Works of Prof. Robt. H. Thurston. Published by JOHN WILEY & SONS, 53 E. Tenth Street, New York. The Publishers and the Author will be grateful to any of the readers of this volume who will kindly call their attention to any errors of omission or of commission that they may find therein. It is intended to make our publications standard works of study and reference, and, to that end, the greatest accuracy is sought. It rarely happens that the early editions of works of any size are free from errors ; but it is the endeavor of the Publishers to see them removed immediately upon being discovered, and it is therefore desired that the Author may be aided in his task of revision, from time to time, by the kindly criticism of his readers. JOHN WILEY & SONS. 53 EAST TEXTH STREET, Works of Prof. Robt. H. Thnrston. Published by JOHN WILEY & SONS, 53 E. Tenth Street, New York. MATERIALS OF ENGINEERING. A work designed for Engineers, Students, and Artisans in wood, metal, and stone. Also as a TEXT-BOOK in Scientific Schools, show- ing the properties of the subjects treated. By Prof. R, H. Thurston. Well illustrated. In three parts. Part I. THE NON-METALLIC MATERIALS OF ENGINEER ING AND METALLURGY. With Measures in British and Metric Units, and Metric and Reduction Tables 8vo, cloth, $2 00 Part H. IRON AND STEEL. The Ores of Iron : Methods of Reduction ; Manufacturing Processes; Chemical and Physical Properties of Iron and Steel : Strength, Duc- tility. Elasticity and Resistance ; Effects of Time, Temperature, and repeated Strain ; Methods of Test ; Specifications ... 8vo, cloth, 3 .50 Part HI. THE ALLOYS AND THEIR CONSTITUENTS. Copper, Tin, Zinc, Lead, Antimony. Bismuth, Xickel, Aluminum, etc.: The Brasses. Bronzes; Copper-Tin-Zinc Alloys: Other Valuable Alloys: Their Qualities, Peculiar Characteristics: Uses and Special Adaptations: Thurston's "Maximum Alloys": Strength of the Alloys as Commonly Made, and as Affected by Special Conditions: The Mechanical Treatment of Metals 8vo, ctoth, 2 30 " AB intimated above, this work will form one of the most con well as modern treatises upon the Materials wed in all torts at Constructions. As a whole it forms a very comprehensive and pract book for Engineers, both Civil and Mechanical." America* MacMimitt. ' We regard this as a most useful book for reference in its departments : it should be in every Engineer's Horary." Jfetnaifal Krujinetr. MATERIALS OF CONSTRUCTION. A Text-book for Technical Schools, condensed from Thurston's "Materials of Engineering." Treating of Iron and Steel, their ores, Miiifm Inn . properties and uses: the useful metals and their alloys, especially brasses and bronzes, and their " kalchoids " : strength, ductility, resistance, and elasticity, effects of prolonged and oft- repeated loading, crystallization and granulation : peculiar metals : Thurston's " maximum alloys"; stone: timber; preservative pro- cesses, etc., etc. By Prof. Robt. H. Thurston, of Cornell University. Many illustrations Thick 8vo, cloth, 500 "Prof. Thursion has rendered a great service to the profession by the publication of this thorough, yet comprehensive, text-book. . . . The book meets a long-fe'.t want, and the well-known reputation of its author is a sufficient guarantee for its accuracy and thoroughness." Building. TREATISE ON FRICTION AND LOST WORK IN MACHIN- ERY AND MTT.T. WORK. Containing an of the variou: experiments to deduce the laws of Friction and Lubricated Surfaces, etc. By Prof. Robt. H. Thurston- Copiously illustrated.. vo. cloth, 3 00 'I;, is not too high praise to say that the present treatise is exhaustive and a complete renew of the whole subject-" American Engineer. STATIONARY STEAM ENGINES. Especially adapted to Electric Lighting Purposes. Treating of the Development of Steam-en srines the principles of Construction and Economy, with description of Moderate Speed and High Speed En- gines. By Prof. R. H. Thurston ..12mo. ctotb. 1 ."At " This work must prove to be of great interest to both manufacturers and users of steam-engines "Snider and TVomf-trarter. explanation of the Theory of Friction, and an account i Lubricants in general use, with a record of various DEVELOPMENT OF THE PHILOSOPHY OF THE STEAM- ENGINE. By Prof. R. H. Thurston 12mo, cloth, $0 75 "This small book of forty -eight pages, prepared with the care and pre- cision one would expect from the scholarly Director of the Sibley College of Engineering, contains all the popular information that the general student would want, and at the same time a succinct account covering so much ground as to be of great value to the specialist." Public Opinion. DESIQNS> CON - For Technical Schools and Engineers. By Prof. R. H. Thurston. (183 engravings in text.) Second edition 8vo. cloth, 5 00 "We know of no other treatise on this subject that covers the ground so thoroughly as this, and it has the further obvious advantage ol being a new and fresh work, based on the most recent data and cognizant of the latest discoveries and devices in steam boiler construction." Mechanical Neics. STEAM-BOILER EXPLOSIONS IN THEORY AND IN PRAC- TICE. Containing Causes of Preventives Emergencies Low Water Con- sequences Management Safety Incrustation Experimental In- vestigations, etc., etc., etc. By H. H. Thurston, LL.D., Dr. Eng., Director of Sibley College, Cornell University. With many illus- trations 12mo, cloth, 150 "Prof. Thurston has had exceptional facilities for investigating the Causes of Boiler Explosions, and throughout this work there will be found matter of peculiar interest to practical men." American Machinist. " It is a work that might well be in the hands of every one having to do with st<-am boilers, either in design or use." Kngineering Newt. A HAND BOOK OF ENGINE AND BOILER TRIALS, AND THE USE OF THE INDICATOR AND THE BRAKE. By R. H. Thurston, Director of Sibley College, Cornell University. Second edition revised 5 09 "Taken altogether, this book is one which every Engineer will find of value, containing, as it does, much information in regard to Engine and Boiler Trials which has heretofore been available only in the form of scat- tered paper* in the transactions of engineering societies, pamphlet reports, note-books, etc." Railroad Gazette. CONVERSION TABLES. Of the Metric and British, or United States WEIGHTS AXD MEAS- URES. With an Introduction by Robt. H. Thurston, A.M., C.E. 8vo, cloth, 1 00 " Mr. Thnrston's book is an admirably useful one, and the very difficulty and unfamiliarity of the Metric System renders such a volume as this almost indispensable to Mechanics, Engineers, Students, and in fact all classes of people." Mechanical News. REFLECTIONS ON THE MOTIVE POWER OF HEAT. And on Machines fitted to develop that Power. From the original French of N. L. S. Carnot. By Prof. R. H. Thurston .... 12mo, cloth, 2 00 From Mons. Haton de la Goupilliere, Director of the Ecole Nationale Superieure da Mints de France, and President of La Sociite d' Encourage- ment Jtour V Industrie Nntionule: ' I have received the volume so kindly sent me. which contains the trans- lation of the work of Carnot. Yon have rendered tribute to the founder of the science of thermodynamics in a manner that will be appreciated by the whole French people." A MANUAL OF THE STEAM ENGINE. A companion to the Manual of Steam Boilers. By Prof. Robt. H. Thurston. 2 vols 8vo, cloth, 12 00 Part I. HISTORY, STRUCTURE AND THEORY. For Engineers and Technical Schools. (Advanced courses.) Nearly 900 pages 8vo, cloth, 730 Part II. DESIGN, CONSTRUCTION AND OPERATION. For Engineers and Technical Schools. (Special courses in Steam Engineering.) 8vo, cloth, 750 TEXT BOOK OF THE PRIME MOTORS. For the Senior Year in Schools of Engineering. By Prof. R. H. Thurston. Ready, Fall of '98. PART I, HISTORY, STRUCTURE, AND THEORY OF THE STEAM-ENGINE. A MANUAL STEAM-ENGINE FOR ENGINEERS AND TECHNICAL SCHOOLS; ADVANCED COURSES. PART I. STRUCTURE AND THEORY. BY ROBERT H. THURSTON, A.M., LL.D., DR. ENG'G; DIRECTOR OF SIBLEY COIJ.EGE, CORNELL UNIVERSITY ; FORMERLY OF THE U. S. N. ENGINEERS ; PAST PRESIDENT AM. SOCIETY MECH. ENGRS. ; AITHOR OF " A HISTORY OF THE STEAM-ENGINE," " MANUAL OF STEAM- "MATERIALS OF ENGINEERING/' ETC., ETC., ETC. NEW YORK: JOHN WILEY & SONS, 53 EAST TENTH STREET. 1891. COPYRIGHT, 1891, BY ROBERT H. THURSTON ROBERT DRUMMOTO, Elfctrot\rper, 444 & W, Pearl Street, New York. FEMUS BROS.. Printers, .328 Pearl Street, New York or PREFACE. In the work of which this is the first volume, the endeavor has been to condense the essential facts and principles consti- tuting the theory' of the steam-engine, both in the ideal form usually assumed by older writers and in the actual form famil- iar to the practitioner, and also to give the more important facts and methods of its design, construction, maintenance, operation and trial. The first part contains the salient points i of theory and an account of the gradual development of the %} engine from the crude forms of earlier times to the elegant t "* and efficient types familiar to the engineer of to-day, and also a description of the general structure and the various special v forms of the modern engine. The second volume gives the t principles of general design, of the construction of the details of the machine, and the methods of operation and repair found satisfactory in recent practice. In the construction of this work, it has been assumed that the reader is familiar with the higher mathematics and the principles of thermal physics, and generally well-read in those subjects which constitute the essential scientific basis of the professional training of the engineer. This assumption, which, a generation ago, would have been unjustifiable, is to-day per- fectly reasonable. The profession of engineering has become one of the learned professions in a single generation, a conse- quence of the rapid development of the system of technical education now forming an essential and, often, the most exten- sive department of modern education in all civilized countries. The book is intended especially for the use of educated, prac- tising engineers and of students, undergraduate and graduate, 334 210995 VI PREFACE. in those technical schools which are sufficiently extensive in curriculum, and which have so large a student body as to jus- tify specialization and the offering of advanced courses of instruction ; institutions which include graduate schools of pro- fessional, specialized, work ; for example, in the mechanical engineering of railways, of naval construction, of steam-engine building. In the introduction of the reference to the use of this work in technical schools, in its title, it is not assumed that many such schools can find time or place for such a treatise. It is considered that possibly a few may find in it work for the sen- ior year of their undergraduate course, and that still fewer among existing schools may find the two volumes and appro- priate collateral reading suitable work for a year in graduate schools of steam-engineering. It is only in the highest class of such undergraduate schools and in a few special graduate schools that it would be justifiable to attempt such an ex- tended course of instruction in this department. It is in part for such cases in Sibley College and elsewhere that it has been prepared. Referring to the general plan and to the special and char- acteristic matter of the work, it will be observed that it differs greatly from other treatises on the subject, and that an at- tempt is here made to construct a theory of application for the real engine. In earlier works, no such attempt was made. The thermodynamic theory, that of the ideal engine, was long since completed ; but the same statement could not be made in regard to the real engine. It has seemed to the Author that the subject has now reached such a stage, in its develop- ment, though still by no means complete or wholly satisfac- tory, that some advance might be made toward that end which only would be accepted by the practitioner as the true purpose of applied theory. In this belief, he has planned and worked out this scheme, in which he has endeavored to embody the most recent and useful results of the later researches of engi- neers and physicists looking toward this reduction of the theory of the steam-engine to a practically applicable form. PREFACE. Vll The work will, ere long, undoubtedly, seem, in view of further progress, crude and unsatisfactory ; but we may at least hope that it cannot be long before some later writer will achieve full success. In the construction of the theory of the engine ideal and real the purely thermodynamic theory is first given form, and in this the general methods of Rankine and Clausius, substantially identical, and, after a generation, entirely unchanged by their successors, are adhered to. In detail, the work of Clausius, and his methods, are mainly followed in the production of the principal equations of thermodynamics ; then, in application, the course taken by Rankine is adopted. Rankine's initial processes are too obscure for the first part of the work, but those of application are admirably simple and convenient. Clausius. developing his equations with beautiful precision, and in simple, logical, and exact mathematical ways, is less satisfactory when we come to deal with the practical problems of the engineer. Combining the two, we obtain what has seemed to the Author a much more satisfactory system than either, as originally presented. The theory of the Real Engine, the " experimental theory " as Him called it, is neces- sarily still incomplete and imperfect. The facts and laws of internal wastes of heat in the engine are as yet too imperfectly understood to permit the framing of an exact theory of this part of the subject ; but, fortunately, so much work has been done that we are now come to a point which permits us to for- mulate a provisional theory, and to adopt processes of compu- tation sufficiently accurate, in many cases, to at least afford the engineer some assistance in his endeavor to anticipate what may be hoped for in the performance of the machine, the design of which he may have taken in hand. The treatise of Professor Rankine, now ranked among the noblest of the engineer's classics, was published in 1859. The Author, then just out of college and engaged in steam-engine design as a special line of professional work, in the old firm of Thurston, Green & Co., probably like many other young en- gineers, read the work with avidity, anticipating that it might Vlii PREFACE. give him an applied theory of the heat-engines, and a guide in their design and proportioning. But the results of thermo- dynamic computation were in such evident disaccord with the practice of the time that he threw it aside as disappointing and misleading. Later, during ten years and more of service in the U. S. N. Engineer Corps, a considerable part of the time in active service at sea, during the civil war and later, and dur- ing a half-dozen years of duty at the Naval Academy, detailed to give instruction in the departments of physics, chemistry, and applied mechanics, the works of Rankine, of Clausius, and of their numerous successors and imitators, were in constant use by the Author, and he still found that the same broad gulf between the pure and the applied theory, or rather the same deficiency of an applied science of the heat-engines, rendered it impossible for the engineer to make practical use of works on thermodynamics in his work of constructing engines for speci- fied conditions. Practical experience was the only guide a light only from the past. It was only when Professor Cotteriil made the experimental work of Clark, of Hirn, of Isherwood, and of Emery a basis for his beautiful treatise on " The Steam-engine considered as a Heat-engine" that engineers began to find the thermodynamic theory, now supplemented by something ap- proximating a satisfactory study of losses of heat and of work, really useful in office-work. In the course of, now, twenty-five years of unintermitted employment as a specialist in technical college work, of thirty years of practical experience and work in the design, the con- struction, the management, and the scientific investigation of the principles of the steam-engine, the Author has been much interested in watching the gradual closing of this gap between the ideal and the real case, and the slow but steady growth of a philosophy of the real heat-engine competent to at least direct and aid, if not to form an exact science of the subject. In this development of an applied science, the honors are won by the engineers who have undertaken however crudely, judged by the refined methods o-f modern science to ascertain by experimental investigation precisely how heat-energy en- PREFACE. IX tering the engine is distributed by transfer and transformation into useful and useless work, and to what extent it is subject to waste as heat. The mathematical physicists gave us the thermodynamic theory ; but the engineers have been com- pelled to supply the essential complement, in order that we might make the science useful in engineering. When it be- came possible to write out a correct balance-sheet of itemized receipts and expenditures, it was possible for the engineer to make the science of the steam-engine the basis of the most refined operations of his art in the design and construction of the engine and its adjustment to its purposes with maximum economical result. The long-established thermodynamic theory of the heat- engines, supplemented by what is rapidly coming to be a well- understood extra-thermodynamic theory of wastes, constitutes the complete theory of the machine, its operation, and its efficiency. The attention of scientific men and engineers, throughout the world, has now* become so earnestly drawn toward this matter, and researches are so generally in progress, under the direction of so many skilled investigators, that it cannot be long before this thermal division of the theory of the engine will be as well developed and as well understood as is now the thermodynamic. That it will ever be possible to secure as simple expression of the physical laws involved can perhaps hardly be hoped, still less expected. The simple expressions adopted by the Author seem to him likely to prove representa- tive of a class which will always supply the engineer with his working equations. As far as accuracy is concerned, the best that can ever be said of them, probably, is that they enable us to predict, more closely than the pure thermodynamic theory, the probable performance of the engine. In other words, they give the engineer processes of application, where, formerly, theory r was often useless and sometimes even misleading. The supplementing of the pure theory of the ideal engine by the physical theory of the real engine gives us a theory of application that enables us to ascertain, in a general way, the X PREFACE. effects of variation of the conditions of operation, to approxi- mately compute the demand for steam and fuel, and to deter- mine the most economical proportions and method of use of the machine, as affected by the commercial conditions of its environment. It is only now that the true problem of the engineer in this field can be solved, the problem : How may a given quantity of mechanical energy and power be obtained, by transformation from its potential form in fuel at minimum total cost ? The fact that this is the first attempt to give some consistency and unity to the theory of the real engine will be possibly accepted as a justification of the perhaps somewhat over-liberal introduction of illustrative examples, and of the occasional repetition of statements of the more essential facts and principles. The concluding chapter in the first part of* the work repre- sents an attempt to make the later facts and recent theory of the engine a basis for an investigation impossible of completion earlier. The beautiful method of Rankine, modified by the introduction of the theory of the thermal wastes of the real engine, becomes applicable to the solution of a great variety of problems which were, formerly, entirely beyond the reach of the designer or of the operator of the machine. They are problems, nevertheless, of extreme importance, and, in fact, constitute the first step in the logical series of processes which lead to the final perfection of the design of an engine precisely adapted to its place and purpose, mechanically and commer- cially. As now applicable to the case of the real engine, they permit the substitution of a more accurate and correct method for that unscientific " guesswork " of earlier practice which is responsible for so many and such unfortunate failures of the designing engineer in the adaptation of the machine to its work. The Author is convinced that here, as in the further investigation of the internal wastes of the engine, the highest talent of the skilled in research may for a long time find profitable employment in effecting closer approximations and in finding better and more exact systems of development. The now familiar distinction between the ideal and the PREFACE. XI real engine also makes it easy to bring into strong relief the principles controlling the reduction of the wastes which con- stitute the distinctive feature of the latter, and to show how the various familiar expedients for narrowing the range be- tween the two cases operate. The theory of the compound engine, of jacketing, of superheating, can to-day be readily constructed and the influence of these and other expedients looking toward the same end may be clearly seen. It thus becomes now possible to intelligently employ them and to judge when and to what extent, their use is desirable and justi- fiable on the ground of ultimate economy. The designer is beginning to find use for his theory, as now made an applied theory, in every direction. This will be further illustrated in the second part of this work when the proportioning of the compound engine is taken in hand. The general principles are exhibited in Chapter VI of the first part ; while the com- putation of dimensions comes properly into the second, which includes the designing of parts in detail. The computations of efficiencies for the single and multiple-cylinder engines, intro- duced into Chapter VI in Part I, as in all other cases, must be taken as illustrative only. The engineer must, in every case in his own practice, satisfy himself as to the exact conditions involved and determine for himself the precise values of the quantities to be employed in his own computations. No two cases are likely to involve the same conditions or give the same figures. Part II deals with the designing, the construction, the operation and maintenance, and the determination of the power and efficiency of the engine. The principles of both parts of the work are summarized by a chapter on specifications and contracts. The discussion of the principles of regulation, of governor-construction, of the action of reciprocating parts, of the designing and proportioning of valve-motions, also fall into this division of the work. In the preparation of the whole, every known available source of information has been resorted to, and. in many instances, in the absence of such records of fact, the Author has, as in the Xll PREFACE. preparation of his work on the Materials of Engineering, at an earlier date, been compelled to resort to experiment and to secure by direct investigation the facts considered by him essential to the completion of his task. Fortunately, the rapid progress of technical schools, and the general introduc- tion of research as a feature of their higher work, are making this part of the work vastly easier and more satisfactory by constantly bringing into light new areas of the previously unexplored field. It has been the intention of the Author to give every essential reference to such authorities as he has con- sulted ; their number and variety may give some idea of the magnitude of the task which has been here assumed, and justify, in some small measure, its imperfections. A MANUAL OF THE STEAM-ENGINE. PLAN. PART I. STRUCTURE AND THEORY. CHAPTER I. HISTORY OF THE STEAM-ENGINE. II. STRUCTURE OF MODERN ENGINES. III. PHILOSOPHY OF THE STEAM-ENGINE- IV. THERMODYNAMICS OF GASES AND VAPORS. V. THEORY OF THE STEAM-ENGINE. VI. COMPOUNDING ; JACKETING ; SUPERHEATING. VII. EFFICIENCIES OF THE STEAM-ENGINE. APPENDIX. PART II. DESIGN, CONSTRUCTION, OPERATION. CHAPTER I. DESIGN OF THE STEAM-ENGINE. II. VALVES AND VALTE-MOTIONS. III. REGULATION; GOVERNORS; FLY-WHEELS; INERTIA-EFFECTS. IV. CONSTRUCTION AND ERECTION. V. OPERATION ; CARE AND MANAGEMENT. VI. ENGINE AND BOILER TRIALS. VII. SPECIFICATIONS AND CONTRACTS. VIIL FINANCE; COSTS AND ESTIMATES. CONTENTS. CHAPTER I. THE HISTORY OF THE STEAM-ENGINE. ART. PAGE 1. The Purpose of the Heat-engine i 2. General Methods of Energy-transformation I 3. Heat Engines classified 2 4. Steam-engines classified , 2 5. Origin of the Steam-engine 3 6. Hero's Engine 3 7. Early Knowledge of Steam * 5 S. Steam in the Middle Ages 5 9. The Marquis of Worcester's Engine 5 10. Savery's "Fire-engine" 8 n. Performance of Savery's Engine n 12. Newcomen's Engine 12 13. Its Merits and Demerits 16 14. James Watt iS 15. The Newcomen Model 19 16. Watt's Single-acting Engine 22 17. Watt's Double-acting Engine 23 1 8. Later Pumping Engines 2; 19. Early Compound Engines 27 20. The Stationary Engine 33 21. The Locomotive Engine. Steam Fire-engines 34 22. Early Marine Engines 45 23. Later Marine Engines 57 24. Recent Use of Multiple-cylinder Engines - 68 25. Process of Development of the Steam-engine 73 26. The Philosophical Study of this Development. 77 XVI CONTENTS CHAPTER I THE STRUCTURE OF THE MODERN STEAM-ENGINE. ART. ''AGE 27. Structure and Uses of the Steam-engine 82 28. Classification of Engines into Types ' . . 82 29. Steam-engines classed 83 30. The Designer's Aim ; Principles of Design 85 31. General Principles of Construction 86 32. Exigencies of Operation 36 33. The Stationary Engine; Older Forms 87 34. The Mill or Factory Engine; Corliss and Greene Engines; Simple and Compound Forms 9; 35. High-speed and Low-speed Engines; Simple and Compound Forms. .. 116 36. Single-acting and H igh-speed Engines 1 50 37. Pumping-engines 163 38. Portable Engines; Agricultural Engines 1 79 39. Road Locomotives and Rollers 187 40. The Locomotive-engines 193 41. Marine Engines 211 42. Standard Forms; Compound Screw-engine 217 43. Adaptation of Structure to increasing Steam-pressure 229 44. Peculiar Types of Steam-engine; Experimental Engines 231 CHAPTER III. THE PHILOSOPHY OF THE STEAM-ENGINE. 45. The Scope of the Philosophy of Heat-engines 2^3 46. Nature of the Processes studied . . . 243 47. Character, Source, and Transformations of Energy 245 48. Chemical Principles involved 245 49. Physical Principles ; Thermodynamics 246 50. Mechanical Principles 247 51. Energetics and Thermodynamics 249 52. The Ideal and the Real Engine 250 53. Nature of the Scientific Problem 251 54. Outline of the Progress of this Philosophy 251 55. Origin and Form of the Mechanical Theory of Heat 253 56. The Science of Thermodynamics 256 57. General Theory of Steam-engines 257 58. Carnot's Work ; De Pambour ; Tate 258 59. Clausius's Labors 261 60. Rankine and his Work ; Thomson 263 61. The Thermodynamics of To-day 267 62. Limitations of Thermodynamic Theory 267 COA'TEJTTSi xvil ART. f-AGE 63. Watt's and Smeaton's Discoveries ,..,, 268 1 64. The Best Ratio of Expansion 271 65. Cylinder-condensation ; Clark's Researches 271 66. Hirn's Investigations; Dwelsoauvers-Dery. . . .- 274 67. Isfaerwood's Experiments; Cotterill 275 65. Status of the Theory of 1850 277 t-j. The Three Periods of this Philosophy 279 70. Work still to be done: Outlook 221 71. Plan of Succeeding Portion of this Work 2=2 CHAPTER IV. THERMODYNAMICS OF THE GASES AND VAPORS. HEAT-UTILIZATION BY TRANSFORMATION. 72. Thennodynamics of the Steam-engine 290 73. Definition of Thennodynamics 291 74. Thermodynamics as a Branch of Energetics 297 7;. Energetics denned and discussed : The Fundamental Law 298 76. Matter; Force; Work; and Energy 299 77. Law of Energetics 304 78. Newton's Laws and Energetics 305 79. Algebraic Expressions in Energetics 307 50. Thermodynamics a Restricted Case of Energetics; Thermodynamics deaned 309 51. Basis and Laws of Thermodynamics 310 2. Expressions of the First Law; The Mechanical Equivalent of Heat. .. 312 53. The First Law and the Heat-engines 315 24. The Second Law of Thermodynamics 315 85. The Steam-engine and the Second Law 319 56. The General Fundamental Thennodynamic Equations 319 87. The Relations of the two Laws 321 55. Thermodynamics and the Constitution of Matter 322 89. Solids; Liquids; Gases; Fusing and Boiling Points; The Kinetic Theory. 322 90. External and Internal Work 327 91. Heat and Temperature; Absolute Scale 328 92. Quantities of Heat; Calorimetry 333 93. Specific, Latent, and Total Heats: Computation of Latent and Total Heat of Steam 336 94. The Critical Physical Conditions and Temperature 350 95. The Perfect Gas; Definition; Equation 354 96. Thermodynamics of the Perfect Gas 355 97. Thermodynamics of Work and Energy 36$ 98. Thermodynamics of Imperfect Gases and of Vapors 373 99. Thermodynamics of Steam ; Factors of Evaporation : Tables 376 CONTENTS. 100. Regnault's Work; Stored Energy in Steam; Steam Power 383 101. General Thermodynamic Equation for Steam; Thermodynamic Func- tion. - 389 102. Expansion ; Thermal Lines for Steam and Vapors 594 103. Construction of the Thermal Lines 400 104. Cyclical Thermodynamic Operations 410 CHAPTER V. THERMODYNAMICS OF THE STEAM-ENGINE. WASTES OF ENERGY ; EFFICIENCY. 105. Thermodynamics of the Steam-engine 421 106. The Steam-engine as a Heat-engine , . . j . 422 107. The Real distinguished from the Ideal Engine 423 loS. The Wastes of the Steam-engine 426 109. The Thermodynamic Wastes 427 no. The Physical or Thermal Wastes 429 in. The Mechanical or Dynamic Wastes; Back-pressure and Clearance.. 430 112. The Ideal Cases ; Heat transformed ; Adiabatic Condensation 431 113. Special Cases ; Use of Saturated Steam ; Jacketed Engines 444 114. Efficiency of Cyclical Operations 447 115. Conditions of Maximum Efficiency. . . 449 116. Theory of Efficiency of Ideal Engines 450 117. Computations of Ideal Engine Efficiencies. Examples of Application 454 118. Limit of Actual Engine Efficiency .. 466 119. Real Engines and their Cycles 467 120. Distribution of Energy in Real Steam-engines 467 121. Method of Operation ; Limits of Temperature 470 122. Methods of Waste in Actual Engines 471 123. Magnitudes and Distribution of Losses ; Back-pressure 476 124. The Unavoidable Thermodynamic Waste in Actual Cases 482 125. Conditions of Maximum Efficiency of Fluids 483 126. Heat-wastes by Conduction and Radiation 483 1 27. Methods of Reduction of such Losses 487 128. Steam-consumption; Magnitude of Cylinder-condensation 488 129. Laws governing Loss by Internal Condensation 499 130. Theory of Internal Condensation and Waste .. 517 131. Restriction of Cylinder-condensation ; Superheating; Steam-jackets; Highspeed 534 132. Friction of Engine and Efficiency of the Machine 540 133. Investigation of Internal Engine Friction 558 134. Variation and Distribution of Internal Friction 565 135. Conditions of Real Maximum Efficiency of Machine 570 136. Conditions of Maximum Total Efficiency of the Steam 571 157. Actual Efficiencies and Economy of p CHAPTER VL MO.TIPLI-CTIIXDE* OK COTtPOCXD EXGIXES; KEDCOXG WASTES; JACKETS; SOHXHEATRG. 133. Geneial Theory of Multiple-cylinder Engines. ................ ..... 554 139. The Wastes of toe Compound Engine ...... ..................... ii 140. The Amelioration of Wastes : Jacketing; Superheating. ............. 590 141. The Problems of Compounding ................................. .. 59? 142. The Three Fundamental Principles. ....... ~ ....................... 593 143. The First Step in Compounding ......................... . ........ 59 & 144. Extent of Economical Expansion... ....... ... .................... 597 145- Influence of SBperfcearing; Jacketing; Engine-speed. ............... 593 146. The Number of Cylinders in Series. .............................. 602 147, Influence of Size of Engine ...................................... 604 140. Solutions of Problems relating to Performance- ....... . ............ 604 149. Examples of Computations of Efficiency ........................... 611 150. General Results of Experiment. ................................... 614 151. Balance of Forces. Efficiency of Mechanism and Distribution of T>, , , ..,-,--- JL-fc.* FiCSSHTCS. . ....-.-~ - . . - - - ...................................... D2O 152. Steam jackets on Simple and Multiple-cylinder Engines ............ 622 153. Action of the Jacket in Detafl. .................................... 627 154. Jacket-wastes K. Cylinder-wastes ................................. 632 15 5 . Computation of Efficiency and Jacket-waste ........................ 636 156. Limitations of Jacket-action: its Maximum Efficiency ............... 643 157. Jackets on Multiple-cylinder Engines. ............................. 654 I5S. Jacketing and Superheating. ...................................... 6* 159. Jackets on " Highspeed Engines.". ................... _". ....... 656 160. Temperatures and Pressures in Jackets ........................... 658 161. Quality of Steam : Condition of Surfaces. ......................... 659 162. Jacketing the Heads and Piston ................................. 66 1 163. Proportions of Engine with Jackets. ............................. 66 1 164. Defective Jacketing ; A!r in Jackets ........... ................. 663 16=. Experience with Jackets; Experimental Results .................... 664 166. Conclusions relative to Jacketing: Engine-efficiency and the Jacket; Testimony ........................... . ....................... 66i 167. Superheated Steam as a Working Fluid, ........................... 671 i63. The Steam-engine and Superheated Steam ......................... 671 169. Limit in Superheating. Outlook ................................... 675 170. Experience and Testimony. Conclusions relative to Superheating... 6So 171. Compression and Clearances: Back-pressure ..................... 683 172. The Binary-vapor System ........................................ 697 xx CONTENTS. CHAPTER VII. THE EFFICIENCIES OF THE STEAM-ENGINE. ART. PAGE 173. Mathematical Treatment of Engine-efficiencies 705 1 74. The Several Efficiencies of the Engine 705 175. Thermodynamic Efficiency 709 176. Thermodynamic Demand for Heat, Steam, Fuel 709 177. Actual Efficiency of Working Substance 712 178. Estimates of Heat, Steam, Fuel 713 179. Efficiency of the Machine and the Engine 714 180. Actual Thermal Lines and " Curves of Efficiency" 71$ 181. Ratios of Expansion at Maximum Efficiencies 725 182. Size of Engines; Efficiency of Capital 741 183. Efficiencies of the Ideal Engine 746 184. Rankine's Diagram of Ideal Efficiency 749 185. Theory of Efficiencies for Real Engines 752 186. Curves of Efficiency for Real Engines 756 187. Thurston's Curves of Real Efficiency 757 1 88. Solution of Practical Problems. ... "59 189. Construction of Efficiency. Diagram from Actual Cases 762 190. Method of Use of Diagrams of Efficiency 765 191 . Estimation of Costs 766 192. Statement of Results 768 193. Relation of Costs and Profits 772 194. Profits at a fixed Expansion 774 195. Cost of Engine as affecting the Best Ratio of Expansion 775 196. Back Pressure as modifying Economy 776 197. Deductions from the Investigation of Costs 77 198. Variation of Cylinder-condensation 783 199. Efficiency Problems solved by Inspection 784 200. Conclusions relative to Maximum Efficiencies 785 201. Absolute Limits to Expansion 786 MANUAL OF THE STEAM-ENGINE. PART I. CHAPTER I. THE DEVELOPMENT OF THE STEAM-ENGINE. 1. The Purpose of any Heat-engine is the useful and economical transformation, in the largest possible degree, of the heat-energy derived from combustion, or other source, and temporarily stored, in greater or less quantity, in a fluid capa- ble of variation of pressure and volume with changes of heat and of temperature and pressure. In all familiar forms this heat is derived from the combustion of coal, or of some prod- uct of fuel-distillation, natural or artificial, and is transferred from the products of combustion to the working fluid, which may be gas, air, steam, or other vapor ; or it may be that the storage medium and the vehicle of transfer, the working fluid, is the mixture composing those products of combustion them- selves. 2. The General Methods of Energy -transformation are the same for any working substance. It is caused to undergo such changes of pressure, volume, and temperature as will effect the conversion of a portion of the stored heat-energy into mechanical energy, usually by driving a piston, but very rarely by the reaction of a jet passing out from under high pressure and at very high velocity. During these changes the fluid drives the piston forward by its expansion at comparatively high temperature and pressure, and is, later, compressed by the 2 A MANUAL OF THE STEAM-ENGINE. piston on its return-stroke at a lower temperature and pressure; the net work done being thus a positive quantity and measured by the difference in the amount of work done, positively and negatively, in the complete revolution of the crank of the engine and a double-stroke of the piston. 3. Heat-engines are classified variously: as according to the physical state of the*ir working fluids ; according to the specific fluid used ; or according to the method of their opera- tion of that fluid. Thus we have gas-engines, vapor-engines, binary-vapor engines ; or, we have steam-engines, ammonia or carbon-disulphide engines ; petroleum-vapor engines; illuminat- ing-gas engines; or, engines employing working fluids of con- stant or variable weight. All are, however, subject to the same general principles of heat-transformation and, ordinarily, to the same methods of thermal or thermo-dynamic, or of dynamic, waste. In all cases their operation involves the thermo-dynamic science of the purely ideal engine, combined with the physical science of heat as applied to the phenomena of real engines. The steam-engine represents simply a single case among numerous heat-engines and motors ; and its problem is merely a single application of principles involved in the philosophy of all. 4. The Definition of a Steam-engine maybe enunciated thus: The steam-engine is a machine designed and constructed especially for the purpose of converting the heat-energy stored in the vapor of water, in as large proportion as may be practicable, into dynamical, or mechanical, energy, and to apply that energy as directly and effectively as possible to the performance of useful work. It may consist of a single element, or vessel, as in the oldest form of steam-engine to be presently described ; or it may, as in modern forms of engine, consist of a train of mechanism of considerable complexity. It may actuate a reciprocating sys- tem, as in pumping-engines of several forms ; or it may turn a shaft ; it may even impel a projectile, as in Perkins' steam- THE DEVELOPMENT OF THE STEAM-ENGINE. 3 gun ; but, in all cases and in all forms, it is a thermo-dynamic machine, subject to thermo-dynamic and thermal losses and to wastes of dynamical energy. 5. The Origin and Growth of the Steam-engine are historically notable for great antiquity and long and, until within a century, slow progress. Precisely when the power of steam began to attract the attention of mankind is quite un- known ; but it was certainly before history had begun to record any other than political events and before any industrial devel- opments, any inventions, any useful art had become a matter of notice among historians. The people of some early pre- historic time deified their great mechanics and inventors, as they did their great warriors ; but at the beginning of historic times this appreciation of those classes had largely ceased. The first period of invention of the steam-engine was one of purely speculative knowledge, and it was known, at some time before the Christian era, as simply a toy, and the force of steam was only thought of as possibly applicable to the purposes of the priestly prestidigitators of that time. This period of specula- tion continued until the middle of the seventeenth century, when the Marquis of Worcester and his contemporaries and predecessors sought to make useful application of the latent powers of steam. A second period of application was thus inaugurated which* continued up to the end of the first quarter of the nineteenth century ; when, the inventions of Watt and others having revealed the value, the power, and the wide adaptability of the machine, in all its principal forms, a third period of refinement and of improvement in all details and all applications brought the engine into substantially its existing form.* 6. Hero's Engine is described by Hero the Younger of Alexandria and dated about 120 B.C., and here we find the first record of the early history of the steam-engine. In the home of Euclid, the great geometrician, and possibly contemporary with that talented engineer and mathematician * History of the Steam-engine ; R. H. Thoiston. New York : ton Co. International Series. 4 A MANUAL OF THE STEAM-ENGINE. Archimedes, Hero produced a manuscript which he entitled "Spiritalia seu Pneumatica." The work is still extant, and has been several times republished. In it are described a number of interesting though primitive forms of water and heat engines, and, among the latter, that shown in Fig. I,* an apparatus moved by the force of steam. This earliest of steam-engines consisted of a globe sus- pended between trunnions, through one of which steam enters through pipes from the boiler below. The hollow bent arms cause the vapor to issue in such a direction that the reaction produces a rotary movement of the globe, just as the rotation of reaction water-wheels is produced by outflowing water. It is quite uncertain whether this machine was ever more than a toy, although it has been supposed by some authorities that it was actually used by the Greek priests for the purpose of producing motion of other apparatus in their temples. It seems sufficiently remark- able that, while the power of steam had been, during all the many centuries that man has existed upon the globe, so universally displayed in so many of the phenomena of natural change, mankind lived almost up to the Christian era without mak- ing it useful in giving motion even to a toy ; but it must excite still greater surprise that, from the time of Hero, we meet with no good evidence of its applica- tion to any practical use for many hundreds of years. Here FIG. i. HERO'S ENGINE, B.C. 200. and there, in the pages of history and in special treatises, we find a hint that the knowledge of the force of steam is not forgotten ; but biographers and his- * Vide Woodcroft's " Translation of Hero." The cut is from Thurston's His- tory of the Steam-engine THE DEVELOPMENT OF THE STEAM-ENGINE. 5 torians have devoted little time to the task of seeking and recording information relating to the progress of this and other important inventions and improvements in the mechanic arts. 7. Early Knowledge of Steam and of its power was con- fined to the understanding that the vapor of water was capable of exerting some force in its exit from closed vessels, and that it might be given application to a few simple and unimportant operations. Hero shows a variety of such applications, some of them very ingenious but all of no importance. For example, he sketches and describes methods of applying the expansive force of steam to the opening and closing of temple doors, to the working of various automata, and to the production of sounds. Nothing indicates that any ancient writer or mechanic had the slightest idea or expectation of the future use of this, to them, concealed power in the operations of the arts. 8. Steam-power in the Middle Ages was but little better understood and appreciated than in earlier times. " /Eolipiles," such as Hero's machine for use as a turnspit, and the various forms of apparatus in which steam was produced and from which it was allowed to issue in a jet for the purpose of " blow- ing the fire," seem to have been the earliest and latest produc- tions of this period ; although predictions of a later applica- tion to important purposes were sometimes made by the speculative philosophers and inventors of those centuries succeeding the tenth and up to about the beginning of the seventeenth. At this latter date a number of crude schemes and rude forms of apparatus, as those of Porta (1601), of Da Caus (1615), and of Branca (1629), were suggested by various ingenious philosophers and writers ; but none seems to have been actually constructed and used, even experimentally, until later. 9. The Marquis of Worcester, and Papin the distin- guished contemporary physicist and philosopher, were the first of these schemers who seem to have actually constructed their apparatus. O A MANUAL OF THE STEAM-ENGINE. In 1663 Edward Somerset, second Marquis of Worcester, published a curious collection of descriptions of his inventions, couched in- obscure and singular language, and called a " Cen- tury of the Names and Scantlings of Inventions by me already practised." One of these inventions is an apparatus for raising water by steam. The description was not accompanied by a drawing, but the sketch here given probably resembles his contrivance very closely. Steam is generated in the boiler D, and thence is led into the vessel A, already nearly filled with water. It drives the water in a jet out through a pipe, F or F ' . The vessel A is then shut off from the boiler and again filled " by suction," after the steam has condensed, through the pipe G, and the operation is repeated, the vessel B being used alternately with A. This apparatus was used for the purpose of elevating water for practical purposes at Vaux- hall, near London. It was still earlier used at the home of Worcester, Raglan Castle, where the openings cut in the wall for its reception are still to be seen. The separate boiler, as here used, constitutes a very important improvement upon the preceding forms of apparatus, although ENG.NE, A.D. 1650. thg j dea was or j g i na l w j t h Porta. The " water-commanding engine," as its inventor called it, was, therefore, the first instance in the history of the steam- engine in which the inventor is known to have " reduced his invention to practice." It is evident, however, that the invention, important as it was, does not entitle the marquis to the honor claimed for him by many authorities of being the inventor of the steam-engine. Somerset was simply one of those whose works collectively make the steam-engine. The invention of the Marquis of Worcester was revived twenty years later by Sir Samuel Morland, but in what form is not now known. In a memoir which he wrote upon the sub- ject in 1683, he exhibited a degree of familiarity with the properties of steam that could hardly have been expected of THE DEVELOPMENT OF THE STEAM-ENGINE, 7 any one at that early date. In his manuscript, now preserved in the Haarlem Collection of the British Museum, he states the size of the cylinders required in his machine to raise given quantities of water per hour, and gives very exactly the relative volumes of equal weights of water and of steam under atmos- pheric pressure. He tells us that one of his engines, with a cylinder six feet in diameter and twelve feet long, was capable of raising 3240 pounds of water through a height of six inches, 1800 times an hour. From this time forward the minds of many mechanicians were earnestly at work on this problem the raising of water by aid of steam. Hitherto, although many ingenious toys, embodying the principles of the steam-engine separately, and sometimes, to a certain extent, collectively, had been proposed and even occasionally constructed, the world was only just ready to profit by the labors of inventors in this direction. But, at the end of the seventeenth century, English miners were beginning to find the greatest difficulty in clearing their shafts of the vast quantities of water which they were meeting at the considerable depths to which they had penetrated, and it had become a matter of vital importance to them to find a more powerful aid in that work than was then available. They were, therefore, by their necessities, stimulated to watch for, and to be prepared promptly to take advantage of, such an invention when it should be offered them. The experiments of Papin, and the practical application of known principles by Savery, placed the needed apparatus in their hands. When Louis XIV. revoked the Edict of Nantes, the persecu- tions at once commenced drove from the kingdom some of its greatest men. Among these was Denys Papin, a native of Blois and a distinguished philosopher. He studied medicine at Paris, and, when expatriated, went to England, where he met the celebrated philosopher Boyle, who introduced him into the Ro)^ Society, of which Papin became a member and to whose " Transactions " he contributed several valuable papers. He invented, in 1680, the " Digester," in which substances, unaffected by water boiling under atmospheric pressure, can be 8 A MANUAL OF THE STEAM-ENGINE. subjected to the action of water boiling under high pressure, and thus thoroughly " digested " or cooked. The danger of bursting these vessels caused him, in 1681, to invent and apply the lever safety-valve* now an indispensable appurtenance to every steam-boiler. In 1690 he constructed a working model of an engine, con- sisting of a steam-cylinder with a piston which was raised by steam pressure, and which descended again when the conden- sation of the steam produced a vacuum beneath it. This appa- ratus the inventor proposed to use as a motor for working pumps and for driving paddle-wheels ; but he never built a successful working machine on this plan, so far as we can ascertain.f Papin, in 1707, proposed to avoid the loss due to conden- sation of steam in the vessel to some extent at least by the use of his piston, which he interposed between the steam and the water. + This engine is in principle a Marquis of Worcester en- gine, in which the piston is introduced to separate the steam from the water which it impels, and thus to reduce the amount of loss by condensation. This engine was never constructed except experimentally, however, and is principally of interest in a history of the steam-engine from the fact that it was a use- ful suggestion to succeeding inventors. 10. Savery's "Fire-engine" was the first among all the earlier devices which came into actual use in the application of the energy stored in steam to the purposes of industry. The constant and embarrassing expense and the engineer- ing difficulties presented by the necessity of keeping the British mines, and particularly the deep pits of Cornwall, free from water, and the failure of every attempt previously made to provide effective and economical pumping machinery, were * Other forms of safety-valve had been previously used. f " Recueil des diverses Pieces touchant quelques nouvelles Machines et autres Sujets philosophiques," M. D. Papin, Cassel, 1695. J " Nouvelle Maniere de lever d'Eau par la Force de Feu, mise en Lumi- fere." Par M. D. Papin, Docteur en Medecme, Professeur en Mathematique a Cassel, 1707. THE DEVELOPMENT OF THE STEAM-NGINE. 9 noted by Savery, who, July 25, 1698, patented the design of the first engine which ever was actually employed in this work. A working model was submitted to the Royal Society of London in 1699,* and successful experiments were made with it. This engine is shown in Fig. 3, as described by Savery him- self in 1702 in the " Miners' Friend." L L is the boiler, in which steam is raised, and through the pipes O Oit is alternately let into the vessels P P. Suppose it to pass into the left-hand vessel first. The valve J/ being closed and r being opened, the water contained in P is driven out and up the pipe 5 to the desired height, where it is discharged. The valve r is then closed, and ?lso the valve in the pipe O. The valve J/ is next opened, and condensing water is turned upon the exterior of P by the cock K, leading water from the cistern X. As the steam contained in P is con- densed, forming a vacuum, a fresh charge of water is driven by atmospheric pressure up the pipe T. Meantime, steam from the boiler has been let into the right-hand vessel/*, the cock W having been first closed and R opened. The charge of water is driven out through the lower pipe and the cock R, and up the pipe 5 as before, while the other vessel is refilling preparatory to acting in its turn. The two vessels thus are alternately charged and discharged as long as is necessary. Savery 's method of supplying his boiler with water was at once simple and ingenious. The small boiler D is filled with water from any convenient source, as from the stand-pipe 5. A fire is then built under it, and when the pressure of steam in D becomes greater than in the main boiler Z, a communication is opened between their lower ends and the water passes under pressure from the smaller to the larger boiler, which is thus " fed " without interrupting the work. G and A^ are gauge-cocks by which the height of water in the boilers is determined, and these attachments were first adopted by Savery. Here we find, therefore, the first really practicable and * "Transactions of the Royal Society," 1699. 10 A MANUAL OF THE STEAM-ENGINE. FIG. 3. SAVERY'S ENGINE, A.D. 1699. commercially valuable steam-engine. Thomas Savery is entitled to the credit of having been the first to introduce into gen- eral use a machine in which the power of heat, acting through the medium of steam, was rendered use- ful. It will be noticed that Savery, like the Marquis of Worcester and like Porta, used a boiler separate from the water-reservoir. He added to the " water-commanding engine" of the Marquis the system of surface- condensation, by which he was en- abled to change his vessels when it became necessary to refill them ; and the secondary boiler, which enabled him to supply the working boiler with water without interrupting its action. The machine was capable of work- ing uninterruptedly for a period of time only limited by its own endurance. Savery never fitted his boilers with the safety-valve, although it was subsequently used on Savery engines by Desaguliers ; and in deep mines he was com- pelled to make use of higher pressures than his rudely-con- structed boilers could safely bear. The introduction of his machines was therefore greatly retarded by the fear, among miners, of the explosion of his boilers. In fact, such explosion did occur on more than one occasion. The Savery engine was improved, about 1716 or 1718, by Dr. Desaguliers, who attached to it Papin's safety-valve, and substi- tuted a jet-injection from the stand-pipe into the " forcing- vessels " for the surface-condensation of Savery's original arrangement. The Savery engine, however, after all improve- ment in design and construction, though a working and a useful machine, was still a very wasteful one. The steam from the boiler, passing into the cold, wet water-reservoir or forcing- vessel, was condensed in large quantity, and also to a very THE DEVELOPMENT OF THE STEAM-ENGINE. II serious extent, by coming into actual contact with the water itself. n. The Performance of the Savery Engine was thus evidently unsatisfactory, as judged from the modern stand- point ; yet, as the first machine applying natural forces to a great task, and for the first time accomplishing it, it was a grand success. The operation of deep mines had become im- practicable where water was met with in any considerable quantity, and, in some cases, hundreds of horses had been kept employed, at enormous and even fatal expense, to keep the lower levels in working. These were displaced by steam and the Saver}" engine, and mines which must otherwise have been abandoned were once more made profitable. The defects of this class of engines were nevertheless great. Their enormous consumption of fuel was one serious difficulty everywhere except in the coal districts ; their heavy pressures needed at deep shafts and for high lif ts gave rise to dangers which threatened constantly both life and property when, as was very usual, the workmanship of the " forcing-vessel *" was defective. In fact, the invention of the Savery engine was introductory to the steam-boiler .explosion : several of the boilers exploding while at work and doing some damage. This new and intimidating experience, and the evident wastefulness of the machine, led mechanics, very soon, to study the problem anew with a view to improvement in these respects : its extrava- gant consumption of fuel, the inconvenient necessity of placing it near the bottom of the mine to be drained, and of putting in several for successive lifts where the depth was considerable, and, especially, the risk which its use with high pressures in- volved even in its best form, had considerably retarded its introduction, and it therefore came into use very slowly, not- withstanding its superiority in economic efficiency over horse- power. Many years after Savery "s death, in 1774. Smeaton made the first duty-trials of engines of this land. He found that an engine having a cylindrical receiver 16 inches in diameter and 22 feet high, discharging the water raised 14 feet above the 12 A MANUAL OF THE STEAM-ENGINE. surface of the water in the well, making 12 strokes, and raising 100 cubic feet per minute, developed 2 horse-power, and con- sumed 3 hundredweight of coals in four hours. Its duty was, therefore, 5,250,000 pounds raised one foot per bushel of 84 pounds of coals, or 62,500 "foot-pounds" of work per pound of fuel. An engine of slightly greater size gave a duty about 5 per cent greater.* 12. Newcomen's Engine. The first important step taken towards remedying the defects of Savery's machine was taken by Thomas Newcomen and John Cawley, or Galley, two me- chanics of the town of Dartmouth, Devonshire, England, who produced what has been known as the Atmospheric or Newco- men Engine. Newcomen was a blacksmith, and Cawley a glazier and plumber. It has been stated that a visit to Corn- wall, where they witnessed the working of a Savery engine, first turned their attention to the subject ; but a friend of Savery has stated that Newcomen was as early with his general plans as Savery. After some discussion with Cawley, Newco- men entered into correspondence with Dr. Hooke, proposing a steam-engine, to consist of a steam-cylinder containing a piston similar to those of Huyghens's and Papin's engines, and driving a separate pump, similar to those generally in use where water was raised by horse or wind power. Dr. Hooke advised and argued strongly against their plan ; but, fortunately, the obstinate belief of the unlearned mechanics was not overpowered by the dis- quisitions of their distinguished correspondent, and Newcomen and Cawley attempted an engine on their peculiar plan. This succeeded so well as to induce them to continue their labors, and in 1705 to patent f in combination with Savery, who held the right of surface-condensation, and who induced them to allow him an interest with them an engine combin- ing a steam-cylinder and piston, surface-condensation, and a separate boiler and separate pumps. In the atmospheric en- * History of the Steam-engine, R. H. Thurston, p. 45 ; Farey on the Steam-engine, p. 125. f It has been denied that a patent was issued ; but there is no doubt that Savery claimed and received an interest in the new engine. THE DEVELOPMENT OF THE STEAM-ENGINE. 13 gine as first designed, the slow process of condensation by the application of the condensing water to the exterior of the cyl- inder to produce the vacuum caused the strokes of the engine to take place at very long intervals. An improvement was, however, soon effected which immensely increased this rapidity of condensation. A jet of water was thrown directly into the cylinder, thus effecting for the Newcomen engine what Desa- guliers had previously done for the Savery engine. As thus improved, the Newcomen engine is shown in Fig. 4. Here d is the boiler. Steam pass- es from it through the cock i The elasticities of steam, at various temperatures greater than that of boiling water, and an approximation to the law which it follows at other temperatures. 5 -I How much water, in the form of steam, was required, at every stroke, by a small Newcomen engine, with a wooden cylinder six inches in diameter and twelve inches stroke. (6) The quantity- of cold water required, at every stroke, to condense the steam in that cylinder, so as to give it a working power of about seven pounds on the square inch. After these well-devised and truly scientific investigations. Watt was enabled to enter upon his work of improving the steam-engine with an intelligent understanding of its "Tinting defects, and with a knowledge of their cause. It was on a Sunday afternoon, in the spring of 1765, that he devised his first and his greatest invention the separate condenser. His object in using it was, as he says himself, to keep the cylinder as hat as the steam that entered it. He was therefore the first to apprehend and to state a problem which the modern engineer is still vainly endeavoring completely to solve. Watt was, at this time, twenty-nine years of age. Having taken this first step and made such a radical improvement, the success of the invention was no sooner determined than others followed in rapid succession as consequences of the exigencies arising from the first radical change in the old Newcomen en- gine. But in the working out of the forms and proportions of 4JPtHffc in the new engine, even Watt's powerful mind, with its stores of happily-combined scientific and practical information, was occupied for years. In attaching the separate condenser, he first tried surface condensation ; but this not succeeding well, he substituted th jet. Some provision became at once necessary for preventing the filling of the condenser with water. Watt at first intended adopting the same expedient which worked satisfactorily with the less effective condensation of 22 A MANUAL OF THE STEAM-ENGINE. Newcomen's engine, i.e., leading a pipe from the condenser to a depth greater than the height of the column of water which could be counterbalanced by the pressure of the atmosphere ; but he subsequently employed the air-pump, which relieves the condenser, not only of the water, but of the air which also usually collects in considerable volume, and vitiates the vacuum. He next substituted oil and tallow for the water previously used in lubrication of the piston and keeping it steam-tight, in order to avoid the cooling of the cylinder incident to the use of water. Still another cause of refrigeration of the cylinder, and consequent waste of power in its operation, was seen to be the entrance of the atmosphere, which came in at the top and followed the piston down the cylinder at each stroke. This the inventor concluded to prevent by covering the top of the cylinder, and allowing the piston-rod to play through a "stuff- ing-box," which device had long been known to mechanics. He accordingly not only covered the top, but surrounded the whole cylinder with an external casing or " steam-jacket," and allowed the steam from the boiler to pass around the steam- cylinder and to press upon the upper surface of the piston, where its pressure was readily variable and therefore more manageable than that of the atmosphere. It also, besides keeping the cylinder hot, could do comparatively little harm should it leak by the piston, as it might be condensed and readily disposed of. 16. The Single-acting Engine of Watt was now fully de- veloped from the " atmospheric engine " of Newcomen. As improved it is shown in Fig. 6, which represents the engine as patented in April, 1769. Watt's first engine was erected with the pecuniary aid of Dr. Roebuck, the lessor of a coal, mine on the estate of the Duke of Hamilton, at Kinneil, near Borrowstounness. This engine, which was put up at the mine, had a steam-cylinder eighteen inches in diameter. In the figure, the steam passes from the boiler through the pipe d and the valve c to the cylinder casing, or steam- jacket, Y Y, and above the piston b, which it follows in its THE DEVELOPMENT OF THE STEAM-ENGINE. descent in the cylinder a, the valve / being at this time open to allow the exhaust to pass into the condenser h. The piston now being at the lower end of the cylinder, and the pump-rods at the opposite end of the beam y thus raised, and the pumps filled with water, the valves c and / close, while e opens, allowing the steam which remains above the piston to flow beneath it, until, the pressure becoming equal above and below by the weight of the pump, it is rapidly drawn to the top of the cylinder, while the steam is displaced above, passing to the underside of the piston. Now the valve e is closed, and <:and /are again opened, FlG - ^.-WATT'S PUMXG- E N-G..NE, A . D . 1769. and the down-stroke is repeated as before. The water and air entering the condenser are removed, at each stroke, by the air-pump *, which communicates with the condenser by the passage s. The pump q supplies condensing-water, and the pump A takes away a part of the water of condensation, which is thrown by the air-pump into the " hot- well " k, and with it supplies the boiler. The valves are moved by valve-gear very similar to Beighton's, by the pins m m in the " plug-frame " or " tappet-rod " n n. The engine is mounted upon a substantial foundation, B B. F is an opening, out of which, before starting the engine, the air is driven from the cylinder and condenser. 17. Watt's Double-acting Engine was the next of his great inventions ; and his scheme of the expansion of steam was quite as important. Watt conceived the idea of economizing some of that power, 24 A MANUAL OF THE STEAM-ENGINE. the loss of which was so plainly indicated by the violent rush of the exhaust steam into the condenser, and described the ad- vantages that would follow the use of steam expansively, by means of a "cut-off," in a letter to Dr. Small, of Birmingham, dated Glasgow, May, 1769. He also planned a " compound engine." This invention of the expansion of steam, which, in importance, was hardly exceeded by any other improvement of the steam-engine, was adopted at Soho in 1776, but the patent was not obtained until 1782. FIG. 7. WATT'S ENGINE, A.D. 1780. During this interval, Watt invented the crank and fly-wheel, but, as the former had been first patented by Wasborough, who is supposed to have obtained a knowledge of it from workmen employed by Watt, the latter patented several other methods of producing rotary motions, and temporarily adopted that known as the " sun-and-planet wheels," subsequently using the crank. The adaptation of the steam-engine to the produc- tion of rotary motion was soon succeeded by the introduction of the Double-acting Engine, the Fly-ball Governor, the Counter, the Steam-engine Indicator, and other minor but THE DEVELOPMENT OF THE STEAM-EXGIKE. 2 valuable improvements, which where the final steps by which the Watt steam-engine became applicable to driving mills, to use on railroads, to steam-navigation, and to the countless pur- poses by which it has become, as it has already been denomi- nated, the great material agent of civilization. Fig. 7 represents the Watt Double-acting Engine. It will be noticed that it differs from the Single-acting Engine in hav- ing steam-valves, B B t and exhaust-valves, E E, at each end of the cylinder, thus enabling the steam to act on each side of the piston alternately, and practically doubling the power of the engine. The end of the beam opposite to the cylinder is usually connected with a crank-shaft. 18. The Later Pumping engine of this type is shown in the succeeding figure, exhibiting the principal form of pump- ing-engine as now constructed. F::- 1 -7--I C: Fig. 8 represents the Cornish pumping-engine, which, in spite of its great weight and high cost, is still in use. It wfll be seen that it is the engine of James Watt in all its 26 A MANUAL OF THE STEAM-ENGINE. general features, with the addition, in its operation, of the ap- plication of Watt's idea of expansion of steam to something approximating the extent customary at the present time. It is single-acting, and has a steam-jacket and a plug-rod valve-gear, J K. The improvements are principally in the form and proportions of its parts, and in its adaptation to high steam and " short ' cut-off.' " A is the steam-cylinder, B C the piston and rod, D the beam, and the pump-rod. The condenser is seen at G, and the air-pump at H. The steam- cylinder is " steam-jacketed," and is surrounded by a casing, O, composed of brickwork or other non-conducting material. Steam is first admitted above the piston, driving it rapidly downward and raising the pump-rod. At an early point in the stroke the admission of steam is checked by the sudden closing of the induction-valve, and the stroke is completed under the action of expanding steam assisted by the inertia of the heavy parts already in motion. The necessary weight and inertia are afforded in many cases, where the engine is applied to the pumping of deep mines, by the immensely long and heavy pump-rods. Where this weight is too great, it is counter- balanced ; and where, as when used for the water-supply of cities, too small, weights are added. When the stroke is com- pleted, the " equilibrium-valve " is opened, and the steam passes from above to the space below the piston, and, an equilibrium of pressure being thus produced, the pump-rods descend, forcing the water from the pumps and raising the steam-piston. The absence of the crank or other device which might de- termine absolutely the length of stroke compels a very careful adjustment of steam admission to the amount of load. Should the stroke be allowed to exceed the proper length, and should danger thus arise of the piston striking the cylinder-heads, the movement is checked by buffer-beams. The regulation is effected by a " cataract," a kind of hydraulic governor, consist- ing of a plunger-pump with a reservoir attached. The plunger is raised by the engine, and then automatically detached. It falls with greater or less rapidity, its velocity being determined by the size of the eduction orifice, which is adjustable by hand. THE DEVELOPMENT OF THE STEAM-ENGIXE. 2/ When the plunger reaches the bottom of the pump-barrel, it disengages a catch, a weight is allowed to act upon the steam- valve, opening it, and the engine is caused to make a stroke. When the outlet of the cataract is nearly closed, the engine stands still a considerable time while the plunger is descending, and the strokes succeed each other at long intervals. When the opening is greater, the cataract acts more rapidly, and the engine works faster. This has been regarded until recently as the most economical of pumping-engines, and it is still gener- ally used in Europe in freeing mines of water. 19. The Compound Engine originated in Watt's time. Fig. 9 represents the first " compound " or " two-cylinder " engine. This class of engines, in which the steam exhausted from one cylinder is further expanded in the second, was first introduced by Hornblower, in 1781, and was patented, in combination with the Watt condenser, by Woolf, at a later date (1804), with a view to adopting high steam and considerable expansion. The Woolf engine was to some extent adopted, but was not suc- cessful in competing with Watt engines where the latter were well built, and, like Honiblower's engine, was soon given up. The compound engine has come up again within a few years, and with what is mow considered high steam and con- siderable expansion, and designed with more intelligent refer- ence to the requirements of economy of working steam in this manner, it is gradually displacing other forms of engine. The engine patented by Hornblower in 1781 was first de- scribed by the inventor in the " Encyclopaedia Britannica." It consists, as is seen by reference to the engraving, of two steam- cylinders, A and B A being the low- and B the high-pressure cylinder the steam leaving the latter being exhausted into the former, and, after doing its work there, passing into the condenser, as already described. The piston-rods, C and D, are both connected to the same part of the beam by chains, as in the other early engines. These rods pass through stuffing- boxes in the cylinder-heads, which are fitted up like those seen on the Watt engine. Steam is led to the engine through the pipe, G Y, and cocks, a, b. c, and d. are adjustable, as required, 28 A MANUAL OF THE STEAM-ENGINE. to lead steam into and from the cylinders, and are moved by the plug-rod, W, which actuates handles not shown. K is the exhaust-pipe leading to the condenser. V is the engine feed- pump, and X the pump-rod carrying the pump-buckets at the bottom of the shaft. The cocks c and a being open and b and d shut, the steam passes from the boiler into the upper part of the steam-cylinder, B\ and the communication between the lower part of B and the top of A is also open. Before starting, steam being shut off from the engine, the great weight of the pump-rod, X, FIG. 9. HORNBLOWER'S COMPOUND ENGINE, 1781. causes that end of the beam to preponderate, the pistons stand- ing, as shown, at the top of their respective steam-cylinders. The engine being freed from all air by opening all the valves arid permitting the steam to drive it through the engine and out of the condenser through the "snifting-valve," O, the valves b and d are closed, and the cock in the exhaust-pipe opened. THE DEVELOPMENT OF THE STEAX-EXGIXE. 2O, The steam beneath the piston of the large cylinder is immediately condensed, and the pressure on the upper side of that piston causes it to descend, carrying that end of the beam with it, and raising the opposite end with the pump-rods and their attachments. At the same time, the steam from the lower end of the small high-pressure cylinder being let into the upper end of the larger cylinder, the completion of the stroke finds a cylinder full of steam transferred from the one to the other with corresponding increase of volume and decrease of pressure. While expanding and diminishing in pressure as it passes from the smaller into the larger cylinder, this charge of steam gradually resists less and less the pressure of the steam from the boiler on the upper side of the piston of the small cylinder, B, and the net result is the movement of the engine by pressures exerted on the upper sides of both pistons and against pressures of less intensity on the under sides of both. The pressures in the lower part of the small cylinder, in the upper part of the large cylinder, and in the communicating paiiijni are evidently all equal at any given time. When the pistons have reached the bottoms of their respective cylinders, the valves at the top of the small cylinder, B, and at the bottom of the large cylinder. A. are closed, and the valves c and d are opened. Steam from the boiler now enters beneath the piston of the small cylinder: the steam in the larger cylinder is exhaused into the condenser, and the steam already in the small cylinder passes over into the large cylinder, follow- ing up the piston as it rises. Thus, at each stroke a small cylinder full of steam is taken from the boiler, and the same weight, occupying the volume of the larger cylinder, is exhausted into the condenser from the latter cylinder. Referring to the method of operation of this engine, Prof. Robison demonstrated that the effect produced was the same as in Watt's single-cylinder engine a fact which is com- prehended in the law enunciated many years later by Rankine, that, ** so far as the theoretical action of the steam on the pis- 3O A MANUAL OF THE STEAM-ENGINE. ton is concerned, it is immaterial whether the expansion takes place in one cylinder, or in two or more cylinders." It was found, in practice, that the Hornblower engine was no more economical than the Watt engine ; and that erected at the Tin Croft Mine, Cornwall, in 1792, did even less work with the same fuel than the Watt engines. The plan unsuccessfully introduced by Hornblower was subsequently modified and adopted by others among the con- temporaries of Watt ; and, with higher steam and the use of the Watt condenser, the " compound " gradually became a standard type of steam-engine. Arthur Woolf, in 1804, re-introduced the Hornblower or Falck engine, with its two steam-cylinders, using steam of higher tension. His first engine was built for a brewery in London, and a considerable number were subsequently made. Woolf expanded his steam from six to nine times, and the pumping-engines built from his plans were said to have raised about 40,000,000 pounds one foot high per bushel of coals, when the Watt engine was raising but little more than 30,000,- ooo. In one case a duty of 57,000,000 was claimed. The accompanying engraving exhibits a modern and success- ful type of compound engine, which may be taken for compari- son in style, general design, proportions, and performance with the earlier forms of pumping-engine. It was designed by Mr. E. Reynolds and is in operation in the city of Milwaukee, where it was constructed. Here the pumps are in line with the steam-cylinders, bring- ing the working-strain direct to the plungers. The valve-gear has a cut-off on both cylinders, which allows the steam to be worked from boiler-pressure down to 8 or 9 pounds. The cylinders are steam-jacketed. The pump, condenser, boiler feed-pumps, and air-chambers are placed below the floor. The contract re- quired a delivery of 12,000,000 gallons of water, 150 feet high, every 24 hours, and a duty of 97,000,000 foot-pounds for every IOO Ibs. of coal consumed. 