steam 
 in steam boilers, are so constructed that they do not 
 show the absolute or tme value of the pressure of the 
 steam, but show the pressure, per square inch, above that of 
 the atmosphere. The pressure of the atmosphere is 14.7 
 (often taken as 15) pounds per square inch. In order, 
 then, to obtain the absolute value, /, of the pressure of 
 the steam it is necessary to add 14.7 to the gauge 
 pressure. 
 
22 STEAM ENGINES AND BOILERS. 
 
 Tables giving the different properties of steam for 
 different pressures are termed Steam Tables ; and are all 
 based upon experiments made by Regnault. Table I, in 
 this work, is a Steam Table. 
 
 In the first column is given the gauge pressure, per 
 square inch, of the steam, calculated upon the assumption 
 that the atmospheric pressure is 14.7 pounds per square 
 inch. The gauge pressure is given rather than the abso- 
 lute pressure, as the author considers it the more conven- 
 ient of the two to use in practice. 
 
 In the second column is given the temperatures, to the 
 nearest degree, in Fahrenheit degrees, of the steam 
 formed under the different pressures. 
 
 In the third column is given, in heat units, the total 
 heat above 32; i. e., the total quantity of heat required 
 to raise one pound of water from 32 to the temperature 
 of the steam, and then turn it into steam. 
 
 In the fourth column is given, in heat units, the latent 
 heat of the steam. 
 
 In the fifth column is given the volume, in cubic feet, 
 of one pound of the steam. 
 
 16. SUPERHEATED STEAM. When steam is sepa- 
 rated entirely from the presence of water and heated it 
 becomes superheated, and approaches the condition of 
 a gas ; the higher its temperature is raised the more and 
 more it departs from the nature of a vapor and approaches 
 that of a gas. The more nearly it assumes the condition 
 of a gas, the more nearly will the equations of a gas 
 apply to it. 
 
CHAPTER II. 
 
 THEORY OF THE STEAM ENGINE. 
 
 17. THEORETICAL HEAT ENGINE. A heat engine may 
 be defined as a machine for converting heat into work. 
 
 In the theoretical heat engine we suppose, what never 
 exists in reality, that we have a machine that works with- 
 out friction and that is made of materials that will act as 
 perfect conductors or non-conductors of heat, as desired. 
 These suppositions are made in order that the problems 
 may be simplified in the beginning. After we have dis- 
 cussed the theoretical engine we can discuss the real 
 engine, with its attending complications of friction and 
 losses of heat by radiation and conduction. 
 
 In all engines, theoretical or otherwise, the heat is 
 brought from its source to the engine by what is termed 
 the working fluid; this may be a liquid, a liquid and vapor, 
 or a perfect gas. In the theoretical engine, it is supposed 
 that all the changes through which the working fluid 
 passes, during the transformation of heat into work, take 
 place in the engine itself; the working fluid is supposed 
 to always remain in the engine and the same portion of 
 the fluid is supposed to be used over and over again. 
 
 1 8. CYCLE. The term cycle, as applied to a heat 
 engine, means a number of consecutive scries of changes in 
 the condition of the working fluid, such that the final condi- 
 tion of the fluid, at the end of the series, is, in all respects, 
 the same as was the initial condition at the beginning of the 
 series. 
 
 In every cycle three processes are gone through : 
 
 (23) 
 
24 STEAM ENGINES AND BOILERS. 
 
 1. A quantity of heat is given to the working fluid by 
 a hot body* 
 
 2. A part of the heat received by the working fluid is 
 given to a cold body. / 
 
 3. A part of the heat received by the working fluid is 
 transformed into external work. 
 
 As the working fluid is, in all respects, in precisely the 
 same condition, as to temperature, pressure, and volume, 
 at the end of the cycle that it was at the beginning, the 
 internal work done during the cycle must amount to zero, 
 and no heat can have been used, therefore, to do internal 
 work. It follows, then, that the total amount of heat 
 given to the working fluid during a cycle, must be equal 
 to the sum of that given by the working fluid to the cold 
 body and that converted into work. Let H be the total 
 quantity of heat received from the hot body ; U the 
 quantity given to the cold body by the working fluid; 
 and W that quantity transformed into external work. 
 Then, if all are expressed in mechanical units, 
 
 (31) H= U+ W. 
 
 Equation (31) may be considered as the principal 
 equation for the cycle of the theoretical heat engine. 
 
 H can usually be calculated when the working fluid 
 employed is known, and when the conditions under 
 which the heat is received are known. 
 
 W can always be obtained from the work diagram, 
 formed by plotting the various changes of pressure and 
 volume of the working fluid during the cycle* 
 
 If is sometimes difficult to calculate, but if the working 
 fluid and the conditions under which the cooling takes 
 place are known, there will be no trouble. 
 
 As an example of a cycle, assume that the co-ordinates 
 of the point a in Fig. 5 represent the pressure and volume 
 of one pound of the working fluid of a perfect engine. 
 
THEORY OF THE STEAM ENGINE. 
 
 25 
 
 Let P lt V\ t and 71, be the initial pressure, volume, and 
 absolute temperature, respectively, of the fluid. 
 
 Fig. 5. V 
 
 Suppose the working fluid is heated at the constant 
 volume V\ until the pressure is^/2, and the absolute tem- 
 perature is 72. The line ab will represent the changes of 
 volume and pressure during this process. 
 
 Next, let the fluid receive heat at the constant pres- 
 sure P 2 until its volume is J/2, and its absolute temperature 
 is Ts. be will represent the changes of volume and pres- 
 sure during this part of the cycle. 
 
 Now, let the hot body be removed and a cold one be 
 substituted for it, and let the working fluid be cooled at 
 the constant volume Vi until the pressure is PI, and its 
 absolute temperature is T. cd will represent the changes 
 of volume and pressure during this process. 
 
 Let the fluid be further cooled at the constant pressure 
 PI until the volume is V\ y and the absolute temperature is 
 71. When this has been done, the cycle will have been 
 completed and the fluid will have arrived at its original 
 condition. 
 
 The heat given to the working fluid is made up of 
 two parts : 
 
 I. That taken in while being heated at constant volume, 
 equal AT V ( 71 71), 
 
26 STEAM ENGINES AND BOILERS. 
 
 2. That taken in while being heated at constant pres- 
 sure, equal K^ ( T$ T* ). 
 Therefore, 
 
 The heat given by the working fluid to the cold bod}* 
 is also made up of two parts : 
 
 1. That emitted while being cooled at constant vol- 
 ume, equal K v ( T$ T ). 
 
 2. That emitted while being cooled at constant pres- 
 sure, equal K^ (T 71). 
 
 Therefore, 
 
 U= K v (T 3 T) + /ip (T, TO. 
 
 The external work done is represented by the area of the 
 
 work diagram abed 
 
 Therefore, 
 
 W=(P 2 Pi) (F 2 Fi). 
 
 If the values of H, U, and W y as derived, are substituted 
 in (31), we have 
 
 ff v (T 2 TO + /f p (T s T 2 ) = K v (T 3 T 4 ) + 
 K p (T 4 Ti) + (A A) (F a Fi). 
 
 The changes that the working fluid is supposed to pass 
 through during the cycle may be any we choose. In the 
 Carnot cycle, named after Sadi Carnot, the changes 
 are : 
 
 1. The fluid receives heat while expanding isothermally. 
 
 2. The fluid expands adiabatically. 
 
 3. The fluid is cooled while being compressed isother- 
 mally. 
 
 4. The fluid is compressed adiabatically. 
 
THEORY OF THE STEAM ENGINE. 27 
 
 J 
 
 19. THERMODYNAMIC EFFICIENCY. This term is used 
 to denote the ratio of the work done during a cycle, to the 
 total heat taken by the working fluid from the hot body. 
 The algebraic expression for the efficiency is 
 
 w W - U 
 
 E== U~ ~H' 
 
 The external work done by a heat engine is equal to the 
 product of the heat used, H, and the efficiency, E, or 
 W= HE. 
 
 As will be seen later, the Carnot cycle is the most effi- 
 cient of all possible cycles for any working fluid; and the 
 expression for the efficiency of this cycle is 
 
 (33) 
 
 71 is the absolute temperature at which the working 
 fluid receives its heat. 
 
 T-2 is the absolute temperature at which the working 
 fluid emits its heat to the cold body. 
 
 20. PERFECT GAS ENGINE. The perfect gas engine is 
 supposed to be a theoretical engine using a perfect gas 
 as a working fluid. When a gas is used as the working 
 fluid, all the calculations necessary to determine the heat 
 received or emitted by the gas, during a cycle, can readily 
 be made, since all the properties of a perfect gas are well 
 known. 
 
 For instance, in Art. 1 8, it was shown that for a perfect 
 engine using one pound of any fluid, the expressions for 
 Hj U, and W for the cycle used, are 
 
 JF=(P 2 -Pi)(F 2 -Fi). 
 
28 STEAM ENGINES AND BOILERS. 
 
 If the fluid had been a perfect gas, it will be easy to 
 show that H 7= W t as it ought. 
 
 To do this, let us refer to Fig. 5, remembering that for 
 
 PV 
 a perfect gas -y : = R, and K^ = K v + R, and determine 
 
 the va.lues of 71, T-2, T 3 , and 71, in terms of P^ V\ t P?, 
 and V* 
 
 Putting these values of 71, 7*, 7J, and 71, in the ex 
 pressions for ^T and U t we get 
 
 , 
 
 From (35), H U= (P 2 PI) (Fi F 2 ) 
 
 But - p - = i, from (14), and, therefore, we have 
 
THEORY OF THE STEAM ENGINE. 
 
 29 
 
 proved algebraically that 
 
 f g m n 
 
 Fig. 6. 
 
 If the cycle of work of the perfect gas engine be the 
 Carnot cycle, Fig. 6 represents the diagram of work. The 
 point a represents the initial condition of one pound of the 
 gas, where its pressure is P lt its volume Vi, and its absolute 
 temperature 71. During the first period of the cycle it 
 expands isothermally from a to b, where its pressure is P> 2 , 
 its volume Vi, and its absolute temperature 71. Next it 
 expands adiabatically from b to d, where its pressure is 
 /s, its volume V s , and its absolute temperature Ti. Then 
 it is compressed, and heat is taken from it, so that it con- 
 tracts isothermally from d to c, where its pressure is P^ 
 its volume V\ and its absolute temperature T- 2 . During 
 the last period it is adiabatically compressed from c to a, 
 thus completing the cycle. 
 
 While the gas expanded isothermally from a to b, the 
 
 
30 STEAM ENGINES AND BOILERS. 
 
 heat given to it was that necessary to do the external 
 work, represented by the area abmf, which, from (16), is 
 
 Pi Fi hyp. log. -?-. Therefore, 
 
 (36) H=Pi Fi hyp. log. ~. 
 
 v\ 
 
 The heat emitted by the gas to the cold body, is equal 
 to the work done during isothermal compression from d 
 to c, represented by the area cdng, which, from (16), is 
 
 P* V\ hyp. log. ~- Therefore, 
 
 (37) U= P 4 Fi hyp. log. -~. 
 
 The external work done during the cycle is represented 
 by the area abdc. Area abdc = area abmf + area bdnm 
 area acgf area cdng. But, as has been shown in Art. 
 12, area acgf= area bdnm, and, therefore, W= area abdc 
 = area abmf area cdng. Since area abmf = H, and 
 area cdng = U, we get from (36) and (37), 
 
 (38) W= Pi Fi hyp. log. j^ P 4 F 4 hyp. log. ~. 
 
 * 1 K4 
 
 From (9) we have P l V = 71 R and P F 4 = T 2 R; 
 and since ac and &/ are adiabatic lines, we have, from 
 
 (25), 
 
 M7-1 
 
 From this relation we get - = . 
 
THEORY OF THE STEAM ENGINE. 31 
 
 Putting for Pi Fi, its value, 71 R t for P^ V its value, 
 > R, anc 
 and (38), 
 
 (39) 
 
 T7 -rr 
 
 i> R, and for -JL its value, 1 we have, from ( 36), ( 37 ), 
 
 H=RT l hyp. log. IL. 
 
 U= R T 2 hyp. log. II. 
 
 W= R (T! T 2 ) hyp. log. 2 . 
 
 M. 
 
 The efficiency of the perfect gas engine working ac- 
 cording to the Carnot cycle is, from (39), 
 
 
 Since this expression for E does not involve any special 
 function or property of the working fluid, we say : 
 
 The efficiency of all heat engines, using any working 
 fluid according to the Carnot cycle, is as given by (40), 
 71 T-2 
 71 ' 
 
 As a further proof, let us suppose that the perfect gas 
 engine is used to run in the reverse direction a heat 
 engine using a working fluid that is more efficient than 
 the perfect gas. The working fluid in the second engine 
 would take heat from the cold body at a temperature T-i\ 
 would have work done upon it, instead of doing work ; 
 and would give heat to the hot body at a temperature 
 71. The second engine is transforming work into heat 
 instead of heat into work. It is evident, therefore, that 
 since the working fluid of the second engine is in pre- 
 cisely the same condition at the end of the cycle that it 
 was at the beginning, the heat given to the hot body 
 must equal the sum of that taken from the cold body and 
 that resulting from the transformation of work into heat. 
 It follows also, that if the second engine is more efficient, 
 
32 STEAM ENGINES AND BOILERS. 
 
 as supposed, than the perfect gas. engine, it will give to 
 the hot body more heat than the perfect gas engine trans- 
 forms into work. But as all the work done by the perfect 
 gas engine is used to run the second engine, the two to- 
 gether form a system by means of which heat is either 
 being created or made to pass from a cold to a hot body 
 without any disappearance of energy or change of any 
 kind in the conditions of the working fluids. That is, by 
 an arrangement of machinery, heat is either created or 
 made to pass from a cold to a hot body without any com- 
 pensation. 
 
 This conclusion is contrary to all our experience as to 
 the action of heat, and to our knowledge of the transform- 
 ation of heat into energy, and, therefore, cannot be con- 
 sidered true. Hence, the second engine is not more 
 efficient than the perfect gas engine. 
 
 If it were supposed that the second engine ran the per- 
 fect gas engine in a reverse direction, the same argument 
 would show that the second engine cannot be less effici- 
 ent than the perfect gas engine. 
 
 We are, therefore, forced to conclude that, since the 
 second engine is neither more efficient nor less efficient 
 than the perfect gas engine, the two engines have the 
 same efficiency. 
 
 By a method of proof that belongs to a more advanced 
 work than this, it can be shown that the Carnot cycle is 
 the most efficient of all possible cycles. Care must be 
 
 taken to remember that the efficiency of the heat engine 
 
 'p *p 
 
 is - : only when working according to the Carnot 
 
 T\ 
 
 cycle. 
 
 It would be well for the student to work out the ex- 
 pressions for the work done by, and the efficiency of, the 
 perfect gas engine working according to a number of 
 the cycles given under the head of Problems. 
 
 21. PERFECT STEAM ENGINE. The perfect steam 
 
THEORY OF THE STEAM ENGINE. 33 
 
 engine is a theoretical engine using water and steam as 
 the working fluid. 
 
 In the actual steam engine the working fluid is 
 usually considered as being steam only. This is due 
 to the fact that the steam engine really consists of 
 two parts that, in practice, are separated and are 
 considered always as being separate and apart from 
 one another. These parts are the engine, proper, and the 
 boiler. The steam receives its heat while in the boiler, 
 from which it passes to the engine and there does work ; 
 then it leaves the engine and usually passes out and away. 
 The steam drawn from the boiler is replaced by an amount 
 of water necessary to make a quantity of steam equal to 
 that taken away. In some cases, the steam, after leaving 
 the engine, is condensed and returned to the boiler. In 
 such cases, the actual engine approaches nearer to the 
 perfect engine than in any other, as here the same work- 
 ing fluid is used over and over again. In the perfect 
 steam engine the water is supposed to be converted into 
 steam while in the engine, and the engine itself takes the 
 place of both engine, proper, and boiler, in the actual 
 engine. The changes that the steam passes through dur- 
 ing one cycle of the perfect steam engine, may be sup- 
 posed to be exactly the same that it would pass through 
 in an actual engine and boiler together, if the losses of 
 heat due to radiation and conduction are neglected, and, 
 therefore, the work diagram of a cycle of the perfect 
 steam engine will be the same as the work diagram of 
 the real engine. 
 
 The cycle, then, that the perfect engine will be assumed 
 to make will be that which approaches nearest to the cycle 
 of the actual engine. 
 
 In Fig. 7, let a represent the initial condition of one 
 pound of water, just on the point of boiling, whose volume 
 is Vvr, pressure per square foot is PI, and temperature is 
 ti F. Let heat be given to the water so that it will be all 
 
 3 
 
34 STEAM ENGINES AND BOILERS. 
 
 converted into steam at the temperature t\ F. The line 
 showing the change in volume will be the line ab, parallel 
 to X, since the pressure remains constant. At b the 
 
 volume of the steam will be V\, the volume of one pound 
 
 p 
 
 of steam under a pressure per square inch of . When 
 
 all the water has been converted into steam, let the hot 
 body be taken away and let the steam expand from b to 
 d. In the actual engine the line of expansion bd is not 
 an adiabatic line, but usually approaches nearer the 
 equilateral hyperbola, unless the expansion is great, whose 
 equation is PI V\ = PI Vi = PV. We will suppose, then, 
 in order that the cycle of the perfect steam engine may 
 approach as nearly as possible to that of the real engine, 
 that the steam loses some heat while expanding from b to 
 d, and that bd is an equilateral hyperbola. While ex- 
 panding from b to d, part of the heat in the steam is being 
 transformed into work, and some of the steam is being 
 condensed ; so that, at d the fluid in the engine is a mix- 
 ture of water and steam at a volume V*, pressure per 
 square foot PI, and temperature / 2 F. At d it is sup- 
 posed that the engine is put in contact with a cold body, 
 corresponding to the condenser of the actual engine, and 
 all the steam is condensed at the uniform temperature 
 /2 F. The line showing the change in volume during the 
 condensation is dc, parallel to OX, since the pressure is 
 constant. The point c represents one pound of water, 
 whose volume is Vz, under a pressure per square foot of 
 P-2, and at a temperature / 2 F. Now, the engine is 
 again put in contact with the hot body until the tempera- 
 ture of the water is increased from fa to A, and the pres- 
 sure raised from P% to PI, thus completing the cycle. 
 The line ac represents the change in volume and pressure 
 during this last period of the cycle, and it is sufficiently 
 accurate to consider it as parallel to OY ; the volume at 
 c is equal to the volume at a. 
 
THEORY OF THE STEAM ENGINE. 
 
 35 
 
 The total quantity, H, of heat given to the water dur- 
 ing the cycle is, evidently, the heat required to raise 
 the temperature of the water from h to t\ t plus the latent 
 heat of evaporation at t\ ; it can be obtained from Table I, 
 
 m 
 
 Fig. 7. 
 
 in this work, or it may be calculated by using the ap- 
 proxmate formulae given in Art. 15. 
 
 The work, W, done during the cycle is represented in 
 the work diagram by the area abdc. From the figure, it 
 is seen that area abdc = area abng + area bdmn area 
 dcgm. 
 
 Area abng = Pi ( Fi F v ). 
 
 Area bdmn = \PdV = PiV -- = P x Fi /W- Zo^. -^ 
 
 Area dcgm = A ( F2 Fs). 
 
36 STEAM ENGINES AND BOILERS. 
 
 Therefore, 
 
 F> 
 W = area abdc = PI ( Fi F w ) + PI Fi hyp. log. -y- 
 
 -P 2 (F 2 - Fa). 
 
 V w and Pa are usually so small that they may, without 
 error, be considered as zero, and the expression for W 
 becomes 
 
 (41) W = Pi Fi l + fty/>. log. ~ - P 2 F 2 . 
 
 The value of U t the quantity of heat emitted by the 
 fluid during the cycle, cannot be calculated directly, as 
 we do not know the quantity of heat emitted during 
 expansion from b to d> nor the exact quantity of steam 
 condensed during compression from d to c. The value 
 of U t however, is given by the expression 
 
 U=H W. 
 
 The efficiency of the engine working according to the 
 given cycle is, 
 
 P! Fi (1 + hyp. log. -^ )- P 2 F 2 
 
 (42) E =- = ^ - 
 
 H H 
 
 If the engine had followed the Carnot cycle its 
 efficiency would have been 
 
 22. THEORETICAL DIAGRAM OF THE REAL ENGINE. 
 In order that all may fully understand the explanation of 
 the action of the steam in the engine, those who are not 
 
THEORY OF THE STEAM ENGINE. 
 
 37 
 
 f *o 
 
38 STEAM EXGIXES AXD BOILERS. 
 
 familiar with the names of the different parts of the 
 engine should refer to Figs. 8 and 9. 
 
 The steam is taken from the boiler to the " steam 
 chest " of the engine, through the u steam pipe." From 
 the steam chest it passes through the " steam ports " 
 into the " cylinder," and there moves the " piston." 
 The motion of the piston is communicated through the 
 " piston rod " to the " connecting rod," then to the 
 " crank," by means of which the " crank shaft " is given 
 a rotating motion. While the piston moves from one 
 end of the cylinder to the other, makes one " stroke," 
 the crank makes half a revolution. 
 
 The "point of cut-off" is that point in the stroke at 
 which the piston is when steam ceases to be admitted to 
 the cylinder: thus, the point of cut-off is at one-quarter 
 stroke, if the steam ceases to be admitted at the instant 
 the piston has finished one-quarter of a stroke. 
 
 The action of the steam in the cylinder is as follows : It 
 begins to enter the cylinder when the piston is beginning 
 its stroke, and by its pressure forces the piston forward. 
 As the piston moves forward steam is generated, at a 
 constant pressure, in the boiler, and flows into the cylin- 
 der ; so that the volume displaced by the piston is kept 
 constantly filled with steam at the boiler pressure. When 
 the piston reaches the point of cut-off the valve closes 
 communication between the steam-chest and the cylin- 
 der, and steam can no longer enter the cylinder. From 
 this on to the end of the stroke, the steam expands and 
 drives the piston forward simply by its expansive force. 
 As the piston reaches the end of its stroke the valve 
 opens the exhaust port, and the steam at once rushes out 
 of the cylinder into the place of exhaust, until the pres- 
 sure in the cylinder becomes about equal to that of the 
 place into which the steam is exhausted. If the engine ex- 
 hausted into the atmosphere, the pressure of the steam in 
 
THEORY OF THE STEAM ENGINE. 
 
 39 
 
40 STEAM ENGINES AND BOILERS. 
 
 the cylinder would drop almost to the atmospheric pres- 
 sure when the exhaust port is opened. In order to empty 
 the cylinder of the steam remaining in it, the piston is 
 forced back to its original position, against whatever 
 pressure there may be in the place of exhaust, either by 
 the pressure of steam admitted on the other side of the 
 piston or by the momentum of the fly-wheel fixed to the 
 shaft. 
 
 To make the diagram of work done by the engine 
 during one forward and backward stroke, assume, in Fig. 
 IO, that ao represents the absolute pressure, Pi, in pounds 
 per square inch, of the steam entering the boiler. Since 
 the steam enters at constant pressure up to the point of 
 cut-off, the line ab will represent the volume, V\, in cubic 
 feet, of the steam admitted to the cylinder at a pressure 
 per square foot of 144 P\. 
 
 From the point of cut-off the steam expands until the 
 piston reaches the end of the stroke, when the volume 
 of the steam is, in cubic feet, V^ and its pressure is P$ 
 pounds per square inch, as represented by the point c. 
 The line of expansion, be, may be assumed as the equi- 
 lateral hyperbola, whose equation is P\ T/i=P 2 V<z=PV. 
 
 When the exhaust port is opened, at the end of the 
 stroke, the pressure immediately falls to P s , as represented 
 at d. 
 
 On the return stroke, the piston moves against the 
 constant " back pressure " Ps, as represented by the 
 line de. 
 
 During the forward stroke of the piston, the steam does 
 the work on the piston represented by the area abcfo; 
 and during the return stroke, the piston does the work on 
 the steam represented by the area edfo. Therefore, the 
 effective work done by the steam, for each forward stroke 
 of the piston, is represented by the area of the diagram 
 abcde. 
 
THEORY OF THE STEAM ENGINE. 
 
 From the figure, we see that 
 
 area abcfo = area abgo + area 
 area abgo = 144 PI Fi, 
 
 41 
 
 f F 
 
 L4|pd 
 
 e-/ Fi 
 
 area bcfg == 144 |PdF= 144 PI Fi ^ / =144P 1 Fi hyp.log.~- 
 
 Therefore, the work done during a forward stroke is 
 
 (43) Wi = area a6c/o = 144 PI FI (1 + hyp. log. ). 
 
 Fig. 10. 
 
 If we call P m the mean forward pressure in pounds per 
 square inch on the piston during the forward stroke, then, 
 since the work done is equal to the pressure per square 
 foot multiplied by the volume swept through in cubic feet, 
 we have 
 
 (44) 
 
 Fi = 144 P m F a . 
 
42 STEAM ENGINES AND BOILERS 
 
 From (43) and (44) we get 
 
 -f hyp. log. ~ 
 
 P __v LL 
 
 ^ m ~ F 2 
 
 v, 
 
 The ratio ^ represents the number of times the steam is 
 
 Vl V\ 
 
 expanded. If this ratio be denoted by r, the cut-off, ~y , 
 
 will be ; and the expression for the mean forward pres- 
 sure becomes 
 
 1 + llyp ' log ' r 
 
 (46) P m = 
 
 On the return stroke, the work, W-2, done by the piston 
 on the steam is that represented by the area edfo, and, 
 from the figure, 
 
 (47) TF 2 = area edfo = 144 P 3 F 2 . 
 
 Since the effective work, W$ t done by the steam on 
 the piston is equal to that done on the forward stroke 
 minus that done on the return stroke, we have, 
 
 (48) TF 3 = TFi TF 2 = 144 P m F 2 144 P 3 F 2 . 
 
 If we let PQ be the mean effective pressure per square 
 inch on the piston, we shall have 
 
 (49) TF 3 = 144 P e F 2 = 144 P m F 2 144 P 3 F 2 . 
 Therefore, from (46) and (49), 
 
 (50) P e = P m _P 3 = 
 
THEORY OF THE STEAM ENGINE. 43 
 
 If A is the area of the piston in square inches, and L is 
 the length of stroke in feet, then 
 
 Put this value of p2 in (49) and we get 
 
 (52) W s = P e LA. 
 
 Now let -A 7 " be the number of forward strokes the engine 
 makes per minute. For a double acting engine, one that 
 takes steam on both sides of the piston, jVwill be equal 
 to twice the number of revolutions made by the engine 
 per minute ; and for a single acting engine, N will be equal 
 to the number of revolutions made per minute. Count- 
 ing the revolutions made by an engine is an easy method 
 of determining the value of N. 
 
 The work, IV, done per minute by the engine is, evi- 
 dently, N W%, and, therefore, from (52), 
 
 (53) W= P e L AN. 
 
 If H. P. represents the horse power of the engine, 
 
 C54) HP= -V- - Pe LAN 
 
 33UOO " 3oOOU 
 
 The diagram abcde, in Fig. 10, is termed the theoretical 
 Indicator Diagram of the real engine. The actual dia- 
 gram differs from that in Fig. 10 in that, owing to the 
 friction of the steam in the ports and the mechanical 
 imperfections in the valves, the corners of the diagrams 
 are always more or less rounded. The line ed has been 
 drawn as if the back pressure were constant, while as a mat- 
 ter of fact it is not ; the exhaust usually closes before all of 
 the steam has been forced from the cylinder, on the 
 return stroke, and thus confines a greater or less quantity 
 
44 STEAM ENGINES AND BOILERS. 
 
 of steam in the cylinder and which is compressed as the 
 piston is forced back. The amount of this compression 
 may be great or small, depending upon the type of 
 engine, but the greater it is the greater is made the 
 mean back pressure, P s . The absolute value of P$ for 
 engines that exhaust into the atmosphere will vary from 
 16 to 20 Ibs., depending upon the engine ; and for con- 
 densing engines, those that exhaust into a condenser, the 
 absolute value of P s will vary from 3^ to 8 Ibs., or even 
 higher. The dotted lines, in Fig. 10, show how the theo- 
 retical diagram must be changed to conform to the actual 
 diagram. 
 
 23. CLEARANCE. In the real engine the piston must 
 not touch the end of the cylinder when at the end of the 
 stroke, and there is, therefore, a space of greater or less 
 volume between the piston and the cylinder end. In 
 addition to this volume there is, also, the volume of the 
 steam ports that must be filled by steam. The sum of 
 these two volumes form what is termed the clearance, 
 or clearance volume of the engine. 
 
 The clearance is prejudicial to thermodynamic effi- 
 ciency of the real engine, as it preserves a volume 
 of what might be termed non-active steam subject to 
 condensation ; it usually increases the amount of steam 
 required to do a given amount of work, and decreases the 
 number of times the steam is expanded for a given cut-off. 
 
 If c represents the volume in cubic feet of the clearance, 
 the volume occupied by the steam at the point of cut- 
 off will be V\ + c; and at the end of the stroke, the 
 volume of the steam will be Vi + c. The real number of 
 times, n, the steam is expanded will be 
 
 T7" 
 F2 
 
 I/I 
 
THEORY OF THE STEAM ENGINE. 
 
 45 
 
 That is, the clearance has reduced the number of 
 expansions, r, in the ratio of 
 
 If we call m the ratio of the clearance volume, c y to the 
 volume, J/2, swept through by the piston in one stroke, 
 
 we shall have m = and, from (55), 
 
 (55a) 
 
 1 -f 
 
 O k 
 
 Fig. 11, 
 
 In Fig. II let a b c d e represent the diagram of an 
 engine with a clearance volume c; and let, as before, the 
 expansion line b c be an equilateral hyperbola. 
 
 The volume occupied by the steam at cut-off, repre- 
 sented by the line h b, is V\ -+ c = a b -j- h a ; and the 
 pressure per square inch during admission is the initial 
 pressure, P\ t represented by the line b g. The volume 
 occupied by the steam at the end of the stroke, repre- 
 sented by the line i d, is Vi-\-c = ed-}-ie; and the 
 
46 
 
 STEAM ENGINES AND BOILERS. 
 
THEORY OF THE STEAM ENGINE. 
 
 47 
 
48 STEAM ENGINES AND BOILERS. 
 
 pressure per square inch against which the piston moves 
 during the return stroke is PS, represented by the line df. 
 The work done during the forward stroke is represented 
 by the area a b c f k. By inspection we see that 
 
 = hbgo-\-bcfg h a k o. 
 hbgo = 144 PI ( Fi + c). 
 
 + c 
 bcfg= 144 I Pd V = 144 P! (Fi+c) hyp. log. T/2 
 
 /ri -i 
 144 I Pd F = 
 
 JFo4- n 
 
 F 2 +c 
 
 but ^ = n, from (55), and hence 
 v\-\-c 
 
 b cfg == 144 Pi (Fi + c) hyp. log. n. 
 hako = 144 PI c. 
 
 Therefore 
 a b cf k = 144 P l ( V 1 + c) (1 + hyp. log. n) 144 PI c. 
 
 If we let P'm represent the mean forward pressure per 
 square inch, the work done during the forward stroke is 
 144 P'm V-2. Putting this expression equal to the expres- 
 sion for a b c f k, given above, we have 
 
 144 P' m F 2 = 144 P! ( Fi + c) (1 + hyp. log. n) PI c. 
 From which we have 
 
 l ( 1 + hyp. log. ) - 
 
 But - . = ;;z, and from (55) 
 
 14- 
 
 F 2 _ 1 + m 
 
 F 2 w F 2 
 
 Therefore 
 
 (556) P' m = Pi (1 + m) ^^EJVK^vfi-y^ __ PI m> 
 
 n 
 
THEORY OF THE STEAM ENGINE. 49 
 
 The mean effective pressure per square inch, P' et is evi- 
 dently the mean forward pressure, P' m , less the back 
 pressure, P- A . Hence 
 
 (55c) P'e=P' m P3 
 
 n 
 
 This expression gives the true mean effective pressure 
 per square inch when clearance is taken into account. 
 The effect of clearance is not only to reduce the number 
 of times the steam is expanded, but also to very mate- 
 rially change the expression for the mean effective pres- 
 sure, as can be seen by comparing (50) and (55^). 
 
 24. EFFICIENCY OF THE ACTUAL ENGINE. The thermo- 
 dynamic efficiency of the actual engine is expressed by 
 the same equation as the efficiency of the perfect steam 
 engine, and is 
 
 *=J. 
 
 Where Wis the work done by a given weight of steam, 
 and //is the total heat in mechanical units, required to 
 raise the temperature of the same weight of water from 
 the initial temperature of the water up to the temperature 
 of the steam and there turn it into steam. 
 
 The work done per stroke by an engine is, from (52), 
 P e L A, and the volume, in cubic feet, of the steam, at the 
 
 -IT 
 
 initial pressure, used per stroke is V\= . 
 
 L A 
 
 From (51), F2= ; and, therefore, the volume of 
 
 144 
 
 steam used per stroke is 
 
 LA 
 
 (5G) 
 
 144r 
 
 If s is the volume in cubic feet of one pound of steam 
 4 
 
50 STEAM ENGINES AND BOILERS. 
 
 at the initial pressure, as given in Table I, the weight, S, 
 of steam used per stroke will be 
 
 Let k\ t as in (29), be the total quantity of heat, in me- 
 chanical units, required to raise the temperature of one 
 pound of water from the initial temperature of the watef 
 to the temperature of the steam and there convert it into 
 steam. Then the heat, HI, required for the weight, S, of 
 steam used per stroke will be, from (57), 
 
 (58) 
 
 144 r s 
 
 Since the work done per stroke is P e L A, and the heat 
 used per stroke is //i, the efficiency of the engine is 
 
 As the perfect steam engine had its efficiency de- 
 creased by departing from the Carnot cycle, so too, the 
 efficiency of the actual engine is less than that of the 
 perfect engine the more it departs from the cycle of the 
 perfect engine. In the perfect engine the expansion is 
 always continued until the pressure of the steam is*that 
 corresponding to the temperature of the feed water. In 
 Fig. 7, let dm be the pressure of the steam correspond- 
 ing to the temperature of the feed water, then the work 
 done by the perfect steam engine would be represented 
 by the area abdc y which is greater than the work that 
 would be done by the actual engine, by the area d'de. 
 
 The actual engine loses a great deal of heat by radia- 
 tion and conduction, which results in a condensation of 
 
THEORY OF THE STEAM ENGINE. 
 
 51 
 
52 STEAM ENGINES AND BOILERS. 
 
 the entering steam ; and the volume of steam that must 
 be applied to the engine is Fi, plus that required for 
 clearance, plus that required to compensate for what is 
 condensed. 
 
 A part of the work, resulting from the transformation 
 of the heat of the steam, is used in overcoming the 
 friction of the moving parts of the actual engine ; so 
 that the engine has a mechanical efficiency as well as a 
 thermodynamic efficiency, and the two must be care- 
 fully distinguished from one another 
 
CHAPTER III. 
 
 TYPES AND DETAILS OF ENGINES. 
 
 25. CLASSIFICATION OF ENGINES. Engine builders 
 usually classify their engines in two great classes as 
 follows : 
 
 1. Condensing Engines. 
 
 2. Non-condensing Engines. 
 
 Condensing engines are those that exhaust the steam 
 into a condenser; they may be either simple, have but a 
 single cylinder, or compound, have two or more cylinders. 
 While a condensing engine maybe a simple engine, most 
 of them are compound and expand the steam a greater 
 number of times than could be well done in a simple 
 engine. The mean back pressure, P 3 in Art. 22, is 
 always less than atmospheric pressure in the case of a 
 condensing engine. 
 
 Non-condensing engines are those that exhaust the 
 steam into the atmosphere ; and, while they may be either 
 simple or compound, they are usually simple. The mean 
 back pressure in these engines is always greater than the 
 atmospheric pressure, when the engine is running 
 properly. 
 
 Engines are sometimes classified according to whether 
 they are used on land or on the ocean, as Land engines 
 and Marine engines. 
 
 They may be classified according to the position of the 
 cylinder, as Vertical engines or Horizontal engines. 
 
 (53) 
 
54 
 
 STEAM EXGINES AND BOILERS. 
 
 In this work, all engines will be considered as coming 
 under one of the following heads : 
 
 1. Plain Slide Valve Engines. 
 
 2. Automatic High Speed Engines. 
 
 3. Corliss Engines. 
 
 There are engines on the market that on account of 
 peculiarities of design it would be extremely difficult to 
 
 Fig. 15. Horizontal Section. 
 Cylinder, Dick and Church Engine, 
 
 determine exactly under which head they would belong; 
 but such engines must be considered simply as connect- 
 ing links, in which an endeavor has been made to obtain 
 all the good qualities of the engines of two or more 
 types. Such engines are often, however, unfitted for any 
 special kind of work, as they possess to a certain degree 
 qualities that make them better than is necessary for 
 some work, and yet do not possess the same qualities to 
 
TYPES AND DETAILS OF ENGINES. 55 
 
 a sufficiently high degree to make them well fitted to do 
 other special work. 
 
 26. PLAIN SLIDE VALVE ENGINES. These engines are 
 usually plain in appearance, and use a simple form of D- 
 valve. Some are heavy, well made, and made of good 
 material; others are slight in weight, poorly made, and' 
 made of the poorest material. To this type of engines 
 belong most, if not all, of the very cheap engines. 
 Engines of this type, however, will stand more hard usage 
 and neglect than perhaps any other on the market; good 
 ones, of course, will stand more than cheap, poor ones. 
 They have rather gone out of fashion at present, and yet, 
 for some conditions and some kinds of work, they are 
 good engines. 
 
 Engines of this type have a fixed cut-off, which can 
 only be changed by re-adjusting the engine, and they 
 regulate by throttling the incoming steam so as to reduce 
 the initial pressure in the cylinder. The cut-off usually 
 occurs at about three-fourth stroke ; the clearance is about 
 ten to twelve per cent of the volume swept through by the 
 piston ; and there is little compression of Che exhaust steam. 
 It results, therefore, that as the steam has practically no 
 expansion, these engines are not economical in the use of 
 steam. 
 
 The mean back pressure for engines of this type may 
 be taken as about seventeen or eighteen pounds absolute. 
 
 In favor of engines of this type it may be said that they 
 are simple in construction ; require very little attention ; 
 are difficult to put much out of order, and are easily 
 repaired when deranged. They are suitable for out-of- 
 the-way places where facilities for repairs are few, and 
 for places where fuel is cheap and the work to be done is 
 practically constant. 
 
 The mechanical efficiency, as well as the thermody- 
 namic efficiency, of engines of this type is often small. 
 
OO STEAM ENGINES AND BOILERS. 
 
 In Fig. 8 is shown a section of an engine of this type, 
 and in Fig. 9 is shown a side view of one. 
 
 27. AUTOMATIC HIGH SPEED ENGINES. This type of 
 engines may be considered as the modern type, as it has 
 been evolved since the beginning of the great use of 
 electricity, and, indeed, is the result of the demand for an 
 engine to be used to run electric machinery. With the 
 
 Fig. 16. Cross-section. 
 Cylinder, Dick and Church Engine. 
 
 advent and great use of dynamos there was at once a 
 demand for small engines that could run at a high rota- 
 tive speed, that would be fairly economical under fluctu- 
 ating loads, and, above all, would run at a uniform speed 
 under great changes of load. The plain slide-valve type 
 of engines could not be said to satisfy any one of these 
 conditions; the Corliss engine did not satisfy the first 
 
TYPES AND DETAILS OF ENGINES. 57 
 
 condition as to high rotative speed, and, then, they were 
 too large, and, for small plants, occupied too much space. 
 Engines of this type are termed high speed not on 
 account of the speed of the piston, but on account of 
 the number of revolutions they will make per min- 
 ute. The speed of the engine is kept almost con- 
 stant by automatically changing the point of cut-off and 
 the amount of compression to suit the various fluctuations 
 of the load. The increase or diminution in the number 
 of revolutions will usually be about one per cent, or less, 
 for a sudden change of from full load to no load, or no 
 load to full load. This increase or diminution of speed, 
 however, will seldom last more than a few revolutions. 
 The number of revolutions made by an engine of the 
 automatic high speed type will depend upon the length 
 of stroke and upon the make ; the shorter the stroke 
 the greater the number of revolutions. Ordinarily, the 
 number of revolutions that an engine of this type will 
 
 make may be obtained by the formula, N= ~ 
 
 v L l 
 
 Where N is the number of revolutions made per min- 
 ute ; and L, the length of the stroke in inches. 
 
 On account of the high speed of rotation, engines of 
 this type must have large, ample bearings ; all parts must 
 be carefully proportioned, fitted and adjusted, and made 
 of good material. The greatest source of trouble with 
 these engines, which is overheating of bearings, can 
 usually be traced to poor materials and workmanship. 
 
 Engines of this type almost invariably use some form 
 of balanced valve, which is automatically made to change 
 the amount of steam admitted to the cylinder in such a 
 manner that the amount of steam admitted is nearly 
 proportional to the work to be done by the engine. 
 
 The cylinders of engines of this type are usually of 
 comparatively large diameter and short stroke ; the 
 diameter is usually between 0.60 and 0.80 of the 
 
58 
 
 STEAM ENGINES AXD BOILERS. 
 
 stroke, and is often equal to the length of the stroke. 
 These proportions of cylinders mean a short engine for a 
 given horse power, and a comparatively large clearance. 
 The clearance varies from about 5 to 10 per cent of the 
 volume swept through by the piston ; it may usually be 
 
 o> 
 
 "I 
 
 t 3 
 
 taken as about IO per cent for those engines having a 
 single valve, and 4 to 6 per cent for those having a system 
 of multiple valves. 
 
 The mean back pressure for engines of this type may 
 be taken as about eighteen or twenty pounds absolute. 
 
TYPES AND DETAILS OF ENGINES. 59 
 
 Most engines of this type have a center crank, although 
 some are made with a side crank. 
 
 Summing up, it may be said in favor of engines of this 
 type that they are fairly economical in the use of steam ; 
 occupy small space for a given power ; regulate well 
 under a fluctuating load ; and, as compared to engines of 
 the Corliss type, are of small first cost. 
 
 The engines of this type require careful attention to be 
 paid to the bearings, on account of the high speed of 
 rotation, and to the adjustments of the valves and other 
 moving parts. All bearings must be kept in good con- 
 dition and well lubricated. 
 
 Figs. II and 12 illustrate engines of this type. 
 
 28. CORLISS ENGINES. Under this head the author 
 includes, in addition to the engines of the pure Corliss type, 
 all of those engines that, even though not having the Cor- 
 liss valve gear, have more of the characteristics of the 
 Corliss engines than of the engines of the types already 
 described. Engines of this type, while having a high 
 velocity of piston, have a rather slow speed of rotation; 
 even the smaller sizes seldom make more than 100 revo- 
 lutions per minute. This is due principally to the nature 
 of the valve gearing used to operate the valves. An aver- 
 age value of the number of revolutions made per minute 
 by engines of this type will be given by the equation 
 
 N= y -, where L is the length of stroke in inches. 
 
 V J^i 
 
 The cylinders of engines of this type are usually of 
 comparatively small diameter and long stroke. The dia- 
 meter varies from one-third to two-thirds the length of the 
 stroke, but is usually about one-half the length of the 
 stroke. These proportions of cylinders mean a long 
 engine, occupying much space, for a given horse-power. 
 
 Engines of this type usually use a system of multiple 
 valves, which, by means of suitable mechanism, are made 
 
60 
 
 STEAM ENGINES AND BOILERS. 
 
 to cut-off the steam to suit the requirements of the load, 
 without changing the amount of compression of the ex- 
 haust steam. There is usually one steam valve and one 
 exhaust valve for each end of the cylinder, and the gov- 
 erning mechanism changes the action of the steam valve 
 only. 
 
 In order to preserve a uniform velocity of rotation, the 
 engines of this type not only have the cut-off automati- 
 
 Fig. 18. 
 Cylinder, Porter-Allen Engine. 
 
 cally changed to suit the varying fluctuations of the load, 
 but are provided, also, with large heavy fly-wheels, in 
 which surplus energy is stored when the load is de- 
 creased, and from which energy may be drawn when 
 the load is suddenly increased. By the aid of the au- 
 tomatic cut-off valves and the large fly-wheels, the varia- 
 tion in speed of engines of this type may be made as 
 small as desired. 
 
TYPES AND DETAILS OF ENGINES. 61 
 
 The clearance in engines of this type is usually about 
 2 per cent of the volume swept through by the piston, 
 although it varies from I to 4 or 5 per cent of that 
 volume. 
 
 The mean back pressure for engines of this type may 
 be taken as about 16 to 18 pounds absolute. 
 
 As the engines of this type make comparatively few 
 revolutions per minute, the bearings are not so apt to get 
 hot as in the case of engines of the automatic high 
 speed type. 
 
 This type of engines is the most economical of all 
 types, and for large establishments requiring much power 
 is undoubtedly the best. The engines of this type, how- 
 ever, are of greater first cost, and occupy more space 
 than do engines of the automatic high speed type. 
 They require considerable care and attention, and have a 
 number of small, light parts to be kept in repair and 
 adjustment. 
 
 Engines of this type are illustrated by Figs. 13 and 14. 
 
 29. CYLINDER AND VALVE CHEST. The cylinders of 
 engines are made of cast iron, with walls sufficiently 
 thick to stand the stress induced by the pressure of the 
 steam, and, also, the straining due to the motion of the 
 piston back and forth. The thickness should be such as 
 to allow at least one reboring. They are all true cylinders 
 inside, but the shape of the outside will 'depend upon the 
 style of engine and the maker. Most cylinders for short 
 stroke engines overhang the beds of the engines ; some are 
 cast solid with the beds, others are cast separate and 
 bolted on. This last form is perhaps the better, as the 
 cylinder can then be rebored with less trouble. 
 
 The steam chest is usually cast with the cylinder, 
 although it is sometimes cast separate and bolted on. Its 
 form and dimensions depend upon the valve, ports, and 
 type of the engine. 
 
STEAM ENGINES AND BOILERS. 
 
 
 o 
 ti 
 
TYPES AND DETAILS OF ENGINES. 63 
 
 The ports should be large, with smooth surfaces and 
 without any sharp or abrupt changes in direction. The 
 area of cross-section of the ports should be such that the 
 steam will travel at a velocity between 100 and 1 50 feet per 
 second when passing into the cylinder. The ports should 
 slope from the cylinder towards the steam chest, so that 
 all water that is condensed in the cylinder may easily 
 drain away. 
 
 Fig. 20. 
 Cylinder of Corliss Engine. 
 
 All cylinders should be provided with drip cocks, for 
 draining the cylinder and steam chest. 
 
 Some of the various methods of inserting the heads, 
 and protecting the cylinders by lagging, are shown in the 
 cuts of cylinders in this work. 
 
64 STEAM ENGINES AND BOILERS. 
 
 30. PISTON. The main point to be considered in con- 
 nection with a piston is tightness, as a leaky piston 
 reduces the efficiency of the engine very materially. For 
 engines of the high speed automatic type, where the 
 weight of the reciprocating parts is used to aid in regu- 
 lating the engine, weight is of an advantage rather than a 
 disadvantage ; while in the case of engines of the Corliss 
 type, weight is a disadvantage. The pistons of engines 
 of the automatic high speed type are, usually, much 
 thicker in proportion to the diameter, than those of the 
 Corliss type. 
 
 Pistons are usually made tight by using as "packing 
 rings," split cast iron rings that are turned slightly larger 
 in diameter than the bore of the cylinder. When they 
 are in the cylinder, the elasticity of the cast iron keeps 
 the rings pressed out against the cylinder, and thus pre- 
 vents the passage of the steam. The piston may be a 
 single casting, with grooves into which the packing rings 
 are sprung, or may be built up, as shown in Fig. 2 1 . There, 
 A is the "spider;" C, the "chunk" or "bull "ring; D, 
 the "packing ring;" and E, the "follower plate." 
 The bolts marked O are for adjusting the bull ring so 
 that it will always run true in the cylinder, even if the 
 center of the piston rod should not coincide with the 
 center of the cylinder. 
 
 31. CROSS-HEAD. The cross-head consists of the body 
 of the cross-head, the " slippers " or bearing surfaces, and 
 the " cross-head pin." 
 
 The cross-head is guided in its backward and forward 
 motion by the bearing surfaces of the top and bottom 
 "guides." Center crank engines have usually two top 
 guides and two bottom guides, as the cross-heads are 
 made with two sets of bearing surfaces, one at each end 
 of the cross-head pin, as shown in Fig. 22 ; while side 
 crank engines have usually one top guide and one bot- 
 tom guide, as the cross-heads have the general form 
 shown in Fig. 23. For automatic high speed engines, the 
 
TYPES AND DETAILS OF ENGINES. 
 
 65 
 
 bearing surfaces are usually plane surfaces, as shown in 
 Fig. 22 ; while for Corliss engines, they are usually V- 
 shaped, or cylindrical as shown in Fig. 23. Engines are 
 usually run "over," so as to bring the pressure of the 
 cross-heads always on the bottom gudes : that is, the en- 
 gines are run so that an observer facing an engine with 
 his left hand towards the cylinder, sees the fly-wheel re- 
 volve from left to right. The bearing surfaces of the 
 cross-heads are usually made of some anti-friction wear- 
 ing metal, such as Babbitt metal, and care should be 
 
 Fig. 21. 
 
 taken to keep them well lubricated. It is always best 
 to have some arrangement by means of which adjust- 
 ment may be made for the wear of the slippers, so as to 
 keep the line of motion of the center of the cross-head 
 pin coincident with the center line of the cylinder. If 
 there is no means of adjusting for the wear, and the line 
 of motion of the center of the cross-head pin is not coin- 
 cident with the center line of the cylinder, the friction on 
 the cross- head pin and crank pin is increased, and, also, 
 the cross-head will run loose in the guides and cause a 
 knocking noise when the load on the engine is suddenly 
 changed. 
 
 The cross-head pin is sometimes cast solid with the 
 body of the cross-head, and then turned up either by hand 
 
66 
 
 STEAM ENGINES AND BOILERS. 
 
 or, if the shape of the cross-head permits, by machinery ; 
 often, however, the pin is made separate and put into the 
 cross-head. This last method gives no advantage, to the 
 user of the engine, over the method of making the pin and 
 cross-head body one casting, unless the pin is put into 
 the body in such a way that it can be removed at any 
 time for returning. Separate pins are usually made of 
 steel. Many engine builders flatten the top and bottom 
 of the cross-head pin in order to reduce the wear. It is 
 
 Fig. 22. 
 Cross-head, Porter-Allen Engine. 
 
 doubtful, however, whether this practice attains its ob- 
 ject. Ample facilities should be provided for good and 
 proper lubrication of the cross-head pin. 
 Cross-heads are shown in Figs. 22 and 23. 
 
TYPES AND DETAILS OF ENGINES, 
 
 67 
 
 Fig. 23. 
 Cross-head, Ide Engine. 
 
68 STEAM ENGINES AND BOILERS. 
 
 32. CONNECTING ROD. The motion of the cross-head 
 is transmitted to the crank-pin through the connecting 
 rod, which is always made either of wrought iron or steel. 
 If it is assumed that the crank-pin moves with a uniform 
 velocity, the length of the connecting rod will have a 
 marked influence upon the velocity of the cross-head. 
 If the connecting rod could be so arranged that it would 
 always remain parallel to the line of motion of the piston, 
 then the distance that the piston has moved from the end 
 of its stroke, for a given movement of the crank, would 
 always be equal to the distance from the position of the 
 
 Fig. 24. 
 
 crank-pin when on dead center to the foot of a perpen- 
 dicular let fall from the crank-pin on the line of motion 
 of the piston. 
 
 In Fig. 24, let B represent the cross-head of an engine, 
 which being rigidly connected to the piston has the same 
 motion as the piston ; and let the line BC represent the line 
 of motion of the piston. Also, let A represent the center 
 of the crank-pin revolving about C and connected to B 
 by the connecting rod BA. Now, if the rod were infinitely 
 long it would always remain parallel to the line BC t and 
 the distance that the piston would have moved while the 
 crank moved from a\ to A would be equal to the distance 
 a\ d. Since, however, the connecting rod, BA, does not 
 remain parallel to BC, but is oblique to it, for all positions 
 
TYPES AND DETAILS OF ENGINES. 
 
 69 
 
 of the crank -pin except at a\ and #2, the distance, b\ B, 
 that the piston actually is from the end of its stroke is 
 not equal to a\ d. As will be shown 
 in Art. 47, it is known that during 
 the forward stroke the distance the 
 piston moves from the end of the 
 stroke, for a given motion of the 
 crank-pin, is greater than it would 
 be if there were no obliquity to the 
 connecting rod ; and during the re- 
 turn stroke, the movement of the 
 piston is less than it would be if there 
 were no obliquity. 
 
 The length of the connecting rod 
 is usually made equal to three times 
 the length of the stroke for Corliss 
 engines, and about two and a half 
 times the length of the stroke for 
 automatic high speed engines. 
 
 The cross-section of the connect- 
 ing rod of a Corliss engine is usually 
 a circle, and that of the connecting 
 rod of an automatic high speed en- 
 gine is usually a rectangle whose 
 greatest dimension is the depth of 
 the rod. 
 
 The connecting rod has at one end 
 the " cross-head pin brasses," and at 
 the other, the " crank-pin brasses." 
 The "brasses " are castings of brass, 
 fastened to the connecting rod in 
 various ways, which form the bearing 
 surfaces of the rod on either the 
 cross-head pin or the crank-pin. In 
 
 order that, as the brasses wear, the length of the rod, 
 measured from center of cross-head brasses to center of 
 
70 
 
 STEAM ENGINES AND BOILERS. 
 
 crank-pin brasses, may remain constant, it is necessary to 
 provide a means of taking up the wear. 
 
 In Fig. 25 is shown a connecting rod whose cross-head 
 
 Fig. 26. 
 Connecting Rod, Porter-Hamilton Eogine. 
 
 end is of a solid box form, into which the brasses fit; the 
 crank -pin end has the brasses attached to it by means of 
 a " strap/' held by a gib and key. The method of taking 
 up the wear of the brasses is indicated in the cut. 
 
 Fig. 27. 
 Connecting Rod, Woodbury Engine. 
 
 In Fig. 26 is shown a connecting rod whose crank end 
 is of the " marine " type, sometimes known as " club 
 ended; " the cross-head end has the strap attached to the 
 rod by a bolt, and a gib and key. 
 
TYPES AND DETAILS OF ENGINES, 
 
 71 
 
72 
 
 STEAM ENGINES AND BOILERS. 
 
 Fig. 27 shows a connecting rod whose cross-section is 
 I-shaped. The method of attaching the brasses and 
 taking up the wear is clearly shown. 
 
 33. CRANK. Those engines that have the crank 
 between the two main bearings of the shaft are center- 
 crank engines ; and those that have the crank on the same 
 side of both the shaft bearings are side-crank engines. 
 
 Fig. 29. 
 
 Most center-crank engines are of the automatic high 
 speed type, and have the crank and the shaft forged out of 
 one solid piece of iron or steel. Where this is the case it 
 is, usually, customary to fasten to each arm of the 
 crank a cast iron disk provided with a balance weight 
 to balance the weight of the crank and a part of the 
 weight of the connecting rod. The method of fastening 
 these balancing disks to the crank differs for different 
 makes of engines. Some center-crank engines have a 
 
TYPES AND DETAILS OF ENGINES. 
 
 73 
 
 built up crank ; the shaft is made of two pieces, to the 
 end of each of which is fastened a disk or wheel, and 
 these disks are then fastened together by the crank pin. 
 The disks are, usually, forced on the pieces of the shaft 
 by hydraulic pressure, and then keyed. The pin is, also, 
 forced into the disks by hydraulic pressure. 
 
 The diameter of the crank-pin of center-crank engines 
 is almost invariably the same as, of slightly greater 
 
 Fig. 30. 
 
 than, the diameter of the shaft ; and it's length is usually 
 equal to that of the cross-head pin. 
 
 In Figs. 28 and 29 are shown the forms of center- 
 cranks that have been described. Fig. 28 shows the 
 crank of the Woodbury engine, and Fig. 29 shows the 
 built up center-crank of the Straight Line engine. 
 
 Side crank engines may have simply a crank, forced by 
 hydraulic pressure onto the end of the shaft, into which 
 
74 STEAM ENGINES AND BOILERS. 
 
 the crank-pin is forced; or they may have a disk, termed 
 the crank-disk, forced onto the end of the shaft, which 
 carries. the crank-pin. 
 
 Most engines of the Corliss type have simply a crank, 
 while the side-crank engines of the automatic high speed 
 type, usually, have a crank-disk. 
 
 The crank-pin of side-crank engines is, usually, about 
 the same size as the cross-head pin. The method of 
 fastening the crank-pin into the crank, or the crank-disk, 
 varies with different makes of engines. Some are simply 
 forced into the hole, provided for them, by hydraulic 
 pressure; others are forced in, and then have a nut 
 put on the back ; while others are fastened in by other 
 methods. 
 
 It is of the utmost importance that ample provisions be 
 made for the proper lubrication of the crank-pin of all 
 engines, whether side-crank or center-crank. 
 
 34. MAIN BEARINGS. It is important that the main 
 bearings of an engine be large, lined with a good 
 wearing metal, and have proper facilities for lubricating. 
 Small bearings, or those not having proper provisions for 
 distributing the oil over the bearings, are apt to give 
 trouble by running too' hot and being constantly in 
 danger of cutting. 
 
 The caps to the main-bearings are those pieces that go 
 down over the shaft after it is in the bearings. They are 
 sometimes put on in a horizontal position and other times 
 are inclined at an angle of about 30. 
 
 In Fig. 30 is shown a section of the main bearing of 
 the Porter-Allen Automatic Engine. It is made in four 
 parts, viz., the bed, or bottom part; the side boxes, or 
 side parts ; and the cap, or top part of the bearing. By 
 screwing up the nuts marked a, the wedges may be 
 raised, and the side boxes pressed out and tightened 
 against the shaft. 
 
TYPES AND DETAILS OF ENGINES. 
 
 75 
 
 In Fig. 31 is shown a section of the main bearing of 
 the Porter-Hamilton Engine. 
 
 35. ECCENTRIC. The eccentric is simply a cast iron 
 disk through which the shaft passes and which moves the 
 valve of the engine. In the case of engines of the plain 
 slide valve type, and, also, of the Corliss type, the 
 eccentric is fastened to the shaft either by a key or by a 
 set screw. The advantage of the set screw over the key 
 
 Fig. 31 
 
 is that it allows the relative position of the eccentric on 
 the shaft to be changed at will ; and the disadvantage is 
 that at times the eccentric may slip and change its 
 relative position without that fact being known. 
 
 The distance that the center of the eccentric is from 
 the center of the shaft is its eccentricity. The eccentric 
 is equivalent to a crank whose length is equal to the 
 eccentricity, and takes the place of such a crank. As the 
 shaft is turned, the eccentric turns and moves the valve of 
 the engine back and forth as if it were connected to a 
 crank whose length is equal to the eccentricty of the 
 eccentric. 
 
76 
 
 STEAM ENGINES AND BOILERS. 
 
 On most engines of the automatic high speed type, the 
 eccentric is not fastened to the shaft, but the opening 
 through which the shaft passes is larger than the shaft ; 
 so that the relative position of the eccentric and, also, the 
 eccentricity can be automatically changed by the gov- 
 
 Fig. 32. 
 
 erning device. Changing the eccentricity, of course, 
 changes the travel of the valve, and, as we shall see later, 
 this affects the point of cut-off. 
 
 36. GOVERNORS. It is impossible to discuss here the 
 governing device of either the automatic high speed type 
 
TYPES AND DETAILS OF ENGINES. 77 
 
 of engines or the Corliss type, as that involves the dis- 
 cussion of the valve mechanisms that will be given later. 
 The governor used on engines of the plain slide valve 
 type is a " throttling governor," which is attached to the 
 steam pipe and which decreases the pressure of the enter- 
 ing steam by " throttling," or partially closing an admis- 
 sion valve. In Fig. 32 is shown a section of one of these 
 governors. The opening A is connected to the steam 
 chest, and the opening B to the steam pipe, so that the 
 steam passes through the valve C before entering the 
 engine. The gear wheel D is run by means of a belt, 
 from the shaft of the engine to the wheel E, and it, in 
 turn, runs the gear wheel F y which moves the balls G. 
 As the speed of the balls G increases, the centrifugal 
 force makes them rise, and in doing so they force down 
 the valve-stem H t and partly close the valve C. The 
 faster the engine runs, the faster the balls G move, and 
 the more the valve C is closed ; the slower the engine 
 goes, the slower the balls move, and the more the valve C 
 is opened. The valve C, thus automatically opens wider to 
 admit steam if the engine begins to slow down, and partly 
 closes, thus shutting off the steam, if the engine begins 
 to speed up. By properly adjusting the governor, by 
 means of the screw 7", the speed of the engine may be 
 fairly controlled within certain limits. 
 
CHAPTER IV. 
 
 ADMISSION OF STEAM BY VALVES. 
 
 37. OPENING AND CLOSINGTHE PORTS BY THE VALVE. 
 As has been explained, the valve is worked by an eccen- 
 tric which is fastened to the shaft; and the eccentric is 
 equivalent to a crank whose length is equal to the 
 eccentricity of the eccentric. The motions of the 
 eccentric and the valve, therefore, bear the same relations 
 to one another that the motions of the crank and piston 
 do. During one complete revolution of the shaft the 
 valve makes one complete forward and one complete 
 backward motion, and the length of each of these 
 motions is equal to twice the eccentricity of the eccentric. 
 If we neglect the obliquity of the eccentric rod, which 
 changes the motion of the valve in the same way that the 
 obliquity of the connecting rod changes the motion of 
 the piston, the valve will make one-half of its forward, or 
 backward, motion while the eccentric makes a quarter of 
 a revolution, and the relation of the motion of the valve 
 to that of the eccentric will be very much simplified. 
 In all that follows, except when otherwise stated, the 
 obliquity of the connecting rod, and of the eccentric rod, 
 will be neglected ; and the motions of the valve and the 
 piston will be discussed as if the rods were of infinite 
 length. 
 
 The valve is said to be in " mid-position " when it has 
 reached the middle of its forward or backward motion. 
 
 The " travel" of the valve is the total distance that it 
 moves in one direction, either forward or backward, and 
 is equal to twice the eccentricity of the eccentric. 
 (78) 
 
ADMISSION OF STEAM BY VALVES. 79 
 
 The simplest valve is the plain Z?-valve, shown in Fig. 
 33. There, a represents the steam chest, into which the 
 steam passes from the boiler ; c represents the exhaust 
 port, through which the exhaust steam passes out of the 
 engine.; di and d^ represent the steam ports, through 
 which the steam passes into the cylinder from the steam 
 chest. In the figure, the valve is supposed to be in mid- 
 position and is shown as lapping over and beyond the 
 ports, at each end, a distance marked o ; it is also shown 
 as lapping over the ports, towards the inside, the distance 
 marked i. 
 
 The distance o is the outside or steam lap, which is, the 
 distance the valve extends over the edges of the steam ports 
 on the outside. 
 
 The distance i is the inside or exhaust lap, which is, tJie 
 distance t/ie valve extends over the edges of the steam ports 
 on the inside. 
 
 In Fig. 33, let C represent the center of the shaft, and 
 A, the center of the eccentric ; so that AC is the eccentri- 
 city of the eccentric, and represents the equivalent crank. 
 When the valve is in mid-position, as shown in the figure, 
 the center of the eccentric is at B, and the valve has made 
 half of its travel. While the valve is in this position, it is 
 evident that no steam can enter or leave through either 
 of the ports, d\ or </ 2 . If the shaft is revolved right- 
 handed, the valve will move from its mid-position towards 
 the right; and when the center of the eccentric has 
 reached any point such as D, the distance that the valve 
 will have moved from mid-position will be equal to the 
 distance, CE, from the center of the shaft to the line DE, 
 which is drawn perpendicular to AC. If, when the cen- 
 ter of the eccentric gets to D, the distance CE is equal to 
 o, the outside lap, the steam will be just on the point of 
 entering the port d\. Now, as the shaft continues to 
 revolve, the valve will continue to move towards the right, 
 and become farther and farther from mid-position. As 
 
80 
 
 STEAM ENGINES AND BOILERS. 
 
 the port was just about to open when the center of the 
 eccentric was at D y it is evident that when the center of 
 
 the eccentric is at any point such as Di, beyond D, and 
 the valve has moved the distance CE from mid-position, 
 
ADMISSION OF STEAM BY VALVES. 81 
 
 the port has been opened the amount EE\ y equal to 
 CEi CE. When the center of the eccentric gets to the 
 point F y the valve will have reached the end of its travel 
 and will be the distance CF from mid-position ; the port 
 will be open the amount EF, equal to CF CE. As the 
 shaft continues to revolve, the center of the eccentric will 
 move from .F towards G, and the valve will move towards 
 the left and gradually close the port. When the center 
 of the eccentric has gotten to the point G, such that the 
 distance, CE, of the valve from mid-position is equal to o y 
 the outside or steam lap, the port will be just closed. 
 When the center of the eccentric has reached the point 
 B\ t the valve will again be in mid-position ; and when it 
 has gotten to A, the valve will have reached the end of 
 its travel towards the left. 
 
 It is evident, from the figure, that no motion of the 
 valve towards the left of mid-position can open the port 
 d\ to the space a of the steam chest ; and, as the valve is 
 always to the left of mid-position while the center of the 
 eccentric is anywhere on the arc B\ AB t it follows that 
 the port d\ cannot be open to the steam chest while the 
 center of the eccentric moves from B\ to B. As it has 
 been shown that the port d\ is open only while the center of 
 the eccentric moves over the part DG of the arc BFBi, it 
 follows that, during one revolution of the shaft, the port d\ 
 is. open only during the time that the center of the 
 eccentric moves from D to G. 
 
 It is evident, from the figure, that the larger is the out- 
 side lap, equal to the distance CE, the smaller is the arc DG; 
 and the smaller is the lap, the larger is the arc DG. If 
 the outside lap were zero, the port would remain open 
 during half a revolution of the eccentric, or while the 
 center of the eccentric traveled over the arc BFB\. 
 
 Referring again to Fig. 33, let us discuss the opening 
 and the closing of the port d\ to the exhaust port c, during 
 one revolution of the shaft. 
 6 
 
82 STEAM ENGINES AND BOILERS. 
 
 From the figure, it can be seen that no movement of 
 the valve towards the right of the mid-position will open 
 di to c, and, therefore, at no time during the motion of 
 the center of the eccentric from B to B\ is the port d\ in 
 communication with c. When the center of the eccen- 
 tric gets to B\ the valve is again in midposition, and as it 
 continues to revolve, the valve moves towards the left. 
 When the center of the eccentric gets to the point //, such 
 that the distance CK is equal to, z, the inside or exhaust 
 lap, the port di is just on the point of opening to the 
 exhaust port, c. As the motion of the eccentric con- 
 tinues, the port becomes more and more open to c; 
 and when the center of the eccentric has reached any 
 point such as Z, the port d\ is open to c the amount KK\ t 
 equal to CK\ CK. When the center of the eccentric 
 gets to A t the valve is at the end of its travel towards the 
 left; and as the center continues to revolve, the valve 
 moves toward the right, and the opening of the port d\ to 
 the exhaust port, c, becomes smaller and smaller until, 
 when the center is at Hi, where the distance CK\s equal 
 to the exhaust lap, the communication of d\ with c is 
 closed. 
 
 From what has been said, it is now easy to follow the 
 various openings and closings of d\ during one revolution 
 of the shaft. Let us start with the valve in mid-position, 
 and the center of the eccentric at B, and consider the 
 shaft as revolving right-handed. When the center of the 
 eccentric gets to D, the port d\ is opened to the steam 
 space a, so that steam may enter the cylinder, and it con- 
 tinues open until the point G is reached. During the 
 movement of the center of the eccentric from G to H 
 the port d\ is closed, and no steam can enter from a nor 
 leave by the exhaust port, c ; but at H the port di is 
 opened to c> so that the steam may leave the cylinder, 
 and it continues open until Hi is reached. 
 
ADMISSION OF STEAM BY VALVES. 83 
 
 It is usual to say the steam port is open, when d\ is open 
 to a; and to say the exhaust port is open, when d\ is 
 opened to c. 
 
 By an analysis similar to that made for the port d-^ it 
 can be shown that, during one revolution of the shaft, the 
 port d<i is, also, open once for the admission of steam and 
 once for its exhaust; the difference between the two ports 
 is that di would be open for the admission of steam dur- 
 ing the semi-revolution B\ AB, instead of the semi-revolu- 
 BFB\ t and would be open for its exhaust during the 
 semi-revolution BFB\ y instead of the semi-revolution 
 BiAB. 
 
 38. RELATIVE MOVEMENTS OF THE PISTON. AND VALVE. 
 In Fig. 34, the piston is shown at the left-hand end of 
 the cylinder, ready to begin its stroke toward the right ; 
 and the valve is shown in such a position that the steam 
 port is open by the amount marked /. The shaft is rep- 
 resented by two points, C and C\. C is the center of 
 the crank shaft ; CD is the crank ; and the circle DGHF 
 is the circle described by the crank-pin during one revo- 
 lution. C\ represents, also, the center of the shaft, and 
 the circle A\D^G\H is the circle described by the center 
 of the eccentric during one revolution of the shaft. Of 
 course, C and C\ ought to coincide, as they both repre- 
 sent the center of the same shaft ; they are put one above 
 the other, as shown, simply to avoid confusion in the 
 drawing, and for the sake of clearness. 
 
 The steam port is open the amount /, and the steam is 
 entering the cylinder to the left of the piston. The center 
 of the eccentric is at the point D\ t and the crank-pin is 
 on the dead center at D. The shaft is supposed to revolve 
 right-handed, as in Art. 37. 
 
 The distance / is the lead, which may be defined as 
 the amount the steam port is open when the piston is at the 
 beginning of its stroke. 
 
84 STEAM ENGINES AND BOILERS. 
 
 As the crank and the eccentric are both fixed to the 
 shaft, they must preserve the same relative positions ; and 
 the center of the eccentric will always be ahead of the 
 crank-pin, by the angle D\ C\ A\. 
 
 The angle B\ C\ D\ is the angle of advance, equal to 
 D\ C\ AI 90, and is defined as the angle the center line 
 of the eccentric makes with a perpendicular to the line of 
 motion of the piston, when the crank is on the dead 
 center. 
 
 If we make C\ N equal to the steam lap, and C\ K 
 equal to the exhaust lap, and draw the lines F\ G\ and 
 LI H\ perpendicular to A\ C\ and intersecting the circle 
 at the points F\, G\, Li, and H\, we shall have, from the 
 reasoning of Art. 37, the point, F\, at which the center of 
 the eccentric is when the steam port is opened ; the point, 
 GI, at which the steam port is closed ; the point, H\, at 
 which the exhaust port is opened ; and the point, L\ t at 
 which the exhaust port is closed. Since C\ A 7 " is equal to 
 the steam lap, o, of the valve, and C\ R is the distance 
 the valve is from mid-position when the center of the 
 eccentric is at D\, it follows that the lead, /, is equal to 
 Ci R Ci N; and Ci R = o + /. And as Ci R is the 
 distance the valve has moved from mid-position while the 
 eccentric turns through the angle B\ C\ D\, it follows that 
 the angle of advance is the angle through which the eccen- 
 tric must be turned in order to move the valve from mid- 
 position a distance equal to the steam lap plus the lead. 
 
 Therefore, for a given steam lap of valve and a given 
 eccentricity, the greater the angle of advance is made, the 
 greater becomes the lead ; and the less the angle of 
 advance is made, the less becomes the lead. If the angle 
 of advance is equal to the angle B\ C\ F\, the lead would 
 be zero and the valve would be said to be " blind ; " if the 
 angle of advance should be less than the angle B\ C\ F\ 
 C\ R would be less than C\ N 9 and the lead would be 
 negative. Again, for a given lead and eccentricity, the 
 
ADMISSION OF STEAM BY VALVES. 
 
 85 
 
86 STEAM ENGINES AND BOILERS. 
 
 angle of advance will be increased, if the steam lap is 
 increased; and be decreased, if the steam lap is decreased. 
 
 In finding the position of the crank for different posi- 
 tions of the eccentric, we start with the position, D, of 
 the crank when the eccentric is at D\, and, as their 
 positions relative to one another are fixed, we know that 
 they must both turn through the same angle in the same 
 time. The position, G, of the crank-pin when the steam 
 port is closed, is obtained by making the angle DCG 
 equal to the angle D\ Ci G\. From the figure it is seen ' 
 that the greater the angle of advance becomes, for a 
 valve with a given steam lap, the less becomes the angle 
 D\ Ci GI and its equal, DCG, and, therefore, the earlier 
 will be the point ofcut-off; also, the larger the steam lap, 
 the less is the angle FI C\ Gi, and, therefore, for a given 
 lead, the less will be the angle Di Ci Gi and its equal, 
 DCG, and the earlier will be the cut-off. From this 
 follows a general proposition, which always holds for the 
 slide valve, as follows, the greater the angle of advance, 
 for a given eccentricity and steam lap y the greater will be 
 the lead, and the earlier will be the cut-off; the greater the 
 steam lap, for a given eccentricity and lead, the greater will 
 be the angle of advance, and the earlier will be the cut-off. 
 
 To find the position, //, of the crank-pin when the 
 exhaust port opens, or release occurs, make GCH equal 
 to G\ C\ H\, or make Z>7/equal to D\ C\ H\. Anything 
 that will make the angle D\ C\ H\ or its equal, DCH t 
 smaller will make the release occur earlier. Now, increas- 
 ing the angle of advance throws Di farther towards //i, 
 and decreases the angle D\ C\ H\\ increasing the exhaust 
 lap, C\ K, throws Hi farther towards A\, and increases the 
 angle D\ C\ H\. It follows, therefore, that, for a given 
 eccentricity and exhaust lap, increasing the angle of 
 advance makes the release occur earlier ; and, for a given 
 angle of advance and eccentricity, increasing the exhaust 
 lap makes the release occur later. 
 
ADMISSION OF STEAM BY VALVES. 87 
 
 The position, L, of the crank-pin when compression 
 begins, or the exhaust port closes, is best obtained by 
 making the small angle D C L, below DC, equal to the 
 small angle D\C\L\. Anything that causes the angle 
 DI Ci LI to be large, will make the point L be farther from 
 D, and will make the compression begin earlier. The 
 angle D\ C\ LI may be increased by making the angle of 
 advance, i C\ D\, greater or by increasing the exhaust 
 lap, thus throwing L\ farther towards A\. It follows, 
 then, that, for a given eccentricity and exhaust lap, an 
 increase in the angle of advance makes the compression 
 begin earlier; and, for a given eccentricity and angle oj 
 advance, an increase in the exhaust lap makes the com- 
 pression begin earlier. 
 
 Finally, the position, F, of the crank-pin when admis- 
 sion begins, or the steam port is opened, is obtained by 
 laying off, below D C, the angle D C F equal to the angle 
 D\ C\F\. It is evident, from the figure, that, for a given 
 eccentricity and steam lap, an increase in the angle of 
 advance makes the admission occur earlier; and, for a 
 given eccentricity and angle of advance, an increase in the 
 steam lap makes the admission occur later. 
 
 It will be noticed, from what has been explained, that, 
 for a given eccentricity, steam lap, and exhaust lap, an 
 increase in the angle of advance makes the lead greater, 
 and makes the ports open and close earlier. 
 
 When the positions of the crank-pin are known for the 
 different positions of the valve, it is very easy to deter- 
 mine the positions of the piston, provided the obliquity of 
 the connecting rod is neglected, since the distance the 
 piston is from the beginning of its stroke is always equal 
 to the distance from the dead center to the perpendicular 
 let fall, on the line of motion of the piston, from the cen- 
 ter of the crank-pin. Thus, when the crank-pin is at G, 
 the piston is at the distance Dg from the beginning of its 
 
88 STEAM ENGINES AND BOILERS. 
 
 Since G is the position of the crank-pin when cut-off 
 takes place, g is the " point of cut-off," and Dg expressed 
 as a fraction of the stroke is the " cut-off." 
 
 That point in the stroke at which the piston is when the 
 exhaust port is opened, is called the " point of release; " 
 that point in the stroke at which the piston is when the 
 exhaust port is closed, is the " point of compression ; " 
 and that point in the stroke at which the piston is when 
 the steam port is opened, is called the " point of admis- 
 sion.'* The "point of cut-off" has already been defined. 
 