32 A MANUAL OF THE STEAM-ENGINE. The principal dimensions of the engines are: Diameter high-pressure cylinder ...................... inches, 34 Diameter low-pressure cylinder ....................... " 66 Diameter of pump .................................. " 41.78 Diameter of pump-plunger ........................... 30 Length of stroke .................................... " 60 The performance of this engine may be compared with those reported for Savery's, Newcomen's, 'and Watt's machines to obtain some idea of the progress of modern times in the economical use of steam. The following are the results of the trial : Duration of trials ............................... hours, 48 Steam-pressure in engine-room ................... pounds, 74-8l Vacuum by gauge ................. ^ .............. inches, 26.25 Water-pressure gauge ............................ pounds, 62.02 Total head, including suction-lift ................ " 67.29 Revolutions of engine per minute ........................ 25.51 Piston speed per minute ............................. feet, 255.10 Coal consumed .................................. pounds, 32.395 Duty in foot-pounds, per 100 pounds of coal consumed.. .104,820,431 Exceeding the duty and the capacity guaranteed under the ordinary, every-day conditions, and the actual weight of coal consumed being charged up without deductions of any kind. The progress of steam-pumping engine efficiency, from the time of Newcomen and of Watt to date, is seen in the follow- ing figures : 1769 Newcomen (by Smeaton) ......................... 7,000,000 1772 " " ........................... 12,000,000 1776 Watt ........................................... 21,600,000 1778 " expansive .................................. 26,600,000 1830 Cornish ........................................ 86,585,000 1880 Compound ....................................... 100,000,000 1885 ....................................... 110,000,000 1890 ....................................... 120,000,000 The duties given are those either guaranteed or actually resulting from trials. The fuel demanded per horse-power per hour thus has decreased from about 35 pounds in Smea- tion's Newcomen engines, and 8 in Watt's best work, to 2 THE DEVELOPMENT OF THE STEAM-ENGIXE. 33 pounds in the Cornish, and to less than 1.75 in later engines of the compound type: the minimum given above being 1.5. Even this figure has been reduced with later engines of the three- and four-cylinder types. 2O. The Stationary Engine is, as has been already seen, an evolution from the earlier types of pumping-engine, and is a product of the fertile and fruitful brain of James Watt. The Watt double-acting engine, turning a shaft, regulated by a " fly-wheel " and controlled by the Watt governor, represents the type of the modern stationary engine as well as that of Watt's own time. The changes which have occurred since that period have been mainly in matters of detail. The old " parallel motion " guiding the head of the piston- rod has now become generally superseded by the guides and sliding cross-head. The valve-gear has been simplified and bet- ter adapted to efficient action as a " cut-off " gear. The gover- nor has been so attached as to adjust the steam supply to work momentarily performed, by variation of the point of cut-off, and, revolution by revolution, fixing the ratio of expansion. The general design and construction of the engine have been modi- fied in the direction of simplicity, cheapness, and lightness, combined with strength. The use of the direct-acting engine, rather than the beam-engine, is now general, and, for all but " high-speed " engines which make 1 50 to 300 revolutions or more per minute, some form of "detachable valve-gear" is employed. The first successful " drop cut-off " engine was that of F. E. Sickels, of 1841, which employed "puppet-valves" on the steam side, which could be detached and allowed to fall into their seats at any desired point in the stroke, by a detaching mechanism operated either by hand or by the governor. To prevent injury by the impact of the valve on the seat, a " dash- pot " was used, consisting of a vessel, containing either water or air, into which a loosely-fitted piston was fitted. This piston, attached to the valve-stem, directly or indirectly, rose and fell with the latter, and when the valve was about to strike the seat at the end of its descent, the fall was checked and the 34 A MANUAL OF THE STEAM-ENGINE. valve " eased " down to the seat by the resistance of the fluid in the dash-pot, on which the piston fell, and through which, for a very short distance, it then forced its way. Modifications of these devices were devised by G. H. Cor- liss in 1849, an d constitute the so-called Corliss engine of the present time, which will be described later. Many other in- ventors have since constructed still other engines of the same general character. The latest improvements of the stationary engine relate to what are distinctively known as the " high-speed " engine, and have led to the production of engines especially adapted to driving machinery at very high speeds of revolution. In the most successful engines of this type it is usual to make the engine itself of the simplest possible design ; to adopt a simple valve-motion, and to secure regulation by means of a governor placed on the main shaft and adjusting the point of cut-off by shifting the eccentric. A single valve is often used. These engines will be fully described in the next chapter. Where the cost of securing the needed condensing water is not too great, and where the steam-pressure is moderate, a condenser may be economically added to the non-condensing engine, thus obtaining a gain in power of considerable amount and an increase in economy of steam and of fuel, if the engine is well proportioned to its work when thus altered, of often one third three pounds and two pounds of good coal per horse- power and per hour being common figures for such engines working non-condensing and condensing. The gain in power is often one fourth or one third. But with increasing pressure of steam this gain becomes lessened. 21. The Locomotive was one of the fruits of the inventive genius of Watt and his contemporaries. When the steam-engine had so far been perfected that the possibility of its application to other purposes than the eleva- tion of water had become generally recognized, the problem of its adaptation to the propulsion of carriages was attacked by many engineers and inventors. As early as 1759 Dr. Robison called the attention of Watt THE DEVELOPMENT OF THE STEAM-ENGINE. 35 to the possibility of constructing a carriage to be driven by a steam-engine. Watt, at a very early period, proposed to apply his engine to locomotion, and contemplated using either a non- condensing engine or an air surface-condenser. He included the locomotive-engine in his patent of 1784, and his assistant, Murdoch, in the same year made a working-model locomotive which was capable of running at a rapid rate. The first actual experiment was made, as is supposed, by a French army officer, Nicolas Joseph Cugnot, who in 1769 built a steam-carriage, which was set at work in presence of the French Minister of War, the Due de ChoiseuL The funds required were furnished by the Comte de Saxe. Encouraged by the partial success of the first locomotive, Cugnot, in 1770, constructed a second, which is still preserved in the Conserva- toire des Arts et Metiers Paris. This more powerful carriage was fitted with two non-condensing single-acting cylinders thir- teen inches in diameter. Although the experiment seems to have been successful, there appears to have been nothing more done with it. An American of considerable distinction, Nathan Read, patented a steam-carriage, 1790.* In 1804 Oliver Evans completed a flat-bottomed boat to be used at the Philadelphia docks, and, mounting it upon wheels, drew it by its own steam engine to the river-bank. Launching the craft, he propelled it down the river, using its steam-engine to drive its paddle-wheels. Evans's "oructor ampltibolis*' as he named the machine, was the first road-locomotive that we find described after Cugnot's time. Evans asserted that carriages propelled by steam would soon be in common use : and offered a wager of three hundred dollars that he could build a "steam- wagon" that should excel in speed the swiftest horse that could be matched against it. Trevithick and Vivian built a locomotive-engine in 1804 (Fig. 1 1) for the railway at Merthyr-Tydvil, in South Wales, which was quite successful, although sometimes giving trouble *" Nathan Read and his Steam-engine." Xew York : 36 A MANUAL OF THE STEAM-ENGINE. by slipping its wheels. This engine had one steam-cylinder 4! inches diameter, and carried forty pounds steam. Colonel John Stevens, of Hoboken, was undoubtedly the greatest engineer and naval architect living at the beginning of the present century. Without having .made any one super- latively great improvement in the mechanism of the steam- engine, like that which gave Watt his fame ; without having the J_L FIG. ii. TREVITHICK'S LOCOMOTIVE, 1804. honor of being the first to propose navigation by steam, or steam-transportation on land, he exhibited a far better knowl- edge of the science and of the art of engineering than any man of his time, and he entertained and urged more advanced opin- ions and more statesmanlike views, in relation to the economi- cal importance of the improvement of the steam-engine, both on land and water, than seem to have been attributable to any other leading engineer of that time. """In" 1812 he published a pamphlet embodying " Documents tending to prove the Superior Advantages of Railways and THE DEVELOPMENT OF THE STEAM-ENGINE. 37 Steam-carriages over Canal Navigation." * At this time the only working locomotive in the world was that of Trevithick and Vivian, at Merthyr-Tydvil, and the railroad itself had not grown beyond the old wooden tram-roads of the collieries. Yet Colonel Stevens says in this paper : " I can see nothing to hinder a steam-carriage moving on its ways with a velocity of one hundred miles an hour " adding in a footnote : " This astonishing velocity is considered here merely possible. It is probable that it may not, in practice, be convenient to exceed twenty or thirty miles per hour. Actual experiments can only determine this matter, and I should not be surprised at seeing steam-carriages propelled at the rate of forty or fifty miles an hour." He proposed rails of timber, protected when necessary by iron plates, or to be made wholly of iron. The car-wheels were to be of cast iron, with inside flanges to keep them on the track. The steam-engine was to be driven by steam of fifty pounds pressure and to be non-condensing. He gives 500 to JOOO pounds as the maximum weight to be placed on each wheel, shows that the trains or " suites of car- riages," as he calls them will make their journeys " with as much certainty and celerity in the darkest night as in the light of day," shows that the grades of proposed roads would offer but little resistance, and places the whole subject before the public with accuracy of statement and evident appreciation of its true value. In 1814 George Stephenson, to whom is generally accorded the honor of having first made the locomotive-engine a success, built his first engine at Killingworth, England. In 1815 he applied the blast-pipe in the chimney, by which the puff of the exhaust steam is made useful in intensifying the draught, and applied it successfully to his second locomotive, here seen in section (Fig. 12). This is the essential character- istic of the locomotive-engine. In 1815, therefore, the modern locomotive steam-engine came into existence, for it is this * Printed by T. & ]. Swords, 1160 Pearl Street, New York, 1812. 21C3D5 38 A MANUAL OF THE STEAM-ENGINE. invention of the blast-pipe that gives it its life, and it is the mechanical adaptation of this and of the other organs of the steam-engine to locomotion that gives George Stephenson his greatest claim to distinction. In 1825 the Stockton and Darlington Railroad was opened, and one of Stevenson's locomotives, in which he employed his " steam-blast," was successfully used, drawing passenger as well FIG. 12. STEPHEN-SON'S LOCOMOTIVE, 1815. as coal trains. Stephenson had at this time become engineer of the road. The time required to travel the distance of twelve miles was two hours. One of the most important and interesting occasions in the history of the application of the non-condensing steam-engine to railroads, as well as in the life of Stephenson, was the open- ing of the Liverpool and Manchester Railroad in the year 1829. When this road was built, it was determined, after long and earnest discussion, to try whether locomotive-engines might not be used to the exclusion of horses, and a prize of 500 was offered for the best that should be presented at a date which was finally settled at the 6th of October, 1829. Four engines competed, and the " Rocket," built by Stephenson, received the prize. This engine (Fig. 13) weighed four and one fourth tons, with its supply of water. Its boiler was of the fire-tubular type, a form that had grown into shape in the hands of several THE DEVELOPMENT Of THE STEAM-EXGIXE. 39 inventors,* and was three feet in tKamrtrr^ six feet long, with twenty-fire three-inch tubes* extending from end to end of the boiler. The steam-blast was carefully adjusted by experiment, to give the best effect. Stiry" pressure was carried at fifty pounds per square inch. The average speed of the Rocket on its trial was fifteen miles per hour, amf $* imyfrnnm was nearly double that, twenty-nine miles an hour; and afterward, running alone, it reached a speed of thirty-five miles. In America the locomotive was set at regular work on railroads, for the first time, on the 8th of August, 1829. This first locomotive was buOt by Fos- ter, Rastrick &Co-, at Stourbridge, Eng- land, and was purchased by Mr. Horatio Alien for the Delia- ware and Hudson Canal Company's road from Carbondale to Honesdale, Pennsylvania. It was at about this time (1831) that Mr. Horatio Allen introduced the first eight-wheeled locomotives ever built, and gave them a form which was the prototype of a recentiy-baih locomotive which has been brought out in Great Britain. In this year, also, an engine, the De Witt Clinton, was buflt for John B. Jervis of the Mohawk and Hudson Railroad. At about the time of the opening of the early railroads, the introduction of steam-carriages on the common highway had become a favorite idea with engineers.f In December, 1833, about twenty steam-carriages and traction road-engines were running or weie in course of con- struction in and near London. In our own country the roughness off roads discouraged inventors, and in Great Britain, even, the successful introduc- i & COL, Kew Yotfc. 1879. 4O A MANUAL OF THE STEAM-ENGINE. tion of road-locomotives, which seemed at one time almost an accomplished fact, finally met with so many obstacles that even Hancock and Gurney, the most ingenious, persistent, and successful of constructors, gave up in despair. Hostile legisla- tion procured by opposing interests, and possibly also the rapid progress of steam-locomotion on railroads, caused this result. The steam-blast of Hackworth, the tubular boiler of Seguin, and the link-motion of Stephenson constitute the essential features of the modern locomotive-engine. Locomotives have gradually and steadily increased in size and power from the date of their introduction. The Rocket, which first proved con- clusively, in 1829, the value of steam-locomotion, weighed 4^ tons. In 1835 Robert Stephenson, who had constructed it with his father, writing to Robert L. Stevens, said that he was making his engines heavier and heavier, and that the engine of which he enclosed a sketch weighed nine tons, and could draw " 100 tons at the rate of sixteen miles an hour, on a level." Locomotives are now built weighing seventy tons, and even pne hundred, and powerful enough to draw more than 2000 tons at a speed of twenty miles an hour. The modern loco- motive consists of a boiler, mounted upon a strong light frame of forged iron, by which it is connected with the wheels. The largest engine yet constructed in the United States is said to have a weight of about 200,000 pounds, which is carried on twelve driving-wheels. A locomotive has two steam-cylinders, either side by side within the frame, and immediately beneath the forward end of the boiler, or on each side and exterior to the frame. The engines are non-condensing and of the simplest possible construction. The whole machine is carried upon strong but flexible steel springs. The steam-pressure is usually more than a hundred pounds. The pulling-power is generally about one fifth the weight under most favorable conditions, but becomes as low as one tenth on wet rails. The fuel em- ployed is wood in new countries, coke in bituminous-coal districts, and anthracite coal in the eastern part of the United States. The general arrangement and the proportions of loco- THE DEVELOPMENT OF THE STEAM-ENGINE. 4! motives differ somewhat in different localities, as will be seen later. The common three-ported slide-valve was invented by Mur- doch, while with Watt, about 1799. This valve, driven by a system of single loose eccentrics and stops, for either forward or backward gear, was adopted by Stephenson and others, and probably by some of the first builders of the marine engine, as well as on the locomotive, as early as or earlier than 1820. At about this latter date the heart-shaped cam and its frame came into temporary use, to be superseded in 1840 or 18142 by the so-called Stephenson link. The two eccentrics, for forward and backward motion, with their hooks and the wedge-motion, were also in use during this period, the hooks being the favorite arrangement, towards its close, on locomotives. The link continues in use as, on the whole, the most satisfactory gear, although, since 1855-60, many modifications and the later class of " radial " gears have been brought into competition with it. After their introduction, the growth of railroads and the use of locomotives extended in the United States and in Europe with great rapidity. The first railroad in the United States was built near Quincy, Massachusetts, in 1826. In 1850 there were about 700 miles in operation ; in 1860 there were over 30,000, and in 1890 about 160,000 miles of completed road in the United States ; and the rate of increase has risen in 1873 to above 7000 miles per year, as a maximum, and the consumption of rails for renewal alone amounts to probably a million tons yer year. 42 A MANUAL OF THE STEAM-ENGINE. The now standard engine for any given class of traffic has assumed such exact proportions and such generally accepted form that the engines of any two well-known builders, though readily distinguishable by the expert engineer, appear to the inexperienced observer to be duplicates. Thus the two engines here shown, the one by the Baldwin Works, the other by the Brooks Company, have every essential feature common ; and all are more or less obviously related and modernized forms of the older types of engine. FIG. 15. BROOKS ENGINE. The tubular boiler has been given better proportions and has greatly gained in size ; the steam-blast and smoke-pipe are as used in Stephenson's day ; the whole system of " running gear " is that of Stephenson ; the bell, sand-box, and whistle are characteristic of American practice, but are substantially the same with all American builders. The frame and the gen- eral external arrangements differ from those of the British engine, presently to be shown ; but in even this comparison, the main characteristics of the locomotive-engine remain equally distinguishable and equally striking in both forms. The Gooch and Allan forms of link were brought out about 1855, both giving nearly equal lead at both ends, and simple kinematic chains. Engelmann, in 1859, substituted pins and links for the sliding-block, while Stewart and Fink had already adopted (1857) a single eccentric.* The Von Waldegg-Wal- schaerts gear came out in 1861. * Trans. Engrs. of Scotland; Nov., 1800. THE DEVELOPMENT OF THE STEAM-ENGINE. 43 Hackworth's, the first radial gear, came out in 1859, an< ^ many years later (187888) those of Brown, Marshall, Joy, and Strong. The " drop," the " trip," or the " detachable " gears came in in 1840 with the Hogg, the Sickels (1841), the Corliss (1849), the Greene (1855), and numerous others, both in Europe and the United States. The Steam Fire-engine is still another form of transportable engine, and is peculiarly an American production. As early as 1830, Braithwaite and Ericsson, of London, Eng- land, built an engine with steam and pump cylinders of 7 and 6^ inches diameter, respectively, with 16 inches stroke of piston. This machine weighed 2\ tons, and is said to have thrown 150 gallons of water per minute to a height of between 80 and 100 feet. It was ready for work in about 20 minutes after lighting the fire. The first attempt made in the United States to con- struct a steam fire-engine was probably that of Hodge : who built one in New York in 1841. It was a strong and very effective machine, but was too heavy for rapid transportation. The late J. K. Fisher, who throughout his life persistently urged the use of steam-carriages and traction-engines, design- ing and building several, also planned a steam fire-engine. Two were built from his designs by the Novelty Works, New York, about 1860, for Messrs. Lee & Larned. They were " self-propellers," and one of them, built for the city of Phila- delphia, was sent to that city over the highway, driven by its own engines. The other was built for and used by the New York Fire Department, and did good service for several years. These engines were heavy but powerful, and moved at good speed under steam. The Messrs. Latta, of Cincinnati, soon after succeeded in constructing comparatively light and very effective engines, and the fire department of that city was the first to adopt steam fire-engines definitely as their principal re- liance. The steam fire-engine has now entirely displaced the old hand-engine. It does its work at a fraction of the cost of the latter. It can force its water to a height of 225 feet, and to a 44 A MANUAL OF THE STEAM-ENGINE. jJllii THE DEVEIJQPMEXT OF THE STEAM- EXC1XE. 45 distance of more than 500 feet horizontally, while the hand- engine can seldom throw it one thud these distances : and the "steamer" may be relied upon to work at full power many hours if necessary, while the men at the hand-engine soon be- come fatigued, and require frequent relief. In the modern standard steam fire-engine, Fig. 16. recipro- cating engines and pumps are adopted. There are pairs of engines and companion-pumps,, working on cranks, set at right angles, and turning a balance-wheel set hg-JiwM them. Such machines illustrate the most remarkable concentration of power in small compass, with lightness and strength of parts. As constructed by the best builders, they are composed of cfcoJC"* materials, are exceedingly carefully and well propor- tioned, and are beautifully finished. Their boilers contain little water, and are crowded with J^Jf'ipg surface ; they there- fore make steam with great rapidity ; their pumps have large pacn^gFt and valves of small lift, and deliver large volumes of water easily; and they are arranged on a carriage permitting rapid and easy haulage. The heaviest of these engines rarefy weigh much over three tons, and they are made as light as two 22- The Earif Marine Engine was an early outgrowth of the work on the steam-engine in the latter part of the eighteenth and early portion of the nineteenth century. In 1690 Papin proposed to use his piston-engine to drive paddle-wheels to propel vessels ; and in 1707 he applied the steam-engine which he had proposed as a pumping-enginc to driving a model boat on the Fulda, at CasseL His pumping- engine forced up water to turn a water-wheel, which, in torn, was made to drive the paddles. An account of his experiment is to be found in manuscript in the correspondence between Leibnitz and Papin, preserved in the Royal Library at Ham- over. December 21, 1736, Jonathan HuHs took out an English patent for the use of a steam-engine for ship-propulsion, pro- posing to employ his steamboat in towing. He proposed using the Newcomen engine, fitted with a counterpoise weight, and a 46 A MANUAL OF THE STEAM-ENGINE. system of ropes and grooved wheels, which, by a peculiar ratchet-like action, gave a a continuous rotary motion. There is no positive evidence that Hulls ever put his scheme to the test of experiment, although tradition does say that he made a model, which he tried with such ill success as to prevent his further prosecution of the experiment. In 1774 the Comte d'Auxiron, a French nobleman and a gentleman of some scientific attainments, constructed a steam- boat, and tried it on the Seine, with the aid of M. Perier. This experiment proving unsuccessful, M. Perier built another boat, which he tried independently in 1775, but was again unsuccess- ful, owing principally to the small power of his engine. In 1778, and again 1781 or 1782, the French Marquis de Jouffroy, who, in his later experiments, used quite a large vessel, suc- ceeded in obtaining such good results as to encourage him to persevere, but, political disturbances driving him from his coun- try, his labors terminated abruptly. About 1785, John Fitch and James Rumsey, two ingenious American mechanics, were engaged in experiments having in view the application of steam to navigation. Rumsey's experi- ments began in 1774, and in 1786 he succeeded in driving a boat at the rate of four miles an hour against the current of the Potomac, at Shepardstown, Maryland. Rumsey employed his engine to drive a great pump, which forced a stream of water aft, thus propelling the boat forward. This same method has been tried by the British Admiralty in the Water-witch, a gunboat of moderate size, using a centrifugal p-ump to set in motion the propelling stream, and with some other modifica- tions which are decided improvements upon Rumsey's rude ar- rangements, but which have not done much more than did his toward the introduction of " hydraulic propulsion," as it is now called. John Fitch was an ingenious Connecticut mechanic. After roaming about until forty years of age, he finally settled on the banks of the Delaware, where he built his first steam- boat. In 1788 he obtained a patent for the application of steam to navigation. His boat was sixty feet long and twenty feet wide. The propelling apparatus was a system of paddles, THE DEVELOPMENT OF THE STEAM-ENGINE. 47 which were suspended by the upper ends of their shafts, and moved by a series of cranks, one to each, taking hold at the middle, and giving them almost exactly the motion which is imparted to his paddle by the Indian in his canoe. Fitch's boat, when tried at Philadelphia, was found capable of making eight miles an hour. It was laid up in 1/92. In 1788 Patrick Miller, James Taylor, and William Symming- ton attached a steam-engine to a boat with paddle-wheels, which had been built by the first-named, and tried it for the first time on Dalswinton Lake, in Dumfriesshire, Scotland. This boat having attained a speed of five miles an hour, another was constructed and was tried in 1789. This vessel was driven by an engine of twelve horse-power, and made seven miles an hour. This result, encouraging as it was, led to no further immediate action, the funds of the experimenters having failed. In 1801, however, Symmington was employed by Lord Dundas to construct a steamboat, with a design of substituting steam for horse-power on canals. The Charlotte Dundas, as this boat was named, was so evidently a success that the Duke of Bridgewater ordered eiglit similar vessels for his canal ; but his death, soon afterward, prevented the order being filled. At this time, several American mechanics were also still working at this attractive problem. In i8o2-*3, Robert Fulton, with Mr. Joel Barlow, in whose family he resided, and Chan- cellor Livingston, who had also then taken up a temporary residence in Paris, commenced a small steamboat eighty six feet long and of eight feet beam. The hull was altogether too slight to bear the weight of the machinery, and, when almost completed, the little craft literally broke in two, and sank at her moorings. The wreck was promptly recovered and rebuilt, and in August, 1803, the trial-trip was made in presence of a large party of invited guests. The experiment was sufficiently successful to induce Fulton and Livingston to order an engine of Messrs. Boulton and Watt, directing it to be sent to America, where Livingston soon returned. In 1806 Fulton followed, 4 8 A MANUAL OF THE STEAM-ENGINE. reaching New York in December, and at once going to work on the vessel for which the English firm sent the engine, with- out being informed of its intended use. In the spring of 1807 the Clermont (Fig. 17), as the new boat was christened, was launched from the ship-yard of Charles Brown, on the East River, New York. In August the machinery was on board, FIG. 17. THE CLERMONT, 1807. and in successful operation. The hull of this boat was one hundred and thirty-three feet long, eighteen feet beam, and seven feet in depth. The boat soon afterwards made a trip to Albany, making the distance of one hundred and fifty miles in thirty-two hours running time, and returning in thirty hours. The sails were not used on either occasion. This was the first voyage of considerable length ever made by a steam-vessel, and the Clermont was soon after regularly employed as a passenger-boat between the two cities. Fulton, though not to be classed with James Watt as an inventor, is entitled to the great honor of having been the first to make steam-navigation an every-day commercial success, and of having thus made the first application of the steam- engine to ship-propulsion which was not followed by the retire- ment of the experimenter from the field of his labors before success was permanently insured. The engine of the Clermont (Fig. 18) was of rather peculiar THE DEVELOPMENT OF THE STEAM-EXGIXE. 49 form, the engine being coupled to the crank-shaft by a bell-crank, and the paddle-wheel shaft being separated from the crank- shaft, but connected with the latter by gearing. The cylinders were twenty-four inches in diameter and of four feet stroke. The paddle-wheels had buckets four feet long, with a dip of two feet. FIG. sS. Kxaxe OF THE CLEKMOXT. 1807. Subsequently, Fulton built several steamers and ferry-boats, to ply about the waters of the States of New York and Connecticut. The Clermont was a boat of but 160 tons burden : the Car of Neptune, built in 1807, was 295 tons ; the Paragon, in 1811, measured 331: the Richmond, 1813, 370 tons: and the Fulton the First, built in 1814 '15, measured 2475 tons. The latter vessel, whose size was simply enormous for that time, was what was then considered an exceedingly formidable steam-battery, and was built for the United States Navy. Before the completion of this vessel, Fulton died of disease resulting from exposure. February 24, 1815, and his death was mourned as a national calamity. The prize gained by Fulton was, however, most closely con- tested by Colonel John Stevens, of Hoboken, who has been already mentioned in connection with the early history of rail- roads, and who had been, since 1791, engaged in similar ex- periments. In 1789 he had petitioned the Legislature of the State of New York for an act similar to that granted Living- ston, and stated that his plans were complete and on paper. In 1804, while Fulton was in Europe, Stevens had com- pleted a steamboat sixty-eight feet long and fourteen feet beam, which combined novelties and merits of design in a A MANUAL OF THE STEAM-ENGINE. FIG. 19. S manner that was the best possible evidence of remarkable in- ventive talent, as well as of the most perfect appreciation of the nature of the problem which he had proposed to himself to solve. The steamboat boiler of 1804 (Fig. 19) was built to bear a working pressure of over fifty pounds to the square inch, at a time when the usual pressures were from four to seven pounds. It con- sists of two sets of tubes, closed at one end by solid plugs, and at their opposite extremities screwed into a stayed water and steam reservoir, which was strengthened by hoops. jj ie W jj i c O f t jj e i ower portion was inclosed in a jacket of iron lined with non-conducting material. The fire was built at one end, in a furnace inclosed in this jacket. The furnace-gases passed among the tubes, down under the body of the boiler, up among the opposite set of tubes, and thence to the smoke-pipe. The engine (Fig 20) was a direct-acting, high- pressure condensing en- gine of ten inches diam- eter of cylinder, two feet stroke of piston, and drove a screw of four blades, and of a form which, even to- day, appears quite good. The first of Stevens's boats performed so well that he im- mediately built another one, using the same engine as before, but employing a larger boiler, and propelling the vessel by twin-screws (Fig. 21), the latter being another instance of his use of a device brought forward long afterward as new, and since frequently adopted. This boat was sufficiently success- ful to indicate the probability of making steam-navigation a commercial success, and Stevens, assisted by his sons, built a FIG. 20. MACHINERY OF TWIN-SCREW STEAMER OF 1804. THE DEVELOPMENT OF THE STEAM-EXCItfE. $1 boat which he named the Phoenix, and made the first trial in 1807. just too late to anticipate Fulton. This boat was driven by paddle-wheels. The Phoenix, shut out of the waters of the State of New York by the monopoly held by Fulton and Liv- ingston, was placed for a time on a route between Hoboken and New Brunswick : and then, anticipating a better pecuniary Fie. zi. SinrasV Tvix-Kxns. 1*05- return, it was concluded to send her to Philadelphia to ply on the Delaware. At that time no canal offered the opportunity to make an inland passage, and in June, 1808, Robert L. Stevens, a son of John, started with Captain Bunker to make the passage by sea. Although meeting a gale of wind, he arrived at Philadelphia safely, having been the first to trust himself on the open sea in a vessel relying entirely upon steam-power. From this time forward the Messrs. Stevens, father and sons, continued to con- struct steam-vessels. The steam-engine in most general use for sea-going ships when the introduction of the screw compelled its withdrawal,, with the paddle-wheel which it drove, was that shown in Fig. 22. which represents the side-lever engine of the steamer Pacific, as designed by Charles \V. Copeland. In the sketch, A is the steam-cylinder: HCthe side-rods, or links, connecting the cross-head in the piston-rod with the end- centre, D, of the side-lever D E F t which vibrates about the main centre E, like the overhead beams. A cross-tail at G is connected with the side-lever and with the connecting-rod GH\ 5 2 A --MA-NO At Of THE STEAM-ENGINE. which latter communicates motion to the crank //, turning the main shaft/. The air-pump and condenser are seen at O M. This engine was one of the earliest and best examples of the type, and perhaps the first ever fitted with a framing of wrought-iron. ,8 49 . After the experiments of Stevens, we find no evidence of the use of the screw, although schemes were proposed and various forms were even patented, until about 1836. In 1836 Francis P. Smith, an English farmer who had be- come interested in the subject, experimented with a screw made of wood and fitted in a boat built with funds furnished by a Mr. Wright, a London banker. He exhibited it on the Thames and on the Paddington Canal for several months. In February, 1837, by an accident, a part of the screw-blade was broken off, and the improved performance of the boat called attention to the advisability of determining its best propor- tions. In 1837 Smith exhibited his courage and his faith in the THE DEVELOPMENT OF THE ^TEAM-ENGINE. 53 reliability of his little steamer by making a coasting-voyage in quite heavy weather, and the performance of his vessel was such as to fully justify the confidence felt in it by its designer. The British Admiralty soon had its attention called to the per- formance of this vessel, and to the very excellent results at- tained by the Archimedes, a vessel of 237 tons burden, which was built by Smith and his coadjutors in 1838 and tried in 1839, at- taining a speed of eight knots an hour. By the performance of the Archimedes, the advantages of screw-propulsion, especially for naval purposes, were rendered so evident that the British Government built its first screw-vessel, the Rattler, and Brunei adopted the screw in the iron steamer Great Britain, which had been designed originally as a paddle-steamer. Simultaneously with Smith, Captain John Ericsson was en- gaged in the same project. He patented, July, 1836, a propel- ler which was found at the first trial to be of such good form and proportions as to give excellent results. His first vessel was the Francis B. Ogden, named after the United States Consul at Liverpool, who had lent the inventor valuable aid in his work. The boat was forty-five feet long, eight feet beam, and drew three feet of water. It attained a speed of ten miles an hour, and towed an American packet-ship, the Toronto, four and a half miles an hour on the Thames. This was a splendid success. Ericsson built several screw-boats, and finally, meeting Cap- tain Robert F. Stockton, of the United States Navy, that gen- tleman was so fully convinced of the merits of Ericsson's plans that he ordered an iron vessel of seventy feet length and ten feet beam, with engines of fifty horse-power. The trial of the Stockton, in 1839, was eminently satisfactory. The vessel was sent to America under sail, and the designer was soon in- duced to follow her to this country, where his later achieve- ments are well known. The engines of the Stockton were direct-acting, the first examples of engines coupled directly to the crank-shaft, without intermediate gearing, that we meet with after that of John Stevens. Soon after Ericsson arrived in the United States he obtained an opportunity to design a screw- 54 A MANUAL OF THE STEAM-ENGINE. steamer for the United States Navy, the Princeton, and, at about the same time, the English and French governments had screw-steamers built from his plans, or from those of his agent in England, the Count de Posen. In these ships the Amphion and the Pomona the first horizontal, direct- acting engines ever built were used. They were fitted with double-acting air-pumps, having canvas valves and other novel features. In these ships the Amphion and the Pomona the first horizontal, direct-acting engines ever built were used. They were fitted with double-acting air-pumps, having canvas valves and other novel features. From 1840 the screw gained favor rapidly, and finally began to displace the paddle for deep-water navigation. Progress in this direction was at first somewhat slow. In 1840, and dur- ing the following ten years, many experiments were instituted between the performances of screw and paddle steamers with- out definitely settling engineering practice. The reason was, probably, that the introduction of the rapidly-revolving screw, in place of the slow-moving paddle-wheel, necessitated a com- plete revolution in the design of their steam-engines. And the unavoidable change from the heavy, long-stroked, low-speed engines, previously in use, to the light engines, with small cyl- inders and high piston-speed, called for by the new system of propulsion, was one that necessarily occurred slowly, and was accompanied by its share of those engineering blunders and accidents that invariably take place during such periods of transition. The earliest days of screw propulsion witnessed the use of steam of ten or fifteen pounds' pressure, in a geared engine using jet-condensation, and giving a horse-power at an expense of perhaps seven or eight pounds of coal per hour. A little later came direct-acting engines with jet-condensation, and steam at twenty pounds pressure, costing about five or six pounds per horse-power per hour. The steam-pressure rose a little higher with the use of greater expansion, and the economy of fuel was further increased. The introduction of the surface- THE DEVELOPMENT OF THE STEAM-ENGINE. 55 condenser, which began to be generally adopted some ten or fifteen years ago, brought down the cost of power to between three and four pounds in the better class of engines. At about the same time, this change to surface-condensation helping greatly to overcome the troubles arising from boiler- incrustation, which had checked the rise in steam-pressure above about twenty-five pounds, and it being at the same time learned by engineers that the deposit of the scale and sulphate of lime in the marine boiler was determined by temperature rather than by the degree of concentration, and that all the lime entering the boiler was deposited at the pressure just mentioned, a sudden advance took place. Careful design, good workmanship, and skilful management made the surface-con- denser an efficient apparatus, and, the dangers of incrustation being thus lessened, the movement toward higher pressures recommenced and progressed so rapidly that, now, over one hundred pounds per square inch is very usual, and three hun- dred and fifty pounds has been attained in marine engines built by the Messrs. Perkins, who are said to have reached the remarkable economy of a horse-power for each pound of com- bustible in the fuel consumed in the boiler. These high pressures, and the greater expansion of the steam, in turn, produced another revolution in engine-construc- tion. It at last became generally known that one of the most serious losses of heat, and consequently of power, in the steam- engine, when expansion is carried to a considerable extent, occurs in consequence of condensation and the deposition of moisture upon the interior of the cylinder, which moisture, when the exhaust takes place, carries, by its re-evaporation, large quantities of heat into the condenser, without deriving any power from it. This loss is also, in some degree, prevented by dividing the expansive working of the steam among two or more cylinders, as in the compound system. Here the heat wasted in either cylinder is less, in consequence of the lessened range of temperature ; and that lost by one cylinder is carried into the second, and there, to some extent, utilized. The amount of saving effected by this means is considera- 56 A MANUAL OF THE STEAM-ENGINE. ble so great, in fact, as to have produced a complete revolution in engineering practice in the construction of marine engines by the best-known builders. They, under the lead of John Elder, adopted the Woolf engine, which had, in earlier times, with lower steam, less expansion, and less intelligent engineer- ing, proved apparently a failure. To-day all sea-going steamers are fitted with multi-cylinder engines having surface-condensers, and with tubular boilers, which are fitted, frequently, with superheaters. The latest and largest of the paddle steamers of the Cunard line, the Scotia, built in 1862, was 379 feet long, and of 3871 tons burden ; crossing the Atlantic in less than nine days. The engines were side-lever, and 100 inches diameter of cylinder, 12 feet stroke, making 18 revolutions per minute, and producing 4500 horse-power. The marine two-crank compound screw-engine was intro- duced still later into the United States. The George W. Clyde was built by the Messrs. Cramp in 1871 ; who, in 1885, also built a triple-expansion engine from the designs of Mr. See, for the Peerless steam-yacht, as an experiment to de- termine the value of the system. Its success led to their per- manent adoption of that type. The U. S. S. Vesuvius, in 1889, had such engines, and developed 4440 I. H. P., with a weight of machinery of but 252 tons ; and gave a speed of 21.65 knots, with about 900 tons displacement. The engines of the U. S. S. Newark, of the same kind, and horizontal and direct-acting, developed 11.64 horse-power per ton weight, a total of 8860 I. H. P. The later development on the ocean included the steamers Teutonic and Majestic, built in 1889-90. The former crossed the Atlantic, from Queenstown to New York, in 5 days, 19 hours, 5 minutes, the quickest trip recorded at its date. These vessels are of 10,000 tons burden, 17,000 horse-power, and 582 feet long, 57^ feet beam, and 39^- feet depth. They have twin-screws, with independent triple-expansion engines. They carry 1600 people, of whom 1300 are passengers and 168 in the engineer's crew. THE DEVELOPMENT OF THE STEAM-ENGINE. 57 The steam-cylinders are of 43, 68, and I ID inches diameter, and 5 feet stroke, making, at speed, 82 revolutions per minute. The surface-condensers each contain 20 miles of brass tubes, \ inch diameter. The propellers are 19 feet diameter and 28^ feet pitch ; twin-screws, with four blades. Twelve boilers, containing 84 furnaces, with steam at 180 pounds, supply the engines. The feed-water amounts to 120 tons, the condensing water to 4000 tons, per hour, and the coal burned to 320 tons per day. The thrust on the two propellers is about 75 tons, total* (See Fig. 24.) The advances made in steam-navigation since the days of Stevens and Fulton may perhaps be best realized on com- paring a modern steam-yacht of similar dimensions with the little screw boat of 1804. That here shown, as built by the Douglas Co., at Waukegan, Illinois, has very nearly the same measurement 26 feet length, 6 feet beam but it weighs only FIG, 23. SMALL STKAH-YACHT. one ton, carries an engine of 3 effective horse-power, and has a speed of about six miles an hour, a higher speed than that of Fulton's Clermont, a boat of five times its length. 23. The Later Phases of construction are given in more detail in 24. By the year 1880, the standard form of marine engine, for large powers and for long voyages, had become the "compound," or double-cylinder type, expanding steam from a pressure of 75 to 90 pounds (5 to 6 atmospheres), by gauge, through two cylinders, " in series," into a condenser, * London Engineer, Dec, 19, 1890, $8 A MANUAL OF THE STEAM-ENGINE. the expansion terminating at 7 to 10 pounds per square inch ( to f atmosphere) above vacuum. The largest engines were constructed with a pair of low-pressure cylinders, to reduce the difficulties experienced in the attempt to make so large a single low-pressure cylinder ; and these were called " three-cylinder compound engines." In 1890, " triple-expansion engines" had become common, employing three cylinders li in series," and using steam of loto 12 atmospheres pressure (150 to 180 pounds per square inch by gauge), and the largest of these were given twin low-pressure cylinders. Speeds of piston of 600 to nearly 1000 feet, and 70 to 90 revolutions per minute, were usual, with engines of 5 feet stroke and more, producing 10,000 to 20.000 I. H. P. in the propul- sion of the largest and fastest steamships. Meantime, the weight of machinery fell from about 1000 to 400 or 450 pounds per horse-power. Ratios of expansion were restricted, usually, to 3 or 5 in simple, 7 to 8 in compound, and 12 to 15 in triple-expansion engines, and the cost in fuel consumed dropped from 2^ or 3 pounds per I. H. P. per hour to 2^ and 2 and to i or even less, under favorable conditions. The steady rise in steam-pressures during the century is best illustrated by naval steam-engineering. In the time of Watt and up to about 1840, the usual pressure in the low-pressure side- wheel engines of that period was from 4 to 7 pounds ( to ^ atmosphere) by gauge, and the rude flue-boilers then in use were of the simplest and weakest forms. By the middle of the century the fire-tubular boiler had come into quite common use, and pressures had risen to double those above stated. Between 1850 and 1860, the customary pressures in new engines and boilers had become 20 to 25 pounds (i| to if atmospheres) and, the introduction of the surface-condenser removing the princi- pal difficulty, the later rise in pressure was rapid and has never ceased. At the pressure then reached, the deposition of the calcium sulphate contained in sea-water was complete and the conse- TOE DEVELOPMENT OF THE STEAJi-EXGlXE. 59 quent loss of economy was very serious. The use of the sur- face-condenser, by reducing this loss,, produced a gain of 15 or 20 per cent. . The type of boiler was next made the cylindrical, Scotch, form, with large flues serving as furnaces and the gases re- turned through tubes, both flues and tabes enclosed in one cylindrical shell, and, the compound engine introduced, the pressures rising rapidly to 60 or 75 pounds (4 or 5 atmospheres), by gauge, these changes respiting in a further economy of 30 or even 40 per cent in engines designed during the decade 1860-70. The next ten years carried pressures for compound engines up to 90 and 120 pounds (6 and 8 atmospheres) and the triple-expansion engine, coming into use, 1875-801, die jMca&uic has risen one fourth or one third more, this type giv- ing a gain of 15 or 20 per cent over the earlier compound _ The following have been considered fair average figures, as representing what was good and standard practice at the dates given, and as illustrating the piugmat fr^fr' 1 in wnnmin* engi- neering in the period 1870-90: Cooflpcrl H.F. .:,-:: :- : - I .-: ~- 1*30 50 X.I 375 = :: : ^ 480 jSo Tii|ili ---------- iSgo :-- i-3 * ' 450 In exceptional cases, as in torpedo-boats, the progiebe. in Hgin^raingfriachfncr>, but not in efficiency, has been still greater. piston speeds having risen to above 1000 feet per minute. The weights of the two- and of the three-cyunder compound engine, as now customarily buflt. are not very different. Forexample, the following, as given by Mr. Hall in 1887, gives the weights of two selected TWD Cyfl. Tbrce Cy - -' 1150 lifo : : 457 60 ;. . ,' A MANUAL OF . THE STEAM-ENGINE. The difference is here rather less than ten per cent, in favor of the later type. The gradual reduction of weights of steam machinery dur- ing the period succeeding the middle of the nineteenth century- is best illustrated by reference to the changes effected in naval work. The minimum weight in 1850 was about 200 pounds each, engines and boilers, per I. H. P., 400 pounds total ; while these figures were reduced by 1860 to about 175 and 350; in 1870 to 150 and 300; in 1880 to 125 or 140, and 275 or 280; in 1885 to 80 or 90 for engines, and 100 for boiler, less than 200 total; and in 1 890 to 40 or 50, 70 or 75, and 100 to 125 total, and even less in exceptional cases, as in fast yachts and torpedo- boats. The lightest examples are as low as 60 or 80 pounds, total, per horse-power. The adoption of simple types, of high engine-speed, and of forced draught is the secret of the rapid gain at the later dates. According to Sennett, the reduction in weight of the ma- chinery of naval vessels has steadily progressed since the early part of the nineteenth century, and since the advent of steam navigation. In 1832, with side-lever paddle-wheel engines, flue- boilers carrying but 4 Ibs. of steam, and jet-condensers, there was but 1.45 I. H. P. obtained per ton of weight. Tubular boilers and 9 Ibs. pressure increased the power to 3.14 I. H. P. per ton in 1845 oscillating engines and 14 Ibs. of steam to 4.72 I. H. P. per ton in 1850; screw engines and 20 Ibs. of steam to 5.52 I. H. P. in 1857 : anci the surface-condenser and 30 Ibs. of steam to 7.5 I. H. P. per ton in 1870. The compound engine with 6b Ibs. of steam only gave 6.4 I. H. P. per ton of machinery in 1876, but greatly reduced the total weight carried on account of reduced coal consumption. Triple compound engines produce a saving in fuel, rather than of weight, to be carried. The increase of weight due to compound and triple compound engines is chiefly caused by the heavier boilers re- quired for the higher pressures, though the engines are also generally somewhat heavier. The introduction of forced blast has enabled the weight of the boiler to be reduced, and this, with high speed, reduces the weight of the engine so that tor- THE. DEVELOPMENT OF- THE STEAJt-EXGJXE. 6l pedoJboat machinery in 1880 gave 3jj66 I. H. P. per ton of weight, and in a last steamer butft in 1882, 12.36 L H. P. was obtained per ton of weight. The later progress and current practice in the application of steam-power in smaH boats is well shown by the facts in the department of naval construction ; and especially in the recent introduction of surface-condensation and compounding and of a forced draught. About 1863-5, the naval steam-launch was about 40 feet long, was fitted with a high-pressure engine of 25 H. P. T and had a speed of 6 knots. In 1870 the speed and power had risen to 8J knots and 50 H. P.: in 1880 to nearly ten knots with nearly the same power, in consequence of im- 62 A MANUAL OF THE STEAM-ENGINE. proved lines and higher efficiency of machinery and reduced weights. At this date, a boat sixty feet long, with engines of 150 H. P., and weighing 6 tons, attained a speed of 15 knots (17^ miles, nearly). Recent trials of simple and compound engines, in competition, as reported to the British Admiralty, gave 7^ and 4 pounds of fuel as respectively required. Their weights were nearly the same : 180 and 150 pounds, nearly, per I. H. P.* By the introduction of forced combustion in the boiler-room, of steam steering, and of anchor- and cargo-hoisting machin- FIG. 25 THE NEW YORK. ery, and various other changes, the number of tons trans- ported per person employed on shipboard has been increased from 2 to 3^ between 1860 and 1890, or about doubled in the present century. The speeds of passenger-steamers now often exceed 20 knots (about 23 miles) an hour for an average, crossing the Atlantic. The mean of sixteen voyages of the City of New York, the City of Paris,t and the Teutonic was about six days and a quarter, between New York Bay and Queenstown harbor (1890). In contrast with the Clermont, we may note the principal * Machinery of Small Boats; A. Spyer ; Trans. Brit. Inst. N. Archts., XXVIIth Session. f From paper by Mr. C. E. Emery in the Scientific American Supplement, 1890. THE DEVELOPMENT OF THE STEAM-ENGINE. 63 features of the steamer New York, built eighty years later, for the same route, by the Harlan & Hollingsvvorth Company, and " engined " by the W. & A. Fletcher Company. (Fig. 25.) The dimensions of hull are as follows : Length on the water-line 301 feet. Length over all 311 " Breadth of beam, moulded 40 " Breadth of beam, over guards 74 " Depth, moulded 12 "3 ins. Draught of water 6 " Tonnage (net, 1091.89) i$5 2 -S 2 The wheels are aft of the centre of length, instead of for- ward a great improvement in the appearance of the boat. The engine is a beam-engine, with a cylinder 75 inches dia- meter and 12 feet stroke of piston, provided with Stevens' cut- off. The use of a surface-condenser, instead of a jet-con- denser, in this river steamer, is a change made to overcome the evil of using mixed salt and fresh water in the boilers, as the tides extend to Albany and the water changes from salt to fresh en route. Another change is the return to the use of Stevens' feather- ing wheels. These are 30 feet 2 inches diameter outside of buckets. There are twelve curved steel buckets to each wheel. Each bucket is 3 feet 9 inches wide and 12 feet 6 inches long. The wheels are overhung, and they have a bearing on the hull only. The feathering is effected in the usual manner by driv- ing and radius bars, operated by a centre placed eccentric to the shaft and held by the " A-frame " on the guard. These wheels were introduced in the New York for the purpose of gain- ing speed, and the trial-trip shows that the builders' expecta- tions were completely fulfilled. Absence of jar is another gain obtained by the use of these wheels, and the comparatively thin buckets enter the water so clean and smooth that one notices, not the shake so common on boats with the ordinary wheels, but an almost entire absence of it. Steam is supplied to the engine by three return-flue boilers, 64 A MANUAL OF THE STEAM-ENGINE. each g\ feet diameter of shell, 1 1 feet width of front, and 33 feet long, constructed for a working pressure of 50 pounds per square inch. Each boiler has a grate-surface of 76 square feet or 228 square feet in all, and with the forced draught produce 3850 horse-power. The exterior is of pine, painted white relieved with tints and gold. The interior is finished in cabinet work, and is all hard wood, ash being used forward of the shaft on the main deck, and mahogany aft and in the dining-cabin. Ash is also used in the "grand saloons" on the promenade deck. The saloon-sides are almost entirely of glass, and the windows so low that persons seated inside have an opportunity to view the scenery. The Puritan, Fig. 26, illustrates the adaptation of this type of steamer, so nearly perfected by Robert L. Stevens, to that kind of navigation, intermediate between river, or still-water, and oceanic, which permits the retention of some features of the former, while modifying the shape of hull and type of engine to meet the demands of " outside " navigation. The plans of this steamer are by Mr. Pierce, the details of hull-construction by Mr. Faron, and the machinery by the W. & A. Fletcher Co. The principal dimensions are as fol- lows : Length over all, 420 feet ; length on the water-line, 404 feet; width of hull, 52 feet; extreme breadth over guards, 91 feet ; depth of hull amidships, 21 feet 6 inches ; height of dome from base-line, 63 feet ; whole depth, from base-line to top of house over the engine, 70 feet. Her total displacement, ready for a trip, is 4150 tons, and her gross tonnage 4650 tons. The ship is fire-proof and unsinkable, having a double hull, divided into 59 water-tight compartments, 52 between the hulls and 7 made by athwartship bulkheads. In the fastenings of hull and compartments there were used 700,000 rivets, and upwards of thirty miles of steel angle-bar. Her decks are of steel, wood-covered. Her masts are of steel, and hollow, to serve as ventilators, and are 22 inches in diameter. Her pad- dle-wheels are encased in steel. The hull is of " mild steel," twenty per cent stronger than 66 A MANUAL OF THE STEAM-ENGINE. iron. The wheels are of steel, and are 35 feet in diameter out- side the buckets. The buckets are 14 feet long and 5 feet wide, each bucket of steel inch thick, and weighing 2800 pounds without rocking arms and brackets attached. The total weight of each wheel is loo tons. The wheels are " feathering," and turn at the rate of 24 revolutions a minute. The boat has a compound, vertical, beam, surface-condensing engine of 7500 horse-power. The high-pressure cylinder is 75 inches in diameter, and 9 feet stroke of piston. The low-pres- sure cylinder is 110 inches in diameter, and 14 feet stroke of piston. The surface-condenser has 15,000 square feet of cool- ing surface and weighs 53 tons. Of condenser-tubes of brass there are 14^ miles. Her working-beam is 34 feet in length from centre to centre, 17 feet wide, and weighs 42 tons. The section of beam-strap measures 9i X ni inches. The main centre of the beam is 19 inches in diameter in its bearings. The shafts are 27 inches in diameter in main bearings, and 30 inches in gunwale bearing. They weigh 40 tons each. The cranks weigh 9 tons each. The crank-pin is 19 inches in diameter and 22 inches long. The boilers contain 850 square feet of grate-surface and 26,000 square feet of heating surface. The products of com- bustion pass through two super-heaters, 8 feet 10 inches inside diameter, and 12 feet 4 inches outside diameter, by 12 feet high; thence into two smoke stacks, the top of each being 101 feet i inch from the keel. The dining-saloon is 108 feet 4 inches in length, by 30 feet in width, and 12 feet in height. There are 12 miles of electric- lighting wire, and, including annunciators, fire-alarm, etc., there are twenty miles of wire and twelve thousand feet of steam-pipe. There are capacious gangways and staircases, lofty cornices, and ceilings supported by tasteful pilasters, the tapering columns of which, in relief, flank exquisitely-tinted panelling throughout the length of her saloons. Every con- venience known to civilization, and which can contribute to the ease and comfort- of the traveller on land or when afloat, is in- cluded in the internal arrangements of this floating caravansary. THE DEVELOPMENT OF THE STEAM-ENGINE. 67 The electric-light currents are generated by four dynamos, each designed with a capacity of 400 lights, or a total of 1600 lights, but capable of maintaining 1850 lights if required. These great steamers have all the essential features of the earlier river-boats of Stevens : the same long, flat, shallow hull, the widely-extended guards and main deck ; the " hog-frames" stiffening the whole structure ; the same type of " beam-engine," as a rule : and the high deck-houses ; but the progress of the century is seen in their enormous size, great power and speed, and their innumerable conveniences and luxuries. The fleets of vessels employed on the great lakes between the United States and Canada have become mainly steam- fleets ; the principal part of the lake transportation of ores, tim- ber, and grain being now carried on in craft like that seen in the accompanying illustration, a type of vessel peculiarly American. The figure represents the Tuscarora, built at Cleveland, by the Globe Iron Works, for the Lehigh Valley fleet, at a cost of about $250,000. Vessels of this class are built of steel and fitted with multiple-cylinder engines, and are both fast and economical. The Tuscarora is 312 feet over all, 40 feet beam, and 25^ feet deep. The weight of hull exceeds 1600 tons. She has OS A MANUAL OF THE STEAM-ENGINE. two flush steel decks, the top covered with 3-inch pine, and an additional' tier of deck-beams below, or a third deck. The water-bottom runs clear aft, and there are three longitudinal keelsons on either side of the main keelson. The triple-expan- sion engines have 24-, 38-, and 6t-inch cylinders of 42 inches stroke. There are three boilers, 12 X \2\ feet, carrying 160 pounds of steam. '" The growth of tonnage on these lakes now exceeds 100,000 tons per annum ; or about the same as the total of the At- lantic and Pacific coasts. The steamers employed are usually very similar in general construction to that here illustrated, the high deck-houses and cabins of the river steamer being necessarily omitted as a matter of safety, and the comparatively smooth and low house of the ocean steamer substituted. The deeper water also permits the use of the screw on the largest vessels. 24. Recent Applications of the multiple-cylinder engine have become usual in every department of steam-engineering. The efforts of Hornblower and of Wolff and their contemporaries failed, partly because of the active business competition of Boulton and Watt, who possessed at the time enormous advan- tages and immense power, but mainly because the steam-pres- sures and speeds of piston then adopted were too low, and the practicable range of expansion was too small, to permit the advantages of the more complex type of engine to become obvious and important. But when the steam-pressure carried on other engines began to rise toward three and four atmospheres, the ratios of expansion to exceed three or five, the serious wastes arising from initial cylinder-condensation began to be seen, and were found to place an early limit to economically increased expansion. This limit, as well as the economical operation of the engine at the earlier limit, was promptly modified when the new construction was adopted ; and it was found that not only was the efficiency of the engine at ratios of expansion then considered maxima greatly increased, but that it was possible to economically extend expansion very much farther than was practicable in a single cylinder. As steam-pressures continued THE DEVELOPMENT OF THE STEAM-EXGIXE. 69 to rise, and as expansion was correspondingly increased, the gain by compounding became more observable and important, and the new engine found more general application; nntil now it is employed almost exclusively in marine engineering, and very extensively in other departments. The increase of steam-pressure above one hundred pounds per square inch, above six or seven atmospheres, has led to the introduction of the triple-compound, or "triple-expansion." engine, and pres- sures exceeding ten atmospheres are already making the " quadruple-expansion " engine a desirable type where great economy of fuel is essential. In all cases, in marine engines, it is found advisable, in good types of engine, to expand steam down to from ten to eight pounds per square inch above per- fect vacuum, to about a half atmosphere pressure, to secure best results. The better the design the lower this limit. The advantages of the multicylinder engines have become so evident that, since about 1870; they have been adopted as standard by the .navies of the world, in spite of the obvious objections to high steam and their inflexibility of power adjust- ment in modern warfare. Multiple-cylinder marine engines are used to the almost entire exclusion of the older forms of simple engine. Although invented by Horn blower in 1781, and, in the more common types, by Wolff in 1804, it was only when, a half-century later still, Messrs. Randolph and Elder in the screw- steamer Brandon (1854) and the paddle-steamers Valpa- raiso and Xica and others, still later, of the Pacific Steam Navigation Co.. made this type practically a success, that it attracted the general attention of engineers. From that time it has steadily and rapidly displaced the simple engine. The gain of the two-cylinder compound engine, when compared with the standard simple marine engine, was found to be from 20 to 40 per cent, averaging in those early days probably 33 per cent. This was enough to secure their general introduc- tion with great rapidity, once the fact was established. The most common form given the two-cylinder compound engine, of the. best construction, is that shown in a succeeding 70 A MANUAL OF THE STEAM-ENGINE. illustration (Chap. II, Fig. 112), and is that almost universally adopted for vessels of the merchant marine. Many designs, dif- fering greatly among themselves and from the above, have been introduced into the ships of the fighting classes in the navy, having mainly in view the reduction of their vertical dimen- sions and getting them well below the water-line and out of reach of shot. It is also sometimes attempted in naval engines to so make their steam-connections that either or both cylinders may be supplied with steam directly from the boilers, should any exigency or an emergency make it desirable. The principles of designing, of proportioning, and of construction are precisely the same, however, whatever the method of grouping the engine-cylinders or their details and accessories. In the cases, becoming common in the United States, but comparatively rare in Europe, in which the engine is proposed to be made a beam-engine and is to drive paddle-wheels, the usual method of compounding is to place the two cylinders at the same end of the beam and as closely together as possible. In the Buckeye State, designed by Mr. Erastus Smith about the middle of the century, the low-pressure piston was an annulus working between the exterior surface of the high-pressure and the internal surface of the low-pressure cylinder ; both pistons being connected to a common cross-head and, by the same pair of links, to the extremity of the beam. The compound engines of the City of Fall River were found to give higher efficiency, by one fourth or one third, than the simple engines customarily employed on Long Island Sound in the same work.* Perhaps as near an approach to ideal efficiency as has yet been recorded, all things considered, is that of M. Normand's torpedo-boat in the French navy, No. 128; the engines of which are reported to have demanded but 0.462 kilogs of fuel per horse-power and per hour (1.16 Ibs. per British H. P.). These engines were "receiver-compounds," with steam * Report on the City of Fall River, by Messrs. Sague and Adger ; with intrt duction by R. H. Thurston; Jour. Frank. Inst., July, 1884. THE DEVELOPMENT OF THE STEAJi-ElfGIXE. /I entering at 4.3 atmospheres (70 Ibs.), with clearances of 10.6 and 614 per cent.* The power attained was 940 I. H. P., the displacement of the hull being about 35 tons ; and speed not far from 10 knots, the maximum,, when driven, being 21 knots. The principal source of this exceptional economy is presumed to be a remarkably effective system of feed-water heating by intermediate steam to 212* F.; full compression in the small cylinder ; and a slight degree of superheating by " wire-drawing "* the steam. The boiler-steam had a pressure nearly three times as great as that in the steam-chest. M. Normand has since, nevertheless, substituted the triple-expansion engine for the compound.* The Triple-expansion Engine has succeeded the ordinary two- cylinder compound machine in regular work of the merchant kvy for long routes, and is also occasionally adopted for station- ary engines where the cost of fuel is such as will justify the some- what increased cost of construction. By its use, it is found practicable to raise the steam-pressure to above ten atmospheres (150 Ibs. and upward! and to increase the ratio of expansion to 15 or more, with good results. The great cost of fuel and the value of tonnage-space on shipboard have hastened this advance in marine-engine design. Mr. O. E. Seaton, comparing sister- ships fitted with the two types of engine, found this change to produce a saving of about 20 per cent over the two-cylinder compound engine, a difference substantially that predicted by computations assuming the usual differences of pressure and ratios of expansion and a reduction by one-third of the cylinder- wastes. ** Triple-expansion** engines were introduced as early as 1874 by Mr. A. C. Kirk in designing the machinery- of the S.S. Pro- pontis of Liverpool, the steam being supplied at 160 pounds pressure by water-tube boilers of the Rowan type : Mr. Kirk ob- serving that a ratio of expansion exceeding 2\ was not practically more advantageous than this value : as higher ratios so exag- gerate internal wastes as not to be economical in a single * OCoal Repon: Mem. de h Soc. des log. Ciriis: Dec. *go: P" *M- t Ibid. 72 A MANUAL OF THE STEAM-ENGINE. cylinder. The result was a considerable gain in economy of steam and fuel. This type of engine in the long voyage between London and Australia (1880) has given similar economy, saving 500 tons in the voyage and permitting the carrying of 500 tons additional freight. Quadruple expansion in engines carrying 175 to 200 pounds steam has been introduced (1885), and promises still further advantage should it prove practicable to construct satisfactory boilers. Quadruple-expansion, four-cylinder, compound engines are adopted occasionally when steam-pressures are higher than advisable for triple expansion, and permit the economical em- ployment, often, of twice the pressure, or more, customary in ordinary compound engines and a third, or more, higher than with triple expansion ; and the best ratios of expansion are cor- respondingly increased ; 20 and 25 being not unusual values. In the arrangement of this engine, the cylinders are variously grouped by the different designers ; all of whom, however, endeavor to secure a combination of lightness, compactness, small clearance-spaces, and good steam-distribution, with uni- form rotatory action on the crank-shaft. A common design mounts two cylinders on the upper ends of the other two, thus, in effect, producing a pair of " tandem " engines, with the two cranks at right angles and with properly proportioned receiv- ers ; in other designs, three cranks are employed in order to secure more uniform turning moments, and in such examples one crank is acted upon by two cylinders ; while the others are connected to a single piston each. A less compact and more weighty and costly design applies each of the four pistons to each of four cranks, giving admirably good rotative effect, but sacrificing something of the advantages of the other types. For boiler-pressures exceeding 15 atmospheres (above about 225 pounds per square inch) the quadruple-expansion engine is unquestionably an economical form, and for marine pur- poses, or where fuel is very costly, it is likely to supersede even the triple-expansion engine. THE-0EVELOPMENT OF THE '-STEAM-ENGINE. 73 25. The Process of Development of the steam-engine is, fn resume, as follows : * A century ago, James Watt had just begun to introduce the first engines belonging to a, then, new type.f A century be- fore (1698), the ingenuity and practical skill of Captain Savery had conferred an enormous benefit upon the mining industries, and through them upon the world, by applying the " fire-en- gine " of the Marquis of Worcester to raising water from the then rapidly deepening mines. Savery used steam of 8 to 10 atmospheres (120 to 150 pounds) total pressure, in some cases: and he is entitled to fame as the first to introduce that now familiar concomitant of civilization, the steam-boiler explosion. The usual pressure was 3 atmospheres. These engines de- manded about 30 pounds of coal, per horse-power per hour, as a minimum. The apparatus of Savery was not what would to- day be called a steam-engine, at all. It was not a train of mechanism, involving moving parts, cylinder, piston, crank, and fly-wheel. H uyghens ( 1 680) and Papin ( 1 690) proposed true en- gines with steam-pistons traversing their cylinders, and forming, on the whole, much such a train of mechanism as is now so well known ; but the Newcomen engine was the first of this type to come into practical use. A writer of that time states that " Mr. Newcomen 's invention of the fire-engine enabled us to sink our mines to twice the depth we could formerly do, by any other machinery: " but " every fire-engine of magnitude con- sumes 3000 worth of coal per annum." The coal-consump- tion was, at best, about 20 pounds per hour and per horse- power. It was this engine that Watt found in operation, when he entered upon the stage. Watt was not simply a mechanic ; he was a real philosopher, and a truly scientific investigator. He found that the sources of loss in engines were the conductivity and radiating power * Stationary Steam-engines ; R. H. Thurston ; N. Y., J. Wiley & Sons, f History of the Growth of the Steam-engine. International Series. N. Y., D. Appieton & Co. t Mem. Acad. ScL; Paris, 1680. Ada EnuKtontm; Leipsic, 1690. >j Mintralegia CormttbUnfis; Price ; 1778. Appendix. 74 A MANUAL OF THE STEAM-ENGINE. of the steam-cylinder, the alternate heating and cooling of the metal at each stroke, the imperfect vacuum, and the wastes from boiler and steam-pipes. To correct these defects, he clothed his boilers and steam-pipes with non-conductors, sometimes even making boiler-shells of wood. Smeaton had already covered the pistons and cylinder-heads with wood. Watt made a more practicable improvement, however, when he devised the steam- jacket. He attached a separate condenser, closed the cylinder at the top, made the engine double-acting, and finally adapted the engine to drive machinery, fitting it with shaft and fly- wheel, throttle-valve and governor, and thus making the steam- engine such as we see it to-day, in all essential particulars. His engine was substantially complete by the year 1784.* Later changes have been a succession of refinements, and of developments in application. Stephenson, and his contem- poraries, applied steam on railroads ; Stevens, Fitch, and Evans, and, finally, Fulton, in the United States, and Bell and others, in Europe, introduced steam navigation ; Sickels in- vented the " detachable " cut-off valve-gear ; Corliss introduced the peculiar type of engine that has given him fame, and so attached its governor as to determine the point of cut-off au- tomatically, and thus to regulate the engine. Robert L. and Francis B. Stevens designed the American river steamboat, and its beam-engine, with so simple and effective a valve-gear that it remains, to-day, still standard. The compound engine, even, was brought out by contemporaries of Watt, and thus every prominent feature and essential detail of the modern steam-engine was introduced at, or before, the middle of the nineteenth century. Yet practice has been steadily changing since his time ; and the form and proportions of the steam-engine, and the methods of steam distribution, have been undergoing constant changes. In the days of Watt, steam was worked at about 7 pounds pressure, per square inch, in stationary engines ; they were al- ways fitted with condenser and air-pump, were slow in move- * History of the Growth of the Steam-engine, p. 119. Farey on the Steam- engine. THE DEVELOPMENT OF THE STEAM-EXCIXE. 75 ment, and were, consequently, of small power in proportion to their size ; they wasted heat and fuel to such an extent as to de- mand 6 or 8 pounds of coal per horse-power and per hour. It is true that Wolff, in 1804, expanded 6 or 8 times, using high- er steam, and obtained the horse-power with 4 pounds of fuel per hour, and that John Stevens and Oliver Evans, in the United States, and Trevithick, in Great Britain, had already used still higher steam in non-condensing engines : but these examples simply illustrated the fact that isolated examples which lead standard practice by a half-century, or more, are to be observed during the growth of every art. Although the principles of steam-engine economy were, in the main, well understood by Watt and his competitors, and have become well settled in later years, we are still far from a completely satisfactory solution of the problem, which, as stated by the Author elsewhere, may be enunciated thus : To construct a machine which shall, in the most perfect manner possible, convert the energy of heat into mechanical power: the heat being derived from the combustion of fuel, and steam being the receiver and conveyer of that heat. Watt's first condenser has been seen to have been a surface- condenser. He immediately afterward adopted a jet-con- denser, however, to obtain " a surface sufficiently extensive to condense the steam of a large engine," and to avoid the diffi- culties that might arise should the condensing water " crust over the thin plates "* of the surface-condenser. The surface-condenser was used by Mr. S. Hall, in 1838. on the steamship Wilberforce. This condenser had 2374 copper tubes, 8 feet long and one-half inch in diameter, placed verti- cally in a box. cooling surface about 2486 square feet, and 8.72 square feet of condensing surface per horse-power. The tubes became coated with mud, and were removed ; the surface- being changed to a jet-condenser. In 1859 the P. & O. Steamship Co. adopted surface-condensation on the Moulton. The condenser had 1 178 tubes. 5 feet 10 inches long, f inch in diameter, 0.05 inch thick, or a surface of 4200 square feet. 2.42 square feet of condensing surface per I. H. P. The tubes were 7 6 A MANUAL OF THE STEAM-ENGINE. packed with linen tape and screwed glands. The circulating water was controlled by a centrifugal pump, probably the first independent circulating-pump ever used. The tubes were ver- tical and the refrigerating water ascended them on the outside. Since that date their use has become general ; the pioneers in the United States having been Lighthall and Sewall. The general introduction of electric-lighting systems, which ordinarily employ " dynamos " driven at very high velocities of rotation, brought about a remarkable and radical change of practice in steam-engine design and construction. The de- mand became imperative for a motor system which should provide power with decreased weight and volume of engine and machinery, and this concentration of power required to be accompanied by a corresponding increase in speed of engine- piston and of rotation, and a much better regulation. Expe- rience has generally led to the adoption, where practicable, of independent engines to each dynamo, and only the high speed of the modern engine is, ordinarily, considered suitable to this work. Steam-pressures have risen, since the improvement of the steam-engine by Watt was begun, somewhat as follows, at sea and in condensing engines : Year. A.D. l8OO St lb o tc earn Pressure; s. atr 5 o t 7 i ' 10 20 20 I 25 I 30 l 60 2 90 4 120 5 200 8 nos. I- I- 2 4 6 8 20 1810 c " 1820 c " 1830 IO " 1840 1C" 1850 1C" 1860 20 " 1870 1880 60 " 1885 i 800 . . . . 100 " In many cases, considerable variations from these figures have been observed ; but they may be taken as representative THE DEVELOPMENT OF THE STEAM-ENGIXE. 77 of what was generally thought good practice at the several dates. The history of progress in marine engineering in the latter half of the nineteenth century is exceedingly instructive. As the power of the engine is, if properly proportioned, in the ratio of its speed of piston or, with any one engine, to its revolutions in the unit of time, these speeds have risen from 500 or 600 feet to 1000, and from 40 or 50 to 80 and 100 revolutions, with even large engines. Simple engines at 25 pounds pressure have been superseded by compound engines at 60 to 80 and these by triple and quadruple expansion from 150 and 200 pounds ; while gaining 30 per cent or more in the first step and 20 or more in the second, all costs considered. Forced draught at 6 inches water pressure has been used, and the speed of similar ships raised from 10 or 12 knots to 15 and then to 1 8 and 20, each square foot of heating surface giving, in some cases, 20 horse-power. In 1 890 the combined power of all the prime movers in the world using steam as the working fluid was not far from 100,- OOO,OOO horse-power, of which the United States had about 15,000,000, Great Britain the same, France and Germany, col- lectively, a similar amount, and the balance was distributed among other nations. Taking the horse-power as the equiv- alent of the \vork of five men, as an average, including over- time, the work of steam is the equivalent to that of a popula- tion of working men amounting to 500,000,000, to a total population of 2,500,000,000, or to about quadrupling the work of the globe. 26. The Philosophical Study of this development will be seen to give rise to the following : We may rapidly note the prominent points of improvement, and the most striking changes of form; and may thus obtain some idea of the general direction in which \ve are to look for further advance. Beginning with the earlier machines, we there found a single vessel performing the functions of all the parts of a modern pumping-engine ; it was at once boiler, steam-cylinder, and 78 A MANUAL OF THE STEAM-ENGINE. condenser, as well as both a lifting and a forcing pump. The Marquis of Worcester, and, still earlier, Da Porta, divided the engine into two parts ; using one part as a steam-boiler, and the other as a separate water-vessel. Savery duplicated those parts of the earlier engine which acted the several parts of pump, steam-cylinder, and condenser, and added the use of the jet of water to effect rapid condensation. Newcomen and Cawley next introduced the modern type of engine, and sepa- rated the pump from the steam-engine proper : in their engine, as in Savery's, we notice the use of surface-condensation first ; and, subsequently, that of a jet of water thrown into the midst of the steam to be condensed. Watt finally affected the crowning improvement of the single-cylinder engine, and com- pleted this movement of differentiation by separating the con- denser from the steam-cylinder, thus perfecting the general structure of the engine. Here this movement ceased, the several important processes of the steam-engine now being conducted each in a separate vessel. The boiler furnished the steam; the cylinder derived from it mechanical power; the vapor was finally condensed in a separate vessel ; while the power, which had been obtained from it in the steam-cylinder, was transmitted through still other parts to the pumps, or wherever work was to be done. Watt and his contemporaries also commenced that move- ment toward higher pressures of steam, used with greater ex- pansion, which has been the most striking feature noticed in the progress of the steam-engine since his time. Newcomen used steam of barely more than atmospheric pressure, and raised 105,00x3 pounds of water one foot high, with a pound of coal consumed. Smeaton raised the steam-pressure to eight pounds, and increased the duty to 120,000. Watt started with a duty of double that of Newcomen, and raised it 320,000 foot-pounds per pound of coal, with steam at ten pounds. To-day, Cornish engines of the same general plan as those of Watt, but worked with forty to sixty pounds of steam, and expanding three to six times, do a duty that will probably average, with good or- dinary engines, above 600,000 foot-pounds per pound of coal. THE DEVELOPMENT OF THE STEAM-EXGINE. 79 The increase of steam-pressure and expansion which has been seen since Watt's time has been accompanied by a very great improvement in workmanship, a consequence of rapid increase in the perfection and the wide range of adaptation of machine-tools, of higher skill and intelligence in designing engines and boilers, increased piston-speed, greater care in obtaining dry steam, and in keeping it dry until thrown out of the cylinder either by superheating, or by steam-jacketing, or by both means combined ; and it has been further accom- panied by greater attention to the important matter of provid- ing carefully against losses by conduction and radiation, and by internal wasteful transfer of heat. The use, finally, of the "compound," or the multicylinder, engine for the purpose of reducing friction, as well as of saving some of that heat which is usually lost in consequence of internal condensation and re-evaporation due to great expansion, has still further aided in this progress and giving a duty of 1,000,000 or more. An important consequence of the still unchecked rise of piston-speed in the modern steam-engine is the approach to a limit beyond which the now standard form of " drop cut-off/' or "detachable" valve-gear, cannot be used. For the piston would, at that limit of speed, reach the end of its stroke before the dropped valve could reach its seat, and the point of cut-off and degree of expansion could no longer be determined accurately and invariably by the governor. This limit has probably already been attained in some engines ; and the engineer is driven back to the use of the older types of " posi- tive-motion " valve-gearing, and is compelled to devise special forms of governor which shall have sensitiveness, and yet power sufficient to control these less tractable kinds of mechanism. and to invent reliable and durable forms of balanced valves, and to practise every available expedient for making the movement of the valve, and its adjustment by the regulator, perfectly easy. Positive motion and ease of adjustment by the governor are, therefore, evidently the requisites of a successful valve-gear for the high-speed engine which will succeed the standard engine of to-day for many purposes. 8O A MANUAL OF THE STEAM-ENGINE. We may now summarize the results of our examination of the development of the steam-engine thus : (1) The process of improvement has been one, primarily, of " differentiation ;" the number of parts has been continually increased, while the work of each part has been simplified, a separate organ being appropriated to each process in the cycle of operations. (2) A kind of secondary process of " differentiation" has, to some extent, followed the completion of the primary one, in which secondary process one operation is conducted partly in one and partly in another part of the machine. This is illus- trated by the cylinders in series of the multicylinder engine. (3) The direction of improvement has been marked by a continual increase of steam-pressure, greater expansion, special provision for obtaining dry steam, higher piston-speed, careful protection against loss of heat by conduction or radiation in- ternally, as well as externally, and, in marine engines, by surface- condensation. The direction of further improvement, as indicated by science as well as by our review of the actual steps already taken, would seem to be : En resume, working between the widest attainable limits of temperature, and the saving of heat previ- ously wasted in the apparatus or rejected from it. Steam must enter the machine at the highest possible temperature, must be protected from waste or loss of heat, and must retain, at the moment before exhaust, the least possible proportion of originally available heat. He whose inventive genius, or mechanical skill, contributes to effect either of these objects to secure either the use of higher steam with safety, or the more effective conversion of heat into mechanical power with- out waste, or the reduction, by transformation into work, of the temperature of the rejected working-fluid confers an inestimable boon upon mankind. In detail, in the engine proper the tendency is, and may be expected to continue, in the near future at least, toward higher steam, greater expansion in more than one cylinder, steam- jacketing, superheating, a careful use of non-conducting pro- THE DEVELOPMENT OF THE STEAM-ENGINE. 8 1 tectors against waste, and higher piston-speed with rapid rotation, and to the adoption of special proportions and of forms of valve-gear adapted to such high-speed engines. In the boiler, more complete combustion, without excess of air passing through the furnace, is sought, and a more thorough absorption of heat from the furnace-gases. The latter may be ultimately found most satisfactorily attainable by the use of a mechanically-produced draught, in place of the far more wasteful method of obtaining it by the expenditure of heat in the chimney. In construction, we may anticipate the use of better materials, as already seen in the substitution of " mild steels" for the cruder material, iron, and more careful workman- ship, especially in the boiler, and still further improvement in forms and proportions of details. In management there is an immense field for improvement, which improvement we may feel assured will rapidly take place, as it is now becoming well understood that care, skill, and intelligence are absolutely essential to economical management, as well as to safety, and that they repay liberally all the ex- penditure of time and money that is requisite to secure them. CHAPTER II. STRUCTURE OF THE STEAM-ENGINE. 27. The Structure and Uses of the Steam-engine have been well defined and mutually adapted, each to the other, since the middle of the nineteenth century, and in such manner as to have led to the production of certain fairly definite forms of engine ; which are each employed very generally, sometimes exclusively, for equally specific purposes. Thus : the modern mill-engine, simple or compound, is com- monly a direct-acting, horizontal engine at least for moderate and large powers with effective provision for adjusting the point of cut-off by the action of the governor ; the engine em- ployed especially to drive fast machinery is commonly a machine having a " positive-motion " valve-gear and as simple of construction, as compact, and as well balanced as the art of the builder can make it ; while the locomotive and the marine engines are each of a type which has been the product of years of change and of evolution which have resulted in their very perfect adaptation to their peculiar work. It has thus hap- pened that engines are divided into classes ; each class having its characteristic form and structure, and its own special nomen- clature. 28. The Classification into Types has been usually fol- lowed in substantially the manner indicated in the scheme given in the next article. It is not invariably the fact, how- ever, that the classification with reference to use is adhered to in the actual use of engines ; and it is often the fact that one type is applied to the purposes ordinarily considered specially appropriate to another class. For example : we find the port- able engine, and sometimes a retired locomotive, doing duty as 82 STRUCTURE OF THE STEAM-EXCISE. 83 a stationary, mill, engine ; as may also be the case sometimes with an engine constructed on what are recognized generally as the characteristic plans of the marine engine. Nevertheless, as a rule, each kind of work is best performed by a form of engine which has been found, by the experience of years, to be the best for that place. The engineer is therefore inclined to be somewhat cautious in accepting any suggestion looking to interchange of duties in this manner. According to Weisbach's system, the various piston-engines may be grouped under the following classes :* I. According to the number of cylinders : (1) Single cylinder. (2) Multiple-cylinder engines. IL With reference to the construction of cylinders : {!) Fixed cylinder. (2) Movable cylinder. In the first case, the engines are (a) Vertical. (J) Horizontal (r) Inclined. In the second case, they are (a) Oscillating. (*) Rotary. III. With reference to the action of the steam : (1) Single acting. (2) Double-acting. IV. With reference to the transmission of the steam-power : (1) Direc^acting. (2) Indirect-acting. And in the latter case either {a) With balance lever, or beam. () Without lever or working beam. 29. ^t^a-^i JIM** . Classed %rf9fK"g to their purpose and use, as in the following scheme, may be taken as practically including all existing standard and approved types. * Weistaacli s Mechanics, roL n. put 2. 45*. P- 8S- 84 A MANUAL OF THE STEAM-ENGINE. STANDARD TYPES OF ENGINES. GENERAL CLASS. Stationary, or Mill, Engines : Moderate Speed or High Speed. Agricultural Engines. Pumping engines. Crank and fly-wheel. Direct-acting. Portable Engines and Semi-portable Engines. Steam Fire-engines. Road Locomotives. Railway " Marine Engines. Paddle-engines. Screw-engines. Special Types. Engines may also be classed according to structure: as simple or compound; as direct acting, beam, vertical, inverted, horizontal, or inclined : or as condensing or non-condensing ; high-pressure or low-pressure ; or as reciprocating, vibrating, as steam-turbines, or as rotary engines ; or as directly con- nected or geared ; as jet-condensing or surface-condensing. They are very frequently designated by the name of the in- ventor, designer, or constructor : as the Watt, the Corliss, or the Porter engine. In the first classification that by reference to proposed use the title is sufficiently indicative of its own reason and meaning ; and this is commonly the case with the nomenclature based on structural characteristics. A simple engine does its work in a single cylinder; while a "compound or multicylin- der engine has two or more cylinders," so connected " in series" that the steam exhausted from one shall be successively worked, under decreasing pressures, in the others. STRUCTURE OF THE STEAM-ENGINE. 85 Direct-acting engines are directly connected from head of piston-rod and the cross-head to the crank ; beam-engines have a '' working-beam " interposed : and the geared engine drives its load as the screw-shaft in marine engines by means of pinions on the crank-shaft and gears on the screw-shaft ; thus enabling the latter -to be driven at higher speed than the former, or, in very rare instances, the reverse. Vertical, in- verted, horizontal, or inclined engines are so named to indicate the direction of their k4 centre-lines " and their position. Con- densing and non-condensing engines are distinguished by the fact that the ^AUUf possesses a condenser. The condenser, however, is not always made to produce a vacuum, when high steam-pressures are adopted : it is occasionally worked at at- mospheric pressure, and is then simply either a heater or an expedient for securing pure feed-water for the boilers. Reciprocating engines are those the usual type in which the piston moves backward and forward in a true cylinder; vibrating engines constitute a rare type in which the piston swings in an arc inside a cylinder of appropriate form ; while rotary engines are those in which the piston continuously revolves on an axis, usually parallel to its own plane. The classification adopted by the Author as that which will be followed in the arrangement of this work is the first, as pre- sented in the table above ; but separate articles or chapters will be devoted to such modifications as are comprehended in the other methods of classing engines falling under those heads. 30. The Principles and Aim in Designing any engine, as guiding the selection of type and details, are such as will insure the most exact adaptation of the machine to the specified work. The ultimate purpose is always to secure the best pos- sible combination of minimum first cost with minimum run- ning expenses. That is the best engine which, at the end of a life terminated either by its own wear and tear and natural decay, or by the substitution of a later and better form, gives the best total effect, as measured on the books of the treasurer, and as including interest on first cost, regular operating ex- 86 A MANUAL OF THE STEAM-ENGINE. penses, compensation of attendant labor, rents, insurance, oil, fuel, and incidentals, making the sum of all such charges a minimum. Hence the stationary engine may be chosen without much regard to weight or space occupied ; locomotive and marine engines must be light, compact, and powerful ; and the latter must be chosen and constructed, especially for long voyages, with primary regard to high economy in use of fuel. In all cases, other things equal, a direct application of the engine to its intended work is desirable ; and it thus happens that we may prefer an engine of moderate speed for mill-work and a " high- speed engine" for driving dynamo-electric machines. In dis- tricts remote from coal-fields every known method is applied to insure maximum economic efficiency ; while among coal- mines steam-jacketing, superheating, or "compounding" are expedients which have no interest for either the engineer or his client. It is such considerations as these which sometimes lead to the use of one standard form of engine where another type would ordinarily be employed as a portable engine to drive a factory, where to be used temporarily, or as when cramped for space ; as in the application of locomotive boilers in the torpedo fleet. 31. The Principles of Construction of the selected type of engine are determined by precisely the same considerations. The engine must be so built that the costs of maintenance shall be made a minimum for the life of the machine. It must be as light as possible, yet the strength of every part must be sufficient to make it safe against all ordinary contingencies ; bearings must not only be designed in proper number, location, and dimensions, but they must be made of good material for their purpose ; good material and good workmanship will invari- ably, " in the long-run," afford full compensation for their cost. It is the consideration of these principles and the deductions from a now long period of extensive and continuous experi- ence which have led to the production and use, for their pre- scribed purposes, of the several standard types of engine to be presently described. STRUCTURE OF THE STEAM-EXG1XE. 87 32. The Exigencies of Operation determine many mat- ters of detail in every type of engine; and the designing engineer, or the purchaser or user, of an engine can never be secure of a satisfactory result unless the conditions of operation and possible accidents and exigencies are considered. Thus : lubrication must be absolutely continuous and certain on en- gines working at high speed of rotation ; provision must be made, especially with marine engines, and elsewhere where " priming " or " foaming " may endanger the engine, for the safe expulsion of water from the steam-cylinder ; reversing- gears must be fitted to rolling-mill engines ; an adjustable dis- tribution of steam is essential in the case of the locomotive. 33. The Stationary Engine has a variety of forms, differ- ing with the special nature or with the location of the ma- chinery to be driven. It is usually a simple engine ; but is getting to be more and more frequently ** compound," or even ** triple-expansion ;" it is usually driven at moderate speed, and has a " detachable valve-gear" or " drop cut-off ;" but it is often of the high-speed type, with a positive-motion valve-gear and a shaft-governor. Among the most common forms are : (1) The Mill-engine ; (2) The Pumping-engine, and others of the moderate low- speed class; (3) The High-speed Engine, of various kinds, but mainly used for mills or electric-lighting establishments ; and a few peculiar forms that need not be here considered. Each of these types or forms is built both simple and com- pound ; the latter will be specially considered in a distinct chapter. The best known and most generally used class of stationary engines at the present time, as has been stated, is that which has the so-called " drop cut-off," or " detachable valve- gear." The oldest well-known form of valve-motion of this description is the Sickels cut-off, previously mentioned, pat- ented by Frederick E. Sickels about the year 1841. It was introduced by the inventor in a form which especially adapted it to the beam-engine used on the Eastern waters of the 88 A MANUAL OF THE STEAM-ENGINE. United States, and was adapted to stationary engines by Messrs. Thurston, Greene & Co., of Providence, R. I., who employed it for some years before any other form of " drop cut-off " came into general use. The Sickels cut-off consisted of a set of steam-valves, made independent of the exhaust-valves, and each raised by a catch, which could be thrown out, at the proper moment, by a wedge with which it came in contact as it rose with the opening valve. This wedge, or other equivalent device, was so adjusted that the valve should be detached and fall to its seat when the pis- ton reached that point in its movement, after taking steam, at which expansion was to commence. From this point, no steam entering the cylinder, the piston was impelled by the expand- ing vapor. The valve was usually the double-poppet. Sickels subsequently invented what was called the " beam-motion," to detach the valve at any point in the stroke. As at first ar- ranged, the valve could only be detached during the earlier half-stroke, since at mid-stroke the direction of motion of the eccentric-rod was reversed and the valve began to descend. By introducing a " wiper " having a motion transverse to that of the valve and its catch, and by giving this wiper a motion coincident with that of the piston by connecting it with the beam or other part of the engine moving with the piston, he obtained a kinematic combination which permitted the valve to be detached at any point in the stroke, adding a very simple contrivance which enabled the attendant to set the wiper so that it should strike the catch at any time during the forward movement of the "beam-motion." On stationary engines, the point of cut-off was afterward determined by the governor, which was made to operate the detaching mechanism, the combination forming what is some- times called an " automatic " cut-off. The attachment of the governor so as to determine the degree of expansion had been proposed before Sickels's time. One of the earliest of these contrivances was that of Zachariah Allen, in 1834, using a cut- off valve independent of the steam-valve. The first to so attach the governor to a drop cut-off valve-motion was George STRUCTURE OF THE STEAM-ENGINE. 89 H. Corliss, who made it a feature of the Corliss valve-gear, already referred to, in 1849. 1 tne vear l8 55 N. T. Greene introduced a form of expansion-gear, in which he combined the range of the Sickels beam-motion device with the expan- sion-adjustment gained by the attachment of the governor, and with the advantage of flat slide-valves at all ports both steam and exhaust. Many other ingenious forms of expansion valve-gear have been invented, and several have been introduced, which, prop- erly designed and proportioned to well-planned engines, and with good construction and management, should give economi- cal results little if at all inferior to those just named. Among the most ingenious of these devices is that of Babcock & Wil- cox, in which a very small auxiliary steam-cylinder and piston is employed to throw the cut-off valve over its port at the in- stant at which the steam is to be cut off. A very beautiful form of isochronous governor was used on this engine, to regu- late the speed of the engine by determining the point of cut-off, In some forms of Wright's engine the expansion is adjusted by the movement, by the regulator, of cams which operate the steam-valves so that they shall hold the valve open a longer or shorter time, as required. The Older Forms of stationary engines were usually simple in design, of plain construction, durable, economical in first cost and in maintenance ; but, as compared with more recent engines, wasteful of steam and fuel. But little space need be here given to their description. They were either beam- engines or direct-acting, and their valves and gear, from the first quarter of the century, consisted often of a single three- ported slide-valve like that of the modern locomotive, driven by a single eccentric and effecting the desired expansion and compression of steam by the lap and lead of the valve, in a manner to be described in a succeeding chapter. The beam- engine gradually fell into disfavor, on account of its size and cost, and was displaced very generally, by the middle of the century, by the horizontal direct-acting engine ; and the in- creased steam-pressures and improved economy of the non 90 A MANUAL OF THE STEAM-ENGINE. condensing engine also resulted in the increasing employment of that form of machine, to the exclusion of the condensing engine, which is, however, still much used, especially for large powers. Where economy was particularly sought, the engine was often fitted with a separate cut-off valve, often mounted on the back of the main valve ; sometimes, however, as a distinct organ in its own valve-chest. In the most common system that of Mayer this cut-off valve consisted of two blocks slid- ing on the back of the main valve, actuated by an independent eccentric, and capable of being separated or brought together, as desired, by a right and left screw, in such manner as to vary the point of cut-off to any required extent. The eccentric is set with or 180 from the crank, accordingly as the cut-off is effected by the inside or the outside edges of the cut-off blocks. Where much power is required, the stationary engine is now usually a horizontal direct-acting engine, having a more or less effective cut-off valve-gear, according to the size of en- gine and the cost of fuel. A good example of the simpler form of this kind of engine is the small horizontal slide-valve engine, with the Meyer system of valve-gear. This form is a very effective machine, and does excellent work when properly proportioned to yield the required amount of power. It is well adapted to a ratio of expansion of from four to five. Its disadvantages are the difficulty which it presents in the at- tachment of the regulator, to determine the point of cut-off, by the heavy work which it throws upon the governor when attached, and the rather inflexible character of the device as an expansion valve-gear. The best examples of this class of engine have heavy bed-plates, well-designed cylinders and de- tails, smooth-working valve-gear, the expansion-valve adjusted by a right-and left-hand screw, and regulation secured by the attachment of the governor to the throttle-valve. The engine shown in the accompanying illustration (Fig. 28) is an example of an excellent stationary engine, and is simple, strong, and efficient. The frame, front cylinder-head, cross-head guides, and crank-shaft " plumber-block," are cast STRUCTURE OF THE STEA3/-EXGINE. QI in one piece. The cylinder is secured against the end of the bed-plate, as was first done by Corliss. The crank-pin is set in a counterbalanced disk. The valve-gear is simple, and the governor effective and provided with a safety-device to pre- vent injury by the breaking of the governor-belt. In this ex- ample all parts are made to exact size by gauges standardized to Whitworth's sizes. With many engines (as is seen in Fig. 29) two supports are placed the one under the main bearing, and the other under the cylinder to take the weight of the engine : and through them it is secured to the foundation. A valve is sometimes used consisting of two pistons connected by a rod and worked by an ordinary eccentric. By a simple arrangement these pistons have always the same pressure inside as out, which prevents any leakage ; and they are said always to work equally as well and free from friction under high as under low pressure. Engines of the class just described are especially well fitted, by their simplicity, compactness, and solidity, to work at the high piston-speeds which are gradually becoming generally adopted in the effort to attain increased economy of fuel by 9 2 A MANUAL OF THE STEAM-ENGINE. the reduction of the immense losses of heat which occur in the expansion of steam in the metallic cylinders through which we are now compelled to work it. FIG. 29. HORIZONTAL STATIONARY ENGINE. The technical expressions " right-hand " and " left-hand " engines are thus defined as applied to engines of this class : Stand by the end of the cylinder, face the shaft and observe the position and direction of the main driving-pulley, and class the engine as follows : Right-hand engines have the main driving-pulley on the right of the observer. Left-hand engines have the main driv- ing-wheel on the left of the observer. Forward-running engines move the top of the main driving- pulley away from the observer. Backward-running engines move the top of the main driv- ing-pulley towards the observer. In deciding on the direction in which an engine is to run, it is well to remember that forward-running engines are prefer- able, on account of the thrust of the connecting-rod being received on the lower guides, which are always stiffer and better lubricated than the upper. One of the neatest and best modern designs of stationary engine for small powers is seen in Fig. 30, which represents a " vertical direct-acting engine," with base-plate a form which is a favorite with many engineers. The engine shown in the engraving consists of two principal parts, the cylinder and the frame, which is a tapering column STRUCTURE OF THE STEAM-EXGIXE. 93 having openings in the sides, to allow free access to all the working parts within. The slides and pillow-blocks are cast with the column, so that they cannot become loose or out of line; the rubbing surfaces are large and easily lubricated. Owing to the vertical position, there is no tendency to side wear of cylinder or piston. The packing-rings are self-adjusting : the crank is counterbalanced ; the crank-pin, cross-head pin, piston- 94 A MANUAL OF THE STEAM-ENGINE. rod, valve-stem, etc., are made of steel ; all the bearing-surfaces are made large, and accurately fitted ; and the best quality of Babbitt-metal only should be used for the journal-bearings. The smaller sizes of these engines, from 2 to 10 horse- power, usually have both pillow-blocks cast in th.e frame, giving a bearing each side of the double cranks. They are built by some constructors in quantities, and parts duplicated by special machinery, which secures great accuracy and uniformity of workmanship, and allows of any part being quickly and cheaply replaced, when worn or broken by accident. The next figure is a vertical section through the same engine. FIG. 3.. VERTICAL STATIONARY ENGINE. (Scale T V) Engines fitted with the ordinary rigid bearings require to be erected on a firm foundation, and to be kept in perfect line. If, by the settling of the foundation, or from any other cause, they get out of line, heating, cutting, and thumping result. To obviate this, modern engines are often fitted with self-adjusting STRUCTURE OF THE STEAM-ENGINE. 95 bearings throughout ; this gives the engine great flexibility and freedom from friction. The preceding figure shows clearly how this is accomplished. The pillow-block has a spherical shell turned and fitted into the spherically-bored pillow-block, thus allowing a slight angular motion in any direction. The connecting-rod is forged in a single piece, without straps, gibs, or key, and is mortised through at each end for the reception of the brass boxes, which are curved on their backs, and fit the cheek-pieces, between which they can turn to adjust themselves to the pins, in the plane of the axis of the rod. The adjust- ment for wear is made by wedge-blocks and set-screws, as shown, and they are so constructed that the parts cannot get loose and cause a break-down. The cross-head has adjustable gibs on each side, turned to fit the slides, which are cast solidly in the frame, and bored out exactly in the line with the cylin der. This permits it freely to turn on its axis, and, in connec- tion with the adjustable boxes in the connecting-rod, allows a perfect self-adjustment to the line of the crank-pin. The out- board bearing may be moved an inch or more out of position in any direction, without detriment to the running of the engine, all bearings accommodating themselves perfectly to whatever position the shaft may assume. The ports and valve-passages are proportioned as in loco- motive practice. The valve-seat is in this instance adapted to the ordinary plain slide- or D-valve, should it be preferred ; but the balanced-piston slide-valve works with equal ease, and at the same time gives double steam and exhaust openings, which greatly facilitates the entrance of the steam to, and its escape from, the cylinder. The vertical direct-acting engine is some- times, though rarely, built of very considerable size ; these large engines are more frequently seen in rolling-mills than elsewhere. 34. The Mill or Factory Engine of latest date is very generally horizontal, direct-acting, with a detachable expansion- valve, a governor operating by adjusting the point of detach- ment and closing of the valve ; which latter is closed quickly either by gravity or by a spring, or, sometimes, by steam- pressure. In a few instances, engines have been built in which A MANUAL OF THE STEAM-ENGINE. STRUCTURE OF THE STEAM-ENGINE. 97 the valve continuously rotates, closing without reciprocation.* When of small size, the stationary is made non-condensing ; when of large power, it is very frequently a condensing engine. When large and where economy is very essential, it is frequently a "compound," and often a "triple-expansion," engine; the steam-pressure being carried higher as a higher ratio of expan- sion is adopted. In many cases, as in cotton-mills making fine grades of product, or for electric-lighting, precise regulation of speed is required, and this may determine the choice of type of engine. The best-known engine of this class is the Corliss engine. It is very extensively used in the United States, and has been copied very generally by European builders. Fig. 32 repre- sents the Corliss engine. The horizontal steam-cylinder is bolted firmly to the end of the frame, which is so formed as to transmit the strain to the main journal with the greatest direct- ness. The frame carries the guides for the cross-head, which are both in the same vertical plane. The valves are four in number, a steam- and an exhaust-valve being placed at each end of the steam-cylinder. Short steam-passages are thus secured, and this diminution of clearance is a source of some economy. Both sets of valves are driven by an eccentric oper- ating a disk or wrist-plate, E (Fig.33),which vibrates on a pin projecting from the cylinder. Short links reaching from this- wrist-plate to the several valves, D D, FF, move them with a pe- culiarly varying motion, open- ing and closing them rapidly, and moving them quite slowly when the port is either nearly open or almost closed. This effect is ingeniously secured by FIG 33 _ CORLISS ENGISE VALVE . MOTJON . so placing the pins on the wrist- * Report on Machinery and Manufactures at Vienna in 1873; R. H. Thurs- ton; Washington, Gov't Printing Office; 1875. 9 8 A MANUAL OF THE STEAM-ENGINE. plate that their line of motion becomes nearly transverse to the direction of the valve-links when the limit of movement is approached. The links connecting the wrist-plate with the arms moving the steam-valves have catches at their extremities, which are disengaged by coming in contact, as the arm swings around with the valve-stem, with a cam adjusted by the gov- ernor. This adjustment permits very perfect regulation by automatic variation of the ratio of expansion by the governor. The standard form of Corliss valve is very well exhibited FIG. 34. THE CORL NGINE-CYL1NDKF by the illustrations here given, which are taken from the draw- ings of Mr. Harris. Those marked A are the steam-, and those marked B are the exhaust-valves. Both consist, as is seen, of cylinders, parts of which have been cut away, leaving the working and bearing surfaces of no greater extent than is necessary to subserve the purposes of the valve. These surfaces are of the simplest possible form and are easily fitted up in the lathe. In order that they may come to a bearing with certainty, and without regard to the position of the spindle relatively to the valve, STRUCTURE OF THE STEAM-ENGINE. 99 they are made with a longitudinal slit into which fits, without jamming, the blade of the rock-shaft. The valves are thus allowed to come to a bearing, and even to wear down in their seats without causing leakage. The next figure shows the arrangement of this valve as seen in longitudinal section of the chest. As this maker con- structs it, the stem goes through a fitted opening, without stuffing-box, and the slight drip is carried off from the closed FIG. 35. HAJUUS-CORIJSS VALVES. space at D\ thus none escapes into the engine-room. The steel collar at F % which is shrunk on the stem, fits into the recess at a and serves as a packing. As the tendency of the stem to shift outward always causes the collar to wear to a fit, it is not likely often to wear leaky. Another detail of interest in the Corliss engine is the " dash- pot." When the valve is suddenly closed, some device is necessary to prevent jar at the instant of its coming to rest. This device is the dash-pot. The form adopted by Corliss con- sists of a shallow cup into which a piston on the valve-stem fits, 100 A MANUAL OF THE STEAM-ENGINE. cushioning the enclosed air, and thus checking the motion of the valve without shock. This dash-pot, made by Watts, Campbell & Co., who have successfully introduced Corliss en- gines into electric-light establishments in New York City and elsewhere, is that seen in the figures. The annular piston, E, E, fits the cylinder, D, D, , E, and a space, seen above B, forms a vacuum-chamber which assists the spring or weight, closing the valve by the formation of a more or less complete vacuum, as the piston is raised while the valve is opening. A small cock, not seen, is arranged to adjust the degree of exhaustion of this chamber. When the valve has nearly reached its seat, the piston, D, passes the opening FIG. 36. HARRIS-CORLISS VALV from F into the outer space and the enclosed air then acts as a cushion, checking the movement of the valve. The " dash-pot " was invented originally by F. E. Sickels. In the original water dash-pot of Sickels, the cylinder is vertical, and the plunger or piston descends upon a small body of water confined in the base of the dash-pot. Corliss's air dash-pot is now often set horizontally. The Corliss engine is the prototype, of a large number of engines constructed in Europe and America, having the same or very similar structure and methods of operation. The leading features of this machine are thus : (i) The use of four valves two steam and two exhaust so placed as to reduce "clearance" to a minimum. STRUCTURE OF THE STEAM-ENGINE. 101 (2) The use of a rotating valve, capable of being cheaply and readily fitted up, of being easily moved, and of being con- veniently worked by connections outside the steam-spaces. (3> The use of a " wrist-plate," caused to oscillate by a sin- gle eccentric, and directly so connected with all four valves that each may be given a rapid opening and closing movement, and be held open and nearly still, at either end of its range, by swinging the line of connection nearly into the line between centres, thus permitting nearly a full opening of port to be FIG. 37. THE DASH- maintained during an appreciable interval, and a free and com- plete steam supply and exhaust. (4) A beautifully simple and effective method of detaching the steam-valve from the driving mechanism, and of insuring its rapid and certain closure at the proper moment, to produce any desired expansion of steam. (5) A direct connection of the governor, so as to determine the ratio of expansion, while so adjusting the power of the engine to the work to be done that the variation of speed with changing loads becomes a minimum. (6) Making this latter adjustment in such away as to throw the least possible work on the regulating mechanism, and thus IO2 A MANUAL OF THE STEAM-ENGINE. to give the governor the greatest possible sensitiveness and accuracy of action. (7) A form of frame and general design of engine which gives maximum strength and stiffness, with least cost and weight. All these features are combined to form a steam-engine essentially different, in general and in detail, from all earlier engines. In operation, the engine was found to exhibit a remarkable economy of fuel, and a singularly perfect regula- FIG. 38. GREENE ENGINE. tion, and to be far more durable and more economical in cost of repairs, on the average, than was generally supposed possible. The Greene Strain-engine (Fig. 38) has four valves, as in the Corliss. The cut-off gear consists of a bar, A, moved by the steam-eccentric in a direction parallel with the centre-line of the cylinder and nearly -coincident as to time with the piston. On this bar are tappets, C C, supported by springs and adjustable 104 A MANUAL OF THE STEAM-ENGINE. in height by the governor. These tappets engage the arms, B B, on the ends of rock-shafts, E E, which move the steam-valves and remain in contact with them a longer or shorter time, and holding the valve open during a greater or less part of the piston-stroke, as the governor permits the tappets to rise with diminishing engine-speed, or forces them down as speed in- creases. The exhaust-valves are moved by an independent eccentric-rod, which is itself moved by an eccentric-set, as is usual with the Corliss and with other engines generally, at right angles with the crank. This engine, in consequence of the independence of the steam-eccentric, and of the contem- porary movement of steam valve-motion and steam-piston, is capable of cutting off at any point from beginning to nearly the end of the stroke. The usual arrangement, by which steam and exhaust valves are moved by the same eccentric, only per- mits expansion with the range from the beginning to half-stroke. In the Corliss engine the latter construction is retained, with the object, in part, of securing a means of closing the valve by a " positive motion," should, by any accident, the closing not be effected by the weight or spring usually relied upon. There are other engines belonging to the class here con- sidered engines having a detachable cut-off valve closed independently of the motion of the valve-gear, of which space will not permit description. Among these are the Wright engine, constructed by one of the oldest and best known designers in the United States; the Brown engine, a machine which has been extensively adopted for driving mills in New England, and is famous for the excellence of its workmanship and finish, as well as for its durability and efficiency ; the Fitch- burg engine, and others. An ingeniously arranged engine of the class considered in this division of the subject, the Wheelock engine, is seen in the accompanying engraving. The steam-chest is placed below the cylinder, and the steam- and exhaust-valves are set side by side, the latter serving both as induction and eduction valve, and having the same action, nearly, as the common three-ported slide-valve ; while the func- STRUCTURE OF THE STEAM-ENGI.VE. 105 IO6 A MANUAL OF THE STEAM-ENGINE. tion of the former is principally that of a cut-off valve. The latter, or main valve, is set nearest the end of the cylinder, and the exhaust steam is thus permitted to escape directly, and promptly from the engine. The valve and seat are independent, and coned slightly, and may be adjusted to take up wear, or to relieve pressure on the seats. These valves are carried on steel trunnions, and with hardened surfaces of contact are but little subject to wear. The steam or cut-off valve is set farther away from the cylinder than in the standard arrange- ments of Corliss and other builders of that class of engines, and this enables the maker of this engine to secure a single port with reduced clearance and less liability to leakage, should the expansion-valve leak. In the later engines of this class a gridiron valve is used in a shell of the same general form, as illustrated in Volume II. In this engine and it should be the case in every engine in which the regulator is driven by belt the connection from shaft to governor is so made that the breaking of the belt permits an automatic closing of the valve and the stopping of the engine. The regularity of motion of the class of engines described in this section may be inferred from the fact stated in regard to the engine here studied, that it has been known to vary but a half-revolution per minute when five sixths of the load was thrown off. Simple and Compound Stationary Engines are both in com- mon use as mill-engines ; and all the familiar classes of engines are constructed in both forms. Until recently the mill-engine has been very generally a single-cylinder engine, or a pair of sim- ple engines coupled with cranks at right-angles where great power was demanded ; but the Corliss and other mill-engines are now often "compounded," and it is not unusual to compound comparatively small high-speed engines. In such cases the elements of the combination are commonly similar in design to the simple form of the same engine. The combination is often made by constructing a " tandem " engine, in which the cylin- ders are placed in the same line, end to end, and often with their pistons on the same rod. In other cases, the engines are set side by side, actually constituting each a complete engine, STRUCTURE OF THE STEAM-ENGINE IOJ with their cranks set at right-angles for a two-cylinder com- pound, or at angles of 120 for a " triple-expansion," engine, and with a common frame. In such cases, as will be seen later, an intermediate " receiver " is introduced into which the high- pressure cylinder exhausts and from which the low-pressure cylinder takes its supply without seriously affecting the work- ing of the fluid. Nearly all the engines to be described are thus built " com- pound," and some are " triple expansion." The Stationary Multiple-cylinder Engine is rarely given the _ne form as the marine engine. The necessity of having a !_ .ar of cranks, and the objection to the employment of the fly-wheel, do not here exist ; nor does either the volume or the weight of the machine become so vitally important a matter as at sea. The design adopted is, for these reasons, one which will be of minimum first cost, irrespective of these considera- tions. Tke"Tandem " Engine is perhaps the most common form of stationary compound engine. In this type, as shown in the accompanying illustration, the two cylinders are set in line, have a common piston-rod, and drive the same crank. The high-pressure cylinder is commonly placed behind the low- pressure, and the latter is directly attached to the frame of the engine. The exhaust of the smaller cylinder is carried in any convenient manner to the large engine ; but the more direct and the larger the conduits employed, the better. In some cases, the two cylinders are set directly in contact. This plan involves a difficulty, usually, in packing the rod between them, but it has the advantage of great compactness. The Compound Corliss Engine was first introduced by other builders ; but no ore was more successful in the economical working of the machine than was its great originator, the late George H. Corliss. The usual method of compounding this engine for stationary purposes is that known as the " tandem " system, in which the high-pressure cylinder is set behind the low-pressure, both pistons having a common rod and driving a common set of reciprocating parts and having valve-gearing io8 A MANUAL OF THE STEAM-ENGINE. actuated by the same eccentric and rod. The plan is simple, inexpensive, convenient, and compact, and is found to be very satisfactory in operation, the economy attained by it being about as high as that of any other arrangement yet devised. This method is illustrated by Fig. 41, which exhibits a form of the engine designed by Mr. Edwin Reynolds. It is readily seen that it would probably be impossible to find a better method of combining maximum efficiency with minimum cost of con- STXUCTUXE OF THE STAMA'G/y. : ;.:. struct ion than this, or to make a more compact: disposition of parts. It is necessarily of considerable length ; but in other directions has no greater dimensions than the single engine of the simple type. The performance of this type of engine has been most excellent. For example, the engines of the Xourse steam- mfll, as constructed by Mr. Corliss, were found to demand no more than 1.62 pounds of good fuel per horse-power and per hour. The same engine as a simple engine, the high-pressure cylinder disconnected., if equal to the best of its class, under TJmflar conditions of operation, would probably not require less than two pounds ; which may be taken as about the limit of economical working for that type of engine, with a good con- denser and dry steam. One disadvantage of this type of engine the * tandem"" is the length of passage between the exhaust-port of the high- pressure and the induction-passage of the low-pressure cvlin- der when the former is taking steam in the backward stroke ; but this is partly compensated, at least, by the very short pas- sage obtainable for the opposite movement. The valve-gearing; is commonly the same on both cylinders ; but it is often so arranged that the governor operates on the one cylinder onlv. leaving the ratio of expansion of the other to be determined by the measure of expansion in the first. Another not uncommon system of compounding this engine, especially for large powers, is oftener practised in Europe than in the United States. This is the coupling of two engines, side by side, as in common marine practice; while another method sometimes adopted is the adaptation of two independ- ent engines of properly-adjusted sizes to act, the one as the high-, the other as the low-pressure engine of a compound sys- tem. These engines are occasionally set at some distance apart, when the local conditions make that a more convenient disposition. The efficiencies of these several types of com- pound Corliss engines are substantially the same. They are all subject to about one half the internal wastes of the simple engine of qffiilar dimensions, to about doable the external STRUCTURE: OF THE STEAM-ENGINE. in wastes of heat, and have a trifle more friction. On the whole, they will ordinarily give an increased economy amounting to about twenty per cent of the heat and fuel consumption of the simple engine. In some cases the arrangement of a pair of complete engines, of properly selected sizes, in such manner that either the exhaust of one may be used in the other, or steam may be taken direct from the boiler to either, is found advantageous. When less power is demanded, or when one is disabled, the available engine may then be used alone. Economy has been attained by this plan, even when the two engines are placed at considerable distances apart, the precaution being taken to carefully guard against loss of heat between them. The "Cross-compound" type of Corliss engine is illustrated by the accompanying sketch of a pair designed by Mr. Reynolds and built by Allis & Co. for the Namquit Mills. The cranks are set at right-angles, and the receiver is placed beneath the floor. This is a less common variety than the " tandem " form ; but is still often adopted. The general arrangement and disposition of the parts of a triple-expansion engine, as built by the Corliss Co., is seen in Fig. 43. Here the low-pressure cylinder is divided, one of its two elements being coupled with the high-pressure cylinder on the right, and the twin with the intermediate cylinder on the left. The cranks are set at 90. These engines have cylinders 20, 34, 36, and 36 inches diameter and 5 feet stroke of piston. All cylinders are completely steam-jacketed, heads included, and the steam is somewhat superheated. Jet-condensers are used. The capacity of the engine is 1000 I. H. P. or more, and its "duty" is about 135,000,000 pounds ; the fuel used, when of good quality, amounting, on test, to 1.44 pounds per horse-power per hour. "Compounding" simple engines is often a very economical and profitable plan. The method depends mainly upon the design of the engine to be so altered. The common forms of stationary beam-engine are commonly improved by what is called " McNaughting," placing a ne- / high-pressure cylinder 112 A MANUAL OF THE STEAM-ENGINE. STRUCTURE OF THE STEAM-ENGINE. beside the old cylinder and connecting it to the beam either at the old air-pump centre, if condensing, or to the point at which the air-pump would have been attached, if the engine be non-condensing. The vertical marine engine may sometimes be altered into the compound form by placing the new cylin- der above the old and the two pistons on a common rod. 114 A MANUAL OF THE STEAM-ENGINE. Many engines cannot be satisfactorily compounded, and others only by the establishment of a separate complete high-pres- sure engine in close proximity to the old and arranging the latter to take its steam from the former. The gain to be anticipated by such improvement and alter- ation of type will depend upon the character of the altered machine. Should it be a very wasteful engine, enormous gains may be anticipated if, while adding the new construction, the old is put in good order. For cases in which the old en- gine is reasonably economical, the gain is simply that due to reduction of cylinder-condensation, and this is at least partly compensated by the friction of the added parts. Savings as great as one half are not unusual in such cases as the first, and as little as ten per cent, in cases like the second, are common. Whether such a gain is, on the whole, financially advantageous is still another question to be settled for each case. Rolling-mill Engines are often constructed especially for their work. For heavy mills they are often made to reverse. The last figure illustrates a common form of reversing-engine. The engine frames are heavy cast-iron girders having a bearing the entire length on the foundation. On the top side of the frames are the main journals. These journals are provided with means for taking up wear and adjusting the helical gears which transmit motion from one shaft to the other. The main valves are placed under the cylinders, the valve- chambers forming a part of the cylinder casting, thus bringing the steam-ports on the lower side of the cylinder, to allow water of condensation to pass out through the exhaust-ports without danger to either cylinder or head. As an additional means of safety the builders often use " snifting-valves " on each end of the cylinder. Where very heavy rolls are employed, as in making armor- plate, for example, an engine is often demanded which may be instantly reversed, driving with equal facility in either di- rection. Fig. 45 exhibits such an engine as built by the Allis Co., from Mr. Reynolds's plans, for Messrs. Carnegie, Phipps & Co. of Pittsburgh. The fly-wheel is here, also, dispensed STRUCTURE OF THE STEAM-ENGINE. 11$ with, and the engines are designed for high speeds of rotation and very heavy work. The steam-cylinders are forty inches diameter by fifty-four inches stroke, with Reynolds' Corliss valve-gear without the drop cut-off mechanism ; the speed of the engines is controlled by the operator, and is varied in every-day practice from 5 Il6 A MANUAL OF THE STEAM-ENGINE. revolutions to 120 revolutions per minute. Power from the crank-shaft is transmitted to the roll-shaft by means of a pair of shrouded helical-tooth steel gears. The reversing mechanism, operated by steam, is controlled by a lever on the engineer's platform; from this position he has unobstructed view of all parts of the engine and roll-train. 35. High and Low Speed distinguish a more modern type from those engines already described. Classified with refer- ence to their method of driving machinery, we may thus desig- nate the two classes : (1) Engines which may be used in driving by belt, and which are not adapted for direct connection. (2) Engines especially designed and constructed to be coupled directly to the " dynamo." The first class of engines is, by many of the more conservative engineers, still preferred to the second. The latter constitute the so-called modern " high-speed " type of engine, and are gradually coming into use ; some engineers adopting them both for direct and for indirect connection. The most experienced engineers are not yet fully in accord in regard to the question whether they have passed the experimental stage in such general application. One of the methods of securing economy in the working of steam has been stated to be the driving of the engine up to the highest safe velocity of piston, and giving it maximum speed of rotation. The time allowed for " initial " condensa- tion of each charge, and for the necessary change of tempera- ture preceding such condensation, is thus reduced, and the amount of steam condensed within the cylinder being thus made a minimum, in any given time, the percentage of loss of the increased quantity of steam worked off by the engine becomes correspondingly less. Engines of this class have a number of advantages, consequent upon their high speed : they are, other things being equal, more economical in the use of steam ; they can be given a very much smaller fly-wheel ; they have, in consequence of the enormously reduced weight of wheel, less friction ; they are more easily STRUCTURE OF THE STEAM EXCISE. IIJ held to their speed by the governor ; they are less subject to variation of speed between beginning and end of any one stroke : and they are often less troublesome and expensive to connect to the load than slow- running engines. These ad van- tages are common to all classes of engines, if they can be driven up to high speeds. The class here considered is better fitted to realize these advantages than the older forms of engines, because they are especially designed for high speed. The objection to this type of engine is the increased risk of wear, and of accident, due to their rapid motion, and espe- cially the danger that when accidents do occur they may be more serious than with engines working at ordinary speeds. The precautions taken by builders of fast engines are all directed toward meeting this contingencj-, making their ma- chines safe against accident. These precautions are seen to be the strengthening, and especially the stiffening, of all the parts exposed to the stresses due to the action of inertia in the reciprocating pieces : the adjustment of all parts to each other in such a manner as to avoid spring; the use of the best material, and of an effective system of lubrication : and the securing of the most perfect workmanship. As actually constructed, they are of proportionallj- shorter stroke than the preceding types, and are consequently more subject to internal waste by cylinder-condensation and have large clearance and " dead " spaces, and thus, also, both exag- gerate internal heat-waste, and become liable to greater loss of cushion-steam. As a rule, in actual work, this class of engine is not usually distinguished by peculiarly high economi- cal results, in competition with the " low-speed " engines. The latter, on the other hand, usually are at a disadvantage for fast running, both through complication of parts and the use of a detachable valve. TJu Porttr-Allcn Engine was the first of the class known as * high-speed " engines. Its designers were Mr. C. T. Porter and Mr. J. F. Allen, the latter being the inventor of its valve- gear : while the former was the pioneer in the introduction of engines of this class. riS MANUAL OF THE STEAM-ENGINE. STRUCTURE OF THE STEA31-EXGIXS. 119 In the Allen engine (Fig. 46), the cylinder and frame are connected as in the engine seen in Fig. 25, and the crank-disk, shaft-bearings, and other principal details are not essentially different. The^ valve-gear differs in having four valves, one at each end on the steam as well as on the exhaust side, all of which are balanced and worked with very little resistance. These valves are not detachable, but are driven by a link attached to and moved by an eccentric on the main shaft ; the position of the valve-rod attachment to which link is deter- mined by the governor, and the degree of expansion is thus adjusted to the work of the engine. The engine has usually a short stroke, not exceeding twice the diameter of cylinder, and is driven at very high speed, generally averaging from 600 to 800 feet per minute.* This high piston-speed and short stroke give high velocity of rotation. The effect is, therefore, to produce an exceptional smoothness of motion, while per- mitting the use of small fly-wheels. Its short stroke ^-n^M*^ solidity to be attained in a bed of rigid form, making it a self- contained engine, adapted to heavy work, and requiring but a small foundation. The journals of the shaft, and all cylindrical wearing-sur. faces of such engines, are finished by grinding, and are thus made perfectly cylindrical. The crank-pin and cross-head pin are hardened before being ground. The joints of the valve- gear consist of pins turning in solid ferrules in the rod-ends, both hardened and ground. After years of constant use thus, no wear occasioning appreciable lost time in the valve-move- ments occurs. Where great steadiness of motion is desired, the expense of coupled engines is often incurred. Quick-running engines do not often require to be coupled ; a single engine may give greater uniformity of motion than is usually obtained with coupled engines at ordinary speeds. The governor used on this engine is known as the Porter governor. It is given power and delicacy by weighting it * Or not fer from 600 limes the cube root of the length of stroke, mil mi in feet. 120 A MANUAL OF THE STEAM-ENGINE. down, and thus obtaining a high velocity of rotation, and by suspending the balls from forked arms, which are given each two bearing-pins separated laterally so far as to permit consid- erable force to be exerted in changing speeds without cramping those bearings sufficiently to seriously impair the sensitiveness of the governor. In "high-speed" engines, the possibilities in the direction of increasing speeds are sought to be made the most of. Their market is not only to be found in the domain of the electrical generation of light, and electrical transmission of power, but in older fields of work as well. The loss of power in the " jack- shafts," or " first-motion shafts," of mills and workshops driven by the low-speed engines is an item of no inconsiderable amount in many cases. The tendency is now observable toward the adoption of the higher speed of engine, in direct connection with the main line of shafting, even where not quite as econom- ical in the use of steam, through the intermediary of a single belt or pair of gears, or even by directly attaching the crank- shaft of the engine to the main line by a coupling. Mr. Allen's invention of a valve-gear placed in the hands of Mr. Porter, who was endeavoring to design a " high-speed " engine, the device needed to carry out the idea. This arrangement consists of a single eccentric driving a link-motion to operate the steam-valve and to work the exhaust at the same time. The link is controlled by a Porter governor, and is so connected and driven that the gear may be readily and quickly adjusted by the governor to any desired point of cut-off. The eccentric and link are shown in the next illustration. The eccentric is set on the shaft in such a position that its motion is coincident with that of the crank. The link is a slotted curved arm, forming one piece with the eccentric- strap, pivoted at the middle on trunnions sustained by an arm rocking about a pin set in the bed of the engine. The upper end of the link carries a pin, from which a rod leads off to the exhaust, which is driven without variable connections. The link-block is fitted to work in the slot of the link, from the end nearest the exhaust-rod pin, down to the point opposite the STRUCTURE OF THE STEAM-ENGIXE. 121 pivotal point at which the trunnions are set. \Yhen it is at the upper end, the throw of the valve is a maximum ; when at the lower point, it is a minimum. As the link-block is moved up and down in the slot, the motion of the valve is varied, and the ratio of expansion correspondingly altered. By an in- genious adjustment of a still more ingenious form of valve- motion, it is thus possible to obtain a valve movement of perfect precision at all speeds, and on both the forward and the back- FIG. 47. THE ALLEN LINK. (Scale -ft-) ward stroke, with a quicker closing action, as the cut-off is later. The steam is allowed to enter the cylinder, at nearly boiler pressure, almost up to the point of cut-off, and the ex- pansion line is a smooth curve very nearly from the junction with the steam line. The four valves are shown in the next figure, which is a section through the steam-cylinder showing valve, ports, and general construction. The two valves at the upper side of the cylinder are the steam-valves ; the lower are the exhaust- valves. This section is, however, horizontal, the valves being set on their edges at either side of the cylinder. The exhaust- 122 A MANUAL OF THE STEAM-ENGINE. valves are so placed as to drain the cylinder of any water that may have entered with the steam, or may have been produced by internal condensation. Both sets of valves are so made, and set, as to be well balanced, and so as to be capable of hav ing the wear taken up when it occurs. The steam-valves are provided with packing-plates, which are adjustable by hand, to STRUCTURE OF THE STEAM-ENGINE. 123 make them steam-tight, as well as to secure a perfect balance. Each valve is placed in a separate valve-chest, and can be in- dependently adjusted. Each valve opens four ports; each is so set that it is actuated by a rod in the line of its own centre ; and all are thus rendered but little liable to either wear or leakage. The rock-shaft arm on the intermediate rock-shaft, between the eccentric and the steam-valve stem, assists in secur- ing the quick opening and closing motion essential to a satis- factory distribution of the steam. The features which have been described are not necessarily distinctive of a " high-speed engine." A positive-motion valve- gear, and a good steam-distribution, are desirable in such engines, and the first point is, in fast-running machines, an essential requisite ; but the engine, so far as it has been de- scribed, may be as well considered a slow as a fast engine. There are some details which are essentially and peculiarly characteristic of the class to which this machine is assigned. Among these points are the strength and rigidity of parts which distinguish such engines ; the great nicety of fitting ; the excellence of all material in every part exposed to the straining action of inertia, and the minor modifications of details to adapt them to service in a machine in which play in joints or bearings will make trouble. The bed is stiff and solid, especially in those parts which take the stresses of the reciprocating pieces. It is broad and deep, with the line of thrust of piston-rod carried close to its surface between the guides, and with a box form which gives great resistance to forces tending to twist it. The steam-cylin- der is secured to the bed by the end, a construction adopted by Corliss many years ago, and one which gives all desirable strength, with freedom from those strains which come of con- nection of two large masses at different and constantly varying temperatures. The main journal-boxes are made in four pieces, and are set up by adjustable wedges, so set as to avoid the springing of the shaft that is sometimes found to occur with a less effective arrangement. The main-shaft journals, and the journals of the crank-pins, are made with especial care, skil- 124 A MANUAL OF THE STEAM-ENGINE. fully ground to size and form, and nicely finished before the engine is assembled. The pin is of " mild " steel, carefully case-hardened to give it a surface that will wear well and will not " cut." The provisions for lubrication in such engines are among the most important of its details. The action of inertia in the moving parts is made by Mr. Porter the means of securing smoothness in working and evenness of crank-pin pressures. At the beginning of the stroke the inertia of the piston, its rod, the cross-head, and to a certain extent the connecting-rod, of all reciprocating parts, causes them to offer a certain resistance to the accelerated motion which they are compelled to take up. This resistance becomes less and less up to zero at half-stroke, the point at which their velocity is a maximum. Passing this point, they are rapidly retarded, and this same property of inertia causes them to offer a resistance to retardation, which resistance now is felt as an impelling force at the crank-pin. Thus, the effect of the presence of these heavy masses in the line of connection produces a reduction of pressure upon the pin at the commencement, and an increase of pressure at the end, of stroke. But in consequence of the varying action of the steam, producing an excess of pressure at the beginning and a deficiency of pressure at the end of stroke, we may combine these two effects, and the result is a comparatively uniform load upon the crank-pin throughout the stroke. This com- pensation is capable of being, in many cases, very nicely adjusted by properly proportioning the weight of the recipro- cating parts. It is evident, however, that at some higher speed, the weight of these parts, as proportioned for strength simply, would be sufficient to give this desirable adjustment of the load on the crank-pin. There is no reason to suppose that this, which would seem to be a natural speed of the steam- engine, may not, at any time, be attained. The Porter-Allen engine, the earliest of the " high-speed " engines, was also one of the first of its class to be constructed as a compound engine. Since the best engines of this type have about the efficiency of good Corliss engines, it is evident STRUCTURE OF THE STEAM-ENGINE. 