 The positions of the piston at the times of the opening 
 and closing of the ports are indicated on the drawing, g 
 is the point of cut-off; h, the point of release ; i, the point 
 of compression ; and /, the point of admission. We are 
 now able to trace the motion of the piston and note the 
 action of the steam. The piston starts at the left end of 
 its stroke and moves towards the right, with steam enter- 
 ing the cylinder during the whole time ; at g the steam is 
 cut-off, and while the piston moves to h, from g, the steam 
 remaining in the cylinder is being expanded. At h 
 release occurs ; the steam begins to leave the cylinder 
 and continues to leave until the piston gets to i t on its 
 return stroke. At i the exhaust port is closed, and the 
 steam remaining in the cylinder is compressed while the 
 piston moves from i to f t on the return stroke. Atf the 
 steam port is opened, and steam begins to enter the 
 cylinder. 
 
 The same kind of analysis can be followed out for the 
 steam entering the cylinder to the right of the piston. 
 The 'point of cut-off, of release, of compression, and of 
 admission, will be the same distance from the end of the 
 stroke ; everything will be the same except that the 
 points of cut-off and release will occur while the piston is 
 moving from right to left, and the points of compression 
 and admission will occur while the piston is moving from 
 left to right. 
 
ADMISSION OF STEAM BY VALVES. 
 
 89 
 
 39. BALANCED SLIDE VALVE. In order to avoid the 
 friction of the plain .D-valve, such as shown in Figs. 33 
 and 34, where the full pressure of the steam presses the 
 valve against its seat, and makes it difficult to move, some 
 form of balanced valve is generally used on automatic 
 high speed engines. A balanced valve not only requires 
 less power to move it, but also wears less than an unbal- 
 anced valve. 
 
 The general form of balanced slide valve in common 
 use is the " Straight Line " valve, or some modification 
 of it. This valve is shown in Figs. 35 and 36. It will be 
 seen that the valve is simply a flat casting, a, with open- 
 
 Fig. 35. 
 
 ings through it, that moves back and forth between the 
 valve seat and a " cover-plate," b. The cover-plate does 
 not rest directly on the valve but on " distance-pieces," 
 c y at the top and bottom of the valve. The cover-plate is 
 sometimes kept in place by means of springs, interposed 
 between it and the steam chest cover; other times the 
 valve is not set exactely vertical, but is slightly inclined, 
 so that the weight of the valve and cover-plate is suffi- 
 cient to keep it in place. The valve shown in Figs. 35 
 and 36 has no special means of correcting for the wear 
 of the valve ; the only way to do this is to reduce the 
 thickness of the distance pieces, c. Some valves are pro- 
 vided with wedges, by means of which the distance pieces 
 
90 
 
 STEAM ENGINES AND BOILERS. 
 
 may be set out and the cover-plate lifted any desired 
 distance from the valve. Fig. 35 shows steam being ad- 
 mitted to the right-hand end of the cylinder and being ex- 
 hausted from the left-hand end, as indicated by the arrows. 
 
 40. PISTON VALVE. The piston valve consists simply 
 of a piston working in a cylinder through which the ports 
 
 Fig. 36. 
 
 are cut. The length of the port is equal to the circum- 
 ference of the piston, less the width of such ribs as may 
 extend across the port. This form of valve is perfectly 
 balanced, but it is difficult to keep it tight and prevent 
 it from leaking. When steam is first turned on to an 
 
ADMISSION OF STEAM BY VALVES. 91- 
 
 engine having a piston valve, care must be taken not to 
 start it up until the steam chest has got thoroughly hot, 
 as the valve is very likely to become hot before the cylin- 
 der in which it works, and to expand and stick, and per- 
 haps cause a breakage somewhere. 
 
 The piston used for the valve is sometimes made tight 
 by the use of cast iron packing rings, other times it is 
 simply turned to a steam tight fit with the cylinder in 
 which it works. 
 
 In Fig. 15 is shown a form of piston valve where the 
 cylinder in which the valve fits is made with thin walls 
 and is surrounded by live steam, so that it heats quicker 
 than the valve and there is not so much danger of the 
 valve sticking. The figure shows steam being admitted to 
 the right-hand end and exhausted from the left-hand end. 
 
 41. MULTIPLE ADMISSION VALVE. With the advent 
 of the automatic high speed engine, there came a demand 
 for a single valve which could be made to cut-off early 
 in the stroke and that would give a large port-opening 
 with a small travel. To meet these requirements, the 
 multiple admission valve was devised. Valves of this 
 type are so made that the opening of the port is not, as 
 shown in Art. 37, equal to the distance the valve is from 
 mid-position minus the steam lap, but is equal to two 
 times this distance for a double admission valve, and four 
 times it for a quadruple admission valve. 
 
 The "Straight Line" valve, shown in Figs. 35 and 36, 
 is a double admission valve. 
 
 42. MEYER VALVE. The Meyer valve consists of two 
 valves, one riding on top of the other; and the advantages 
 it has over the single valves are that the clearance may be 
 made smajler, and the point of cut-off may be changed 
 as desired without in any way changing the points of 
 release or compression, something which cannot be done 
 with a single valve. The valve shown in Fig. 17 is a mod- 
 ified form of a Meyer valve. It consists of the main 
 
92 STEAM ENGINES AND BOILERS. 
 
 valve b, moved backwards and forwards by a hollow valve 
 stem, and the small auxiliary valve c, which rides on b, 
 and is moved by a small valve stem working inside of the 
 hollow valve stem which moves b. In order that steam 
 may enter the cylinder, the port in b must not be covered 
 by c, and it must be over the port in the cylinder. In 
 the figure steam is being admitted into the left-hand end 
 of the cylinder and exhausted from the right-hand end, as 
 indicated by the arrows. D is the steam supply pipe, and 
 K t the exhaust pipe. The cut-off is regulated entirely by 
 the small, riding valve c, while the admission, release, and 
 compression are regulated entirely by the main valve b. 
 
 43. CORLISS VALVE. The Corliss valve is a cylindrical 
 valve, but instead of having a reciprocating motion in the 
 direction of its axis, it has an oscillating motion about its 
 axis. In Figs. 19 and 37 are shown Corliss valves. It 
 will be seen, in Fig. 19, that there are four valves in all, 
 two steam valves at the top of the cylinder, and two 
 exhaust valves at the bottom. The valves are not fast- 
 ened to the stem by which they are moved, but the stem 
 is flattened and simply lies in the valve. The valves are 
 always made so that the steam pressure comes on top of 
 them and the pressure of the steam presses them down on 
 their seats. The moving mechanism of the valves is quite 
 complicated, and has many small parts that must be kept 
 in order. 
 
 The clearance is reduced by making the ports very 
 short and placing the valve close to the cylinder. 
 
 The Corliss valve permits a regulation of the point of 
 cut-off without any change in the release or compression. 
 
 As there are separate steam and exhaust ports, the 
 exhaust steam does not pass out through the same port 
 through which the hot, live steam enters. Whether or 
 not this is any advantage, and conduces to the economy 
 of the engine, is a somewhat undecided question. In Fig. 
 
ADMISSION OF STEAM BY VALVES. 
 
 93 
 
 37 is shown the mechanism by means of which the valves 
 of the Corliss engine are worked. 
 
 The "wrist-plate," A, is made to oscillate about the 
 pin B, by means of the " reach-rod," C, which engages 
 with the " wrist-pin." The wrist-plate is connected by 
 the rod D to the bell crank, , that oscillates about the 
 
94 STEAM ENGINES AND BOILERS. 
 
 N 
 
 valve stem F. At the farther end of E is the pin G which 
 carries the F-shaped lever H. The inner end of H is 
 kept pressed against the cam / by means of a spring ; 
 and the outer end has a hook which engages with a steel 
 block fastened, by means of the bolt K, to an arm, Z, 
 rigidly attached to the valve stem F. The dash pot rod, 
 M t is, also, attached to the arm L. The cam /has a pro- 
 jection on it, and is moved backward or forward by means 
 of the governor rod, not shown in the figure, that is 
 attached to the pin O. 
 
 When the wrist-plate is turned right-handed the crank 
 E is turned left-handed, and the hook on //"engages with 
 the block on K t and thus lifts the lever L and opens the 
 valve. When L is lifted, the dash-pot rod, M, is lifted. 
 After the lever L has been lifted to a certain distance, 
 the inner end of //"strikes the projection on the cam /, 
 which turns H about the pin G, so that the hook is 
 released from the block K. As soon as this takes place, 
 the arm L is made to fall, by the weight of the dash-pot 
 piston and the pressure of the air on top of the piston, 
 and thus close the valve. The function of the dash-pot 
 is to close the valve ; and it is so arranged that by means 
 of a small valve a greater or less vacuum may be main- 
 tained under its piston. 
 
 The governor changes the position of the cam /so that 
 the block K is disengaged early or late, as required to 
 govern the engine, from the hook on H. 
 
 The exhaust valves have no disengaging mechanism, 
 but are simply made to oscillate backward and forward 
 by means of a rod connecting them to the wrist-plate. 
 
 Owing to this peculiar method of closing the valve, the 
 speed of rotation of the engine cannot be great, as the 
 dash-pot piston must have time in which to fall. The 
 writer has known of but few cases where the number of 
 revolutions has exceeded one hundred per minute, and 
 in most cases the engines were small. 
 
ADMISSION OF STEAM BY VALVES. 
 
 ( J5 
 
 The advantages claimed for Corliss valves are : 
 
 I. They permit of a regulation of the cut-off without 
 any change in the release or compression. 
 
 Fig. 38 
 
 2. Short ports, and, consequently, small clearance 
 volume. 
 
 3. Separate steam and exhaust ports, reducing con- 
 densation. 
 
96 STEAM ENGINES AND BOILERS. 
 
 4. Quick, sharp, motion of the valve when cutting off 
 steam. 
 
 44. LINK MOTION. On marine engines, locomotives, 
 and some few land engines, it is necessary to have some 
 device by which the direction of rotation of the crank-shaft 
 may be changed. The mechanism usually used is the 
 link motion. The engine is provided with two eccentrics, 
 keyed to the crank-shaft, each of which is connected by 
 an eccentric rod to the end of a link. A block, connected 
 by a suitable mechanism to the valve, slides along a 
 groove cut in the link. When the block is at one end of 
 the link it has all the motion of the eccentric connected 
 to that end, and very little of the motion of the other 
 eccentric ; when the block is in the middle of the link it has 
 a little motion, backward and forward, that is the result 
 of the motions of both eccentrics. One of the eccentrics 
 is the " forward " eccentric, and the other is the " back- 
 ward " eccentric. When the motion of the valve, on 
 account of the position of the block, is due more to the 
 " forward " than to the " backward " eccentric, the engine 
 runs forward ; and when influenced more by the "back- 
 ward " than the " forward " eccentric, the engine will run 
 backward. The position of the block in the link may be 
 changed by moving the block and keeping the link in the 
 same position ; or by keeping the block at rest and 
 moving the link, as is done in the Stephenson link 
 motion. 
 
 In Fig. 38 is shown a small vertical engine with a link 
 motion. A is the " link; " B is the " block" that, in this 
 case, is fastened directly to the valve stem ; C is the 
 " reversing lever" by means of which the link is moved so 
 that the position of the block in it may be changed. 
 
CHAPTER V. 
 
 VALVE DlAGRAMSo 
 
 45. ZEUNER VALVE DIAGRAM. A valve diagram is a 
 diagram that will show, at once, the steam lap, exhaust 
 lap, lead, distance the valve is from mid-position, and, 
 also, the amount the port is open for a given position of 
 the crank. By means of valve diagrams, all the various 
 problems connected with the motion of valves may be 
 solved. There are several systems of valve diagrams, 
 each of which is considered better than the others by those 
 who use it ; and as, in the opinion of the author, the 
 Zeuner diagram is better for all uses than any other, it 
 will be used in this work. 
 
 In Fig. 39, let AA' represent the stroke of an engine 
 drawn to any desired scale, and the circle ABA', the path 
 of the center of the crank pin, or the crank-circle. Also, 
 let nm be the travel of the valve drawn to any desired 
 scale, which may or may not be the same as the scale of 
 AA'. The distance On will be equal to the eccentricity 
 of the eccentric, and the circle nAi m will be the path of 
 the center of the eccentric. When the crank-pin is at A t 
 the center of the eccentric will be at Ai, and YOA\ will 
 be the angle, of advance. Now, if the crank moves from 
 AO to any position as BO, the center of the eccentric 
 will move from A\ to Bi, and the angle AOB will be 
 equal to the angle AiOBi. Draw B\b perpendicular to 
 the line AA ; then, neglecting the obliquity of the eccen- 
 tric rod, when the crank is in the position BO, the valve 
 will be moved from mid-position a distance equal to Ob. 
 To find the distance Ob by the method just described, it 
 
 r (97) 
 
98 
 
 STEAM ENGINES AND BOILERS. 
 
 was necessary to draw three lines, OB, OB\, and Bib, 
 and to make the angle A\OB^ equal to the angle AOB. 
 
 Draw OB' so that the angle B'OA' will be equal to the 
 angle BOA, and H O will be the position of an imaginary 
 crank which starts from A O when the real crank starts 
 from AO and moves with the same velocity as, but in 
 
 Fig. 39. 
 
 the opposite direction to, the real crank. Draw A\a per- 
 pendicular to OB' . In the two right triangles, OB\b and 
 OAia, we have OAi equal OB\, and the angle B\0b equal 
 the angle A\0a. Therefore, the two triangles are equal, 
 and Oa is equal to Ob : or Oa is equal to the distance the 
 valve is from mid-position when the crank has moved 
 through the angle AOB, equal to A OB'. From this, it 
 is seen that if, instead of considering the real crank, we 
 consider the motion of an imaginary crank revolving in 
 the opposite direction to, but with the same velocity as, 
 the real crank, the distance that the valve is from mid- 
 position, for a given angular motion of the crank, may be 
 obtained by drawing only two lines, OB' and A\a. 
 
VALVE DIAGRAMS. D9 
 
 Since the position of the point AI is fixed, for a given 
 eccentricity and angle of advance, and the angle A\aO is 
 a right angle, the point a will always fall upon the circum- 
 ference of the circle drawn upon OA\ as a diameter. This 
 gives us, then, an extremely simple means of obtaining 
 the distance the valve is from mid-position after the crank 
 has moved through any given angle. 
 
 In Fig. 40, let AA' t as before, represent the stroke of 
 the engine, and ADBA' the path of the crank-pin; also, 
 let the angle YOA\ be the angle of advance ; and let OA\ 
 be, to any desired scale, the eccentricity of the eccentric, 
 equal to half the travel of the valve. Upon OA\ 9 as a 
 diameter, draw the "valve circle " OaA^. From the pre- 
 ceding paragraph, it follows that if OB represents any 
 position of the imaginary crank, at any instant, Ob will 
 represent the distance the valve is form mid-position at 
 that instant. That is, by drawing one line we determine, 
 at once, the angle the crank has turned through and the 
 distance the valve is from mid-position. Care must be 
 taken to remember that OB does not represent the real 
 crank of the engine, but an imaginary crank that revolves 
 with same velocity as the real crank, but in the opposite 
 direction. 
 
 Neglecting the obliquity of the connecting rod, the dis- 
 tance the piston would have moved from the end of its 
 stroke, while the crank moved through an angle equal to 
 A' OB, would be B^A '. And if, as we supposed, the real 
 crank moved in the direction from A to Y t the piston 
 would have moved the distance B\A' from the left-hand 
 end of the stroke and not from the right-hand end. 
 
 If we describe the arc dc y with O as a center and a 
 radius equal to the outside or steam lap of the valve, the 
 distance the steam port is open, when the crank has 
 moved through the angle equal to BOA' , will be equal to 
 Ob Ob' ; that is, it will be equal to the distance the 
 valve is frjm mid-position minus the steam lap. 
 
100 
 
 STEAM ENGINES AND BOILERS. 
 
 If the lines OC and OD be drawn through c and d, 
 respectively, OC will represent the position of the 
 imaginary crank when steam begins to enter the 
 cyclinder, and OD its position when steam is cut-off; 
 because, for those positions, the distance the valve is from 
 mid-position is equal to the steam lap. 
 
 When the crank is on the dead center, the imaginary 
 crank is at OA' t and the distance the valve is from mid- 
 position is Oa, so that the lead is a' a. 
 
 Fig. 40. 
 
 The valve is open its maximum distance when the 
 imaginary crank is in the position of the line OA\, and 
 then the valve is at the right-hand end of its travel. 
 
 If the line DD\ is drawn perpendicular to AA', the 
 distance A ' D\ will be the distance the piston is from the 
 beginning of the stroke at the point of cut-off. 
 
 If the line OA\ be continued to ^2, so that OA 2 is 
 
VALVE DIAGRAMS. 101 
 
 equal to OAi, and another valve circle be drawn on 
 as a diameter, the exhaust port may be discussed. 
 Draw the arc fg t with O as a center and a radius equal to 
 the exhaust lap. Then, for any position of the imaginary 
 crank, such as O K, the exhaust port is open the distance 
 kk\ y equal "to the distance, Ok, the valve is to the left of 
 mid position minus the exhaust lap, Oki. 
 
 If OF and OG are drawn through the points/and g t 
 respectively, OF will be the position of the imaginary 
 crank when release occurs, and OG its position when 
 compression begins ; since, for those positions, the dis- 
 tance the valve is from mid-position is equal to the 
 exhaust lap. 
 
 46. VALVE DIAGRAM PROBLEMS. By assuming a num- 
 ber of the variables. in the valve diagram, in Fig. 40, as 
 known, various problems can be made up, all of which can 
 be solved by the proper use of the valve diagram. The 
 solution of every problem will necessitate a good, clear, 
 understanding and knowledge of the relation of the various 
 parts of the diagram to one another. For the sake of 
 making the student familiar with the use of the valve 
 diagram and to give him practice in the use of it, a number 
 of the most important problems likely to be met with 
 in practice will be solved in detail. 
 
 Problem I. Given the point of admission, the point of 
 cut-off, and the travel of the valve ; find the angle of ad- 
 vance, the steam lap, and the lead. 
 
 Referring to Fig. 40, we see that since Od is equal to 
 Oc, being the radii of the steam lap circle, the arc Od is 
 equal to the arc Oc, and, therefore, the arc dA\ is equal to 
 the arc cA\. That is, the line OA\ bisects the angle between 
 the positions of the imaginary crank at admission and at 
 cut-off. The construction, therefore, is as follows : 
 
 In Fig. 41, let AA\ be the stroke of the engine drawn to 
 any desired scale ; A\ B\, the distance from the end of 
 
102 
 
 STEAM ENGINES AND BOILERS. 
 
 the stroke to the point of admission ; and Ai C\, the 
 distance from the beginning of the stroke to the point of 
 cut-off. On A\A as a diameter, construct the crank 
 circle ACA\B. Draw the lines B\.B and C\ C perpendicu- 
 lar toy^iand intersecting the crank circle at B and C, 
 respectively. Now draw OB and OC, and they will rep- 
 resent the positions of the imaginary crank at admission 
 and cut-off, respectively. Draw Om, bisecting the angle 
 COB, and lay off Om, according to any desired scale, 
 equal to the given eccentricity of the eccentric, or half 
 
 Fig. 41. 
 
 the travel of the valve, m will be the position of the 
 center of the eccentric when the real crank is in the 
 position OA ; and the angle YQm will be the required 
 angle of advance. 
 
 On Om as a diameter, draw the valve circle intersecting 
 C at c y OA at a, and OB at b. With O as a center and 
 a radius equal to Oc y equal Ob, draw the arc cdb inter- 
 secting OA at d. cdb is an arc of the steam lap circle ; Ob 
 is the steam lap ; and da is the lead. 
 
 Problem 2. Given the point of admission, the point of 
 
VALVE DIAGRAMS. 
 
 103 
 
 cut-off, and the steam lap ; find the angle of advance, the 
 eccentricity, and the lead. 
 
 An inspection of Fig. 40 shows that the valve circle 
 passes through the points of intersection of the steam 
 lap circle with the lines showing the position of the 
 imaginary crank at admission and at cut-off. Hence the 
 following construction : 
 
 In Fig. 42, let AA\ be the stroke of the engine, drawn 
 to any scale, and the circle A CA\B, the crank-circle ; A\ B\, 
 the distance of the point of admission from the end 
 of the stroke ; and A\ C\ t the distance of the point of 
 cut-off from the beginning of the stroke. Draw BB\ and 
 
 Fig. 42. 
 
 CC\ perpendicular to AA\ and intersecting the crank- 
 circle at the points B and C> respectively. Draw OB and 
 OC to represent the position of the imaginary crank at 
 admission and cut-off, respectively. With as a center 
 and a radius, Ob, equal, on any desired scale, to the 
 steam lap, draw the steam lap circle cutting OB and 
 OC at b and c, respectively. Now pass a circle 
 through the points c, O, and b, and it will be the 
 required valve circle. The center of the valve circle may 
 be found by the ordinary method of finding the center of 
 a circle that shall pass through three given points ; or, if 
 
104 STEAM ENGINES AND BOILERS. 
 
 desired, the diameter Om of the required circle may be 
 obtained by drawing, at c, the line cm perpendicular to 
 OC and continuing it until it meets, at m, the line bm 
 drawn perpendicular to Ob at b y and then connecting the 
 points O and m. 
 
 The center of the eccentric is at m when the crank is 
 on the dead center; the angle YOm is the angle of 
 advance ; the line Om is the required eccentricity, equal 
 to half the travel of the valve ; and da is the required 
 lead. 
 
 Problem j. Given the point of admission, the point of 
 cut-off, and the lead ; find the angle of advance, the eccen- 
 tricity ', and the steam lap. 
 
 As explained in Problem i, the diameter of the valve 
 circle always bisects the angle between the positions of 
 the imaginary crank at admission and at cut-off. From 
 Fig. 42, we see that the lead, da, is equal to Oa Od; 
 and, since Od is equal to Ob, we have da = Oa Ob. 
 But from the triangle Oma, we have Oa == Om cos. mOa; 
 and from the triangle Omb, we have Ob = Om cos. mOb. 
 Therefore, da = Oa Ob = Om \cos. mOa cos. mOb~\. 
 
 Since the angles mOa and mOb are constant for a given 
 admission and cut-off, it follows that da will vary directly 
 as Om. Therefore, to solve the problem proceed as 
 follows : 
 
 In Fig. 43, let AA\ be the stroke of the engine ; A C A\ B, 
 the crank circle; OB and OC, the positions of the imag- 
 inary crank, obtained as in the preceding problems, at 
 admission and cut-off, respectively. Bisect the angle 
 COB by the line Om, and the angle YOm will be the 
 angle of advance. 
 
 On the line Om take any point, such as m, and from it 
 draw md perpendicular to O B, and ma perpendicular to 
 OA. With O as a center and a radius Od, draw an arc 
 cutting OAi at e. ea would be the lead for an eccentricity 
 equal to Om. As has been shown, the lead is directly 
 
VALVE DIAGRAMS. 
 
 105 
 
 proportional to the eccentricity, and the given lead is to 
 ea as the required eccentricity is to Om. Therefore, 
 make Of equal to ea, and Og equal to the given lead. 
 Connect the points / and m, then, through g t draw gn 
 parallel to fm and intersecting Om in the point n. 
 On is the required eccentricity. 
 
 Draw, through n, the line ndi parallel to md and inter- 
 secting OB at d\, Odi will be the required steam lap. 
 
 Y 
 
 C 
 
 Fig. 43. 
 
 Having found the angle of advance and the eccentric- 
 ity, the valve circle may be drawn if desired. 
 
 Problem 4.. Given the point of cut-off, the lead, and the 
 maximum opening of the port ; find the angle of advance, 
 the eccentricity, and the steam lap. 
 
 This problem is met with in steam engine designing 
 more than perhaps any other relating to the valve, 
 and it is probably the most difficult to solve exactly. 
 It is usually solved by trial and approximation. The 
 exact solution is usually difficult for the student, because 
 the reasons for the different steps in the construction of 
 the diagram are seldom fully understood. In order to 
 
106 
 
 STEAM ENGINES AND BOILERS. 
 
 explain thoroughly the principles involved, let us suppose 
 that in Fig. 44 the problem has been solved, and let us 
 determine the relations that exist between the different 
 parts of the diagram. In the diagram, Orn is the eccen- 
 tricity ; Ob t the steam lap ; ba, the lead ; and dm, the 
 maximum opening of the steam port. AI C\ is the dis- 
 tance from the beginning of the stroke to the point of 
 
 Fig. 44. 
 
 cut-off, and OC is the position of the imaginary crank at 
 cut-off. Draw am, and, since the arc Oam is a semi- 
 circle, am will be perpendicular to OA. Also draw cm, 
 and, since Ocm is a semi circle, it will be perpendicular 
 to OC. Draw bh at right angles to OA ; it will intersect 
 cm at n. Through ;, draw hm parallel to OA and inter- 
 
VALVE DIAGRAMS. 107 
 
 secting bh at h. km will be equal to ba, the lead. Now, 
 with as a center and a radius equal to Om, draw the 
 arc mk intersecting OA at k; then draw kg at right angles 
 to OA and intersecting hm at g. kg will be equal to bk, 
 equal to dm, the maximum opening of the steam port. 
 Now, since Oc is equal to Ob, and the angles ncO and 
 nbO are right angles, if we draw the line On it will bisect 
 the angle, cnb, between the line nb, at right angles to the 
 imaginary crank on dead center, and the line cm, at right 
 angles to the imaginary crank at cut-off. 
 
 Continue On until it cuts gk at /, and then draw Im. 
 Draw ns parallel to hg and intersecting kl at s. With n 
 as a center and a radius equal to ns, draw an arc cutting 
 Im at r. Draw nr, and it will be parallel to Om, as may 
 be proved as follows : 
 
 In the two similar triangles Ins and 10k, we have 
 
 - - -_ But In and /zrare sides of the triangle 
 
 Inr-, also 10 and Om are sides of the triangle 10m. 
 Therefore, since the triangles Inr and Olm have their 
 sides proportional and the angle nlm common to both, 
 they must be similar; and the line nris parallel to Om. 
 
 In the same way it can be shown that if the lines rs and 
 mk be drawn they will be parallel. 
 
 Knowing the relations that have been shown to exist 
 between the various parts of the diagram, the solution of 
 the problem becomes as follows : 
 
 Let AA\, in Fig. 45, represent the stroke of the engine, 
 drawn to any scale, and ACA\, the crank circle; 
 A\ C\, the distance the piston is from the beginning of 
 its stroke at the point of cut-off; and OC, the position of 
 the imaginary crank at cut-off. 
 
 Make Od, according to any desired scale, equal to the 
 given lead ; and Oa, equal to the given maximum opening 
 of the steam port. 
 
 Through (9 and a, respectively, draw Ob and ^/perpen- 
 dicular to OA. Through d, draw cd at right angles to 
 
108 
 
 STEAM ENGINES AND BOILERS. 
 
 OC. Bisect the angle ceb by the line O'e, and prolong it 
 until it intersects af at /.* Connect / and d by the line 
 fd; and draw eg parallel to OA and intersecting fa at g. 
 With e as a center and a radius eg, draw the arc /* cut- 
 ting df 'at ^5. Connect the points * and h, and then draw 
 */0' parallel to eh and intersecting <9'/at 0'. 
 
 Fig. 45. 
 
 The angle Oeh is the required angle of advance ; and 
 O'd is the required eccentricity. Draw O'b parallel to 
 OA and intersecting Oe at b. O'b is the steam lap. 
 
 A line through d parallel to a line through h and g will 
 pass through the intersection of fa and Ob prolonged. 
 
 * Thereat of the solution is simply the solution of the well-known geo- 
 metrical problem : Given two lines and a point, to find a point on one of the lines 
 which is equally distant from the other line and the given point, fe and/a are the 
 given lines and d is the given point O', the required point on fe, is equally 
 distant from d and the line/a prolonged. 
 
VALVE DIAGRAMS. 
 
 109 
 
 Problem 5. Given the angle of advance, the eccentricity, 
 and the point of compression ; find the exhaust lap and the 
 point of release. 
 
 In Fig. 46, let AA\ be the stroke of the engine, drawn 
 to any desired scale, and the circle ABAi, the crank 
 circle. Draw the line OB, making the angle YOB equal 
 to the given angle of advance. Lay off AD\ equal to the 
 distance of the point of compression from the beginning 
 of the return stroke, and, then, draw D D at right 
 angles to AA\. Connect and Z>, and OD will be the 
 position of the imaginary crank at the beginning of com- 
 pression. 
 
 Fig. 46. 
 
 Continue OB to /#, so that Om is equal to the given 
 eccentricity, and on Om as a diameter draw the valve 
 circle Ocmd, intersecting the line OD at d. Od is the 
 required exhaust lap. 
 
 With as a center and a radius equal to Od, draw an 
 arc cutting the valve circle at c. Through c, draw the 
 line OC y and it will represent the position of the imaginary 
 crank when release takes place. Draw CCi perpendicular 
 
110 STEAM ENGINES AND BOILERS. 
 
 to AAi, and A\C\ will be the distance of the point of 
 release from the beginning of the stroke. 
 
 Problem 6. Given the point of compression, the point of 
 release, and the eccentricity ; find the angle of 'advance and 
 the exhaust lap. 
 
 An inspection of Fig. 46 will show that the line Om 
 bisects the angle COD, which is formed by the lines 
 indicating the positions of the imaginary crank at release 
 and at compression. Hence the construction for the 
 solution of the problem is as follows : 
 
 In Fig. 46, let AA\ be the stroke of the engine, and let 
 the circle ACAi be the crank circle. Let OC be the 
 position of the imaginary crank at release, and OD its 
 position at the beginning of compression. Draw OB bi- 
 secting the angle COD, and on it make Om equal to the 
 given eccentricity. On Om, as a diameter, draw the 
 valve circle cutting OC at c, and OD at d. 
 
 The angle YOB is the required angle of advance, and 
 Oc, equal to Od, is the required exhaust lap. 
 
 47. EFFECT OF THE OBLIQUITY OF THE CONNECTING 
 ROD ON THE POINT OF CUT-OFF. In Fig. 47, let A\ A 2 
 represent the stroke of an engine; O, the center of the 
 crank shaft ; OA-, the crank ; and AA\, the length of the 
 connecting rod. Suppose the crank to revolve as indi- 
 cated by the arrow. 
 
 Make Ab equal to A\B\, and draw bB' perpendicular to 
 AA' and cutting the crank circle at B '. If the obliquity 
 of the connecting rod were neglected, the crank would be 
 in the position OB' when the piston has moved through 
 the distance A\B\ on its forward stroke. With B\ as a 
 center and a radius equal to AA\, describe an arc cutting 
 the crank circle at B. OB will be the actual position of 
 the crank when the piston has gotten to B\. It makes no 
 difference where B\ is taken ; the construction will always 
 show that, on the forward stroke of the engine, the obli- 
 
VALVE DIAGRAMS. 
 
 Ill 
 
 quity of the connecting rod makes the actual position of 
 the crank lag behind the position it would occupy if there 
 were no obliquity: that is, in order that the crank shall 
 turn through a given angle A OB', the piston must move 
 
 through a greater distance than the distance, Ab, that it 
 would move through if there were no obliquity. It fol- 
 lows, therefore, that on the forward stroke the actual dis- 
 
112 STEAM ENGINES AND BOILERS. 
 
 tance of the piston from the beginning of the stroke at 
 the point of cut-off is greater than indicated by the valve 
 diagram, by an amount depending upon the obliquity of 
 the connecting rod. In other words, the obliquity of the 
 connecting rod makes the cut-off occur later, on the for- 
 ward stroke, than indicated by the valve diagram. 
 
 Let C\ be any position of the piston on the return 
 stroke. Make cA' equal to C\ Az t and draw cO perpen- 
 dicular to AA' and intersecting the crank circle at O. 
 OO would be the position of the crank, when the piston 
 is at C\ on the return stroke, if there were no obliquity to 
 the connecting rod. With C\ as a center and a radius 
 equal to AAi draw an arc cutting the crank circle at C. 
 OC will be the actual position of the crank when the piston 
 is at C\ on the return stroke. The construction shows 
 that, for a given movement of the piston on the return 
 stroke, the obliquity of the connecting rod makes the 
 crank keep in advance of the position it would be in if 
 there were no obliquity ; that is, in order that the crank 
 shall turn through a given angle A' OC, the piston must 
 move through a less distance than the distance, A'c, that 
 it would move through if there were no obliquity. It 
 follows, then, that, on the return stroke, the actual distance 
 of the piston from the beginning of its stroke at the point 
 of cut-off is less than indicated by the valve diagram, by 
 an amount depending upon the obliquity of the connect- 
 ing rod. In other words, the obliquity of the connecting 
 rod makes the cut-off occur earlier, on the return stroke, 
 than indicated by the valve diagram. 
 
 From what has been said, it is evident that if the steam 
 laps of a valve be made as determined by the valve dia- 
 gram, and the valve be set with equal lead on the head 
 end and crank end of the cylinder, the point of cut-off will 
 occur earlier on the return stroke than on the forward stroke, 
 unless there is some special means of equalizing the points 
 of cut-off. The usual manner of equalizing the points 
 
VALVE DIAGRAMS. 113 
 
 of cut-off is to set the valve with a somewhat greater 
 lead on the head end of the cylinder than on the crank 
 end. The exact amount that the lead on the head end 
 ought to be made greater than that on the crank end, 
 depends upon the obliquity of the connecting rod, the 
 eccentricity of the eccentric, and the lead on the crank 
 end. It may be determined by making a valve diagram 
 for each end of the cylinder, and using in each diagram 
 the positions of the imaginary crank as determined by 
 taking into account the obliquity of the connecting rod. 
 
 48. SWINGING ECCENTRICS. Automatic high speed 
 engines regulate by changing the angle of advance or the 
 eccentricity of the eccentric, or both, and thus change the 
 point of cut-off. As no changes in the angle of advance or 
 the eccentricity can affect the dimensions of the valve, the 
 steam lap and the exhaust lap must always remain the 
 same for the same valve. 
 
 In order to understand how the cut-off and lead will 
 be affected by a change in the eccentricity and angle of 
 advance, for a given eccentric and a given valve, let us 
 refer to the valve diagram in Fig. 48. There, ABA\ is 
 the crank circle ; OB is the position of the imaginary 
 crank at cut-off; OC is the position of the imaginary 
 crank at admission ; YOm is the angle of advance ; Om 
 is the eccentricity ; and Ob, equal to Oc, is the constant 
 steam lap. m is the position of the center of the eccen- 
 tric when the real crank is on the dead center ; and ad is 
 the lead. The line md is perpendicular to Od, since the 
 angle Odm is inscribed in a semi-circle. 
 
 Now, suppose the center of the eccentric to be shifted 
 to mi from m; then the angle of advance will be YOrni, 
 and the eccentricity will be Om\. By the change we 
 have decreased the angle of advance and increased the 
 eccentricity. The new valve circle, drawn on Om\ as a 
 diameter, intersects the lap circle at the points b\ and c\; 
 
 8 
 
114 
 
 STEAM ENGINES AND BOILERS. 
 
 OB\ is the new position of the imaginary crank at cut-off; 
 and OC\ is the new position of the imaginary crank at 
 admission. 
 
 By making, then, the angle of advance less and the 
 eccentricity greater, we have made the cut-off occur 
 later. If we should consider m 1 the original position of 
 
 the center of the eccentric and m its final position, we 
 see that by increasing the angle of advance and decreas- 
 ing the eccentricity, we make the cut-off occur earlier. 
 We obtain, therefore, the following propositions: 
 
VALVE DIAGRAMS. 115 
 
 1. To make the cut-off occur later, make the angle of 
 advance less and the eccentricity greater. 
 
 2. To make the cut-off occur earlier, make the angle of 
 advance greater and the eccentricity less. 
 
 It now remains to see what effect is produced on the 
 lead by changing the angle of advance and the eccen- 
 tricity. In Fig. 48 it is seen that changing the center of 
 the eccentric from m to m has changed the lead from ad 
 to ad\. Draw m\d\ and, since the angle Od\m\ is inscribed 
 in a semi-circle, it will be perpendicular to OA\. Since 
 adi is greater than ad, the line m\d lies to the right of md. 
 Therefore, it is seen that if, when the cut-off is changed, the 
 lead becomes greater, the center of the eccentric will lie to 
 the right of a line drawn through its original position per- 
 pendicular to the center line of the engine. 
 
 If the lead had remained constant, ad\ would be equal 
 to ad and the line m\d\ would coincide with md. There- 
 fore, it follows that, if the lead remains constant when the 
 cut-off is changed, the center of the eccentric will remain on 
 a line drawn through its original position perpendicular to 
 the center line of the engine. 
 
 If ad\ were less than ad, the lead would be less than 
 before and the line md would lie to the left of md. That 
 is, if the lead is decreased when the cut-off is changed, the 
 center of the eccentric will lie to the left of a line drawn 
 through its original position perpendicular to the center line 
 of the engine. 
 
 Very few engines preserve a constant lead under vary- 
 ing cut-offs, owing to the difficulty of making the center 
 of the eccentric have a straight-line motion, as it must in 
 order that m\ may always fall on md. 
 
 On most engines of the automatic high speed type 
 the eccentric is swung about a pin outside the shaft, so 
 that, as the angle of advance is changed, the center, m, of 
 the eccentric moves in the arc of a circle whose center is 
 the center of this suspending pin. Making the eccentric 
 
116 STEAM ENGINES AND BOILERS. 
 
 swing about the pin effects a continual variation in the 
 lead, as the point of cut-off is changed, and the way in 
 which the lead varies depends upon the relative positions 
 of the center of the suspending pin, the center of the 
 shaft, and the center of the eccentric. Usually, 
 although not always, the lead is made to decrease as the 
 cut-off becomes later. Often, the lead is made zero for 
 cut-off at one-quarter stroke, negative for points of cut- 
 off later than one-quarter, and positive for points of cut-off 
 earlier than one-quarter. In such cases, the center of the 
 shaft is between the center of the suspending pin and 
 the center of the eccentric. 
 
 The position of the center of the suspending pin is 
 found by assuming three required positions of the center 
 of the eccentric, and finding the center of a circle that will 
 pass through these positions. The center of this circle 
 will be the required center of the suspending pin. 
 
 In Fig. 49 is shown a diagram of a governor similiar 
 to that used on the Straight Line engine. R is the eccen- 
 tric, which, as shown, is carried by the frame T t and 
 which has an opening in it through which the shaft passes. 
 The eccentric and frame swing about the pin S, on the 
 governor wheel. When the engine is cutting off at its 
 latest, the center of the eccentric is at n; and when the 
 engine is cutting off at its earliest, the center of the eccen- 
 tric is at a. The center of the eccentric is shown in Fig. 
 49 as at n, and the eccentricity is the distance of n from 
 the center of the shaft. When the engine is run, the 
 centrifugal force of the weight C tends to make it move 
 farther from the center of the shaft. When C moves, it 
 moves about the pin 0, and, by means of the link //", 
 makes the frame, T t and the eccentric, R, move about S 
 as a center ; so that the center of the eccentric moves 
 from n towards a. When C is moved outward by its cen- 
 trifugal force it will bend the spring E, to which it is con- 
 nected by the band P, until the resistance to bending of 
 E is equal to the moving force acting on C ; then the 
 
VALVE DIAGRAMS. 117 
 
 eccentric will be at rest, with its center somewhere between 
 n and a. 
 
 If, on account of an increased load, the speed of the 
 engine should be decreased, the centrifugal force of C 
 would become smaller, and the spring would pull C 
 towards the center of the shaft, and move the center 
 of the eccentric towards n; thus, the cut-off would 
 
 Fig. 49. 
 
 be made later and an increased amount of steam would 
 be admitted into the engine to make it go faster. So, 
 also, if, on account of a decrease in the load, the speed of 
 the engine should increase, the centrifugal force would 
 become greater, and C would move farther from the center 
 of the shaft, thus moving the center of the eccentric 
 toward a, making the cut-off earlier, and reducing the 
 amount of steam admitted to the engine. 
 
CHAPTER VI. 
 
 INDICATORS AND INDICATOR CARDS. 
 
 49. INDICATORS. The indicator is an instrument by 
 means of which the actual work diagram of the steam in 
 the cylinder of an engine is automatically drawn on a 
 piece of paper. The diagram obtained by the use of the 
 indicator is termed an " indicator card." 
 
 There are several indicators, which differ from one 
 another in their details only, for sale on the market. 
 
 In Fig. 50 is shown a view of the Crosby indicator, 
 made by the Crosby Steam Gauge & Valve Co., Boston, 
 Mass. It consists of the " drum " A, on which the paper 
 for the card is held by clips a ; the cylinder F t in which 
 works a steam tight piston connected to the piston, rod 
 G ; and a lever K t which carries a pencil c, at its free 
 extremity. The motion of the engine is reduced by a 
 suitable reducing motion and, by means of a cord D,is com- 
 municated to the drum A. As the piston moves forward, 
 the drum is turned in one direction by the pull on D y 
 and as it moves back, on its return stroke, the drum is 
 turned in the opposite direction by means of a strong 
 spring inside of it, which is shown in the sectional view 
 of the indicator given in Fig. 51. It is evident that if, 
 during the backward and forward motion of the drum, 
 the pencil c had been kept at rest and pressed against the 
 paper, it would have marked on there a line, parallel to 
 the base of the drum, whose length would be propor- 
 tional to the stroke of the engine. 
 
 The steam enters the cylinder F, and presses against 
 the piston and makes it rise ; and it, in turn, makes the 
 pencil c rise. As seen in Fig. 51, the piston in the cyl- 
 (118) 
 
INDICATORS AND INDICATOR CARDS. 
 
 119 
 
 inder is kept down by a spring that must be compressed 
 before the piston can rise. The springs used to keep the 
 piston down are numbered and named according to the 
 number of pounds pressure per square inch required to 
 raise the pencil c through one inch : thus, a No. 40 
 spring, or a 40 Ib. spring, is a spring that, when in the 
 indicator, will require an effective pressure of 40 Ibs. per 
 square inch to make c rise one inch. 
 
 Fig. 50. 
 
 By means of the system of levers, shown in Fig. 50, con- 
 necting Kto the frame of the indicator and to the piston 
 rod G, the pencil c is made to move in a straight line 
 parallel to the axis of the drum A. It is in the system 
 of levers for making c move in a straight line, that indi- 
 cators on the market differ most. 
 
 The handle E can be so adjusted by turning it to the 
 right or left, that when it is pressed forward, so that its 
 inner end strikes against the stop B, the pencil c will 
 
120 
 
 STEAM ENGINES AND BOILERS. 
 
 press with any desired pressure against the paper on the 
 drum A. When the pencil is pressed against the paper 
 it makes a line, every point of which represents, at once, 
 the position of the piston in its stroke and the pressure 
 of the steam at the same instant. The position of the 
 piston is indicated by the distance of the point from the 
 ends of the card; and the pressure of the steam is 
 referred to the "atmospheric line," obtained by shutting 
 off the cylinder of the indicator from the cylinder of the 
 engine, putting it in communication with the air, and 
 then pressing the pencil against the paper. 
 
 Fig. 51. 
 
 50. ADJUSTMENTS AND CONNECTIONS OF INDICATORS. 
 In order that the results obtained by the use of an indi- 
 cator may be of value, it is necessary that the various 
 parts should be in adjustment and act as they are designed 
 to act. If an indicator is tested, and it is in adjustment, 
 it will be found that : 
 
 I. The pencil will move in a straight line parallel to 
 
INDICATORS AND INDICATOR CARDS. 121 
 
 the axis of the drum ; and the line obtained by moving 
 the pencil and keeping the drum at rest,will be at right 
 angles to the line obtained by keeping the pencil at rest 
 and moving the drum. 
 
 2. For equal amounts of increase in the pressure on the 
 piston, the pencil will rise equal distances. 
 
 The motion of the pencil must be adjusted by the 
 maker of the instrument; and if it is not correct the in- 
 strument should not be used for important work, as the 
 cards obtained from it would be distorted, and would be 
 apt to give a wrong impression of the real action of the 
 steam in the cylinder of the engine. 
 
 The springs used in the cylinder of the indicator should 
 always be tested hot, so that, when being tested, they will 
 be as nearly as possible in the same condition as when in 
 actual use. It is not necessary that the springs should be 
 exact, provided the error is constant, and can be deter- 
 mined. 
 
 It is important that the friction of the pencil be as 
 little as possible and that the play, or back lash, in the 
 joints of the levers, for producing the straight line motion 
 of the pencil, should be as small as possible. The fric- 
 tion of the pencil on the paper must be reduced to the 
 minimum, by adjusting the pencil so that it presses against 
 the paper with sufficient force to just make a mark and 
 no more. 
 
 The piston of the indicator should be a nice fit in the 
 cylinder, and it is preferable to have it too loose rather 
 than too tight. The fit will be about right if the piston 
 will be moved down the cylinder by its own weight, when 
 the spring is removed. The piston, and all the moving 
 parts attached to it, should be as light as is consistent with 
 strength. 
 
 The drum of the indicator should be light and should 
 move easily on its axis. Its cross-section should be a per- 
 fect circle ; and its axis of rotation should coincide with 
 
122 STEAM ENGINES AND BOILERS. 
 
 the axis of the cylinder. The tension of the spring in the 
 drum should be regulated so that the inertia of the drum 
 will not lengthen the cards too much ; it should be greater 
 for high speed, than for low speed engines. 
 
 The indicator is connected to the cylinder of the engine 
 by a piece of half-inch pipe; and, while much differ- 
 ence of opinion seems to exist as to whether or not the card 
 obtained with a short connection, having as few bends as 
 possible, is materially different from that obtained with a 
 long connection, having several bends, it is, undoubtedly, 
 true that the long connections do no good ; and, there- 
 fore, the connections should be as short as possible. 
 Where the load on an engine fluctuates through wide 
 ranges, it is almost impossible to determine with any 
 degree of accuracy, from the cards of an engine, whether 
 or not the valves are properly adjusted, unless cards are 
 taken at the same time from both ends of the engine. 
 To do this, it is necessary to have two indicators, one at 
 each end of the cylinder ; they should be so arranged 
 that when the pencil of the one is pressed against its 
 paper, the pencil of the other will, also, be pressed against 
 its paper. Where two indicators cannot be arranged to 
 work together, so that cards may be taken simultaneously 
 from each end of the cylinder, and a single indicator is 
 used, it should be connected to the ends of the cylinder 
 so that it will not be necessary to change its position in 
 order to take a card from either end of the cylinder. 
 The best method of making the connections for a single 
 indicator is to connect both ends of the cylinder to a 
 single pipe, along the side of the cylinder, and in the 
 middle of this pipe put a three-way cock, to which the 
 indicator may be attached. Makers of indicators make 
 special three-way cocks for indicator connections. 
 
 51. REDUCING MOTIONS. As the diameters of the 
 drums of indicators are, usually, either ij or 2 inches, 
 
INDICATORS AND INDICATOR CARDS. 123 
 
 their circumferences will be about 5 or 6 inches ; and, as 
 the length of the card taken on an indicator must be 
 considerably shorter than the circumference of the drum, 
 the cards will usually be 3 inches long for a drum ij 
 inches in diameter, and about 4 inches long for a drum 2 
 inches in diameter. The drum is connected to some 
 point on the engine that, by a suitable " reducing 
 motion," makes the drum move through a distance equal 
 to the desired length of the indicator card. The motion 
 of this point must be such that the drum of the indicator 
 will make one complete movement in one direction, dur- 
 ing the same time that the engine makes one stroke ; also, 
 the ratio of the velocity of turning of the drum, at any 
 instant, to the velocity of the piston, at the same instant, 
 ought to be a constant quantity. If this last requirement 
 is not fulfilled, the card will be distorted, shortened up at 
 some places and lengthened out at others, so that an 
 event which occurs at, say, one quarter of the stroke of 
 the engine, will be shown on the card as occurring either 
 before or after one quarter stroke. To test the accuracy 
 of a reducing motion, put the engine on dead center, so 
 that the piston 'is just beginning its stroke, and mark the 
 position of the pencil on the indicator card. Now divide 
 the distance through which any chosen point on the cross- 
 head moves, during one revolution, into a number, such as 
 four or eight, of equal parts, and make a mark at each 
 point of division. Move the piston forward until the 
 chosen point on the cross-head coincides with the first 
 division mark, and mark the position of the pencil on the 
 drum ; then move the cross-head to the next division 
 mark, and mark, again, the position of the pencil on the 
 drum. Continue moving the cross-head forward one 
 division, and marking the corresponding motion of the 
 drum, until the piston has made one stroke. Take the 
 card off the drum and determine whether or not the dis- 
 tance between any two successive marks is always the 
 
124 STEAM ENGINES AND BOILERS. 
 
 same ; if it is, the reducing motion is correct, but if it is 
 not, the reducing motion is defective. 
 
 The commonest form of reducing motion is the " pen- 
 dulum motion," shown in Fig. 52. It consists of a bar, 
 A, slotted at one end, and suspended by a pin, B, at the 
 other end. A pin, c, fastened to the cross-head, fits in 
 the slot at the lower end of the bar ; and a pin, D, is fast- 
 ened to the bar. The string from the drum of the indi- 
 cator is tied to D. As the engine moves backward and 
 forward, the pin c makes the bar oscillate about B as 
 a center. At any instant, the ratio of the velocity of the 
 
 Fig. 52. 
 
 /? D 
 drum to the velocity of the piston is equal to ~~n^> As 
 
 Be changes for different positions of the piston, this 
 ratio is not a constant one. The point D moves in the 
 arc of a circle whose center is B; and, therefore, the 
 direction of the string, leading from D to the drum of the 
 indicator, is constantly changing. This makes a slight 
 error in the motion of the drum. If Be is not made less 
 than twice the length of the stroke of the engine and, 
 when in mid-position, is perpendicular to the direction of 
 the motion of the piston, and the string is lead off per- 
 pendicular to Be in mid-position, it will be found that 
 the errors of the motion will be small, and the motion 
 will give fairly good results. 
 
INDICATORS AND INDICATOR CARDS. 125 
 
 The length of the card given by this motion is equal to 
 the length of the stroke of the engine multiplied by the 
 length of BD and divided by the length of Be. 
 
 The " Brumbo Pulley," shown in Fig. 53, is a motion 
 devised to overcome the errors of the simple pendulum 
 motion. It is more elaborate then the simple pendulum 
 motion. It consists of a link, A, which is suspended by 
 a pin, B, and to which is fastened an arc, D, whose center 
 coincides with that of the pin B. The lower end of A is 
 connected to the cross -head, by the link C. It is usual to 
 make the link A, when in mid-position, perpendicular to 
 the line of motion of the piston. 
 
 By assuming the length of the links A and C, and 
 plotting the required motion of the drum, for given 
 motions of the piston, a form of arc may be obtained that 
 will give a perfectly correct motion to the drum of the 
 indicator. It is usual, however, to make D the arc of a 
 circle ; and, then, the motion is not exact, but the error 
 due to the obliquity of the string leading from D is 
 avoided, as its direction is not changed. 
 
126 STEAM ENGINES AND BOILERS. 
 
 In Fig. 54 is shown the " pantograph " used on long 
 stroke engines. It gives a perfect motion if properly 
 used. 
 
 The instrument is made of a number of light wooden 
 links joined together as shown. When used, the pivot B 
 is fastened, by means of the thumb screw on its end, to 
 any convenient support. The pin A is dropped into an 
 opening either in the cross-head itself or in a piece 
 fastened to the cross-head ; so that, while B remains 
 stationary, A has the motion of the cross-head. The 
 cord leading to the indicator is fastened to a pin, E, in 
 the cross-head bar DC, and should be lead off parallel to 
 the line of motion of the piston. 
 
 Fig. 54. 
 
 This instrument may be used either in a horizontal or a 
 vertical position, whichever is the more convenient, and 
 will give equally good results in either position. 
 
 The length of the card depends upon the ratio of the 
 distance BE to the distance BA, and upon the stroke of 
 the engine. For a given position of the cross-bar, BC, 
 and the pin, E, in it, the ratio of BE to BA is a constant 
 one, no matter how long the instrument maybe stretched. 
 The position of the cross-bar, DC, may be changed by 
 changing the holes in which the pins D and C are 
 placed. The bar DC must always be parallel to the left- 
 
INDICATORS AND INDICATOR CARDS. 127 
 
 hand bar passing through B. The pin, E, on the cross- 
 bar, DC, must be placed so that it is on the line BA. The 
 joints of the instrument must be kept tight and well 
 lubricated. 
 
 The length of the card given by this instrument is 
 equal to the length of the stroke of the engine multiplied 
 by the length of BE and divided by the length of BA. 
 
 In Fig. 55 is shown one of the many forms of "re- 
 ducing wheels/' used in connection with high speed 
 engines. Its construction is evident from the figure. 
 The cord from the large drum leads to the cross-head of 
 the engine, and that from the small drum leads to the 
 indicator. 
 
 Fig. 55. 
 
 52. CORD FOR INDICATOR. The cord used for trans- 
 mitting the motion of the reducing mechanism to the 
 drum of the indicator, should be a good quality of strong, 
 cotton, cord that has but little stretch. Where the dis- 
 tance from the reducing mechanism to the indicator is 
 great, it is preferable to use good steel wire instead of 
 cord. 
 
128 STEAM ENGINES AND BOILERS. 
 
 In leading off from the reducing motion, the cord should 
 always run, for a short distance at least, parallel to the 
 direction of motion of the piston of the engine. If this is 
 not done, there will be an error due to the obliquity of the 
 cord. 
 
 In changing the direction of the cord it should be 
 passed over small guide pulley-wheels, made for that 
 purpose. 
 
 It is customary to have a loop in the end of the lead- 
 ing, cord in which may be caught the hook that is usually 
 attached to the end of the cord fastened to the drum of the 
 indicator. By unfastening the hook from the loop, the 
 indicator will be disconnected from the engine and 
 stopped, and the card on the drum may be changed ; by 
 catching the hook in the loop, the indicator may be put 
 in motion again. 
 
 53. TAKING THE INDICATOR CARD. To take a card, turn 
 steam on the indicator and wait until it has got thoroughly 
 warm ; connect the drum to the reducing motion ; open 
 the communication between one end of the cylinder of 
 the engine and the cylinder of the indicator ; press the 
 pencil against the paper, and hold it there while the 
 engine makes one revolution ; then shut off the indicator 
 from the engine, and at once take the atmospheric line. 
 If the indicator is connected so that a card may be taken 
 from both ends of the engine, take a card from one end, 
 then, as rapidly as possible, shut off that end and take 
 the card from the other end, before taking the atmos- 
 pheric line. 
 
 While one man is taking the indicator card, another 
 ought to be getting the number of revolutions of the 
 engine. 
 
 54. To DETERMINE THE HORSE-POWER FROM THE INDI- 
 CATOR CARD. The indicator card gives us the real 
 
INDICATORS AND INDICATOR CARDS. 
 
 129 
 
 "work diagram" of the steam in the cylinder, and, as 
 has been explained in Article 22, the area of this diagram 
 represents the work done, by the steam on the engine, each 
 time steam enters the cylinder. Therefore, if we get the 
 area of the diagram in square inches and divide it by the 
 length of the diagram in inches, we shall obtain the mean 
 height of the diagram. If this mean height be multiplied 
 by the number of the indicator spring we shall get the 
 mean effective pressure, P e , per square inch, of the steam 
 
 Fig. 56. 
 
 on the piston ; and if we put this value of Pe in the 
 equation for the horse-power of an engine, as given by 
 (54) of Art. 22, we get 
 
 P e L AN 
 
 H. P.= 
 
 33000 
 
 As explained in Art. 22, L is the stroke of the engine 
 in feet ; A, the area of the piston in square inches ; and N t 
 the number of times per minute the engine takes steam. 
 If the engine is double acting, N is equal to the number 
 
130 STEAM ENGINES AND BOILERS. 
 
 of strokes, or twice the number of revolutions made per 
 minute. P e , for a double acting engine, ought to be taken 
 as the mean of the values of P e derived from the cards 
 from both ends of the cylinder. 
 
 The best method of determining the area of an indicator 
 card is to use the Amsler Planimeter, shown in Fig. 56. 
 The card is fastened to a drawing board, or the smooth 
 top of a table, and the point A of the instrument pressed 
 into the drawing board or table, so that it cannot move. 
 The tracing point, B, of the instrument is now put at any 
 convenient point on the line of the card, and the reading 
 of the scale on the wheel C is determined by means of 
 the venier , which enables one to read to the hundredth 
 part of a square inch. The tracing point, B, is now moved 
 around, always in a right-handed direction, on the line of 
 the card until it returns to the point from which it was 
 started. The scale on the wheel is again read, and the 
 difference between the last reading and the first reading, 
 of the scale en C, is the area of the diagram in square 
 inches. Measure the length of the diagram; then divide 
 the area of the diagram by the length of the diagram, and 
 the result multiplied by the number of the indicator 
 spring, is the mean effective pressure, P e , to be used in 
 calculating the horse-power. 
 
 The price of planimeters is now so small that it is 
 rather unusual for any person who has an indicator to be 
 without a planimeter, but for the sake of those who do 
 not have one, the method of obtaining the value of P e 
 without the use of the planimeter is given. In Fig. 57, 
 let AB represent the atmospheric line of the card. 
 Through A, draw AC in any convenient direction. Take 
 any convenient, small distance, AD, on AC. From D lay 
 off successively nine equal distances, DF, FG, GH, etc., 
 to N ; and make each of these distances equal to twice the 
 length of AD. Now lay off NC equal to AD, and draw 
 BC. Through the points D, F, G, H, etc., on AC, draw 
 
INDICATORS AND INDICATOR CARDS. 
 
 131 
 
 lines parallel to BC and intersecting AB at the points 
 d>f,g, h, etc. Through the points d y f,g, /z, etc., draw 
 lines, IT, 22, 33, 44., etc., perpendicular to AB and, each, 
 intersecting the bounding line of the card in two points. 
 
 Get the sum of the distances //, 22, 33, 44., etc., and 
 divide it by ten ; multiply this quotient by the number of 
 the indicator spring, and the result will be the value of 
 mean effective pressure, P et to be used in determining the 
 horse-power of the engine. 
 
132 
 
 STEAM ENGINES AND BOILERS. 
 
 55. To FIND THE RATIO OF CLEARANCE OF THE ENGINE 
 FROM THE INDICATOR CARD In Fig. 58 we have a card 
 whose atmospheric line is AB. That part of the bound- 
 ing line of the card from I to 2 is made during admission 
 of the steam to the cylinder ; that part from 2 to 3 is 
 made during expansion of the steam, after cut-off at 2 ; 
 that part from 4 to 5 * s made during the return stroke, 
 while the exhaust valve is open ; and that part from 5 to 
 6 is made during compression, after the exhaust valve 
 
 Fig. 58. 
 
 closed at 5. The part from 3 to 4 is made at the end of 
 the stroke, when the pressure suddenly falls, from the final 
 pressure of the steam after expansion, to almost the atmos- 
 pheric pressure ; and the part from 6 to I is made when 
 the steam begins to enter the cylinder, just before the 
 beginning of the forward stroke. 
 
 To find the ratio of the clearance volume to the volume 
 swept through by the piston during one stroke, draw AA\ 
 perpendicular to the atmospheric line ; and lay off AA l 
 so that, according to the scale of pressures of the card, it 
 will be equal to the atmospheric pressure, 14.7 Ibs. per 
 square inch. Through A\, draw A\B parallel to AB. 
 
INDICATORS AND INDICATOR CARDS. 133 
 
 Now take any two points, such as a and b, on the com- 
 pression line 56. Through a draw a line parallel to AB, 
 and continue it until it intersects, at c, a line drawn 
 through b perpendicular to AB; also, through a draw a 
 line perpendicular to AB, and continue it until it intersects, 
 at </, a line drawn through b parallel to AB. Draw cd 
 and continue it until it intersects A\B\ at 0, the "origin " 
 of the card. 
 
 Through O, draw OY perpendicular to AB and inter- 
 secting it at e. Then, the ratio of Ae to AB will be the 
 ratio of the volume of clearance, at that end of the 
 cylinder from which the card was taken, to the volume 
 swept through by the piston in one stroke. This con- 
 struction is based upon the supposition that the curve 
 56 is an equilateral hyperbola. The ratio obtained 
 may, or may not, be the same for both ends of the 
 cylinder. 
 
 56. To FIND THE WEIGHT OF STEAM USED PER HOUR 
 PER HORSE-POWER. Take any point,/, near the end of 
 the expansion line, and through it draw the line fg 
 parallel to AB and intersecting the compression line at^. 
 
 Let the ratio obtained by dividing the length offg by 
 the length of AB be denoted by X. 
 
 The volume of the steam, at the pressure by the gauge 
 equal to the pressure corresponding to hf t that is used 
 per stroke is equal to the volume swept through by the 
 piston, in one stroke, multiplied by X. Since the volume, 
 in cubic feet, swept through by the piston per stroke is 
 
 LA XLA 
 
 , the volume of steam used per stroke is . 
 
 144 144 
 
 If the number of strokes made per minute is N, the 
 number made per hour will be 60 A 7 ", and the volume of 
 steam, at a gauge pressure corresponding to hf y used per 
 hour will be 
 
 GO XL AN $ XL AN 
 144 ~12~ 
 
STEAM ENGINES AND BOILERS. 
 
 Let s be the volume, in cubic feet, of one pound of 
 steam at the gauge pressure corresponding to the pressure 
 /{/", as obtained from Table I ; then the weight of steam 
 used per hour by the engine will be 
 
 s 12 s 
 
 From (54), we have that the horse-power of the engine 
 If. P. = 
 
 is 
 
 P e L AN 
 
 53000 
 
 The weight of steam used per hour per horse-power 
 will be, from (61), 
 
 S _ 165000 X_ 13750 X 
 H. P. : ~\l~sJ\~ sP e 
 
 X and P e are obtained from the indicator card, and s is 
 obtained from Table i. 
 
 57. INTERPRETATION OF THE ACTION OF THE VALVES 
 FROM THE APPEARANCE OF THE INDICATOR CARD. In 
 studying the cards shown in this article, the student must 
 remember that each card is drawn to illustrate some 
 special defect, which is made very prominent and which 
 may be much less prominent on a card from an engine. 
 
 Wire-drawing or Throttling is indicated by the admis- 
 sion line gradually dropping, from the beginning of the 
 stroke to the point of cut-off, below a line drawn parallel 
 to the atmospheric line through the point indicating the 
 initial pressure of the steam, as shown at 12 in Fig. 59. 
 Wire-drawing is due, in the case of non-throttling engines, 
 to the valve not opening far enough to admit the steam 
 to the cylinder, or to bad and poorly designed ports. In 
 the case of throttling engines, the wire-drawing is due to 
 the action of the governor, and is always to be expected. 
 
INDICATORS AND INDICATOR CARDS. 135 
 
 Too Great an Expansion is indicated by the expansion 
 line extending down below the initial back pressure and 
 forming a loop, as shown at j^ in Fig. 59. The pressure 
 of the steam at the end of the stroke is less than the 
 initial back pressure, and when the exhaust valve is 
 opened the pressure in the cylinder is raised instead of 
 being lowered. 
 
 The area of the loop at 345, must be subtracted from 
 the area 1256. The small loop means negative work ; 
 since, while the loop is being formed, the forward pressure 
 
 Fg. 59. 
 
 on the piston is less than the back pressure. In measur- 
 ing the area of such a card with the planimeter, the 
 instrument will, of itself, subtract the area of the small 
 loop, if the tracing point be moved down and around 
 over the expansion line just as the pencil moved when 
 the loop was formed. 
 
 Early Admission, which is a result of too much lead, is 
 indicated by the line 61, in Fig. 60, slanting backwards, 
 and by the sharp, backward-pointing beak at I. 
 
 Early Release is indicated by the line 34, in Fig. 60, 
 slanting forward, and by the sharp, forward-pointing beak 
 at 4. 
 
 In the case of engines with single valves, early release 
 will, if the valve is properly made, always accompany 
 early admission, but in the case of engines that have 
 
136 STEAM ENGINES AND BOILERS. 
 
 separate steam and exhaust valves, early release need 
 not accompany early admission. 
 
 Fig. 60. 
 
 In the case of single valve engines, early admission 
 and early exhaust may be corrected by turning the eccen- 
 tric backward on the shaft, so as to reduce the angle of 
 advance. 
 
 When there are separate exhaust and steam valves, the 
 manner of correcting early admission, or early exhaust, 
 depends upon the valve gear. 
 
 Late Admission, which is a result of too little lead, is 
 indicated by the line 61, in Fig. 61, slanting forward, and 
 by the sudden rounding at 6. 
 
 Late Release is indicated by the line 34, in Fig. 61, 
 slanting backward, and by the sharp, beak-like point 
 at 3. 
 
 When the exhaust and admission are controlled by the 
 same valve, late release will always, if the valve is prop- 
 erly designed, accompany late admission ; both may be 
 corrected by turning the eccentric forward on the shaft, 
 so as to make the angle of advance greater. 
 
 Where there are separate exhaust and steam valves, 
 late exhaust need not accompany late admission, and the 
 
INDICATORS AND INDICATOR CARDS. 
 
 137 
 
 manner of correcting either will depend upon the valve 
 gear. 
 
 Fig. 61. 
 
 Too Great Compression is shown by the compression 
 line being carried above the initial line of pressure and 
 forming a loop, as shown at I in Fig. 62. 
 
 Fi?. 62. 
 
 This can sometimes be remedied by turning the eccen- 
 tric backward, so as to make the angle of advance less. 
 Where there are separate steam and exhaust valves, the 
 
138 STEAM ENGINES AND BOILERS. 
 
 exhaust valves must be changed so that they will not 
 close so early in the return stroke. 
 
 Leak During Compression is indicated by a break in 
 the compression line, as shown at 67 in Fig. 63. 
 
 In case a card such as shown in Fig. 63 is obtained, the 
 piston should be tested for tightness. To do this, remove 
 the head of the cylinder, after the steam has been shut 
 off, and block the engine in such a position that the steam 
 port admitting steam to the crank end of the cylinder is 
 open; then turn on the steam and note whether or not 
 
 any passes the piston. If the piston leaks it should be 
 made tight at once. 
 
 If the piston is tight and all the drip cocks are closed 
 tight, a break in the compression line, as shown at 67 in 
 Fig. 63, indicates a leak from the cylinder into the 
 exhaust port. 
 
 Leak During Expansion. In order to determine 
 whether or not there is any leakage into, or out of, the 
 cylinder during expansion, it is necessary to draw the 
 theoretical expansion line as follows : 
 
 In Fig. 64, let AB be the atmospheric line; AAi be 
 equal to the atmospheric pressure, according to the 
 scale of pressures of the card ; and let O be the " origin " 
 of the card, found from the compression line by the 
 method described in Art 55. 
 
INDICATORS AND INDICATOR CARDS. 
 
 139 
 
 Take any point, c, on the expansion line, close to the 
 point of cut-off; through it draw Cc parallel to AB, and 
 cD perpendicular to AB. Care must be taken to choose 
 the point c in such a position that there can be no doubt 
 but that the steam valve is closed. 
 
 IB. 
 
 Fig. 64. 
 
 Through O draw any line intersecting Cc, at n, and 
 cD, at m. Draw through n a line perpendicular to AB, 
 and continue it until it intersects, at f t a line drawn 
 through m parallel to AB. 
 
 The point /is a point on an equilateral hyberbola, here 
 assumed to be the theoretical expansion line. By repeat- 
 ing the construction, any number of points may be found 
 on the desired curve ; and the curve may afterwards be 
 drawn in. 
 
 Let cd be the theoretical expansion line. If the 
 expansion line of the indicator card is below the theoret- 
 ical line, it indicates condensation or leakage out of the 
 cylinder, or both ; while, if the expansion line of the card 
 is above the theoretical line, it indicates leakage of steam 
 past the steam valve into the cylinder. 
 
140 
 
 STEAM ENGINES AND BOILERS. 
 
 Where the number of times the steam is expanded is 
 large, the expansion line of the card will always fall below 
 the theoretical line. This is due to the fact that, for a 
 large number of expansions, the expansion line is not an 
 equilateral hyperbola, as has been assumed in this work. 
 
 Fig. 64a. 
 
 Indicator Cord too Long. When the cord connecting 
 the drum of the indicator to the reducing motion is too 
 long the drum is allowed to move back and come to rest 
 before the piston gets to the head end of its stroke. The 
 effect of this on the card is as shown in Fig. 64a. On the 
 card from the head end of the cylinder, marked H t there 
 appears the vertical line 12; and on the card from the 
 crank end of the cylinder, marked C, there appears the 
 vertical line 34. 
 
CHAPTER VII 
 
 COMPOUND ENGINES AND CONDENSERS. 
 
 58. COMPOUND ENGINES. While any engine in which 
 the steam is used in more than one cylinder is a com- 
 pound engine, the term has come to be restricted, by 
 custom, to those engines in which the steam is used in 
 but two cylinders, a high pressure cylinder and a low 
 pressure cylinder. The steam enters the high pressure 
 cylinder on leaving the boiler, and there expands a certain 
 number of times ; after leaving the high pressure cylinder 
 the steam passes into the low pressure cylinder, where it 
 is expanded more. By using two cylinders for a given 
 number of expansions, the number of expansions in each 
 cylinder is made much less than it would be if there were 
 but one cylinder, and, therefore, the range of pressures 
 in each cylinder is made less. As the range of tempera- 
 tures, of expanding steam, depends upon the range of 
 pressures, the use of two cylinders, to obtain a given 
 number of expansions, will reduce the range of tempera- 
 tures in each cylinder. 
 
 The losses in an engine are always of two kinds, 
 thermodynamic and mechanical. 
 
 The thermodynamic losses are due to radiation of heat 
 from the walls of the cylinder, and the heating of the 
 metal of the cylinder; they bring about an increase in the 
 comsumption of steam, per horse power per hour, by 
 condensing the steam in the cylinder. It has been found 
 that the condensation of steam in a cylinder is decreased 
 by well lagging the cylinder with non-conducting 
 materials ; by increasing the speed of rotation of the 
 engine, thus decreasing the length of time each particle 
 
 (141) 
 
142 STEAM ENGINES AND BOILERS. 
 
 of steam is in contact with the metal of the engine ; by 
 reducing the number of expansions in the cylinder, thus 
 reducing the range of temperatures of the steam during ex- 
 pansion ; and, finally, by decreasing the radiating surface 
 of the cylinder. 
 
 The mechanical losses are due to the friction of the 
 moving parts, and are decreased by good workmanship 
 and materials in construction ; by reducing the number 
 of moving parts ; and by care and good management 
 while running. 
 
 The whole object of compounding is to reduce the 
 amount of steam used, per horse-power per hour, by 
 reducing the losses in the engine. As the lagging of a 
 simple engine can be made just as good and efficient as 
 that of a compound engine, there can be no reduction 
 of losses on that account; the speed of rotation of the 
 simple engine may be just as great as that of the com- 
 pound, and, therefore, there can be no reduction on that 
 account; two cylinders expose more surface for radiation 
 than one, and therefore, compounding increases the losses 
 due to this; but the range of expansion in each cylinder 
 of a compound engine is less than it would be in a single 
 cylinder engine of the same total number of expansions, 
 and there is, then, a reduction of loss in the compound 
 engine on this account. 
 
 The mechanical losses may be, and usually are, greater 
 in the compound engine of the same power than they are 
 in the single cylinder engine. 
 
 Summing up then, the compound engine tends to 
 increase the thermodynamic losses by increasing the radi- 
 ating surface, and also tends to increase the mechanical 
 losses by increasing the number of moving parts ; but it 
 tends to decrease the thermodynamic losses by decreas- 
 ing the range of temperatures of the steam in the cylinders, 
 by reducing the number of expansions in each. 
 
 When the reduction of losses is greater than the increase, 
 
COMPOUND ENGINES A^D CONDENSERS. 143 
 
 the compound engine should be used. With low pressures 
 and a small number of expansions, the single cylinder 
 engine is more economical than the compound engine. 
 It is probably safe to say that for pressures under 
 sixty pounds, by the gauge, the single cylinder condens- 
 ing engine is more economical than a compound engine; 
 but for pressures above sixty pounds, by the gauge, the 
 compound engine is more economical. The higher the 
 pressure and the greater the number of expansions, the 
 greater is the economy of the compound engine as com- 
 pared to the single cylinder engine. In the case of non- 
 condensing engines the single cylinder engine is probably 
 more economical for all pressures under ninety pounds", 
 by the gauge, but above this it is probable that the com- 
 pound engine is the better to use. 
 
 As the single cylinder engine has its limit, at which it 
 becomes less economical than the compound engine, so 
 the compound engine becomes less economical than the 
 triple expansion engine, where the steam is expanded 
 successively in three cylinders, for pressures greater than 
 about one hundred and twenty pounds by the gauge. 
 
 Up to about four expansions, it is probable that the 
 single cylinder engine is more economical than the com- 
 pound engine ; for from four to six expansions, there is 
 not much choice between the two engines, so far as 
 economy is concerned ; for from six to ten expansions, 
 the compound engine is the more economical. For a 
 greater number of expansions than ten, it will usually be 
 found better to use a triple expansion engine. 
 
 Compound engines are usually classified under two 
 heads, viz., Tandem Compound, Cross-compound. 
 
 59. TANDEM COMPOUND ENGINES. Tandem compound 
 engines are those which have the two cylinders placed 
 one in front of the other. There are two pistons, one for 
 each cylinder; one piston rod; one connecting rod; and 
 one crank. The steam flows as directly as possible from 
 
144 STEAM ENGINES AND BOILERS. 
 
 the high pressure cylinder into the low pressure cylinder, 
 and the connecting pipes are usually made small. There 
 is no " receiver," or vessel into which the steam flows, 
 between the high pressure cylinder and the low pressure 
 cylinder. 
 
 The tandem compound engine occupies less space than 
 the cross-compound. 
 
 60. CROSS-COMPOUND ENGINES. The two cylinders of 
 the cross-compound engine are placed side by side, and 
 there is for each cylinder, a separate piston rod, connect- 
 ing rod, cross-head, and crank. The steam often passes 
 into a " receiver " after leaving the high pressure cylinder, 
 and there remains until it passes into the low pressure 
 cylinder. The cranks are usually set at an angle of 90 
 with one another ; so that when the high pressure piston 
 is at the end of the stroke, the low pressure piston is in 
 mid-position and has half a stroke to complete before it 
 is ready to take steam ; it is on this account that it is 
 always necessary to have a receiver for cross-compound 
 engines whose cranks are at 90. 
 
 The cross-compound engine occupies more space than 
 the tandem compound engine, but by having two piston 
 rods, two connecting rods, and two cranks, it really be- 
 comes equivalent to two engines connected to the same 
 shaft, each of which need be only about half the power of 
 the single cylinder engine to do the same work. And, 
 therefore, all the parts of the cross-compound engine 
 may be lighter and smaller than the same parts on 
 either a single cylinder engine or a tandem compound 
 engine. 
 
 The twisting effort of the crank shaft is made more uni- 
 form by having the cranks at 90, as when one piston is 
 exerting its maximum effort the other is exerting a much 
 less effort, and, therefore, the engine becomes easier to 
 govern. 
 
COMPOUND ENGINES AND CONDENSERS. 145 
 
 61. RATIO OF CYLINDERS OF COMPOUND ENGINES. 
 The ratio of the volume of the low pressure cylinder 
 to the volume of the high pressure cylinder may be de- 
 noted by K, and, since the strokes of the two cylinders 
 of a compound engine are usually the same, we have 
 
 jyi 
 K = p. Where D is the diameter of the low pressure 
 
 cylinder, and d the diameter of the high pressure cylinder. 
 The value of K ought to be made to vary with the 
 pressure of the steam and the number of times the steam 
 is expanded. Designers usually try to make the value of 
 K such that the " drop," or fall in pressure of the steam 
 between the high pressure cylinder and the low pressure 
 cylinder, shall be small, when the work of the engine 
 is divided so that it is the same in each cylinder. 
 
 The value of ./T varies from 2j to 4 for automatic high 
 speed engines; and from 3 to 4^ for engines of the 
 Corliss type ; it is always equal to the quotient obtained 
 by dividing the total number of times the steam is 
 expanded by the number of times it is expanded in the 
 high pressure cylinder. 
 
 62. THE HORSE-POWER OF COMPOUND ENGINES. In 
 determining the horse-power of a compound engine from 
 which indicator cards have been taken, work up the card 
 for each cylinder just as if it were the card from a single 
 cylinder engine; and having found the mean effective 
 pressure for each cylinder, calculate the horse-power of 
 each by the method explained, in Art. 54, for a single 
 cylinder engine. The sum of the horse-powers developed 
 in the two cylinders will be the horse-power of the 
 engine. 
 