12$ that the opportunity offered for economical improvement is here equal, and the result of the experiment has been as sat- isfactory. The usual methods of compounding are substan- tially the same as those familiar in the case of the Corliss en- gine, and they may be expected to exhibit a similar ratio of improvement when compared with the corresponding simple machine. In some cases this gain is not sufficient to compen- sate the increased cost and complication, added expense of maintenance, and greater weight and volume ; but at pressures exceeding sixty or seventy-five pounds it is found that they give real advantage, and the more as the pressures and ratios of expansion are increased. At still higher pressures, as for those exceeding 125 or 150 pounds, it is probable that still further subdivision of the total expansion-ratio, and the con- struction of the triple-expansion engine, would prove to be an improvement ; while at pressures exceeding 200 or 225 pounds the quadruple-expansion machine would be as profitable, com- paratively, as in those departments of application in which they have been already set at work. A maximum ratio of ex- pansion of about three in each cylinder is probably advisable. Another engine of this class is that first designed by Mr. J. W. Thompson, and known as the " Buckeye engine." This engine was not a radical competitor of the pioneer engine ; but was, from the beginning, a moderately-high-speed engine. It was fitted with a positive motion, " automatic " or self- adjusting valve-gear, and a balanced valve, and had sufficient stability and excellence of workmanship to make it safe at high speeds ; while the peculiarities of its construction were such as gave it a very high place as an economical machine. In this case the cylinder is carried on a pedestal, as is that of the Corliss engine, usually; the frame consists of a girder unit- ing the cylinder and the main pillow-block and carrying the guides ; the crank-shaft end is carried by another pillow-block. The main frame is, however, supported by a strut which is now usually seen in other engines, and which takes the load tending to spring the girder under the guides. The valves are so constructed that the steam enters balance- 126 A MANUAL OF THE STEAM-ENGINE. pistons, through which it passes to the interior of the valve, where the boiler-pressure is constantly maintained when the engine is at work. The balance-pistons are packed with sprung rings and followers, and fitted to work steam-tight on faces on the cover-plates of the valve. Coiled steel springs serve to hold the pistons to their seats on the valve when FIG. 49. PLAN OF VALVES. steam is shut off. From the interior of the valve the steam is admitted to the cylinder through ports in its faces as they are alternately brought by its movement to coincide with the cylinder-ports. The cut-off valve is formed by two plates shown at v v, Fig. 49, rigidly connected by rods h h h' h'. These plates work on seats surrounding the valve-ports, which ports they alternately cover at times relatively to the piston-travel, determined by the STRUCTURE OF THE STEAM-EtfGWE. 12" governor. The governor is of a type that has not been seen in engines previously described. In the common "fly-ball governor " the two balls revolve about a vertical spindle, to which they are attached by a pair of arms in such a manner that they may take any position that the resultant action of gravity, centrifugal force, and the pull on the supporting arms may give them. A defect common to all governors of this class is that the force tending to pull the balls downward is perfectly uniform. The position taken by the balls, at any fixed speed of engine, is always the same ; the connection of the balls with the regulating mechanism is one which alwavs preserves a fixed relation between the position of the governor- balls and the position of the regulating apparatus. Thus it happens that the engine can never be kept precisely at speed, unless the speed is such as will give the governor exactly its normal position and, at the same time, such that the valves shall supply just the normal quantity of steam to the engine. If we can substitute for the action of gravity a force which can be made to vary with change in the position of the balls, in such a way that the variation in the opening of the throttle, or in position of the point of cut-off, shall go on until the en- gine comes to speed, irrespective of all other conditions, we shall have what is known as an " isochronous " governor, and shall be able to secure the right speed, whatever changes occur in steam-pressure or in load, provided that there is steam enough to drive the load at that speed with the least expansion for which the engine is designed. Such a result can be reached by substituting the tension of a spring, properly set, for the action of gravity. The form of governor here illustrated is. or can be made to be. of this class. It simply requires that the spring tension shall be given a certain easily determined relation to the effort of centrifugal force. A governor of this character, when well made and adjusted, will open the throttle-valve, or will increase the ratio of ex- pansion, as the steam-pressure diminishes or as the load is in- creased, and will continue to move in the proper direction in- definitely, or until the machine comes to speed, or until the 128 A MANUAL OF THE STEAM-ENGINE. engine is doing all that it can do. In this governor (Fig. 50) two levers are set on either side the crank-shaft, in a frame or a pulley to which they are pivoted at b, b. These rods carry weights, A, A, which may be adjusted to any desired position by means of the bolts seen in the cut. The outer end of each rod is linked to the loose eccentric, C, C, by the rods B, B, and is controlled by the springs F, F, which resist the effort of centrifugal force tending to throw the weights outward. As the weights swing outward or inward, as the one or the other of the two opposing forces predominates, the eccentric is turned on the shaft in such a manner as to give the valves that motion which is necessary to produce the proper distri- FIG. 50. THOMPSON'S GOVER bution of steam to bring the engine to its speed. The ad- justment of this regulator to its work is easily obtained by the shifting of the weights along the levers, or by increasing or diminishing their amount, as is found necessary. The general arrangement of this system and the appearance of an engine of this class are illustrated in the accompanying engraving. A dash-pot has sometimes been used on the governor to correct the tendency to violent fluctuation when nearly isochro- STRUCTURE OF THE STEAJt-EJCGIJCE. tag nous, and this was probably the first case of its use on this class of engines. The independence of the cut-off and main valves, in con- sequence of the use of two eccentrics, permits any ratio of expansion to be adopted that may be desired, and the fact that the cut-off eccentric is set, at starting, nearly " with the crank." gives a wide range detenninable by the governor, nearly from full-stroke to complete suppression. As the governor shifts the eccentric about the shaft, it gives increased angular advance and a shorter and shorter cut-off. Here the main valve is actuated as in the common forms of valv: but its eccentric, instead of being set ahead of the crank, follows, the exhaust- and steam-openings being, by the structure of the valve, reversed, and their acting edges trans- posed. By carrying the pivot of the cut-off rock-shaft on the main rock shaft arm, uniform travel of the cut-off valve on the back of the main valve is secured, whatever the variation of cut-off. This insures uniform wear. In this, as in all engines similarly regulated, any mishap to governor or its connections stops the engine, a " run-away engine "" being thus impossible. In some cases, the use of an independent cut-off valve actu- ated by an " automatic " regulation system is adopted with the simpler forms of valve. The following figure illustrates STRUCTURE OF THE STEA3t-EXGI&E. IJI such a plan, as constructed by Stnrtevant, for all powers up to 150 H. P. Here the passages in the main valve, for the admission of steam, do not extend through the entire thickness of the valve. Within the main valve is a cylindrical seat in which nuts a piston-valve, which receives from its eccentric a differential movement relatively to that of the main valve, just before the beginning of the stroke, opening the passage into the cylinder. The valve returns to cut off the steam at a time determined by the governor. As, at this time, the two valves are moving in opposite directions,, this action is very prompt. This form of cut-off valve has very little motion in its seat. and is subject to no lateral pressure. The main valve is set to cut off at three-quarters stroke. The main valve is habtw^J by pressure-plates upon its back. The SlTaigklJim* E*gi*e differs as radically from the two preceding as do they from each other. In this engine we find but a single valve, which does duty both as a distributing and as a cut-off valve. This engine is the invention of, and is designed by, Prof. J. E. Sweet, and has some interesting points, which wffl bear much more extended study than they can be given in the space which can here be allowed. The engine takes its name from its peculiar form of frame, which is seen to consist of two perfectly straight diverging struts extending from the end of die cylinder directly to the two main bearings, thus carrying the fine of resistance to the puM and push of die connections exactly along its own central line. The engine is carried on three points as is the practice with " surface-plates,'"' which must have an absolntdly invariable system of supports, to avoid danger of ""spring. These are under the main bearings, and beneath the steam- cylinder. The two journals receive equal loads; the crank-pin is not subject to the deflecting forces met with where a crank is overhung: danger of unequal wear of journals, and of spring- ing the pin, is thus avoided. The fly-wheel is placed in twin form between the fVE*** bearings, and also serves as a crank as STRUCTURE OF THE STEAM-fJSfGIA'E. 1JJ wdl as balance-wiled. By its action at this point it intercepts heavy and objectionable stresses, which, otherwise, might he transmitted to the mam shaft ; and the reciprocating action of counterweights and equilibrating parts is dins only felt within a mass of metal which can resist them with safety and without affecting the main journal; which is also less liable to spring under the loads transmitted through ft. To secure better dis- tribution of wear, the crank-shaft is allowed some end-play. The steam-cylinder has the valve-chest placed at the end nearest the crank, and the ports and passages are carried as in those engines. The valve-stems have no stuffing-boxes, but pass into the chest through unusually long and carefully fitted holies in a hub, made about five one-thousandths of an inch larger than the rod inside the Babbitt-metal bushing, for a length of six diameters, or more. The hub is loose in the hole in the end of the valve-chest, and is packed at the ends by a washer fitted on a flat seat on the inside. The piston-rod is similarly fitted. Ira this engine, wear is a voided at the cross-head pin by cutting away the surfaces which do little or no work, and thus securing overrunning surfaces, which are not subject to this distorted wear to so great an extent. The valve is what may be called a " piston-valve ~ of rect- angular section, the space in which it slides having, therefore, also a rectangular section. Tk* wmpntmd form of the Sweet engine is one of the best of illustrations of the compactness which may be given the "tandem type of the machine. The engine is buflt, as to its high-pressure cylinder and working parts, precisely like the standard type of the simple engine of the same design. It has exactly the same characteristic form of frame and methods of connection and of steam-distribution and governor. Directly behind the high-pressure cylinder, however, is placed the larger, low-pressure, cylinder, the whole forming,, practically, one struc- ture. The whole machine can be taken apart and reassembled without disturbing the cylinders or the frame. Both pistons, which are mounted on one rod, can be removed and replaced ; 134 A MANUAL OF THE STEAM-ENGINE. the intermediate head coming away with its stuffing-box through the larger cylinder. The packing of the rod between the two cylinders is a metallic sleeve, solid and free from liability to produce trouble or to require readjustment, once in place STRUCTURE OF THE STEAM-ENGINE. 135 and properly fitted. It is /ree from liability to wear or to bear upon the rod in such a manner as to produce undue friction and heating, while it is loose enough to work smoothly and yet tight enough to prevent leakage of steam past its shell. The valve of the low-pressure cylinder is worked by an independent, fixed, eccentric, and the expansion is adjusted by the action of the governor, affecting the point of cut-off on the high-pressure cylinder, precisely as in the simple engine. Where the load is fairly steady this arrangement is perfectly satisfactory. The inventor has also planned a triple-expansion vertical engine of equal simplicity. TJie Armington arid Sims Engine is of the same general class with the last described forms of engine, but differs from them in its details and in its proportions, somewhat, and especially in the form of its valve, and in the devices in- termediate between governor and valve. In this engine the " piston " valve is used, combined with a double port. The following engraving, Fig. 55, presents a view of this en- gine. The bed, or frame, is seen to be similar to that of the Porter-Allen engine, heavy, solid, stiff, taking the bending stresses of the guides at its upper surface, and insured against twisting strains by the box form of its section. Two main pillow-blocks carry its steel crank-shaft, and support the two wheels, one of which is a balance-wheel, and the other of which is the pulley, from which the engine is belted to its work ; or, perhaps oftener, both being used in driving, thus equalizing the load on the shaft and preventing tendency to wear out of line. The steam-cylinder is overhung, and the exhaust-pipe is carried down below the floor, clear of the foundation, which latter has a minimum extent and cost, while sufficiently heavy and strong enough to carry the engine steadily. In some cases the frame is made with but one pillow-block, and the crank is overhung. The journals are calculated for the speeds and pressures adopted. The lubrication is a matter of vital importance in all engines of this class. In this engine the "sight feed " is used, in which each drop of oil falls through a clear space, on its way 136 A MANUAL OF THE STEAM-ENGINE. to the point to be oiled, in full view of the man in charge, and any failure of the oil to " feed " is thus promptly detected. The crank-pin is supplied by a "wiper," which takes its supply of the lubricant from the oil-cup at every revolution of the crank. This device has been used, in very similar form, by the Author, on fast marine engines, with perfect satisfaction. A governor, of the same type as that exhibited in the arti- cles describing the " Buckeye " and the "Straight Line "en- gines, is secured to the arms of the pulley on the frame, and FIG. 55. AKMINGTON & SIMS ENGINE. adjusts the position of the eccentrics which give motion to the valve through a rod and valve-stem, the connection between which two parts is made at a point at which they can be conve- niently supported by a rock-shaft and arm carried at the middle of the length of the frame. The cranks are two disks in which the balancing mass can be secured at any desired point. The cylinder, steam-chest, and valve-seat are all in one cast- ing. The steam-chest is in direct communication with the boiler, and the valve, which is of the piston form with a double steam- STRUCTURE OF THE STEAM-EXGIffE. Itf port, is surrounded by the " live steam," thus taking steam at the middle and exhausting it at the ends of the chest. The valve moves precisely as does the ordinary locomotive slide- valve, and the steam is introduced, at the beginning of the stroke, through a double length of port, and hence with un- usual promptness when the engine is running at high speed. The total " dead space " in these engines, including piston- clearance, is sometimes as low as 5 per cent on large gfags, In all cases, compression should fill this space at ever}* stroke. This piston-valve possesses a novelty in the double port. Its advantages are the ease and cheapness with which it can be made and fitted, and with which it can be replaced when worn ; its perfect balance and ease of working under any practicable steam-pressure, its permanence, tightness, and remarkable durability when properly cared for and used with boilers sup- plied with good water. Its disadvantages are the rapidity with which it sometimes wears, when it is not kept well lubri- cated, or when it is exposed to the action of steam carrying over from the boiler acidulated or dirty water, the danger of injury to the cylinder or its heads when priming occurs, and the proneness of the attendant to neglect its repair. The governor is the same, in principle, as those already de- scribed as adapted to the adjustment of the eccentric on the main or the governor shaft. It has the two weights carried on, and forming a part of arms pivoted to the governor pulley, and re- volving in the vertical plane as usual in that class of governors, The position of these weights, as determined by the speed and the action of the springs, determines the position of the eccen- trics, and thus the position and motion of the valve, and the point of cut-off, flying out and giving a higher ratio of expan- sion as the load on the engine is diminished, or as steam-pres- sure rises in the slightest degree, and a lower ratio as these conditions are reversed. In the device here adopted, however, the valve is driven by an eccentric which is * duplex." One eccentric is set inside another, and connected to the governor arms in such a way that, as the weights separate with increas- ing speed of engine, both eccentrics are turned on the shaft so 138 A MANUAL OF THE STEAM-ENGINE. as to cause their " throws " to coincide, or to separate as may be necessary. When they coincide, the travel of the valve is due to a greater total throw, and is a maximum ; when they are separated as far as possible the travel is reduced to a mini- mum. The action is almost precisely the same as that of a " Stephenson link," worked between full and mid-gear. When the two eccentrics give maximum travel, the action is that of the link-motion in full gear ; when they are at opposite sides of the shaft, the action is that of a link in mid-gear. By set- ting them at intermediate points, the throw is made that is required to give an intermediate action of the valve, and thus the distribution of steam is made to accord with the demands of the work by such a variation of the ratios of expansion and of compression as is obtained by the link-motion, and, in this case, with the advantage in promptness of opening and of closure obtainable with a double-ported valve. The range of action given in this engine is sufficient to permit a range of cut-off from o to about three-quarters stroke. The lead re- mains unchanged, and the compression increases as the ratio of expansion is increased. The springs of the governor are used in compression. Among the first of the " single-valve automatic " engines to find a place in electric lighting was the Armington & Sims engine, which was also one of the earliest to be built as a compound engine. An experimental engine was built about 1880 ; but the engine was not constructed as a multiple-cylinder engine regularly and as a standard type until some years later. The form given this engine is seen in the accompanying illustration, which represents the machine as constructed to give 100 horse-power at high speed. The regulation and the general construction of each of the two elements of the com- pound engine are similar to those already described in the simple engine. The two cranks are placed opposite, and this gives that perfection of balance which cannot be secured by any other device. It is also the best method of obtaining transfer of steam from the one engine to the other with minimum loss of pressure. The attainment of a speed of 800 STRUCTURE OF THE STEAX-EXGIXE, 159 revolutions a minute is not unusuaL Both cylinders are steam- jacketed. Such engines are usually made up to about 200 horse-power. In the type here shown, the cranks being opposite, the engine balanced, it can safely be run at a high speed : the peculiar form of the valve provides for quick ad mis- sion of steam, and the large wearing surfaces insure it more or less fully against leakage : the pistons and stuffing-boxes used are more easily got at than ordinarily with engines of the " tandem " type. 140 A MANUAL OF THE STEAM-ENGINE. In the Idc engine, of this class, shown herewith, a similarly compact form of " automatic " engine is illustrated ; with its shaft-governor, and peculiarly solid frame. The top of the frame extends from cylinder to main bear- ing, the full width of bearing. The caps are put on at an angle, which gives an adjustment in line with the wear of the parts. The- adjustment is given by reducing the thickness of the liner plates, and the cap is always drawn up solid. A straight vertical web of metal connects the upper and lower portions of the frame, and forms a stiff girder. This web extends from the cylinder to the front side of bearing, close to the crank-disk. The fly-wheel is set as close as possible .to the crank, in order to reduce the strain on the shaft. The base of the frame is rectangular, and forms a box girder, the top of which forms STRUCTURE OF THE STEAM-ENGINE. 14! the bearing for the lower guide, which receives the pressure of the connecting-rod. Piston-valves are used, and, in this engine, the steam-chest is bored out and fitted with bushings which have supporting bars to prevent the valve catching upon the ports. When worn they can be withdrawn and new ones inserted, and a new valve introduced, without delay. FIG. 58." CROSS " COMPOUX-D TXGIXE. Fig. 58 represents an automatic compound engine de- signed by Mr. F. H. Ball, especially for use in driving dynamo electric machinery. The illustration represents engines using steam at 125 pounds pressure, and of 250 horse-power each. It was thought best to build these engines in the form of a double engine rather than the " tandem " type of compound, because it was believed that higher rotative speed could be successfully used where the work was distributed over twc sets of crank-pins and journals of smaller sizes, rather than with the use of a single set of bearings of larger size, as in the case of a tandem engine developing the combined power of the double compound. 142 A MANUAL OF THE STEAM-ENGINE. The cylinder-dimensions selected after working up a large number of provisional diagrams were as follows: High-pressure cylinder: diameter 13"; stroke 16". Low- pressure cylinder : diameter 25"; stroke 16". The maximum power attained on trial was 325 I. H. P. The next figure illustrates the same make of engine com- pounded in the more usual way, a " tandem," compound, high-speed engine, for electric-lighting or other purposes, which is found to be one of the best combinations of efficiency with simplicity and small cost. FIG. 59. TANDKM COMPOUND HIGH-SPEED ENGINE. Nearly all makers now use this method of compounding for all cases except where, as in marine engines, a double engine with cranks at right-angles is considered desirable on other grounds. They are nearly as simple in form, as cheap of construction, and as inexpensive in repairs as the simple engine. An engine designed by Mr. Ide, Fig. 60, illustrates both the " tandem " form of compound high-speed engine, and some features of design of peculiar interest. This engine has its running parts covered in to insure that the oil, which is freely supplied, may not be wasted or spattered about, to the injury of surrounding objects, while thus also obtaining thoroughness STRUCTURE OF THE STEAM-EKGIKE. 143 144 A MANUAL OF THE STEAM-ENGINE. of lubrication approximating that of the "oil-bath." This gives, when fully effected, very great decrease in the wasted energy of internal friction of engine and corresponding increase of efficiency. The design is simple, inexpensive of con- struction, and embodies details of construction coming to be generally recognized as essential to high efficiency. The engine has a shaft-governor, controlled by a dash-pot, and thus enabled to regulate more closely. Its running parts are usually of steel. The low-pressure cylinder is bolted direct to the engine- bed, and to the head of this cylinder is cast the high-pressure cylinder. By this arrangement steam from the high-pressure cylinder has a short, direct passage into the low-pressure cylinder, and four stuffing-boxes are dispensed with on the rods between cylinders, reducing friction and dispensing with considerable external radiating surface. The cylinders and steam-chests are encased with a finished iron jacket, with two-inch air-space, between cylinder and jacket, filled with non-conducting material. Both cylinder- heads are protected in the same manner. The head between the cylinders is cored out leaving a space, which is filled with non-conducting materials. The next figure exhibits the same type of engine as arranged for a " cross-compound " by the Harrisburg Co. The " tandem " engine has an advantage in small cost, in com- pactness, and small friction ; but the cross-compound, with cranks at 90, has no " dead-centres," is somewhat steadier in its revolution, and has lighter stresses on its running parts. A receiver is here needed, and is seen between the two engines. It is made an expansion-piece to avoid temperature-strains. In designing the twin form, or cross-compound engine, it is advisable to secure compactness without sacrificing accessi- bility; independence of parts exposed to independently vary- ing temperatures, and a nice adjustment of steam-distribution with respect to both the cylinders and the intermediate re- ceiver. The next figure illustrates the arrangement of the Harrisburg engine as seen from behind the cylinders. 146 A MANUAL OF THE STEAM-ENGINE. In the plans it is to be noted that the power to be given off by the engines is transferred through the intermediately situated pulley fly-wheel, which is the only element separating the two machines. The shaft is made of minimum length ; the space afforded by the mounting of the wheel in this manner also serves to admit the two valve-chests and a very short 1 : [ 1 : 1 i J 1 E I ; 1 i pn :l: I : 1 1 i : i i ! 1 : 1 | 1 I :i!i I ti i ; 1 | 1 1 : : 1 1 1 t ; , 1 i 1 1 ;i: 1 1 iFio. fa. SECTION : CROSS-COMPOUND ENGINE. connection serving as receiver and constructed with an ex- pansion-piece, to avoid introduction of strains. The whole design, which is now a not uncommon one, illustrates well the most compact possible form of this engine. These points are also observable in the next illustration, in which a plan of the Porter compound is given. Where, as STRUCTURE OF THE STEAM-ENGINE. 147 in this case, the valve is on a level with the centre-line of the engine, care must be taken to secure immunity from danger FIG. 3.-Puwc or Ri from water entering the cylinders, by the use of an automatic relief-valve, or a " breaking-cap." OF Tf $TEAM-EJTGaC. 149 Tlie engraving on page 146 shows the usual construction of foundation, which may be either brick or stone, but is com- monly prefened of brick with, often, stone blocks on which the engine is immediately supported. Where,, as often in rolling-mills, the power of the engine must be transmitted along the shaft, a fly-wheel of the simpler kind may be placed between the cylinders, and still greater compactness thus sometimes attained. Thus, in Fig. 63, the plan of a Porter- Afflen rolling-mill engine, this arrangement is made, the shaft being extended to the right, toward the roIl-iraitnL to which ft is coupled as shown. The arrangement of die machine, in detail, illustrates the special methods of combining two engines of this type, as dictated by its ^pp**-"! construction. Tkf Ldxssmg tmgimf. planned by Mr. Jarvis, illustrates still another design of the -tandem "" compound variety. In this case both steam-chests are on the same side, giving short connection between the two chests, and diminishing the sur- face exposed to steam, which exposure is detrimental to economy. It is seen in Fig. 64. The shaft-governor, keyed to the shaft, obviates danger due to the breaking of belts or gears. This governor is of the class in which the eccentric is hung on an arm, which allows it to swing across the shaft by levers pivoted to the spider of the wheel In its details it is the design of Prof. R. C Carpenter. To obtain the astatic or isochronous property, the gov- ernor must be so arranged that with a slight variation in speed it may move through its entire range. This end is that the weights with their arms remain against the inner stops until the speed has nearly reached its governing range. A slight additional increase would then cause the weight and . arms to move, if the increase were not checked, through the entire range of action. This action is restrained by the air dash-pot, seen in Fig. 65. Inertia is made to act usefully by so pivoting the arms that, when the governor is in operation, the I5O A MANUAL OF THE STEAM-ENGINE. such a position that a line drawn through their centre of gravity perpendicular to the radius will pass to one side of the arm-pivot. The force due to inertia, when the speed changes, acts nearly along this line, and tends to turn the arm about the pivot, and thus move the eccentric in the same manner FIG. 65. CA as the centrifugal force, and acting most quickly, it gives the governor a greater sensitiveness. 36. The Single-acting High-speed Engine is a peculiar but now familiar type. In the "single-acting engine," the steam drives the piston in but one direction, and the return- stroke must be made without the production of useful work. In the "double-acting engine," the steam acts upon the piston in both directions, and with practically equal effect. Thus, a more regular action is secured with a given weight of balance- STRUCTURE OF THE STEAM-EXGIXE. !$! wheel, or the same regularity with a wheel of less weight than is required for the other form of engine. This smoothness off motion is one of the most essential features of steam-engine economy. At the speeds which have been lately attained, however, the inertia of moving parts becomes so great that moderate variations in the impelling power become com- paratively insignificant, and have no perceptible effect upon the smoothness of revolution of the crank-shaft. The double-acting engine evidently possessed greater power than its predecessor, when of the same size, and the - efficiency of the machine" was correspondingly increased. But the very conditions which have been thus made to aid in securing regularity have introduced a new difficulty: At every revolution of the engine, the crank * turns the centre "" twice ; and, at every passage of the centre, the direction of pressure upon the crank-pin is reversed, thus producing a shock which varies with the difference of pressure, the suddenness with which it is felt at the pin, and the extent of the " lost motion " between the pin and its bearings. Some lost motion must always be permitted, to avoid danger of heating the journal and injury to the machine. The counteracting adjust- ments are found to be, usually, the utilization of the inertia of the reciprocating parts ; the adoption of heavy compression, and very careful adjustment of the fit of the brasses on the pin. With skilful use of these expedients, and with the in- troduction of perfection of workmanship, and of qualities of material, such as have only been attained in late years, the "high-speed engine " has been made successful at as high as 300 and even, in some cases, 600 or more revolutions per minute. But much higher speeds than these are sometimes de- manded ; and engines must, in the future, be buflt to run. regularly, steadily, and safely, at, probably, very much higher velocities. This may, ultimately, lead to radical changes in the design of the now standard forms of fast engines. Nev- ertheless, the limit of speed has by no means been reached, even at the higher of the above speeds, with the common type 152 .A MANUAL OF THE STEAM-ENGINE. of engine. The speed of even 450 times the cube root of the length of stroke, now a common figure, and over three times that given by Watt's rule, is occasionally greatly exceeded. Ericsson designed an engine, some years ago, for electric light- in^, which ran, for years, at 1250 revolutions per minute, without accident. The piston-speed was about twice that of FIG 66. ERICSSON'S ENGINE. (Sc the average " high-speed " engine, and nearly ten times that adopted by Watt. The object of the inventor was to design a steam-engine for the special work of driving small dynamo-electric machines, and hence to secure great stability and strength, a minimum number of parts requiring lubrication, and absolute certainty that the parts retained should be, at all times, thoroughly supplied with the lubricant. The engine is therefore made a " half-trunk " engine, the trunk, F, F, Fig. 66, serving as an STRUCTURE OF THE STEAM-ENGINE. 153 oil-reservoir. The joint in the eccentric-rod is provided with a piston moving in a cylindrical guide, N, which is also an oil- reservoir. The cylinder, C, and base-plate, B, are in one cast- ing, upon which is set the hollow frame supporting the crank- shaft, H , and balance-wheel. Every journal and rubbing part has an oil-reservoir and special provision for effective lubrication. There comes a time, in the attempt to secure smooth work- ing, and as speeds are increased, when the weight of running parts, as calculated for strength only, becomes as great as is desirable to effect this object by their inertia ; there comes a time, also, as compression is increased, when the " cushioned " steam is carried up to boiler-pressure, and this would seem the natural limit. The next device adopted by the engineer, in chronological order, is that of preventing the lift of the brasses of the crank-pin and of the cross head pin when turning the centres, while still leaving the freedom of fit required to give safety from heating. This last expedient is that which has led to the construction of a class of engines which are as peculiar and as typical as either of the classes which have been already described. Westing/wuse's Engine belongs to this class, and is here taken as its representative. The change of construction characteristic of this type of engine is a return to the original " single-acting " plan of engine. The simple form of this engine, Figs. 67, 68, has two cylinders, A A, fitted with single- acting pistons, D D, forming trunks filling the bore of the cylinder, giving a long steam-tight bearing, and taking the con- necting-rod pin, A B, at a point at which no tendency to rock the piston can be produced. The top of the piston is cored out to prevent transfer of heat from the working to the non- working end. The rods, F F, take hold of the crank-pins within an inclosed chamber, C, forming part of the engine- frame, E C. This frame and bed-plate also acts as a reservoir for oil lubricating the journals and pistons, which oil floats on water and is dashed up over the moving parts so enclosed, at every revolution of the engine. No other attention is required 154 A MANUAL OF THE STEAM-ENGINE. than to keep a supply of oil in the chamber, by filling as loss occurs by leakage. In fact, the whole engine is thus shut in by its frame, and its working parts are invisible while working an arrangement at once a means of security and convenience. The valve adopted in this engine is a piston-valve of the class already described, but having some peculiarities specially adapting it to its use in this engine. Its guide, /, Fig. 67, is a '- 7 r - : ' '' / ' lISSIl FIG. 67. WESTTNGHOXTSE BNOINF. (Scale ^.1 piston traversing a cylinder separating the exhaust space from the chamber below. This one valve, V, distributes steam to both cylinders, the two cranks being set directly opposite each other. This adjustment of the cranks also gives a perfect STRUCTURE OF THE STEAJf-EXGlXE. 155 balance of reciprocating parts, and secures smoothness of move- ment off the whole machine, whatever speed may be adopted ; and exceptional speeds of 1000 revolutions, or more, per min- ute are reached without observable vibration. The governor, /, and its action, are precisely like the same parts in engines of this class described earlier. It actuates the eccentric, and determines the point of cut-off by varying the throw of the valve, while retaining constant lead. The governor is usually so adjusted that it will not come into play until the engine falls one per cent below, or rises one per cent above, the normal speed ; its full traverse is effected, also, 156 A MANUAL OF THE STEAM-ENGINE. within this range, the intention being that the speed shall never vary more than one per cent from that fixed as its proper ve- locity. The range of expansion is from o to about f stroke. One of the dangers to which fast-running engines are pe- culiarly exposed is that of injury by the entrapping of water in the cylinder, and the plunging of the piston against the mass of incompressible fluid which then fills the clearance-spaces. In this engine, in addition to the relief-cocks, or valves, which are always fitted to such engines, a safeguard is introduced in the form of what engineers are accustomed to call the " break- ing-piece," a part which is made purposely weaker than other portions of the machine, exposed to a common danger, so that this piece may go when danger arises. This piece is always one the replacement of which will give little trouble, and make but little expense. Such a breaking-piece is made to form a part of the cylinder-head. This may be knocked out without injury to any important, or costly, part of the structure.* The Single-acting Multicylilider Engine is often adopted for work in which high speed of rotation is an advantage. The Westinghouse compound engine, illustrated in the engraving, is a good typical representative of this class, and is one of the simplest devices of its kind. A single piston-valve, set hori- zontally above the two cylinders, distributes the steam and is regulated by a shaft-governor which properly varies its throw. The cranks are set opposite each other ; the motions of the pistons are synchronous in opposite directions, and no receiver is needed. Both engines are single-acting, and high compres- sion does away, largely, with the wastes due to considerable clearance. The cut-off in the high-pressure cylinder is effected by the lap of the valve. It has been found possible by this arrangement to bring down the consumption of steam to less than 20 pounds (9 kilos) per horse power per hour when con- *The Author planned an engine, about the year 1860, in which the whole cylinder-head was made a safety-valve which could lift and discharge the water into the chamber behind it. the cover of the latter being bolted on, while the cylinder-head was only held in place, against a faced joint, by steam-pressure. STRUCTURE OF THE STEAM-ENGINE. 157 densing, and below 25 pounds (i I kilos) when working non- condensing. In such single-acting engines, it is usually irifehded that the rod shall never leave the crank-pin, in order that pounding may not occur. It is therefore evidently necessary that they 158 A MANUAL OF THE STEAM-ENGINE. should be so proportioned and speeded that the action of the inertia of their reciprocating parts shall not produce stresses, on turning the centre, in excess of the sum of weights and steam-pressure. An ingenious modification of the enclosed single-acting com- pound type of engine, the "central-valve engine" of Mr. Wil- lans which is also interesting as having been the subject of ex- ceptionally complete scientific in- vestigation is seen in Fig. 70.* It was studied as a simple, a com- pound, and a triple-expansion en- gine ; being easily adapted to either system. As here shown, its three cylin- ders are placed in series and " tan- dem." The valves are on one rod, driven by a single eccentric on the crank-pin ; the rod being in the axis of the engine and the valves within the hollow piston- rod. Cut-off is effected by the passage of the ports into metallic rings in the ends of the cylinders, and is adjustable by hand or by the governor. Compression is effected in the separate cushion- chamber, f These engines are usually grouped in pairs, with cranks at right-angles. F,a. 7 o.-W ILI . A Ks'E NGINE . (Scaled) Ag the valve . faces move with the pistons, the valve-motion must here be taken from the pins to secure the desired movement relatively to the pistons. * The discussion of this paper is remarkably interesting. Trans. Brit. Inst. C. E. ; March, 1888; 1887-1889; No. 2306; vol. xciii. f Ibid , vol. Ixxxi. p. 166. STRUCTURE OF THE STEAAf-ENGIXE. '59 The work on the main journals and pins is substantially all on the upper 4i brass " of the latter and the lower of the former, FIG. 71. TRIUMPH ENGINE, and the crank-pin working-side is never expected to leave the pin. The eccentric-rod, like the connecting-rod, is always l6o A MANUAL OF THE STEAM-ENGINE. in compression, and the main bearings also are always under constant downward thrust. Lubrication is secured, by the Westinghouse method, by the dipping of the crank into a pool of oil and water in the crank-case. The guide-pistons are arranged to produce the needed cushion by compressing the air in the compression-chambers and this is adjustable as may prove to be advisable. The governor is of the now familiar Hartnell type. Another recent and peculiar example of this class of en- closed engines is the so-called 'Triumph" engine of Mr. Eickershoff, a " valveless " engine, in which the piston of one of its elements serves to distribute the steam to the others. It consists of three engines, side by side, each having the general construction shown in Fig. 71, coupled to cranks set at angles of 120. Its simplicity is its striking feature, having neither valves, eccentrics, piston- or valve-rods, cross-heads nor stuffing-boxes. The distribution is remarkably good. Regu- lation is effected by a throttling-governor on the steam-chest. With the exception of the cut-off, each piston controls the steam in the cylinder next preceding in the order of rotation, and when acting as a valve is at or near its maximum speed, while at the same moment the pistons in the preceding cylin- der are at their slowest speed. This simple expedient controls the steam in this engine in a manner remarkable for its very great efficiency. The indicator-diagram here given was taken from a 7 x 14x8 inch engine, non-condensing. XX is the atmospheric line ; AB is the admission-line in the high-pressure cylinder; BC, the steam-line ; C, the point of cut-off ; CD, expansion-line for high-pressure cylinder only; D, point of release to low-pressure cylinder; DEF, expansion-line, showing expansion in both high- and low-pressure cylinders, represented also by expansion- line LM of the low-pressure card ; F, point of compression in the high-pressure cylinder connection with the low-pressure closing ; FA is the compression-line. In the low-pressure card KLis the admission-line ; LM, the expansion-line, corresponding to line DEFoi the high-pressure STRUCTURE OF THE STEAM-EXGIXE. 161 card ; M is the point of cut-off of the high-pressure cylinder, cor- responding with compression-point F of the high-pressure card : JAVisthe expansion-line for the low-pressure cylinder only; X is the point of release to the exhaust ; NP is the exhaust- line ; PQ, line of back-pressure ; QK, compression-line. It must be remembered that the piston in the cylinder from which the high-pressure card is taken is 120 in advance of the piston in the cylinder from which the low-pressure card is taken. The FiG. 72. bOHCATOB-DIAGKAXS. ratio of the clearance to the volume of the high-pressure cylinder is such that the compression is always brought to initial pres- sure, irrespective of change in load. By this means the cylin- der-walls are brought to the temperature of the entering steam and condensation prevented, and shock in passing the centres is avoided. The plan of enclosing the " running parts " of the engine to insure freedom from dust, flooded journals, and exemption from expense in finishing small parts, is illustrated, in a 162 A MANUAL OF THE STEAM-ENGINE. special case, as here shown, an upright single-valve automatic engine designed by Sturtevant. In this case, a pair of engines FIG. 73.-' are set with cranks opposite to secure a balance, and a single valve answers for both. An excellent and often practised arrangement of oil-cups is here shown ; all being of the STRUCTURE OF THE STEAM-ENGINE. I6 3 sight-feed " class, all set in view and together, and where readily accessible. This general plan is adopted for engines of 10 to 35 horse-power. 37. Pumping-engines are built, as a rule, compound, and will be considered as such in the chapter relating to that Ha of constructions. Their principal types may, however, be properly described here. A simple form of pumping-engine without fly-wheel is the now common " direct-acting steam-pump." This engine is generally made use of as a forcing- and fire-pump, and wherever the amount of water to be moved is not large, and where the pressure is comparatively great. The steam-cylinder, AR f and feed-pump. Fig. 74. are in line, and the two pistons have usually one rod in common. The two cylinders are connected by a strong frame, and two standards fitted with lugs cany the whole, and serve as a means of bolting the pump to the floor or to its foundation. The method of working the steam-valve of the modern steam-pump is very ingenious and peculiar. As shown, the pistons are moving toward the left ; when they reach the end 164 A MANUAL OF THE STEAM-ENGINE. of their stroke, the face of the piston strikes a pin or other contrivance, and thus moves a small auxiliary valve, /, which opens a port, , and causes steam to be admitted behind a piston, or permit steam to be exhausted, as in the figure, from before the auxiliary piston, F, and the pressure within the main steam-chest then forces that piston over, moving the main steam-valve, G, to which it is attached, admitting steam to the left-hand side of the main piston, and exhausting on the right-hand side, A. Thus the motion of the engine operates its own valves in such a manner that it is never liable to stop working at the end of the stroke, notwithstanding the absence of the crank and fly-wheel, or of independent mechanism, like the cataract of the Cornish engine. There is a very consider- able variety of pumps of this class, all differing in detail, but all presenting the distinguishing feature of auxiliary valve and piston, and a connection by which it and the main engine each works the valve of the other combination. In some cases these pumps are made of considerable size, and are applied to the elevation of water in situations to which the Cornish engine, described in the preceding chapter, was formerly considered exclusively applicable. Fig. 75 illustrates such a pumping-engine, as built for supplying cities with water. This is a Worthington " compound " direct-acting pumping- engine. The cylinders, A B, are placed in line, working one pump, F, and operating their own air-pumps, D D, by a bell- crank lever, connected to the pump-buckets by links. Steam exhausted from the small cylinder, A, is further expanded in the large cylinder, B, and thence goes to the condenser, C. The valves are moved by valve-gear which is actuated by the piston-rod of a similar pair of cylinders placed by the side of the first. These valves are constructed substantially on the plan of the Corliss and are thus very fairly balanced, are easily and promptly moved, and give little clearance. By connecting the valves of each engine with the piston-rod of the other, it is seen that the two engines must work alternately, the one making a stroke while the other is still, and then itself stopping a moment while the latter makes its stroke. STRUCTURE OF THE STEAM-ENGINE. 165 166 A MANUAL OF THE STEAM-ENGINE. Water enters the pump through the induction-pipe, E, passes into the pump-barrel through the valves, V F, and issues through the eduction-valves, T T, and goes on to the " mains " by the pipe, G, above which is seen an air-chamber, which assists to preserve a uniform pressure on that side the pump. The " high-duty attachment," U U, of the later engines of this type performs an exceedingly important office in a very ingenious yet simple manner. It consists of a pair of plungers working in oscillating barrels, U U, attached to a cross-head on each piston-rod common to engine and pump. Water-pres- sure is introduced behind these plungers and retained as nearly uniform as practicable as the engine makes its stroke. It is at once seen that this pressure resists the motion of the engine from the beginning to the middle of its stroke. At mid-stroke, the centre-lines of the plungers are perpendicular to the Line of the rod ; they counterbalance each other, and the action of the pair is neutral as respects the engine. Beyond half-stroke this pressure aids the steam, and the more as the end of stroke is approached. The irregular action of the expanding steam is thus met by a correspondingly variable opposite action of "equalizers," and it is easy, with high ratios of expansion, even, to thus secure a very uniform pressure in excess of the resistance of the water-column, by careful proportioning of parts and of pressures. By this simple and ingenious device, due to Mr. C. C. Worthington, it is possible to increase the ratio of expansion in the direct-acting engine very greatly with corresponding gain in duty; the engine thus entering the class known as " high-duty engines." This attachment thus does the duty of a fly-wheel, often, of enormous weight, and thus increases effectively the efficiency of the engine as a machine. It works properly, with the same variations of pressures, at all speeds, and is also, at times, a safety-attachment, stopping the engine in case of a breakage in the mains. In the " equalizer " system, let A = total area of section of plungers; p = pressure admitted upon them ; STRUCTURE OF THE STEAM-ENGINE. 167 1 68 A MANUAL OF THE STEAM-ENGINE. L = their full, joint, load ; T = thrust in line with piston-rod ; 8 = angle of axis of equalizer with vertical. Then the total load and the stress on the t\vo equalizer-rods is L = Ap = r'cot e T= Apsin = L sin Q; At mid-stroke # = o and T o = L. At the extreme positions, 0,, a , T=Ap sin lt = Ap sin 2 ; and these values should be made to approximately equal the initial load on the engine-piston, less the resistance in the pump at starting, and to the latter quantity, less the terminal pressure of engine-piston, at the end of stroke. The alti- tude of the equalizer-trunnions above the centre-line of the engine, and the length of stroke thus fixed, are the elements determining the quantity of work done in the equalizer-cylin- ders and the completeness of equalization. The stroke, s, should have such extent that the work per stroke may be equal to the alternate excess and deficiency of the work of the engine, in the earlier and the later half-stroke, respectively, above and below that demanded, in the same time, at the pump. A small sketch illustrating this equalization will be found in the chapter on Engine-trials. Beam pumping-engines are now almost invariably built with crank and fly-wheel, and very frequently are compound engines. The illustration on page 169 represents an engine of the latter form. A and B are the two steam-cylinders, connected by links and parallel motion, CD, to the great cast-iron beam, EF. At the opposite end of the beam, the connecting-rod, G, turns a crank, H, and fly-wheel, LM t which regulates the motion of the engine and controls the length of stroke, averting all danger of accident occurring in consequence of the piston striking either cylinder-head. The beam is carried on handsomely- STKl'CT*~RE OF TOM STMAM-JSHGOOL 169 shaped iron columns, which, with cylinders* pomp, and fly- wheeL are supported by a substantial stone foundation. The pump-rod, I r works a double-acting pump, / and the resistance to the issuing water is rendered uniform by an air-chamber, K r within which the water rises and falls when pressures tend to vary greatly. A revolving shaft. -V. driven from the fly-whcd abaft, carries cams, OP, which move the lifting-rods seen directly over them and the valves which they actuate. Be- tween the steam-cylinders and the columns which carry the beams is a well, in which are placed the condenser and air- pump. Steam is carried at 60 or 80 pounds pressure, and ex- panded from 6 to 10 times. A later form of double-cylinder beam pmnping-engine is that invented and designed by E. D. Leavittt. and shown in Figs. 78 and 79. The two cylinders are placed one on each side the centre of the beam, and are so inclined that they may be coupled to opposite ends of it, while their lower ends are placed dose together. At their upper ends a valve is placed at each end of the connecting steam-pipe. At their lower ends a single valve serves as exhaust-valve to the high-pressure and as steam-valve to the low-pressure cylinder. The pistons move I/O A MANUAL OF THE STEAM-ENGINE. in opposite directions, and steam is exhausted from the high- pressure cylinder directly into the nearer end of the low- pressure cylinder. The pump, of the " Thames-Ditton " or " bucket-and-plunger " variety, takes a full supply of water on FIG. 78. THE LEAVITT WATER-WORKS ENGINE. the down-stroke, and discharges half when rising and half when descending again. The duty of this engine is reported as ex- ceeding 1 10,000,000 foot-pounds for every too pounds of coal burned. The duty of a moderately good engine is usually considered to be from 60 to 70 millions ; while 100,000,000 is a high figure. STRUCTURE OF THE STEAM-EXGIXE. 171 The Wolff and Receiver types are the two most familiar forms of pumping-engine. The Wolff engine is so designed that the motions of the two pistons are coincident in time, as when both are attached to the same end of a working-beam. Fig. 79. It is often found advantageous to add a second, high-pressure, cylinder to a low-pressure engine, thus converting it into a compound engine. This is usually done by placing the new cylinder beside the old and connecting it to the beam through the old air-pump links. This compounding system is FIG. 79. THE commonly known as " McXaughting," from the first engineer to practise it. In such cases, the steam-passages lead from either end of the one cylinder to the opposite end of the other, and no intermediate receiver is needed. Where, as in the Gaskill engine of the Holly Mfg. Co., Figs. 80, 81, and 82, the proportions of the cylinder are such, the diameter being great in proportion to the stroke, that it is possible to introduce a beam in the manner shown, and to secure alternation of move- ment, the intervening steam-passages become of minimum length, and " dead-space" is made comparatively small, with \7 2 MANUAL OF THE STEAM-ENGINE. STRUCTURE OF THE STKAJf-EHGlXE. 73 very advantageous economical results; while the engine be- comes very compact. When, as is sometimes the fact, the two cylinders are placed at opposite ends of the beam, the latter being of com- mon proportions and the engine of long stroke, the centre- fines of the cylinders are separated by a distance equal to from 174 A MANUAL OF THE STEAM-ENGINE. FIG. 82. COMPOUND PUMPING-ENGINE. STRUCTURE OF THE STEAM-EXGIXE. 1/5 two to three times the length of stroke, and the steam-passage* and dead-spaces become seriously large. This objection has been met by Dr. Leavftt by inclining the cylinders, as in Figs. 78 and 79, and throwing their lower ends in under the main beam-centre, thus considerably shortening the connecting pipes. A Corliss Pmrnpimg-cmguu. designed by that great engineer for the water-works of Pawtucket, IL I., has been reported as doing, continuously, a " duty" of over 120^0000000. This *g"nr, Fig. 83, consists of a pair of horizontal steam-cylinders, side by side, driving a pair of double-acting pumps, each in line with one of the engine-cylinders and the two having a common 176 MANUAL OF THE STEAM-ENGINE. piston-rod. A bell-crank lever and suitable links connect the engines with the single balance-wheel, placed between and above them. The smaller cylinder takes steam of about ten FIG. 84. VERTICAL TRIPLE-EXPANSION ENGINES. atmospheres absolute pressure (127 pounds by gauge), and its exhaust passes across to the larger cylinder, whence it is passed into the condenser, below the engine. The ratio of expansion is from 15 to 20, and the speed of engine 50 revolutions per minute. STRUCTURE OF THE STEAJi-EXGlXE. 1/7 The pomps are fitted with a large number of small and light valves and thus are subject to very little waste by leakage or back-flow of water while they are seating, and demand very little power in their operation. As in all engines of this kind, a receiver is attached between the engine-cylinders, and in this case the steam is superheated both before entering the engine and while passing from the one cylinder to the other. The valve-gear is of the usual Corliss type, the expansion variable on both cylinders. Fig. 84 illustrates a type of vertical triple-expanding pump- ing-engines for water-works, such as have been designed by Mr. Reynolds and the Allis Co. for a number of large cities. Their capacity averages about 20,000^000 gallons per day. jj The cylinders are attached to heavy A-frames which are secured to the bed-plates. In the A-frames, the guides are formed for the cross-heads. The plungers move with the cranks, which are set 120 degrees apart to insure a constant and steady flow of water in the delivery-mains. The pumps have outside-packed plungers of the single-acting type, one plunger being located under and operated by each piston. Each plunger is connected to its steam-piston by four rods attached to the cross-heads. The condenser and pumps are placed in a pit below the engine-room floor. The pump-valves are mounted on cages, and so arranged that any series of valves can be easily removed or replaced. All the operations of the engine are performed from one central position by the engineer. The engraving following illustrates a pair of vertical triple- i expansion pumping-enghies which were designed by Mr. Rey- nolds for the city of Allegheny, Pa., to pump six million gal- lons of water, each twenty-four hours, against a head of 220 feet, and develop a duty of ninety-five million foot-pounds for each one thousand pounds of water fed to the boilers. The duty obtained by a twenty-four-hour run was over 107.000.000 foot-pounds. This type is a favorite with many builders, as it bongs all parts within a small floor-plan, yet gives accessibility of parts, FIG. 85. -T ISO -.A MANUAL OF THE STEAM-ENGINE. a moderate size and cost of foundation for a given capacity, and direct connection of the cylinders in series and the pumps. The section at the left is so made as to give a good idea of the arrangement of steam-passages and of water-connections. This design is seen to be a direct connected engine set on end. A design of blowing-engine, of air-pumping, for large blast- furnaces, illustrating well the compactness, stiffness, and neat- ness attainable in such designs, and also the form of valve- motion adopted with the poppet-valve, is shown in the outline engraving on page 179.* This design is by Messrs. Gordon, Strobel & Lawrence. The steam-cylinders are 42 and the blast-cylinder 84 inches in diameter, their common stroke 4 feet. The box-form of frame permits great stiffness and ad- mits the placing of the two cylinders in line, the main (i 5-inch) shaft beneath, and a convenient general arrangement of valve- gearing. In the latter, as seen, a rock shaft, actuated directly by the eccentric-rod, produces the vibration of the "wipers" raising the " toes," which, in turn, raise and depress the valves. A trip-arrangement permits a variable cut-off from one to three-fourths stroke, and a constant lead is maintained. The lift of the steam-yalve varies from f- inch to 2-J inches, as the ex- pansion decreases. The action of the exhaust is unaffected by that of the steam-valve. The air-valves are so large in total area that, at the working-speed, no observable loss of pressure occurs at their ports. The depth of piston is one fourth the diameter in the steam-cylinder and one eighth in the blast-cyl- inder. This engine makes about 35 revolutions per minute, with 60 pounds of steam and cut-off at . 38. Portable Engines are such as may be conveniently moved from place to place. They are generally of small size, moderate power, compact construction, non-condensing, em- ploying steam of high pressure in cylinders worked at high piston-speed, and produced in boilers of the tubular class and which commonly serve, also, as engine-frames. In some cases, * Reproduced by permission from the Iron Age o* STRUCTURE OF THE STEAM-ENGINE. l8l they consist of engine and boiler mounted on a common bed. Often they are mounted on wheels, in \vhich case they are usually known as " agricultural engines." Road-locomotives, which are self-impelling portable engines, are much used in some parts of the world, and the steam "road-roller" is a road-locomotive which has heavy rollers in place of wheels, and which may be used in rolling the surface FIG. 87. SEMI-PORTABLE ENGINE. (Scale of macadamized or other roads. Similarly, a "steam fire-en- gine " is a portable engine carrying a steam-pump which may be used in extinguishing fires. The " semi-portable " engine in Fig. 87 is not fastened to the boiler, and is therefore not .affected by expansion, nor are the bearings overheated by conduction or by ascending heat 1 82 A MANUAL OF THE STEAM-ENGINE. from the boiler. The fly-wheel is at the base, which arrange- ment secures steadiness at the high speed which is a requisite for econ- omy of fuel. The boilers are of the upright tubular style, with internal fire-box, and are intended to be worked at 150 pounds pressure (10 atmospheres) per inch. These boil- ers are fitted with a baffle-plate and circulating-pipe, to prevent priming, and also with a fusible plug, which will melt and prevent the crown- sheet of the boiler burning, if the water gets low. Another illustration of this class of engine, as built in small sizes, is seen in Fig. 88. The peculiarity of this engine is that the cylinder is placed in the top of the boiler, which is upright. By this arrangement the engine is constantly drawing from the boiler the dryest steam, and there is thus no liability of serious loss by condensation, which is rapid, even in a short pipe, when the engine is separate from the boiler. The engine illustrated is rated at 10 horse-power. Among the earliest of American engineers to turn attention to this department of construction were Messrs. Babcock & Wilcox. The style of engine which was designed and intro- duced by them has now become almost as generally accepted as standard among builders of small engines as has the Corliss engine among constructors of drop cut-off engines. It has been copied in all parts of Europe, as well as in the United States. It may be taken as representative of the best methods of construction of this class of machinery in this country, and as exhibiting the elegance in proportions, and that excellence of material and workmanship, which are now becoming recognized as desirable in steam-engines of even the smallest size. FIG. 88. SEMI-PORT (Scale A STMUTTUSE Of THE STEAM-ENGINE- 183 Figs. 30 and 31 exhibit the form of the engine here to be described. It is a ~ vertical engine "" mounted upon a base plate of neat and strong form, and with the steam-cylinder bolted by the lower head to a very strong and very graceful frame. 1~Mc mam journals are earned m bearings JUBSJ meted in the frame, and consequently free from liability to loss of perfect alignment, or to unequal wear. The valve is either a plain locomotive-slide or, preferably, a piston-valve. The Latter is fitted in a detachable seat, which can be easily removed for renewal of seat and valve, should accident or wear ever make k necessary. The vertical position of the engine pievenb. wear within fhe cylinder becoming serious or unsymmetricaL The pistons are hollow, and are packed with rings set with *"*%* spring to keep them up to a bearing. The cross-head has its gibs turned to fit the guides in the frame, which latter are part of the casting of the frame and are bored out in line with the cylinder, and cannot puiiilillly g 6 * out f fine. The engine above referred to is of small size 4 or 5 hone- power and has been iiUMiiaBy designed for electric-fighting purposes. The governor regulates by adjusting the supply off steam passing to the engine through a throttle-valve a method which seems to have been here more successful than is usual in engines having to perform so t^rarHng a. kind f work. The speed of this engine is usually 250 to 300 revolutions per minute. Larger engines of this style are often constructed, ranging up to TOO horse-power. These engines, when of 15 to IOO horse-power, are properly classed as stationary engines ; they are given an independent crank-shaft pillow-block and a counterbalanced disk-crank. In these engines, of all sizes, the modern innovation of the use of steel for running parts is very generally introduced. The rods, pins, and minor parts are of this metal; the bearings are usually of bronze fined with Babbitt-metal, and are given large area. Crank-shafts are either of M^cl or of hammered iron. The later work of the best English builders has given 184 A MANUAL OF THE STEAM-ENGINE. remarkable economical results. Some of these portable engines have exhibited, at competitive trials, an economical efficiency equal to that of the largest marine engines. The causes of this remarkable economy are readily learned by an inspection of the engines, and by observation of the method of managing them at test-trials. The engines are very carefully designed. The pistons travel at high speed. Their valve-gear consists usually of a plain slide-valve, supplemented by a separate ex- pansion-slide, driven by an independent eccentric, and capable of considerable variation in the point of cut-off. This form of expansion-gear is very effective at the usual ratio of expansion, which is not far from four or five. The governor is usually attached to a throttle-valve in the steam-pipe, an arrangement which is not the best possible under variable loads, but which produces no serious loss of efficiency when the engine is driven, as at competitive trials, under the very uniform load of a brake and at very nearly maximum capacity. The most successful engines have steam-jacketed cylinders with high steam and considerable expansion. The boilers are, as are also all other heated surfaces, carefully clothed with non-con- ducting material, and well lagged over all. The details are carefully proportioned, the rods and frames are strong and well secured together, and the bearings have large rubbing- surfaces. The connecting-rods are long and easy-working, and every part is capable of doing its work without straining and with the least friction. In handling the engines at the competitive trial, experienced and skilful drivers are selected. The difference between the performances of the same engine in different hands has been found to amount to from 10 to 15 per cent, even where the competitors were both considered exceptionally skilful men. In manipulating the engine, the fires are attended to with the utmost care ; coal is thrown upon them at regular and fre- quent intervals, and a uniform depth of fuel and a perfectly clean fire are secured. The sides and corners of the fire are looked after, especially. The fire-doors are kept open the least possible time ; not a square inch of grate-surface is left STRUCTURE OF THE STEAM-ENGINE. 185 unutilized, and every pound of coal gives out its maximum of calorific power, and in precisely the place where it is needed. Feed-water is supplied as nearly as possible continuously, and with the utmost regularity. In some cases the engine-driver stands by his engine constantly, feeding the fire with coal in handfuls, and supplying the water to the heater by hand by means of a cup. Heaters are invariably used in such cases. The exhaust is contracted no more than is absolutely necessary for draught. The brake is watched carefully, lest irregularity of lubrication should cause oscillation of speed with the chang- ing resistance. The load is made the maximum which the engine is designed to drive with economy. Thus all conditions are made as favorable as possible to economy, and they are preserved as invariable as the utmost care on the part of the attendant can make them. These trials are usually of only three or five hours' duration, and terminate before it becomes necessary to clean fires. Agricultural Engines. The next illustration represents the portable, " agricultural," steam-engine as built by one of the earliest and best manufacturers of such engines in the United States. In the boilers of these engines the heating-surface is given less extent than in the stationary engine-boiler, but much greater than in the locomotive, and varies from 10 to 20 square feet per horse-power. The boilers are made very strong, to enable them to withstand the strains due to the attached en- gine, which are estimated as equivalent to from one tenth to one eighth that due to the steam-pressure. The engine is mounted, in this example, directly over the boiler, and all parts are in sight and readily accessible to the engineer. Compound Portable Engines have been found to exhibit great economy as compared with the simple engine, notwith- standing the fact that the advantages of compounding are gen- erally supposed to be less on small than on large engines. The plan adopted is usually that of placing the two engines side by side, connecting them to cranks, on a common crank-shaft, set at right-angles, and providing a receiver of moderate size to take the exhaust of the smaller and to supply steam to the 1 86 A MANUAL OF THE STEAM-ENGINE. larger cylinder. In some instances, the Wolff system of two pistons having simultaneous opposite motions and without receiver is adopted, a plan admissible with small engines, but less suitable for large powers. The compounding of engines FIG. 89. T of this class, which are usually of less than 25 horse-power, has been found to produce a saving of, often, twenty-five per cent of the fuel and steam. Steam Fire-engines have become standard in general plan and arrangement of details. These are probably the best illustra- tions of extreme lightness, combined with strength of parts and working power, which have ever been produced in any branch of mechanical engineering. By using a small boiler crowded with heating-surface, very carefully proportioned and arranged, and with small water-spaces ; by adopting steel for running- gear and working parts wherever possible ; by working at high STRUCTURE OF THE STEAM-ENGIXE. l8/ piston-speed and with high steam-pressure ; by selecting fuel with extreme care by all these expedients, the steam fire- engine has been brought, in this country, to a state of efficiency far superior to anything seen elsewhere. Steam is raised with wonderful promptness, even from cold water, and water is thrown from the nozzle at the end of long lines of hose to great distances. But this combination of lightness with power is only attained at the expense of a certain regularity of action which can only be secured by greater water and steam capacity in the boiler. The small quantity of water contained within the boiler makes it necessary to give constant attention to the feed, and the tendency, almost invariably observed, to serious foaming and priming not only compels unintermitted care while run- ning, but even introduces an element of danger which is not to be despised, even though the machine be in charge of the most experienced and skilful attendants. Even the greatest care, directed by the utmost skill, would not avail to prevent frequent explosions, were it not for the fact that it rarely, if ever, happens that accidents to such boilers occur from low water, unless the boiler is actually completely emptied of water. In driving them at fires, they frequently foam so violently that it is utterly impossible to obtain any clew to the amount of water present, and the attendant usually keeps his feed-pump on and allows the foaming to go on. As long as water is passing into the boiler it seems unlikely that any portion will become over- heated and that accident will occur. (See page 191.) 39. Road Locomotives and Rollers are built, necessarily, with even greater care and of greater strength than the ordi- nary portable engine ; since they are exposed to rougher usage and more serious strain. In this, as in the class of engines last described, the draught is obtained by the blast of the exhaust-steam which is led into the chimney. The usual consumption of fuel is from 4 to 6 pounds pei hour and per horse-power, burning from 1 5 to 20 pounds on each square foot of grate, and each pound evaporat- 1 88 A MANUAL OF THE STEAM-ENGINE. ing about 8 pounds of water. A usual weight is, for the larger sizes, 500 pounds per horse-power. Road-engines are arranged to propel themselves, as in the Mills road-engine or locomotive, of which the accompanying engraving is a representation. This engine is proportioned for hauling a tank containing 10 barrels, or more, of water and a grain-separator over all ordinary roads, and to drive a thrashing- machine or saw-mill, developing 20 or 25 horse-power. This example of the road-engine has a boiler built to work at 250 FIG. 90. THRASHER'S ROAD-ENGINE. (Scale fg.) pounds of steam ; the engine is designed for a maximum power of 30 horses. It has a balanced valve and automatic cut-off, and is fitted with a reversing-gear for use on the road. The driving-wheels are of wrought-iron, 56 inches diameter and 8 inches wide, with cast-iron driving-arms. Both wheels are drivers on curves as well as on straight lines. The engine is guided and fired by one man, and the total weight is so small that it will pass safely over any good country bridge. A brake is attached, to insure safety when going down-hill. Although designed to move at a speed of about three miles per hour, the STRUCTURE OF THE STEAJt-EXGIXE. 