 In calculating the horse-power that a compound engine 
 ought to develop, for given conditions as to absolute 
 steam pressure, total number of expansions of the steam, 
 number of strokes per minute, diameters of low and high 
 
 10 
 
146 STEAM ENGINES AND BOILERS. 
 
 pressure cylinders, and length of stroke, proceed as if 
 there were but one cylinder, of the same size as the low 
 pressure cylinder, in which the total expansion of" the 
 steam took place. If the horse-power obtained by 
 assuming that all the work was done in the low pressure 
 cylinder be multiplied by a factor, whose value depends 
 upon the type of the compound engine, the result will be 
 equal to the horse-power the compound engine ought to 
 develop under the given conditions. 
 
 Let A be the area, in square inches, of the low pressure 
 piston ; L, its length of stroke, in feet ; N t the number of 
 strokes made by the low pressure piston per minute ; , 
 the total number of times the steam is expanded in the 
 compound engine ; and C, a factor whose value depends 
 upon the type of the compound engine. The horse- 
 power of the engine will be given by the equation 
 
 
 P e is the mean effective pressure, which, by substituting 
 E for r in (50), is found to be 
 
 
 PI is equal to the gauge pressure of the steam in the 
 boiler plus 14.7. P 3 is the average back pressure, and may 
 be assumed to be between two and a half and five pounds 
 per square inch, for condensing engines. 
 
 The value of the factor C will vary from 0.75 to 0.90 
 for automatic high-speed engines, and from 0.80 to 0.90 
 for engines of the Corliss type. 
 
 63. CONDENSERS. Condensers are usually associated 
 in the minds of most people with compound engines, 
 
COMPOUND ENGINES AND CONDENSERS. 147 
 
 although there is no reason why a condenser should not 
 be used with a single cylinder engine, provided there is a 
 good supply of water. 
 
 There are two kinds of condensers in use at present, viz., 
 the jet condenser and the surface condenser. 
 
 The jet condenser is more generally used on land, 
 because it is simpler ; not so apt to get out of repair ; and, 
 where the water is good, gives as good results as the 
 surface condenser, if not better. When the jet con- 
 denser is used, the exhaust steam from the engine enters 
 the " condensing chamber," where it comes in contact 
 with the condensing water, in the form of spray, and is 
 condensed. The condensed steam, together with the 
 condensing water, is pumped out of the " condensing 
 chamber " into the " hot well," by means of a pump called 
 the " air pump." Part of the water in the hot well is 
 pumped back into the boiler by the " feed pump," and 
 the remainder is allowed to run to waste. 
 
 The condensing water is sprayed, when it enters the 
 condensing chamber, by means of a rose fixed on the end 
 of the injection pipe, or by means of a perforated plate, 
 called the "spattering plate," fixed inside of the con- 
 densing chamber. 
 
 The principal parts of a jet condenser are, the con- 
 densing chamber, the air pump, and the hot well. 
 
 The air pump of jet condensers is sometimes worked by 
 the engine, being connected to it by a belt, but is often 
 provided with an independent steam cylinder of its own. 
 Condensers whose air pump is worked independent of the 
 engine are known as " independent condensers." Con- 
 densers of this class will pump their own condensing 
 water ; but they ought not be expected to draw water 
 more than 12 or 15 feet, as there are a great number of 
 joints about a condenser that are often difficult to keep 
 tight, and the water flows into the condensing chamber 
 against whatever pressure there may be there. The 
 
148 
 
 STEAM ENGINES AXD BOILERS. 
 
 smaller the height through which the air pump lifts the 
 condensing water, the better will the condenser work. 
 
 In Fig. 65 is shown a section of an " independent con- 
 denser." A is the steam inlet ; B is the water inlet ; Fis 
 the condensing chamber ; G is the air pump, worked by 
 the steam cylinder K ; and J is the outlet to the hot well. 
 
 Fig. 65. 
 Worthington Independent Condenser. 
 
 When the surface condenser is used, the condensing 
 water passes through a number of small copper or com- 
 position tubes, on the outside of which the steam to be 
 condensed circulates. The steam coming in contact with 
 the cold surface of the tubes is condensed and falls to 
 the bottom of the condenser, from where it is pumped, by 
 the " air-pump," into the hot well. The condensing 
 
COMPOUND ENGINES AND CONDENSERS. 
 
 149 
 
 water is either drawn or forced through the condenser 
 tubes by the " circulating pump." 
 
 The surface of the tubes in contact with the steam 
 forms the condensing surface of the condenser. The 
 
 tubes are always of very small diameter, and the metal of 
 which they are made is as thin as is consistent with safety. 
 Sometimes, instead of the steam circulating on the outside 
 of the tubes, it passes through them, and the condensing 
 water circulates on the outside. 
 
 The principal parts of the surface condenser are : the 
 
150 STEAM ENGINES AND BOILERS. 
 
 condensing surface, being the surface of a great number 
 of very small tubes ; the air pump ; the circulating pump ; 
 and the hot well. 
 
 The great point in favor of the surface condenser is the 
 fact that the steam, after being condensed, is returned to 
 the boiler and used again without coming in contact with 
 the condensing water. The same water for making steam 
 is used over and over in the boiler, without any new feed 
 water except what is necessary to supply the loss due to 
 leakage of the boiler and the various connections from 
 the boiler to the engine and condenser. As but little 
 fresh feed water is needed, the boiler may be kept very 
 free from scale and sediment. This, of course, is a great 
 point in its favor for use at sea, or where the water is bad 
 and likely to form scale in the boiler. 
 
 The main objection to the surface condenser was that 
 when the tubes got hot they expanded, and then were 
 likely to become loose and leak. They were, also, 
 likely to "creep; " that is, work out of the bearing at one 
 end. Both of these objections have been overcome in 
 the Wheeler condenser, shown in Fig. 66, by fastening 
 the tubes at one end only. 
 
 An explanation of this condenser is unnecessary as 
 everything is clearly shown in the figure. 
 
 64. EFFECT OF THE CONDENSER ON THE POWER OF THE 
 ENGINE. Condensing the exhaust steam from an engine 
 diminishes the back pressure by creating a partial vacuum 
 behind the piston. This vacuum is generally spoken of 
 as being so many "inches of mercury;" each inch of 
 mercury representing a diminution of about half a pound 
 in the back pressure, and therefore, a corresponding in- 
 crease in the mean effective pressure on the piston. 
 
 It is seldom that the vacuum maintained by a condenser 
 will exceed 26 inches of mercury, while the usual vacuum 
 will be about 24 inches. It is usual to assume that the 
 difference between the back pressure without the con- 
 
COMPOUND ENGINES AND CONDENSERS. 151 
 
 denser and the back pressure with the condenser, is equal 
 to the pressure corresponding to the vacuum maintained 
 by the condenser. 
 
 The equation for the horse-power of an engine is, from 
 
 (54), 
 
 P e LAN 
 
 33000 
 
 Now, if we suppose that the speed of the engine is to 
 be the same after the condenser is attached, as it was 
 before, L, A, and N will be constants and the horse- 
 power will vary directly as P& varies. From equation (50) 
 we have 
 
 (65) P. = P, + *P^-0 _ P, 
 
 If /a is the average back pressure without the con- 
 denser; P'z, the average back pressure with the con- 
 denser ; /e, the mean effective pressure without the 
 condenser; P' e , the mean effective pressure with the 
 condenser ; H. P., the horse-power of the engine without 
 the condenser ; and H' . P'., the horse-power with the con- 
 denser; we have 
 
 p f l + h vp- l y- r \ - 
 (66) * f- r. 
 
 H. P. V J e p / 1 + ]>np. log. r\ _ p 
 
 1 ~~ ~ " 
 
 Equation (66) shows how many times greater the horse- 
 power of the engine is with a condenser than it is with- 
 out a condenser. 
 
 Suppose that it is desired that the power of the engine 
 should not be increased, but that it should remain the 
 same, and that the cut-off should change so that the 
 engine will use less steam with the condenser than without 
 it. Let rbe the number of times the steam is expanded 
 without the condenser, and r', the number of times it is 
 expanded with the condenser. 
 
 In this case we have H. P. = H'. P'., and, therefore, 
 P e = P' or 
 
152 STEAM ENGINES AND BOILERS. 
 
 (67) pi (l+?W. l9-r) _ 
 
 r 
 
 r, (1 + hyp. loq. r') 
 
 * i -, '- ./ 3. 
 
 From this we get 
 
 (68) 1 + l*yp* log- r' __ 1 + ft?//?, toff, r (P 3 p^) 
 
 This equation can be solved by trial, using Table 2. If 
 there were no clearance to the engine and Fwere the 
 volume in cubic feet of the cylinder of the engine, the 
 volume of the steam used per stroke without the 
 
 Y 
 
 condenser would be ; and the volume used with the 
 r 
 
 condenser would be , The fraction of saving would be 
 
 Z Z 
 
 (69) y = L *=i r -. 
 
 r 
 
 From y, given by (69), must be subtracted the fraction 
 obtained by dividing the quantity of steam required to run 
 
 Y 
 
 the condenser by -. 
 r 
 
 If, instead of increasing the work done by the engine 
 or changing the cut-off, it should be desired that 
 the engine should do the same work with the condenser, 
 and cut-off at the same point, that it did without the 
 condenser, but use a lower absolute pressure of steam in 
 the boiler, we would have, since P e = P' e and the value 
 of r is not changed, 
 
 fnc\\ -D (1 H~ hyp. log. r) 
 
 (70) ^i- -P% = 
 
 jy, (1 -{-hyp.log. r) 
 
COMPOUND ENGINES AND CONDENSERS. 153 
 
 P'l is the absolute boiler pressure that is carried when 
 the condenser is used. 
 From (70) we have 
 
 , (A P's) r 
 
 65. AMOUNT OF CONDENSING WATER REQUIRED. The 
 number of pounds of water required to condense one 
 pound of steam depends upon the temperature of the 
 steam when it leaves the engine, and upon the initial and 
 final temperatures of the condensing water. The tem- 
 perature of the steam when it leaves the engine depends 
 upon the absolute pressure, P 2 , of the steam at the end of 
 the forward stroke, j ust before the exhaust valve is opened. 
 The expression for this final absolute pressure may 
 
 n 
 
 for all ordinary purposes be taken as P 2 = PI is the 
 
 initial absolute pressure of the steam, and r is the num- 
 ber of times the steam is expanded. 
 
 The gauge pressure of the steam, or pressure above 
 the atmosphere, when it enters the condenser is PI 
 
 14.7- 
 
 Let / be the latent heat of one pound of steam at a 
 gauge pressure of Pz 14.7, and t\ the corresponding 
 temperature. The values of / and t\ may be obtained 
 from Table I. Also, let fa be the initial temperature of 
 the condensing water, and fa the final temperature. 
 
 The heat given out by one pound of the steam when it 
 condenses will, evidently, be / + t\ fa\ and the heat 
 taken up by every pound of the condensing water will be 
 /a fa\ therefore, the number of pounds, W, of water 
 required to condense one pound of steam from the engine 
 will be, 
 
 I 4- ti * 8 
 
 (72) W = 
 
 ta 
 
154 STEAM ENGINES AND BOILERS. 
 
 4 should be taken as 110, for the ordinary work of 
 condensers. 
 
 The value of fa depends upon the source of supply of 
 the water and the climate of the location of the engine ; 
 it will be greater in summer than in winter. It will 
 usually be safe to take the value of fa as 80. 
 
CHAPTER VIII. 
 
 HEAT AND COMBUSTION OF FUEL. 
 
 66. STEAM MAKING. The steam used in an actual 
 engine is made in an apparatus that is often spoken of as 
 the boiler or the boiler plant. It consists of three main 
 parts, each, in a manner, dependent upon the other two, 
 and yet in many ways distinct from them. These parts 
 are, the furnace, the boiler proper, and the chimney. 
 
 In Fig. 67 is shown a section of a furnace and boiler 
 such as is in common use everywhere in this country. 
 The various parts are lettered so that their relations to 
 one another may be seen at once. 
 
 The part termed the furnace is the part in which the 
 heat, afterwards converted by the engine into work, is 
 generated by the combustion of fuel. 
 
 The boiler is simply a closed vessel which contains the 
 water of which the steam used in the engine is formed. 
 The boiler may be of any shape or size. 
 
 The chimney is the part which carries off the products 
 of combustion. 
 
 The fuel is put in the furnace on the grate, and is there 
 burned. During the combustion of the fuel heat is gen- 
 erated; a part of this heat is given directly to the boiler, 
 by radiation from the hot fuel, and a part is carried off by 
 the gases generated by the combustion. These gases 
 pass out of the furnace into the chimney, and from there 
 they pass into the air. On the way from the furnace to 
 the chimney, the hot gases are made to come in contact 
 with the boiler ; and as the boiler is cooler than the gases, 
 a part of the heat they contain is given up to it. The 
 heat thus obtained by the boiler is transmitted to the 
 
 (155) 
 
156 
 
 STEAM ENGINES AND BOILERS. 
 
 water, which is gradually heated and, finally, converted 
 into steam. 
 
 The dimensions and proportions of the furnace depend 
 
 upon the heat required by the boiler per unit of time, the 
 kind of fuel, and the type or kind of furnace. 
 
 The dimensions and proportions of the boiler depend 
 upon the amount of steam required by the engine per unit 
 
HEAT AND COMBUSTION OF FUEL. 157 
 
 of time, the conditions under which the steam is gen- 
 erated, and the type of the boiler. 
 
 The dimensions and proportions of the chimney depend 
 upon the kind of fuel, the amount used by the furnace 
 per unit of time, and the temperature at which the hot 
 gases pass off. 
 
 67. STEAM REQUIRED PER HOUR. In all problems 
 relating to boilers it is necessary to know, as a basis upon 
 which to design the furnace, the boiler and the chimney, 
 the number of pounds of steam required per hour and the 
 conditions under which it must be made. 
 
 If we are designing a boiler to supply steam for an en- 
 gine of given dimensions and power, using steam at a 
 given initial gauge pressure, we may calculate the number 
 of pounds of steam that will be used per hour by the 
 engine and to this add a per cent to cover leakage and 
 condensation, and thus obtain the number of pounds of 
 steam the boiler will probably be called upon to supply 
 per hour. 
 
 From (57) of Art. 24, we have that the weight of steam 
 used per stroke by an engine is 
 
 LA 
 
 144 r s 
 
 If N is the number of strokes made by the engine per 
 minute, the weight, W\ t of steam used by the engine per 
 minute will be 
 
 (73) Wi = N S = 
 
 To make allowances for waste from various sources, for 
 the amount of steam used by the pumps, and for that 
 condensed in the engine, the amount of steam the boiler 
 ought to be designed to supply per minute may be 
 
 taken as W. As the steam required to be supplied 
 
158 STEAM ENGINES AND BOILERS. 
 
 per hour is 60 times that required per minute, the expres- 
 sion for, W, the number of pounds of steam required to 
 be supplied by the boiler per hour is 
 
 ,70 W - 6 X8 IF.-- 
 
 ^ } l ~ 
 
 144 r a ~ 8rs 
 
 68. HEAT REQUIRED PER HOUR. Having assumed or 
 determined the number of pounds of steam required per 
 hour, it is next necessary to determine, if it is not already 
 known, the pressure by the gauge, and the initial temper- 
 ature of the " feed-water," or water entering the boiler. 
 
 Let P be the pressure per square inch, by the gauge, 
 of the steam in the boiler ; //", the total heat of evapora- 
 tion above 32, in heat units, of one pound of steam at the 
 gauge pressure P; t, the initial temperature of the feed- 
 water. 
 
 H must be taken from Table I ; while /depends upon 
 the source of supply of the feed water, and upon con- 
 siderations that will be discussed later. 
 
 It is evident that, since H is the heat required to raise 
 the temperature of one pound of water from 32 to the 
 temperature of the boiling point corresponding to the 
 gauge pressure P and then to turn the water into steam, 
 the heat required to raise one pound of water from a 
 temperature / to the boiling point corresponding to P 
 and then turn it into steam, will be H (t 32). 
 The heat required, then, to evaporate H' 7 pounds of water 
 'per hour, under the given conditions, will be 
 
 (75) Hi = W [_H (t 32)]. 
 
 From equation (75), it is evident that, for a given value 
 of IV, H\ will be smaller as we make H smaller and as 
 we make /larger, and hence the latter should always be 
 as large as possible. 
 
HEAT AND COMBUSTION OF FUEL. 159 
 
 The value of H depends upon the pressure by the 
 gauge at which the steam is formed and upon nothing 
 else; and as is seen by an inspection of Table I, the 
 higher is the pressure of the steam in the boiler, the 
 greater is the value of H. It is also seen, however, that 
 the value of H increases very slowly as the pressure in- 
 creases. Thus, the value of H corresponding to a pres- 
 sure of 75 Ibs., by the gauge, is 1179.4, and the value of H 
 corresponding to a pressure of 150 Ibs., by the gauge, 
 is 1193.5 ; so that, while the pressure has been increased 
 by 75 Ibs., H has been increased by but 14.1 heat units. 
 
 The value of / depends upon the source of supply of 
 the feed-water and upon whether or not the feed-water is 
 heated before it is forced into the boiler. It is customary 
 to force the feed-water through a " feed-water heater " 
 before it enters the boiler. As feed-water heaters will be 
 discussed farther along, it will suffice to say that they usu- 
 ally consist of a number of tubes, surrounded by exhaust 
 steam from the engine, through which the feed-water is 
 forced before it enters the boiler. The water, while pass- 
 ing through the tubes of the heater, has its temperature 
 raised by the heat imparted to it by the exhaust steam. 
 The heat in the exhaust steam would be lost if it were not 
 taken by the feed- water; so that the feed- water heater, by 
 raising the temperature of the feed-water, is a heat saving 
 appliance, and a valuable adjunct to any engine and 
 boiler plant, where there is exhaust steam escaping into 
 the atmosphere. 
 
 The greater / is made, the less will be the value of //i 
 for given values of W and H. 
 
 Instead of speaking of the number of heat units a 
 boiler will require per hour it is customary to speak of 
 "the equivalent water from and at 212" that it will 
 evaporate per hour. 
 
 The equivalent water from and at 212 is the number 
 of pounds of water that could be evaporated by the expend- 
 
160 STEAM ENGINES AND BOILERS. 
 
 iture of the same number of heat units actually used by 
 the boiler, if the water entered the boiler at 212 and was 
 converted into steam at a temperature of 212. 
 
 Since the heat required to convert one pound of water 
 at a temperature of 212, into steam at 212 is equal to 
 the latent heat of water at atmospheric pressure, about 
 966 heat units, it is seen that the expression for "the 
 equivalent water from and at 212," W ot is' 
 
 The factor H ~~ (t ~ 32) is called the " factor of 
 966 
 
 evaporation," and may be defined as, the factor by which 
 the water actually evaporated by a boiler must be multi- 
 plied in order to reduce it to " equivalent water from and at 
 
 212. " 
 
 In Table 3 will be found factors of evaporation for 
 different gauge pressures of steam and different tempera- 
 tures of feed water. 
 
 Equation (76) gives us a means of determining the 
 heat required per hour for a boiler, when we know the 
 equivalent water from and at 2 1 2 required to be evaporated 
 per hour. As will be seen later, boilers are often assumed 
 as being able to evaporate 34} Ibs. of water from and at 
 2 1 2 per hour per horse-power. Upon this assumption, 
 W Q = 34^ B, where B is the horse-power of the boiler, 
 and the expression for H\ becomes, 
 
 (77) J3i = 966 W = 33327 B. 
 
 69. FUEL REQUIRED PER HOUR. The number of 
 pounds of fuel required to supply the heat necessary for 
 the boiler per hour, depends upon the heat developed by 
 the combustion of one pound of the fuel and upon the 
 amount of heat that is lost, in various ways, by the furnace, 
 
HEAT AND COMBUSTION OF FUEL. 161 
 
 the boiler and the chimney. If we take the amount of heat 
 developed by the combustion of one pound of the fuel 
 and from this quantity subtract the amount that is lost, 
 we shall obtain the quantity of heat used by the boiler 
 per pound of fuel ; and the total quantity of heat required 
 per hour divided by the quantity used per pound of fuel 
 will give us the number of pounds of fuel that must be 
 burned per hour in the furnace. 
 
 It is evident, therefore, that it is extremely important 
 that we should know the amount of heat developed by 
 the complete combustion of one pound of the fuel in the 
 furnace. 
 
 Combustion may be defined as a rapid oxidation, accom- 
 panied by the evolution of light and heat. 
 
 In all fuels there are certain elements that will not 
 burn, but which remain after combustion and form ash; 
 and there are other elements that are in the fuel in such 
 small quantities that their presence may be neglected. 
 The principal elements in all fuels, whether gaseous, 
 liquid, or solid, are carbon, hydrogen and oxygen. 
 
 The carbon may be present either in a free, uncom- 
 bined state or in combination with a part of the hydrogen. 
 
 The hydrogen is always present either in combination 
 with the oxygen or with a part of the carbon. We always 
 assume that a part of the hydrogen is in combination with 
 all of the oxygen, and that the rest is in some sort of 
 combination with part of the carbon. 
 
 It is generally assumed that the oxygen in a fuel is in 
 combination with a part of the hydrogen, and is present 
 as water. The oxygen, of course, does not burn, but 
 simply reduces the amount of hydrogen that is available 
 for combustion. 
 
 Upon combustion, the carbon in a fuel may form one 
 of two compounds : 
 
 I. If the combustion is complete, every atom of the 
 carbon will take up, and enter into combination with, two 
 
 11 
 
162 STEAM ENGINES AND BOILERS. 
 
 atoms of oxygen and form carbon dioxide, or carbonic 
 acid gas as it is sometimes called, whose chemical symbol 
 is CO*. 
 
 2. If there is a lack of oxygen and the combustion is 
 not complete, every atom of the carbon will combine 
 with one atom of oxygen and form carbon monoxide, 
 whose chemical symbol is CO. 
 
 It has been determined by experiments that when one 
 pound of carbon is completely burned, so as to form 
 carbon dioxide, there is evolved, by the combustion, 
 14,500 heatunits ;* also, thatwhen one pound of carbon 
 is burned to form carbon monoxide, there is evolved 
 4,400 heat units. Thus there is a difference of 10,100 
 heat units between the amounts of heat evolved by the 
 complete and the partial combustion of one pound of 
 carbon. It is customary, in all discussions as to the heat 
 of combustion of fuels, to assume that all the carbon in 
 the fuel is completely burned to carbon dioxide. 
 
 Hydrogen, when burned, enters into combination with 
 oxygen, in the proportion of two atom of hydrogen to one 
 of oxygen, and forms water, whose chemical symbol 
 is H*O. 
 
 It has been determined by experiments that one pound 
 of hydrogen, on being burned, will evolve 62,032 heat 
 units, or about4.28 times as many heat units as are evolved 
 by the complete combustion of one pound of carbon. 
 When one pound of hydrogen burns it unites with eight 
 pounds of oxygen ; so that, with the oxygen present in 
 any fuel there is always united one-eighth of its weight of 
 hydrogen. If, then, we subtract from the total weight of 
 hydrogen present in a fuel, one-eighth of the weight of 
 the oxygen, the remainder will be the weight of free 
 hydrogen in the fuel, or the weight of hydrogen that will 
 be burned. 
 
 To obtain the theoretical amount of heat that will be 
 
 * The heat evolved by the complete combustion of one pound of carbon 
 varies slightly with the source from which the carbon is obtained, and recent 
 experiments have shown that it is probably nearer 14,600 than 14,500. 
 
HEAT AND COMBUSTION OF FUEL. 163 
 
 evolved by the combustion of one pound of fuel, it is nec- 
 essary for us to first learn, from a chemical anaylsis, the 
 weights of carbon, hydrogen, and oxygen in one pound 
 of the fuel. The weight of carbon multiplied by 14,500, 
 will give the number of heat units that will be evolved by 
 the complete combustion of the carbon ; and the weight 
 of free hydrogen, equal to the total hydrogen less one- 
 eighth of the weight of the oxygen, multiplied by 14,500 
 times 4.28, will give the heat that will be evolved by the 
 combustion of the hydrogen in the fuel. The sum of the 
 heats evolved by the carbon and by the free hydrogen 
 will be the total heat evolved by the combustion of one 
 pound of the fuel. Putting what has been said in mathe- 
 matical language, we see that the expression for the the- 
 oretical amount of heat, h, evolved by the complete com- 
 bustion of one pound of fuel is 
 
 (78) h = 14500 [~C+ 4.28 ( H' - 
 
 C is the weight, in pounds, of carbon in one pound of 
 the fuel. H' is the weight, in pounds, of hydrogen in one 
 pound of the fuel. O is the weight, in pounds, of oxygen 
 in one pound of the fuel. 
 
 Owing to the fact that, in most fuels, there is always a 
 small quantity of substances, other than carbon and 
 hydrogen, that burn and give off more or less heat, and 
 that a part of the total heat evolved is used in decompos- 
 ing the elements before they can burn, the theoretical 
 amount of heat obtained by the use of equation (78) is 
 not exactly equal to the heat actually evolved by the 
 combustion of one pound of the fuel. Equation (78), 
 however, may be used when no other means is at hand 
 for determining the amount of heat evolved by one pound 
 of a fuel. 
 
 The principal fuels used in boiler furnaces are wood 
 and coal. 
 
 Wood is seldom used, on account of the expense, 
 
164 STEAM ENGINES AND BOILERS. 
 
 except in special establishments where the refuse con- 
 sists largely of shavings, saw-dusts, and pieces of wood 
 that must be got rid of. In such cases, of course, it is 
 much better and cheaper to use this refuse as fuel than it 
 is to buy coal. Wood burns rapidly and with a bright 
 flame, but does not evolve much heat. It is customary 
 to consider one pound of wood equivalent to 0.4 pounds 
 of coal. 
 
 Coal is more extensively used as a fuel, in boiler fur- 
 naces, than any other substance. Although the mining 
 engineer classifies coal into several groups or classes, it 
 will suffice for us to consider all coal used in boiler fur- 
 naces as either anthracite or bituminous coal. 
 
 Anthracite coal is a hard, dense coal containing a large 
 per cent of carbon and a small per cent of volatile 
 matter; it is slow to ignite and burns at a high tempera- 
 ture with little or no visible flame. 
 
 Bituminous coal is somewhat soft and easily broken ; it 
 usually contains from 20 to 50 per cent of volatile 
 matter ; it ignites easily and burns freely with quite a 
 flame. 
 
 Coke is the residue obtained after distilling off the 
 gases from certain kinds of bituminous coals; it is not 
 very dense, but contains a high per cent of carbon. 
 
 In Table 4 is given the heat developed by the complete 
 combustion of one pound of various fuels. 
 
 The loss of heat by a furnace, boiler, and chimney 
 may be ascribed to four causes : 
 
 1. Incomplete combustion. 
 
 2. Radiation. 
 
 3. Hot gases escaping out of the chimney. 
 
 4. Dropping of fuel through the grate into the ash-pit. 
 The loss due to incomplete combustion is the most 
 
 serious of all losses. It may be that, when the coal is 
 put into the fire, there is not a sufficient amount of air to 
 burn the volatile gases that pass off, so that the greater 
 
HEAT AND COMBUSTION OF FUEL. 165 
 
 part of them will not be burned. Or, it may be, that 
 owing to a lack of air, the carbon is not completely 
 burned to carbon dioxide, but is burned only to carbon 
 monoxide. If the carbon is not completely burned, 
 there is a loss of 10,100 heat units for every pound of 
 carbon converted into carbon monoxide. 
 
 The loss by radiation may be reduced by a careful and 
 correct setting of the furnace and boiler, and by taking 
 precautions to have just as little hot surface exposed as 
 possjble. 
 
 The loss due to the hot gases escaping up the chimney 
 may be estimated if we know the temperature, t\, of the 
 air entering the furnace and the temperature, &, of the 
 gases entering the chimney. The specific heat of one 
 pound of chimney gases may, without serious error, be 
 taken as equal to that of ordinary atmospheric air, or 
 0.24 ; so that every pound of gas escaping out of the 
 chimney carries off 0.24 (fa t\) heat units. 
 
 The heat carried off by the gases in the chimney can- 
 not be said to be wasted, unless there is some fault in the 
 design of the boiler plant, as this heat is used to produce 
 the draft. It will be seen later that the amount of air 
 entering the furnace depends upon the draft of the chim- 
 ney, which, in turn, depends upon the height of the chim- 
 ney and upon the temperature of the air outside, and that 
 of the gases inside of the chimney. The temperature of 
 the gases in the chimney should be sufficient to produce 
 the required draft, and no more. 
 
 The loss due to dropping of fuel through the grate 
 ought not to be large, if the grate is properly proportioned 
 and care is exercised in firing the furnace. Some loss, 
 of course, is always bound to occur, but when this loss is 
 large there should be a change either of the grate or fire- 
 man, or perhaps of both. 
 
 The sum total of all the heat lost in the various ways, 
 per pound of the coal consumed, will amount to from 20 
 
166 STEAM EXGIXES AND BOILERS. 
 
 to 50 per cent of the total heat of combustion. For the 
 best boiler plants, where care is exercised in firing, the 
 amount of heat used per pound of coal may be taken as 
 from 70 to 80 per cent of the heat of combustion ; for 
 good boiler plants the amount may be taken as from 60 
 to 70 per cent of the heat of combustion ; and for poorly 
 designed plants, poorly fired, the amount will be from 40 
 to 60 per cent of the total heat of combustion. 
 
 Therefore, if K represents the fraction of the total heat 
 of combustion that is utilized, the heat utilized per pound 
 of coal will be, from equation (78), 
 
 (79) h = Kh = 1T1 4500 C + 4.2 
 
 If, now, we divide the total heat, H\, required per hour, as 
 given in (75) or (77), by the heat utilized, ^ , per pound 
 of coal we obtain the amount of coal, F t that it will 
 be necessary to burn per hour in the furnace. 
 
 Therefore, the expression for 
 
 (80) 
 
 70. AIR REQUIRED FOR COMBUSTION. The air admit- 
 ted to a furnace for the" combustion of a fuel is a me- 
 chanical mixture, consisting principally of oxygen and 
 nitrogen ; these gases are present in the proportion, by 
 weight, of 23 per cent of oxygen and 77 per cent of 
 nirtogen ; by volume, the proportion in which they are 
 present is 20 per cent of oxygen and 80 per cent of nitro- 
 gen. The oxygen, only, is used in combustion ; the 
 nitrogen is inert, and so far as aiding combustion is 
 concerned, is useless. 
 
 From chemistry we learn that when two substances 
 unite chemically they always do so in a certain fixed 
 proportion, by weight. It is known that one pound of 
 
HEAT AND COMBUSTION OF FUEL. 167 
 
 hydrogen always requires eight pounds of oxygen for its 
 complete combustion into water, H^ 0; also, that one 
 pound of carbon requires \ of a pound of oxygen for its 
 combustion to carbon monoxide, CO, and f of a pound 
 of oxygen for its combustion to carbon dioxide, CO-2. 
 
 Therefore, if we assume complete combustion of the 
 carbon and of the free hydrogen, the number of pound? 
 of oxygen required per pound of fuel will be, 
 
 (81) 
 
 C is the total carbon, H* the total hydrogen, and O the 
 total oxygen in one pound of the fuel. 
 
 Now, since, as has been said, there is only 23 per cent, 
 by weight, of oxygen in the air, the weight of air, A y 
 
 required to supply 0\ pounds of oxygen will be, A = - 
 
 Putting for Oi its value, and neglecting fractions, we get 
 the following expression for the pounds of air required 
 for the complete combustion of one pound of fuel. 
 
 (82) A = 12 C -f 36 ( H f V 
 
 Ordinarily, we may assume that 12 pounds of air will 
 be needed for the complete combustion of one pound of 
 coal; and as one pound of air at 32 occupies a volume 
 of I2j cubic feet, the volume of air, at 32, required for 
 the complete combustion of one pound of coal may be 
 taken as 150 cubic feet. 
 
 It has been found that in the boiler furnace there is 
 always needed more air than is actually necessary for the 
 combustion of the fuel, in order to dilute the gases of 
 combustion and to make sure that every particle of hydro- 
 
168 STEAM ENGINES AND BOILERS. 
 
 gen and carbon will come in contact with the amount of 
 oxygen necessary to burn it. The amount of air for dilu- 
 tion, as the surplus air is called, depends upon how inti- 
 mately the air for combustion and the combustible gases 
 are mingled and mixed. It has been found that it is 
 advantageous to have the air enter in a number of streams 
 rather than in a large body, and that the higher the veloc- 
 ity of the entering air the less the quantity required for 
 dilution. Experience has shown that in the case of nat- 
 ural or chimney draft, the amount of air required for dilu- 
 tion will be about equal to the amount required for com- 
 plete combustion; while in the case of forced draft, the 
 amount of air required for dilution will be about equal to 
 one-half that required for combustion. 
 
 Therefore, we may say that for chimney draft it is nec- 
 essary to supply 24 pounds of air to the furnace for each 
 pound of coal burned; and for forced draft, 18 pounds 
 of air are required per pound of coal. Of course, the 
 greater the quantity of air we supply to the furnace, over 
 and above that actually required for combustion, the 
 greater will be the loss of heat due to the temperature of 
 the escaping gases. Again, the greater the quantity of 
 air supplied per pound of coal burned the larger must be 
 the chimney to carry off the gases from the furnace. 
 
 It is evident, therefore, that the amount of air supplied 
 to the furnace should be no more than the quantity act- 
 ually necessary for proper combustion. 
 
 71. RATE OF COMBUSTION. By the rate of combustion 
 is meant the number of pounds of fuel that is burned per 
 square foot of grate surface per hour. 
 
 There are two limits to the rate of combustion, a max- 
 imum and a minimum. 
 
 The maximum rate depends upon the kind of fuel and 
 the force of the draft ; and where the draft is great enough 
 to supply the amount of air required for combustion, the 
 
HEAT AND COMBUSTION OF FUEL. 169 
 
 maximum limit will be reached only when the draft be- 
 comes so great as to blow the fuel off of the grate bars. 
 It is evident that this limit will depend somewhat upon 
 the density of the fuel. It is probable that the greatest 
 rate of combustion has been attained in locomotives, 
 where a rate of about 120 pounds of anthracite coal has 
 been reached. Of course, this is not a rate that is con- 
 tinued for any great length of time. 
 
 The minimum rate of combustion depends upon the 
 kind and nature of the fuel and the construction of the 
 grate of the furnace ; it is the rate at which it is possible 
 to keep a bright clear fire just on the point of burning 
 through in places, and so admitting a body of cool air to 
 chill the furnace. For anthracite coal, the minimum rate 
 of combustion in boiler furnaces is about 4 pounds ; and 
 for bituminous coal, it is about 10 pounds. 
 
 The rate of combustion, with chimney draft, for an- 
 thracite coal, will vary from 7 to 20 pounds, the average 
 being about 12 pounds; for bituminous coal, the rate will 
 vary from 12 to 40 pounds, the average being about 20 
 pounds. 
 
 The whole tendency of modern practice is towards 
 forced draft and high rates of combustion. 
 
 72. THE FURNACE. In Fig. 67 the furnace under the 
 boiler is shown in section. It will be seen that the " grate 
 bars " rest on the " bridge wall " at the back end, and on 
 the " dead plate " at the front end. Where the grate is 
 long, it is customary to make it up of two lengths of 
 " grate bars " supported at the middle by a " bearing 
 bar." 
 
 The grate bars are made of cast iron and of different 
 shapes for different kinds of fuels. There are quite a 
 number of patented grate bars on the market, for each of 
 ivhich the inventor claims certain advantages. 
 
 In Fig. 68 is shown a view of a common form of grate 
 
170 
 
 STEAM ENGINES AND BOILERS. 
 
 bar. The bars are made single or double, in order that, 
 by using a number of single and double bars, grates of 
 any desired width may be built up. There are lugs, 
 marked A in Fig. 68, which prevent the bars from being 
 
 Fig. 68. 
 
 packed too close together, and which cause the formation 
 of air spaces, through which the air for combustion enters 
 from the " ash-pit." The area of the openings for the 
 admission of air between the grate bars, ought to be made 
 to depend, somewhat, upon the kind of coal burned, but 
 is usually about one-half the total area of the grate. 
 
 Where very fine coal is used the area of the openings 
 should be less than where coarser coal is burned, in order 
 that there may not be a great waste by the dropping of 
 coal, through the openings, into the ash-pit. 
 
 In Fig. 69 is shown a somewhat different style of grate 
 bar that is quite extensively used. 
 
 The grate bars are seldom made longer than four feet ; 
 and grates are seldom made longer, measured from the 
 
 Fig. 69. 
 
 furnace door to the bridge wall, than seven feet. If a 
 grate is longer than seven feet it becomes almost impos- 
 sible to fire and stoke it properly, and the end next to the 
 bridge is very apt to be useless, if not detrimental. The 
 grate is usually built with a slope, from the front of the 
 
HEAT AND COMBUSTION OF FUEL. 171 
 
 furnace towards the bridge wall, of from one-half to one 
 inch fall for every foot in length. 
 
 The dead-plate at the front of the grate is sometimes 
 made quite large, although it is usually rather small. 
 
 The doors of the furnace should be made double, and 
 should have perforations in them. The perforations are 
 for the admission of air, which aids in the combustion of 
 the gases passing off from the fuel on the grate and, 
 also, cools the door and prevents it from burning out. 
 The inner part, or lining, of the door is to prevent the 
 outer part, or door proper, from being too highly heated 
 by the heat radiated from the burning fuel on the grate. 
 
 The furnace shown in Fig. 67 is what is termed an 
 external furnace, since it is exterior to the boiler. Some- 
 times, however, the furnace is contained in the boiler 
 itself, as shown in Fig. 73, when it is termed an internal 
 furnace. 
 
 73. FIRING THE FURNACE. The term "firing" is 
 applied to the work of putting the fuel in the furnace, and 
 keeping the fire in a clean, bright condition. To the 
 uninitiated it would seem as if the whole thing to be done, 
 in feeding a furnace, would be to open the furnace door 
 and throw the fuel in on the grate ; it has been found, 
 however, that in order to preserve a good, hot, fire, it is 
 best to adopt some system of firing. 
 
 There are three systems in common use, each of which 
 has its advocates. These systems are, the spreading, the 
 alternate, and the coking. 
 
 In the spreading system, the fresh charge of coal is 
 spread in a layer over the whole area of the grate. This 
 is perhaps the most common system, and if the fire is fed 
 frequently, with small quantities of fresh fuel at each 
 charge, it will give good results. If, however, the fire is fed 
 at rather long intervals, with a large quantity of fuel at each 
 charge, the fire will be chilled every time fresh fuel is put 
 
172 STEAM ENGINES AND BOILERS. 
 
 on it. This chilling of the fire will result in the incom- 
 plete combustion of the gases in the furnace and a loss of 
 heat. 
 
 The alternate system can only be used to advantage 
 with a wide grate. In this system, the fresh fuel is put 
 alternately on each side of the grate in sufficient quanti- 
 ties to cover about one-half of the whole surface. The 
 whole area of the grate is never covered, at any one time, 
 with fresh fuel ; so that, the whole fire is never chilled. 
 The gases that pass off from the fresh fuel on one side of 
 the grate, come in contact with the surplus hot air coming 
 through that side of the grate on which there is no fresh 
 fuel, and are burned. This system of firing does not re- 
 quire such care and watchfulness on the part of the fire- 
 man, as does the spreading system, but as has been said, 
 it can be used to advantage only in the case of rather 
 broad furnaces. 
 
 The coking system is the system that has been adopted 
 in all mechanical stoking devices. In it, the fresh charge 
 of fuel is put just inside the door of the furnace, on the 
 dead plate, and allowed to remain there until the greater 
 part of the most volatile gases are driven off; then the 
 coal is pushed farther back into the furnace, where a part 
 of it is burned and all of the gases are driven off, and a 
 fresh charge is put on the dead plate. Each succeeding 
 charge pushes the charges preceding it further towards 
 the end of the furnace, and the charges are put in at such 
 intervals that each will be completely burned during its 
 passage from the dead plate to the bridge wall. The 
 gases, evolved from the charge on the dead plate, are 
 obliged to pass over the hot bed of fire and come in con- 
 tact with the surplus air coming through the back end of 
 the grate ; and, as both the gases and the air are at a high 
 temperature, there is a strong probability that all the 
 gases will be burned. This method of firing works 
 equally well with bituminous coal and anthracite coal, 
 
HEAT AND COMBUSTION OF FUEL, 
 
 173 
 
174 STEAM ENGINES AND BOILERS. 
 
 but is of more value where bituminous coal is used, on 
 account of the large per cent of volatile gases such coal 
 contains. 
 
 It is impossible to say that anyone of the three systems 
 of firing is better than another; anyone will give good 
 results if it is properly carried out, and any one is better 
 than no system at all. To get good results as to evapora- 
 tion and rate of combustion, it is absolutely necessary 
 that care be exercised in the firing; good results cannot 
 be obtained by careless, bad firing, where the coal is 
 thrown into the furnace in any way and in large quanti- 
 ties at a time. 
 
 The fire should be kept bright, and free from dirt and 
 clinkers, and of as nearly a uniform thickness over the 
 whole grate as possible. A bright, clean fire will always 
 give better results than one that is dirty, and full of 
 clinkers and ash. 
 
 The thickness of the bed of coals has quite a marked 
 influence upon the economy of the combustion. The 
 best thickness will depend largely upon the fuel to be 
 burned, but it may safely be said that it should not be 
 allowed to be less than six inches for a good, hot fire. It 
 is seldom- that the thickness of the fire is allowed to be 
 greater than twelve inches. Experiments, with the same 
 coal, have shown that a fire six inches thick gave poorer 
 results, as to evaporation, than a nine-inch fire ; and the 
 nine-inch fire gave poorer results than a twelve-inch fire. 
 Care should be taken to see that the fire never burns 
 through in spots, leaving a portion of tne grate uncovered 
 by hot coals. 
 
 74. MECHANICAL STOKERS. There are several forms 
 of mechanical stokers on the market, and almost all -of 
 them feed the coal, from a hopper, onto the front part of 
 the furnace, where it is partially burned, and from where 
 it is gradually .made to move back along the grate to the 
 
HEAT AND COMBUSTION OF FUEL. 175 
 
 bridge wall. The rate of feeding of the fuel and the rate 
 of combustion must be such that all of the coal will be 
 burned on its way from the furnace door to- the bridge 
 wall. If the rate of feeding is too great, the fuel will not 
 be completely burned when it reaches the end of the 
 grate, and a part of it will be forced into the ash pit, and 
 be lost ; while if the rate of feeding be too small, the part 
 of the grate next to the bridge wall will not be completely 
 covered with live coals, and cold air will leak through 
 and chill the gases on their way to the chimney. 
 
 The grates of almost all mechanical stokers are usually 
 inclined at a considerable angle to the horizon, and the 
 coal is made to move from the dead-plate/to the bridge 
 wall by a movement of the grate bars. This movement 
 is generally derived from a shaft that is rotated by a s\nall 
 engine. 
 
 It is probable that the Roney Mechanical Stoker is. one 
 of the most used and best known mechanical stokers in 
 this country. Fig. 70 shows the Roney Mechanical 
 Stoker as applied to the ordinary return tubular boiler. 
 In Fig. 71 is shown the stoker in detail. 
 
 Referring to Fig. 71, it is seen that the grate is inclined 
 from the front of the furnace towards the bridge wall ;,and 
 that the grate bars are arranged as steps, with their 
 lengths at right angles to the direction of the length of 
 the boiler. The coal is fed into the "coal hopper,". and 
 from there is pushed onto the "dead plate ;" the^coal falls 
 onto the front grate bars and is made to move from one 
 grate bar to another, towards the bridge wall, by an oscil- 
 lating motion of the grate bars. This motion of the grate 
 bars is derived from the " rocker bar," which is moved 
 back and forth by the " connecting rod. ' The " connect- 
 ing rod " derives its motion from the " agitator," that is 
 connected, by means of the "link," to the "disk-crank." 
 The disk-crank is rotated by the shaft to which it is fast- 
 ened. By the motion of the rocker arm the grate bars 
 
176 
 
 STEAM ENGINES AND BOILERS. 
 
HEAT AND COMBUSTION OF FUEL. 177 
 
 are made to assume an inclined position, and then a stepped 
 position. When the bars are in the inclined position, the 
 coal tends to slide down the grate towards the bridge wall. 
 When the agitator is moved out towards the end of its stroke 
 it strikes a nut on the end of the connecting rod and 
 moves the rod until the grate bars assume the inclined 
 position. As the agitator moves inward, it pushes on the 
 pusher and forces coal from the hopper onto the grate and, 
 also, forces the coal on the grate down the grate bars, 
 which remain in their inclined position until the agitator 
 strikes the inside nut on the connecting rod. Thus, it is 
 seen that during about half the time of one revolution of 
 the disk crank, the coal on the grate may move towards 
 the bridge, and during the other half of the time it is at 
 rest on the grate. By means of the " feed wheel/' the 
 pusher may be adjusted so that it will be moved forward 
 during any desired part of the forward motion of the 
 agitator. The amount of coal fed to the furnace depends 
 largely upon the adjustment of the pusher, although in 
 some cases the weight of the coal, in the hopper and on 
 the grate, will cause a movement of the coal along the 
 grate. By adjusting the leek nuts on the connecting rod, 
 the movement of the grate bars may be adjusted. Also, 
 everything may be made to occur quicker or slower by 
 running the disk crank at a high or low speed. 
 
 75. HAWLEY DOWN DRAFT FURNACE. One of the 
 latest, successful, improvements in furnaces for boilers 
 may be said to be the down draft system of the Hawley 
 Down Draft Furnace Co. In this system, two grates are 
 used, one above the other, as shown in Fig. 72. 
 
 The upper grate is made up of a number of tubes, C, 
 connected to the drums A and B. The drums, A and B, 
 are connected to the boiler, so that there is always a 
 circulation of water through the drums and through the 
 tubes. The bottom grate, D y is of the ordinary kind. 
 
 12 
 
178 
 
 STEAM ENGINES AND BOILERS. 
 
 / l\ I V 
 i \ ^ 
 
 Id X \ /- ; 
 
 /\ 
 
 SB 
 
HEAT AND COMBUSTION OF FUEL. 179 
 
 All the fresh fuel is put on the upper grate, through 
 the doors F, and air is admitted, also through F t over the 
 fuel. By the arrangement of the furnace, the air and 
 gases of combustion are made to pass down through the 
 upper grate in order to reach the chimney. All the fine 
 particles of coal, and partially burned coal, drop between 
 the upper grate bars and fall onto the lower grate ; so that, 
 the lower grate is always covered with a thick layer of 
 hot coals. Air is admitted through the ash pit, and it 
 passes up through the hot coals on the lower grate ; a 
 part of this air is used in burning the coals on the lower 
 grate ; the remainder comes in contact with the hot, 
 combustible, gases from the upper grate and burns them. 
 
 This furnace has given good results as a preventer of 
 smoke. 
 
CHAPTER IX. 
 
 BOILERS. 
 
 76. TYPES OF BOILERS. Before considering the dif- 
 ferent types, it will be well to define certain terms used 
 in referring to boilers. 
 
 The grate surface is the area of the grate of the fur- 
 nace of the boiler. 
 
 The heating surface is the area of the surface of con- 
 tact of the hot gases with the boiler, while on their way 
 from the furnace to the boiler chimney. 
 
 The shell is the main vessel in which is contained the 
 water and steam. 
 
 The water space is the volume of that part of the boiler 
 occupied by the water. 
 
 The steam space is the volume of that part of the boiler 
 occupied by the steam. 
 
 All classifications of boilers are based, generally, upon 
 peculiarities in the design of the shell, or in the relative 
 position of the heating surface and grate surface. Boilers 
 are, also, often classified according to the place where 
 they are to be used. Among the different classifications 
 may be mentioned the following: marine boilers, land 
 boilers ; upright boilers, horizontal boilers ; internally fired 
 boilers, externally fired boilers; fire-tube boilers, water- 
 tube boilers. 
 
 A marine boiler is one that is used on vessels ; and a 
 land boiler is one that is used on land. 
 
 An upright boiler is one having the axis of the shell 
 (180) 
 
BOILERS. 
 
 181 
 
 vertical ; and a horizontal boiler is one having the axis of 
 the shell horizontal. 
 
 An internally fired boiler is one that has its furnace 
 inside the shell of the boiler ; and an externally fired 
 boiler is one that has its furnace exterior to the shell. 
 
 A fire-tube boiler is one a part of whose heating sur- 
 face is the internal surfaces of a number of tubes sur- 
 rounded by water ; and a water-tube boiler is one a part 
 of whose heating surface is the external surfaces of a 
 number of tubes filled with water. 
 
 77. OLD TYPES OF BOILERS. Under this head has 
 been included those forms of boilers that were first used, 
 and that are still used to a large extent in England, but 
 
 Fig. 73. 
 
 that are seldom met with in this country. The principal 
 among these may be said to be the Cornish boiler and 
 the Lancashire boiler. 
 
 The Cornish boiler is an internally fired boiler, with a 
 cylindrical shell. The furnace is contained in a large 
 cylindrical flue running the whole length of the boiler 
 from front to rear. In Fig. 73 is shown a longitudinal 
 section of a Cornish boiler, and in Fig. 74 is shown a 
 
182 
 
 STEAM ENGINES AND BOILERS. 
 
 cross-section of one. The furnace is in the flue A, and 
 the products of combustion pass through A to the rear of 
 the boiler, where they divide into two portions, and return 
 through the passages B to the front of the boiler, they 
 then enter C and pass through it to the chimney. 
 
 Fig. 74. 
 
 The Cornish boiler has, always, but a single furnace and 
 a single flue. 
 
 The Lancashire boiler, like the Cornish boiler, is an 
 internally fired boiler, but it differs from the Cornish 
 boiler in having two furnaces and, for a part of its length, 
 two flues. The two flues of the Lancashire boiler are 
 united into a single flue near the back end of the boiler. 
 The distinguishing features of the Lancashire boiler are 
 the two furnaces and the two flues uniting in the single 
 flue a short distance from the back end of the boiler. 
 
 The Cornish and Lancashire boilers built to-day are 
 almost always provided with " Galloway tubes " across the 
 flues. These are shown in Fig. 75, and are simply tubes, 
 a, of the shape of a truncated cone, placed in an inclined 
 
BOILERS. 
 
 183 
 
 position across the large flue b. They facilitate the cir- 
 culation of the water in the boiler and increase the heating 
 surface. 
 
 In many of the modern forms of Cornish or Lanca- 
 shire boilers, the gases pass under the boiler from the 
 
 Fig. 75. 
 
 rear towards the front, instead of along the sides, and 
 pass along the sides on the way to the chimney. That 
 is, in Figs. 73 and 74, the gases pass to the front through 
 the passage C, after leaving A, and then pass off to the 
 chimney through the passages B. 
 
 78. RETURN FIRE-TUBE BOILERS. Boilers of this 
 type are usually spoken of as " return tubular boilers," 
 and are more used in this country than those of any other 
 type. 
 
 In Figs. 67 and 76 are shown views of a boiler of this 
 type. 
 
 These boilers, as seen from the cuts shown, are cylin- 
 drical, externally fired, boilers. The gases pass from the 
 furnace under the boiler to the '* back connection," and 
 
184 
 
 STEAM ENGINES AND BOILERS. 
 
^BOILERS. 
 
 185 
 
 from there pass to the front through a number of tubes 
 or flues. If the tubes are of greater diameter than six 
 inches, they are usually spoken of as flues. The number 
 of tubes varies with the diameter of the shell of the 
 boiler and the diameter of the tubes. 
 
 The heating surface of a return tubular boiler consists 
 of that part of the surface of the shell in contact with 
 the gases ; of the outside surface of the tubes, the surface 
 in contact with the water ; and that part of the ends, 
 or heads, of the boiler with which the gases come in 
 contact. The area of the surface of the shell that is in 
 
 I 
 
 Fig. 77. 
 
 contact with the gases depends upon the setting of the 
 boiler; although it is customary to assume, what is not 
 always true, that two-thirds of the area of the shell is 
 exposed to the hot gases. It is usually customary to 
 neglect, as unimportant, the parts of the heads in contact 
 with the gases. It is evident, then, that the heating sur- 
 face of the shell will be obtained by multiplying two- 
 thirds the outside circumference of the shell, in feet, 
 by the length, in feet ; and the heating surface of the 
 tubes will be obtained by multiplying the outside cylin- 
 drical surface of one tube by the number of tubes in 
 
186 
 
 STEAM ENGINES AND BOILERS. 
 
BOILERS. 
 
 187 
 
 the boiler. Therefore, let D denote the diameter, in 
 feet, of the shell of the boiler; /, the length in 
 feet ; d, the outride diameter, in inches, of each tube ; 
 and N, the number of tubes. Then the heating 
 
 2 
 
 surface of the shell will be, 3.1416 X -- Dl ; and that 
 
 *J 
 
 Fig. 79. 
 
 Fig. 80. 
 
 3.14.16 dlN 
 
 of the tubes will be . The total heating sur- 
 face, S, will be 
 
 (83) 
 
 = 2.1 Dl + 0.262 dlN. 
 
 The tubes used in return tubular boilers are sold accord- 
 ing to their external diameter; and the diameters in most 
 
188 
 
 STEAM ENGINES AND BOILERS. 
 
 00 
 
 bfl 
 
BOILERS. 189 
 
 common use are 3, 3^, and 4 inches. The diameter of 
 the tube used in a boiler is somewhat limited by its 
 length, as the length should not exceed sixty times the 
 diameter. 
 
 The diameters of the shells of return tubular boil- 
 ers vary from about 30 inches to 84 inches; and the 
 lengths of the shells will vary from about 6 feet to 20 
 feet, although the usual lengths are from 12 to 16 feet. 
 
 Boilers whose diameters do not exceed 72 inches, and 
 whose lengths are not greater than 18 feet, may be 
 obtained with the bottom of the shell made of a single 
 sheet of iron or steel, and the top part made of one or 
 more sheets. The advantage of a single sheet on the 
 bottom of an externally fired boiler, is that there are then 
 no rivets to come in contact with the hot gases. 
 
 The ends of tubes less than six inches in diameter 
 are fastened in the heads of the boilers by " expanding" 
 them, as shown in Fig. 77, and those six inches, or more, 
 in diameter are riveted to the heads. 
 
 79. WATER-TUBE BOILERS. Boilers of this type are 
 not as much used as those of the return fire-tube type, 
 but they are becoming more and more extensively used 
 every day. The first cost of these boilers is usually much 
 greater than that of boilers of other types. The heating 
 surface of these boilers is made up of such a variety of 
 surfaces that it is impossible to give any general rule for 
 determining it, that will be applicable to all kinds of 
 water-tube boilers. It must suffice to say that the heat- 
 ing surface is the total surface of those parts of the boiler 
 in contact with the hot gases. 
 
 It is impossible to illustrate and explain all the different 
 varieties of water-tube boilers, but they may be distin- 
 guished into three classes, each of which may be illus- 
 trated. 
 
190 
 
 STEAM ENGINES AND BOILERS. 
 
 *\jfcv.5 .*.. S_ 
 
 mi 
 
 tc 
 
BOILERS. 191 
 
 In the first class are included those water-tube boilers 
 that have a number of tubes fastened together into sets 
 by common headers or legs, and these common headers 
 connected 'to a drum containing water and steam. The 
 form of the headers, connecting the ends of the tubes, 
 depends upon the make of the boiler and the number of 
 tubes connected into one set. From all boilers of this 
 class, it is possible to remove one set of tubes without 
 in any way injuring the other sets. It is probable that the 
 greater number of all the water-tube boilers on the market 
 belong to this class. 
 
 As an example of this class of water-tube boilers, the 
 Babcock and Wilcox boiler is shown. 
 
 Fig. 78 shows a section of this boiler; Fig. 79 shows an 
 enlarged view of the connection of the tubes to the head- 
 ers, and of the connection of the headers to the water and 
 steam drum. In Fig. 80 is shown a front view of one of 
 the headers. It will be seen that each header, both at 
 the front and the rear, is entirely independent of the 
 others, and that by taking off the hand-hole covers, a in 
 Figs. 79 and 80, one of which is placed on the headers 
 opposite the end of each tube, the tubes may be exam- 
 ined, or taken out if desired. 
 
 In some forms of water-tube boilers, of this class, the 
 headers are so arranged that the water from the lower 
 tubes must flow through the headers of the upper tubes 
 before it can enter the water and steam drum. 
 
 The Heine boiler will serve to illustrate what might be 
 termed the second class. In this class would be included 
 all those water-tube boilers that have the ends of all the 
 tubes fastened into one common header at each end of 
 the boiler. 
 
 Fig. 8 1 shows a perspective of a Heine boiler ready 
 for shipment ; Fig. 82 shows a section; and Fig. 83 shows 
 the method of fastening the tubes to the header, and the 
 
192 
 
 STEAM ENGINES AND BOILERS. 
 
 details of the hand holes, one of which is placed opposite 
 the end of each tube. In Fig. 83, T represents the ends 
 of the tubes fastened to the header; 0, hollow stay-bolts 
 bracing the walls of the header; and J t h, H t and b, parts 
 of the hand-hole cover. 
 
 In the third class of water-tube boilers, would be 
 included those that have two or more large drums con- 
 nected by nearly vertical water-tubes. 
 
 Fig. 83. 
 
 This class is illustrated by the Stirling boiler; a section 
 of which is shown in Fig. 84, and a half-front elevation 
 in Fig. 85. 
 
 80. VERTICAL BOILERS. Until of late years almost all 
 vertical boilers made were of small size, but now large 
 ones are being made and used. These boilers are usually 
 what might be termed internally fired ; and they are liked 
 on account of the small floor area occupied by them. 
 
 In Fig. 86 is shown a half-section and half-elevation of 
 a small vertical boiler, such as is in common use in this 
 country. 
 
 The heating surface in these boilers consists of the sur- 
 
BOILERS. 
 
 193 
 
 Fi. 84. 
 Stirling Boiler, 
 
 13 
 
194 STEAM ENGINES AND BOILERS. 
 
 face of the furnace and of the outside surface of the tubes 
 through which the gases pass. The tubes of these small, 
 vertical boilers are usually of 2 or 2j inches outside 
 diameter. 
 
 81. MARINE BOILERS. While any boiler used on a 
 vessel is, or ought to be, called a " marine boiler/' custom 
 has generally confined the name to boilers similar to that 
 show in section in Fig. 87, and in half-elevation and half- 
 section in Fig. 88. 
 
 These boilers are always internally fired ; they make 
 steam rapidly and occupy but a small amount of space. 
 The tubes used in marine boilers are usually about 2j 
 inches in external diameter. 
 
 82. RATING OF BOILERS. Most boilers are usually 
 rated as being of a given number of horse-power. 
 By the term horse-power, when applied to a boiler, is 
 meant the horse-power of the engine to which the boiler 
 is capable of supplying steam. Of course, it is at once 
 evident that the power of a boiler will vary between very 
 wide limits, depending upon the efficiency in the use of 
 steam of the engine to which it is attached. 
 
 In order that there might be some uniformity in the 
 rating of the boilers tested at the Centennial Exposition, 
 at Philadelphia, in 1876, the judges decided that one 
 boiler horse-power should mean thirty pounds of water 
 per hour, evaporated from an initial temperature of 100 
 F., under a boiler pressure of seventy pounds by the 
 gauge. This is equal to 34^ Ibs., per hour, of equivalent 
 water from and at 212. This standard of rating has 
 become almost universally adopted, and one horse-power 
 for a boiler may be considered as the evaporation of 34 J 
 pounds of water per hour from and at 212, or its 
 equivalent.* 
 
 * This has been adopted as the standard boiler horse-power by the American 
 Society of Mechanical Engineers. 
 
BOILERS. 
 
 195 
 
 Fig. 85 
 Stirling Boiler. 
 
196 STEAM ENGINES AND BOILERS. 
 
 When, however, boilers are sold and no test is made to 
 determine the amount of steam they will make, they 
 cannot be rated according to the standard of 34^ pounds 
 of water per hour from and at 212; and manufacturers 
 usually rate them according to the number of square feet 
 of heating surface. There is no uniformity among manu- 
 facturers as to the number of square feet of heating 
 surface that shall be necessary for one horse-power, nor 
 is any distinction made as to the difference in efficiency 
 of the different parts of the heating surface. Some 
 manufacturers of return tubular boilers rate their boilers 
 on the basis of I2j square feet of heating surface per 
 horse-power, while others rate their boilers on a basis of 
 15 square feet of heating surface per horse-power. 
 
 Manufacturers of water-tube boilers usually rate their 
 boilers on a basis of 10 or n square feet of heating sur- 
 face per horse-power. 
 
 Vertical boilers are usually rated upon a basis of 12 
 square feet of heating surface per horse-power. 
 
 When comparing the prices asked by different manu- 
 facturers for boilers of the same rated horse-power, it is 
 necessary to compare carefully the areas of the heating 
 surfaces, in order to determine whether or not the boilers 
 are rated on the same basis. 
 
 83. APPENDAGES TO A BOILER. Under this head are 
 included pressure gauges, water gauges, gauge cocks, 
 safety valves, feed-water heaters, and other small parts of 
 a boiler that need some short description. 
 
 Pressure Gauges. The most common form of pressure 
 gauge is shown in Figs. 89 and 90. In Fig. 90 the pres- 
 sure gauge is indicated by a. It has a dial face graduated 
 to show pressure in pounds per square inch above the 
 atmosphere, so that when the pressure in the boiler is 
 simply that of the atmosphere the gauge will indicate zero 
 pounds. Fig. 89 shows a pressure gauge with the dial 
 
BOILERS. 
 
 197 
 
 Fig. 86. Vertical Boiler. 
 
198 
 
 STEAM ENGINES AND BOILERS. 
 
 face removed, so that the inside mechanism can be seen. 
 The steam enters, through #, the flexible, bent tube b, 
 shown in section at e y and by its pressure tends to 
 straighten the tube. As the tube straightens, it moves the 
 arc c ; which in turn moves the hand d by means of a 
 
 Fig. 87. 
 Marine Boiler. 
 
 small pinion fastened to the axis of d and gearing 
 with c. By properly adjusting the position the hand d y 
 and the strength of the tube /5, the gauge may be made 
 to correctly indicate pressures. 
 
 Syphon. The syphon is simply, a bent piece of J 
 inch pipe, shown at b in Fig. 90, to which the gauge is 
 always fastened. The syphon is used in order to keep 
 the tube of the pressure gauge filled with water, and thus 
 
BOILERS. 
 
 199 
 
 t 
 
200 STEAM ENGINES AND BOILERS. 
 
 prevent the very hot steam from coming in direct contact 
 with it. 
 
 Water Column. The water column is a casting to 
 which is fastened a number of the small appendages to a 
 boiler. In Fig. 90, A indicates the water column. To it 
 is fastened the pressure gauge a, the gauge cocks c, and 
 the water gauge d. The upper part of A is connected 
 to the steam space of the boiler, and the lower part to the 
 water space; so that the water stands at the same level 
 in the water column that it does in the boiler. 
 
 Gauge Cocks. The gauge cocks c, in Fig. 90, are for 
 determining the position of the water line in the boiler. 
 There are usually three gauge cocks, about three inches 
 apart. The water line should be just about the middle 
 cock, so that if the upper cock is opened, steam will 
 escape; if the middle cock is opened, a mixture of steam 
 and water will escape ; and if the lower cock is opened, 
 water will escape. Boilers are sometimes provided with 
 two sets of gauge cocks, one fastened to the water 
 column and one fastened directly to the shell of the 
 boiler. 
 
 Water Gauge. The water gauge or, as it is sometimes 
 called, the water glass, is indicated by d, in Fig. 90. It 
 is a glass tube communicating with the steam space of A 
 at the top, and with the water space at the bottom. If 
 the tube is open and not choked at any point, the level 
 of the water in the water gauge will be the same as that 
 of the water in the boiler ; so that the water in the gauge 
 will enable one to see at a glance where the level of the 
 water stands in the boiler. The glass tube has, usually, 
 about twelve inches exposed to view; and the middle 
 gauge cock is at about the middle of the glass tube. 
 The lower end of the glass tube is about on the level of 
 the tops of the tubes of the boiler, in the case of a return 
 fire-tube boiler. 
 
 Safety Valve. A safety valve is a valve which, when 
 
BOILERS. 
 
 201 
 
 Fig. 90. 
 
202 
 
 STEAM ENGINES AND BOILERS. 
 
 the pressure of the steam becomes equal to a given 
 amount depending upon the setting of the valve, is opened 
 by the pressure of the steam, and allows some of the 
 steam to " blow off" into the atmosphere; it thus pre- 
 vents the pressure in the boiler from becoming too great. 
 There should be at least one safety valve on every boiler, 
 and it is desirable to have two safety valves to every 
 boiler, in order that if, for any reason, one of the valves 
 should fail to act the other would act. 
 
 Fig. 91. 
 
 There are two kinds of safety valves in common use on 
 boilers generating steam for steam engines, the lever 
 safety valve and the pop safety valve. 
 
 In Fig. 91 is shown a lever safety valve. It consists of 
 a valve, in the body A, to which is a spindle B t that 
 presses against a lever, D. The lever is free to swing 
 about the pin C, and carries a poise, W, whose position on 
 the lever may be changed at will. The steam presses 
 
BOILERS. 
 
 203 
 
 against the bottom of the valve, in the body A, and tends 
 to force the spindle, B, upwards. In order that the 
 spindle may rise and allow the valve to open, the lever 
 must be moved about the pin, C, as a center; but the 
 weight of the lever, D t and the poise, W, tends to keep 
 the lever from moving. It is evident that the valve will 
 not open until the moment of the force acting on the 
 valve becomes equal to the sum of the moments of the 
 weight of the lever and the weight of the poise. 
 
 Fig. 92. 
 
 Let, in Fig. 91, V be the area of the valve in square 
 inches; P t the pressure of the steam, by the gauge, at 
 which the valve will blow off; a, the distance, in inches, 
 from the center of Cto the center of the spindle B; b, the 
 distance, in inches, to the center of the poise ; c, the dis- 
 tance, in inches, to the center of gravity of the lever; w t 
 the weight, in pounds, of the lever ; W, the weight, in 
 pounds, of the poise ; and m, the weight, in pounds, of 
 the valve. 
 
204 STEAM ENGINES AND BOILERS. 
 
 Then, it is evident from Fig. 91, that 
 
 (84) PVa = cw + b W -f ma 
 
 From (84) we get 
 
 In a given safety valve, the only thing that can be 
 changed is the distance, b, that the poise is from the 
 center of the pin C; and the greater b is made, the higher 
 will be the pressure at which the valve will blow off. 
 
 A " pop " safety valve is a safety valve in which the 
 valve is held down on its seat by a spring, instead of a 
 lever and poise. In Fig. 92 is shown a section of a 
 " pop " safety valve such as is manufactured by the Con- 
 solidated Safety Valve Co. The valve is set to blow off 
 at different pressures by adjusting the tension of the 
 spring by means of the nuts at the top. 
 
 The only objection to a pop safety-valve is the noise it 
 makes when it opens. 
 
 Feed- Water Heater. We have already shown how 
 the amount of heat required to evaporate a pound of 
 water is reduced by increasing the temperature of the feed 
 water before it enters the boiler. Whenever it is possible, 
 the exhaust steam of a non-condensing engine should be 
 used to heat the feed -water, instead of being allowed to 
 pass off into the atmosphere. The apparatus in which 
 the feed-water is heated before entering the boiler is 
 termed a " feed-water heater." 
 
 In Fig. 93 is shown a National feed-water heater. 
 As seen in the cut, the feed-water is made to pass through 
 a coil of pipe, before entering the boiler, that is surrounded 
 by the exhaust steam. 
 
 Sometimes a feed-water heater is made to serve the 
 double purpose of heating the feed-water, and of catching 
 all the sediment and impurities that would otherwise be 
 
BOILERS. 205 
 
 deposited in the boiler, when the water has been heated 
 as hot as it becomes in the heater. 
 
 Feed Pipe. The feed pipe is the pipe through which 
 the water enters the boiler. It is often attached to the 
 shell of the boiler near the back, or to the bottom of the 
 front end. Neither of these positions, however, is to be 
 recommended, as in either case the comparatively cool 
 feed-water impinges upon the hottest part of the shell. 
 
 tXHA'JSt flfE 
 
 It is better that the feed pipe should be attached to the 
 front end of the boiler a few inches below the water line, 
 and be carried back into the boiler; and the water should 
 be allowed to escape from the pipe through small perfora- 
 tions in it, rather than through the open end. 
 
 Bloiv-off Pipe. Every boiler should have a blow-off 
 pipe, by means of which it may be emptied of the water 
 it contains. 
 
206 
 
 STEAM ENGINES AND BOILERS, 
 
BOILERS. 207 
 
 Valves. The steam pipe, for taking steam from the 
 boiler to the engine, should have a valve close to the 
 boiler. 
 
 The feed pipe should have two gate valves, close to the 
 boiler, with a check valve between them. 
 
 The blow-off pipe should not have a valve on it, but 
 should have a good plug-cock. 
 
 Feeding Apparatus. The feed-water is usually forced 
 into the boiler by means of a pump, called a feed-water 
 pump, although the injector is often used. 
 
 84. SETTINGS OF BOILERS. The setting of a boiler 
 means the general arrangement of furnace, boiler, and 
 chimney relative to one another, and the manner in which 
 the furnace and boiler are inclosed and built in. Of 
 course, the setting will depend largely upon the type and 
 construction of the boiler, but for the ordinary return 
 fire-tube boiler there are two recognized standard settings, 
 viz., the full-arch front setting, and the half-arch front 
 setting. 
 
 Fig, 76 shows a perspective view of a return fire-tube 
 boiler with a half-arch front setting ; and Fig. 94 shows 
 one with a full-arch front setting. 
 
 When two or more boilers are set side by side, with 
 common front and rear walls, they form what is termed a 
 " battery " of boilers. All the boilers of a battery may, 
 or may not be connected to the same chimney. 
 
 The setting for return fire-tube boilers, recommended 
 by the Hartford Steam Boiler Inspection and Insurance 
 Company, described in The Locomotive for February, 
 1895, is shown in Figs. 95, 96 and 97. 
 
 In this setting the furnace is supposed to be lined with 
 fire-bricks, and the walls are made very thick. The 
 company, in its description of the setting, says: 
 
 " The width of the furnace in the settings advocated 
 by this company is six inches less than the diameter of 
 
208 
 
 STEA3I ENGINES AND BOILERS. 
 
 the boiler. Beginning just above the grate, the side walls 
 batter at such angle as to make them 3" clear of the 
 boiler at the center, where the walls project inward and 
 close against the boiler. This batter gives greater sta- 
 bility to the walls, and another special feature of it is, 
 that it allows the heated gases to rise without impinging 
 against the walls of the setting, and they flow away from 
 
 Fig. 95. 
 
 the wall and distribute themselves evenly over the whole 
 heating surface of the shell. The removal of soot and 
 ash from the shells is also facilitated, and, moreover, it is 
 found that these deposits do not form so readily when the 
 walls are battered as they do when the walls are straight, 
 and the space between them is correspondingly con- 
 tracted. The batter also increases the volume of the 
 combustion chamber, and allows of a more thorough 
 mixing of the oxygen and furnace gases, the result being 
 that complete combustion of the fuel is greatly facilitated. 
 The bridge-wall slopes back from about four inches above 
 the grate, at an angle of 40, in order that the radiant 
 heat from the fire may be diffused over a large portion 
 
BOILERS. 
 
 209 
 
 of the boiler shell. The flame bed back of the bridge- 
 wall slopes down to the level of the boiler-room floor. 
 It is paved for easy cleaning, and the combustion cham- 
 ber is large enough to make examinations and repairs to 
 the boiler comparatively easy. The cleaning door in 
 the rear wall is placed on a level with the flame bed in 
 order that ashes may be readily removed, and as it is 
 
 Fig. 96. 
 
 below the currents of highly-heated gases loss by radia^ 
 tion through the door is largely prevented. The loss or 
 waste of heat from this cause is often very great and it 
 has not generally received the attention it deserves. 
 Another point that demands more attention than it 
 usually receives, is the liability of leakage of cold air 
 through the walls of the setting, with the resulting reduc- 
 tion of furnace temperature. To avoid loss of tempera- 
 ture from this cause heavy double walls are constructed 
 in this company's settings, the outside walls of a battery 
 having a two-inch air space between them. The division 
 
 H 
 
210 
 
 STEAM ENGINES AND BOILERS. 
 
 walls between two or more boilers should have a half-inch 
 clear space between them, to allow free and independent 
 expansion of the walls. With a solid wall and one or 
 more boilers of the battery stopped, one side of the wall 
 separating a boiler in use from another one out of use 
 would be hot and greatly expanded, while the other side 
 of it would be cool ; the result being that the bonded or 
 
 Fig. 97. 
 
 solid wall must necessarily be severely strained or injured, 
 and the joints in the masonry quite probably broken by 
 the unequal expansion. Excessive leakage of air is likely 
 to follow. These criticisms apply to all solid-built boiler 
 settings. While the heavy double walls are somewhat 
 more expensive in first cost, the increased economy and 
 capacity of the boilers, as well as the greater durability 
 of the settings, fully warrant their construction. The 
 results obtained in many large plants fully sustain this 
 statement. 
 
 The exposed portions of the boiler shells above the 
 settings are covered with plastic non-conducting covering 
 2$" thick. This is much lighter than brick, is a better 
 non-conductor, and does not exert a sensible thrust upon 
 
BOILERS. 211 
 
 the setting walls as a brick arch does. If leaks occur 
 along the joints of the covered part of the boiler, they are 
 quickly noted by the discoloration of the covering, and 
 may be stopped before the injury from corrosion occurs. 
 The illustrations give the general arrangement of the 
 settings above described, in which it is desired to combine 
 durability with simplicity in design and construction, and 
 at the same time to obtain good results from the boilers, 
 both in economy and in capacity." 
 
CHAPTER X. 
 
 CHIMNEYS. 
 
 85. CHIMNEYS. Chimneys are to carry the products 
 of combustion away from the boiler, and, by so doing, 
 produce a draft that will cause fresh air to enter 
 the furnace and carry with it the oxygen to be used 
 
 Fig. 98. 
 
 in combustion. They are made either of brick or 
 metal; and usually have either an octagonal or circular 
 cross-section. A circular, inside, cross-section is better 
 than either a square or an octagonal cross-section, as it 
 offers less resistance to the flow of the gases. A square, 
 inside, cross-section is, really, equivalent only to a cir- 
 cular cross-section whose diameter is equal to that of a 
 (212) 
 
CHIMNEYS. 
 
 213 
 
 circle inscribed in the square ; this is so as the corners of 
 square chimneys become almost dead spaces, on account 
 of the excessive resistance there to the flow of the gases. 
 The passage through which the gases pass, after leav- 
 ing the boiler or battery of boilers, on their way to the 
 
 chimney, is termed the " breeching ; " it may be large or 
 small, long or short, depending upon the number of boil- 
 ers connected to it and the distance from the boilers to 
 the chimney. 
 
 In the case of a single boiler, or a small battery of boil- 
 
214 STEAM ENGINES AND BOILERS. 
 
 ers, the chimney is usually made of No. 16 sheet iron, 
 and is carried directly by the breeching. Fig. 98 shows 
 the breeching of a sheet iron stack for a single boiler with 
 a half-arch front setting ; and Fig. 99 shows the breech- 
 ing for a battery of two boilers, with a full-arch front 
 setting. 
 
 In the case of a large battery of boilers, a number of 
 small, sheet iron chimneys, to each of which will be con- 
 nected two or three boilers, may be used, or all the 
 boilers may be connected to a single large chimney. 
 
 Brick chimneys, usually, have two walls with an air 
 space between them. The inner wall may extend up the 
 whole height of the chimney or only a part of the way to 
 the top. The outer wall is for stability, and forms the 
 body of the chimney; while the inner wall is simply a 
 lining to prevent the hot gases from coming in contact 
 with the outer wall, and it should be made entirely of fire 
 brick laid in clay, or, at least, should be lined with fire 
 brick. This lining is necessary, as ordinary brick-work will 
 not stand the heat of the hot gases without deteriorating 
 very much. 
 
 Brick chimneys are very much used, although they are 
 expensive, and are apt to open at the joints and let cold 
 air leak into the inside. 
 
 In Fig. icois shown a section of a large brick chimney 
 
 Iron chimneys, of large size, made of thick sheet iron, 
 are becoming more and more extensively used every day. 
 They are usually cheaper than brick chimneys, and are 
 perfectly air tight. They may or may not be lined with 
 fire brick, although it is preferable to have them lined. 
 