189 Telocity of the piston may be increased so that four miles per hour may be accomplished when necessary. This is an excellent example of this kind of engine as con- structed at the present time. The strongly-built boiler, with its heater, the jacketed cylinder, and light, strong frame of the engine, the steel running-gear, the carefully-covered surfaces of cylinder and boiler, and excellent proportions of details, are illustrations of good modern engineering. Fig. 91 is an engraving of a road-roller as built by one of the most successful among the firms engaged in this work. The structure of such an engine, if of the better class, illus- trates many specially interesting features of modern construc- tion. They are often made with single engines; but. as in this case, a pair coupled at right-angles, as in the locomotive, is preferable ; and it may often be advisable to compound them. There should be no danger of the machine getting stalled by reason of the engine " catching on the centre." These ma- chines are made of from ten to fifteen tons weight : the valve- 190 A MANUAL OF THE STEAM-ENGINE. motion is usually the common locomotive gear ; the best have steel running parts and steel boilers ; a brake is fitted to the driving-wheels; and special noiseless safety-valves are used. The gearing should be of annealed cast-steel, and the driving- wheels are best made of a mixture of peculiarly strong iron, as " car-wheel " iron with new No. i foundry-iron. This class of road-locomotive was brought into use about FIG. 92. R 1829 on French roads, and about 1865 in England and her colonies. The Author has made a trial of one of these machines constructed by very successful British builders (see above fig- ure), to determine its power, speed, and convenience of work- ing and manoeuvring. The following were the principal di- mensions : Weight of engine, complete, 5 tons 4 cwt 11,648 pounds. Steam-cylinderdiameter 7| inches. Stroke of piston IO < Revolutions of crank to one of driving-wheels 17 Driving-wheelsdiameter 60 inches. breadth of tire 10 " weight, each 45 o pounds. STRUCTURE OF THE STEAM-ENGINE. igi Boiler length oreralL...... 8 feet. " diameter of shell 30 " thickness of shell tr inch. fire-box sheets, outside, thickness " Load on driving-wheels, 4 tons 10 cwt 10,080 pounds. The boiler was of the ordinary locomotive type, and the engine was mounted upon it, as is usual with portable engines. The steam-cylinder was steam-jacketed, in accordance with the most advanced practice here and abroad. The crank-shaft and other wrought-iron parts subjected to heavy strains were strong and plainly finished. The gearing was of malleableized cast-iron, and all bearings, from crank-shaft to driving-wheel, on each side, were carried by a single sheet of half-inch plate, which also formed the sides of the fire-box exterior. Its per- formance was thoroughly satisfactory. As the marine engine illustrates the highest result of ap- plication of invention and engineering talent to production of economy of fuel, and the most elaborate and perfect type of engine, so the steam fire-engine exemplifies the result of the same application of genius to the production of a machine in which everything is subordinated to quickness and power in action. Thus, referring to Fig. 93, that of an engine designed by the Manchester Locomotive Works, we find that, in this class of engine, the demand for lightness, strength, compactness, quick action, and large and concentrated power is met, generally, by the use, as here seen, of the vertical tubu- lar boiler, with the exhaust-blast of the locomotive, with tubes crowded in more thickly than would be desirable or safe with the horizontal form ; large steam and water pipes, double- acting pumps, set vertically, as a rule, in the larger sizes, large steam-cylinders, a large air-chamber, and a steel or wrought- iron frame. The whole is mounted on springs of great strength and flexibility combined. Large fire engines of this kind will weigh three tons, and will .throw 1000 gallons a min- ute, in a 2-inch stream, to a distance of 300 or 325 feet, or to a height of 200 feet or more. Their steam-cylinders are as large as 9 or 10 inches diameter, and pumps 5f or 6, with a stroke of STRUCTURE OF THE STEAM-ENGINE. 193 6 to 9 inches. Only the best of materials can be used in such machinery as this. The balance obtainable by the use of three engines is especially useful in the case of the steam fire-engine; where smoothness and steadiness of action is necessary on so unsub- stantial a base. Here, also, the use of three attached pumps, as in Fig. 94, gives a very valuable gain in smooth-working of the water-side of the machine. With skilful designing, the added weight is comparatively unimportant ; since it only affects the engine and is to probably usually a sensible ex- tent compensated by reduced size, or by greater efficiency of the boiler and by decided gain in reduction of friction and greater " throw" of the stream leaving the hose-nozzle. The details of the design by Mr. Knaust, here shown, so far as con- cerns the peculiarities of this class of engine, can be readily seen and need no special description. The steam fire-engine is sometimes constructed as a " fire- boat" of enormous power, the whole steam-power of the main boilers being there available. The New Yorker, designed by Mr. Cowles, for example, displaces 351 tons, has a speed of 15 knots, has four steam-pumps, each of 1 6-inch steam- and lo-inch water-cylinders, capable of discharging 10,000 gallons per minute to a maximum distance of 250 feet in a 5-inch stream, or to less distances in a number of smaller streams. 40. The Locomotive Engine is the best known example of sustained power, with minimum weight, which has yet been produced by the mechanical engineer. A locomotive has two steam-cylinders, either side by side within the frame, and immediately beneath the forward end of the boiler, or on each side and exterior to the frame. The engines are non-condensing, and of the simplest possible con- struction. The whole machine is carried upon strong but flexi- ble steel springs. The steam-pressure is usually more than loo pounds. The pulling-power is generally about one fifth the weight under most favorable conditions, and becomes as low as one tenth on wet rails. The fuel employed is wood in new countries, coke in bituminous-coal districts, and anthracite coal STRUCTURE OF THE STEAM-EXG1XE. IQ5 in the eastern part of the United States. The general arrange- ment and the proportions of locomotives differ somewhat in different localities. The peculiarities of the American type (Fig. 95 ) are the truck, //, or bogie, supporting the forward part of the engine, the system of equalizers, or beams which distribute the weight of the machine equally over the several axles, and minor differences of detail. The cab or house, r. protecting the engine-driver and fireman, is an American de- vice, which is gradually coming into use abroad also. The American locomotive is distinguished by its flexibility and ease of action upon even roughly-laid roads. In the sketch, which shows a standard American engine in section, A B is the boiler. C one of the steam-cylinders, D the piston, E the cross-head, connected to the crank-shaft, F. by the connecting-rod. G H the driving-wheels, 1 J the truck-wheels, carrying the truck. KL : M N is the fire-box, O O the tubes, of which but four are shown. The steam-pipe, R S, leads the steam to the valw- chest, T, in which is seen the valve, moved by the valve-gear. L~ I " and the link. If. The link is raised or depressed by a lever, JT, moved from the cab. The safety-valve is seen at the top of the dome, at Y, and the spring-balance by which the load is adjusted is shown at Z. At a is the cone-shaped ex- haust-pipe, by which a good draught is secured. The attach- ments , c. d. r, f y g whistle, steam-gauge, sand-box, bell, head-light, and " cow-catcher " are nearly all peculiar, either 196 A MANUAL OF THE STEAM-ENGINE. in construction or location, to the American locomotive. The locomotive is furnished with a tender, which carries its fuel and water. A standard passenger-engine on railways in the United States has four driving-wheels, 5i feet diameter ; steam-cylin- ders, 17 inches diameter and 2 feet stroke ; grate-surface 15^ square feet, and heating-surface 1058 square feet. It weighs 63,100 pounds, of which 39,000 pounds are on the drivers and 24, 100 on the truck. The freight-engine has six driving-wheels, 54f inches in diameter. The steam-cylinders are 18 inches in diameter, stroke 22 inches, grate-surface 14.8 square feet, heat- ing surface 1096 feet. It weighs 68,500 pounds, of which FIG. 96. THE AMERICAN TYPE OF PASSENGER-ENGINE. 48,000 are on the drivers and 20,500 on the truck. The former takes a train of five cars up an average grade of 90 feet to the mile. The latter is attached to a train of 1 1 cars. On a grade of 50 feet to the mile, the former takes 7 and the latter 17 cars. Tank-engines for very heavy work, such as on grades of 320 feet to the mile, which are found on some of the mountain lines of road, are made with five pairs of driving-wheels, and with no truck. The steam-cylinders are 20^- inches in diame- ter, 2 feet stroke; grate-area, 15! feet; heating-surface, 1380 feet ; weight with tank full, and full supply of wood, 112,000 pounds ; average weight, 108,000 pounds. Such an engine has hauled 1 10 tons up this grade at the speed of 5 miles an hour, STRUCTURE OF THE STEAM-ENGIXE. 197 the steam-pressure being 145 pounds. The adhesion was Jbout 23 per cent of the weight. In checking a train in motion, the inertia of the engine itself absorbs a seriously large portion of the work of the brakes. This is sometimes reduced by reversing the engine and allowing the steam-pressure to act in aid of the brakes. To avoid injury by abrasion of the surfaces of piston, cylinder, and the valves and valve-seats, M. Le Chatelier introduced a jet of steam into the exhaust-passages when reversing, and thus prevented the ingress of dust-laden air and the drying of the rubbing surfaces. This method of checking a train is rare- ly resorted to except in case of danger. The introduction of the " continuous " or " air " brake, which can be thrown into action in an instant on every car of the train by the engine- driver, is so efficient that it is now almost universally adopted. It is one of the most important safeguards which American ingenuity has yet devised. In drawing a train weighing 1 50 tons at the rate of 60 miles an hour, about 800 effective horse- power is required. A speed of 80 miles an hour has been sometimes attained, and 100 miles has probably been reached. The standard locomotive-engine has a maximum life which may be stated at an average of about 30 years. The annual cost of repairs is from 10 to 15 per cent of its first cost. On moderately level roads, the engine requires a pint of oil to each 25 miles, and a ton of coal to each 40 or 50 miles run. The compound locomotive engine is now coming to be adopted. This involves considerable changes of proportions, increasing the volume and weight of steam-cylinders, but en- abling the designer to more than proportionally decrease the weight of boiler and the quantity of fuel carried. Xo serious objection to their use has been experienced, however, and no difficulty in the construction of the " double-cylinder " type of engine for the locomotive. Many such engines have been constructed. They will be referred to again. The increasing demands upon the railways of the United States have recently brought about considerable changes in the forms of engine employed. The standard " American " type cf 198 A MANUAL OF THE STEAM-ENGINE. locomotive is much less generally employed for slow and heavy traffic, and its place has, on the trunk lines, been taken by 8-, IO-, and 12-wheeled engines of great weight. Even in pas- senger service, engines with six and ten coupled wheels are displacing it in many cases. For "switching " or "shunting" heavy trains, engines of 40 tons weight, with six coupled wheels and 17- to I clinch cylinders of 24 inches stroke, are used. The weights on the drivers are usually 5 to 7 times the adhesion demanded. In Europe, with lighter trains and shorter runs, as a rule, but with higher speeds, the single pair of drivers, the opposite extreme of practice, seems preferred. On both continents the compound locomotive is rapidly com- ing into use. The modern developments of the locomotive-engine, which have been seen to involve no change of general construction, have been mainly the refinement of details, the introduction of a few recent inventions, as the extended smoke-box, and the application of the air-brake. The engine is to-day the locomotive of George and Robert Stephenson. But while the type remains unchanged in its essentials, there are now in use a great number of designs of engine differing among each other in proportions and often widely in external appearance, designs which have been produced in the endeavor to adapt the machine to specific kinds of work or to special localities and purposes. Thus the fast passenger and STKCCTCKE OF THE STEAX-EXGIXE. - /.- the slow freight, or " goods," engine have very different pro- portions and appear like quite different machines. The common standard passenger-engine is of the type illustrated in the accompanying figure, as built by the Rogers Works, in which a comparatively recent device, the " extension smoke-box," is shown, acting as a trap and temporary recep- tacle for hot ashes and cinders carried through the tubes and for- merly thrown out to set fire to buildings or vegetation or to annoy the people on the train. Ten- and twelve-wheeled engines are employed for the heaviest kinds of work. These locomotives weigh from 45 to 75 tons, and occasionally even more, of which nearly all is car- ried on coupled driving-wheels of not far from 4 feet diameter. The cylinders are 20 to 22 inches in diameter, and stroke of piston usually about 2 feet. They have 25 to 35 square feet of grate-surface and 1500 to 2500 feet of heating-surface. The alternate pairs of wheels have " blank," or unconed. tires, to permit easy movement around curves. Their details are similar to those elsewhere described as made for standard pas- senger-engines. Where the fine is of narrow gauge, as often in new coun- tries, or wherever it is found desirable to concentrate more hauling power than the usual forms of engine would give, special designs have been sometimes adopted. The Fairhe engine is one of these. This plan unites two engines, back to 200 A MANUAL OF THE STEAM-ENGINE. back, in effect, giving a twin arrangement of engines and of boiler, united at the fire-box. The plan is costly but effective. A simpler system of concentration of power is that of Forney, which unites engine and tender on one frame and thus secures increased weight and adhesion, as seen in the engraving here given ; which gives a total weight of 60,000 pounds on a nar- row and comparatively short wheel-base, and makes an ex- ceptionally handy and easily worked engine. The "tank-engine," of which the last illustrates one form, is sometimes constructed on a very large scale. Thus, loco- motives built at the Baldwin Locomotive Works, Philadel- phia, for the Grank Trunk Railway, to be used in the St. Clair tunnel, under the bed of the St. Clair River, between FIG. 99. FORNEY LOCOMOTIVE. Port Huron, Mich., and Sarnia, Ont., have five pairs of 50-inch driving-wheels on each side of the boilers, the cab in the centre of the boiler, extending out over the two tanks. The cylinders are 22.28 inches, and the boiler 74 inches in diameter, to carry 160 pounds of steam. Each locomotive with tanks filled weighs 200,000 pounds, the ave- rage weight in running order, with tanks half-filled, being 180,000 pounds. Compound Locomotives are less common than compound stationary engines. They are, however, gradually becoming used where fuel is expensive and give, when well designed, very marked economical advantages. The usual system STRUCTURE OF THE STEAM-EXGIXE. 2:: places a high-pressure cylinder on one side and a low-pressure cylinder on the other, the latter being commonly arranged to take steam direct from the boiler when starting or whenever, for any reason, it is desirable. Some of the more interesting and successful designs of compound locomotive-engine are those of which outline illustrations follow, selected from Professor Woods' mono- graph.* That of Von Borries is exemplified by Figs. I oo and 101 : the one exhibiting the arrangement adopted in a heavy en- gine on the Prussian State Railways^ the other a Spanish engine of less power. .- : ::.: .' - The former has cylinders 18.1 and 25.6 inches diameter. 24.8 inches stroke, weighs 88,250 pounds, and has 1420 square feet of heating-surface and 16 feet grate-surface. The driving-wheels are 52.4 inches diameter, and the steam-pressure 175 pounds s; A. T. Woods. M.M.E. : X. Y., Van Aisdafe. 1891. ; Feb. i. 1=59. 2O2 A MANUAL OF THE STEAM-ENGINE. The second engine is of 86,200 pounds weight, with 16- and 23-inch cylinders, 24 inches stroke of pistons, tfa feet diameter of drivers, the pressure I/O pounds. FIG. 101. SPANISH ENGINE. The arrangement of both engines involves the peculiar form of starting-valve devised by Von Borries, which is seen in the next figure. In the sketch, a is the receiver-pipe to the FIG. ioia. VON BORRIES VALVE. high-pressure, b that to the low-pressure cylinder. The valve, v, is seen as in ordinary working when " under way," and the STRUCTURE OF THE STEEAM-ENGINE. 203 arrows show the course of the steam. Attached to the back of this valve are two plungers, c c, constituting the starting- valve. When the throttle-valve is opened, steam enters the pipe d, passing back of the plungers, forcing the valve to its seat, f, at the same time opening the ports h //, through which, and the passage b, it goes on to the large cylinder. When the engine starts, the exhaust occurs from the small cylinder and the receiver-pressure rises, this valve becomes equilibrated, returns to the position shown, and, once thus started, the engine acts as compound, and so continues until, after shutting off steam, this equilibrium is lost and the engine starts again, later, as a simple machine. This device is in extensive use. In the Worsdell form of engine, Fig. 102, the construc- tion is as seen in the sketch.* A is the steam-pipe, B the starting-valve connection, C the receiver, D the exhaust-pipe, and v and Fare the starting and the intercepting valves. The engine here taken for illustration is an English passenger-locomotive, having 16- and 2O-inch cylinders, 24 inches stroke, drivers 8of inches in diameter. The steam- pressure the same as the pre- ceding, and the weight of engine 97,000 pounds, of which 68,000 rests on the driving-wheels. The areas of heating and grate surface are, respectively, 1323^ and 17^ square feet. Joy's valve-gear is employed. The construction of the valves is seen in the next figure. The flap-valve is the intercepting-valve, seen as in regular * Engineering; March 30^ 1888. THE WORSDELL EXCIXE. 204 A MANUAL OF THE STEAM-ENGINE. working. Its spindle is connected with the small piston at a, as shown. The starting-valve is set in a pipe or casing connected with the former, as seen in the sketch. A valve held in place by a spring connects the pipe b with the piston a. The starting-valve is worked by the engine-driver, the same motion closing the intercepting-valve, and the locomotive starts as a simple engine. The rise of pressure in the receiver Valve C fit FIG. 103. PLAN AND SECTION, WORSDELL'S VALVE. presently restores the valves to the position shown and the engine at once becomes compound. The plan, more usual in marine engineering, of employing one high-pressure and two low-pressure cylinders is illustrated in the next sketch, that adopted on the Northern Railway of France.* In the figure, A is the main steam-pipe, B the valve- * Engineering; Dec. 6, 1889. STRUCTURE OF THE STEAM-ENGINE. 2O$ chest, C C the receiver, all attached to the small cylinder, and D D are the two low-pressure exhaust-pipes. The cylinders, h and / /, are high- and low-pressure, respectively, and the whole plan is readily traced out. The cranks of the latter are set at right angles, and the high-pressure crank at 135 degrees with each. All are on one shaft, the middle one of three driving-axles. The high-pressure valve-gear is the Rider modification of the Meyer system, permitting any desired expansion in the high- pressure cylinder. When thrown completely over, the cut-off FIG. 104. DIVIDED L. P. CYUXDER. valve permits the steam to blow through the small cylinder, and thus the engine is converted into the common form, the two low-pressure becoming the driving-engines. This engine has cylinders of 17 and 19.7 inches diameter and 27.6 inches stroke, driving-wheels (six) 64.9 inches diame- ter. 1225 square feet of heating-surface, 13 feet grate-surface, weighs 106,176 pounds, of which 91,000 rests on the drivers, and the steam-pressure by gauge is 199 pounds. 206 A MANUAL OF THE STEAM-ENGINE. The Mallet system, now much employed and well known, is exhibited in the next figure. FIG. 105. THE MALLET SYSTEM. Here A and B are the steam-pipe* and receiver, and C the exhaust-pipe. D is a starting-valve, taking steam through E, and F is the " intercepting-valve." The pipe G serves to con- vey the exhaust from the small cylinder when working non- compound. A pressure-reducing valve is placed between starting-valve and receiver. When in ordinary operation as a compound engine, the pressure of boiler-steam keeps the in- tercepting-valve closed against receiver-pressure. On starting from rest, however, this valve is relieved and steam passes over into the low-pressure cylinder, the pair then working as simple engines. The engine can thus start any load that the standard machine can take. Once started, this and other compounds have less hauling power than the simple type ; but no such reduction occurs as to interfere with any ordinary work. STRUCTURE OF THE STEAM-ENGINE. 207 In all these engines, automatic relief-valves are desirable, on the large cylinder especially, since they must be expected to add to the priming the water of cylinder-condensation in larger proportion than in cases of restricted ratios of expansion. The Webb system, as introduced on the London and Northwestern Railway of Great Britain for both passenger and heavy traffic, is exhibited in the accompanying illustra- tion. It precisely reverses the arrangement last described, there being two high-pressure and one low-pressure cylinder, their relative position being the reverse of the preceding. FIG. 106. THE WEBB COMPOUND. The pipes A A and B B take steam to the small cylinders, and C and D D convey the rejected steam to the large cylin- der. The former are placed ahead of the latter and are con- nected to an independent axle, no coupling or parallel rods being used, and the two axles " keeping time " only through the automatic adjustment produced by their o\vn operation. 208 A MANUAL OF THE STEAM-ENGINE. Where more than two pairs of coupled drivers are employed, the added axles are coupled to the small engines and their axles by means of parallel rods. This engine has the following dimensions : diameter of cylinders, 14, 14, 30 in.; stroke, 24 in.; wheels, diameter, 75 in.; steam-pressure, 175 Ibs.; weight, 99,350 Ibs.; heating-surface, 1457 sq. ft.; grate, 20.55 sc l- ft- Two thirds the total weight is on the drivers. The valve-motion is that of Joy. An en- gine of this type, experimentally tried between New York and Philadelphia, making regularly 87 miles in 2 hours, with 7 stops, and 200 or 225 tons weight of train, excelled the simple engine by 25 per cent in economy of fuel-consumption. The parallel rod is always felt to be a source of danger and of waste of power in the locomotive, and this plan is considered decidedly advantageous in this respect. On the other hand, the low- pressure cylinder produces a comparatively irregular " torque " on the axle to which it is coupled. The Pitkin system, as introduced by Mr. A. J. Pitkin of the Schenectady Works, is seen in Fig. 107, below. FIG. 107. THE PITKIN COMPOUND. It includes one high- and one low-pressure cylinder, with an ingenious intercepting-valve, seen in the next illustration. The receiver has a volume fifty per cent greater than that of STRUCTURE OF THE STEAM-ENGINE. 209 the small cylinder, and the clearance in the latter is about ten per cent, a proportion shown by the indicator to be desirable with the proportions of valves employed. The valves are ar- ranged and the general disposition of parts is as in the standard engine of the old form. The intercepting-valve, as here seen in section, is as at the FlG. toS- Pmtix's IvnERCKFTDCC-VALVK. instant of starting and before compound working begins, the ports c and d closed and no connection existing between the receiver and the large cylinder ; while the latter receives steam through a reducing- valve and the port a and the passage b. On starting, the exhaust from the small cylinder fills the receiver, and the back-pressure taking effect, through e, on the intercepting-valve and destroying its equilibrium, it at once moves over and the large cylinder takes its steam prop- erly for compound working. The dash-pot, A, prevents too sudden movement. This engine has the following dimensions : cylinders, diam- eter, 20 and 29 in.; stroke of piston, 24 in.; ratio of cylinders, 2.1 : diameter drivers (6), 68 in.; weight of engine, 126,800 Ibs.: heating-surface, 1677 sq. ft.; grate-surface, 28.57 ^ About 80 per cent of the total weight is on the drivers. 2IO A MANUAL OF THE STEAM-ENGINE, Mr. Von Borries estimates a saving of 15 per cent and upward as an offset to an increase of first cost amounting to 2 or 3 per cent. He also finds his engines to exceed the common type in hauling power by from 5 per cent on heavy engines to 10 per cent, or more, in fast passenger-service ; a conclusion sustained by Mr. Lapage. The increased weight of cylinders and accessories, for a given power, is more than compensated by the decreased weight of boiler required. The compound locomotive engine has been sometimes found to use as little as 22 pounds (10 kilos) of steam per hour and per horse-power ; which is about two thirds or three fourths the quantity demanded by similar engines uncompounded. M. Mallet communicated to the French Society of Engi- neers (1883) a note from M. Borodin, giving the results of ex- periments to determine the relative economy of the simple FIG 109. BRITISH EXPRESS ENGINE. and the compound system of engine for locomotives. The en- gines experimented with were those designed for the railway from Bayonne to Biarritz by M. Mallet. The trials extended over a considerable period of time, and the comparisons were made fairly complete. The result showed the compound sys- tem to have an economy of from 10 to 20 per cent, according to the conditions under which they are carried out. The prac- ticable variation in the ratio of expansion is often very greatly restricted in the compound engine. The use of the steam- jackets with which the engines were provided did not prove to be of advantage. The expenditure of steam was greater when they were in use than when they were shut off. STRUCTURE OF THE STEAM-ENGINE. 211 Fig. 109 represents the type of engine often adopted on English roads for very high speeds and with comparatively light loads. This engine has regularly made 200 miles in four hours, and somewhat similar engines have made 250 miles in five hours, and even 400 miles in eight hours. The diameter of the drivers, in this example, is 8 feet, the steam-cylinder 1 8 inches, and the stroke of piston 28 inches. This type was in use even earlier than 1880; at which date the performance just stated had been attained. British engines of this last-described type have done ex- traordinary work. Such locomotives on the longer main lines, between London and Glasgow, make an average of 50 miles an hour for 400 miles. The Midland Railway employs engines with cylinders 18x26, a single pair of drivers 7 feet 4 inches diameter; with 1240 feet of heating-surface and 20 feet of grate, to haul trains of 225 to 250 tons weight, at nearly 50 miles an hour, and with a fuel-expenditure of 26 pounds per mile. Compound engines of recent construction have wheels 7f feet in diameter, and have made nearly ninety miles an hour. One of Mr. Worsdell's engines has, for illustration, 20 and 28 by 24 inch cylinders, 7 feet 7^ inch drivers (single pair), 1 140 feet of heating and 20 feet of grate, and has attained an aver- age of over 50 miles an hour on 26.4 pounds of coal per mile ; the train, engine included, weighing something over 300 tons. The steam-pressure carried is 175 pounds. 41. The Marine Engine, on the rivers of the United States, remains largely as it was left by the earlier engines. It is a beam-engine, of moderate steam-pressure, driving the radial paddle-wheel : the details are little, if at all, altered. The pressure of steam is now sometimes as high as 60 pounds per square inch or even more. The valves are of the disk or poppet variety, rising and falling vertically. They are four in number, two steam and two exhaust valves being placed at each end of the steam-cylinder. The beam-engine is a pecu- liarly American type, seldom if ever seen abroad. Fig. 1 10 is an outline sketch of this engine as built for a steamer plying on the Hudson River. This class of engine is 212 A MANUAL OF THE STEAM-ENGINE. usually adopted in vessels of great length, light draught, and high speed. But one steam-cylinder is commonly used. The cross-head is coupled to one end of the beam by means of a pair of links, and the motion of the opposite end of the beam is transmitted to the crank by a connecting-rod of moderate 1J. -irrvr Via ill FIG. no. EAM-ENGINE. length. The beam has a cast-iron centre surrounded by a wrought-iron strap of lozenge shape, in which are forged the bosses for the end-centres, or for the pins to which the con- necting-rod and the links are attached. The main centre of the beam is supported by a " gallows-frame" of timbers so ar- ranged as to receive all stresses longitudinally. The crank and shaft are of wrought iron. The valve-gear is very usually of STRUCTURE OF THE STEAM-EXCISE. 21$ the form known as the Stevens valve-gear, the invention of Robert L. and Francis B. Stevens. The condenser is placed immediately beneath the steam-cylinder. The air-pump is placed close beside it, and worked by a rod attached to the beam. Steam-vessels on the Hudson River have been driven by such engines at the rate of 20 miles an hour. This form of engine is remarkable for its smoothness of operation, its economy and durability, its compactness, and the latitude which it permits in the change of shape of the long, flexible vessels in which it is generally used, without injury by " getting out of line." For paddle-engines of large vessels, the favorite type, which has been the side-lever engine, is now rarely built. For smaller vessels, the oscillating engine with feathering paddle-wheels is still largely employed in Europe. It is very compact, light, and moderately economical, and excels in simplicity. The usual ar- rangement is such that the feathering-wheel has the same action upon the water as a radial wheel of double diameter. This reduction of the diameter of the wheel, while retaining maximum effectiveness, permits a high speed of engine, and therefore less weight, volume, and cost. The smaller wheel- boxes, by offering less resistance to the wind, retard the prog- ress of the vessel less than those of radial wheels. Inclined en- gines are sometimes used for driving paddle-wheels. In these the steam-cylinder lies in an inclined position, and its connect- ing-rod directly connects the crank with the cross-head. The condenser and air-pump usually lie beneath the cross-head guides, and are worked by a bell-crank driven by links on each side the connecting-rod, attached to the cross-head. Such en- gines are used to some extent in Europe, and they have been adopted in the United States navy for side-wheel gunboats. They have also been used on ferry-boats plying between New York and Brooklyn. The non-condensing direct-acting engine is used principally on the Western rivers of the United States, is driven by steam of from 100 to 150 pounds pressure, and exhausts into the at- mosphere. It is the simplest possible form of direct-acting en- 214 A MANUAL OF THE STEAM-ENGINE. gine. The valves are usually of the " poppet " variety, and are operated by cams which act at the ends of long levers having their fulcra on the opposite side of the valve, the stem of which latter is attached at an intermediate point. The engine is hori- FIG. ni.-S zontal, and the connecting-rod directly attached to cross-head and crank-pin without intermediate mechanism. The paddle- wheel is used, sometimes as a stern-wheel, as in the plan of Jonathan Hulls of 1737, sometimes as a side-wheel, as is most usual elsewhere. STRUCTURE OF THE STEAM-ENGINE. 21$ Special designs of marine engine are sometimes found de- sirable for small powers. That here illustrated, for example, as designed by Shipman, is very similar in general arrangement to some forms of semi-portable engine, the engine and boiler having a common base. Larger sizes, however, are separated. The boiler is water-tubular, of the general form of that first used by Stevens. The engine, either simple or compound, is vertical and of the usual standard type, with link-motion, when used as a yacht-engine, and having a reverse-lever. The essential feature of this motor is that it is an auto- matic petroleum-burning engine, designed for use where a moderate amount of power is required. When steam has been generated, no further attention is required beyond that of open- ing and shutting the steam-valve whenever the engine is started or stopped, the fire, speed, and water-feed being arranged as to adjust themselves automatically. Two small aspirators or atomizers, taking steam from the boiler, take up the petroleum fuel, from a chamber below, and drive it into the furnaces in fine spray. Torches ignite this spray as it passes inward. The steam and petroleum supply of the atomizers is regulated by a diaphragm connected to a valve in the steam-pipe. This diaphragm is exposed to steam-pressure on the one side, and is held down by a spring, loaded to a certain pressure, on the other. Its movement is conveyed to the valve by a rod, and it thus regulates the amount of steam passing to the atom- izers. The water in the boiler is kept at a constant level by means of a float, connected to a tap in the suction-pipe of the pump. This float is placed in a chamber which is joined to the top and bottom of the boiler, and rises or falls with the level of the water. The movement is conveyed, by means of levers, to the tap in the suction-pipe, which it opens or closes as the water- level changes. The speed of the engine is regulated by means of a gov- ernor. When once steam is up, the fires, the water-supply, the oiling, and the speed of the engine require no further attention. 216 A MANUAL OF THE STEAM-ENGINE. When first starting, a sufficient pressure is required in the boiler to work the atomizers, and for this a hand air-pump is pro- vided. In vessels, in nearly all cases, the ordinary screw-engine is adopted, and is direct-acting. Two engines are placed side by side, with cranks on the shaft at an angle of 90 with each other. In merchant-steamers, the steam-cylinders are usually FIG. i ia. COMPOUND MARINE ENGINE. vertical and directly over the crank-pins, to which the cross- heads are coupled. The condenser is placed behind the engine- frame, or, where a jet-condenser is used, the frame itself is sometimes made hollow, and serves as a condenser. The air- pump is worked by a beam connected by links with the cross- head. The general arrangement is like that shown in Fig. 112. For naval purposes such a form is objectionable, since its height is so great that it would be exposed to injury by shot. In naval engineering the cylinder is placed horizontally. STRUCTURE OF THE STEAM-ENGINE. 21 7 The trunk-engine, in which the connecting-rod is attached directly to the piston and vibrates within a trunk or cylinder secured to the piston, moving with it, and extending outside the cylinder, like an immense hollow piston-rod, has been fre- quently used in the British navy. It has rarely been adopted in the United States. 42. Standard Forms of marine engines, in nearly all steam-vessels built for the merchant-service, and in some naval vessels, have come to be some modification of the compound engine. Figs. 112 and 113 represent the usual form of the two-cyHnder compound engine. Here A A, B B are the small and the large, or the high-pressure and the low-pressure, cylinders respectively. C C are the valve-chests. G G is the ^!I_. FIG. nj. COWPOCXB MARTVI Fxcrv* (SECTTOK). condenser, which is invariably a surface-condenser. The con- densing water is sometimes directed around the tubes con- tained within the casing, G G, while the steam is exhausted around them and among them, and sometimes the steam is condensed within the tubes, while the injection-water which is sent into the condenser to produce condensation passes around 2l8 A MANUAL OF THE STEAM-ENGINE. the exterior of the tubes. In either case, the tubes are usually of small diameter, varying from five eighths to half an inch, and in length from four to seven feet. The extent of heating- surface is usually from one half to three fourths that of the heating-surface of the boilers. The air and circulating pumps are placed on the lower part of the condenser-casting, and are operated by a crank on the main shaft at N\ or they are sometimes placed as in the style of engine last described, and driven by a beam worked by the cross-head. The piston-rods, T S, are guided by the cross- heads, V V, working in slipper-guides, and to these cross-heads are attached the connecting-rods, XX, driving the cranks, M M. The cranks are now usually set at right-angles ; in some engines this angle is increased to 120, or even 180. Where it is arranged as here shown, an intermediate reservoir, P O, is placed between the two cylinders to prevent the excessive variations of pressure that would otherwise accompany the varying relative motions of the pistons, as the steam passes from the high-pressure to the low-pressure cylinder. Steam from the boilers enters the high-pressure steam-chest, X, and is admitted by the steam-valve alternately above and below the piston as usual. The exhaust steam is conducted through the exhaust passage around into the reservoir, P, whence it is taken by the low-pressure cylinder, precisely as the smaller cylinder drew its steam from the boiler. From the large or low-pressure cylinder the steam is exhausted into the con- denser. The valve-gear is usually a Stephenson link, ge, the position of which is determined, and the reversal of which is accomplished, by a hand-wheel, o, and screw, m np, which, by the bell-crank, k i, are attached to the link, ^v. The "box- framing" forms also the hot-well. The surface-condenser is cleared by a single-acting air-pump, inside the frame, at T. The feed-pump and the bilge-pumps are driven from the cross- head of the air-pump. The "tandem compound" marine engine, Fig. 114, is a simpler and less expensive construction, but it is so subject to uncertainty in starting and so liable to become fixed "on the STRUCTURE OF THE STEAM-EXGINE. 2I 9 centre," that if adopted at all for marine work, it is very gener- ally duplicated, the two engines having cranks at right angles, and thus its special advantage sacrificed. Such a combination is, however, excellent as a " quadruple-expansion " engine, the second set of steam-cylinders taking steam from the first, and FK_ TT TAXOTEW Cowocsro ETQME. (Scale .) a pair of two-cylinder compound engines of different size being thus grouped to give four cylinders " in series." The latest types of Marine Engine are those compounded engines in which the number of engines in series is three, or even more, usually driving three equidistant cranks, and those which are designed to drive two, or even three, screws inde- pendently. In the extension of the principle of compounding 220 A MANUAL OF THE STEAM-ENGINE. in multiple-cylinder engines, it is probably desirable to restrict the number of cranks to three, even with a pair of low-pressure cylinders, or in the quadruple-expansion engine ; both as a mat- ter of economy and to secure smooth-working with minimum FIG. 115. TRIPLE-EXPANSION ENGINE. friction. The balance is usually practically perfect and the full advantage of compounding is attained. In these cases the construction of all the engines which constitute an element of the compounded machine is commonly substantially the same in general, the differences being prin- STRUCTURE OF THE STEAM-ENGINE. 221 cipally in the proportions of the steam-cylinder and its acces- sories. The triple-expansion engine thus usually consists, as a whole, of three similar simple engines, side by side, so ar- ranged, as to size of cylinder and disposition of pipes and valves, that they work as a series in taking and exhausting steam. There are, however, a number of successful arrange- 222 A MANUAL OF THE STEAM-ENGINE. ments of three- and of four-cylinder engines driving but two cranks and in which the " tandem " disposition of cylinders is adopted with good results. The engraving represents one set of the triple-expansion engines of the twin-screw sister-ships, the City of Paris and the City of New York. Their general arrangement is well shown. Each set drives one screw. The magnitude of these great engines is indicated by the altitude of the working platforms and the reversing wheel. This may be taken to represent a standard and very satisfactory disposition of parts and general proportion of engines. A good sample set of figures for the proportions and per- formance of these engines are : Steam-cylinders, diameter, inches ......... 45, 71, 113 Stroke of pistons, feet ........................... 5 Ratios of volumes. . . I ; 2.489; 6.304 01-0.402 ; i ; 2.53 Steam-pressure, per gauge, Ibs .................. 148 Rev. per min ................... . ............... 87 Vacuum, inches ......................... ....... 26 Mean pressures, Ibs ..................... 64 ; 32 ; 14 Indicated power, H. P ....................... 1 9, 1 75 Temp, feed-water, Fahr ......... . ............. 1 19 " sea-water ........................ 54 Area H. S., sq. ft ........................... 50,250 " G. S., " " ........................... i ,294 " cond. surf ............................. 33,ooo I. H. P. per sq. ft. G. S ....................... 14.8 H - s " " " condens. surface. . . . -- = 0.58 Ratio H. S. to G. S ........................... 38.8 " " C.S ........................... 1.52 These figures are given by the engineer officers of the ship for a passage across the Atlantic made in 5 days, 19 hours, 34 STRUCTURE OF THE STEAM-ENGlffE. 22$ minutes, at its date the quickest on record. One day's run was 311 sea-miles,* The arrangement of these engines in twin-screw steamers is seen in the next figure, which exhibits the machinery of the steamer Columbia of the Hamburg-American Line, a ship ?K 07. TOTUB-I 1 1 1 mmm of 12,000 tons displacement and about 15,000 horse-power: each set of triple-expansion engines, as shown, having half that power. The cylinders are 40. 66. and 101 inches diameter, and the stroke of piston 66 inches. The shafts are of steel. 2oi inches diameter, driving screws of manganese bronze 18 feet diameter and of 32 feet pitch. These engines have driven the * Am. Machinist; Feb. 12, iSgi. 224 A MANUAL OF THE STEAM-ENGINE. Columbia 3045 knots New York to Southampton in 6 days, 15 hours, or 19.15 knots per hour. FlG. Il8. QUADRUPLH-EXI'ANSION ENGINE. FlG. An illustration of a standard type of quadruple-expansion marine engine is seen in the section herewith given. This is a STRUCTURE OF Tff STEAM-E&GIA'E. 22$ Scotch engine of 550 horse-power, cylinders loj. 14, and 20 inches diameter, and 20 inches stroke off piston. Only the low-pressure cylinder is jacketed. The cranks being set at right angles, the two pairs off pistons have not synchronous mo- tion, and a receiver or large connecting pipes most be adopted in this arrangement to insure good pressure-changes between tile second and third cylinders. The most extraordinary concentration off steam-power is illustrated in the more recent constructions off torpedo-boats. These little craft are given the lightest possible hulk, fine lines, unencumbered decks, and maximum power, everything being made subordinate to speed. That here figured, the Aviete (page 226), a Thoraeycroft boat built for the Spanish Govern- ment, has made 26 knots an hour (over 30 statute miles). The hull is but 147^ feet long, off 14^ feet beam, and 5 feet draught, or but a trifle longer than Fulton's dermont. Speeds exceeding 20 knots are common with this dass of boat. This type of boat has been given as much as 1600 indicated horse-power, steam being worked at 150 pounds pressure in water-tubular boilers, driving a hull displacing 100 tons,, at speeds off from 25 to 26 knots. The coal consumed at stand- ard half-speed 10 knots is about ft tons as a minimmp. Twin-screws are used. On long runs these, the M measured- mile trial,'* results are not usually approached very doseh/- In this work, the water-tube boiler is. in many cases, substi- tuted for the ordinary ~ shell " fire-tube form with good re- salts. The coal-consumption ranges not far from 2 pounds per I. H. P. per hour in good work. The naval engine of recent times is distinguished by a combination of strength, lightness, compactness, and power, which makes it the most remarkable of all the achievements of modern engineers and mechanics. This is exemplified by the later engines built for boats of the class here illustrated. The triple-compound engine has cylinders 14. 20, and 31^ inches diameter, 16 inches stroke, and taking steam, at 200 pounds pressure, from water-tube boilers rated at 1300 horse-power, and sometimes actually exceeding that figure. ~ White metal "" 226 A MANUAL OF THE STEAM-ENGINE. STRUCTURE OF THE STEAM-ENGINE. 227 is used in all bearings, and both oil and water are supplied to all especially important journals. The low-pressure valve is bal- anced by an adjustable arrangement, and the piston-rings are made of an alloy requiring no lubrication, thus securing, among other advantages, a better action of the condenser. The frames and all parts not necessarily cast are of forged steel. General experience, in brief, indicates the compound engine as customarily employed to exhibit an increase in economy over the simple engine which it displaced amounting to about 30 per cent, and a superiority of 20 or 25 per cent of the triple- expansion engine, with steam at 140-160 pounds, over the compound at 90-100 ; while the latter has not been found to show much advantage with increasing pressures. The reasons for the facts are readily seen on studying, as elsewhere, the theory of the engine. Similarly the quadruple-expansion en- gine exhibits superiority, in less degree, at 200 pounds, over the triple-expansion. The three-crank engine also is found to possess advantages over the two-crank, in efficiency of mechanism and smoothness of operation, and to demand, often, even less repair. With similar size of low-pressure cylinder, this form of triple-expan- sion engine may give considerably greater power than the com- pound, with less serious stresses on the working parts ; and this difference, again, makes it practicable to build the former at as small cost as the latter, when of equal power. The latest type of river and sound steamers is illustrated by the Plymouth of the Fall River Line between New York and New England, traversing Long Island Sound. The dimensions of the Plymouth are as follows : Feet. Inches. Length overall..... 366 Length on water-line , 351 S Breadth over guards 87 Breadth of boll 50 Depth at lowest point of sheer 21 Draught of water, light II Distance from keel to topmast-head 119 Distance from keel to dome-deck 55 3 Distance from keel to top of boose on dome 59 3 228 A MANUAL OF THE STEAM-ENGINE, STKUCTUKE OF THE STEAlf-EXGIXE. 22O, The ship is constructed on the double hull, bracket plate and longitudinal system, securing safety for the ship as regards either sinking or destruction by fire. The designers and con- structors were the same as of the Puritan, previously described. The Plymouth is fitted with a four-cylinder, double-in- clined, triple-expansion, direct-acting engine of 5500 indicated horse-power. The high-pressure cylinder. 47 inches diameter, takes steam at a pressure of 160 pounds per square inch. The intermediate cylinder is 75 inches in diameter. The high- pressure and intermediate cylinders are placed forward of the centre of the shaft, and are connected to crank-pins, placed at right-angles. Abaft the shaft are two low-pressure cylinders, each 8i inches in diameter. One low-pressure is connected to the same crank-pin as the high-pressure cylinder, and the other to the same crank-pin as the intermediate cylinder. All pistons have a stroke of & feet 3 inches. Each of the two low- pressure cylinders is supplied with its own air-pump and sur- face-condenser, with independent centrifugal circulating pump. The high-pressure cylinder alone has an adjustable drop cut- off. On all the other cylinders the cut-off is fixed. The engine keelsons and frames are made of steel, strength- ened in the usual manner with angles and intercostals. The wheels are of the feathering type, 30 feet diameter outside the buckets. Each wheel has 12 curved steel buckets, each being 4 feet wide and 13 feet 3 inches long. 43. Adaptation of Structure to economical requirements is evidently one of the essential elements of successful appli- cation of the steam-engine to best advantage. As will be shown elsewhere, for every pressure and every engine there is always a certain best ratio of expansion, all things considered; and the proper number of steam-cylinders in series in the multiple-cylinder engine is fixed by the steam-pressure adopted. It thus happens that, as pressures have risen, the compound engine has displaced the simple engine, at sea, and the ** triple- expansion" engine has, at pressures exceeding about ten atmos- pheres (135 Ibs. by gauge) begun to displace the older double- cyiinder compound engine ; and even the "* quadruple-expan- 230 A MANUAL OF THE STEAM-ENGINE. sion" engine, with its four cylinders in series, has been adopted for pressures considerably exceeding the latter. The structure of these engines is essentially similar to that FIG. 122. BAILEY-FKIEDRICH MOTOR. of the older compound, the high-pressure cylinder of the latter becoming, in turn, an intermediate cylinder. These forms will be described more fully later. STRUCTURE OF THE STEAM-ENGINE. 231 In illustration of the above : The " domestic" or other small motors are often given peculiar and ingenious forms to secure automatic operat-on and relief from cost of attendance. The Friedrich Motor is a combined engine and boiler The engine is a high-expansion engine, fitted with a governor determining the amount of expansion automatically, accord- ing to the work. A surface-condenser condenses the exhaust steam, and a feed-pump returns it to the boiler. Thus the water is used over and over again, and no incrustation takes place in the boiler. It is stated that a four-horse engine of this kind requires about 135 pounds of coke in six hours. The boiler generates its steam mainly in tubes suspended in a furnace extending the full width and length of the boiler. The boiler-top consists partly of the lower part of the engine- frame, which there forms a steam-dome, with the steam-cylin- der suspended in it, and the remainder is a plate which is readily removed for access to the interior for inspection and cleaning. The furnace is fitted with a fuel-hopper or magazine, and above this is an air-valve acted upon automatically by the steam, in such a manner as to lift it and pass air over the fire whenever the generation of steam is too rapid and the pressure too high, thus regulating the consumption of the fuel according to the demand. The whole is mounted upon a base-plate, fitted below the fireplace with an ash-pan, as seen, charged with water to keep the floor cool and preserve the grate-bars. 44. Special Types of steam-engine are occasionally used experimentally and temporarily, or are permanently employed where found to be specially adapted to some peculiar purpose. Thus the single-acting engine has been found to have its own special field ; the Cornish engine was long used exclu- sively for a mine-pump ; the rotary engine finds its place, and even a steam-turbine is successfully applied to driving machin- ery in which an enormous speed of rotation is demanded. The superiority of a rotary motion for a steam-engine is ap- 232 A MANUAL OF THE STEAM-ENGINE. patently so evident that many attempts have been made to overcome the practical difficulties to which it is subject. One of these difficulties, and the principal one, has been the pack- ing of the part which performs the office of the piston in the straight cylinder. The often claimed advantages of the rotary engine are the reduction in the size of the engine, claimed to result from the great velocity of rotation ; the avoidance of great accidental strains, especially noticed in propelling ships ; and a great saving of the power which is, erroneously, asserted to be expended in the reciprocating engine in overcoming the inertia while changing the direction of the motions. These advantages, so far as they exist, adapt the rotary engine, in an especial manner, to the purposes of steam fire-engines. In the Holly steam fire-engine, seen in Fig. 125, eccentrics and sliding-cams, which are frequently used in rotary engines, are avoided. Corrugated pistons, or irregular cams, are adopted, forming chambers within the cases. In the engine the steam enters at the bottom of the case, and presses the cams apart. The only packing used is in the ends of the long metal cogs, which are ground to fit the case and are kept out by the momentum of the cams, assisted by a slight spring back of the packing-pieces. The friction on the pump, Fig. 124, is said to be less than in the engine. This is the reason given in support of the claim that the rotary engine forces water to a given distance with less steam-pressure than is necessary to drive reciprocating engines. The smaller amount of power necessary to do the work, the less strain and consequent wear and tear upon the whole machine, are said to make it durable and reliable. The pump being chambered, its liability to injury by the use of dirty or gritty water is lessened ; and it is stated that it will last for years, pumping gritty water that would soon cut out a piston-pump. This engine contains two rotating cams, each of which is also a gear having eight short teeth, arranged in pairs, with one long tooth and one deep space between. The short teeth are for the purpose of insuring that the two cams rotate STRUCTURE OF THE STEAM-EXGIXE. 233 exactly together. The long teeth are abutments for the steam, forming, as they do, steam-tight joints with the walls FIG. rrj. ROTARY E.VCT.VB. of the case in which they rotate, and with the deep spaces in which they engage. The steam entering at the bottom of the case tends to press the abutments apart and thus cause rotation of the pistons in opposite directions. The tightness of the joints of the teeth with the case is insured by packing- pieces set out by springs. The steam is discharged at the FTC. \*4. ROTAT PCMF. top of the case. The heads of the cams are turned to fit the flat ends of the case, which are provided with recesses for lubricant. 234 A MANUAL OF THE STEAM-ENGINE. STRUCTURE OF THE STEAM-ENGI\E, 235 In the construction of the pump three long teeth are introduced to each cam, and fewer guide-teeth. The water enters at the bottom of the case, and is discharged at the top. The revolution of the pump-pistons in opposite directions causes a vacuum in the case, and the water is caught by the abutments and swept out of the case. The greater number of teeth is given in order to insure greater steadiness of stream than would be given by only two long teeth upon each piston. 236 A MANUAL OF THE STEAM-ENGINE. The motion being continuous and the connections tight, the stream is unintermittent. The journals of the engine and pump run in long bearings. There are suitable stuffing-boxes to insure steam and water-tight joints for the shafts. The certainty of rotation of the cams is further insured by well- cut gear-wheels on the shafts outside the steam and water cases. The steam-cams are given greater diameter than those for the water, to permit a greater water-pressure to be maintained ; the steadiness of this water-pressure is further insured by an air-chamber. Engines of this class have now been in use many years. A singular device, but one found effective for very low lifts, is illustrated in Fig. 126, as built by Allis for the city of Chicago, 111. A vertical engine of economical type, and designed for a somewhat high speed of rotation, is connected to the shaft of a screw-propeller of suitable dimensions and proportions, but differing from the marine screw in the greater area of its blades. This raises water from a low level on the one side to a higher level on the other with satisfactory economy. FIG. 127. THE " AUTOMATIC An interesting modification of the Corliss principle in the adaptation of the " automatic" system of shaft-governor regu- lation is illustrated in the accompanying engraving. In this arrangement, the Payne engine, the advantages of the pecul- iar kinematic movement of Corliss and of his form of valve, STXUCTUZM OF THE STEAM-ENGINE. 2tf are combined in the positive-motion system of gearing essen- tial to the * high-speed *" engine. As in some other engines, the steam- and exhaust-valves are here in the same shell, and the small clearance of this form of engine, the peculiar movement of the valves, and the exact regulation of the shaft-governor, and the high-speed system, are combined in a very compact machine. The illustration herewith given represents a compound en- gine with automatic expansion-gear as designed by Fowler & Co. of Leeds, G. R, for stationary purposes. The use of rope-transmission, now in extensive use, is here exhibited, the fly-wheel being suitably grooved to carry it. The cut-off mechanism is adjusted by the governor seen on the horizontal shaft above the high-pressure steam-chest. The cut shows weH, also, the various important accessories of the engine : its pass-over steam-pipe, relief-valves, indicator-motion, and sys- tem of lubrication, as well as the general features of a carefully considered design. The Slfam-htrbiMf constitutes a class of steam-engine which, although the first invented and familiar, as a type, to all engineers from the days of Hero the Younger, and known to have a high theoretical and moderately high actual effi- 238 A MANUAL OF THE STEAM-ENGINE. ciency, has been only experimentally used until a very recent date. That of Hero has been illustrated in Fig. I. The Atwater engine of about 1840 was of this type, and was said to be as economical as the engines of the time of equal power. Steam-turbines of the inward-flow type have been used by Gorman and others.* The later " compound " steam-turbine has recently been somewhat extensively employed in the operation of dynamo- electric machinery. It consists of two sets of parallel-flow tur- bines set, in twin series, on one shaft on either side the induc- tion-pipe, thus balancing. The passages are gradually enlarged as the volume of the steam increases with its progressive ex- pansion. The turbines thus alternate with their guide-blades, and both the vanes and the blades are carefully proportioned and set to secure maximum attainable efficiency at the proposed speed of rotation, their pitches and depths being suitably varied. The computed efficiency, without allowances for wastes, is about 87 per cent. The actual consumption of steam is found to be 35 to 40 pounds per electrical horse-power pro- duced, and per hour as steam-pressures rise from 60 to 90 pounds by gauge. The speed of rotation ranges from 5000 or 10,000 revolutions per minute upward, according to size and steam-pressure; 1 8,000 and 20,000 being common speeds for the smaller sizes. Dow's turbine is an inward-flow wheel with concentric sets of guides and vanes in series, and is said to have attained 35,000 revolutions per minute, working regularly at 25,000, consuming 55 pounds of steam per horse-power per hour. Only the most perfect construction is here admissible. The theory of this type of machine is that familiar to the hydraulic engineer, and the speeds of orifice for maximum effi- ciency are well known to be infinite in the Hero class of tur- bine and approximately one half the final velocity of flow in * Rankine, p. 538. STRUCTURE OF THE STEAM-EXCISE. 239 the guide-blade turbine. Since these speeds are impracticable in their use, a certain loss of energy is thus inevitable. In compensation for this loss, in the steam-turbine, is the fact that it is* not subject to that fluctuation of temperature of parts exposed to contact with the steam which results in large wastes by cylinder-condensation in the common forms of steam-engine. A gain of from 25 to 50 per cent, as compared with the latter, in this way, is to be counted upon. The Dow turbine, as built for work, in connection with the Howell torpedo, gives an average of about 1 1 horse-power in coming up to speed in regular working, at 60 pounds steam- pressure, and weighs from loo to 1 50 pounds, or not far from 13 pounds per horse-power.* Its fly-wheel rim attains a speed of nearly 7 miles an hour at 10,000 revolutions per minute. The designer estimates its power at 150 pounds steam-pres- sure and the same speed at 40 horse-power, or one horse-power to 3.75 pounds weight, and states that this may be still further reduced to the extraordinary minimum of 2\ pounds weight per horse-power, a figure well within the estimated allowable maximum for use in aeronautic work. The steam-turbine of Parsons, Fig. 129, is an engine con- sisting of a series of turbines, the different pairs of guides and wheels being so placed that the fluid passes successively from one pair to the next. Of the two forms, radial and axial flow, only the latter have been used here. Two series of cylindrical turbines are used, arranged symmetrically to the right and left of the central steam-inlet, the exhaust taking place from the two ends. In this manner a balance is obtained, and the bear- ings are relieved of end-pressure. Oil is forced through the bearings by a pump. The bearings are thus forcibly deluged with oil, which returns to a reservoir. The governor is a suc- tion fan mounted upon the spindle and connected with a dia- phragm, which operates the throttle-valve against the power of a spring. Its action is found to be rapid and certain. Such engines have been successfully employed in driving Electrical World; April 18, 1891. 240 A MANUAL OF THE STEAM-ENGINE. electric machinery and in "spinning" the "fly" of the Howell torpedo. For alternating electric currents, this system pos- sesses the peculiar advantage of permitting a " dynamo" to be employed having but two poles. It. may be readily driven continuously at speeds exceeding 10,000 revolutions per minute, STRUCTURE OF THE STEAM-EXGISCE. 2.: and, like the Dow turbine, elsewhere icfeiied to, has been driven at 20^000 and upward. With the lower speeds of revo- lution usual with ordinary engines, the number off poles required generally approximates the quotient IZJOQO divided by tine speed off engine, if directly connected. The best off these machines have demanded from 35 pounds of steam per horse-power per hour,, upward, according to pres- sure employed. It may be assumed that they wiH require not for from the weight where/, Iks between 50 and aoo pounds per square inch by gauge, and the appaiatus is operated under favorable condi- tions ; the value of * tying between 350 and 400 with dry steam. In the United States, the substitution of the Dow turbine for the sy interns previously in use, for torpedoes, has brought down die weight and volume of marliinMy from the earlier mhmnnm of 560 pounds and three cubic feet per "^*"* to 75 pounds and one cubic foot. ^Exfcwimtfrntal Emgimts or steam-engines designed es- pecialy for purposes of instruction and research, are now fre- quently UHisli lifted, and especially in equipping European schools. Such engines arc illustrated in the frontispiece of this volume, as buffi: for Owens College, Manchester, G. B. :* while other forms designed by American engineers and as con- structed for Sibfiey College, Cornell University, and for the Massachusetts Institute of Technology, will be represented in a later chapter (VoL II.) on Engine Trials. In the design of such engines, the problem is ordinarily to make aH adjustments cover a wide range ; in order that the laws affecting variation of pressures, temperatures, speeds, steam-distribution, as determinimig efficiency, may be SUims- trated ; as wefl as to secure a means of investigating problems still unsolved and of checking results previously obtained but 7--.; -.-.?: r- -:--- . := --:!-: . J I 242 A MANUAL OF THE STEAM-ENGINE. requiring confirmation. The engine illustrated consists of a triple-expansion combination so arranged that each element may be worked and tested independently, if desired, as well as either compounded or triple-expansion. The type adopted is that familiar in marine engineering, with inverted cylinders, jacketed on sides and ends, and each jacket separately piped to permit its action to be ascertained. The working-pressure is 200 pounds as a maximum ; the piston-speed may attain 1000 feet per minute; the Meyer ex- pansion-valves give a range of expansion from r = 1.5 to r = oo. The cylinders are 5, 8, and 12 inches diameter, 10, 10, and 15 inches stroke. The engine can be worked either condensing or non-condensing. This engine was designed under the supervision of Professor Reynolds and built by Messrs. Mather & Platt. A surface-condenser is used containing 160 square feet sur- face, and is served by an air-pump, driven by the largest engine, 9 inches diameter and 4^ inches stroke. Hydraulic brakes are employed, which are simply adaptations of the centrifugal pump. On trial the engine worked admirably and economically, demanding but 1.33 pounds of fuel per horse-power per hour; the efficiency being 0.20 at 200 pounds pressure. The efficiency of machine was about 0.80. The performance of the engine, in all respects, is reported to be eminently satisfactory. (See 128, Chap. V.) CHAPTER IIL THE .PHILOSOPHY OF THE STEAM-ENGINE. 45. The Scope of the Philosophy of the Ste^ m -engine, and a complete history of the development of the Theory o f the Steam-engine, would include, first, the history of the Mechanical Theory of Heat; secondly, the history of the Science of Thermodynamics, which has been the outgrowth of that theory ; third, the history of the application of the Science of Heat-transformation to the case of the Steam-engine ; and, fourthly, an account of the completion of the Theory of the Steam- and other Heat-engines by the introduction of the theory of losses by the more or less avoidable forms of waste, as distinguished from those necessary and unavoidable wastes indicated by the pure theory of thermodynamics. The first and second of these divisions are treated of in works on thermo- dynamics and in treatises on physics. The third division is briefly considered, and usually very incompletely, in treatises on the steam-engine ; while the last is of too recent develop- ment to be the subject of complete treatment, as yet, in any existing works. Our principal object is, here, simply to collect into a condensed form, and in proper relations, these several branches of the subject, leaving for an appropriate time and place that more full and complete account which might now. for the first time in history, be prepared. 46. The Nature of the Processes observed in the opera- tion of the steam-engine are such as wfll illustrate many of the most important principles and facts which constitute the physi- cal sciences, The steam-engine is an exceedingly ingenious hot very imperfect machine for transforming the heat-energy 244 A MANUAL OF THE STEAM-ENGINE. obtained by the chemical combination of a combustible with the supporter of combustion into mechanical energy. The original source of this energy is found far back of its first ap- pearance in the steam-boiler. It had its origin at the begin- ning. When the solar system had been formed from the nebu- lous chaos of creation, the glowing mass which is now called the sun was the depository of a vast store of heat-energy, which was thence radiated into space and showered upon the attend- ant worlds in inconceivable quantity and with unmeasured in- tensity. During the past life of the globe, the heat-energy received from the sun was partly expended in the production of forests and the storage of an immense quantity of carbon, which had previously existed in the atmosphere, combined with oxygen, as carbonic acid. The geological changes which buried these forests resulted in the formation of coal-beds and the storage of a vast amount of carbon, of which the affinity for oxygen remained unsatisfied until finally uncovered by man. Thus we owe to the heat and light of the sun, as was pointed out by George Stephenson, the incalculable store of energy upon which the human race is dependent for life. This coal, thrown upon the grate in the steam-boiler, takes fire, and, uniting again with the oxygen, sets free heat in pre- cisely the same quantity that it was received from the sun and appropriated during the growth of the tree. The actual energy thus rendered available is transferred, by conduction and radi- ation, to the water in the steam-boiler, converts that water into steam; and its mechanical effect is seen in the expansion of the liquid into vapor against superincumbent pressure. Trans- ferred from the boiler to the engine, the steam is there per- mitted to expand, doing work, and the heat-energy with which it is charged becomes partly converted into mechanical energy, and is applied to useful work. Thus we may trace the store of energy received from the sun and contained in our coal through its several changes until it is finally set at work; and we might go still farther and ob- serve how, in each case, it is again usually re-transformed and again set free as heat-energy. THE PHILOSOPHY OF THE STEAAI-EXGIXE. 24$ 47. The Nature, Sources, and Transformations of En- ergy in these several processes are thus easily traced. The transformation which takes place in the furnace is a chemical change ; the transfer of heat to the water and the subsequent phenomena accompanying its passage through the engine are physical changes, some of which require for their investigation abstruse mathematical operations. A thorough comprehension of the principles governing the operation of the steam-engine, therefore, can only be attained after studying the phenomena of physical science with sufficient minuteness and accuracy to be able to express with precision the laws of which those sciences are constituted. The study of the philosophy of the steam-engine involves the study of Chemistry and Physics, and of the science of Energetics, of which the science of Thermodynamics is a branch. This sketch may, therefore, include an outline of the growth of the several sciences which together make up its philosophy, and especially of the science of thermodynamics, which is peculiarly the science of the heat-engines.* 48. The Chemical Principles involved in the action of all the steam-engines are those illustrated in the combustion of the fuels. All essential elements of this part of the philos- ophy of heat-engines are now at least approximately know r n, and it is perfectly possible for the engineer, knowing the composition and physical structure of his fuel, to compute very exactly the quantity of heat-energy stored in its mass and the amount probably to be realized in the furnace in which it is consumed and stored in the working-fluid to be sent forward into his engine. In all cases, he is supplied, as fuel, with a certain known composition of carbon, hydrogen, and their compounds, unim- portant proportions of other combustible elements, as sulphur, and a quantity of incombustible mineral matter, forming, finally, ash and clinker, or cinders. The union of these com- * For a somewhat detailed account of the early and mediaeval progress of the sciences, see the " History of ihe Steam-engine," by the Author, chapter vii : International Series ; New York, D. Appleton & Co. 246 A MANUAL OF THE STEAM-ENGINE. bustible elements and compounds with the oxygen of the air produces a definite and easily calculable amount of heat-energy, of which a part, equally easy of computation when the extent, nature, location, and arrangement of the absorbing, or " heat- ing," surfaces are known, is taken up for useful purposes ; while the rest is sent up-chimney or otherwise wasted. The physical, as well as the chemical, character of the fuels and the greater or less completeness of their combustion and the consequent character of the discharged furnace-gases aids in determining the final result and the total efficiency of the system. 49. The Physical Principles involved in the storage, transfer, and utilization of heat in the steam-engine are those which relate to the transfer, storage, and re-transfer of heat- energy in the passage of that energy from the furnace-gases to the boiler, its storage in the water and steam, and its transfer to the engine, with continuous loss and waste, until finally, a part being transformed into mechanical energy and more or less usefully applied, the remainder is finally discharged from the engine and entirely lost and wasted, as a source of power. Conduction, radiation, convection of heat, and heat conversion into other kinds of energy, are the physical phe- nomena involved in these operations. In some cases these processes are somewhat obscure and remained for many years but little understood. This is especially the fact with respect to those operations which go on within the engine cylinder in the course of the cycle there performed and which involve the introduction of the steam and its temporary storage into a cooler space in which it is partly condensed by surrender of heat to the enclosing walls ; the gradual reduction of temperature and pressure of the steam with increasing expansion of volume, and with restora- tion of that heat, in part, to the fluid, and finally the discharge of the steam from the cylinder at a still further reduced tem- perature, with complete restoration of the heat previously stored in the walls of that vessel. The application of the principles of physics to this series of changes is quite as essemial to a complete theory of the real heat-engine as is that THE PHILOSOPHY OF THE STEAM-EXGINE. 