 In Fig. 101 is shown an elevation and section of a steel 
 plate chimney, such as is made by the Philadelphia En- 
 gineering Works, Philadelphia, Pa. 
 
 86. DRAFT OF CHIMNEY. By the draft of a chimney is 
 meant the difference in pressure of the gases in the chim- 
 
CHIMNEYS, 
 
 215 
 
 Fig. 100. 
 
 Fig. 101. 
 
216 STEAM ENGINES AND BOILERS. 
 
 ney and that of the air on the outside, measured at, or 
 near, the base of the chimney. It is this difference in 
 pressure, or draft, that makes the air flow into the furnace 
 and force the gases out through the top of the chimney. 
 When the draft is due to the difference in temperatures 
 of the gases in the chimney and the air outside, and to 
 the height of the chimney, it is termed a natural draft ; 
 but when the pressure forcing the air into the furnace is 
 that due to a fan or blower, the draft is termed a forced 
 draft, since it is usually much greater than the ordinary, 
 natural, draft. Of course, there is no sharp line of 
 demarkation between natural and forced drafts ; as a nat- 
 ural draft may be very high, and a forced draft may be 
 very low. 
 
 The draft is usually spoken of as being of so many 
 " inches of water." This method of expressing the draft 
 gives the head of water, in inches, that is equivalent to 
 the difference between the pressure of the air and that of 
 the gases inside of the chimney. The number of inches 
 of draft is measured by means of a U-tube, shown in Fig. 
 102. The legs of the tube are first filled about half full 
 with water ; then, one end of the tube is inserted through 
 a hole in a piece of cork that fits tightly into an opening 
 in either the breeching, near the chimney, or the base of 
 the chimney itself; the other end of the tube is left open 
 to the air. The water will stand higher in the leg in 
 communication with the hot gases than in the one in 
 communication with the air; and the distance, in inches, 
 that the surface of the water in the one leg is above the 
 surface of the water in the other leg is the draft in inches 
 of water. 
 
 Except in the case of very high chimneys, the draft of 
 furnaces having natural draft will seldom exceed three- 
 fourths of an inch, and is ordinarily about one-half an 
 inch. The draft in furnaces using forced draft is only 
 limited by the ability of the fan or blower to create it. 
 
CHIMNEYS. 
 
 217 
 
 87. VELOCITY OF THE GASES PASSING THROUGH THE 
 CHIMNEY. The velocity of the flow of the gases through 
 the smallest cross-section of the chimney is determined 
 by the law of the flow of gases under a small pressure. 
 We know, from physics, that for small pressures, the 
 velocity, in feet per second, with which a gas will flow 
 
 Fig. 102. 
 
 from a vessel in which the unbalanced pressure per square 
 foot, /, is that equivalent to a head, h, of the gas, is 
 
 (86) v = y^h 
 
 v is the velocity of flow, in feet per second, of the gas. 
 g is equal to the constant 32. h is the head, in feet of 
 gas, equivalent to the pressure, p, per square foot, that 
 causes the gas to flow. 
 
 If the gas has a density, or weight per cubic foot, of D t 
 
 then 
 
 = p, and h == . 
 
218 STEAM ENGINES AND BOILERS. 
 
 In the case of a chimney, the pressure causing the gas. 
 to flow is equal to the difference between the pressures 
 inside and outside of the chimney. 
 
 Let Fig. 103 represent a chimney, whose height in feet 
 is H, with an opening at the bottom. Also, let PI be the 
 pressure, per square foot, of the gases inside the chim- 
 ney ; Po, the pressure, per square foot, of the air outside 
 the chimney ; D\, the density of the gases inside the 
 chimney ; Do, the density of the air outside ; and P, the 
 pressure, per square foot, of the air at the top of the 
 chimney. 
 
 Then, evidently, P = P + HDo ; P l = P + HD^ ; and 
 the pressure that forces air into the opening, and the 
 gases out of the chimney, is 
 
 Po Pi = H (Do - A). 
 
 The head, h, in feet of hot gas equivalent to the pres- 
 sure Po Pi is, from what has been said before, equal to 
 the pressure divided by the density of the hot gas. 
 Therefore, 
 
 Po- A (Do 
 ks _____ =H^- 
 
 From (86) we know that the velocity with which the 
 hot gas will tend to flow, when under a pressure equiva- 
 lent to a head h t is 
 
 (88) F= 12= 
 
 Experience has shown, however, that the velocity of 
 the gases in a chimney is reduced by friction, until it is 
 only from one-third to one-half what it would be if there 
 were no friction. Therefore, if we let / represent a factor, 
 varying between one-third and one-half, by which the 
 theoretical expression in (88) must be multiplied in order 
 to obtain the actual value, u, of the velocity of the flow 
 of the gases, we have 
 
CHIMNEYS. 
 
 219 
 
 (89) 
 
 The density of air at 32 F., or 493 absolute, is 0.08, 
 and it is sufficiently accurate for us to assume, as is al- 
 most true, that the density of the gases in the chimney is, 
 also, 0.08 at 32 F. 
 
 Now, if the absolute temperature of the air outside of 
 the chimney is To, and that of the gases inside is 7i we 
 
 Fig. 103. 
 
 know, from what has been said in Chapter I, that, since 
 the density of a gas is inversely as its volume, 
 
 1 
 
 
 KO 
 
 0.08 X 493 
 -- _ -- 
 
 TO 
 
 0.08 X493 
 
 "IT 
 
 , and 
 
220 STEAM ENGINES AND BOILERS. 
 
 Therefore, 
 
 A __ Ti_ 
 A = To ; 
 
 and the expression for u, as given in (89), becomes 
 (90) u = 8 
 
 The temperature of the gases in chimneys is, ordinarily, 
 between 400 F. and 550 F. ; so that the value of 71 will 
 be between 861 and ion. The temperature of the 
 outside air varies with the locality and the seasons of the 
 year, but it may be assumed as 60 F., or 521 absolute. 
 
 7" 1 
 
 Therefore, the value of yr may be taken as varying from 
 
 1.6 to 2. 
 
 As the density of the air varies greatly from time to 
 time, depending upon the amount of moisture in the air, 
 and as the density of the gases inside of the chimney also 
 varies greatly, the value of u can never be very accurately 
 obtained by an equation. The result obtained by the 
 use of (90) is apt to differ more or less from the true value 
 of u, because in (90) it has been assumed that the temper- 
 ature of the gases is the same at all parts of the chimney, 
 whereas it really becomes less the nearer we approach 
 the top. 
 
APPENDIX. 
 
 CARE OF BOILERS. 
 
 As it is very important that everbody having anything 
 to do with the operation of a boiler plant should know 
 how to care for the boilers, there is inserted, here, the 
 rules to be observed in order to prevent accidents, to 
 economize fuel, and to preserve the boiler, that are given 
 by the Fidelity and Casualty Company in its little book, 
 The Engineer's Manual. 
 
 How to Prevent Accidents. 
 
 1. SAFETY VALVES. These should be of ample 
 size and kept in working order. The valve should be 
 tried daily ; this is best done by allowing the pressure to 
 rise gradually until the valve just "simmers," noting the 
 pressure by the steam gauge at the moment. Freedom 
 of action may of course be ascertained by hand, but it 
 cannot be known by this means that the valve will blow 
 off when the proper pressure is attained. Neglect and 
 overloading of this most important adjunct are prolific 
 causes of boiler explosions. Each boiler should have its 
 own safety valve, and no stop valve should be permitted 
 between it and the boiler. See cut " A " (not given here). 
 This illustrates the worst combination of safety and stop 
 valves that could well be contrived. 
 
 2. PRESSURE GAUGE. It is absolutely necessary that 
 the pressure gauge should be trustworthy, and if there is 
 any reason to question its readings, it should be compared 
 with one known to be accurate. The gauge should be 
 
 (221) 
 
222 STEAM ENGINES AND BOILERS. 
 
 fitted to a " loop " filled with water, which transmits the 
 pressure and prevents contact of steam with the gauge 
 spring. Attach the gauge directly to the boiler and not 
 to the steam pipe, to prevent fluctuations of pressure 
 readings. 
 
 3. WATER LEVEL. Before starting, make sure that 
 there is plenty of water in the boiler by trying the gauge 
 cocks. While running do not depend on the gauge glass, 
 but try the gauge cocks often. The water line should be 
 kept at a regular height, and should never be less than 
 three or four inches above the " fire line." The gauge 
 glass should be blown out frequently to see that it is not 
 chojced ; it is an excellent plan to try the gauge cocks 
 every fifteen minutes. Both gauge and cocks must be 
 kept clean. 
 
 4. DAMPER. Do not close the damper entirely while 
 there is fire on the grates, as gas may collect in the tubes 
 and cause an explosion. 
 
 5. FEED PUMP OR INJECTOR. These should be kept in 
 order, and should be of ample size for all requirements. 
 The feed pump, however, ought not to be so large as to 
 render it difficult to feed the boiler continuously at a slow 
 rate of speed. It is always safer to have two means of 
 feeding. An injector should be used when no feed-water 
 heater is provided, as it prevents the contraction of tubes 
 and plates where the feed water comes in contact with 
 them. 
 
 6. Low WATER. The blow-out apparatus should be 
 kept tight, as any leakage here may give rise to low 
 water, with the result of overheating the plates. In case 
 of low water, fresh coal, or better still, wetted ashes, must 
 be thrown on the fire at once. Do not turn on the feed, 
 
APPENDIX. 223 
 
 though if already in motion, allow it to continue, nor start 
 or stop the engine, or lift the safety-valve until the boiler 
 has cooled down. After a case of low water the tube 
 ends in the upper rows should be examined for leaks. 
 
 7. INCRUSTATION, CORROSION. Boilers should be kept 
 free from scale, as its presence increases the liability of 
 burning or cracking the plates and predisposes to 
 explosion. The surest method for preventing internal 
 corrosion is to abandon the use of the water which causes 
 it, but if this is impracticable, a sharp lookout should be 
 kept for defects. Leaks of seams and fittings, drippings 
 from pipes, exposure to the weather, contact of the boiler 
 with brick-work, etc., are causes of external corrosion, 
 and should be at once remedied. 
 
 8. BLISTERS, CRACKS, AND BURNT PLATES. When 
 these occur they should receive attention at once. Burnt 
 places and blisters should be cut out and a patch put on 
 inside the boiler to avoid making a pocket for the 
 collection of sediment. 
 
 9. FUSIBLE PLUGS. These are required by law in 
 some States. To keep them in an efficient condition 
 their surfaces, both on the fire and water sides, must be 
 often scraped clean, but notwithstanding all precautions, 
 they are unreliable. 
 
 10. STARTING THE ENGINE. The engine should be 
 started slowly, in order not to make a violent change in 
 the condition of the water and steam, and when 
 possible, the engine should be stopped gradually. The 
 sudden opening or closing of a large stop-valve may pro- 
 duce a violent rush of steam and water against that part 
 of the boiler whence the steam is drawn, the percussion 
 of which may be sufficient to rupture the boiler. 
 
224 STEAM ENGINES AND BOILERS. 
 
 How to Save Fuel. 
 
 1. FIRING. The fire should be kept level and of some- 
 what greater thickness at the bridge wall. This promotes 
 a uniform consumption of fuel, as the air passes more 
 freely through the fire near the bridge and the greater 
 thickness retards its passage. Fuel supplied regularly in 
 small quantities, combined with an even distribution, 
 produces the best results. When anthracite coal is used, 
 the average thickness of the fire should be 6 to 8 inches ; 
 with bituminous coal, it should be 8 to 10 inches; with 
 coke, 10 to 12 inches. If the draft is poor, however, a 
 thin fire must be used. Do not fire with large lumps. No 
 fragment ought to be larger than a man's fist. 
 
 Complete combustion is only attained when the fuel is 
 burning with a bright flame all over the grate. Blue 
 flames, dark spots and smoke are evidences of the lack 
 of the necessary air which ought to be supplied above 
 the grate. Fires should be " cleaned " no oftener than 
 necessary. In using a caking coal, it is advantageous to 
 make use of a " coking fire," i. e., firing in front and 
 breaking up with a slice bar, and shoving back when 
 coked. The practice of wetting coal before throwing it 
 on the fire is a bad one, as it wastes heat and produces 
 corrosion. 
 
 2. FEED- WATER. Heating the feed-water, either by 
 means of exhaust steam or the waste gases in the chim- 
 ney, adds to the economy of a steam plant. Each in- 
 crease in the temperature of the feed-water of 1 1 F. 
 means a saving of fuel of one per cent. No saving in 
 fuel is effected by the use of an injector, but the employ- 
 ment of one promotes the longevity of a boiler by intro- 
 ducing the feed-water at a temperature so high that no 
 injurious contractions are caused in any part of the 
 boiler. 
 
APPENDIX. 225 
 
 3. CLEANING. The heating surfaces of a boiler, both 
 inside and out, should be kept clean, in order to prevent 
 a serious waste of fuel. The thickness of the soot or 
 scale which is allowed to accumulate ought never to 
 exceed T ^ of an inch. 
 
 4. LEAKS IN BRICK-WORK. Cracks or openings m 
 the brick-work should be carefully stopped. The admis- 
 sion of air, except at the places provided for it, impairs 
 the draft, cools the gases on their way to the tubes, 
 and sometimes causes jets of flame to impinge so strongly 
 on the shell as to injure the plates. 
 
 5. COVERING. Radiation from the dome and the top 
 of the boiler is a source of waste. A covering of asbestos 
 or other suitable non-conducting material should be pro- 
 vided as a protection. 
 
 6. BLOWING OUT. The bottom blow-out cock should 
 be kept tight to prevent loss by leakage. A plug cock is 
 the simplest, surest and most durable valve for this pur- 
 pose. When the feed water is of a hard or muddy nature, 
 the boiler should be blown out frequently. A boiler 
 should be emptied every week or two, and filled afresh. 
 The proper manner to use a surface blow-off is to open it 
 for about fifteen seconds every hour rather than for a 
 longer time at greater intervals. 
 
 How to Lengthen the Life of the Boiler. 
 
 1. BANKING FIRES. Contraction and expansion, caused 
 by change of temperature, shorten the life of a boiler. 
 For this reason it is better to bank the fires at night 
 instead of drawing them. 
 
 2. LEAKS, Leaks, whether in boiler or fittings, should 
 be repaired at once. Leaks often give rise to corrosion. 
 
 15 
 
226 STEAM ENGINES AND BOILERS. 
 
 3. FILLING UP. Wear and tear of a boiler, arising 
 from unequal expansion and contraction, is increased by 
 allowing the feed- water to enter at too low a temperature. 
 If the use of cold water is unavoidable, the feed-pipe 
 should always be extended into the interior of the boiler. 
 It should enter horizontally through the front head, near 
 one side, and a few inches below the water-line, thence 
 extending back to within a few feet of the back head, 
 crossing over and discharging downward between the 
 tubes and shell. By this means the feed-water is heated 
 nearly to the temperature of water in the boiler, and is 
 discharged at the coolest part of the boiler. The use of 
 an injector or feed-water heater renders this extension of 
 the feed-pipe unnecessary. 
 
 4. BLOWING OUT. A boiler should never be emptied 
 while the brick-work is hot. When this is done the sedi- 
 ment is baked on the plates, making it difficult to remove. 
 
 5. RAPID FIRING. Steam should be raised slowly in 
 a boiler having thick plates or seams exposed to the fire, 
 else overheating or burning results. The greatest effect 
 of a fire on a boiler bottom takes place immediately 
 behind the bridge, and if a seam is located here there is 
 liability of burning the lap. It is best in such cases to 
 change the position of the bridge, so that the seam comes 
 over the bridge, or better still, over the furnace. 
 
 6. MOISTURE. The exterior of a boiler should be 
 protected from moisture, as it brings about corrosion and 
 consequent weakening of the boiler. 
 
 7. GALVANIC ACTION. Sometimes boilers may be 
 protected from the action of corrosive agents present in 
 the water by means of zinc. As a rule one square inch 
 of surface of zinc to every fifty pounds in the boiler is 
 
APPENDIX. 227 
 
 sufficient. The plates should be placed in perfect metallic 
 contact with the iron and renewed as they are wasted by 
 oxidation. 
 
 8. DISUSE OF BOILER. If it is intended not to use the 
 boiler for some time, the boiler should be emptied of its 
 water, dried thoroughly by pans of charcoal, and after 
 placing pans of lime in the interior, closed to prevent 
 oxidation. If this is impracticable, the boiler should be 
 filled with water in which common soda is dissolved. 
 
TABLE I . 
 
 PROPERTIES OF STEAM. 
 
 Pressure 
 by the 
 Gauge. 
 
 Temperature. 
 
 Total 
 Heat above 
 32. 
 
 Latent 
 Heat. 
 
 Vol. of 
 one Ib. of 
 Steam. 
 
 13 
 
 119. 
 
 1118. 
 
 1031. 
 
 223. 
 
 12 
 
 137. 
 
 1124. 
 
 1019. 
 
 135. 
 
 11 
 
 150. 
 
 1128. 
 
 1010. 
 
 98.9 
 
 10 
 
 160. 
 
 1131. 
 
 1003. 
 
 78.3 
 
 9 
 
 168. 
 
 1133. 
 
 997. 
 
 65.0 
 
 8 
 
 175. 
 
 1135. 
 
 992. 
 
 55.9 
 
 7 
 
 181. 
 
 1137. 
 
 988. 
 
 48 9 
 
 - 6 
 
 187. 
 
 1139. 
 
 984. 
 
 43.6 
 
 5 
 
 191.8 
 
 1140.4 
 
 980.1 
 
 39.31 
 
 -.- 4 
 
 197. 
 
 1142. 
 
 977. 
 
 35 8 
 
 3 
 
 201. 
 
 1143. 
 
 974. 
 
 33.3 
 
 2 
 
 205. 
 
 1144. 
 
 971. 
 
 30.6 
 
 -.. 1 
 
 208. 
 
 1146. 
 
 968. 
 
 28.4 
 
 
 
 212.0 
 
 1146.6 
 
 965.7 
 
 26.56 
 
 1 
 
 215. 
 
 1148. 
 
 964. 
 
 25.0 
 
 2 
 
 219. 
 
 1149. 
 
 961. 
 
 23.6 
 
 3 
 
 222. 
 
 1150. 
 
 959. 
 
 22.3 
 
 4 
 
 224. 
 
 1150. 
 
 957. 
 
 21.2 
 
 5 
 
 227.1 
 
 1151.2 
 
 955.1 
 
 20.16 
 
 6 
 
 230. 
 
 1152. 
 
 953. 
 
 19.3 
 
 7 
 
 232. 
 
 1153. 
 
 952. 
 
 18.4 
 
 8 
 
 235. 
 
 1154. 
 
 950. 
 
 17.7 
 
 9 
 
 237. 
 
 1154. 
 
 948. 
 
 17.0 
 
 10 
 
 239.4 
 
 1154.9 
 
 946.4 
 
 16.30 
 
 11 
 
 242. 
 
 1156. 
 
 944. 
 
 15.7 
 
 12 
 
 244. 
 
 1156. 
 
 944. 
 
 15.2 
 
 13 
 
 246. 
 
 1157. 
 
 942. 
 
 14.6 
 
 14 
 
 248. 
 
 1158. 
 
 941. 
 
 14.2 
 
 15 
 
 249.7 
 
 1158.1 
 
 939.3 
 
 13.71 
 
230 
 
 STEAM ENGINES AND BOILERS. 
 
 Pressure 
 by the 
 Gauge. 
 
 Temperature. 
 
 Total 
 Heat above 
 32. 
 
 Latent 
 Heat. 
 
 Vol. of 
 one Ib. of 
 Steam. 
 
 16 
 
 252. 
 
 1159. 
 
 938. 
 
 13.3 
 
 17 
 
 253. 
 
 1159. 
 
 937. 
 
 12.9 
 
 18 
 
 255. 
 
 1160. 
 
 935. 
 
 12.5 
 
 19 
 
 ^257. 
 
 1160. 
 
 934. 
 
 12.2 
 
 20 
 
 258.7 
 
 1160.9 
 
 932.7 
 
 11.85 
 
 21 
 
 260. 
 
 1161. 
 
 932. 
 
 11.6 
 
 22 
 
 262. 
 
 1162. 
 
 931. 
 
 11.3 
 
 23 
 
 264. 
 
 1162. 
 
 929. 
 
 11.0 
 
 24 
 
 265. 
 
 1163. 
 
 928. 
 
 10.7 
 
 25 
 
 266.7 
 
 1163.3 
 
 927.1 
 
 10.36 
 
 26 
 
 268. 
 
 1164. 
 
 926. 
 
 10.2 
 
 27 
 
 270. 
 
 1164. 
 
 925. 
 
 9.95 
 
 28 
 
 271. 
 
 1165. 
 
 924. 
 
 9.75 
 
 29 
 
 273. 
 
 1165. 
 
 923. 
 
 9.54 
 
 30 
 
 273.9 
 
 1165.5 
 
 922.0 
 
 9.34 
 
 31 
 
 275. 
 
 1166. 
 
 921. 
 
 9.16 
 
 32 
 
 277. 
 
 1166. 
 
 920. 
 
 8.98 
 
 33 
 
 278. 
 
 1167. 
 
 919. 
 
 8.81 
 
 34 
 
 279. 
 
 1167. 
 
 918. 
 
 8.63 
 
 35 
 
 280.5 
 
 1167.5 
 
 917.3 
 
 8.45 
 
 36 
 
 282. 
 
 1168. 
 
 917. 
 
 8.31 
 
 37 
 
 283. 
 
 1168. 
 
 916. 
 
 8.16 
 
 38 
 
 284. 
 
 1169. 
 
 915. 
 
 8.02 
 
 39 
 
 285. 
 
 1169. 
 
 914. 
 
 7.87 
 
 40 
 
 286.5 
 
 1169.3 
 
 913.0 
 
 7.73 
 
 41 
 
 288. 
 
 1170. 
 
 912. 
 
 7.61 
 
 42 
 
 289. 
 
 1170. 
 
 911. 
 
 7.48 
 
 43 
 
 290. 
 
 1170. 
 
 911 
 
 7.36 
 
 44 
 
 291. 
 
 1171. 
 
 911. 
 
 7.23 
 
 45 
 
 292.2 
 
 1171.1 
 
 909.0 
 
 7.11 
 
 46 
 
 293. 
 
 1171. 
 
 908. 
 
 7.01 
 
 47 
 
 294. 
 
 1172. 
 
 907. 
 
 6.91 
 
 48 
 
 295. 
 
 1172. 
 
 907. 
 
 6.81 
 
 49 
 
 296. 
 
 1172. 
 
 906. 
 
 6.71 
 
 50 
 
 297.5 
 
 1172.7 
 
 905.2 
 
 6.61 
 
 51 
 
 299. 
 
 1173. 
 
 904. 
 
 6.52 
 
 52 
 
 300. 
 
 1173. 
 
 904. 
 
 6.43 
 
APPENDIX, 
 
 231 
 
 Pressure 
 by the 
 Gauge. 
 
 Temperature. 
 
 Total 
 Heat above 
 32. 
 
 Latent 
 Heat. 
 
 Vol. of 
 one Ib. of 
 Steam. 
 
 53 
 
 301. 
 
 1174. 
 
 903. 
 
 6.34 
 
 54 
 
 302. 
 
 1174. 
 
 902. 
 
 6.25 
 
 55 
 
 302.4 
 
 1174.2 
 
 901.6 
 
 6.16 
 
 56 
 
 303. 
 
 1174. 
 
 901. 
 
 6.08 
 
 57 
 
 304. 
 
 1175. 
 
 900. 
 
 6.00 
 
 58 
 
 305. 
 
 1175. 
 
 900. 
 
 5.93 
 
 59 
 
 306. 
 
 1175. 
 
 899. 
 
 5.85 
 
 60 
 
 307.1 
 
 1175.6 
 
 898.4 
 
 5.77 
 
 61 
 
 308. 
 
 1176. 
 
 898. 
 
 5.70 
 
 62 
 
 309. 
 
 1176. 
 
 897. 
 
 5.63 
 
 63 
 
 310. 
 
 1176. 
 
 897. 
 
 5.57 
 
 64 
 
 311. 
 
 1177. 
 
 896. 
 
 5.50 
 
 65 
 
 311.5 
 
 1176.9 
 
 895.1 
 
 5.43 
 
 66 
 
 312. 
 
 1177. 
 
 895. 
 
 5.37 
 
 67 
 
 313. 
 
 1178. 
 
 894. 
 
 5.31 
 
 68 
 
 314. 
 
 1178. 
 
 893. 
 
 5.25 
 
 69 
 
 315. 
 
 1178. 
 
 893. 
 
 5.19 
 
 70 
 
 315.8 
 
 1178.2 
 
 892.1 
 
 5.13 
 
 71 
 
 317. 
 
 1179. 
 
 892. 
 
 5.08 
 
 72 
 
 317. 
 
 1179. 
 
 891. 
 
 5.02 
 
 73 
 
 318. 
 
 1179. 
 
 890. 
 
 4.97 
 
 74 
 
 319. 
 
 1179. 
 
 890. 
 
 4.91 
 
 75 
 
 319.8 
 
 1179.4 
 
 889.1 
 
 4.86 
 
 76 
 
 321. 
 
 1180. 
 
 889. 
 
 4.81 
 
 77 
 
 321. 
 
 1180. 
 
 888. 
 
 4.77 
 
 78 
 
 322. 
 
 1180. 
 
 887. 
 
 4.72 
 
 79 
 
 323. 
 
 1180. 
 
 887. 
 
 4.68 
 
 80 
 
 323.7 
 
 1180.6 
 
 886.3 
 
 463 
 
 81 
 
 324. 
 
 1181. 
 
 886. 
 
 4.59 
 
 82 
 
 325. 
 
 1181. 
 
 885. 
 
 4.54 
 
 83 
 
 326. 
 
 1181. 
 
 885. 
 
 4.50 
 
 84 
 
 327. 
 
 1182. 
 
 884. 
 
 4.45 
 
 85 
 
 327.4 
 
 1181.7 
 
 883.6 
 
 4.41 
 
 86 
 
 328. 
 
 1182. 
 
 883. 
 
 4.37 
 
 87 
 
 329. 
 
 1182. 
 
 883. 
 
 4.33 
 
 88 
 
 330. 
 
 1182. 
 
 882. 
 
 4.28 
 
 89 
 
 330. 
 
 1183. 
 
 881. 
 
 4.24 
 
232 
 
 STEAM ENGINES AND BOILERS. 
 
 Pressure 
 by the 
 Gauge. 
 
 Temperature. 
 
 Total 
 Heat above 
 32. 
 
 Latent 
 Heat. 
 
 Vol. of 
 one Ib. of 
 Steam. 
 
 90 
 
 330.9 
 
 1182.8 
 
 881.0 
 
 4.20 
 
 91 
 
 332. 
 
 1183. 
 
 881. 
 
 4.16 
 
 92 
 
 332. 
 
 1183. 
 
 880. 
 
 4.13 
 
 93 
 
 333. 
 
 1184. 
 
 880. 
 
 4.09 
 
 94 
 
 334. 
 
 1184. 
 
 879. 
 
 4.06 
 
 95 
 
 334.4 
 
 1183.9 
 
 878.5 
 
 4.02 
 
 96 
 
 335. 
 
 1184. 
 
 878. 
 
 4.00 
 
 97 
 
 336. 
 
 1184. 
 
 878. 
 
 3.97 
 
 98 
 
 336. 
 
 1185. 
 
 877. 
 
 3.93 
 
 99 
 
 337. 
 
 1185. 
 
 877. 
 
 3.90 
 
 100 
 
 337.6 
 
 1184.9 
 
 876.0 
 
 3.86 
 
 101 
 
 338. 
 
 1185. 
 
 876. 
 
 3.83 
 
 102 
 
 339. 
 
 1185. 
 
 875. 
 
 3.80 
 
 103 
 
 340. 
 
 1186. 
 
 875. 
 
 3.77 
 
 104 
 
 340. 
 
 1186. 
 
 874. 
 
 3.74 
 
 105 
 
 340.9 
 
 1185.9 
 
 873.8 
 
 3.71 
 
 106 
 
 342. 
 
 1186. 
 
 873. 
 
 3.68 
 
 107 
 
 342. 
 
 1186. 
 
 873. 
 
 3.65 
 
 108 
 
 343. 
 
 1186. 
 
 872. 
 
 3.63 
 
 109 
 
 343. 
 
 1187. 
 
 872. 
 
 3.60 
 
 110 
 
 343.9 
 
 1186.8 
 
 871.4 
 
 3.57 
 
 111 
 
 345. 
 
 1187. 
 
 871. 
 
 3.55 
 
 112 
 
 345. 
 
 1187. 
 
 871. 
 
 3.52 
 
 ' 113 
 
 346. 
 
 1187. 
 
 870. 
 
 3.50 
 
 114 
 
 346. 
 
 1188. 
 
 870. 
 
 3.47 
 
 115 
 
 346.9 
 
 1187.7 
 
 869.3 
 
 3.45 
 
 116 
 
 348. 
 
 1188. 
 
 869. 
 
 3.43 
 
 117 
 
 348. 
 
 1188. 
 
 868. 
 
 3.40 
 
 118 
 
 349. 
 
 1188. 
 
 868. 
 
 3.38 
 
 119 
 
 349. 
 
 1189. 
 
 868. 
 
 3.35 
 
 120 
 
 349.8 
 
 1188.6 
 
 867.1 
 
 3.33 
 
 121 
 
 350. 
 
 1189. 
 
 867. 
 
 3.31 
 
 122 
 
 351. 
 
 1189. 
 
 866. 
 
 3.28 
 
 123 
 
 352. 
 
 1189. 
 
 866. 
 
 3.26 
 
 124 
 
 352. 
 
 1189. 
 
 865. 
 
 3.23 
 
 125 
 
 352.6 
 
 1189.5 
 
 864.9 
 
 3.21 
 
 126 
 
 353. 
 
 1190. 
 
 865. 
 
 3.19 
 
 127 
 
 354. 
 
 1190. 
 
 864. 
 
 3.17 
 
APRENDIX. 
 
 233 
 
 Pressure 
 by the 
 Gauge. 
 
 Temperature. 
 
 Total 
 Heat above 
 32. 
 
 Latent 
 Heat. 
 
 Vol. of 
 one Ib. of 
 Steam. 
 
 128 
 
 354. 
 
 1190. 
 
 864. 
 
 3.14 
 
 129 
 
 355. 
 
 1190. 
 
 863. 
 
 3.12 
 
 130 
 
 355.4 
 
 1190.3 
 
 863.0 
 
 3.10 
 
 131 
 
 356. 
 
 1191. 
 
 863. 
 
 3.08 
 
 132 
 
 357. 
 
 1191. 
 
 862. 
 
 3.06 
 
 133 
 
 357. 
 
 1191. 
 
 862. 
 
 3.05 
 
 134 
 
 358. 
 
 1191. 
 
 861. 
 
 3.03 
 
 135 
 
 358.0 
 
 1191.1 
 
 861.0 
 
 3.01 
 
 136 
 
 359. 
 
 1191. 
 
 861. 
 
 2.99 
 
 137 
 
 359. 
 
 1192. 
 
 860. 
 
 2.97 
 
 138 
 
 360. 
 
 1192. 
 
 860. 
 
 2.96 
 
 139 
 
 360. 
 
 1192. 
 
 860. 
 
 2.94 
 
 140 
 
 360.7 
 
 1191.9 
 
 859.1 
 
 2.92 
 
 141 
 
 361. 
 
 1192. 
 
 859. 
 
 2.90 
 
 142 
 
 362. 
 
 1192. 
 
 858. 
 
 2.88 
 
 143 
 
 362. 
 
 1192. 
 
 858. 
 
 2.87 
 
 144 
 
 363. 
 
 1193. 
 
 858. 
 
 2.85 
 
 145 
 
 363.2 
 
 1192.7 
 
 857.2 
 
 2.83 
 
 146 
 
 364. 
 
 1193. 
 
 857. 
 
 2.81 
 
 147 
 
 364. 
 
 1193. 
 
 857. 
 
 2.80 
 
 148 
 
 365. 
 
 1193. 
 
 856. 
 
 2.78 
 
 149 
 
 365. 
 
 1193. 
 
 856. 
 
 2.77 
 
 150 
 
 365.7 
 
 1193.4 
 
 855.4 
 
 2.75 
 
 NOTE. Although the quantities in the table are not carried out to as many 
 significant figures as in many tables, they are sufficiently exact for practical 
 purposes. The volumes have been calculated upon the assumption that the 
 mechanical equivalent is 778, instead of 772. All the volumes have been calcu- 
 lated up to 201bs. pressure; above that they have been calculated only every 
 five pounds, and the intermediate values interpolated. 
 
234 
 
 STEAM ENGINES AND BOILERS, 
 
 TABLE II. 
 
 HYPERBOLIC LOGARITHMS. 
 
 Number. 
 
 Hyperbolic 
 Logarithm. 
 
 Number. 
 
 Hyperbolic 
 Logarithm. 
 
 Number. 
 
 i 
 
 Hyperbolic 
 Logarithm. 
 
 Number. 
 
 Hyperbolic 
 Logarithm. 
 
 1.0 
 
 0.00 
 
 3.5 
 
 .25 
 
 6.0 
 
 1.79 
 
 8.5 
 
 2.14 
 
 1.1 
 
 0.10 
 
 3.6 
 
 .28 
 
 6.1 
 
 1.81 
 
 8.6 
 
 2.15 
 
 1.2 
 
 0.18 
 
 3.7 
 
 .31 
 
 6.2 
 
 1.82 
 
 8.7 
 
 2.16 
 
 1.3 
 
 0.26 
 
 3.8 
 
 .34 
 
 6.3 
 
 1.84 
 
 8.8 
 
 2.17 
 
 1.4 
 
 0.34 
 
 3.9 
 
 .36 
 
 6.4 
 
 1.86 
 
 8.9 
 
 2.19 
 
 1.5 
 
 0.41 
 
 
 
 6.5 
 
 1.87 
 
 
 
 1.6 
 
 0.47 
 
 4.0 
 
 .39 
 
 6.6 
 
 1.89 
 
 9.0 
 
 2.20 
 
 1.7 
 
 0.53 
 
 4.1 
 
 .41 
 
 6.7 
 
 1.90 
 
 9.1 
 
 2.21 
 
 1.8 
 
 0.59 
 
 4.2 
 
 .44 
 
 6.8 
 
 1.92 
 
 9.2 
 
 2.22 
 
 1.9 
 
 0.64 
 
 4.3 
 
 1.46 
 
 6.9 
 
 1.93 
 
 9.3 
 
 2.23 
 
 
 
 4.4 
 
 1.48 
 
 
 
 9.4 
 
 2.24 
 
 2.0 
 
 0.69 
 
 4.5 
 
 1.50 
 
 7.0 
 
 1.95 
 
 9.5 
 
 2.25 
 
 2.1 
 
 74 
 
 4.6 
 
 1.53 
 
 7.1 
 
 1.96 
 
 9.6 
 
 2.26 
 
 2.2 
 
 0.79 
 
 4.7 
 
 1.55 
 
 7.2 
 
 1.97 
 
 9.7 
 
 2.27 
 
 2.3 
 
 0.83 
 
 4.8 
 
 1.57 
 
 7.3 
 
 1.99 
 
 9.8 
 
 2.28 
 
 2.4 
 2.5 
 
 0.88 
 0.92 
 
 4.9 
 
 1.59 
 
 7.4 
 7.5 
 
 2.00 
 2.01 
 
 9.9 
 
 2.29 
 
 2.6 
 
 0.96 
 
 5.0 
 
 1.61 
 
 7.6 
 
 2.03 
 
 10.0 
 
 2.30 
 
 2.7 
 
 0.99 
 
 5.1 
 
 .63 
 
 7.7 
 
 2.04 
 
 10.1 
 
 2.31 
 
 2.8 
 
 1.03 
 
 5.2 
 
 .65 
 
 7.8 
 
 2.05 
 
 10.2 
 
 2.32 
 
 2.9 
 
 1.06 
 
 5.3 
 
 .67 
 
 7.9 
 
 2.07 
 
 10.3 
 
 2.33 
 
 
 
 5.4 
 
 .69 
 
 
 
 10.4 
 
 2.34 
 
 3.0 
 
 1.10 
 
 5 5 
 
 .70 
 
 8.0 
 
 2.08 
 
 10.5 
 
 2.35 
 
 3.1 
 
 1.13 
 
 5.6 
 
 .72 
 
 8.1 
 
 2.09 
 
 10.6 
 
 2.36 
 
 3.2 
 
 1.16 
 
 5.7 
 
 .74 
 
 8.2 
 
 2.10 
 
 10.7 
 
 2.37 
 
 3.3 
 
 1.19 
 
 5.8 
 
 1.76 
 
 * 8.3 
 
 2.12 
 
 10.8 
 
 2.38 
 
 3.4 
 
 1.22 
 
 5.9 
 
 1.78 
 
 8.4 
 
 2.13 
 
 10.9 
 
 2.39 
 
APPENDIX. 
 
 235 
 
 o 
 
 ri I 
 
 i- 5 
 
 iJ 
 
 H 
 
 8 
 
 
 
 jo earn 
 
 
 f^ o ^s oc i> 
 
 
 
 
 <M O CJ L^ <> O -rf CO TM I-H O Ci QO l^- <X> >O ^ 
 
 
 
 '-^OGOt^ 
 
 
 
 
 'O^ 
 
 
 
 
 
 OOOOOOOOOOOOOOOOO<N 
 
 i-HT-(^HT-lrHr-'i-li-Hr-(THCM(M 
 
236 
 
 STEAM ENGINES AND BOILERS. 
 
 TABLE IV. 
 
 HEATING POWER OF FUELS. 
 
 COMBUSTIBLE. 
 
 C 
 
 H 
 
 
 
 N 
 
 Q 
 
 Ash. 
 
 %%*i 
 
 D - 0> 3 
 ^ A & 
 
 Wood, air dried 
 Peat 
 
 40.4 
 40.8 
 46.1 
 
 86.5 
 
 84.9 
 
 85.3 
 50.1 
 643 
 83.78 
 82.12 
 77.90 
 78.53 
 
 69.80 
 
 83.74 
 82.70 
 
 72 29 
 
 79.81 
 91.50 
 
 81.32 
 
 4.90 
 3.30 
 4.60 
 
 12.00 
 
 13.70 
 
 13.90 
 3.90 
 4.20 
 4.79 
 5.31 
 5.32 
 5.61 
 
 5.26 
 
 4.52 
 
 4.77 
 
 6.53 
 
 5.98 
 3.50 
 
 32.70 
 26.30 
 23.60 
 
 1.50 
 
 1.40 
 
 0.80 
 13.70 
 10.00 
 4.15 
 5.69 
 9.53 
 9.69 
 
 8.35 
 
 0.54 
 
 8.81 
 
 8.28 
 
 4.80 
 2.60 
 
 0.90 
 1.00 
 1.00 
 
 
 
 1.20 
 7.70 
 1.50 
 
 6400 
 6800 
 7600 
 
 19800 
 
 19200 
 
 18100 
 10300 
 11000 
 15100 
 15200 
 14600 
 14900 
 
 12600 
 
 14400 
 14000 
 
 13400 
 
 14400 
 15200 
 
 12200 
 
 " air dried 
 Petroleum, crude, 
 from Baker, Russia 
 Petroleum, heavy 
 crude, from Penn- 
 sylvania 
 Petroleum, common, 
 from Virginia 
 Lignite, American 
 *' Australian... 
 Coal Welsh 
 
 0.90 
 1.00 
 98 
 1.35 
 1.30 
 1.00 
 
 1.33 
 
 1.50 
 1.74 
 
 1.50 
 1.50 
 
 1.50 
 0.60 
 1.43 
 1.24 
 1.44 
 1.11 
 
 2.02 
 
 1.60 
 0.98 
 
 0.43 
 1.35 
 
 0.67 
 
 13.20 
 10.00 
 4.91 
 3.77 
 
 4.88 
 4.03 
 
 6.90 
 
 6.63 
 1.00 
 
 2.72 
 
 6.48 
 
 10.96 
 
 *' Newcastle 
 
 " Lancashire 
 ' Scotch 
 
 " Big Muddy, 
 " Jackson Co., Ill 
 " Johnson Co., 
 Arkansas 
 11 Block Id 
 
 " Hocking Valley, 
 Ohio 
 
 " Coking, Pitts- 
 burgh, Pa 
 " Anthracite 
 " Penn- 
 sylvania, Buck- 
 wheat 
 
 C means per cent of carbon contained in the combustible ; 
 H, the per cent of hydrogen ; O, the per cent of oxygen; N, 
 the per cent of nitrogen, and S, the per cent of sulphur. 
 
PROB LEMS. 
 
 1. How much work is done in lifting a weight of 20 Ibs. 
 through a height of 20 ft. ? Ans., 400 ft. -Ibs 
 
 2. How much work is done in moving a weight of 
 100 Ibs. along a horizontal plane surface against a resist- 
 ance of 10 Ibs. through a distance of 6 ft.? 
 
 Ans., 60ft.-lbs. 
 
 3. If the resistance to be overcome on a railroad is 
 10 Ibs. for each ton of weight of the cars, what horse- 
 power will be required to move a train of cars weighing 
 100 tons at a speed of 40 miles per hour? 
 
 Ans., 107 horse-power. 
 
 4. How many units of heat per minute are equivalent 
 to one horse-power? Ans., 42.4. 
 
 5. A piece of iron weighing 5 Ibs. is heated to 212 de- 
 grees and then dropped into a vessel containing 16.5 Ibs. 
 of water at 60 degrees. If the temperature of the water 
 is increased 5 degrees by the heat from the iron, what is 
 the specific heat of the iron? Ans., 0.112. 
 
 6. The specific heat, c p , of air at constant pressure, ex- 
 pressed in heat units, is 0.24. What is the specific heat 
 expressed in ft. -Ibs. at constant pressure, K p , and at con- 
 stant volume, K y l 
 
 Ans., K p = 186.7 ft.-lbs., K,= 134.4 ft.-lbs. 
 
 7. A quantity of air at a temperature of 60 degrees 
 under a pressure of 14.7 Ibs. per square inch, has a volume 
 of 5 cubic feet. What is the volume of the same air 
 
 (237) 
 
238 STEAM ENGINES AND BOILERS. 
 
 when its temperature is changed to 120 degrees at con- 
 stant pressure? Ans., 5.57 cub. ft. 
 
 8. The volume of a quantity of air at a temperature of 
 60 degrees under a pressure of 14.7 Ibs. per square inch 
 is 10 cub. ft. What is the volume of the same air when 
 the pressure is changed at constant temperature to 60 
 Ibs. per square inch? Ans., 2.45 cub. ft. 
 
 9. Assume that the initial pressure, volume, and abso- 
 lute temperature of a gas are P lf V ly and 7\; and that 
 after a change the final pressure, volume, and absolute 
 temperature are P 2 , V 2 and T 2 . Prove that 
 
 Let the pressure remain constant at P l while the tem- 
 perature is changed from 7\ to T 2 . The volume will 
 change from V t to some volume that we may call V . 
 From (7) we have 
 
 V l V 
 
 (a) -Y=~r 
 
 1 1 1 2 
 
 Now let the absolute temperature remain constant at 
 T 2 while the pressure is changed from P l to P 2 . The 
 volume will change during this change of pressure from 
 V to V 2 . From (8) we have 
 
 (b) P, V> = P 2 V 2 . 
 Multiply (a) by (b) and we have 
 
 P, V l V P 2 V 2 V 
 
 10. The volume of a quantity of air at 70 degrees 
 under a pressure of 16 Ibs. per square inch is 20 cubic 
 feet. What is the temperature of this air when the vol- 
 ume is 4 cubic feet and the pressure is 70 Ibs. per square 
 inch? ' Ans., T= 464.6, and * = 3.6. 
 
PROBLEMS. 239 
 
 11. What is the weight of the quantity of air which 
 occupies a volume of 10 cubic feet at a temperature of 
 100 degrees under a pressure of 50 Ibs. per square inch? 
 
 When the pressure is in pounds per square foot, we know 
 
 P V 
 thatjr- w 53.15, where w is the weight of the air in 
 
 __ PV 50X144X10 
 
 pounds. . 53357- (461 + 10 0) 53.15= 2 ' 4 
 
 12. How much work is done by a quantity of air while 
 expanding under a constant pressure of 80 Ibs. per square 
 inch from a volume of 2 cubic feet to a volume of 6 cubic 
 feet? 
 
 For expansion at constant pressure, the work is equal 
 to the pressure per square foot multiplied by the change 
 of volume, or 
 
 P = 80X144, F 2 = 6, 
 Work = 80X144 (6 -2) = 46080 ft.-lbs. 
 
 13. How much heat, expressed in foot-pounds, must be 
 given to the air during the expansion in Problem 12? 
 
 We know that H = S + L + W. For a perfect gas whose 
 weight is w we know that S = wK v (T 2 7\),andL = O. 
 In this case W = P l (V 2 -V 1 ). Therefore, 
 
 H=WK V (Tt-Tj+Pt (vvj. 
 
 But 
 P l V 2 = R w T 2 and P, V, = R w 7\. Hence w T 2 = ?^l and 
 
 p y 
 w 7\ = L . Put for w T 2 and w 7\ their values and get 
 
240 STEAM ENGINES AND BOILERS. 
 
 Hence, 
 
 H=P 1 (F 3 -.y i )^j = 80Xl44(6-.2)|g 
 
 = 158,500 ft.-lbs. 
 
 14. How much heat is given to a quantity of air while 
 
 P P 
 it changes in such a manner that 7-=-^, from an initial 
 
 volume of 9.23 cubic feet under a pressure of 100 Ibs. 
 per square inch, to a volume of 18.46 cubic feet under a 
 pressure of 200 Ibs. per square inch? 
 
 * 
 
 As before, H = S + W; and 
 S = w K v (T 2 rj; where 
 w is the weight of the air; 
 T 2 the final absolute tem- 
 perature; and Tj the initial 
 absolute temperature. 
 
 W=area abed, in the figure, 
 
 * 
 4 
 
 P V 
 - 2 , and T,= ^-^. Therefore, 
 
 w 
 
 _P 2 V 2 -P 1 V 1 
 H= 
 
 200 X 144 X 18.46 - 100 X 144 X 9.23 
 1.41 - 1 
 
 300X144(18.46-9.23) 
 2 
 
 1,172,000 ft.-lbs. 
 
PROBLEMS. 241 
 
 15. What fraction of the heat in Problem 14 is trans- 
 formed into work? Ans., 0,17. 
 
 16. How much heat must be given to a quantity of air 
 which expands isothermally, at a temperature of 60 de- 
 grees, from a valume of 0.83 cubic feet under a pressure 
 of 60 Ibs. per square inch, to a volume of 3 cubic feet? 
 
 Here, no heat is required to change the temperature of 
 
 the air ; all is used in doing ex- 
 ternal work. 
 
 W=area abed, in the figure, 
 = P 1 F 1 hyp. log. ~\ 
 
 Ans., 9180 ft.-lbs. 
 
 17. How much heat in ft.-lbs. must be given to 1.3 
 cubic feet of air which is heated at constant volume from 
 an absolute temperature of 520 degrees under a pressure 
 of 2 Ibs. per square inch, to an absolute temperature of 
 1000 degrees? 
 
 Since the volume is kept constant, the external work is 
 zero and 
 
 w =-^V Hence 
 K 1 
 
 P V K 
 
 _ _ 
 
 -^ 1.41-1 0.41' 
 
 2X144X1.8 (1000-520), ft 
 
 520 X 0.41 
 16 
 
242 STEAM ENGINES AND BOILERS. 
 
 . 18. How many heat units are given to the air in Prob- 
 lem 17? Ans., 1.08. 
 
 19. In which is there the greater amount of energy: 
 1 Ib. of air at 60 degrees, under a pressure of 100 Ibs. per 
 square inch, or 1 Ib. of air at 60 degrees under a pressure 
 of 15 Ibs. per square inch? Give the reasons for your 
 answer. 
 
 20. Given a quantity of air whose volume is 3 cubic feet 
 at 60 degrees under a pressure of 45 Ibs. per square inch. 
 What is the volume and temperature of this air after it is 
 expanded adibatically until its. pressure is 15 Ibs. per 
 square inch? 
 
 I V = 6.54 cub. ft. 
 
 [ 7 = 378.6; and *=-82.4. 
 
 21. (a) What is the work done during the expansion in 
 Problem 20? (b) What is the heat, in heat units, con- 
 verted into work? 
 
 j (a) 13,170 ft.-lbs. 
 '" ( (b) 16.9 heat units. 
 
 22. Given a quantity of air whose volume is 2 cubic 
 feet at a temperature of 60 degrees under a pressure of 
 80 Ibs. per square inch, (a) What is the weight of the 
 air? (b) What will be the temperature and pressure if 
 the air be expanded adibatically until its volume is 8 
 cubic feet? (c) How much work will be done during 
 this expansion? (d) How much work will be. done if the 
 air be expanded isothermally until its volume is 8 cubic 
 feet? 
 
 Ans., (a) 0.83 Ibs. (b) -166 degrees and 11.3 Ibs. per 
 sq. in. (c) 24,450 ft.-lbs. (d) 32,000 ft.-lbs. 
 
 23. (a) What is the temperature of the steam in a boiler 
 
PROBLEMS. 243 
 
 whose gauge pressure is 90 Ibs.? (b) What is the weight 
 of one cubic foot of the steam? j (a) 330.9 degrees. 
 
 '* | (b) 0.238 Ibs. 
 
 24. How many heat untis are required to heat 16 Ibs. 
 of water from an initial temperature of 60 degrees and 
 evaporate it under a pressure of 30 Ibs. by the gauge? 
 
 Ans., 18,200. 
 
 25. The temperature of the water entering a boiler, in 
 which the gauge pressure is 60 Ibs. per square inch, is the 
 same as the temperature of the steam in the boiler, (a) 
 What is the external work done in evaporating one pound 
 of water? (b) What is the internal work done in evapo- 
 rating one pound of water? . ( (a) 62,300 ft. -Ibs. 
 
 5 ' I (b) 636,600 ft.-lbs. 
 
 26. Given a quantity of air whose temperature is 80 
 degrees; whose pressure is 100 Ibs. per square inch; and 
 whose volume is 2.2 cubic feet. It is made to pass through 
 the following Carnot cycle: It is expanded isothermally 
 until its volume is 4.0 cubic feet; then expanded adia- 
 batically until its temperature is 30 degrees; then com- 
 pressed isothermally; and'finally it is compressed adibat- 
 ically until its volume, pressure, and absolute tempera- 
 ture are the same as at the beginning of the cycle, (a) 
 What is the total quantity of heat, H, given to the air? 
 (b) What is the heat, U, taken from the air? (c) What 
 is the work, W, done during the cycle? (d) What is the 
 efficiency, E, of the cycle? 
 
 H= P t Vi hyp. log. pS- 19,000 ft.-lbs. 
 
 U - P,V, hyp. log. = Pl ft TZ hyp. log. 
 
 V 4 * 1 V I 
 
 = 17,300 ft.-lbs. 
 W=H [7=1,700 ft.-lbs. 
 
 E = ^ = Z>zl? = 0.093. 
 ti l 
 
244- STEAM ENGINES AND BO-ILERS. 
 
 27. One pound of air is made to pass through the fol- 
 lowing cycle: It is expanded at constant pressure; then 
 expanded isothermally; then compressed at constant 
 pressure; and then compressed isothermally until the 
 cycle is completed. What are the expressions for H, U, 
 and E? 
 
 The work diagram is shown 
 in the figure. Let the co-or- 
 dinates of a be V lf P lt 7\; of 
 b be I/ 2 , P lt T 2 ; of c be F 3 , 
 P 2 , 7 2 ; and of d be F 4 , P 2 , 7\. 
 
 During the expansion from 
 a to b the heat given to the 
 pound of air is K v (T 2 7\) + 
 P l (V 2 Vj)', and during the 
 expansion from b to c the heat given to the air is 
 
 PI V 2 hyp. log. ~. Adding these expressions we have that 
 
 "2 
 
 the total heat, H, given to the air is 
 
 H = K, (T 2 - TO +P l (V 2 -VJ +P, V 2 hyp. log. ^ 
 
 2 
 
 p (V V } P 
 
 __- t lV^2 *' \ T> /T7 T7 \ i T) T7 ?.>, 7^^ * 1 
 
 r i 
 
 PI (F 2 FO r 
 
 During the compression from c to d the heat taken from 
 the air must be the same that would be put into it during 
 expansion from d to c, or K v (T 2 7\)+P 2 (V 3 F 4 ); and 
 the heat taken from the air during compression from d to a 
 is 
 
 P l VJL hyp. log. ~. Therefore, the heat, 17, taken from 
 
 the air is 
 
 V- K- T (r, T.) +p t (V,VJ+P 1 V.hyp.log.^. 
 
 . log. &. 
 - 
 
PROBLEMS. 245 
 
 Since P 2 V 3 = P l V 2 , and P 2 V, = P l V lt we have 
 
 P,(V 9 V 4 )^P l (V 9 V l )' t and 
 
 p (Y _ y \ p 
 
 V- ' ( r . + p i (Vf-V^+P, V, hyp. log. 
 
 / ^2 
 
 - Pl ( ^~ Fl) r + P, V. hyp. log. 
 
 r L ^2 
 
 W- HU=P l (VVJ hyp. log. ^ 
 
 ^2 
 W 
 
 28. If in Problem 27, the weight of air used is 0.25 Ib. ; 
 P l is 11,520 Ibs. per square foot; P 2 is 2,200 Ibs. per square 
 foot; Y! is 0.61 cubic foot; and V 2 is 2 cubic feet;, what 
 will H, U, W, and E equal? 
 
 Since the expressions derived for H, U, W, and E, in- 
 volve only the pressures and volumes of the gas, the 
 weight need not be considered. Substitute the values of 
 P lt Vj, and P 2 in the expressions for H, U, W, and E and 
 get: H = 93,300; U= 66,700; W = 26,600; and = 0.285. 
 
 29. Find the expressions for H, U, W, and E, for one 
 pound of air working according to the following cycle: 
 It is heated at constant volume; then expanded adiabati- 
 cally; then compressed at constant pressure to its initial 
 condition. 
 
 The work diagram is shown in the figure. The co-ordi- 
 nates of a are P lt V lt 7\; of 6, P 2 , V lt T 2 ; and of c, P lt 
 V 2 , TV 
 
 During the change from a to 
 b the air is heated at constant 
 volume, no work is done, and the 
 heat put in during this change is 
 /Y V (T 2 7\). During the change 
 from b to c no heat is either given 
 to, or emitted by, the air. Dur- 
 v ing the change from c to a the 
 
246 STEAM ENGINES AND BOILERS. 
 
 same amount of heat is taken from the body that must be 
 given to it for a change from a to c, or, 
 
 Therefore we have 
 
 TT i<r (T T \ l \ 2 *' 
 ri = Kv(l 2 li) = - j 
 
 T L 
 
 t/=/C (TTJ +P, (VVJ, 
 
 W=H U. 
 
 W 
 E-IJJ. 
 
 30. In Problem 29 let P t be 15 Ibs. per square inch; P 2 
 be 80 Ibs. per square inch; V l be 1.3 cubic feet; and V 2 be 
 4.26. Find the values of H, U, W, and E. 
 
 # = 29,700; 7=22,000; ^=7,700; and = 0.26. 
 
 31. Deduce the expressions for H, U, and W for one 
 pound of air for the following cycle: Air expanded at 
 constant pressure, P lf from V l to V 2 ; then expanded 
 adiabatically from V 2 to F 3 ; then compressed at constant 
 pressure, P 2 , from V 3 to V 4 \ then compressed adiabati- 
 cally to its initial condition. 
 
 r-i 
 
 32. In Problem 31, let P t be 12,000 Ibs. per square foot; 
 P 2 be 3,000 Ibs. per square foot; V l be 0.8 cubic foot; and 
 
PROBLEMS. 247 
 
 V 3 be 3.2 cubic feet; and determine the values of H, U 9 
 W, and E. 
 
 # = 99,000; 7 = 66,200; VT = 32,800; and =0.33 
 
 33 Determine the horse-power of a double-acting 
 engine whose cylinder is 13 inches in diameter and which 
 has an 18-inch stroke, when making 220 revolutions per 
 minute while taking steam at 80 Ibs by the gauge and 
 cutting off at \ stroke. Neglect the clearance and as- 
 sume that the mean back pressure is 20.5 absolute. 
 
 Ans., 96.7 horse-power. 
 
 34. An engine has a clearance volume which is 0.08 of 
 the volume swept through by the piston per stroke. If 
 the steam be cut off at stroke, what will be the num- 
 ber of times it is expanded? Ans., 3.86 times. 
 
 35. Assume that the mean back pressure is 19 Ibs. 
 absolute, and that the clearance volume is 10 per cent, of 
 the volume swept through by the piston per stroke; and 
 determine the horse-power developed by a double-acting 
 engine, whose cylinder is 12 inches in diameter and has 
 a 14-inch stroke, when making 260 revolutions per minute, 
 while taking steam at 70 Ibs. by the gauge and cutting off 
 at | stroke. Ans., 97 horse-power. 
 
 36 What is the weight of the steam used per stroke 
 by the engine in Problem 33? Ans., 0.075 Ibs. 
 
 37. Neglect the clearance volume of the engine in 
 Problem 35, and determine the weight of steam used per 
 hour per indicated horse-power Ans., 22.8 Ibs. 
 
 On account of the loss by condensation and other causes, 
 the weight of steam actually used per hour per indicated 
 horse-power will be from \ to J greater than 22.8 Ibs., or 
 between 27 and 31 pounds 
 
248 STEAM ENGINES AND BOILERS. 
 
 38. Assume that the temperature of the water entering 
 the boiler is 150 degrees, and determine the efficiency of 
 the steam in Problem 33. Ans., = 0.117 
 
 39. If it were possible to use the steam in a perfect 
 engine, working according to the Carnot cycle, between 
 the same limits of temperatures as in Problem 38, what 
 would the efficiency, be? Ans., 0.22. 
 
 40. The cylinders of a locomotive are 19 inches in 
 diameter and have a 24-inch stroke; the driving wheels 
 are 7 feet in diameter; and the mean back pressure against 
 which the pistons work is 19 Ibs. absolute. Determine 
 the horse -power developed by the locomotive when taking 
 steam at 150 Ibs. by the gauge and cutting off at f stroke, 
 while traveling at a speed of 40 miles per hour. 
 
 The number of revolutions made per minute by each 
 driving wheel is equal to the number of feet in one mile, 
 5,280, multiplied by the number of miles traveled per 
 hour, and divided by 60 times the circumference of one 
 
 , . . 5280X40 ^ 
 
 dnvmg wheel, ^ n IAW = l^O. Horse-power = 1458. 
 OU X o. 
 
 41. Assume the mean effective pressure to be 40 Ibs., 
 the number of revolutions to be 75 per minute, and the 
 length of stroke to be 42 inches; and detemine the dia- 
 meter of the cylinder of a double-acting engine which 
 will develop 200 horse-power. Diameter = 20 inches. 
 
 42. If the mean back pressure is 20 Ibs. absolute, how 
 many times must steam at an initial pressure of 80 Ibs. 
 by the gauge, be expanded in order that the mean effect- 
 ive pressure shall be 40 Ibs.? 
 
PROBLEMS. 249 
 
 Here we have 
 
 hyp. lg> r = 0.632 rl. 
 
 In order to solve this we must assume various values of r 
 and try them in the equation, we shall finally get a value 
 of r that will satisfy it. 
 
 If r= 3, hyp log. r=1.10; and we have 1.10> 1.89-1 
 
 " r = 4, " " =1.39; " 1.39<2.52-1 
 
 " r = 3.5, " " =1.25; " " 1.25>2.21-1 
 
 " r = 3.6, " " =1.28; " 1.28>2.27-1 
 
 " r = 3.7, " " =1.31; " 1.3K2.34-1 
 r is equal to 3.6, about. 
 
 43 About how many revolutions per minute should be 
 made by an automatic high speed engine whose stroke is 
 18 inches? Ans., 218. 
 
 44. About what should be the diameter of the cylinder 
 of an automatic high-speed engine whose stroke is 16 
 inches? Ans., 12 inches. 
 
 45. About what should be the length of the connecting 
 rod of an automatic high-speed engine whose stroke is 
 14 inches? Ans., 35 inches. 
 
 46. About how many revolutions per minute should be 
 made by a Corliss engine whose stroke is 42 inches? 
 
 Ans., 67. 
 
 47. About what should be the diameter of the cylinder 
 of a Corliss engine whose stroke is 36 inches? 
 
 Ans., 18 inches. 
 
 48. About what should be the length of the connecting 
 rod of a Corliss engine whose stroke is 54 inches? 
 
 Ans., 162 inches. 
 
 49. How does increasing the angle of advance affect 
 
250 STEAM ENGINES AND BOILERS. 
 
 the lead, the point of cut-off, and the point of compression? 
 
 50. Through what distance will the valve move, if the 
 eccentric be turned through an angle equal to the angle 
 of advance? 
 
 51. What must be done to make the cut-off occur later, 
 on a single-valve engine, and not change the point of re- 
 lease or the point of compression ? 
 
 52.* Find the steam lap and the lead of a valve, whose 
 travel is 4J inches, that admits steam when the piston is 
 yij-g- of the stroke before the beginning of the forward 
 stroke, and that cuts off at $ of the stroke. 
 
 Ans., Lap= 1J in.; 
 
 53. Find the steam lap and the lead of a valve, whose 
 travel is 4 inches, that admits steam when the piston is 
 iff of the stroke before the beginning of the forward stroke , 
 ^nd that cuts off at of the stroke. 
 
 Ans., Lap= IJf in.; lead = T 5 T in. 
 
 54. Steam is admitted when the piston is at the begin- 
 ning of the stroke and is cut off at J of the stroke, by a 
 valve whose steam lap is 2J inches. Find the lead, the 
 eccentricity, and the angle of advance. 
 
 Ans., Lead=0; eccentricity = 3 in.; angle of advance 
 = 45. 
 
 55. Steam is admitted when the piston is -jj-j of the 
 stroke before the beginning of the forward stroke, and is 
 cut off at J of the stroke, by a valve whose steam lap is 
 1 T \ inches. Find the lead, the eccentricity, and the angle 
 of advance. 
 
 Ans., Lead = /3- in.; eccentricity = If in.; angle of ad- 
 vance = 63- 15'. 
 
 56. Steam is admitted when the piston has made yj-g of 
 
 *In working the valve diagram problems it will be well to 
 make the crank circle 8 inches in diameter. 
 
PROBLEMS. 
 
 251 
 
 the stroke, and is cut off at -fy of the stroke, by a valve 
 whose lead is - -fa of an inch. Find the steam lap and the 
 eccentricity. Ans., Lap = If J in.; eccentricity = 2^| in. 
 
 There are some , special cases where the construction 
 shown in Fig. 45 fails, and other constructions must be 
 used. The most common case that occurs is when the line 
 eh is so nearly parallel to ef that it is impossible to deter- 
 mine with any accuracy their point of intersection, O' . In 
 such cases the construction must be exactly the same as 
 for Fig. 45 until the point h is fixed, then instead of draw- 
 ing the line eh draw kg, as shown in Fig. 45a. Then draw 
 dk through d parallel to hg, and continue it until it cuts fg 
 prolonged at k. Through k draw O'k cutting Ob at 6, and 
 efatO'. O'b is the steam lap. If O'd be drawn, the angle 
 it makes with Ob will be the required angle of advance. 
 O'd is the eccentricity. 
 
 If the lead be zero, the points 0, d, and e, in Figs. 45 and 
 45a will coincide. In this case the method of Fig. 45 fails 
 but the method shown in Fig. 45a may be used for the 
 
 FIG. 45a. 
 
252 
 
 STEAM ENGINES AND BOILERS. 
 
 solution of the problem. Sometimes it is preferable to use 
 the following method, indicated by Fig. 456: Since he 
 
 lead is zero we know that the crank is in the position OA 1 
 in Fig 456 when the steam is admitted. Let OB represent 
 the position of the crank at cut-off. Now we know that 
 the center of the eccentric is somewhere on the line, OD, 
 bisecting the angle BOA l . Assume any point, a, as a trial 
 center of the eccentric; and draw the valve circle aeO. 
 With O as a center draw the lap circle em, cutting Oa at m. 
 If Oa were the eccentricity and Oe the steam lap, the 
 maximum opening of the valve would be am. But am = 
 Oa Om = OaOe = Oa ( I cos DO A ) . Since the angle 
 DO A, is constant, we see that the maximum opening of 
 the valve is, in this case, directly proportional to the 
 eccentricity. Therefore, make Od equal to ma; and Oh 
 equal to the required maximum opening. Draw da; then 
 draw ha' parallel to da and cutting Oa at a'. Oa' is the 
 required eccentricity. Through a' draw a line perpendicu- 
 lar to OA, and cutting it at e f . Oe' is the required steam 
 lap. 
 
 In Problem 57 the student may use the regular construc- 
 tion shown in Fig. 45 or the construction shown in Fig. 45a. 
 In Problem 58 the regular construction fails, and the con- 
 struction shown in Fig. 45a or that in Fig. 456 must be 
 used. In Problem 59 it will probably be best to use the 
 construction shown in Fig. 45a. 
 
PROBLEMS. 253 
 
 57. Steam is cut off at f of the stroke by a valve whose 
 maximum opening is } of an inch, and whose lead is J of 
 an inch. Find the steam lap, the eccentricity, and the 
 angle of advance. 
 
 Ans., Lap=l in.; eccentricity = 1J in.; angle of ad- 
 vance = 40. 
 
 58. Steam is cut off at \ of the stroke by a valve whose 
 maximum opening is f of an inch, and whose lead is T 1 ^ 
 of an inch. Find the steam lap and the eccentricity 
 
 Ans., Lap= 1 T \ in.; eccentricity = 2^ in. 
 
 59. Steam is cut off at \ of the stroke by a valve whose 
 maximum opening is inch, and whose lead is zero. Find 
 the steam lap, and the eccentricity 
 
 Ans., Lap = 3^2 in.; eccentricity = 3|J in. 
 
 60. The sine of the angle of advance is J|, the eccen- 
 tricity is 2J inches, and the compression begins when the 
 piston has made -fj of the return stroke. Find the exhaust 
 lap and the point of release. 
 
 Ans., Lap=l T \ in.; release begins when the piston is 
 of the stroke from the end of the stroke. 
 
 61. The sine of the angle of advance is }, the eccen- 
 tricity is 2 inches, and the point of compression is ^f of 
 the stroke from the beginning ot the return stroke. Find 
 the exhaust lap and the point of release. 
 
 Lap=l 5 5 in.; release begins when the piston is T J^ of 
 the stroke from the end of the forward stroke. 
 
 62. The point of release is T f ff of the stroke before the 
 end of the forward stroke, compression begins at T \ of 
 the return stroke, and the eccentricity is 3 inches. Find 
 the exhaust lap and the angle of advance. 
 
 Lap =1 }f in.; angle of advance = 50-45 / . 
 
254 STEAM ENGINES AND BOILERS. 
 
 63. Find the center of suspension of the eccentric of 
 an automatic high-speed engine on which the cut-off 
 changes from | to f of the stroke, and the maximum 
 opening of the valve when cutting off ^ stroke is f of an 
 inch. The lead of the valve shall be -f s of an inch positive, 
 for cut-off at J the stroke ; zero, for cut-off at J the stroke ; 
 and T 3 F of an inch negative, for cut-off at f of the stroke. 
 
 64. For an indicator pendulum motion, such as is shown 
 in Fig. 52, what should be the shortest lengths of the 
 distances Be and BD in order to get a card 3 inches long 
 from an engine whose stroke is 18 inches? 
 
 Ans., Bc = 36in. 
 
 65. The indicator card taken from an engine whose 
 cylinder is 13 inches in diameter and which has a stroke 
 of 21 inches, is 3 r 3 ^ inches long, and has an area of 1.46 
 square inches. What was the horse-power developed by 
 the engine if the card were taken with an 80-lb. spring 
 while the engine was making 180 revolutions per minute? 
 
 Ans., 93 horse-power. 
 
 66. On an indicator card 3^ inches long, taken from 
 an engine whose cylinder is 13 inches in diameter and 
 whose stroke is 21 inches, the length of the line corre- 
 sponding to the line fg in Fig. 58 is 2f inches. If the 
 pressure corresponding to the point /, in Fig. 58, be 13 Ibs. 
 per square inch by the gauge, what is' the weight of steam 
 used per stroke by the engine? Ans., 0.0825 Ibs. 
 
 67. If the engine from which the card in Problem 66 is 
 taken, develop 93 indicated horse-power when making 180 
 revolutions per minute, what is the weight of steam used 
 per hour per indicated horse-power? Ans., 19.1 Ibs. 
 
PROBLEMS. 255 
 
 68. Assume c in (63) to be 0.85; E in (64) to be 9; P l 
 to be 105 Ibs., by the gauge; P 3 to be 8 Ibs. absolute; the 
 length of the stroke to be 20 inches; the number of revo- 
 lutions to be 200 per minute; and the ratio of the volume 
 of the low-pressure cylinder to that of the high-pressure 
 cylinder to be 3; and determine the diameters of the cyl- 
 inders of a compound-engine to develop 200 horse-power. 
 
 Diameter of low pressure cylinder = 20.7 in. 
 " " high " " = 12.0 in. 
 
 69. How many times is the steam expanded in the high 
 pressure cylinder in Problem 68? Ans., 3 times. 
 
 70. An engine takes steam at an initial pressure of 80 
 Ibs. by the gauge and expands it 3.7 times against a 
 mean back pressure of 18 Ibs. absolute. How much would 
 the horse-power of the engine be increased by the use of 
 a condenser which reduces the mean back pressure to 6 
 Ibs. absolute ? Ans., 29 per cent. 
 
 71. To what could the number of expansions of the 
 steam in the engine of Problem 70 be changed, and the 
 engine continue to do the same work with the condenser 
 that it did without? 
 
 From (68) we have 
 
 1 + j iy p m l og , r _ 1 + hyp, log. 3.7 18-6 _ 
 " ~~ ~~- 
 
 Therefore, we have 
 
 hyp. log. r = 0.50r-.l 
 If 
 
 r = 3 we ha 
 r 5 
 r = 6 " ' 
 r=5.5 " 
 r=5.4 " 
 r=5.3 " 
 r = 5.4, about. 
 
 ve 1.10> 1.50 1 
 1.61>2.50 1 
 1.79 <3. 00-1 
 1.70<2.75-1 
 1.69<2.70 1 
 1.67>2.65-1 
 
256 STEAM ENGINES AND BOILERS. 
 
 72. To what could the boiler pressure of the steam in 
 Problem 70 be reduced, and the engine continue to do the 
 same work with the condenser that it did without? 
 
 Ans., about 65 Ibs. by the gauge. 
 
 73. If the condensing water enters the condenser at 
 70 degrees and leaves it at 110 degrees, how many pounds 
 of water will be required to condense one pound of steam 
 exhausted from the engine in Problem 70? 
 
 Ans., 26.9 Ibs. 
 
 74. About what is the vacuum, in inches, of Mercury, 
 maintained by the condenser in Problem 70? 
 
 Ans. We may say that, roughly, the difference between 
 the pressure against which the steam is exhausted without 
 and with the condenser is equal to the difference between 
 the mean back pressures without and with the condenser, 
 or to 18 6=12 Ibs. That is, the pressure in the con- 
 denser is 12 pounds less than atmospheric pressure, or is 
 only 3 Ibs. absolute. This corresponds to a vacuum of 
 12X2 = 24 inches. 
 
 75. Calculate the factor of evaporation for a gauge 
 pressure of 75 Ibs. and an initial temperature of the feed 
 water of 135 degrees. 
 
 76. A boiler evaporates 5000 Ibs. of water per hour 
 from an initial temperature of 145 degrees, and under a 
 pressure of 80 Ibs. by the gauge. What is the equivalent 
 water evaporated per hour from and at 212 degrees? 
 
 *Ans., 5515 Ibs. 
 
 77. What is the boiler horse-power of a boiler which 
 evaporates 3080 Ibs. of water per hour from an initial 
 temperature of 135 degrees and under a pressure of 100 
 Ibs. by the gauge? Ans.. 100. 
 
 78. A boiler evaporates 3500 Ibs. of water per hour 
 from an initial temperature of 120 degrees and under a 
 
PROBLEMS. 257 
 
 pressure of 80 Ibs. by the gauge; a second boiler evap- 
 orates 4000 Ibs. of water from an initial temperature of 
 110 degrees and under a pressure of 60 Ibs. by the gauge. 
 Which of the two boilers utilizes the greater amount of 
 heat per hour? 
 
 79. Calculate the number of heat units evolved by the 
 complete combustion of one pound of coal which con- 
 tains 69.8 per cent, of carbon; 5.26 per cent, of hydrogen; 
 and 8.35 per cent, of oxygen. 
 
 Ans., 12,750 heat units. 
 
 80. Calculate the number of heat units evolved by the 
 complete combustion of one pound of petroleum which 
 contains 84.9 per cent, of carbon; 13.7 per cent, of hy- 
 drogen; and 1.40 per cent, of oxygen. 
 
 Ans., 20,700 heat units. 
 
 81. How many pounds of water can be evaporated 
 from and at 212 degrees by the heat evolved by the com- 
 plete combustion of one pound of coal containing 65.2 
 per cent, of carbon; 4.92 per cent, of hydrogen; and 8.64 
 per cent, of oxygen? Ans., 12.65 Ibs. 
 
 82. Assume that one cord of wood weighs 3000 Ibs. 
 and that each pound of wood will evolve 5000 heat units 
 when completely burned, and determine when it is cheaper 
 to buy wood than to buy the coal in Problem 81. 
 
 Cheaper to buy wood as long as one ton (2000 Ibs.) of 
 coal costs more than 1.57 as much as one cord of wood. 
 
 83. If 40 per cent, of the heat evolved by the combus- 
 tion of each pound of the coal in Problem 79 is lost, how 
 many pounds of coal will be required to evaporate 5650 
 Ibs. of water from an initial temperature of 130 degrees 
 and under a pressure of 80 Ibs. by the gauge? 
 
 Ans., 800 Ibs: 
 17 
 
258 STEAM ENGINES AND BOILERS, 
 
 84. Suppose that in burning the coal in Problem 81 it 
 is found that one-half only of the carbon is completely 
 burned, and that the other half is burned to carbon mon- 
 oxide ; what is the heat evolved per pound of coal burned ? 
 
 Ans., 8540 heat units. 
 
 85. How many pounds of air are required for the com- 
 plete combustion of one pound of coal containing 79.65 
 per cent, of carbon, 5.58 per cent, of hydrogen, and 4.64 
 per cent, of oxygen? Ans., 11.4 Ibs. 
 
 86. Assume that 20 Ibs. of .air at 60 degrees are ad- 
 mitted to a furnace for each pound of the coal in Problem 
 85 that is burned; that the specific heat of the gases in 
 the chimney is 0.24; and that the temperature of the 
 escaping gas is 430 degrees ; and determine the number of 
 heat units carried off by the gases per pound of coal burned. 
 
 All the carbon, hydrogen, and oxygen in the coal that 
 is burned is carried up the chimney. Therefore, the weight 
 of the gases carried up the chimney per pound of coal burned 
 is the weight of the air admitted per pound of coal plus 
 the weight of the combustible and volatile matter in the 
 coal, or it is 20 + 0.7965 + 0.0558 + 0.0464, equal 20.9 Ibs. 
 Heat carried off =1850 units. 
 
 87. Determine the area of the heating surface of a 
 return tubular boiler 66 inches in diameter, 16 ft. long, 
 and containing 98 tubes each 3 inch in diameter, that is 
 set so that of the -circumference of its shell is exposed 
 to the hot gases. Ans., 1414 sq. ft. 
 
 88. What would be the area of the heating surface of 
 the boiler in Problem 87 if it were set so that but of the 
 shell was exposed to the hot gases? Ans., 1368 sq. ft. 
 
 89. Assume 12 sq. ft. of heating surface per boiler 
 horse-power, and determine the horse-power of the boilers 
 in Problem 87 and 88. 
 
PROBLEMS. 
 
 259 
 
 90. Assume k in (90) to be J, and determine what will 
 be the velocity of the gases in a chimney 120 ft. high, 
 when the temperature of the gases is 450 degrees and that 
 of the air is 65 degrees. Ans., 25 ft. per second. 
 
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