247 of the principles of thermodynamics to the processes of trans- formation of energy. 50. The Mechanical Principles which are included in a complete theory of the action of the heat-engines will be illustrated in the chapters on the design of the various parts of the engine. It is sufficient here to present a general outline of the modern science. The science of mechanics is of comparatively recent date, and with the publication of Newton's Principia became thor- oughly consistent and logically complete, so far as was possible without a knowledge of the modern principles of energetics, Newton's enunciations of the laws of motion were the basis of the whole science of dynamics, as applied to bodies moving freely under the action of applied forces, either constant or variable. They are as perfect a basis for that science as are the primary principles of geometry for the whole beautiful structure which is built up on them. The three perfect qualitative expressions of dynamical law are : 1. Every free body continues in the state in which it may be, whether of rest or of rectilinear uniform motion, until com- pelled to deviate from that state by impressed forces. 2. Change of motion is proportional to the force impressed, and in the direction of the right line in which that force acts. 3. Action is always opposed by reaction ; action and reac- tion are equal, and in directly contrary directions. We may add to these principles a definition of a force, which is equally and absolutely complete : Force is that which produces, or tends to produce, motion, or change of motion, in bodies. It is measured statically by the weight that will counterpoise it, or by the pressure which it will produce, and dynamically by the velocity which it wiP produce, acting in the unit of time on the unit of mass. The quantitative determinations of dynamic effects o forces are always readily made when it is remembered that the effect of a force equal to its own weight, when the body is free to move, is to produce in one second a velocity of 32.2 248 A MANUAL OF THE STEAM-ENGINE. feet per second, which quantity is the unit of dynamic meas- urement. Work is the product of the resistance met in any instance of the exertion of a force, into the distance through which that force overcomes the resistance. Energy is the work which a body is capable of doing, by its weight or inertia, under given conditions. The energy of a falling body, or of a flying shot, is about ^ its weight mul- tiplied by the square of its velocity, or. which is the same thing, the product of its weight into the height of fall or height due its velocity. These principles and definitions, with the long-settled definitions of the primary ideas of space and time, were all that were needed to lead the way to that grand- est of all physical generalizations, the doctrine of the persist- ence or conservation of all energy, and to its corollary declar- ing the equivalence of all forms of energy, and also to the experimental demonstration of the transformability of energy from one mode of existence to another, and its universal ex- istence in the various modes of motion of bodies and of their molecules. Experimental physical science had hardly become acknowl- edged as the only and the proper method of acquiring knowl- edge of natural phenomena at the time of Newton ; but this soon became a generally accepted principle. In physics, Gil- bert had made valuable investigations before Newton, and Galileo's experiments at Pisa had been examples of similarly useful research. In chemistry, it was only when, a century later, Lavoisier showed by his splendid example what could be done by the skilful and intelligent use of quantitative meas- urements, and made the balance the chemist's most important tool, that a science was formed comprehending all the facts and laws of chemical change and molecular combination. We can now see how, in all the physical sciences, four primitive ideas are comprehended : matter, force, motion, and space which latter two terms include all relations of position. These are the fundamental ideas of mechanics. Based on these notions, the science of mechanics compre- THE PHILOSOPHY OF THE STEAM-ENGINE. 249 bends four sections, which are of general application in the study of all physical phenomena. These are : Statics, which treats of the action and effect of forces only. Kinematics, which treats of relations of motion simply. Dynamics, or kinetics, which treats of simple motion as an effect of the action of forces. Energetics, which treats of modifications of energy under the action of forces, and of its transformation from one mode of manifestation to another, and from one body to another. 51. Energetics and Thermodynamics are the broader and the narrower codes of similar law. Under the latter of the four divisions of mechanical philosophy is comprehended that latest of the minor sciences, of which the heat-engines, and especially the steam-engine, illustrate the most important applications Thermodynamics. This science is simply a wider generalization of principles which have been established one at a time, and by philosophers widely separated both geo- graphically and historically, by both space and time, and which have been slowly aggregated to form one after another of the sciences, and out of which we are gradually evolving wider generalizations, and thus tending toward a condition of scientific knowledge which renders more and more probable the truth of Cicero's declaration : " One eternal and immu- table law embraces all things and all times." At the basis of the whole science of Energetics lies a principle which was enunciated before Science had a birthplace or a name : All that exists, whether matter or force, and in whatever form, is indestructible, except by the Infinite Power which has reated it. That matter is indestructible by finite power became ad- nitted -as soon as the chemists, led by their great teacher Lavoisier, began to apply the balance, and were thus able to show that in all chemical change there occurs only a modifica- tion of form or of combination of elements, and no loss of matter ever takes place. The " persistence " of energy was a later discovery, consequent largely upon the experimental de- termination of the convertibility of heat-energy into other 25O A MANUAL OF THE STEAM-ENGINE, forms and into mechanical work, for which we are indebted to Rumford and Davy, and to the determination of the quantiva- lence anticipated by Newton, shown and calculated approxi- mately by Colding and Mayer, and measured with great prob- able accuracy by Joule and Rowland. 52. The Ideal and the Real Engine must be clearly dis- tinguished in all that follows. The ideal engine of the earlier method is one in which only thermodynamic processes occur. Only transfer of heat from point to point in its cycle of opera- tions, and the conversion of thermal into mechanical energy or the reverse, are assumed as possible ; and the problem studied is that of determining what, under certain specified conditions, is the efficiency of the engine, the proportion o' net work per- formed to gross energy demanded for its accomplishment. Such an engine must be constructed of materials without per- meability to heat, without conducting or heat-storing capacity, absolutely free from friction, and incapable of yielding to im- pressed forces. It is a purely ideal case. The real engine, on the other hand, must be composed of such materials as are available to the engineer. They must have strength, stiffness, toughness, and endurance under load and wear, and must be capable of being given the desired shape and proportions at the least possible expense. Only iron and steel, copper and the familiar alloys meet these requirements ; and, practically, all engines are composed of these substances, and all have their working cylinders made of cast-iron, a sub- stance of high conducting and storing power for heat. These facts make an enormous difference in the behavior of the en- gine both as respects its utilization of heat and its useful application of the energy produced within its working cylinder by heat-transformation. Large quantities of heat are neces- sarily wasted, in the manner already indicated above, when discussing the physical principles involved in the action of the engine ; and a considerable fraction of the power exerted by the steam on the piston of the engine is, in the actual case, lost in the friction of its own journals. Thus the real case must be carefully distinguished from the THE PHILOSOPHY OF THE STEAJI-EXGIXE. 2$l ideal, and the pure thermodynamic theory of the latter consti- tutes bat one element of the theory of the former. 53. The Scientific Problem which confronts the student of the theory of the steam-engine, as a practical case, is thus seen to be the determination of the quantity of heat-energy stored in a given fuel ; the proportion which may be reasonably expected to be developed by its combustion; the amount which should be taken up and stored for useful application in a steam-generator, and the balance wasted at the chimney and elsewhere ; of that which may be taken to the engine through a steam-pipe of known size and condition, of that which will be probably wasted by conduction and radiation, en route, or at the engine and within its cylinder; and finally, the quantity which will be converted into work and, of this, the proportion that will be capable of useful application. The determination of the latter quantity is the measure- ment of a balance after all wastes are deducted ; and the effi- ciency sought is the ratio of this quantity to the mechanical equivalent of all heat-energy supplied to the engine, or to that produced at the furnace, as the case may demand. In detail, therefore, the problem to be solved includes the application of known chemical, physical, and mechanical princi- ples to the determination, one by one, of all these quantities of energy, step by step, from the furnace to the driving-shaft of the engine, and the summation, at each step, of such quanti- ties received or paid out in such manner that a final balance- sheet may be constructed exhibiting every item on both sides the account, and permitting the answering of any question that may arise respecting the receipt and expenditure of energy and mechanical power. 54. An Outline of the Progress of Science in the develop- ment of the philosophy of the steam-engine may be appropri- ately here briefly given. It properly begins with the history of the older philosophies ; but its useful elements, and its actual applications, only date back to a very recent period. As will be seen, the physical sciences have all had an exceedingly slow growth until within the last two or three centuries. The abso- 252 A MANUAL OF THE STEAM-ENGINE. lute impossibility of their promotion except through continu- ous experimentation, and the inability of mankind to construct the apparatus of research until modern times, would have caused this late development of sciences of this class, even had the true scientific spirit existed and the scientific method been known earlier. The physical sciences have, since the beginning of the seven- teenth century, had independent and uninterrupted growth ; but it has been irregular, spasmodic, and unsymmetrical. The science of applied mechanics, as distinguished from its purely mathematical branches, had its origin with Galileo in the first and Newton in the second half of that century ; chemistry may be said to have become a science under the hand of Lavoisier at the close of the eighteenth century ; physics had a longer period of incubation, from the days of Gilbert, and energetics and its minor branch, thermodynamics, have only been con- ceived and organized into sciences in the nineteenth century. Throughout this whole period of modern scientific work, the patient student and careful observer will see that these various sciences, now seemingly independent, are becoming established in closer and closer relations, and are gradually coming to illustrate continually more and more clearly their unquestionable mutual interdependence. All phenomena of motion and change of molecular relation, whether in physics, chemistry, or mechanical action, are subject to the laws of mechanics and of energetics, and a common science must probably sooner or later come to comprehend all. In what follows the development of the science of thermo- dynamics and the gradual construction of the philosophy of the heat-engines only will be considered.* The student is, how ever, advised to study carefully and in a philosophical manner the development of all, and especially in their mutual relations, and in their bearing upon the science of energy, as mechanical and as molecular, and as a science of energy-transformations. * For a more detailed account see the encyclopaedias, or consult the Author's " History of the Steam-engine," chapters vii, vui. THE PHILOSOPHY OF THE STEAM-ENGINE. 253 55. The Origin of the "Mechanical Theory of Heat," as is now well understood, dates, as a speculation, from the days of the earliest philosophies. The contest which raged with such intensity, and sometimes acrimony, among speculative men of science, during the last century, was merely a repetition of struggles of which we find evidences, at intervals, through- out the whole period of recorded history.* The closing period of this, which proved to be an important revolution in science, marked the beginning of the nineteenth century. It was in- augurated by the introduction of experimental investigation directed toward the crucial point of the question at issue. It terminated, about the middle of the century, with the accept- ance of the general results of such experiment by every scien- tific man of acknowledged standing, on either side the Atlantic. The doctrine that heat was material, and its transfer a real movement of substance from the source to the receiver of heat, was thus finally completely superseded by the theory, now be- come an ascertained truth, that heat is a form of energy, and its transformation a change in the location and method of molecular vibration. The Dynamical Theory of Heat was first given a solid basis by the experiments of Count Rumford (Benjamin Thompson), in 1/96-7 of which an account was given in a paper read by Rumford before the Royal Society of Great Britain in 1798, by the experiments of Sir Humphry Davy in 1798-9, and by the later and more precise determina- tions of the value of the mechanical equivalent of heat by Joule and others. James Prescott Joule, as early as 1843, obtained a series of results varying in quantity from 587 to 1026, from which he deduced an equivalent of 770 foot-pounds by the friction of water in small pipes. In the following year Mr. Joule gave a 'mean value of 802 foot-pounds. In 1845 he found 890 as the * The main portion of what follows relating to this subject is abstracted from a paper read by the Author before the British Association for Advancement of Science. Montreal meeting, 1884. For the full paper see Trans. B. A. A. S., 1884" On the Theory of the Steam-engine;" also "The Development of the Philosophy of the Steam-engine;" R. H. Thurston; N. Y., 1889. 254 A MANUAL OF THE STEAM-ENGINE value of the equivalent. Two years later he obtained 781.5 and 782.1 respectively; the mean of which is 781.8. He, in 1849, undertook a final determination of the equivalent, and carried out a series of forty experiments on the friction of water, fifty on the friction of mercury, and twenty on the fric- tion of cast-iron plates, from which he deduced the value, 772 foot-pounds, which was accepted for a generation. His later determination, made for the British Association, 1876, was 774.1, with a possible error of small amount. Still later deter- minations indicate a higher value. Julius Robert Mayer was engaged, at the same time, upon investigations of equal importance, carried on in an entirely different manner. In 1840, a physician on the island of Java, he noticed that the venous blood of his patients was unusually red. He concluded that it was owing to the fact that a less amount of oxidation of the tissues of the body would keep up the bodily heat in a hot country than would be required in a colder one. Following up this thought, he came to the con- clusion that a fixed relation must exist between heat and work. In 1842 he made the attempt to determine this relation numeri- cally. Professor Tyndall thus describes his reasoning : " It was known that a definite amount of air, in rising one degree in temperature, can take up two different amounts of heat. If its volume be kept constant, it takes up one amount ; if its pres- sure be kept constant, it takes up a different amount. These two amounts are called the specific heats under constant vol- ume and under constant pressure. The ratio of the first to the second is as I : 1.421." Dr. Mayer "first saw that the excess .421 was not, as then universally supposed, heat actually lodged in the gas, but heat which had been actually consumed by the gas in expanding against pressure. The amount of work here performed was accurately known ; the amount of heat con- sumed was also accurately known ; and from these data Mayer determined the mechanical equivalent of heat. Even in this first paper he is able to direct attention to the enormous dis- crepancy between the theoretic power of the fuel consumed in steam-engines and their useful effect." "As regards the mechani- THE PHILOSOPHY OF THE STEAM-EXG1XE. 2$$ cal theory of heat, this obscure Heilbronn physician, in the year 1842, was in advance of all the scientific men of the time." In a paper read before the Royal Society in 1878, Joule stated that, taking the unit of heat as that which can raise a pound of water (weighed in a vacuum) from 60 to 61 F. on the mercurial thermometer, its mechanical equivalent, reduced to the sea-level and to the latitude of Greenwich, is 7/2.55 foot- pounds. Favre deduced 753 from the friction of steel on steel, and 807 from the heat absorbed by an electromagnetic engine for the production of work. Him deduced 787 from the fric- tion of liquids, and 775 from the compression of lead. Quintus Icilius deduced 714^ from the heat developed in an electric cir- cuit. By comparing the work expended in revolving the plate of a Holtz electrical machine with the heat produced by the resulting current, Rosetti deduced 776.1 foot-pounds. Le Roux, from the heat produced by rotating a tube full of water in a magnetic field, found 835. Violle, by similar experiments on disks of metal in the place of water, found 793.2 with copper, 794.3 with tin, 797.3 wjth lead, and 792.7 with aluminium. Bartoli deduced 771.12 from the friction of mercury in small tubes. By a careful study of the velocity of sound in gases, Regnault re-determined the ratio of the two specific heats of gases used by Mayer in his first calculation. Regnault's result was 1.3945, instead of 1.421 ; and from this and other data Mayer's calculation, repeated, gave 794.8. Prof. Henry A. Rowland finally made a determination of the equivalent, and his investigations involved many difficult problems in thermometry. He found that the specific heat of water is greater near the freezing-point than at and near 8o c . Rowland's result gives the mechanical equivalent of heat as 778 foot-pounds at 39.2 F., the temperature being measured by a mercurial thermometer, and 783 foot pounds if by an air- thermometer. The value of the mechanical equivalent of heat is thus, very possibly, 778 ft.-lbs. per B. T. U. ; 426.8 kilogrammetres per calorie ; 256 A MANUAL OF THE STEAM-ENGINE. and is considered probably correct to within 0.003 of its own value ; i.e., it may be as low as 776 or as high as 780. 56. The Science of Thermodynamics has for its essential basis the established fact of the dynamical nature of heat, and the fact of the quantivalence of two forms of energy heat and mechanical motion, molecular energy and mass energy. Rest- ing, as it does, on fundamental, experimentally determined, principles, it could have no existence until, during the early part of the present century, these phenomena and these truths were well investigated and firmly established. The first period of the development of the science was occupied almost exclusively by the exposition of the dynamical theory of heat, which lies at the bottom of the whole. Mohr, in 1837; Seguin, in 1839; Mayer, of Heilbronn, in 1842; and Colding, in 1843, ea ch took a step into a field, the limits of which and the importance of which they could at that time hardly have imagined. Mayer had a very clear conception of the bearing of the new theory of heat upon dynamics, and ex- hibited remarkable insight into the far-reaching principles of the new science. He collated the facts more exactly deter- mined later by Joule and others with the principle of the con- servation 01 energy, and applied the rudiments of a science thus constructed to the calculation of the quantity of carbon and expenditure of heat which are unavoidably needed by a mountain-climber, doing a given quantity of work, in the ele- vation of his own body to a specified height. The work of Mayer may be taken as representing the first step in the pro- duction of a Science of Thermodynamics, and in the deduction of consequences of the fact which had, until his time, so seldom engaged the attention of men of science. It was only at about the middle of the nineteenth century that it began to be plainly seen that there existed such a science, and that the dynamic equivalence of heat, and energy in the mechanical form, was but a single fact, which must be taken in connection with the general principles of the persistence of energy, and applied in all cases of performance of work by expenditure of heat through the action of elastic bodies. TOE PHILOSOPHY OF THE STEAJf-EXCIA'E. 257 In 1850, Qausius* adapted Garnet's anvesttigatloims as the correct theory of thermodynamics, to accord with the laws off Modern thermodynamics. Qausius* then stated Caroot's principle as follows : * Whenever heat is converted Into work, amathfr qmamtilj of heat must, during the working cycle, be transferred from a hotter body to a colder body ; the amount transferred depends only on the temperatures between which the transfer Is effected, and not on the nature of the body acting as Its ve- This is Carnot's principle, and a direct consequence of the second law of thermodynamics. 57. The Theory of the Steam-engine, like every other scientific system, rests upon a foundation of facts ascertained by experiment, and of principles determined by the careful study of the laws relating to those facts, and controlling phe- ' mm in properly classed together by that science. Like every other element entering into the composition of a scientific system, this theory has been developed subsequently to the establishment of its fundamental facts, and the history of progress in the art to which it relates shows that the art has led the science from the first. The theory of the steam-engine includes all the phenomena and all the principles involved in the production of power, by means of the steam-engine, from the heat-energy derived from the chemical combination of a combustible with the oxygen of the air acting as a supporter of the combustion. The remaining portion of this chapter will be devoted to the tracing of the growth of the theory of the steam-engine, simply as a mechanical instrument for transformation of the one form of energy into the other of the molecular energy of heat-motion, as stored In the vapor of water, into mass-energy, or mechanical energy, as applied to the driving of mechanism. The theory thus limited Includes a study of the thermodynamic phenomena, as the principal 2$8 A MANUAL OF THE STEAM-ENGINE. and essential operations involved in the performance of work by the engine ; it further includes the consideration of the other physical processes which attend this main function of the engine, and which, inevitably and unavoidably, so far as is to-day known, concur in the production of a waste of energy. Of all the heat sent forward by the steam-boiler to the engine, a certain part, definite in amount and easily computed when the power developed is known, is expended by transfor- mation into mechanical energy; another part, equally definite and easily calculated, also, is expended as the necessarily occur- ring waste which must take place in all such transformations, at usual temperatures of reception and rejection of heat ; still another portion is lost by conduction and radiation to surround- ing bodies ; and, finally, a part, often very large in comparison with even the first and principal of these quantities, is wasted by transfer, within the engine, from the induction to the educ- tion side, " from steam to exhaust," by a singular and interest- ing process, without conversion into useful effect, and by the familiar processes of transfer. The science of thermodynamics only takes cognizance of the first and second, which are some- times among the smallest, of these expenditures. The science of the general physics of heat takes cognizance of the others and enables us to approximately compute their magnitude. The Science of the Steam-engine must, like every other branch of applied science, be considered as the result of two distinct processes of development : the one is what may be called the experimental development of the subject ; the other is the purely theoretical progress of the science. So far as the useful application of correct principles to the improve- ment of the machine is concerned, the latter has always, as is usually the case elsewhere, been in advance of the former in its deduction of general principles ; while, as invariably, the former has kept far in advance, in the working out of practically use- ful results, and in the determination of the exact facts where questions of economic importance have arisen. 58. Carnot's Work lies at the foundation of the science of the steam-engine, and its exposition may be found in his THE PHILOSOPHY OF THE STEAM-ENGIXE. 259 "Reflexions sur la Puissanct Metric* du Feu"* He assumed the truth of the theory of substantial caloric ; nevertheless, in his development of the theory of heat-engines, he enunciated some essential principles, and thus laid the foundation for a theory of the steam-engine which was given correct form, in all its details, as soon as the dynamical theory was taken for its foundation-principle. Carnot asserts that " the motive power of heat is independent of the means taken to develop it ; its amount is determined, simply, by the temperature of the bodies between which the heat is transferred. Wherever there exists a difference of temperature, there may be a development of power. The maximum amount of power obtainable by the use of steam is the maximum obtainable by any means whatever. High-pres- sure engines derive their advantage over low-pressure engines simply from their power of making useful a greater range of temperature." He made use of the device known as the " Carnot Cycle," exhibiting the successive expansions and com- pressions of the working fluid in heat-engines, in the process of change of volume and temperature, while following the series of changes which gives the means of transformation of heat into power with final restoration of the fluid to its initial con- dition, showing that such a complete cycle must be traversed in order to determine what proportion of the heat-energy avail- able can be utilized by conversion into mechanical energy. This is one of the most essential of all the principles compre- hended in the modern science. This " Carnot Cycle " was, afterward, represented graphically by Clapeyron. Carnot shows that the maximum possible efficiency of fluid is attained, in heat-engines, by expanding the working fluid from the maximum attainable temperature and pressure down to the minimum temperature and pressure that can be per- manently maintained on the side of condensation or rejection, i.e., if we assume expansion according to the hyperbolic law, * Reflexions sur la Puissance Motrice da Feu; Paris, 1824; repnbiisbed by Gamhier-Villars: Paris, 1878. See, also, the Author's edition: " Reflections on the Motive Power of Heat, bj N.-L-Sadi Carno*;" with notes; X. Y., J. Wiley A: Sons. 260 A MANUAL OF THE STEAM-ENGINE. by adopting, as the ratio of expansion, the quotient of maxi- mum pressure divided by back pressure. He further shows that the expansion, to give maximum efficiency, should be per- fectly " adiabatic." * He even suggests that the adiabatic ex- pansion of steam may result in its own condensation, a fact a generation later discovered and proven by Rankine and Clau- sius. These principles have been recognized as correct by all authorities, from the time of Carnot to the present day, and have been, not infrequently, brought forward as new by minor later writers unfamiliar with the literature of the subject. In- troducing into the work of Carnot the dynamical relation of heat and work, a relation, as shown by other writings, well understood, if not advocated publicly by him, the theory of the steam-engine becomes well defined and substantially accurate. The Count de Pambour, writing in 1835, and later, takes up the problem of maximum efficiency of the steam-engine, shows the distinction to be drawn between the efficiency of fluid and efficiency of machine, and determines the value of the ratio of expansion for maximum efficiency of engine. He makes this ratio equal to the quotient of maximum initial pressure divided by the sum of the useless internal resistances of the engine, including back pressure and friction, and reduced to equivalent pressure per unit of area of piston. This result has been gen- erally accepted, although sometimes questioned, and has been demonstrated anew, in apparent ignorance of the fact of its prior publication by De Pambour, by more than one later writer. De Pambour, applying his methods to the locomotive, particularly, solved the problem, since distinctively known by his name : Given the quantity of steam furnished by the boiler in the unit of time, and the measure of resistance to the mo- tion of the engine ; to determine the speed attainable. Pro- fessor Thomas Tate, writing his " Mechanical Philosophy," in '853' gives the principle stated above a broader enunciation, thus : " The pressure of the steam, at the end of the stroke, is equal to the sum of the resistances of the unloaded engine, * For definition of this and related terms, see chapter on the Thermody- namics of the - Jam-engine. THE PHILOSOPHY OF T3E STEAM-EA"GI.\E. 26l whatever may be the law expressing the relation of volume and pressure of steam." The development of the Science of Thermodynamics into available and satisfactory form was effected mainly by Pro- fessors Rankine and Clausius, working independently but con- temporaneously from 1849. Combes, in papers presented to and published by the Aca- demic des Sciences, was probably the first to introduce into the theory of the steam-engine the consideration of that phenome- non, discovered by Watt, to check the wasteful effects of which the latter invented the steam-jacket.* That author gradually gave shape to his ideas, as time went on. publishing them in 1845.+ *d. later, in 1863-67.* He even anticipates Rankine and Clausius in one of their most famous discoveries, saying: " La rapatr d'fan. a Fetal dt saturation ft entffremenl secke, st dilatait sans addition mi soustraction de chaltmr ; ft nous anms montrf qne F expansion cst alors Offompagn/e tfitmf Halt/faction part if Ik de rapettr. Ccst a pat pres ainsi qmf Us choses doirmt Sf passer dans /fs machines a vapcmr ordinahres." He goes on to describe very clearly the phenomenon of cyl- inder-condensation ;"* but in his later works he seems to have paid less attention to this action, and may not have fully real- ized its importance: but his conception of the processes in- volved in such wastes, and in the preventive action of the jacket, was exact and well expressed. 59. Clausius' Work began at some time preceding 1850. He applied the modern theory of the steam-engine to the solution of the various problems which arise in the practice of the engineer, so far as they can be solved by the principles of thermodynamics. His papers on this subject were printed in 1850.$ The Count de Pambour had taken a purely mechani- cal mode of treatment, basing his calculations of the work :-} | Principes de la Tbterie Ufrmnqpr de la Chalew. PoggendocTs Annalca, iSsoet srq. of Heat;' translated br W. R. Browne; London. 1879. 262 A MANUAL OF THE STEAM-ENGINE. done in the cylinder of the steam-engine upon the hypothesis of Watt, that the weight of steam acting in the engine re- mained constant during expansion, and that the same assump- tion was applicable to the expanding mass contained in engine and boiler during the period of admission. He had con- structed empirical formulas, published in his work on the theory of the steam-engine, in 1844, for the relation of volume and pressure, during expansion, and had based his determinations of the quantity of work done, and of expenditure of steam in the engine, upon this set of assumptions and formulas, consid- ering the steam to remain in its initial condition of dry and saturated vapor, or of moist vapor, as the case may be, from the beginning to the end of the stroke. Errors were thus in- troduced, which, although not important in comparison with those often occurring when the results of purely thermo- dynamic, and in so far correct, v treatmenl was compared with the actual case, were, nevertheless, sufficiently great to become noticeable when the true theory of heat-engines became known, and correctly applied. Clausius proved that, in the expansion of dry and saturated steam, doing work in the engine, condensation must take place to a certain extent, and that, consequently, the weight of steam in the cylinder must be somewhat reduced by the process of expansion beyond the point of " cut-off." During the period of compression, also, the reverse effect must occur, and the compressed mass must become superheated, if initially dry. He showed that the amount of work actually done in a non-conducting working cylinder must be sensibly different from that estimated by the method of De Pambour. Taking advantage of the re-deter- mination of the constants in Regnault's equations effected by Moritz, Clausius obtains numerical results in the application of the true theory, and deduces the amount of work done in the steam-engine under various conditions such as are met with in practice. He shows how the action of the engine may be made that of the Carnot Cycle, and determines the effect of variation of the temperature of the " prime" steam. The investigation is, in the main, purely theoretical ; no application THE PHILOSOPHY OF THE STEAM-ENGIXE. 263 is made to the cases met with in real work, and the compari- son of the results of the application of the new theory to practice in steam-engineering is left to others. The work of Clausius is, throughout, perfectly logical, and beautifully simple and concise, and his application of the theory to the steam-engine amounts to a complete reconstruc- tion of the work of Carnot, and his followers, upon a correct basis. He develops with mathematical exactness of method and work the fundamental principles of the science of thermo- dynamics, constructs the .* fundamental equations," the so- called " General Equations of Thermodynamics," and, in the course of his work, proves the fact of the partial condensation of saturated steam, when permitted to expand doing work against resistance. 60. Rankine began his work upon the theory of the trans- formation of heat into mechanical energy at about the same time with Clausius (1849), an< ^ published his first important deduction, the form of the General Equation of Thermo- dynamics, nearly simultaneously, but a little earlier.* He gave much attention to the then incomplete work of develop- ment of applied thermodynamics, and produced not only the whole theory of the science, but very extended papers, includ- ing solutions of practical problems in the application of the science to heat-engines. Stating with singular brevity and clearness the main principles, and developing the general equations in substantially the same form, but by less easily followed processes, than his contemporary, he proceeded at once to their application. He determines the thermodynamic functions for air and other gases, exhibits the theory of the hot-air engine, as applied to the more important and typical forms, deduces expressions for their efficiency, and estimates the amount of heat demanded, and of fuel consumed, in their operation, assuming no other expenditure of heat than that required in an engine free from losses by conduction and radia- tion. He next, in a similar manner, applies the theory to the * Trans. Royal Soc. of Edinburgh. 1850 et seq. Sec, also, Rankine's " Mis- cellaneous Papers" and his " Manual of the Steam-engine." 264 A MANUAL OF THE STEAM-ENGINE. steam-engine, proves the fact of the condensation of steam during the period of expansion, estimates the amount of heat, fuel, and steam expended, and the quantity of work done, and determines thus the efficiency of the engine. He makes a special case of the engine using superheated steam, as well as that of the "jacketed" engine, considers the superheated steam-engine, and the binary-vapor engine, and reconstructs De Pambour's problem ; applying the theory in the applica- tion of mechanics to general engineering. Several important text-books, a large volume on shipbuilding, and other works, with an unknown number of papers, published and unpublished, form a monument to the power and industry of this wonderful man and remarkable genius, that may be looked upon as per- haps the greatest wonder of the intellectual world. Thus, Rankine, producing, in part, the same results as Clausius, by his wonderfully condensed method of treatment, turned his attention more closely to the application of the theory to the case of the steam- and other heat-engines, giving, finally, in his "Prime Movers" (1859), a concise yet full exposition of the correct theory of those motors, so far as it is possible to do so by purely thermodynamic treatment. He was unaware, ap- parently, as were all the scientific men of his time, of the ex- tent to which the conclusions reached by such treatment of the case are modified, in real engines, by the interference of other physical principles than those taken cognizance of by his science. Sir William Thomson, partly independently, and partly working with Joule, has added much valuable work to that done by Clausius and Rankine.* In the hands of these great men the science took form, and has now assumed its place among the most important of all branches of physical science. It was Sir William Thomson who discovered and revealed to English readers the remarkable work of Carnot and thus effectively aided in the construction of the science. As stated by Rankine :f *Edio. Trans., 1850 etseq.; Phil. Mag.; and Mathematical and Physical Papers. t Steam-engine; Introduction, p. xxxi. THE PHILOSOPHY OF THE STEAM-EXGIXE. 265 - Professor \\THiam Thomson, adopting the true theory of beat, in 1850,, not only solved some new problems in thermo- dynamics; and devised and carried out. jointly with Mr. Joule, some most important experiments ; but be extended analogous principles to electricity and magnetism, and thereby created what may justly be styled a new science. His papers have appeared in the Transactions of the Royal Society of Edin- burgh for 1851, and subsequently in the Philosophical Maga- zine since 185 1. and the Philosophical Transactions since 1854. Numerical data, without which the theoretical researches before referred to would have been fruitless, were furnished by the ex- periments of Dulong. and MM. Bravais, Martins, Moll, Van Beck, and others, on the velocity of sound : by those of M. Rnd- berg. on the expansion of gases; by the experiments, almost unparalleled for extent and precision, of M. Regnaulton. the properties of gases and vapors, made at the expense of the French Government, and published in the Proceedings and Memoirs of the Academy of Sciences, from 1847 to 1854: and by the joint experiments of Messrs. Joule and Thomson, on the thermic effects of currents of elastic fluids, made at the expense of the Royal Society, and published in the Philo- sophical Transactions for 1854.** Rankine concludes: ""Although the mechanical hypothesis just mentioned may be useful and interesting as a means of anticipating laws, and connecting the science of thermodyna- mics with that of ordinary mechanics, still it is to be remem- bered that the science of thermodynamics is by no means dependent for its certainty upon that or any other hypothe- sis, having been now reduced to a system of principles. or general facts, expressing strictly the results of experi- ment as to the relations between heat and motive power. In this point of view the laws of thermodynamics may be regarded as particular cases of more general laws, ap- plicable to all such states of matter as constitute Energy, or the capacity to perform work, which more general laws form the basis of the sdnue of cmrrgrtics. a science comprehend- 266 A MANUAL OF THE STEAM-ENGINE. ing, as special branches, the theories of motion, heat, light, electricity, and all other physical phenomena." The physicist, as well as the engineer, is still seeking to as- certain more definitely what is the mechanism of heat-energy transmission. It is now well ascertained that both heat and light are originally, in space, methods of vibration, of oscilla- tion, or of translation of particles of a fluid known as the " lumi- niferous sether ;" but the physical characteristics of that fluid are not yet defined with certainty. The researches of Hertz and others seem to indicate the probability that Clerk Max- well's suggestion that this method of transfer of energy may be electromagnetic in character. Professor D. V. Wood, tak- ing up the mathematical physics of the subject, deduces by a simple process, based on probably substantially accurate data,* as follows: (1) This medium transmits energy at the rate of 186,300 miles per second. (2) Heat-energy is transferred from the sun to the earth at the rate of 133 foot-pounds per square foot of section of the transmitted beam. (3) The medium may be taken as possessing the character- istics of the sensibly perfect gas. His process gives at once the essential physical character- istics of a fluid capable of transmitting this known quantity of energy at this observed velocity. It must be a medium of which one pound would occupy about twenty times the volume of the earth ; its tension would be one pound, nearly, per square mile of section ; and its specific heat must be about 4,600,000,000,000, that of water being taken as unity. It would weigh one pound to every 72 X IO 21 cubic feet ; the heat- vibrations are about 6x IO 14 per second ; and it is " everywhere practically non-resisting, uniform in temperature, density, and elasticity," whether in the depths of space and at its own boun- dary, if it has one, or at the surface of the sun or of the largest * Philosophical Magazine, Nov. 1885; Van Nostrand's Science Series, No. 85. THE PHILOSOPHY OF THE STEAM-EXGINE. 267 star in the universe. It would not destroj- the motion of the average comet in a million of millions of years. 6z. The Thermodynamic Theory of the Steam-engine stands, to-day, substantially as it was left by Clausius and Ran- lane and Thomson, at the close of their work in this field, in the decade 1850 to 1860. Many treatises have been published. some of them by men of exceptional ability ; but all have fol- lowed the general line first drawn by these masters, and have only now and then found some minor point to develop. Combes, Zeuner, and other writers have developed the sub- ject in detail, the latter, especially, studying the theory of various working fluids, as of superheated steam, and the phe- nomena of heat-transformation in relation to their effect upon the working substance. The pure theory of thermodynamics was substantially complete, however, long ago. and no impor- tant developments are to be now anticipated, except as ele- ments in the expansion of similar principles into the broader field of energetics. 02. The Limitations of thermodynamic theory and of iis application in the design and operation of heat-engines were first discovered by James Watt. They were systematically and experimentally investigated by Clark, in 1852 and earlier, were observed and correctly interpreted by Him (1855-71, an< d were revealed again by the experiments of Isherwood (18601. and by those of Emery and many other recent investigators on both sides of the Atlantic. These limitations are due to the fact that losses occur in the operation of such engines which are not taken into account by the hitherto accepted theory of the engine, and have no place in the thermodynamic treatment of the case. It is assumed, in the purely thermodynamic theory of the engine, that the expansion of the working fluid takes place in a cylinder having walls impermeable to heat, and in which no losses by conduction or radiation, or by leakage, can occur. Of those losses which actually take place in the real engine, that due to leakage may be prevented, or, if occurring, can be checked ; but it is impossible, so far as is now known, to secure 268 A MANUAL OF THE STEAM-ENGINE. J a working cylinder of perfectly non-conducting material. The consequence is that, since the steam or other working fluid enters at a high temperature and is discharged at a compara- tively low temperature, the surfaces of cylinder, cylinder-heads, and piston are, at one instant, charged with heat of high tem- perature, and at the next moment, exposed to lower tempera- tures, are drained of their surplus heat, which heat is then rejected from the cylinder and wasted. Thus, at each stroke, the metal surfaces, exposed to the action of the expanding substance, alternately absorb heat from it, and surrender that heat to the " exhaust." As the range of temperature worked through in the engine increases, as the quantity of steam worked per stroke diminishes, and as the time allowed for transfer of heat to and from the sides and ends of the cylinder and the piston is increased, the magnitude of this loss increases. These physical phenomena are therefore no less important in their influence upon the behavior of the engine, and upon its efficiency, and are no less essential elements for consideration in the general theory of the engine than those taken into account in pure thermodynamics. Such limitations are studied in Chapter V. 63. James Watt not only discovered the fact of the exist- ence of this method of waste, but experimentally determined its amount in the first engine ever placed in his hands. It was in 1763 that he was called upon to repair the little model of the Newcomen engine, then and still in the cabinets of the University of Glasgow. Making a new boiler, he set up the machine and began his experiments. He found, to his surprise, that the little steam-cylinder demanded four times its own volume, at every stroke, thus wasting, as he says, three fourths of the steam supplied, and requiring four times as much "in- jection-water" as should suffice to condense a cylinderful of steam. All of Watt's first inventions were directed toward the reduction of this immense waste. He proposed to himself the problem of keeping the cylinder "as hot as the steam that entered it ;" he solved this problem by the invention of the separate condenser and the steam-jacket, and the discovery of THE PHILOSOPHY OF THE STEAM-EXGIXE. 269 these limitations of the thermodynamic theory and their re- duction was the source of Watt's fame. John Smeaton, a distinguished contemporary of Watt, seems to have been not only well aware of this defect of the steam-engine, but was possibly even in advance of Watt in at- tempting to remedy it. He built a large number of Xewcomen engines between 1765 and 1770, hi some, if not many, of which he attempted to check loss of this " cylinder-condensation " in engines, some of which were five and six feet in diameter of cylinder, by lining pistons and heads with wood. Notwithstanding the fact that this waste was thus familiar to engineers, from the time of the invention of the modern steam-engine, and was recorded in all treatises on engine con- struction and management, the writers on the theory have never been aware that it gives rise to the production, in the working cylinder, of a large amount of water mingled with the steam. It has often been assumed by engineers themselves that this water is always due to "priming" at the boiler. Rankine, while correctly describing the phenomenon of cylin- der-condensation, attributed the presence of the water in steam- cylinders to the fact of condensation of dry steam doing work by expansion, apparently not until later having noted the fact that this would only account for a very small proportion of the moisture actually present in the average steam-engine. He considered incomplete expansion the principal source of loss, as do usually other writers on thermodynamics. Him published his Memoir e stir FUtilitf dfs Envehppes b Vapeur in 1855.* This memorable paper gives us the first precise analysis of experiments showing the quantitative measures of the thermal action of the walls of the steam-cylin- der. It presents an exact and scientific treatment of the case, and gives indisputable measures of the quantity of heat trans- ferred to the metal, and restored to the steam when too late for transformation into its proportion of mechanical energy. In every experiment, Him measured the quantity of water en- * Bulletin de la Soci& Indnstrielle de Molbouse; t. XXVTI. pp. 105-206. 2/O A MANUAL OF THE STEAM-ENGINE. tering the boiler, and there converted into steam, and compared it with the quantity of steam found, at each step in the engine- cycle, in the cylinder. He even went so far as to determine, by the use of his calorimeter, the quality of the steam entering the engine, in order that his measures of that contained in the cylinder might not be rendered uncertain by the action known as priming or foaming at the boiler. He also, for the first time, determined the weight of water leaving the condenser, and its temperature, thus securing the elements for the method of computation now known as that of Farey and Donkin. He proposed no theory, believing, as he stated expressly, that, at the time, any formulation of a theory was impossible without further knowledge. As a result of his first series of experiments he was able to say : " The influence of the steam-jacket is now clearly ex- plained : it consists in preventing the steam from partially con- densing, and thus lessening the pressure during expansion, by that act itself. As the heat taken from the jacket is, as has been seen, a small fraction of the total heat expended, the power so gained costs very little. Were any doubt now to exist on this point, the following facts would completely remove them : " (i) When the engine is working with jacket in use, if we suddenly shut off the steam and take it directly to the cylinder, the engine continues to work, as before, for some time, as if nothing had happened. The indicator-diagrams are precisely the same as before ; it is only after 10 or 20 minutes that the power of the engine falls off 23^ per cent in this case. It is thus evidently the heat in the walls of the cylinder, and not the simple drying of the steam, which gives us this economy of 23^ per cent. " (2) The jacket actually modifies very sensibly the tem- perature of the steam ; for, while it is acting, the steam ex- hausted into the condenser is at 64 C, at a tension of o ra .o75 while, in the other case, the temperature falls to 58, although its tension rises to o m .O95. . . ." Farther on he says : " Since it is the elevation of tempera- ture of the walls of the cylinder, heated by the steam in the THE PHILOSOPHY OF THE STEAM ENGIXE. 2JI jacket, which is the cause of the improvement, it is not to be doubted, for an instant, that any means of securing such tem- perature will be equally effective and economical." He then proposes the use of a smoke-jacket : but he finds, on trial, that it is of little value, the heat being incapable of passing with sufficient rapidity from the gases in the jacket to the metal of the cylinder. Him, in this memoir, also expressly proposed the measure of the heat consumed by the engine as the true measure of its efficiency. 64. The Best Ratio of Expansion is that which gives best effect under the specified conditions. But this is obviously greater or less, accordingly as the wastes of the engine in- crease more or less rapidly, and as this point, known practi- cally to exist, at which the net effect, after balancing gains and losses, is set at one ratio or another by such variations. The limit of efficiency in heat-engines, as has been seen, is thermodynamically determined by the limit of complete expansion. The causes of the practical limitation of the ratio of expansion to a very much lower value than those which maximum efficiency of fluid would seem to demand have not been always considered, either with care or with intelligence, by writers thoroughly familiar with the dynamical treatment, apart from the modifying conditions here under consideration. These problems are the special subject of Chapter VII. 65. Cylinder-condensation is now knowmto produce very serious modifications of working conditions. Watt, and prob- ably his contemporaries and successors, for many years sup- posed that the irregularity of motion due to the variable pressure occurring with high expansion was the limiting con- dition, and does not at first seem to have realized that the cylinder-condensation discovered by him had any economical bearing upon the ratio of expansion at maximum efficiency. It undoubtedly is the fact that this irregularity was the first limiting condition with the large, cumbrous, long-stroked, and slow-moving engines of his time. Nearly every accepted authority, from that day to the present, has assumed, tacitly, 2J2 A MANUAL OF THE STEAM-ENGINE. that this method of waste has no influence upon the value of that ratio. Thomas Tredgold, writing in 1827, who, but little later than Carnot, puts the limit to economical expansion at the point subsequently indicated and more fully demonstrated by De Pambour, exaggerates the losses due to the practical con- ditions, but evidently does perceive their nature and general effect. He also shows that, under the conditions assumed, the losses may be reduced to a minimum, so far as being depend- ent upon the form of the cylinder, by making the stroke twice the diameter. Mr. D. K. Clark, however, publishing his " Railway Ma- chinery" in 1855, was the first to discuss this subject with knowledge, and with a clear understanding of the effects of condensation in the cylinder of the steam-engine upon its maximum efficiency. Cornish engines, from the beginning, had been restricted in their ratio of expansion to about one fourth, as a maximum, Watt himself adopting a " cut-off " at from one half to two thirds. Hornblower, with his compound engine competing with the single-cylinder engines of Watt, had struck upon this rock, and had been beaten in economy by the latter, although using much greater ratios of expan- sion ; but Clark, a half-century, and more, later, was, neverthe- less, the first to perceive precisely where the obstacle lay, and to state explicitly that the fact that increasing expansion leads to increasing losses by cylinder-condensation, the losses in- creasing in a much higher ratio than the gain, is the practical obstruction in our progress toward greater economy. After a long and arduous series of trials of locomotive- engines, and prolonged experiment looking to the measure- ment of the magnitude of the waste produced as above de- scribed, Clark concludes : " The magnitude of the loss is so great as to defeat all such attempts at economy of fuel and steam by expansive working, and it affords a sufficient expla- nation of the fact, in engineering practice, that expansive working has been found to be expensive working, and that, in many cases, an absolutely greater quantity of fuel has been THE Pff/LOSOPJ/Y OF THE STEAM-ENGINE. "5 consumed in extended expansion working, while less power has been developed." He states that high speed reduces the effect of this cause of loss, and indicates other methods of checking it. He states that " the less the period of admission, relative to the whole stroke, the greater the quantity of free water existing in the cylinder." His experiments revealing these facts were, in some cases, made prior to 1852. But the men handling the engines had observed this effect even before Clark : he states that they rarely voluntarily adopted " a sup- pression of above 30 per cent," as they found the loss greater than the gain. Describing the method of this loss, this author goes on to say that, " to prevent entirely the condensation of steam worked expansively, the cylinder must not only be sim- ply protected by the non-conductor : it must be maintained, by independent external means, at the initial temperature of the steam." He thus reiterates the principle expressed by Watt three quarters of a century before. The same author, writing in 1 877, says : ' The only ob- stacle to the working of steam advantageously to a high degree of expansion in one cylinder, in general practice, is the condensation to which it is subjected, when it is admitted into the cylinder at the beginning of the stroke, by the less hot sur- faces of the cylinder and piston ; the proportion of which is increased so that the economy of steam by expansive working ceases to increase when the period of admission is reduced down to a certain fraction of the stroke, and that, on the con- trary, the efficiency of the steam is diminished as the period of admission is reduced below that fraction." The magnitude of this influence may be understood from the fact that the distinguished engineer, Loftus Perkins, using steam of 300 pounds pressure, and attaining the highest economy known, up to his time, found his engine to consume 1.62 pounds of fuel per hour and per horse-power ; while this figure is now reached by engines using steam at one third that pressure, and expanding about the same amount, and sometimes less. Mr. Humphreys, writing a little later than Clark, shows the consumption of fuel to increase seriously as the ratio of 2/4 A MANUAL OF THE STEAM-ENGINE. expansion is increased beyond the very low figure which con- stituted the limit in marine engines of his time. 66. Him was the first scientific and practical investigatoi on the Continent of Europe. A few writers on thermodynamics had finally come to un- derstand the fact that such a limitation of applied theory existed, and Mons. G. A. Hirn, who, better than probably any authority of his time or earlier, combined a knowledge of the scientific principles involved, with practical experience and experimental knowledge, in his treatise on thermodynamics (1876), concludes : " quit est absolument impossible d'e'difier a priori une the'orie de la machine a vapeur d'eau douce d"un cha- racttre scientifiqnc et exact" in consequence of the operation of the causes here detailed. While working up his experiments upon the performance of engines, comparing the volume of steam used with that of the cylinder, he had always found a great excess, and had, at first, attributed it to the leakage of steam past the piston ; but a suggestion of M. Leloutre set him upon the right track, and he came to the same conclusion as had Watt, so many years before. He explains that errors of thirty, or even up to seventy, per cent may arise from the neglect of the consideration of this loss. Combes had per- ceived the importance of this matter, and De Freminville suggested the now familiar expedient of compression, on the return-stroke, as nearly as possible to boiler-pressure, as a good way to correct the evil. Hirn was the first to show in detail the distribution of heat-wastes and to prove with cer- tainty, on such grounds, that the benefit of extended expan- sion in real engines can only be approximated to that pre- dicted, by the theory of the ideal engine, by special arrange- ments having for their object the reduction of cylinder-waste, such as superheating, "steam-jacketing," and "compounding." His experimental work began at a very early date and in a purely scientific spirit. He had noted the discoveries of Mayer (1842) and of Joule (1846 and later) only after he had himself sought to ascertain the true nature of heat. He pub- lished his conclusions, correct conclusions, in 1848, relating to THE PHILOSOPHY OF THE STEAM-EMG1NE. 2/5 this question as determined by his researches on heat and fric- tion. In 1855 he was able to show that Cannot had accepted the wrong theory in his now famous work ; proved, by experi- ment, that heat actually disappears, as heat, in the operation of tile steam-engine, and showed that, in the actual engine, the steam-jacket, an element in itself wasteful, may be a very im- portant source of economy by checking extra-thermodynamic wastes. Him showed that Mayer's ideas were completely sustained, and that the Rankine and Clausius phenomenon of condensa- tion of steam and similar vapors, during their adiabatic expan- sion,, is actually observable in the steam-engine. His great work on Thermodynamics * was published in 1876, and in it he gave as clear an account of the physical operations taking place within the engine-cylinder as had dark or Isherwood. and produced a theory of the real engine an ** experimental theory" as he called it which has served as the basis for nearly all subsequent work in that direction. Mons. V. Dwelshauvers-Dery supplemented this work of Him by further development of the theory and its application in fuller detail to the processes of heat-transfer in the steam- engine in the years subsequent to 1878.+ From 1873, this in- vestigator worked with Him and his lieutenant, Hallauer, and with M. Grossteste in the construction, upon the basis of ex- periment, of a correct theory of the real, as distinguished from the ideal, engine and its reduction to a practically valuable form. He gives in an " Expose," in the Revue, in 1882, a carefully-written account of this development of the most modern form of the theory of heat-engines. This latest theory was finally completely established by a long and instructive discussion in which the ablest physicists and engineers of Europe were engaged. In its current form, its algebraic ex- pression is that of Dwelshauvers-Dery; but it still requires further development. * Thterie Mecaniqoe de Cbaknr; z tomes; Finis, 1816. f Revue UmretseSe des Mines, de Liege. 2/6 A MANUAL OF THE STEAM-ENGINE. 67. Isherwood's Researches were the first systematically conducted investigations of the latest phase of the problem of steam-engine efficiency in the United States. Mr, B. F. Isherwood was, in 1860, a Chief Engineer in the United States navy, and Chief of the Bureau of Steam Engi- neering. He seems to have been the first to have attempted to determine, by systematically planned experiment, the law of variation of the amount of cylinder-condensation with varia- tion of the ratio of expansion. Experimenting on board the U. S. S. Michigan, a naval vessel fitted with simple and un- jacketed engines, he found that the consumption of fuel and of steam was greater when the ratio of expansion was carried beyond about two than when restricted to lower ratios. He determined the quantity of steam used, and the amount con- densed, at expansions ranging from full stroke to a " cut-off" at one tenth. His results permit the determination of the method of variation, with practically satisfactory accuracy, for the engine upon which the investigation was made, and for others of its class. It was the first of a number of such inves- tigations made by the same hand, and these to day constitute the principal part of our data in this particular direction. The author, studying these results, found that the cylinder-conden- sation there varied sensibly as the square-root of the ratio of expansion, and the method of variation is apparently substan- tially similar for other forms and proportions of engine. The amount of such condensation usually lies between one tenth and one fifth the square-root of that ratio, if estimated as a fraction of the quantity of steam demanded by a similar engine having a non-conducting cylinder, it being here assumed that the engine is one of fair size. The proportion of loss is some inverse function of the size of engine probably nearly in- versely as the diameter of cylinder. Mr. Isherwood, in his works, gives admirably-expressed descriptions of the modus operandi, when considering this waste.* He summarizes his own work, and explains with un- * Engineering Researches; a vols. 410; Philadelphia, 1860. See especially the introduction to volume n. THE PHILOSOPHY OF THE STEAM-EXGIXE. -~~ exampled clearness the method of modification of the best ratio of expansion by these internal and previously unfamiliar v IStCSi Professor Cotterill gives more attention to this subject than any writer up to his time. He devotes a considerable amount of space to the study of the method of absorption and surren- der of heat by the metal surfaces enclosing the steam, con- structs diagrams which beautifully illustrate this action, and solves the problems studied by him with equal precision and elegance of method. He summarizes the experimental work done to the date of writing, and very fully and clearly exhibits the mode of transfer of heat past the piston without trans- formation into work. Professor Cotterill's treatise on the steam-engine, " considered as a heat-engine," is thus most valuable to the engineer.* Mr. Sutcliffe states, as early as 1875, that engines of ap- proved type may sometimes exhibit losses by cylinder-waste exceeding 40 per cent.t He gives the following figures for these losses in the Corliss engines at Saltaire : 7.4 27 per cent. 9-04 36.37 " " 11.4 46.67 " " These figures approach those previously obtained by Isher- wood from a much less approved form of engine. 68. The Status of the Theory of the Steam-engine, about 1850. was becoming well settled as a thermodynamic system, and even the most recent phase had begun to take vague shape. Dr. Albans, writing about 1840, says of the choice of best ratio of expansion : " Practical considerations form the best guide, and these are often left entirely out of view by mathe- maticians. Many theoretical calculations have been made to * The Steam-engine considered as a Heat-engine ; London, 1878. 4 Hopkinson on the Steam-engine Indicator; 7th ed. ; 1875. 278 A MANUAL OF THE STEAM-ENGINE. determine the point, but they appear contradictory and unsat- isfactory." Renwick, in 1848, makes the ratio of initial divided by back pressure the proper ratio of expansion, but correctly describes the effect of the steam-jacket, and suggests that it may have peculiar value in expansive working, and that the steam may receive heat from a cylinder thus kept at the tem- perature of the " prime " steam. John Bourne, the earliest of now acknowledged authorities on the management and con- struction of the steam-engine, pointed out, at a very early date, the fact of a restricted economic expansion. Rankine recog- nized no such restriction as is here under consideration, con- sidered the ratio of expansion at maximum efficiency to be the same as that stated by Carnot, and by other early writers, and only perceived its limitation by commercial considerations, a method of limitation of great importance, but often of less practical effect than is the waste by condensation. In his life of Elder (1871), however, he indicates the existence of a limit in practice, and places the figure at that previously given by Isherwood for unjacketed engines. Thus the theory of the steam-engine stands, at this date, in- complete, but on the verge of completion, needing only a little well-directed experimental work to supply.the doubtful elements. Even these are becoming determined. Isherwood and later engin- eers give facts showing waste to be proportional, very nearly, if not exactly, to the square-root of the ratio of expansion ; and Escher, of Zurich, has shown the loss to be also proportional to the square-root of the time of exposure, or, in other words, to the reciprocal of the square-root of the speed of rotation ; and it only remains to determine the exact method of variation of loss with variation of range of temperature and a rational basis to give the whole of the necessary material for the con- struction of a working theory which may enable the engineer to estimate, in advance of construction, the economic perform- ance of his machine. Dwelshauvers has done much to popularize the modern and accepted theory of the real engine. He has endeavored to exhibit the action of the steam-jacket, to show what is the TOE PHILOSOPHY OF THE STEAM-EJtTGWE. 2J9 modification of die action of the metallic interior of the gngntr, by the introduction of that wasteful dement, to counteract. in many cases, a greater waste ; and he has sought to show the influence of the experimental philosophy of the engine upon the proportions and the working of the condenser. He has observed the fact of a maximum ratio of expansion appro- priate to the condition of maximum efficiency,, as determined by the variation of this waste, previously unobserved, and has engaged in the construction of its theory in accordance with his published theory of heat-expenditure, reducing all to a common basis and philosophy. Some of the work of Dwelshau vers-Dery has been trans- lated by Donkin. and published, from time to time in London EmgimetTrsmg ; other portions remain untranslated, xm\ are onlv to be found in the Rfzue Umtn-ersiHe dies Mines. Simigagiia jia< summarized it welL It probably cannot be long before direct investigation will secure all essential knowledge. When this becomes the case, the remarks of those distinguished physicists and engineers, Hallauer and his great teacher, Him, wfll be no longer based upon apparent fact. Says Him. on this subject " Ma commctiom reste amjomrdkm qtiflU ctedt il y a vimgt ams, mme tkeorie proprememt dite de la machine a Tzapcmr est impossible; la titanic cjcpcnmemtale,etabKe atr If motemr bdmeme et dams toutes les formes oil il a fit fssave. cm me'camiqme afpliqxe pent semle comdmire a des rcsmhats rigom- 60, Three Periods of this Philosophy of the steam-en- gine may be discerned. Chronologically considered, the his- tory of the growth of the theory divides itself distinctly into three parts : the first extending up to the middle of the present century, and mainly distinguished by the attempts of Cannot and of Clapeyron to formulate a physical theory of the thermo- dynamics of the machine ; the second beginning with the date of the work of Rankine and Clausius, who constructed a correct thermodynamk theory ; and the third beginning nearly a gen- eration later, and marked by the introduction into the general 280 A MANUAL OF THE STEAM-ENGINE. theory of the physics of the conduction and transfer of that heat which plays no part in the useful transformation of energy and its application. The first period may be said to include, also, the inaugura- tion of experimental investigation, and the discovery of the nature and extent of avoidable wastes and attempts at their amelioration by James Watt and by John Smeaton. The second period is marked by the attempt, on the part of a num- ber of engineers, to determine the method and magnitude of these wastes by more thorough and systematic investigation, and by the exact enunciation of the law governing the neces- sary rejection of heat, as revealed by the science of thermody- namics. The third period is opening with promise of a com- plete and practically applicable investigation of all the methods of loss of energy in the engine, and of the determination, by, both theoretical and experimental research, of all the data needed for the construction of a working theory. Hirn has recognized these three periods, and has proposed to call the second the " theoretical " and the third the " experi- mental " stage. The Author would prefer to make the nomen- clature somewhat more accordant with what has seemed to him to be the true method of development of the subject. It has been seen that the experimental stage really began with the investigations of Watt in the first period, and that the work of experimentation was continued through the second into the present, the last, period. It is also evident that the theoretical stage, if it can be properly said that such a period may be marked off in the his- tory of the theory of the steam-engine, actually extends into the present epoch ; since the work of the engineer and the physicist of to-day consists in the application of the science of heat-transfer and heat-transformation, together, to the engine. During the second period the theory included only the thermo- dynamics of the engine ; while the third period is about to incorporate the theory of conduction and radiation into the general theory with the already established theory of heat- transformation. The writer would therefore make the classifi- THE PHILOSOPHY OF THE STEAM-EXGIXE. 28 1 cation of these successive stages in the progress here -described thus: 1. Primary Period that of incomplete investigation and of earliest systematic, but inaccurate, theory. 2. Secondary Period that of the establishment of a cor- rect thermodynamic theory, the Theory of the Idtal Engine. 3. Tertiary Period that of the production of the complete theory of the engine, of the true Theory of the Real Engine. 70. Work remaining to be done, as may be now readily seen, is that of determining, by experiment, precisely what are the physical laws governing the transfers of heat between metal and vapor, in the engine-cylinder, and to apply these laws in the theory of the machine. Cotteriil has shown how heat penetrates and traverses the metal, and Grashof has indi- cated the existence of an intermediate and approximately con- stant temperature between the temperatures of the initial steam and of the exhaust, and both have given us some new methods. The Author, while pointing out the nature of the true ** curve of efficiency" of the steam-engine which he was so fortunate as to discover, has shown how it may be made useful in the solution of practical and of theoretical problems in- volved in the applied theory of heat-engines, and many able minds are now engaged upon the theory. There can be little doubt that it will soon become satisfactorily complete. The determination of physical constants and the experi- mental checking of the scientific treatment of the case will undoubtedly furnish employment to able and skilful investi- gators for many years, and the study of the modification of the general theory in its application to the present and the com- ing types of engine will offer a no less important and attrac- tive field of labor for those competent to take up the work and finding opportunities to do so. The philosophy of the construction and of the operation of the multiple-cylinder and of new forms of engine is already well understood, and the algebraic and numerical equations applying to them as a mathe- matical theory are now in process of development. Messrs. Him and Hallauer, Donkin, Dwelshauvers-Dery, Zeuner and 282 A MANUAL OF THE STEAM-ENGINE. Kirsh have already succeeded in effecting some valuable ad- vances in the theory of the real engine, by the introduction of data previously secured by Clark and others. The experimental investigation of Messrs. Gately and Kletschy, to be considered later, and the more exact work since undertaken will ultimately supply all needed data. That in- vestigation, the first attempt at systematic investigation of the methods of variation of the several main losses and wastes, in the steam-engine, with variation of the principal quantities de- termining their magnitudes, was made in the spring of 1884, and upon a plan schemed out by the Author some years earlier (1878). The results gave, roughly, the needed data for the provisional theory of the engine, including physical as well as thermodynamic wastes, the theory of heat-transfer and that of heat-transformation. It has now become practicable to make intelligent and useful estimates of the relative value of alternative plans of construction of proposed new engines, of probable costs of operation, and of efficiencies and best pro- portions of size of engine to power demanded for any given type, size, and design. Some of the most satisfactory data are those obtained by Messrs. Hill,* Willans,f Schneider,;}; English, an d Kennedy. | 71. The Plan of this Work thus logically includes the philosophical study of the gradual development of the modern steam engine out of the germ which existed in ancient times ; the description of the machine of our own day, in its principal forms ; the tracing of the evolution of scientific knowledge of its philosophy to the present time ; the discussion of the sci- entific principles involved in the production, utilization, and wastes of energy in the apparatus and mechanisms employed ; and the useful application of such principles, in the design, the proportioning, the constructing, and the economical operation of engines and transmitting machinery. The succeeding subjects then follow in logical and natural * Mark's Steam-engine Design. f Trans. Brit. Inst. C. E., 1888. t Delaford's Report, 1884. Trans. Brit. Inst. Mech. Engrs., 1887. || Trans. Brit. Inst. Mech. Engrs., 1890. THE PHILOSOPHY OF THE STEAM-ENGINE. 283 order, thus: Chemistry of Combustion ; Physics of Heat-trans- fer and Storage; Thermodynamics: Theory of the Steam- engine, ideal and real ; Design ; Construction ; Operation and Management; Tests of the Machine; Theory of Efficiencies, including finance; Establishments; Specifications, Contracts, and Legal Forms and Business Principles. We thus trace the production of energy in available form and its progress in the process of its utilization, from its first appearance with the combustion of the fuel in which it had been stored, through the several steps by which it passes into the boiler, becomes stored in the steam, and is finally transferred to the engine and there converted in part into mechanical energy, to be use- fully or wastefully applied to the performance of the intended task or to overcome the friction of the mechanism employed. The Fundamental Mechanical Principles involved are, in brief, the following : The object of all mechanism is to produce a certain defi- nite motion of some part or parts the position and form and the methods of connection of which are known and fixed against any resistance that may be met with in the course of such movement. Every machine and every train of mechanism is therefore a contrivance by means of which energy or power available at one point, usually in definite amount and acting in a definite direction and with definite velocity, is transferred to other points, there to do work of definite amount, and there to overcome known resistances with known velocities, The object of the engineer in designing mechanism is to effect this transfer of energy and these transformations at the least cost and with least running expense, and hence with maximum efficiency of apparatus. It is often important tc secure minimum volume and weight of machine, as well as maximum effectiveness in operation. The work of a machine is measured by the magnitude of the resistance encountered and the velocity with which it is overcome. The nature of the work, aside from its simple kinetic character, is as widely variable as are the details of human industry. 284 A MANUAL OF THE STEAM-ENGINE. Prime Movers are those machines which receive energy directly from natural sources, and transmit it to other machines which are fitted for doing the various kinds of useful work. Thus, the steam-engine derives its power from the heat-energy liberated by the combustion of fuel ; water-wheels utilize the energy of flowing streams ; windmills render available the power of currents of air; the voltaic battery develops the energy of chemical action in its cells; and, through the movement of electro-dynamic mechanism, this energy is communicated to other machinery, and thus caused to do work. Machinery of Transmission is used in the transformation of energy supplied by the prime mover into available form, for the performance of special kinds of work, or for simple transmission of power from the prime mover to machines doing that work. The work to be done may be the raising of weights, as in hoisting and pumping machinery; the transportation of loads, as on the railway or in the steamship ; the alteration of the form of solid masses, as in machine-tools ; the overcoming or even the utilizing of frictional resistances, as in brakes ; or any other of the numberless operations performed in mills and factories by machinery. Machines and Machine-tools receive energy, derived originally from prime movers, and transferred to them through machinery of transmission, and apply that energy to special kinds of work to which they are precisely adapted by their design and con- struction. Thus, looms apply such energy to the weaving of cloth ; lathes are especially fitted for the production of parts having circular sections; planing-machines produce straight- lined surfaces. The power demanded by a machine is that needed to do the work for which the machine is designed, plus the addi- tional amount expended by the machine itself, in transferring the first-mentioned quantity from the source of power to which the machine is connected, by transmitting mechanism to the point at which the work is to be done. Where the machine is subject to shock and jar sufficient to permanently distort its parts, or the bearing surfaces, a portion of the power demanded THE PHILOSOPHY OF THE STEAJt-EA'CIXE. - * f is wasted in doing this work ; where the journals heat, consider- able amounts of energy are sometimes lost as heat-energy: in all cases some loss occurs in this way. Where power is trans- mitted by the expansion and compression of elastic fluids, also, energy is often lost in large amounts by transformation into " The power demanded by any machine thus always exceeds that expended by the machine upon its proposed task. Were these wastes not to occur, the power transmitted would be the same in amount at every point in the machine. Work, as a term in the science of engineering, may be defined as that action by which motion is produced against the resistance continuously or intermittently opposed to any mov- ing body. It is measured by the product of the direct com- ponent of the resistance into the space traversed. Where the resistance is variable, its mean value is taken. Thus, if R be the resistance and 5 the space, the work is, for constant fijnbtance, U=RS, ........ (i) in which U is measured in foot-pounds or kilogrammetres. For a variable resistance, R* acting through a space, s r (2) which can be integrated when R is known as a function of s. Resistances, and the forces by which they are overcome, are measured by engineers, usually, either in British or in metric units, as the pound or the kilogramme. Work, and the energy expended in doing work, are thus both measured by the product of the pounds or the kilogrammes of resistance or of effort into spaces of which the measure is usually given in feet or in metres. The unit of work and of energy is thus either the foot-pound or the kUogrammetre. The British and metric measures have definite relations, which are given in tables to be found in all engineers* table- books, 286 A MANUAL OF THE STEAM-ENGINE. Where the motion of the machine or of the part doing v^ork is circular, the space traversed may be measured by the angu- lar motion, a, multiplied by the lever-arm, /, and their pro- duct, multiplied by the force, R, exerted, gives the measure of the work done. Thus : U=aRl in which last expression n is the number of revolutions made in the unit of time. These values are equivalent to the product of the angular motion into the moment of the resistance. Work may also be measured, as in steam, air, gas, or water- pressure engines, by the product of the area of piston, A, the mean intensity of pressure upon it,/, the length of stroke of piston, /, and the number of strokes made. Thus, U=Apln = Aps =fir> ......... (4) when Fis the volume of the working cylinder multiplied by the number of strokes ; in other words, the volume traversed by the piston. Where the force acting, or the resistance, acts obliquely to the path traversed, it is evident that only the component in that path is to be considered. Diagrams exhibiting the amount of work done and the method of its variation are often found useful. In such diagrams the ordinate is usually made proportional to the force acting or to the resistance, while the abscissas are made to measure the space traversed. The curve then exhibits the relations of these two quantities, and the enclosed area is a measure of the work performed. With a constant resistance, the figure is rectilinear and a parallelogram ; with variable velocities and resistances, it has a form characteristic of the methods of operation of the part or of the machine the action of THE PHILOSOPHY OF THE STEAM ENGINE. 287 which it illustrates. In the first case, the area can be obtained by multiplication of the difference of the ordinates by the difference between maximum and minimum abscissas; in the second case, it may be obtained by any convenient system of integration, of which systems that of mechanical integration, as by the " planimeter," is usually best. Power is defined as the rate of work, and is measured by the quantity of work performed in the unit of time, as in foot-pounds or in kilogrammetres, per minute or per second. The unit commonly employed by engineers is the "horse- power," which was defined by Watt as 33,000 foot-pounds per minute, equivalent to 550 per second, or 1,980,000 foot-pounds per hour. This is considered to be very nearly the amount of work performed by the very heavy draught-horses of Great Britain ; but it considerably exceeds the power of the average dray-horse of that and other countries, for which 25,000 foot- pounds may be taken as a good average amount. The metric horse-power, called by the French the chevaL- vafeur, or force de cheval, is about i per cent less than the British, being 542^ foot-pounds or 75 kilogrammetres per second, 4500 kilogrammetres per minute, or 270,000 per hour. These quantities are almost invariably employed to measure the power expended and work done by machines. It is evident that power is also measured by the product of the resistance, or of the effort exerted into the velocity of the motion with which that resistance is overcome, or that force exerted. Since s = vt, U= Rs = Rvt; and when / becomes unity, the measure of the power, or of the equivalent work done in the unit of time, is (5) in which the terms are given in units of force and space as above. The power of a prime mover is usually ascertained by experi- mentally determining the work done in a given time, the trial 288 A MANUAL OF THE STEAM-ENGINE. usually extending over some hours, and often several days. It is measured in foot-pounds or kilogrammetres; the total work so measured is then divided by the time of operation and by the value of the horse-power for the assumed unit of time and the mean value of the power expended thus finally expressed in horse-powers.* The forces acting in machines are distinguished into driv- ing and resisting forces. That component of the force, act- ing to produce motion in any part which lies in the line of motion only, is that which does the work; and this component is distinctively called the " Effort." Similarly, only that compo- nent of the resistance which lies in the line of motion is con- sidered in measuring the work of resistance. In either case, if the angle formed between the directions of the motion of the piece and of the driving or the resisting force be called a, the effort is P = R cos a (6) The other component, acting at right angles to the path of the effort, is . Q = R sin a (7) and has no useful effect, but produces waste of power by in- troducing lateral pressures and consequent friction. Energy, which is defined as capacity for performing work, is either actual or potential. Actual or Kinetic Energy is the energy of an actually mov- ing body, and is measured by the work whichjt is capable of performing while being brought to rest, under the action of a retarding force ; this work is equal to the product of its weight, v* W, into the height, h = , through which it must fall under the action of gravity to acquire that velocity, v, with which it is at the instant moving; i.e., E-U=Wh= W (8) <5 * Custom has not yet settled the proper form of the plural of this word; there is no reason why it should not follow the rule. THE PHILOSOPHY OF THE STEAM-ENGINE. 289 A change of velocity v t to v v causes a variation of actual energy, E^ E v and can be effected only by the expenditure of an equal amount of work . . (9) This form of energy appears in every moving part of evc-ry machine, and its variations often seriously affect the working of mechanism. The total actual energy of any system is the algebraic sum of the energies, at the instant, of all its parts ; i.e., (10) and when this energy is all reckoned as acquired or expended at any one point, as at the driving-point, the several parts having velocities, each n times that of the driving-point, which latter velocity is then v, the total energy becomes Actual energy is usually reckoned relatively to the earth ; but it must often be reckoned relatively to a given moving mass, in which case it measures the work which the moving body is capable of doing upon that mass, when brought by it to its own speed. Potential Energy is the capacity for doing work possessed by a body in virtue of its position, of its condition, or of its intrinsic properties. Thus, a weight suspended at a given height possesses the potential energy, in consequence of its position, E = Wh, and may do work to that amount while de- scending through the height, h, under the action of gravity. A bent bow or coiled spring has potential energy, which be- comes actual in the impulsion of the arrow or is expended in the work of the mechanism driven by the spring. A mass of gunpowder or other explosive has potential energy in virtue 2QO A MANUAL OF THE STEAM-ENGINE. of the unstable equilibrium of the chemical forces affecting its molecules. Food has potential energy in proportion to the amount of vital and muscular energy derivable by its consump- tion and utilization in the human or animal system. These potential energies are not measured by the observed actual energies derived from these substances in any case, but are the maximum quantities possibly obtainable by any perfect system of development and utilization. In practical applica- tion, more or less waste is always to be anticipated. The law of persistence of energy affirms that the total energy, actual and potential, of the universe, or of any isolated system of bodies, is of invariable amount, and that all energy is thus indestructible, although capable of transformation into various forms of physical and chemical energy. Every instance of disappearance of actual energy involves the performance of work, and the production of potential or of some new form of actual energy in precisely equal amount. A stone thrown vertically upward loses kinetic energy as it rises in precisely the amount resistance of the air being ne- glected by which it gains potential energy. A falling mass striking the earth surrenders the actual energy acquired by loss of potential energy during its fall, and the equivalent of the quantity so surrendered is found in the work done upon the soil ; it finally passes away as the equivalent energy of heat motion produced by friction and impact. The potential chem- ical energy of the explosive is the equivalent of the kinetic energy of the flying projectile, and the latter has its equivalent in the work done at the instant of striking and coming to rest, and in the heat produced by the final change of mass-motion into molecular or heat motion. Energy in all its many forms is thus transferable in defi- nite quantivalent proportions, and in all cases changes form when work is done. Work may therefore be defined as that operation which results in a change in the method of manifes- tation of energy, and Energy as that which is transferred or transformed, when work is done. The motion of a projectile is the transfer of energy from one place to another. It is generated at the point of departure, stored as actual or THE PHILOSOPHY OF THE STEAM-ENGINE. 2QI kinetic energy, transferred to the point of destination, and there restored and applied to the production of work. Acceleration and retardation of masses in motion can only be produced by doing work upon them, or by causing them to do work, and thus, by the communication of energy to them or by its absorption from them, in precisely the amount which measures the variation of their actual energy as so pro- duced. Every body which is increasing in velocity of motion thus receives and stores energy ; every mass undergoing re- tardation must perform work, and thus must restore energy previously communicated to it. In every machine which works continuously, and in which parts are alternately accelerated and retarded, energy is stored at one period and restored at another, in precisely equal amounts. Work done upon any machine may thus be expended partly in doing the useful work of the system, and partly in storing energy ; and the same machine may do work at another instant partly by expending the energy received by it, and partly by expending stored energy previously accumulated. Storage or restoration of energy thus always occurs when change of speed takes place. It is evident, since the storage or restoration of energy implies variation of speed, that the condition of uniform speed is that the work done upon the machine shall at each instant be precisely equal to that done by it upon other bodies. The work applied must be equal to that of resistance met at the driving-point. Thus, ^^Ri/', J Pdv=J*Rdv'\ . . . (12) and the effort at each point in the machine will be equal to the resistance, and inversely as the velocity of the point to which it is applied ; i.e., 03) In the starting of every machine energy is stored during the whole period of acceleration up to maximum speed, and this energy is restored and expended while the machine is 2Q2 A MANUAL OF THE STEAM-ENGINE. coming to rest again. This latter quantity of energy is usually expended in overcoming friction. The useful and the lost work of a machine are, together, equal to the total amount of energy expended upon the machine, i.e., to the work done upon it by its "driver." The Useful Work is that which the machine is designed to perform ; the Lost Work is that which is absorbed by the friction and other prejudicial resistances of the mechanism, and which thus waste energy which might otherwise be usefully applied. These two quantities, together, constitute the Total Work or the Gross Work of a machine, or of a train of mechanism. In every case some energy is wasted, and the work done by the machine is by that amount less than the work performed in driving it. In badly proportioned machines the lost work is often partly expended in the deformation and destruction c* the members of the construction ; in well designed and properly worked machinery loss occurs wholly through friction. In machines acting upon fluids this lost work is usually partly wasted in the production of fluid friction i.e., of currents and eddies ; thus producing new forms of actual energy in ways which are not advantageous : even this waste energy is finally converted, like the preceding form, by molecular friction into heat, and is dissipated in that form of molecular energy. Thus all wasted work is lost by conversion from the energy of mass- motion into molecular energy and ultimately disappears as heat. The efficiency of mechanism is measured by the quan- tity obtained by dividing the amount of useful work per- formed by the gross work of the piece or of the system. It is always, therefore, a fraction, and is less than unity ; which latter quantity constitutes a limit which may be approached more and more nearly as the wastes of energy and work are reduced, but can never be quite reached. If the mean useful resistance be R, and the space through which it is overcome be s', and if the mean effort driving the machine be P, and the space through which it acts be s, the total and the net or useful work will be, respectively, Ps, Rs'\ the lost work will be Ps Rs' and the Efficiency = < i. . '. ' "... ';' ' . (14) THE PHILOSOPHY OF THE STEAM-EXGrXE. 2Q3 Counter-efficiency, C, is the reciprocal of the efficiency ; Le., The efficiency and the counter-efficiency of a machine, or of any train of mechanism, is the product of the efficiencies or of the counter-efficiencies of the several elements constituting the train transmitting energy from the point at which it is receive t d to that at which the work is done, i.e., from the M driving" to the " working" point. Friction is thus the principal cause, and usually the only cause, of loss of energy and waste of work in machinery. A given amount of energy being expended upon the driving- point in any machine, that amount will, in accordance with the principle of the persistence of energy, be transmitted from piece to piece, from element to element, of the machine or train of mechanism, without diminution, if no permanent dis- tortion takes place and no friction occurs between the several elements of the train, or between those parts and the frame or adjacent objects. Temporary distortion, within the limit of perfect elasticity, causes no waste of energy; permanent distortion, however, causes a loss of energy equal to the total work performed in producing it. But permanent distortion is due to deficiency of strength and defective elasticity, and is never permitted in well-designed machinery properly operated ; and hence the important principle : The only cause of lost work in mechanism, which is to be anticipated in design and calculated upon in deducing the theory of special mechanism, is the friction necessarily conse- quent upon the relative motion of parts in contact and under pressure. The study of the laws of friction, the construction of its theory, and the experimental investigation of the conditions which determine the loss of efficiency in machinery by friction, are thus obviously of supreme importance to the engineer who designs, the mechanic who constructs, and the operator or manufacturer who makes use of machinery. 294 A MANUAL OF THE STEAM-ENGINE. In engineering, therefore, the principles of pure mechan. ism, of theoretical mechanics, and of pure theory in the science of energetics, or of thermodynamics, are to be studied as intro- ductory to a science of application in which all actions and all calculations are to be considered with reference to the modi- fications produced by the wastes of energy and the alteration of the magnitudes and other properties of forces consequent upon the occurrence of friction. This is to the engineer a vitally important branch of applied science, and it is coexten- sive with the applications of mechanical science. The magnitude of the lost work in machinery and mill- work is variable, but is always very large. It may prob- ably be fairly estimated that one half the power expended in the average case, whether in mill or workshop, is wasted in lost work, being consumed in overcoming the friction of lubri- cated surfaces. That this is true, is evident from the fact that the power demanded to drive the machinery of such establish- ments has been found by Cornut and others to be variable to the extent of 15 or 20 per cent by simple change of tempera- ture indoors from summer to winter, and a reduction of 50 per cent in the work lost by friction has often been secured by change of lubricant. Mr. Fairbairn has found a change to the extent of 10 to 15 horse-power in a cotton-mill from the former cause. The friction of shafting in mills varies, with size and load- ing, from 0.33 to 1.5 horse-power per 100 feet (31 m.) length, averaging for the " main line," with good lubrication, about I horse-power. The loss of power in mills ranges, with differ- ent machines, from 5 to 90 per cent, averaging for cotton and flax mills about 60 per cent, with good management, and in woollen mills about 40 per cent, the efficiencies being there- fore about 40 and 60 per cent for the two cases. The friction of heavy iron-working tools maybe taken at about/ =0.15, the efficiency at 0.85. The loss in the steam-engine is usually nearly constant at all powers, and ranges from 4 pounds per square inch (0.27 atmosphere) on smail engines of 25 to 50 horse-power, down to I pound (0.07 atmosphere) in very large marine-engines: this gives efficiencies ranging from 0.84 to 95 THE PHILOSOPHY OF THE STEAM-ENGINE. 295 or 97 per cent. In a "high-speed" engine intended to drive electric lights the Author found the efficiency to be _. . 0.06 Efficiency = i -=j-, in which U is the work done, calling work " at full stroke" unity. Rules for calculating the magnitude of this loss will be given in later chapters. "Absolute" Power is that measured on the indicator-dia- gram, taken down to the line of zero-pressure, that of perfect vacuum. Taking the steam used per horse-power, per hour, on this basis, permits a comparison to be made, irrespective of differences of back-pressure, either in determining the intrinsic merits of different types or of individual engines of the same type. "Nominal" power is that at which the machine is rated. It may represent, as in the now usual rating of boilers, that which the engine may reasonably be expected to produce under usual conditions; or it may, as in old British practice, which assumes a mean effective pressure of 7 pounds per square inch, simply give a clue to the dimensions of the machine; while its actual working power may be several times greater. The British rule for finding the nominal horse-power of an engine is : Multiply the square of the diameter by the speed of the piston, and divide the product by 6000. Thus : Let d = diameter of piston, / = the length of the stroke, = the revolutions per minute. The speed of the piston is = / X 2 X . Area of piston = d* X .7854. Work done per minute = 5 tensity, until the whole system is occupied by the originally existing energy, at a finally uniform and minimum intensity. Energy confined within a limited space thus continually tends to expand, and to break through its boundaries, and, if not freed from this constraint, it produces a pressure upon the sur- rounding surfaces, which, e.g., is exhibited as tension of en- closed vapors and gases. Freed from confinement, it tends to indefinitely expand. Either form of energy may produce either other form under suitable conditions. Rankine's statement of the ** General Law of the Transfor- mation of Energy" is as follows: * " The effect of the whole actual energy present in a sub- stance, in causing transformation of energy, is the sum of the effects of all its parts." The ajciom, as Rankine calls it, that " any kind of energy may be made the means of performing any land of work" is derived by " induction from experiment and observation." and confirmed by all experience. The science of energetics may be based either upon this principle, so derived, or. probably better, upon the fundamental law stated as underlying all ex- istences : although the latter has, after all, the same basis. The science is one of which, as its great student has said, the subjects are boundless ; and never can, by human labors, be exhausted, nor the science brought to perfection. Professor Balfour Stewart considered the universe to be "composed of atoms with some sort of medium between them as the machine, and the laws of energy as the laws of working of this machine." The Sources of Energy are : (i) Potential: ia) fuel; (S) food : if) head of water ; (, (i) and the value of H can be determined by integration when the method and the rate of variation of heat and the Thermody- namic Function are known. Since, in any case, the quantity of heat, Q, is known to be proportional to the absolute temperature, T, it follows, also, that dH Td, (2) and the value of H can be obtained when (f> is known in terms of T and of constants, or of other independent variables so ex- pressed as to make the above equation integrable. This ex- pression, the basis of the whole theory of heat-engines, shows that the amount of energy transformed is measured by the product of the absolute temperatures of transformation into some function of the changes of condition of the working sub- stance. This Second Law is also more generally expressed by Ran- kine as follows :* If the total actual heat of a homogeneous and * Steam-engine; p. 306. THERMODYNAMICS OF THE IDEAL E \GI\E. $\7 uniformly hot substance be contrived to be divided into any num- ber of equal parts, the effects of those parts in causing uvrk to be performed are equal. This law is one case of a general law ap- plicable to every kind of actual energy ; that is, of capacity for performing work, constituted by a certain condition of each particle of a substance, how small soever, independently of the presence of other particles. The symbolical expression of the Second Law of Thermodynamics is given as follows : Let unity of weight of a homogeneous substance, possessing the actual heat Q, undergo any indefinitely small change, so as to perform the indefinitely small amount of work dU. It is required to find how much work is performed by the disappearance of heat. Conceive Q to be divided into an indefinite number of indefinitely small equal parts, each of which is SQ. Each of those parts will cause to be performed the quantity of work represented by consequently the quantity of work performed by the disap- pearance of heat will be V=Q.*U. or = which quantity is known when Q, and the law of variation of 4?Cf with Q, are known. From the mutual proportionality of actual heat and abso- lute temperature, there follows The Second Law of ThermodynamicSj expressed with ref- erence to absolute temperature. If the absolute temperature of any uniformly hot substance be divided into any number of equal farts, the effects of those parts in causing work to be performed are equal. This law is expressed algebraically as follows : From the t relation between absolute temperature (r) and actual heat (0 it follows that L-Q. dr~ dQ' 318 A MANUAL OF THE STEAM-ENGINE. consequently the expression above, for the work performed by the disappearance of heat, is transformed into U_ _ r_ dU ~ ~dr The first and second laws constitute the basis of the Theory of Thermodynamics. Rankine has shown that the second law must follow from the hypothesis that "sensible heat consists of any kind of steady, molecular motion within limited space ;" and it is now considered as well established, both that heat does consist of such molecular motion, and that the second law is correct. The magnitude of heat-energy must thus be proportioned to the weight of matter 'affected by it, and to the mean square of the velocity of molecular motion. Absolute temperature, prop- erly defined, is proportional to the actual molecular energy of the matter so affected ; and it thus again follows that any con- version of such energy, during any change in the dimensions of the space enclosing it, is proportional to the absolute tem- perature.* Clausius' enunciation of this law is as follows : f " The work which heat is capable of performing, in any variation of the arrangement of parts of any body, is proportional to the abso- lute temperature at which such change occurs." This law evidently asserts the independence of the quantity of work done and the nature of the "working substance;" and it may be taken as a corollary that When, in any heat-engine tracing a cycle, the working sub- stance operates between two fixed temperatures, the work done, or the energy produced, is precisely proportional to the quantity of heat transmitted from the source of heat to the refrigerator, without regard to the nature of the substance adopted as its vehicle as shown by Carnot in 1824. *See Rankine, "On the Second Law of Thermodynamics ;" Trans. Brit. Assoc., 1865; Phil. Mag., Oct. 1865. f Poggendorff's Annalen, 1862. THERMODYNAMICS OF THE IDEAL ENGINE. 319 This was demonstrated by Clausius, who made the princi- ple '* it is impossible for heat to pass, of itself, from a colder to a warmer body" the basis of his argument. Thus, of the whole quantity of heat passing from the heater to the working substance, one part is always transmuted into mechanical work, or energy ; while the remainder goes to the refrigerator, and the ratio of the one quantity to the other is perfectly definite. Professor Wood expresses this law thus : " If all the heat absorbed be at one temperature, and that rejected be at one lower temperature, then will the heat which is transmuted into work be to the entire heat absorbed in the same ratio as the difference between the absolute temperatures of source and refrigerator is to the absolute temperature of the source."* 85. The Steam-engine illustrates the Second Law, both in its operation as a whole and in the details of energy- transformation going on in its inner workings. Not only is it true that two perfect engines, of different power, working under the same thermodynamic conditions perform work by the con- version of precisely proportional quantities of heat ; but it is also true that the work-effect of heat at any instant, in the midst of the steam so doing work by its expansion, is proportional to the quantity of heat at that instant there present and taking its part in the thermodynamic action of the fluid. As will be seen, however, presently, the second law finds important application simply in enabling us to ascertain the total quantity of work, external and internal, required to pro- duce changes of volume and energy in fluids, like the vapors, in which we cannot measure directly the internal forces and internal work. 86. General Algebraic Expressions for Thermodynamic Changes of Energy may be readily deduced directly from the First Law of Thermodynamics. Since only transfers of heat and transformations into mechanical energy, actual or poten- * Thermodynamics, 40. 32O A MANUAL OF THE STEAM-ENGINE. tial, are considered, assuming any small variation of heat, dH, measured dynamically, to take place, producing variations of the physical state of any substance ; if the change of sensible heat be called dS, that of " latent " heat. dL, and of external work, dU, then the first law of thermodynamics is expressed by the equations : dff=dS+dL + dU, (A) and ....... (E) . (C) where, in the last two expressions, dE = dS -\- dL, and is the variation of energy, actual and potential ; while dW '= dL -\- dU, and is the total work done, externally and internally. These are primary and general equations. The quantity E is often called the intrinsic energy of the substance ; L is evidently a potential energy ; while S is a form of molecular kinetic, or actual, energy, which may sometimes be regarded as also in a sense potential. The above are completely general expressions of the GEN- ERAL FUNDAMENTAL EQUATION OF THERMODYNAMICS. It will be observed, however, that, while the law enables us to say that, a given amount of work, dU, being done, and a known quantity of sensible heat, dS, being transferred from the source without transformation, the total quantity of heat demanded for the two changes, occurring simultaneously or successively, will be precisely the sum of the thermal equiva- lent of the first and the thermal measure of the second ; that law does not enable us to say what, in any given case of heat-expenditure, will be the method of distribution of energy in the two forms, or the magnitude of either of the two parts into which it is thus divided. We must evidently find a way of determining dU\ and this, when it includes internal work, may be impracticable, as a matter of observation and direct measurement. It is this subsidiary problem which the second law is called in to solve. THERMODYNAMICS OF THE IDEAL ENGIXE. 321 87. The Relations of the Two Laws of Thermodynamics to the theory of thermodynamic operations and heat-engines are now readily defined. The First Law states that, wherever thermal and mechanical energies are converted, the one into the other, such conversion takes place in the proportion of one thermal unit to each " mechanical equivalent," as previously defined : while the Second Law asserts that, during such conver- sion, whatever proportion of the thermal energy present may be so converted, that proportion is equal to the product of the quantity of heat, or of the absolute temperature, into another factor, the form and magnitude of which are determined by other physical conditions. The first law gives no clue to the method of transformation, and no measure of the total quan- tity of energy transformed in any case ; it simply asserts that so much heat-energy as is converted into the other form is so transmuted with a definite quantivalence. The second law, while merely asserting that the quantity transformed is propor- tional to the total heat present, and to the absolute tempera- ture at which transformation takes place, enables a determina- tion to be made, by its combination with the first law, of the actual quantity of energy so changing form. The first law enables us to construct the second equation of thermodynamics ; the second law, as will be more fully shown later, gives the form and value of its second term. Thus heat, from whatever source derived, once stored within any mass of working substance, becomes subject to these two laws ; and while the first law determines what amount of mechanical en- ergy may be produced per unit of heat-energy transformed, the second law prescribes both the proportion of the total stored heat which, under the given conditions, maybe so transformed, and the proportion of utilized to unutilized heat. A reservoir containing any given amount of heat-energy, no additional amount can be transferred into it, except it be heat of higher temperature ; and, once the added energy enters the reservoir, it cannot be again removed as a distinct quantity of heat of high temperature, but becomes a part of the whole stock of energy, and, in common with the original store, becomes sub- 322 A MANUAL OF THE STEAM-ENGINE. ject, unqualifiedly, to the second law of thermodynamics, in all operations involving transformation. 88. The Thermodynamics of the Constitution of Mat- ter and its physical and chemical changes must be considered before the heat-engines can be intelligently studied ; since, in all of them, variations of temperatures, pressures, and volumes of one or another form of "working fluid " constitute the pro- cess of their action. The physical state of matter is determined by the intensity of internal forces and by the quantity of internal heat, i.e., of heat-energy present in the mass, and it varies as transfer takes place to it or from it by communication with external bodies. The intrinsic energy of the solid body is a form of potential energy, or energy of position ; equilibrium being maintained by the adjustment of volume to temperature, and this energy being developed as kinetic, or in the production of work, as temperature and the stock of sensible heat are reduced. The same is true of liquids, which, however, have a larger stock of molecular, potential, energy, and have, by expansion, lost sta- bility of form. The change of state, traced further, passes through that of the vapors and of the permanent gases, and finally is exhibited the condition of the perfect gas, in which equilibrium exists between external confining pressures and the total tension due the pressure of heat-energy ; in which, also, no internal condensing forces are observable. In the lat- ter case the total heat-energy is exactly proportional to the absolute temperature, and is measured by the continued prod- uct of weight, real specific heat, and absolute temperature. 89. Solids, Liquids, and Gases constitute the three forms of matter into which all kinds are classed. The exact structure and constitution of matter are well understood only so far as the senses, aided by physical apparatus, can observe it ; of its ulti- mate nature nothing is known. So far as our knowledge goes, all forms may be assigned to one or another of three classes. All known kinds of matter are probably capable of taking, under different conditions, definite for each case, either of these forms. Nearly all known liquids, for example, under certain THERMODYNAMICS OF THE IDEAL ENGINE. 323 definite conditions of temperature and pressure, may be solidi- fied, or may be vaporized ; solids are liquefied and vaporized by elevation of temperature ; and all familiar gases may be liquefied, and have even been solidified, by subjecting them to pressure and, at the same time, reducing their temperature. All matter, so far as is known, may be considered as con- sisting of an aggregation of collections of "atoms," or particles, which collections are called molecules, separated by intermo- lecular spaces of greater or less extent, attracting each other with a force which is dependent upon the nature of the substance, and upon its volume, and yet held apart by repellent forces, which seem, usually, to have an intensity dependent principally upon temperature, and may probably be due solely, and in all cases, to the heat-energy present, stored m the substance. The attractive forces are considered to be of two kinds, the one purely attractive, the other giving permanence of form ; the first is the force of " cohesion," the second that of " polarity." ox). Solids have stability both of form and of volume, re- sisting every attempt to alter either; liquids are stable as to volume, but destitute of stability of form ; gases have no sta- bility either of form or volume ; and, at all measurable tem- peratures, constantly tend to indefinite diffusion throughout space. Solids have molecules bound together by cohesive attraction, and held in definite relations of position by polarity ; in liquids polarity becomes unobservable ; in gases only the repellent forces are seen, and equilibrium between attraction and repulsion of molecules can no longer exist. In the passage from one state to another, in many cases, mat- ter passes through intermediate states, solids becoming viscous when liquefying, and liquids becoming imperfectly gaseous be- fore fairly attaining the perfectly gaseous state. The perfect gas is absolutely free from the influence of attractive molecular forces. All known gases are more or less imperfect ; but a few, as oxygen, hydrogen, nitrogen, in their ordinary conditions, may. for all purposes of the engineer, be considered perfect. The Fusing and Boiling Points, or the freezing and liquefy ing temperatures, are, as already stated, fixed for each fluid for 324 A MANUAL OF THE STEAM-ENGINE. every pressure, but variable with change of pressure. Increased pressure usually increases the former and always elevates the latter. An exception, in the case of ice, for example, is seen when fusion is accompanied by contraction ; the melting-point is lowered, in such cases, by increase of pressure. The pressure /> at which the boiling-point becomes a given temperature, T, on the absolute srale is very exactly given, for several liquids, by a formula constructed by Rankine* to represent Regnault's experiments : com. log p = A -^ ; . . . . (i) and, for the reverse determination, T= , , (2) C ' 4TV 2 C in which, for the Fahrenheit scale and pressures in pounds on the square foot, the several quantities are : A log B logC j Water 8.2591 3.43642 5.59873 0003441 0.00001184 Alcohol 7.9707 3.31233 5.75323 0.001812 0.00003282 Ether 7-5732 3.31492 5.21706 0.006264 0.00003924 Carbon disulphide 7-3438 3.30728 5.21839 0.006136 0.00003765 Regnault's own formula, as adapted to the Centigrade scale and to pressures in millimetres of mercury, for temperatures, /, exceeding 100 C., is as follows : logp = a bo? c/3 x , (3) in which x=.t m -\- 20, and a 6.2640348; log b = 0.1397743 ; log a = 9.994049292 10 ; " c = 0.6924351. " ft = 9-998343862 - 10 ; * Philosophical Magazine; 1854. THERMODYNAMICS OF THE IDEAL ENGIXE. $2$ For temperatures between the freezing and boiling points, logp = a -j- bet c& t in which, as corrected by Moritz,* a= 4-7393707; kg = 8.13199071 12 10 ; log a 0.0x368649371 52 ; " c = o/5 1 17407675. " ft = 9-996725536856- 10 ; The temperatures of fusion of metals and those of fusion and of boiling of other substances are given in works on physics and on special materials. The " luminiferous ether "which apparently pervades all space, and which transmits light and heat to us from the sun, is a gas of such exceeding tenuity that it opposes no meas- urable resistance to the bodies of the solar system and of the universe, and is of such slight density and high elasticity as to transmit vibrations with nearly two hundred and fifty thousand times the velocity of those traversing hydrogen gas ; it has therefore one five-hundredth the density of any hydrogen which may exist in the interstellar spaces. The Kinetic Theory of Matter is now generally accepted by men of science. According to this theory, a gas consists of a collection of molecules, simple or complex, which are in ex- tremely rapid motion, and which intermingle freely, coming into collision with each other,t and with the confining surfaces, with a violence which depends upon their velocities ; which velocities, in turn, are determined by the temperature of the mass. The intermolecular spaces, and therefore the free paths of the molecules, are of comparatively great extent. In liquids, the free paths of the molecules become very greatly restricted by the action of now measurable attractive forces; and in solids, in consequence of the confining action of cohesion and of polarity, brought into play by the condensation marking the * Clausios. f Boltzmann suggests that collisions may be rare, if not absolutely impos- sible, the molecules swinging about each other in hyperbolic, comet-like orbits, without contact. 326 A MANUAL OF THE STEAM-ENGINE, further change from the liquid state, the particles can only vi. brate about a fixed point without change of mean position rela- tively to adjacent particles. The state, or the form, of matter is thus determined by the action of forces external and internal. The intensity of inter- nal attractive and repulsive forces, and of external pressure, determines whether a substance may exist in the liquid or the gaseous condition, and the action of polarity produces when the particles are brought closely together, the solid state ; while rise in temperature, by modifying the intensity of the molecu- lar forces and separating molecules, causes the solid to pass through the pasty and viscous condition, and to become liquid at higher temperatures ; it then vaporizes, and finally becomes gaseous, in consequence of separation of particles by the repul- sion produced by heat-motion. The size of the molecule is probably always the same in the same kind of matter ; but different in different substances. Sir William Thomson estimates a molecule of glass as probably less than one twenty-five millionth and more than one two hundred and fifty millionth of an inch in diameter (less than ioolooo and more than TFsVtrFor millimetre). He states that, were a drop of water as large as a pea magnified to the size of the earth, its molecules would then appear to be, in size, be- tween that of a small leaden shot and that of a cricket-ball.* He calculates the number of molecules present in a cubic inch of any perfect gas at atmospheric pressure, and at the freezing point in temperature, to be 10", or one hundred thousand mil- lion million million. According to Avogadro's law, this number is the same for all perfect gases. Plateau f concludes, from experiments made by him upon the tenuity of liquid bubbles, that the radius of molecular at- traction is less than one seven-hundredth of an inch (i milli- metre). WartmannJ makes the range still less. Robison had * Nature; 1870. Silliman's Journal of Science and Art; July 1870. f Smithsonian Report; 1856. j Trans. Soc. Geneva; 1862. THERMODYNAMICS OF THE IDEAL ENGINE. $2? long before * inferred, from experiments with Newton's rings, that the effect of pressure is observable before actual contact, at a distance of about one five-thousandth of an inch (y^ millimetre), and Powell t detects this action at one eleven-hun- dredth of an inch (^ millimetre). 90. Internal and External Work, when change of physi- cal state occurs, are always the immediate cause of change of volume and molecular arrangement. As this alteration of con- dition involves, internally, the application of force to overcom- ing atomic or molecular resistance, or the reverse, with altera- tion of volume, work is consumed or is developed in the process, and an equivalent amount of energy is transformed into, or out of, work. Work so done is entirely independent of external forces and conditions, and its amount is a function, solely, of the forces acting, and of the spaces traversed, or of the altera- tion of volume incident to the physical changes occurring. Such work is called Internal Work, and energy operating in this manner is known as Internal Energy. Changes of volume occurring in any mass, in the presence of other substances, involve the overcoming of external pres- sure, or are facilitated, to some extent, by the action of exter- nal forces. This is equivalent to the production, or to the consumption, of a certain amount of work, which is known as External Work. Energy may thus be expended in the production of either internal or external work, or both ; and, on the other hand, in- ternal energy may be transformed into external work ; or the reverse operation may take place. The amount of external work so performed is evidently de- termined by the magnitude of the change of volume, and by the intensity of external pressures, solely, and is thus not necessarily dependent upon internal conditions. An equation involving both internal and external work, or energy, is evi- dently an equation involving two independent variables. Mechanical Philosophy; voL L f Phil. Trans.; 1834. 328 A MANUAL OF THE STEAM-ENGINE. Thus> when steam, air, or gas expands behind the piston of a heat-engine, the internal work done is measured by the product of the mean intensity of molecular attraction into the change of volume occurring; and this quantity may be much greater than the external work ; in the case of steam, it far ex- ceeds the external work done in driving the piston ; its amount is comparatively small, and is very difficult to measure, in the case of air, and it becomes indefinitely small in the case of the perfect gas ; it is a function of volumes, and of molecular forces. The external work is measured by the product of the mean intensity of pressure on the piston by the volume trav- ersed, and is limited by the resistance to the motion of the piston on the one hand, and by the intensity of molecular re- pulsion on the other. An equilibrium always exists between this latter force and the sum of internal attractive and exter- nal compressive forces. When the fluid expands freely into a vacuum, evidently no external work is done. External work is usually ultimately converted, through mechanical energy, into heat. The Internal Energy of a body is the potential energy, or the capacity to do work, possessed in virtue of the existence of internal repulsive force. The potential energy of a mass ca- pable of condensation under the action of internal attractive forces is another similar and equally important form of energy. Rotational Motion evidently can only be produced or de- stroyed in a fluid by the action of a force which may be de- nominated internal friction, or molecular friction ; hence, such motion cannot exist in a perfect fluid, or, if existing, may be neglected, as being invariable, and need not be taken into ac- count in any accepted theory. 91. Heat, denned and measured, as a Form of Energy, constitutes the principal subject of treatment in the branch of applied physics here studied. The term heat may be used in either of the two senses ; it may represent the sensation due to that physical action which has been described, or it may mean that phenomenon itself. It is in the latter of these two senses that the term is here used ; and heat is to be here con- THERMODYNAMICS OP THE IDEAL ENGINE. 329 sidered only as a form of the energy of molecular motion, or vibration, capable of transfer from one body to another, and of transformation into other forms of energy. In its measure- ment, it is necessary to consider two magnitudes, the one defining intensity, the other its quantity. Since any given amount of energy may exist, whatever its form, either as the energy of a small quantity of matter in rapid motion, or as that of a larger quantity in less violent motion, the rate of heat- motion, and the consequent "intensity" of the heat, must be observed, as well as the quantity. Since heat is energy, and since it is measured by the pro- duct of the mass of matter pervaded by it into its intensity of Wtf action, i.e., by the quantity \Mtf = , it is evident that, whether it pervades one substance or another, and whatever the mode of transfer, the quantity of heat-energy is the same, when the same work is done, or the same kinetic energy is present, and that it is entirely independent of the nature of the substance, having the weight W, or the mass M, and the mo- lecular velocity v, which simply serves as its vehicle. The Physical Effects of Heat, as a form of energy intro- duced into matter, are seen in several distinct classes of phe- nomena : (1) The temperature of the substance rises, the sensation of heat, produced upon the nerves of touch by contact with the body, is intensified, and the tendency to transfer heat to adja- cent bodies is increased. (2) The elasticity of volume of the substance is increased, and its stability of form is decreased. (3) The substance is given increased volume, and, reaching certain definite points in the scale of temperature, is caused to change its physical state, as from solid to liquid, or from the liquid to the gaseous form. (4) External work is performed, i.e., work is done against forces affecting the mass from without. 330 A MANUAL OF THE STEAM-ENGINE. (5) As a secondary effect, the chemical composition of bodies is often altered, elements uniting more readily to form compounds, and compounds changing their constitution, some- times at fixed, sometimes at variable, temperatures; combina- tion being, within certain limits, usually, but not always, accel- erated by increase of temperature. Dissociation sometimes occurs. Reversal of the phenomenon, causing a reversal in the direction of movement of heat, produces heat where it had been expended, and decreases temperature where increase had previously taken place. Dynamically, the effects of transfer of heat are : (1) Change of temperature ; i.e., variation of sensible heat- energy, or of the kinetic energy of molecular motion. (2) Performance of internal work; i.e. : (a) Molecular work, which is often considered to include the preceding. (b) Intermolecular work ; i.e., work done against molecular cohesion, or other attractive forces. (c) Interatomic work ; or similar work done within the mo- lecular, and against the chemical, forces. Temperature measures the intensity of heat and its tendency to transfer itself to surrounding bodies. When two bodies are at the same temperature, they exhibit no tendency to change by transfer of heat from one to the other. Whenever two bodies are brought together, heat is exchanged between them, the hotter yielding to the colder more than it receives from the latter, until they attain a state of common and uniform tem- perature at which the flow of heat ceases, each receiving pre- cisely as much as it loses. The higher the temperature of any body the greater the tendency to expand, and the greater its elasticity of volume, and the less its elasticity and stability of form ; and the colder the mass the more marked the opposite qualities. Two dissimilar substances, however, do not exhibit, usually, the same elasticities at the same temperatures. Temperatures are usually measured by means of thermome- ters of which the scales are conventional, and often differ in THERMODYNAMICS OF THE IDEAL EXGIXE. 33! different instruments. Standard temperatures are so chosen that they may be easily identified and that comparison may be readily effected. The temperature of fusion of ice and the boiling-point of pure water, under mean barometric pressure at the sea-level, are universally accepted standards, and are readily determined and are invariable. The scale of the Centigrade thermometer is constructed by dividing the space between these two temperatures into 100 degrees, the lower point being made the zero. The Fahrenheit scale is thus divided to 180 degrees, and the lower reference-point is called 32. To trans- form these scales, the one to the other, we have ....... (2) in which C and F represent the readings of a common tem- perature on the Centigrade and Fahrenheit scales, respectively. The Absolute Scale of Temperature is constructed on the assumption that its zero represents the real zero of heat-energy, that point at which either the pressure of a perfect gas retained at constant volume, the volume of such a gas under constant pressure, or the product of pressure and volume, when both are variable, will vanish by complete abstraction of heat. Experi- ment shows that the ratio of / O r , this product at the melting- point of ice, to/,1", , the magnitude of the same product at the boiling-point, as above, is, for nearly perfect gases, = i^6i' neariy ' (3) and A g A*V 0-36$ -*= (4) If the difference p,v t pj> 9 corresponds to lotf, as on the Centigrade scale, we have, for the absolute scale, 7\ p t v t o 1-365 * 332 A MANUAL OF THE STEAM-ENGINE. and the temperatures T Q and T l will have the relation T, - r. _ 0.365 A".. _ I^T, _ 100 _ ~ 0.365 ~ 274 For the Fahrenheit division, T, - T 1 80 (7) Generally, any temperature, /, on the common scale, may be determined from the expressioa t >-* -'- 0.365" pv P O V Q . , = 274 , Centigrade ; \ - (9) = 493 *" Jt * " -, Fahrenheit, j pv p v The Absolute Zero is thus found at -274C, or -(493.2-32) = -461 .2 F. . (10) The freezing and boiling points, on the absolute scale, are thus found at -J- 274 C., or -|- 493 F., and at -|- 374 C, or The absolute zero has never been reached experimentally, and its existence and its location on the scale of temperature have only been determined by theory, based upon the now universally recognized laws of transfer of heat-energy. The exact value of the coefficient of expansion for the perfect gas is not known with absolute correctness. It was made 0.3646 to 0.3648 by Rudberg, for air, between the freezing and boiling points, and by Regnault 0.3665 to 0.3670. Rankine assumes THERMODYNAMICS OF THE IDEAL ENGINE. 333 that the perfect gas would give, approximately, 0.365, as above. Taking Regnault's value for air at constant volume, 0.3665 = ^J-y, as is often done, the absolute zero would be found at 459 F., or 272. 9 C., instead of 461 .2 F., or 274 C. The freezing and boiling points, on the absolute scale, then become respectively -j- 49i-4 F., or -}- 273 C., and -f 671^ F., or -f 373 C., instead of -f 493.2 F., or + 274 C., and -f- 673.2 F., or -j- 374 C. The second set of figures are obtained on the assumption that the values for air and the perfect gas are substantially the same, and both sets on the hypothesis that the coefficient remains constant throughout the scale.* 92. Quantity of Heat is thus seen to be entirely distinct from temperature, and is measured by an essentially different unit. Heat as a form of energy and the equivalent of the work, of whatever kind, expended in producing that energy, may evidently be measured by any unit of energy. But any unit of energy is a product of two factors, the one measuring a force, the other a space traversed under the action of that force. Quantity of heat, therefore, is a quantity of energy and it may be similarly measured, by either of the familiar measures of energy, or by its own peculiar unit. The Thermal Unit, or unit of heat-energy, is that invariable quantity of heat which is found to be required to raise the temperature of unity in weight of water one degree in tem- perature when at the lower standard temperature at o Centi- grade, or 32 Fahrenheit. The British Thermal Unit is the heat so required when the unit of weight is the pound, and the scale Fahrenheit ; the Metric Thermal Unit, or Calorie, meas- ured that demanded to heat one kilogramme of water from o C. to i C. Rankine and Maxwell take this quantity at the temperature of maximum density ; but for the purposes of this * Professor Holman concludes that, as the absolute zero is approached, the value of this coefficient approximates a = Cent., or a = Fahr. 334 A MANUAL OF THE STEAM-ENGINE. work the two measures are taken as substantially equal ; they are sensibly the same. Calling the quantity of heat, in any case, measured in British units, Q, and in metric units, Q mi Q = 3.968320,; & = 0.25 1996 <2; log Q = log Q m -fa 5986065 ; log Q m log Q + 14013935. The magnitude of the thermal unit is necessarily invariable ; and the number of thermal units required to produce any given change of temperature in any substance usually increases slightly as that range is higher on the scale of temperatures. Heat is often, especially in applied thermodynamics, most conveniently measured in mechanical units. The determina- tion of the magnitude of the " mechanical equivalent of heat" has been made by processes which involve a comparison of these units both by transformation of mechanical energy into heat and by the reverse operation, but usually by the former method. Calorimeters are instruments constructed for the purpose of Calorimetry, or heat-measurement. They are of various forms, but that principally used in physical and engineering researches consists of an apparatus containing water and fitted with thermometers and scales for measuring variations of tem- perature and quantities of water. The quantity of heat pass- ing into the instrument becomes determinable when the quan- tity of water flowing through it and its variation of tempera- ture become known. It is sometimes convenient to measure the volume, rather than the weight, of water. In this case, the density must be known to permit the calculation of the weight of the liquid. Volkmann has compiled the results of the experiments of Hagen, Matthiessen, Pierre, Kopp, and Jolly, on the expansion of water, and has obtained the following mean results for the volume and density of water at various temperatures on the Centigrade scale : THERMODYNAMICS OF THE IDEAL ENGINE. 335 Tem f Odeg I 2 3 4 5 6 7 : 9 10 I Volume. T C .. ..I OOOI22 Density. 5.999878 >-999933 .999972 -999993 .OOOOOO .999992 .999969 999933 19988s .999819 >.QQQ7iQ Temp. 1 15 dcgr. C Volume. .000847 .001731 .002868 .004250 .007700 .011970 .016940 .022610 .028910 -035740 -04-52-W 20 " 2= ** 30 60 " .... 80 " I OOOlSl ...1.000261 < 100 " The law governing the expansion of water is very exactly expressed by a simple form of equation. Buel has thus calcu- lated in British units the following table, following Watt :* the figures agree with the above to the third place of decimals. VOLUME AND WEIGHT OF DISTILLED WATER AT DIFFERENT TEMPERATURES ON THE FAHRENHEIT SCALE. Temper- ature, iUn ;-.=.-.. Ratio of volume to vol- ume of equal weight at the temperature of maxi- m_~ -er.~::v. Difference. Weight of a cubic foot in pounds. Differ, ence. 32= 39 -2 40 50 60 70 8o e 90* 100 no* 120* .000129 .OOOOOO .000004 .000253 .000020 .001981 .00332 .00492 .00686 .00902 .01143 .OOOI29 .000004 .000249 .000676 .001052 .001339 .00160 00194 .00216 .00241 OO263 62.417 62.425 62.423 62.409 62.367 62.302 02.213 62.119 62.000 61.867 61.720 .OOS .OO2 .014 .042 .065 .084 099 .119 133 .147 ifii 130 140' I5o v 160 170 180* ioo : 200 = 2IO = 2I2 C 220 230= 240" .01411 .01690 .01095 .02324 .02671 1-03033 1.03411 .03807 .04226 .04312 .04668 .05142 -05633 .00279 -00305 .00329 .00347 .00362 .00378 .00396 .00419 .OOOS6 .00356 -00474 .00491 61.556 61.388 61.204 61.007 6o.8oi 60.587 60.366 60.136 59-394 59.707 59-041 59-372 59.096) .168 .184 .197 .206 214 .221 .230 .242 .I3 7 .066 .269 .276 * Watt's Dictionary of Chemistry; art. H ii. p. 113. Weisbach's Mechanics; vol. 336 A MANUAL OF THE STEAM-ENGINE. Temper- ature, Fahren- heit. Ratio of volume to vol- ume of equal weight at the temperature of maxi- mum density. Difference. Weight of a cubic foot in pounds. Differ- ence. 250 .06144 .00511 58.812 .284 26o .06679 00535 58.517 .295 270 .0/233 00554 58.214 303 280 .07809 .00576 57-903 .311 290 .08405 .00596 57.585 .318 300 .09023 .00618 57-259 .326 310 .09661 .00638 56.925 334 320 . 10323 .00662 56.584 341 330 .IIOO5 .00682 56.236 348 340 .11706 .00701 55-883 353 350 .12431 .00725 55-523 360 360 I3I75 .00744 55-I58 .365 370 13942 .00767 54-787 371 380 14729 .00787 54-4H 376 390 15538 .00809 54.030 .381 400 . 16366 .00828 53-645 385 410 . 17218 .00852 53-255 390 420 .18090 .00872 52.862 393 430 .18982 .00892 52-466 .396 440 .19898 .00916 52.065 .401 450 .20833 00935 51.662 403 460 .21790 .00957 51.256 .406 470 .22767 .00977 50.848 .408 480 23766 .00999 50.438 .410 490 .24785 .01019 50.026 .412 500 .25828 .01043 49.611 415 5io . 26892 .01064 49-195 .416 520 27975 .01083 48.778 .417 530 .29080 .01105 48.360 .418 540 30204 .01124 47-941 .419 550 31354 .01150 47.521 .420 93. The Specific Heat, or capacity for heat, of any sub- stance is the ratio of the quantity of heat required to raise the temperature of any given weight one degree, under specified conditions, to the amount demanded to raise the temperature of an equal weight of water one degree when at the lower of the two fixed standards of temperature usually taken as that of melting ice, or the "freezing-point." The specific heat of any substance thus determines what rise or fall of temperature will follow the introduction, or the abstraction, of any given amount of heat. Specific heats are of several kinds. The real specific heat of any substance measures the quantity of heat producing altera- tion of temperature, simply. Apparent specific heat measures THERMODYNAMICS OF THE IDEAL ENGINE. 337 that demanded to produce variation of temperatures, accom- panying other physical changes involving transformations of heat-energy. When these specific heats are measured in me- chanical units of energy, they are sometimes called, as by Ran- kine, "dynamical specific heats" real or apparent, as the case may be. The specific heat of constant volume measures the quan- tity of heat required to produce alteration of temperature without variation of volume. The specific heat of constant pressure is an " apparent " specific heat, and determines the amount of heat demanded to cause variation of temperature in masses of fluid under invariable pressure. In the former of these two cases the specific heat is probably always identical with the real specific heat ; in the latter, the specific heat, which is an apparent specific heat, and the heat transferred, includes a part which does not affect the temperature of the mass, but is essential to operations involving transformations of energy from one form to another. Either form of specific heat may be taken as the quantity of heat, in thermal units, producing a variation of the tempera- ture of unity in weight, of the given substance, one degree, under specified conditions. It is most convenient to make the temperature of maximum density of water (39. I F., or 3.9 C.) the standard. Rankine gives* the following expressions for the specific heat of water : c= i + o.ooo ooo 309 (/ 39.1)'; (Fahr.) . . (i) c m = i + o.ooo ooi (t 3.94)*; (Cent.). ... (2) The total heat, in thermal units, demanded to raise the tem- perature of unity of weight from to / to /, is h =f t -f i J r 0.000 ooo 103 [ (/, - 39-1 >' - (/, - 39-1)'] : (3) =/,-*, +0.000 ooo 33 [ (', - 4)' - (>, - 4)*]. ... (4) The specific heat, c, as determined by experiment is obvi- ously wt Steam-engine ; p. 246. 338 A MANUAL OF THE STEAM-ENGINE. in which w and zv t are the weights of the given substance, and of water, or other standard, used in the experiment, and / and ^ are the ranges of temperature where cooling is performed by the immersion of the given body in that weight of water. The specific heats of solids and liquids are usually so nearly the same, for constant volume and for constant pressure, that the figures are usually given for their capacity for heat without reference to these conditions ; these differences are rarely, if ever, measurable.* It was discovered by Dulong and Petit that, in certain groups, the product of the specific heat of substances and the combining weight is the same for the whole group. This product, for elementary substances, is usually not far from 6.5. Thus we have, calling the real specific heat c,, 64 . c _ = : .~T~> nearly. atomic weight The specific heats of alloys are obtained by multiplying the weight of each constituent by its percentage in the alloy, add these products and divide by 100. Regnault finds that the specific heats of alloys far removed from their fusing-points are the means of the specific heats of their constituents. Dulong and Petit found the specific heat of iron to increase from a mean of 0.1098 between the freezing and boiling points of water and 0.1255 for a range increasing up to 662 F. (350 C). Copper similarly increased from 0.0927 to 0.1013, and zinc from 0.0927 to 0.1015, platinum from 0.0335 to 0.0343 and to 0.03818 at 2192 F. (1400 C.). Holman, finds for the latter,f c = 0.03284-0.00000 3022 (/ 32)4-0.000000000009 (/ 32)"; = 0.0328 + 0.00000 544 /, 4- 0.000000000016 /" . . . (5) * See Constants of Nature, Part II ; Clarke ; Government Print, f Journal Franklin Institute ; Aug. 1882. THERMODYNAMICS OF THE IDEAL ENGINE. 339 for the Fahrenheit and Centigrade scales, respectively. For iron he obtains c 0.10687 4- 0.0000304 (/ 32) -f- 0.0000000238 (/ 32)*; = 0.10687 + 0.0000547 / -|- 0.0000000428 /' (6) The law of Dulong and Petit is equivalent to the statement that the quantity of heat demanded to raise the temperature of an atom of any simple substance, in the solid state, one de- gree is the same for all such elements ; and Neumann's law asserts that all compound solid substances of similar chemical construction require the same quantity of heat per atom, but that this amount is less than for the isolated elements. The specific heat of elementary solids is greater than that of com- pound solids. Woestyn and Gamier find that the specific heat of molecules is equal to the sum of the specific heats of their constituent atoms, a conclusion partly confirmed by Keep. Marked exceptions are noted, however, and Thomson and Tait* enunciate the principle that if a system of material points are acted upon by impulsive forces, more kinetic energy is gen- erated when they are free than when in combination. The following table, mainly from Dulong and Petit and from Pouillet, gives the specific heats of a large number of solids and liquids. SPECIFIC HEATS OF SOLIDS AND LIQUIDS. Alcohol (liquid) 0.61500 J Chalk 0.21485 Charcoal 0.24150 Chloride of barium 0.89570 " " calcium 0.16420 " lead 006641 ' magnesium 0.19460 " " manganese 0.14250 " " strontium 0.11990 " " zinc 0.13618 Cobalt 0.10696 Copper o . 095 15 Corundum 0.19762 Aluminium 0.21430 Ammonia (a vapor). 0.50830 Anthracite coal 0.20100 Antimony 0.05077 Arsenic 0.08140 Benzine 0.45000 Bismuth (solid) 0.03084 .0.03630 Bituminous coal 0.20085 Brass 0.09391 Bromine (liquid) 0. 10700 * Nat. Phil.; 315. 340 A MANUAL OF THE STEAM-ENGINE. Diamond o. 14687 Ether (liquid) 0.50342 Galena 0.05088 Glass o . 19766 Gold 0.03244 Graphite o. 20083 Hydrochloric acid o. 18450 Ice 0.50400 Iceland spar o. 20850 Iodide of mercury 0.04197 " " potassium 0.08191 " " silver 0.06159 Iodine (solid) 0.05412 " (liquid) o. 10822 Iridium .. .0.18870 Iron 0.11379 " (cast) ..0.12983 Lead (solid) 0.03065 " (liquid) 0.04020 Magnesium 0.24990 Manganese 0.12170 Marble 0.20989 Mercury (liquid) 0.03332 (solid) 0.03192 Nickel o. 10863 Nitrate of sodium 0.27821 " " silver 0.14352 Nitre o. 23875 Oil of turpentine (liquid) 0.46727 Olive-oil 0.30960 Oxygen 0.21750 Palladium 0.05928 Petroleum 0.46840 Phosphorus 0.18870 Platinum 0.03243 Potassium o. 16956 Salt 0.17295 Sapphire 0.21737 Selenium 0.07446 Silica 0.19132 Silicon o. 17740 Silver 0.05701 Sodium o. 29340 Steel 0.11700 Sulphide of zinc 0.12813 Sulphur (native) o. 17760 " (purified) 0.20259 " (liquid) 0.23400 Sulphuric acid 0.34300 Tin (solid) 0.05695 " (liquid) 0.06370 Tungsten 0.03342 Water i.ooooo Wood spirit 0.64500 Zinc 0.09555 The specific heats of gases differ from those of the solids, not only in magnitude, but also in method of variation. The specific heat of constant volume, which may be considered as the true measure of the specific heat of the substance, differs greatly from the specific heat of constant pressure. These two specific heats are, however, constant for the perfect gas and approximately so for the, so-called, permanent gases, and their ratio, which is an important quantity in thermodynamic inves- tigation, is also constant. This ratio is given, for air, by Rankine, by calculation from the experiments of Bravois and Martens, and of Moll and Van Beek, on velocity of sound in air, as y =1.408, by Clausius as 1.410, by Masson as 1.419, Weisbach 1.4025, Cazin 1.410, Rontgen 1.4053, and by Kayser as 1.4106; THERMODYNAMICS OF THE IDEAL EXCISE. 34! it is usually taken as 1.41. The experiments of Dulong* give closely confirmatory values, thus : Air, 1.414 f ; ox >~gen, 1.413 ; h>*drogen, 1.409. The ratio of the specific heats of all elemen- tary gases is probably the same, as will be seen later ( 96, Chap. IV). The greater the specific heat of a liquid, evidently, the greater that of its vapor. For all the familiar gases, at tem- peratures far removed from those of liquefaction, these quanti- ties may be assumed to be sensibly invariable. It is hence inferred, also, that the zero of the perfect gas thermometer is an absolute zero marking the absence of all heat-energy, or mo- tion. Experiment gives, with a fair degree of accuracy, values of the specific heat of constant pressure ; but it has not directly determined that of constant volume. These specific heats are usually distinguished by the sym- bols c p and c f , or K p and K, t accordingly as they are measured by thermal or mechanical units, and, when J represents Joule's * mechanical equivalent," It seems probable that c r and K, are always identical with the " real " specific heat of the substance, and that their value is invariable, and entirely independent of physical changes of state. These specific heats relate to units of weight of the fluid, and measure, in thermal units, the heat required to raise its temperature one degree. It is often desirable, however, to refer to another specific heat related to volume, comparing the quantity of heat required to raise unity of volume one degree with that demanded to raise an equal volume of the substance taken as standard * Annales de Chimie et de Physique: xti. 13. f Corrected by later determination of constants, according to Watt. 342 A MANUAL OF THE STEAM-ENGINE. through the same range. The standard almost invariably taken, where gases and vapors are compared, is atmospheric air, and specific heats are given in the tables of books of reference for both air and water as standards. We thus have for gases and vapors two specific heats at constant pressure and two at constant volume, which may be called the densimetric and the volumetric specific heats of constant pressure and of constant volume. The following table gives a number of their values as calculated, by Clausius* mainly from Regnault's data. The specific heat of air at constant pressure was predicted from de- terminations theoretically made by Rankine before experiment had given the correct value. SPECIFIC HEATS OF GASES. S. H Constant .of 'ressure. S. H Constant of Volume. Densi- metric. Volu- metric. Densi- metric. Volu- metric. Air I 0.23/50 o. 1684 I o, I. 1056 o. 21751 .013 o. 1551 1 .018 N 2 0.9713 0.24380 .9970 o. 1727 0.996 Hydrogen H a 0.0692 3 . 40900 .9930 2.4110 0.990 Chlorine Cl a 2 45O2 O. I2OIQ 248 0.0928 I TJO Br, 5 .4772 O.O5552 .280 0.0429 I ^Q5 Nitric Oxide NO I .0384 0.2317 .013 o. 1652 I.OI8 Carbonic Oxide Hydrochloric Acid. . . Carbonic Acid Nitric Acid CO HC1 CO 2 N a O 0.9673 1.2596 1.5201 i . 5241 0.2450 0.1852 0.2869 O.2262 .998 .982 39 45 0.1736 0.1304 0.172 0.181 0.997 0-975 1-55 1.64 H S O o 4805 26 I 16 Carbon disulphide Car buretted H ydrogen cs a CH, CHCls 2.6258 0.5527 0.1569 0.5929 74 38 0.131 0.468 2.04 1.54 Olefiant Gas C,H 4 NH 3 0.9672 0.4040 75 26 0-359 2.06 Alcohol C 2 H 8 O Ether CHi O e 16 6*87 Hydrogen is seen enormously to exceed every other sub- stance in the value of its specific heat as measured for unity of weight. Latent Heat, so called, is not, strictly speaking, heat ; its * Mechanical Theory of Heat; 7; 1879. THERMODYNAMICS OF THE IDEAL ENGINE. 543 measure is the equivalent of the quantity of heat which, in cer- tain classes of operations, is expended in the performance of work, internal, or external, or both ; it has disappeared, as heat, by transformation into mechanical energies, kinetic or poten- tial. Thus, in the fusion of solids and in the vaporization of liquids, and in the expansion of substances with rising tem- perature, increase of volume occurs, in all cases, against resist- ances, either external, or internal and molecular, and the product of the mean intensity, /, of such resistance, into that change of volume, tfoj gives a measure of an amount of work which, according to the general laws of energy, can only be performed by the expenditure of an equivalent amount of some form of energy in this case heat-energy. Of all the heat transferred to the body, a portion, //= U\ must be transformed from the kinetic, sensible, form ; becoming " latent," in the potential forms of " energy of position " of the separated mole- cules, and of external work performed during their displace- ment. It is common, incorrectly, to state that a body, thus expanded by heat, contains a certain quantity of latent heat ; this heat, which has apparently become latent, as was supposed by its discoverers, Dr. Black and James Watt, no longer exists as heat. It is this so-called latent heat, the heat-energy thus transformed, which produces all alterations of volume and all variations of internal and external energy, and which, alone. performs work. Its measure is always (7) in which ft is the intensity of the sum of the internal and ex- ternal resistances to increase of volume. The reversal of such processes causes the restoration of this energy to the form of sensible heat ; the quantity so restored also has the measure just given. Heat which has been appar- 344 A MANUAL OF THE STEAM-ENGINE. ently rendered latent is thus always caused to reappear by such reversal. Clausius calls heat thus transformed " work-heat /" whether it be applied to the performance of internal or of external work. The latent heat of expansion is that heat which disappears by transformation into the potential energy of equivalent work whenever a body is caused to expand by communication to it of that form of energy. Thus, if unity of weight of air is caused to expand at constant pressure in such manner that its tem- perature rises one degree, and its volume increases to such an extent as to retain its pressure unchanged, its rate of accept- ance of heat is measured by its specific heat of constant pres- sure, c = 0.237 ; while, if caused similarly to increase in tem- perature, simply, without expansion, the heat demanded is proportional to c v = 0.168 ; the difference c t c v = 0.069, by transformation, has disappeared as heat, and is the measure of the latent heat of expansion and of. the work and energy de- manded to produce the observed expansion of volume against resisting forces in this case, mainly external work against ex- ternal pressure. In other than the perfect gases, this work of expansion consists partly, and sometimes principally, of inter- nal work done against molecular attractive forces. The difference, c p c v , is always found to be greatest when the mass is most expansible by heat ; and the part c,, which is probably constant for all substances,. under all possible condi- tions, is, as already stated, the real specific heat, while the large quantity, c f , is the real specific heat increased by the quantity demanded as latent heat of expansion. Values of c p c v I may be obtained from the tables. The Latent Heat of Fusion is that quantity of heat-energy demanded to perform that work f the expansion of solids, at constant temperature and at the point of fusion, which, being done, leaves the mass so far expanded that the mutual direc- tional force affecting adjacent molecules becomes inappreci- able, and, stability of form being thus lost, the body becomes liquid. The latent heat of fusion thus measures the work THERMODYNAMICS OF THE IDEAL ENGINE. 345 done, externally and internally, in producing this change of volume against the resisting effort of molecular forces and ex- ternal pressure ; the latter is usually insignificant in amount in comparison with the former ; the work is principally internal work. M. Person finds* the latent heat of fusion of non-metallic substances to be nearly /=(/ + 2 5 6fF.)fo-O, (8) in which / is the temperature, Fahrenheit, and c^ and c t are the specific heats in the liquid and solid states, respectively. The latent heat of fusion of ice is found by experiment to be 142.5 British thermal units, nearly, or, on the metric scale, about 79 calories. During fusion, all the heat-energy applied to the substance is expended in doing the work of expansion, and none is effective in producing increase of the temperature, which remains constant during the whole period of fusion. The introduction and transformation of heat-energy, during the process of fusion, is observed to occur under the operation of three laws, viz. : (1) The temperatures of fusion and of solidification are the same, and are definitely fixed for each substance under any given pressure. (2) This temperature remains constant, heat being slowly supplied, during the whole operation of change of state of the given mass. (3) Change of volume always occurs during this change of state, and is the greater as the quantity of heat so supplied and transformed is the greater. The temperature of fusion is raised, as a rule, by pressure ; the reverse occurs to the extent of O.oi33 F. (o.oc>74 C.) for each atmosphere, in the case of ice, the variation being gen- erally less for substances of high cohesion, and fusing points, and greater for those of low melting points and little strength. The Latent Heat of Ei'aporation is that heat-energy trans- * Annales de Chimie et de Physique; Nov. 1849. 346 A MANUAL OF THE STEAM-ENGINE. formed into potential energy, or into actual energy of other form, when the change of state is that of a liquid undergoing vaporization. Its amount measures the energy demanded to remove the molecules beyond that condition of equilibrium which is the boundary between the liquid and gaseous states, and at which stability of volume, as well as of form, disappears. As will be seen ( 112) on studying the thermodynamic theory of the heat-engines, the magnitude of this quantity measures the work which can be donejDer unit weight, as a maximum by the substance, if used as a working-fluid in heat-engines. It does not at all affect the thermodynamic efficiency or propor- tion of heat transformed into work with any given range of temperature. The three laws above given for fusion hold equally well for this change. The quantity of heat transformed is, however, usually, enormously greater, and its variation with the tempera- ture and the pressure due the boiling-point, or the point of liquefaction, accordingly as the change is produced by the communication or the abstraction of heat, is very considerable. Regnault obtained values of this latent heat, for water, which are very exactly expressed by one of his formulas, slightly modified by Rankine, thus : * /= 1091.7 - 0.695 (t - 32) - o.oooooo 103 (t - 39 - 1 ) 3 : (9) or, similarly applying the correction indicated by the last term, l m = 606.5 0.695 t m o.ooo ooo 333 (/ 4) 3 ; . . (10) in British and metric units, respectively. For the former, the following nearly equivalent expressions may be generally used : /= 1091.7 - 0.695 (*- 32) ) = 1114 -0.695 t \. . . . (11) = 966.1 0.695 (/ 212) ) * Steam-engine; p. 250. See Peabody's Thermodynamics, for these con- stants. THERMODYNAMICS OF THE IDEAL ENGINE. 347 The latent heats of water are greater than those of any other substance. According to Andrews, we have the follow- ing, the latent heat of water being unity : Substance. Latent Heat. Substance. Latent Heat. Water i Bisulphide of carbon 0.162 Wood-spirit 0.492 Oxalic ether 0.136 Alcohol.... ,..0.378 Bromine 0.085 Ether 0.169 Peroxide of tin 0.059 According to Mr. H. Whiting,* the application of the molecular theory of gases to liquids, in combination with the magnetic theory of cohesion, requires certain numerical rela- tions between the physical constants which are in every case obtained, very exactly, by experiment. The most important are the following : (1) " The product of the latent heat, molecular weights, and coefficient of expansion is equal to 8.4 for liquids at tempera- ture zero, expanding by ordinary law." (2) "The product in metric measures of the mechanical equivalent of the latent heat and the density is 1.2 times the product of the coefficient of expansion, the resistance, and the absolute temperature." The Total Heat of Evaporation is the sum of the sensible and latent heats, measured in heat-units, and is constant at any one pressure, but, like the latent heat of evaporation, is vari- able with change of pressure, and, consequently, of the boiling- point. This quantity is sometimes called the " total heat of vapor." Its amount is always calculated from some fixed tern- perature, and is defined as the total heat from that fixed temperature, and at the given temperature, or pressure, of evaporation. Thus, water, fed to a steam-boiler at 60 F., and evaporated at 70 pounds pressure according to the steam- gauge, is said to be evaporated front 60 F. and at 320 F., the boiling-point for the given pressure. This quantity of heat, in thermal units, is // = <(/. -/.) + /,. . . . . (12) * Science Bulletin; 1884. 348 A MANUAL OF THE STEAM-ENGINE. in which c is the specific heat of the liquid, /, /, the range of temperature, and / the latent heat of evaporation at the boiL ing-point, / a . For water we have, as above, according to Regnault, when /, = 32, in British measures, b = i09i.7 + o.305(/ t - 32), = 1082 +0.305*,, V. ... (13) = 1146.6 + 0.305 (/, - 212); and when heated from any higher temperature / deduct c (t t 32), c being the mean specific heat for that range of temperature. L m = 606.5 +0.305*, , ..... (14) in metric units, the heat being measured from the freezing- point ; we deduct ct 9 when the initial temperature, on that scale, is t v The efficiency of steam generators is often measured by the weight of water evaporated by them " from and at " the boiling- point under atmospheric pressure. Experiment determines the weight evaporated under actual conditions ; the above ex- pressions give the total heat required per pound, and this quan- tity divided by the latent heat under the standard conditions, 965.7 thermal units according to Regnault, or 966.1 as corrected by Rankine, gives the equivalent weight desired. For all ordi- nary work this divisor may be taken as 966. The Total Heat of Gasification is always (15) in which, for steam, c = 0.4805, its specific heat under constant pressure, as a gas, and / has very exactly that value found at the freezing-point 1091.7, nearly, for British, or 606.5 in metric measures. THERMODYNAMICS OF THE IDEAL ENGINE. 34Q Supcrktated steam, or "steam-gas.," requires for its produc- tion by the change of the liquid into the vapor under a stated pressure, and elevation to any given temperature, a quantity of heat and energy which is entirely independent of the pressure and temperature at which the boiling-point occurs. The pro- cess involves two distinct operations: (i) the raising of tem- perature, by the transfer to it of sensible heat, from the initial temperature of the substance to its final temperature ; (2) the performance of internal work by the conversion of sufficient heat to separate the molecules from that proximity which char- acterizes the liquid state to their final relative positions in the larger volume and at the final temperature and pressure ; which latter quantities are fixed for the unit of mass by the equation fv / T = constant. Hence, starting from the freezing-point, (16) where H is the total heat, ff the latent heat at T v and K, the dynamically measured specific heat of the gas ; its real dynamic specific heat. Rankine takes for British measures : * Jk = 842^72 foot-pounds, K t = 772 X 0475 = 366.7 foot-pounds; in thermal units, *= 1092, ' = 0-475- The specific heat of superheated steam is found by Zeuner to be variable, thus : / in Ibs. per sq. in. 50 100 200 C, 0.348 0.346 0.344 P-55- 35O A MANUAL OF THE STEAM-ENGINE. Hirn finds the following values for its specific volume : p in atmos. 1345 t Cent. 141 200 200 200 Sp. vol., cu. in. 1.85 0.697 0.522 0.414 It can be readily computed if necessary.* 94. The Critical State is a condition, intermediate between the liquid and gaseous states, which is sometimes observed when vaporization occurs under very high pressures. At the "critical temperature " a gaseous body may be liquefied by pressure; at any higher temperature such liquefaction has never been produced. In the ordinary process of vaporization the mass rises in temperature with but slight, and often no, observable, change of volume, until, at a certain temperature and pressure, fixed for each fluid, the temperature ceases rising with constant volume, and, heat being still introduced at a uni- form rate, volume increases, with temperature constant, and g< ; on increasing until all the fluid has, molecule by molecule, been transformed into the state of vapor. As will be seen later, in the first part of the process the heat is simply transferred as sensible heat, and produces rise of temperature ; in the second period heat is transformed, and an equivalent amount of work is done in the gradual conversion into vapor and the expansion of the mass, during the continuous process of change, against internal and external resistances. When the pressures resisting the expansion are very great, this variation of volume is greatly restricted, and a point may finally be reached at which no such expansion at constant temperature can take place ; the sub- stance all passes, suddenly and completely, into the vaporous condition. The temperature at which this occurs is the " crilx ical temperature" of the substance, and at this point the latent heat of evaporation obviously becomes zero ; the two states ; the liquid and the gas, at this point have a common limit.f * Zeuner's Warmeiheorie ; also Peabody, chap. vii. p. 125. f This has been experimentally shown by Mathias; Comptes Rendus, 1889, p. 470; and Jour. Franklin Inst., Apr. 1890; p. 297. THERMODYNAMICS OF THE IDEAL ENGINE. 351 This phenomenon was observed by M. Cagniard de la Tour in the case of water, as early as 1822. Dr. Andrews has studied this phenomenon here described with great care.* He con- cludes the two fluids to be merely widely-separated illustrations of one physical state ; more correctly, the two states, the liquid and the vapor, have a perfect continuity. The critical tempera- ture of carbonic acid is about 87. 7 F. (3O.9 C.) and at a press- ure of 75 atmospheres; that of ether is 369 F. (187 C.) and at 37.5 atmospheres; for alcohol, 498 F. (258 C.) and 119 at- mospheres, according to M. C. de la Tour ; for carbon disul- phide, 505 F.(263 C.) and 66.5 atmospheres; while for water the temperature rises to 773 F. (410 C), and the pressure is not exactly known, probably nearly 750 atmospheres, as calcu- lated by the Author. At the latter temperature water was found to dissolve glass. M. Cailletet reached the critical tem- perature with nitric oxide at 46.4 F. (8 C.) under 270 at- mospheres, marsh gas at 44.6 F. (7 C.) and 180 atmospheres, oxygen and carbonic oxide at below 2O.2 F. ( 29 C.) and at 300 atmospheres, nitrogen below 55.4 F.(i3 C.) and at 200 atmospheres; hydrogen seemingly approaches this state at 21 F. ( 29 C.) and 280 atmospheres. The so-called per- manent gases may all be reduced to the liquid state by pressure when the critical temperature is reached, and have been so con- densed by M. Cailletet and by M. Pictet, the pressures applied reaching, in some cases, 800 atmospheres and the necessary de- crease of temperature being attained by expansion at initially low temperatures from under these pressures. The following table of temperatures of physical phenomena has been collated by Mr. J. J. Coleman : f PHYSICAL CONDITIONS AND TEMPERATURE. De*. Deg. Fahr. Cent. + 698 +370 Critical point of water = 195 . 5 atmos. pressure. + 311 +155.4 " " "sulphurous anhydride = 78.9 + 285 +141 " " "chlorine = 83.9 " * Philosophical Transactions; 1869. f Trans. Phil. Soc. Glasgow; March 18, 1885. 352 A MANUAL OF THE STEAM-ENGINE. Deg. Deg. Fahr. Cent. + 266 +130 Critical point of ammonia = "5 atmos. pressure. -f-212 -f-ioo.2 " " " sulphuretted hydrogen = 92 " _j_ gg _|_ 37 " " "acetylene = 68 " _|_ 95 _j_ 35.4 " " " nitrous oxide = 75 " _j_ 89 + 3 I -9 " " " carbonic acid = 77 " 4- 50 + io. I " " " ethylene = 51 " " _|_ 32 o Nitrous oxide boils at 32 atmos. pressure Faraday. _^_ 32 o Carbonic acid boils at 36 " " " -j- 14 io Sulphurous anhydride boils " -j- 15 10.5 " Bunsen. io 23 Methyl chloride boils Regnault. io 23 Carbonic acid boils at 19.38 atmos. pressure Faraday. 20 29 Sulphurous anhydride boils in current dry air. Pictet. 20 29 Carbonic oxide and oxygen, air and nitrogen, com- pressed to 300 atmos. in glass tubes, and suddenly expanded, show liquefaction Cailletet. 26 32 Alcohol containing 52 per cent water freezes Pictet. 29 _ 33.6 Chlorine boils Regnault. 29 33.7 Ammonia boils Bunsen. 31 35 Commercial paraffin oil (sp. gr. .810) freezes Coleman. 40 40 Nitrous oxide boils at 8.71 atmos. pressure Faraday. 40 40 Carbonic acid boils at II 40 40 Ethylene boils at 13.5 " " 53 47 Freezing point of Hollands gin and French brandy. Coleman. 60 51 Nitrous oxide boils at 5 atmos. pressure Faraday. 60 51 Carbonic acid boils at 6.75 " " " 60 51 Ethylene boils at 9 " " " 62 52 American petroleum (sp. gr. 790) freezes Coleman. 62 52 Freezing point of extra strong whiskey and rum . . . 62 52 Alcohol containing 40 per cent water freezes " 80 61.8 Sulphydric acid boils ....Regnault. 80 62 Nitrous oxide boils at 3 atmos. pressure Faraday. 80 62 Carbonic acid boils at 3.75 " " " 80 62 Ethylene boils at 6.5 " " " 99 73 Critical point of marsh gas, pressure 56 atmos. Wroblewski. 103 75 Liquefied ammonia freezes. 103 75 Alcohol containing 20 per cent water freezes Coleman. 108 78 Carbonic acid boils Faraday and Regnault. 112 80 Solid sulphurous anhydride melts Mitchell. 123 86 Nitrous oxide boils Faraday. 123 86 Marsh gas boils at 40 atmos. pressure Wroblewski. 128 87.9 Liquid nitrous oxide boils Regnault. THERMODYNAMICS OF THE IDEAL ENGINE. 353 SS. SSL 144 98 Marsh gas boils at 25 aunos. pressure WrtUewtK. 52 102 Amyl alcohol an oily liquid Obemtti. 52 102 Silicon fluoride a white mass " .2 102 Arseniurerted hydrogen liquid 52 102 Hydrochloric acid boils " =2 102 Chlorine orange crystals " 52 - 102 Eihylene boils 54 103 " " 66 no Solid carbonic acid and ether in vacno Faradar. 71 113 Critical point of oxygen, pressure 50 aunos WrtbUvesln. -i 113 Marsh gas boils at 1 6 aunos. pressure 5 115 Solid carbonic acid in vacuo, 25 mm. pressure Deamr. 75 115 Hydrochloric acid gas solid OhewskL 116 Carbon disulphide solid. 180 118 Arseninretted hydrogen white crystals Okesoski. 193 125 Nitrons oxide boils in vacuo Deseur. 200 129 Ether solidifies ObemsK. 202 130 Absolute alcohol solid. 209 134 Amyl alcohol solid ObtmstL 2i3 139 Eihylene boils in vacno " 219 139.5 Critical point of carbonic oxide, press. 55.5 aunos. . " 220 140 " " air. pressure 39.0 atmos " 220 140 Calculated temp, of carbonic acid snow in vacuo (?). . .PictcL 220 140 Hydrogen compressed to 650 atmos. and pressure released produces momentary liquefaction and solidification PicUt. no 140 Oxygen compressed to 320 atmos. and pressure re- leased produces momentary liquefaction Put ft. 231 146 Critical point of nitrogen, 35 atmos. pressure ObraukL 238 150 Ethylene boils in vacno 233 150 Carbonic oxide boils at 20 atmos. pressure " 242 152 Atmospheric air boils at 20 " " -247 155 Marsh gas boils WrobU*ski. -ago; 184 Oxygen boils " 312 191.4 Airboils OttrmK. 31* 191.2 " " WntlraHln. 315 193 Carbonic oxide boils 317 194 Nitrogen boils Olte&ski. 337 205 Atmospheric air boils in vacno " 348 2ii Carbonic oxide solidifies in vacuo " 351 213 Nitrogen boils in vacno " ? Hydrogen at 100 to 200 atmos. liquefies to colorless drops (:n glass tubes 0.2 mm. dia. surrounded by oxygen boiling in vacuo) WnMcwsJd amd OhewtL 354 A MANUAL OF THE STEAM-ENGINE. Deg. Deg. Fahr. Cent. -355 2I 5 Calculated boiling point of hydrogen E. J. Mills. 460 273 Absolute zero. (The critical points above freezing point of water are quoted from Professor Dewar ; Chemical News, Jan. 16, 1885.) 95. The Definition of the Perfect Gas has been seen to be capable of expression by statement either of its physical consti- tution, of its physical properties, or of its thermodynamic equation. It is so constituted that its molecules exert no in- herent cohesive attractions, or mutual repulsions, and it can only be confined, when acted upon by heat, if allowed to ex- pand within a defined volume by the application of external force ; and hence its effort to expand i.e., its pressure, tension, or elasticity, as it is variously called is supposed to be due solely to that energy of molecular motion which we call heat. Its distinguishing physical property is found in the fact that, when reduced to any given volume, and confined within any given space, its total pressure upon the confining-walls, or its total tension, is precisely equal to the sum of the pressures which any number of equal parts would produce, if each were separately enclosed in an equal space. This is equivalent to saying that, the temperature being constant, the tension is in- versely as the volume, which is the law of Boyle and of Ma- riotte. The perfect gas is also found to vary in pressure, or in volume, or to vary in product of pressure and volume, both varying together, directly as the temperature measured from the " absolute" zero, i.e., according to the law of Charles and of Gay Lussac. Experiment thus shows that the more nearly a gas ap- proaches this ideal state, the more perfectly does it illustrate the law of Boyle and Mariotte, the pressure varying inversely as the volume ; and the more exactly does it follow the law of Charles and Gay Lussac, according to which the variation of pressure at constant volume, or of volume at constant pressure, or of the product of pressure and volume, varies directly as the absolute temperature. THERMODYNAMICS OF THE IDEAL ENGINE. 355 TIu Defining Equation of the Perfect Gas is, therefore, as already seen, pv T po pjp, . The quantity of matter considered is commonly taken as unity of weight, and v is here, therefore, the "specific volume," or the volume of unity of weight. The value of R is thus constant for any one gas, and, for different gases, will vary inversely as their densities at stand- ard temperature and pressure. Thus, for the nearly perfect gases, oxygen, hydrogen, nitrogen, and for the mixture, air, the values of R are, respectively, nearly 26.5, 42.3, 30, and 29.3, in metric measures, or 48, 70, 55, and 53, in British measures. Evidently, TD in which D is the density of the gas, as measured by the weight of unity of volume, and Tis absolute temperature. 96. The Thermodynamics of the Perfect Gas involves the determination of the methods of variation of temperature, pressure, and volume, and of variations of quantities of heat and work consequent upon those changes ; in such manner that the General Thermodynamic Equation may be applied to the case. This means the measurement of the quantities entering into the equation and ascertaining their physical relations, and thus the algebraic relations of their symbols ; so that numerical values may be substituted and the equation solved for any given case. The general therm odynamic equation has been seen to be an expression in which the change of heat-energy is measured in terms of two distinct phenomena ; the application of heat to alteration of temperature in any " working fluid," the transfer, 3$6 A MANUAL OF THE STEAM-ENGINE. simply, of heat-energy ; and that producing mechanical energy, or work. We now see that the first of these quantities is meas- ured by the product of the range of temperature of the unit weight, always taken, and the real specific heat ; while the sec- ond must be measured by the product of the intensity of the total pressure of the fluid by the change of volume. Hence dH=dS+dW; in which the equation may be solved when, in the second term of the second member, the relation of/ to v is known; or, when the values of all the quantities involved can be directly ob- tained by observation or other means. The first law of thermodynamics and the experimental measure of the mechanical equivalent of heat enable us to express the specific heat, K v , of constant volume, the "real dy- namical specific heat," in terms of either thermal or dynamical units. The second law of thermodynamics asserts that the value of/ in the second term may be taken as proportional to absolute temperature and, hence, the value of/, at any instant, may be obtained by multiplying the rate of variation of/ with T, -> by T, the absolute temperature of the fluid ; and hence f = T (jr): (> and we have simply to write then to obtain values of the several symbols ; and to determine the value of the partial differential coefficient H^J , by refer- THERMODYNAMICS OF THE IDEAL ENGIXTE. 357 ence to the algebraic expression of the laws of variation of the physic?! characteristics of the fluid. The "Thermodjmamic FiuKtum** is obtained by reference to the second law, also, as originally shown by Rankine, thus:* We have seen that the second law asserts that any effect of heat, being proportional to the quantity of heat acting in its production, is proportional to the absolute temperature of the fluid, and is measured by the product of this quantity by a " thermodynamic function/" the form and magnitude of which for a gas will be presently determined ; that is: (4) when $ represents that function. The Thermodynaumc Equations for Gases are thus obtained by inserting in the general fundamental equations the values of the partial differential coefficients obtained from the charac- teristic equation of the gas. The perfect gas, as has been seen, is defined by the equation = R=*, a constant, in which the subscript, , may be taken to indicate the state of the substance at a standard temperature, as at the melting. point of ice. For all purposes of the engineer, and for nearly all the purposes of the physicist, the permanent gases, so called, may be taken as perfect. The values of the coefficients The general equations thus become, in accordance with these two laws, dH= TdQ = ? -" :; 358 A MANUAL OF THE STEAM-ENGINE. ......... (5) dH= Since the value of the total differential dv in (5) is and, from (6) and (7), (6) R "T dp, ..... (7) JJ.T - = K t = K v -J- R ; Kp K v = R ; . . . (8) and thus, as was first shown by Clausius, both specific heats, that of constant volume and that of constant pressure, and their difference, are found, by thermodynamic science, as well as by experiment, to be constant. Since, from (7), ,~_ vdp+pdv ~~ ' (9) THERMODYNAMICS OF THE IDEAL ENGINE. 359 But since the specific heat at constant pressure, K p , is also fe) we have We may, therefore, unite the three forms of the equations for perfect gases : dH = (K t - = K/tT- vdp (10) in which equation the specific heat at constant pressure ap- pears instead of the specific heat at constant volume inserted in (5). Introducing both specific heats, and eliminating R, we obtain: dH = When a perfect gas expands at constant temperature, ob- viously no internal work can be done, and no change occurs in the amount of sensible heat present in the mass. Hence, under the laws of transference of energy, if no external work is done, a constant weight of such gas, freely ex- panding at constant temperature, requires no heat from exter- nal sources to keep its condition, with respect to heat or energy, unchanged. 360 A MANUAL OF THE STEAM-ENGINE. This conclusion, based upon the law of persistence of energy, has been confirmed by experiments made by Joule and Thomson upon the permanent, or nearly perfect, gases. In the case of the non-permanent gases, such as carbonic acid, it is found by experiment, as by theory, that this conclusion does not hold. In the latter, as in any case in which internal work is done, heat must be introduced during expansion to perform that internal work, if the temperature is to be kept constant, and, reversing the process, heat must be abstracted during com- pression at constant temperature. When external work is done by a perfect gas, expanding at constant temperature, it is obviously necessary to supply heat, to do that work, in exactly equivalent amount, and the heat absorbed is thus a measure of the work so done. When imperfect gases similarly expand, heat is added, as before, in just the amount demanded for conversion into work, and its measure is also the measure of the total work done internally and externally. The thermodynamic function, for the perfect gas, is readily derived from the general equations. Since this function is dH we have Also, L . . . (12) The latter may be deduced directly from the former, by eliminating dv and substituting its value in terms of dp. We have THERMODYNAMICS OF THE IDEAL ENGINE. 361 Substituting in (12), an equation which is perfectly general. For perfect gases, T~ T J \dTh~ vT ' \dTlp and. also, when */t> = o, t-*L\ L ^\ \ _ />\ (<\ fdv\ df~\df} P ^~ \d~p) T \df}* ~ ; WrJ, V^Jr ~ \df)i Substituting in (14), = *,+'-*<-*#,. . . (I5) which is the second equation (12). Collecting the expressions for all, we have and integrating, = AT, log, T+ R log, v + C = K p \og e T-Rlo&p+C = (K V +R} log, T - R log, / + C 362 A MANUAL OF THE STEAM-ENGINE. The value of C, the constant of integration, is here inde- terminable ; but this is a matter of no importance, since it dis- appears in application, differences in values of thermodynamic functions, only, being in such cases considered. &> Introducing the value of -j~ = y, and observing that _ i 7 in which x = 1.405, nearly, for air, and is usually taken as 1.41 for all permanent gases ;* --- = 2.451 ; _ = 3-451. The value of ~^^, for air, is estimated by Rankine at 53.15 foot- * o pounds per degree Fahrenheit, accepting Regnault's determi- nation of the value of p Q v as 26,214 foot-pounds, and taking T at 493.2 Fahr. The applications of the General Equations for Perfect Gases are illustrated by the following cases : (i) Required the amount of heat demanded to produce change of volume at constant pressure. We have * Purely theoretic analysis indicates a possibility that this value of the perfect gas may be y = ^ = 1.405285. Phil. Mag., 1885; p. 520. THERMODYNAMICS OF THE IDEAL ENGINE. 363 Since/ is constant, dp o, and dff = whence, integrating, H = (2) The gas expands or contracts at constant temperature. For this case take But T is constant ; dT = a (3) Expansion is adiabatic or isentropic, i.e., H is constant, dH o. Then dH =K,dT + (K, - K^T d = o, rr Integrating and calling -~ = y, log, T-\- (y i) log,t/ = constant, 364 A MANUAL OF THE STEAM-ENGINE. Tv y ~ l const. = 7X*" 1 . 7\ - W Similarly, from the equation dH = K t dT - (K p - KJT = o we obtain Combining the above, we get Or, from dH = A^h we have */z> , dp r-+f and, as before, and /j^, v = pv y = constant. (4) Required an expression for the work done by a perfect gas expanding at constant temperature, the latent heat of ex- pansion being supplied from some external source of heat, i.e., in isothermal expansion. We have dH = pdv ; pv = constant = p^ , and = M. THERMODYNAMICS OF THE IDEAL ENGINE. 365 .-.U= or, if the ratio of expansion is r = -*, (5) To measure the work done during adiabatic expansion : We have pv 1 = constant = /,?,*. (6) To find the variation of temperature when a gas ex- pands adiabatically, and without doing work ; as when expand- ing from one given volume to another within a space otherwise vacuous : From (i i), v Since the work done by the gas is zero, = KjlT\ dT=o; T= constant 97. The Work performed and Energy expended, by transfer and transformation of heat, are thus readily computed whenever the method of operation is known. As already 3 A MANUAL OF THE STEAM-ENGINE. stated, the variation of pressure with change of volume may usually be represented by some curve of the hyperbolic class, and by algebraic expressions of the general form, pv n = const. pjv? (i) In such cases the work done, by unity of weight, is in which then and, thence, <7_ v n r* - n Pf>? =*-^T'> (4) whence, for gases, Hence, the work done during expansion along a line of which the equation is pp? = pv n is proportional to the differ- ence of the products of pressure and volume at the initial and terminal portions of the curve, and, in the case of gases, to the range of temperature worked through. The change of temper- ature is thus, in all such cases, directly proportional to the quantity of work performed by or upon the expanding or con- tracting fluid. The Heat expended is, in all cases, the sum of the amounts demanded to perform internal work, to do the external work of expansion, and to produce variation of sensible heat. In the perfect gases, the internal work is zero ; the external work is measured as above; and the variation of sensible heat is measured by S=Kv(T, - TJ, . . ;: ., . . (6) being positive for compression and negative for expansion. THERMODYNAMICS OF THE IDEAL ENGINE. 367 Hence, the total heat demanded in any case of hyperbolic expansion, such as the above, must be 5+ U, or Thus it is found that the total amount of heat emitted or received in such changes is directly proportional to the range of temperature, 7\ T t , worked through during such expan- sion or compression. The above is also a proof that, either specific heat being found constant by experiment, the other must be constant as well. For the case of common hyperbolic expansion, in which the law of Boyle and Mariotte is followed, n = I, and the ex- pression for work done, equation (4), becomes H , inde- terminate. In this case, unity of weight being taken, as before, P*v* = P* V * = pv, and C"*dv v U = A", / = A". log, -' = A", log, r, . . (8) / v t in which r is the ratio of expansion. This case is that of isothermal expansion of gases, the heat transferred to or from the fluid being the equivalent of the work done, and wholly transformed. When n exceeds unity, the curve falls under; and when n < i, the line lies above the equilateral hyperbola. In the first case, the temperature of the gas must obviously fall ; in the second case, it must as evidently rise, as expansion pro- ceeds. Isothermal changes are, by definition, those occurring at constant temperature. Adiabatic changes are, by definition, those which occur without gain or loss of heat by transfer to or from the enclosing vessel ; such as may take place in a vessel composed of a non- conducting substance. 368 A MANUAL OF THE STEAM-ENGINE. Isodynamic changes are, by definition, those taking place without variation of internal energy. The work of Isothermal and of Adiabatic Expansion of gas may evidently be now determined by assigning to n, in the ex- pression PV* = constant, proper values, and the quantity of heat-energy transformed may be thus ascertained. For Isothermal Expansion of gases, as already seen, n = i and rdv v = A^ log, - = A?, log. r ; . . (9) 1 which measures the quantity of heat transformed into external mechanical work, or into kinetic energy. Since no change of temperature takes place, no heat is transferred to effect such a change ; and, since no intramolecular forces resist or aid the change of volume, no heat is transformed in that manner. The quantity 7thus measures the total amount of heat transferred, which, measured in thermal units, is, calling A, where Q is the quantity of heat, in thermal units ; / = - j is A " Joule's equivalent." This determination may be effected, also, by comparison of the thermodynamic functions for the initial and final conditions of the fluid, thus : The thermodynamic function at the beginning of expan- sion is and, at the end of the process, ... (12) THERMODYNAMICS OF THE IDEAL EXGIXE. 369 Since the temperature is constant, 7~ s = 7^, the heat ex- pended is (,3) as before, the expanding or compressed mass weighing unity. For air, adopting T. = 493^ R, R = 53.15, and U= 53.157; log,r, ...... (14) and, in metric measures, Ft?r Adiabatu Expansion of gases, there are two equations of condition : The work done during expansion is and if the density is called 8 = 37O A MANUAL OF THE STEAM-ENGINE. Again, u= rv.'-A^ Y r* v ~* dv t/Z/j I/ft For compression, the work is similarly measured ; its value is negative, and heat is produced in place of being expended. The variation of temperature is controlled by the laws ex- pressed in the equations whence ~^ =T l -r~\ ..... (20) r being the " ratio of expansion. The Isothermal and the Isodynamic Lines on a diagram of heat-energy in cases of the expansion of gas are identical in form and location. As has been seen, the whole internal energy of the perfect gas, and, approximately, all that of the permanent gases, is the energy of heat-motion, and is mani- fested as sensible heat, its total amount being proportional to the absolute temperature of the fluid. A line of invariable internal energy, or the isodynamic line, is therefore, for gas, a line of uniform temperature. The equation of this line is obtained directly from the de- fining equation of the gas, thus : T constant; ...... (21) pv RT= constant ..... (22) Calling abscissa and ordinate x and y, v = ax, p = by, and pv RT THERMODYNAMICS OF THE IDEAL EXGIXE. 371 a and b being assigned values to be determined by the scale on which the curve is drawn. The isothermal and isodynamic lines, for gases, are thus again seen to be alike hyperbolic. Since heat must be converted into mechanical energy, when the fluid expands isothermally behind a piston, it is again evi- dent that an amount of heat must be supplied, during such ex- pansion, precisely equal to the external work done, in order that the temperature of the gas shall not vary ; and that dur- ing compression, heat must be abstracted to a similar extent. The Adiabatu or Istntropic Lint, also, represents the method of variation of pressures and volumes when the ~ en- tropy" of the fluid is constant, Le., when no heat is communi- cated to, or emitted from, the gas, all change of temperature of the fluid being due to transformation of energy. Since all energy expended upon external bodies must, in this case, be produced by conversion of heat into mechanical energy, and all heat gained by the substance must be due to the reverse transformation, it is evident that the fluid must cool during expansion, and become heated by compression, when it is en- closed in a non-conducting envelope of variable volume. It thus follows, also, that the expanding fluid will give an adia- batic line which will fall more rapidly from the same initial state i^an its own isothermal, the adiabatic curve thus lying under the isothermal, on the diagram of energy. When com- pression occurs from the same initial state, the adia- batic line lies above the iso- thermal. The relations of the two lines are shown in Fig. 130, in which T, T, T lt T t , are isothennals. and lt t , 2t E It are adiabatics. The in- tersections of the latter with the former being considered as marking initial conditions, the curves are seen to separate, in the manner just indicated, with change of volume in either direction, as explained in 81. 37 2 A MANUAL OF THE STEAM-ENGINE. The equation of the adiabatic line is readily obtained from the characteristic equation of the gas, combined with the special defining conditions of the assumed change, thus : Since no heat-energy is absorbed by, or emitted from, the fluid, in this case, during change of volume, = constant ; dH = Td(f> = o ; d = o. Then d* = K *+%*, ..... (24) dT p v dv = K v - f +- f --; ..... (25) = K v log, T + K, (y i) log, v. (26) Then (f) -g = log, T-\-(y i) log, v = log,(rF Y -'); ..... (27) and, since

? log C =5-59873; -, = 0.00001184; pressures being taken in pounds on the square foot, and tem- perature in degrees Fahrenheit on the absolute scale. The ex- periments of Regnault and of Fairbairn and Tate have furnished the generally accepted values. Unwin has proposed f a simpler formula than Rankine's, which, while not quite as exact, gives more manageable expres- sions for - and its functions ; thus, for vapors generally : -; ....... (12) * Steam-engine; p. 237, 206. Ibid.; pp. 559-564. f Phil. Mag.; April 1886. THERMODYNAMICS OF THE IDEAL ENGINE. 379 I dp nb --=2.3025^ (a log ^"pT = 2. 3 02 5 V -- |^ ;. . . (I 4 ) b* t dp nb (15) -- = 2.3025- For steam, these formulas become : log p = 7.5030 -y; . . . . . (16) r -( _ 7579 Y-\ ~ V 7 .5030 - log// ' i *# 21815 (7- 5Q30- log ff* ,,,, 441-3 T dp 21815 = 2.8782(7.5030 -log/); . . (19) which expressions give remarkably exact results. Metric meas- ures are used throughout. Many simple expressions have been proposed for the rela- tions of pressure and temperature of saturated steam. These, in their simplest forms, are usually of the type : in which, for British measures, as the Fahrenheit scale and ab- solute pressures in pounds on the square inch, values are very 38o A MANUAL OF THE STEAM-ENGINE. nearly a = 0.0085 5 * = - 22 - Thus Mr. Estler makes a = 0.008484, i = 0.222, for all customary working pressures, and obtained a sufficiently close approximation for any ordinary work of the engineer. Internal pressure and work are computed by deducting external pressure and work from the totals. Clausius thus obtained the following values of p for steam of the pressures given, all in millimetres of mercury, of which 760 measure one atmosphere of pressure: TOTAL PRESSURES OF STEAM. Centigrade. External Pressure. Ratio dp Total Pressure dp Ratio P /. T. A- At. Tr- *- T ir- A' IOO 374 760 t 27 200 10146 13-3 I2O 394 1520 2 48.595 19150 12.6 134 408 2280 3 67.020 27277 ii. g 144 418 3040 4 84-345 35172 . 5 152 426 3800 5 100.375 42659 II. 2 159 433 4560 6 116.085 50149 II. O 1 66 440 5320 7 133-445 58502 10.8 171 445 6080 8 146.910 65228 10.7 176 450 6840 9 161.27 72410 10.6 180 454 7600 10 173-425 78561 10.4 199 473 11400 15 239.57 113077 9-9 It is seen that the rate of variation of pressure with the temperature of steam continually increases as pressures and temperatures rise, and that the proportion of internal to ex- ternal work and pressure continually diminishes; but that the latter ratio is large, about ten to one, for the whole range of pressures familiar in standard practice. The specific volume of steam, or the volume of unity of weight, and its reciprocal, the density, have been seen to be capable of easy computation when the latent heat of vaporiza- tion at the given temperature is known ; since this latent heat measures the work done while the force resisting it is calculable as above. From the expressions (3) already given, 98, r*P *. H dp we thus obtain very exact values. THERMODYNAMICS OF THE IDEAL E \GI.\E. 381 Clausius thus obtains the following values, and compares them with the somewhat uncertain figures of Fairbairn and Tate, derived experimentally. Metric measures are employed. SPECIFIC VOLUMES OF STEAM. ' r - Calculated. By Experiment. 117.17 : .: . :- 124.17 398.17 125.41 402.41 137.46 1 - 411.46 144-74 413-74 0-947 0.769 0.651 0.530 0-437 0.941 0.758 0.645 0.514 -:- Adopting his nomenclature, let s and the density of steam ; the results according very perfectly with those obtained in the researches of Messrs. Fairbairn and Tate.* The general equation for steam and vapors thus becomes, since K v = /, as before, }- (3) . dp dT The thermodynamic function for vapor is, as before, in form, ... (4) and is similar in form to that obtained for gases. For steam, the value of K v is the dynamically expressed measure of the specific heat of water, or " Joule's equivalent." Thus, the ex- pression for this function becomes, for any other fluid than steam, of which the specific heat in the liquid state is C, (5) Professor Unwin adopts an empirical expression for the relations of external pressure and the temperature of saturated vapors, having the form,f log/ = a bT~ n -, and (6) y- 1 Rankine; Miscellaneous Papers, p. 423. London Engineer; April g, 1886; p. 277. THERMODYNAMICS OF THE IDEAL ENGINE. 391 in which, when/ is the pressure in pounds on the square inch, T'the absolute temperature reckoned from 461 F., and, for steam, a = 5.8031 ; b = 15,900; n = 1.25, common logarithms being used. This expression gives values agreeing with those obtained by Regnault, to within 0.007, throughout a range extending up to about 25 atmospheres. From the above equation we obtain I dp nb -. = 2.3026^- 45765. /5 ' t dp ,nb -- = 2.3026 .; _ 457^5. = 2.8783(5-8031- log/); J (7) (8) which gives the numerical values which follow. The ratio of total pressure, internal and external, 7*-j~, to external pressure, /, and of latent heat of vaporization to heat transformed into external work, is as below : / dp p'dT p Eq. 8 Rankine Diff. 5 14.69 14.79 .10 10 13.83 13.88 - .05 20 12.96 12.98 .02 40 12.09 12.08 + .01 70 n-39 11.36 + .03 140 10.53 10.49 + -04 200 10.08 10.03 + .05 250 9.80 9-75 + .05 39 2 A MANUAL OF THE STEAM-ENGINE. The ratio of internal pressure, T '-rr p, or of the pressure due internal work, to the external and observed pressure, p, is (9) 45765 = 2.8783(5.8031 -log/)- i J The specific volume of steam, v s, the difference in vol- ume of a pound of steam and of the .water from which it is made, at any given pressure, /, is, as has been seen, a factor by which the total pressure, T -j~ , being multiplied, the product measures the work expended in its evaporation, or its equivalent, the latent heat, H, of vaporization at that pressure. Thus / j* \ ' = //; .... (10) Jt (M) and p being expressed in pounds on the square foot, and s taken as 0.016, 1.8626? An approximate expression for / is, for British units, /= 1443 ojiT 1632 03) The following are a few calculated values of latent heats and of specific volume : THERMODYNAMICS OF THE IDEAL ENGINE. 393 p / r j D-- 5 1000.8 73-03 0.0137 10 978.8 37-96 0.0263 20 954-0 1973 O.O5O6 40 926.2 IO.27 0.0972 70 900.9 6.056 0-1647 140 865.4 3-149 0.3160 200 845.0 2^48 0.4417 250 831-4 1.820 0-5447 The external work of evaporation \sf(v s\ or 268.2/ 59.28 The internal work is _log/> (14) The following table gives the value of T and of /, actual and as computed by the approximate equation. / is here given in pounds on the square inch. /^Fahr. T A::-i. Computed 100 5 6l 0.942 0-953 150 611 3-707 3.706 212 673 14-70 14.62 250 711 29-88 29.67 300 761 67.22 66.82 350 811 I35-U 134-62 400 861 247-75 247.70 432 893 350-73 351-50 394 A MANUAL OF THE STEAM-ENGINE. 102. The Thermal Lines, for Vapors, differ somewhat in form from those found for gases. The exact equations of the expansion lines become, however, so difficult of application, in the theory of the heat-engines, that it has been found advisable to substitute for them approximate expressions of simple form, which may be more conveniently applied. These approximate formulas are usually equations of hyperbolas, of the form pif 1 = constant (i) The value of the index n varies from o for isothermal and isopiestic expansion of moist saturated vapors, to unity, as in the isothermal expansion of gases, and to 1.333 f r tne adiabatic expansion of steam-gas. " The Curve of Saturation " and constant weight is that thermal line, on a diagram of energy, which exhibits the rela- tions of pressure and volume (usually of unity of weight) of the fluid when expanding, and kept constantly in the saturated state. In the case of initially dry, saturated, steam, at all ordinary pressures and temperatures, it would be necessary to supply heat during expansion, and to abstract it during com- pression, in order that the vapor should be kept " dry and saturated ;" i.e., on the point of condensation. The relations of simultaneous pressures, temperatures, and volumes of steam are given elsewhere. It will be seen that they are so com- plicated that the true equation of this curve becomes too cum- bersome for convenient use. Comparison of numerical results has shown, however, that the curve may be very closely repre- sented by equation (i), making n = -fj, according to Rankine, or, a little more nearly, by 1.0646, as given by Zeuner, i.e., pv& = const. ; or, /z/ 1 - 0646 = const. ; . . (2) p and v being the pressure and specific volume of the vapor. The value of this constant, in British measures, is 475, nearly; in metric measures, 1.7. An equivalent expression to the above is p m v = const. THERMODYNAMICS OF THE IDEAL ENGINE. 395 The Specific Heat of Saturated Steam is that quantity demanded, during rise of temperature, to keep unity of weight in the saturated condition, and is measured by dQ dh I I in which the coefficient 0.305, representing the increment of total heat per unit rise of temperature, is obtained from data given by Regnault's experiments. Applying the formula to any familiar pressure and temperature of saturated steam, it is dQ found that -^=, is negative in all ordinary cases, and that, consequently, it is necessary to add heat to a mass of expand- ing steam to keep it dry and saturated, notwithstanding the fact that it continuously falls in temperature as well as in pressure. Should not heat be so supplied, the steam would become a mixture of steam and water, the proportion of steam decreasing with progressing expansion. The negative value of the specific heat of saturated steam and its consequence, partial condensation, were discovered in 1850, independently, by Rankine and Clausius. It has some importance in the theory of the steam-engine. The Isothermal Line for Saturated Steam, or any other vapor, expanding in presence of the liquid from which it is formed, or containing, as is usually the case, in practice, more or less mist, is an isopiestic line, a line of constant pressure. The pressure of saturated steam is a function of tempera- ture, only, and remains constant and invariable so long as the temperature of the liquid and its vapor remains unchanged. The equations for isothermal expansion of steam, or other vapor, are therefore n = o ; p const. =/(/); . . . . (4) = *;/* = $ ......... (5) The line is rectilinear, parallel to the axis measuring vol- umes, and at a greater or less height accordingly as the tem- perature is higher or lower. 39^ A MANUAL OF THE STEAM-ENGINE. The Hyperbolic Expansion of Steam, or other vapor, is not isothermal. The tendency of such expansion, when produced, as it possibly may be, at times, is to dry moist vapor, and to superheat that already dry; the temperature falling at a lower rate than in expansion either adiabatically or as saturated vapor. This case thus differs greatly from that of the hyper- bolic expansion of the perfect gas ; which has been seen to be perfectly isothermal. In the latter case, the supply of heat must be precisely equivalent to the work done ; in the former, heat must be supplied considerably in excess of the equivalent of the external work performed. Hyperbolic expansion of steam, or other vapor, is never met with in practice, except by probably the rarest accident. The assumption made, usually, however, in computing the power of the steam-engine, that the steam expands in this manner, is often sufficiently correct for ordinary work, in prac- tice. The differences between the several curves, as shown by the steam-engine indicator, are, in good practice, seldom important or noticeable. The Adiabatic Line of expanding steam may be obtained by making the thermodynamic function constant, thus : =/ log, T+u j = const., ... (6) and ^0 = o .............. (7) When, in such case, steam, initially dry but saturated, ex- pands from the temperature, pressure, and volume 7^ , /, , z>, , to any other state, T, p, v, the value of

, thus given, pv n becomes known as the value of the constant quantity R i} THERMODYNAMICS OF THE IDEAL ENGINE. 4OI and it becomes easy to calculate the value of / corresponding to any value of v. In illustration, for one pound of initially dry steam, ex- panded adiabatically, ppf>*> =jrs-*x = 475, nearly, and we obtain for successive values of p = / ^ 5 to the nearest unit, volumes in cubic feet, and pressures in pounds on the square foot : v p * P v P 1 475 6 61 15 22 2 216 8 45 20 16 4 97 10 35 25 13 These figures measuring the co-ordinates of the curve, it may be laid down to any desired scale. The existence of sensible error in any figure is shown by the point so erroneously fixed falling outside the smooth curve passing through the other points. The graphical construction is thus a reliable check upon the computation. The geometrical construction of curves of the class, pv u = const., is very easy and often preferred to construction by the preceding method. When n = i, the curve becomes the equilateral hyperbola and may be laid down by the following methods : There are several methods of constructing this curve, of which the simplest are, perhaps, the following, as applied to produce the equilateral hyperbola, the curve of Mariotte, to which the expansion-line, in the best classes of engine, very closely approximates, and which is commonly taken as the standard. Let XX, YY be given asymptotes (i.e., the clearance and true vacuum-lines of the indicator-card), and x any given point, and let xx, xy be its co-ordinates. Extend YO until OY' = YO and draw AP, making Y'P equal to xY and parallel to XX. 402 A MANUAL OF THE STEAM-ENGINE. Divide YO and OY' into similar divisions. Assume an ordinate Om of a point to be found, and draw mx" parallel to XX. At Y' erect Y'n = Om, and draw Pnx" ; the point x" of intersection with x"n is the required point. FIG. 132. THE HYPERBOLA. For in the triangles n/ P, nmx" we shall have nY' : Y'P:: mn : x"m = = x" ; i.e., y" \x\\y\x". Q. E. D. When the expansion-line is true to the hyperbolic curve, it becomes possible to obtain a fairly approximate measure from the diagram of the clearance-space ; or, the latter being known, to determine the real locus of the hyperbolic expansion-curve, as follows : Let S', E, E', V, S represent an indicator-card ; let OX be the line of perfect vacuum ; OY the line at end of cylinder plus the clearance; then OX and OYwill be asymptotes of the hyper- bola E, A, A', E', the curve of expansion. THERMODYNAMICS OF THE IDEAL ENGINE. 403 Take two points on the curve A A', and AK, AC, A'B, and A'ff will be their co-ordinates. Draw AA t and from C t the line CB parallel to A A' ; the point B, where it intersects A'B, will be a point in the line OY. Or, draw HK parallel to A A ', and AT, the intersection with AK t will be such a point. For by Mariotte's law and from the properties of the hyperbola, xy = m ; x'y' = m ; .-. jry = J^X- or, A'D'.BD-AD'.DC. And, from similar triangles (by construction), A'D\ BD \\AD\ DC. Q. E. D. Conversely, having given the clearance and the scale of the indicator, with point of cut-off, to find the expansion4ine. In proportion y y 1 ' '. y :: x" x : x, assume x' and find values of y by constructing the triangle KPH, similar to ADA '. Taking the point of release as a point in the hyperbolic curve, and laying down that curve on the diagram, it will be found, not only that the curve and the expansion-line of the diagram do not coincide, but that the latter falls above the 404 A MANUAL OF THE STEAM-ENGINE. former throughout its length, in nearly all cases, indicating, usually, initial condensation and later re-evaporation, but some- times indicating some leakage as well. If the weight of steam actually drawn from the boiler be taken as the basis of a dia- gram, using its volume as the initial ordinate of the hyperbolic curve, it becomes easy to trace the variations of the whole actual diagram from the ideal indicator-card, as here shown. In any case in which the curve represented by the expan- sion-line is of the class of which the equation is the co-ordinates sought, any one point, /,$;, or pjj^ being given, may be found, and any new point in the ideal curve determined by computation, thus : From the above expression, n log v + log/ = n log v l + log/, ; and if/, and v r are known, for any assumed volume v, the log- arithm of the corresponding new pressure must be log/ = n log v l -\- log/, n log v ; which expression being used to determine several points, the curve may be drawn through them. The values of n have been seen to be as follow : Equilateral hyperbola, . . . . I Curve of steam ; saturation --, or 1.0646 Adiabatic curve, steam, .... 1.035 ~(- o.i^r " gas, .... 1.408 Isothermal " " ..... i.o The variation of the actual ratios of expansion from their apparent values, in engines having large clearance-spaces, is very considerable at high ratios of expansion and in short- stroke engines. The close approximation of the three principal steam-ex- pansion lines is well shown by the accompanying diagram, a THERMODYNAMICS OF THE IDEAL EXGIKE. 405 set of curves shown in various publications, but probably first laid down in this form by Mr. Porter.* AB exhibits the initial volume, as does also CD ; AD and BC represent the initial pressure ; EF is an ordinate, taken at convenience ; and the terminal ordinates are GH, 7J/, and LK. OR is taken at half-stroke ; while CN is the axis of the equilateral hyper- bola, AOG t the upper curve, of which CB and CH are asymptotes. Ordinates measure absolute pressures in pounds FIG. i34--TH TMBI FII 1111 mil per square inch : abscissas represent volumes of unity of weight (i lb.lt Thus BA is the volume (4.73 cu. ft.) of one pound of steam at a total pressure of 90 pounds per square inch; ABCD is the external work done in its production. It is this curve which is commonly assumed to be that of the expansion of steam. The curve AOI is the curve of dry and saturated steam, its co-ordinates representing the simultaneous pressure and volume of the fluid when in contact with the mass of water from which it is produced. The expansion is less, and the rate of fall of pressure greater, than if it were to follow the law * Steam-engine Indicator; p. 1*3. 406 A MANUAL OF THE STEAM-ENGINE. of Mariotte. It is this curve which is assumed to be described when steam expands in well-jacketed engines. The lower line, AOL, is the adiabatic curve, assumed to be obtainable in engines with non-conducting cylinders and approximately in " high-speed engines." The area under this, as under the other curves, represents the work done as the steam expands, and exhibits the gain obtainable by expansion, in each case. In all real engines, however, the expansion-line falls at first more rapidly, and finally more slowly, than either of these curves. As elsewhere seen, this variation from the ideal curve is often very observable. Cylinder Condensation and Leakage produce variations in the diagram, as obtained, which differently affect the different parts of the curve. Leakage can usually be eliminated, and always should be before the engine is set at work regu- larly. The first-named waste is usually irremediable. Its character, laws of variation, and magnitude will be studied in detail in the succeeding chapter. When the exact measure of the quantity of steam expended is obtained by a boiler-trial, it is easy to trace these variations, as in the indicator-diagram, Fig. 135, taken from the engine and worked up by the late Professor C. A. Smith, in which illustration the diagram which should have been produced by the same steam, had there been no initial condensation, is shown with the real diagram.* This indicator-diagram is an unusually good sample, as to form, and was taken from the St. Louis high-service pumping- engine, a machine of 705 I. H. P., 85 inches diameter of cylin- der and 10 feet stroke of piston, making 1 1 revolutions per minute. Taking measures of the abscissas of the two dia- grams, it is seen that the condensation amounts to from about 30 per cent as a minimum to 50 per cent as a maximum, so far as measurable, the actual card illustrating the expansion in a metallic cylinder of the steam, which would have given the larger diagram in an ideal engine with its non-conducting cylinder. The complete ideal diagram would extend propor- * Steam-making; p. 91. THERMODYNAMICS OF THE IDEAL ENGINE. 407 tionally farther toward the right and beyond the limits of the actual figure. When the two lines continue so far separated, it is an indication of large initial condensation, and correspond- ingly great re-evaporation after the exhaust-valve opens ; as the initial condensation is due to, and is proportional to, the re- evaporation. In most cases, however, the engineer, unable to determine these data, assumes the point of release, or the point of intersection of the expansion-line prolonged with the ordinate at the extreme end of the diagram, as that of coinci- 80- FIG. 133. THE REAL AND THE IDEAL CARD. dence of the ideal and the real curve, and draws the hyperbolic curve backward from that as a given point, in the manner already described. A comparison of the ideal diagram thus formed with the actual indicator-card will give a means of judging of the character of the engine studied as a thermo- dynamic machine. Rankine's construction will enable the engineer conveniently to find the absolute mean pressure in the steam-cylinder and the final pressure.* Thus, in Fig. 136, draw AB and AG ; take AC equal to one fourth AB ; from C as a centre, strike the arc BFG\ and AG then measures the stroke of piston plus clear- ance. Take CD proportional, on the adopted scale, to the clearance ; AD then measures the stroke. Make AE the dis- Hutton's Handbook; p. 380. 4 o8 A MANUAL OF THE STEAM-ENGINE. tance to the point of cut-off, and draw the perpendicular EF, which will measure, very closely, the absolute mean pressure ; FIG. 136. MEAN PRESSURES. while EH, measured to the intersection with the line BG, will be approximately the final pressure.* EF I + log, r p m Then -j-^ = = , nearly, the quantity EF being slightly large for large values of r, small for small values, and exact for r = 3.5, nearly. The curve pv n = C may be constructed approximately by the following general method (see Fig. 137).* Starting from L, draw any horizontal line, QC, at a small distance below L, then the question is to find S, the point on the curve which lies on QC. For this purpose, set downwards and and complete the rectangle NT as shown in the figure ; also draw the horizontal line RF to meet the ordinate LNH in F, as shown in the figure. Then bisect DQ in Z, join ZF, and prolong it to meet the horizontal through T in E : a vertical Rankine's Ship-building. f Cotterill; ist ed., p. 340. THERMODYNAMICS OF THE IDEAL ENGINE. 409 through E will be the new ordinate very approximately, and by its intersection with QC will determine 5. For, completing the rectangle TS', as shown by the dotted lines in the figure, the rectangles ZH, ZG are equal, for ZT ~ RG' < RG = FR, and ZN is common. .-. OH OG + NS'\ that is to say, Rectangle NS' = Rectangle OH Rectangle OG. H E FIG. 137. CONSTRUCTION or PARABOLAS. Now if the points LS be taken near enough together, the area of the rectangle NS f may be made to differ as little as we 410 A MANUAL OF THE STEAM-ENGINE. please from the area of the strip of the curve LSN, and the rectangles OH, OG are equal to P, V l , P,V t , respectively, divided by n I ; hence, referring to the formula for the area given above, it is clear that we have determined S, so that it lies on the curve PV n = constant very approximately. The thermal lines being thus constructed, their combina- tion in diagrams of energy representing the cycles of operation of any heat-engine becomes practicable when the construction and method of operation of the engine are given, and the graphical solution of problems relating to work and efficiency may thus be effected. The lines observed in real engines are so different from those of the ideal engine, in nearly all cases, that it is not worth while ordinarily to use the complicated exact expressions found for the latter. The simpler curves above described give quite as satisfactory approximations to the actual forms. The expansion line, usually, in real engines, falls, at the beginning, more rapidly than the common hyperbola, and at the end less rapidly, thus giving a curve of a different class. 104. Cyclical Thermodynamic Operations are such as consist of a series of thermodynamic changes, in such order and of such character that, at the termination of the cyclical period, the initial physical conditions are precisely reproduced. Such cycles were first defined by Carnot, and he was also the first to call attention to the obvious fact that, in such opera- tions, the internal structure and internal variations of energy might be ignored ; since, at the end of each cycle, the working fluid, whatever its nature, "returns to precisely its original state ; that is, to that state considered in respect to density, to temperature, to mode of aggregation." * In such operations, therefore, it is a matter of no importance whether internal forces are known or unknown, large 01 3mall, measurable or indeterminate; whether the fluid be a gas, a vapor, a liquid, or a solid. The changes of internal work and * Reflections on the Motive Power of Heat; edited by R. H. Thurston; N. Y., J.Wiley & Sons; 1890; p. 67, foot-note. THERMODYNAMICS OF THE IDEAL EJTGIA'E. 411 energy, positive and negative, must balance; and their sum must be zero for the cycle. It thus becomes easy, in such cases, as shown by Carnot, to determine the useful effect, the wastes, and the efficiency of any cyclical thermodynamic changes irrespective of the character of the working fluid. Such cycles are illustrated in the well-known "Carnot cycle;" in which the fluid expands (i) isothermally, (21 adia- batically ; (3) is compressed isothermally, and (4) adiabaticaliy ; the latter period being so adjusted as to finally, at its close and at the termination of the cycle, bring the fluid back precisely to its initial temperature, pressure, and volume. Here the work of adiabatic expansion balanced that of adiabatic com- pression; while those quantities performed during the iso- thermal changes, positively and negatively, are in exact propor- tion to the constant absolute temperatures at which the two steps occur. Thus this cycle results in the performance of work by transformation of a proportion of the total heat- energy, * T -, into mechanical energy and the waste of the *! proportion, ~ t as rejected, untransformed, heat. This, as was shown by Carnot, also, is the maximum possible efficiency of any system whatever, and with whatever working fluid the work may be done. It is evident that, with the steam-engine, the same principles and conclusions apply, and the study of the engineer is to endeavor to approach this fraction of efficiency in practice as closely as possible; while also making its absolute value as high as possible by making T t T t a maximum. In order to solve many problems in the thermodynamics of the steam-engine, as of other heat-engines, it is necessary to study the methods of expenditure of heat and of performance of external work, step by step, through a cycle, and thus to ascertain the extent and character of those variations from Caraot's ideal cycle of maximum efficiency which result in loss of heat and dynamical effect. Fig. 138 illustrates the more regular forms of thermo- 412 A MANUAL OF THE STEAM-ENGINE. dynamic cycle met with in the operation of heat-engines. A B and CD are two isothermal lines crossed by two adiabatics, EFand G H. The perfect engine cycle of Carnot \sabcd; the same with the adiabatic lines replaced by lines of constant volume, which are here those of a regenerative action, is seen in a b n m. Others are formed, as e f g k, and fijA, by lines of constant pressure crossing the two pairs of curves, and by lines of constant volume crossing them, as in a bum and o pqr. Many other cycles are formed by other combinations. That A C E G FIG. 138. THE THERMODYNAMIC CYCLE. seen in w s t u v is the ideal steam-engine cycle modified by the usual exhaust line, and drop of pressure at constant volume at t u. //"/is taken as the "atmospheric" line. Here the iso- thermal, w s, corresponds to that portion of A B or C D at the extreme right ; where it becomes asymptotic with O X. The cycle of Carnot, abed, is illustrated in the action of the now well-known type of air-engine of Stirling ; in which a mass of air is permanently enclosed in a working cylinder, in which its variations of pressure, temperature, and volume are pre- cisely such as are above described. It represents the most efficient of all known types of hot-air engine. THERMOD YXA MfCS OF THE IDEAL ENGIXE. 413 The closed cycle, w s t u p, is also well illustrated in the most effective types of modern steam-engine. In the marine steam-engine, for example, the feed-water is taken from the hot- well or the discharge of the surface-condenser, with which such engines are now always fitted ; is forced into the boiler by the feed-pump ; is there converted into steam by accession of heat from the fuel, with consequent expansion into the va- porous state; is next transferred to the working cylinder; where its expansion results in the conversion of a certain pro- portion of its heat into mechanical energy, by a process similar to that just described as in the cycle of Carnot. It first drives the piston at constant pressure and temperature, as is required in a cycle of this form ; next it expands adiabatically. to a minimum temperature and pressure and a maximum volume, precisely as in that cycle ; then it is compressed, at this mini- mum pressure, into the condenser, which removes the heat of compression and preserves its pressure and temperature con- stant, so as to give an isothermal change ; and, finally, being thus reduced to the liquid state, once more, it is once again forced into the boiler, to enter upon another similar cycle to that now completed. The last step, compression as liquid, into the boiler, and its increase of temperature to that of the steam into which it is presently converted, corresponds to the period of adiabatic expansion at the other side of the cycle. To make it exact, however, it is evident that the last step should be the compression of the vapor into liquid, at the higher temperature and pressure, by a purely mechanical action ; instead of its in- troduction, cold, into the boiler, and its elevation, there, to the maximum temperature by heat directly applied. The action of the non-condensing engine is, in essence, the same as that just traced. The steam enters the engine at a maximum temperature and pressure ; drives the piston, up to the point of cut-off, by an isothermal expansion ; is then ex- panded to the back-pressure and corresponding temperature by an adiabatic process, as nearly as the nature of the case will permit; is then rejected into the atmosphere an isothermal process, where it is condensed, the atmosphere being here the 414 A MANUAL OF THE STEAM-ENGINE. condenser ; and it finally reappears as feed-water to be once more passed through the same cycle again. Thus each revolu- tion of the engine illustrates a cycle, in duplicate, one on each side the piston. In the trials of engines, it is necessary, to secure a satisfac- tory result, that the engine should be operated steadily until its " regime '" is fully established, and until it is making cycle after cycle, precisely under the same conditions, before the trial is commenced. This is here especially important because of the facts, to be more fully discussed later, that the reactions between the steam and the cylinder-surfaces are of real impor- tance in the economics of the machine, and that it takes some time to establish uniform action in this respect. Steam and Air being compared, as representative of two ex- treme types of working fluid, it will be found, as indicated by our formulas, which show maximum efficiency of fluid to be dependent upon temperature solely, that the one must be just as efficient as the other as a medium of transformation of heat into mechanical energy, provided the fluids are worked be- tween the same initial and terminal temperatures. The formulas already given enable this comparison to be readily made. Both fluids may be assumed to work in the Carnot cycle. Such a comparison was made by Rankine as early as 1867,* the data and results being, in British units, as follow : DATA. T T E = ' ' = 0.2228. * i U (assumed) 68,420 ft.-lbs. Pressure of steam ................... p l = 5652 ; P l = 39.25 Pressure of air ...................... ./>, = 5050 ; P, = 35. 1 * The Engineer ; Aug. 2, 1867. THERMODYNAMICS OF THE IDEAL ENGINE. 4! 5 Volume of steam, initial, v t i.oo cu. ft. Weight of steam 0.0956 Ibs. Weight of air 1.6113 Ibs. Volume of air, initial, t/, 9.81 cu. ft. Volume of air, atmospheric 22.87 cu. ft. RESULTS. St. -engine. Air-engine. Diff. Heat expended, ft.-lbs 68,420 68,420 o Heat rejected, " 53,i?6 53,176 o Heat transformed into work, ft.-lbs 15,244 15,244 o Work of expansion, ft.-lbs 16,690 68420 5 1,730 Work of compression, ft.-lbs 1446 53,176 5i,73O Work per indicator, net 15,244 15,244 o Efficiency 0.2228 0.2228 o An enormously greater amount of work is thus seen to have been done during the forward stroke of the air-engine than in the case of the steam-engine ; but this is balanced by a pre- cisely equal excess in compression during the return-stroke ; the heat of such compression being necessarily wasted. Both engines thus do exactly the same net amount of work during each cycle, expending the same quantities of heat and exhibit- ing the same efficiencies of fluid. But it is seen that the air- engine must have much the greater bulk, and, consequently, in nearly the same ratio, the greater weight ; and this fact makes the comparison of efficiencies of engine, including both efficiency of fluid and that of mechanism, result much more favorably to the steam-engine. This advantage of the steam-engine be- comes greater at high pressures, and is a vital one under its usual working conditions. In all cases of adiabatic change of volume under pressure, doing external work, we shall have for the thermal change, in dynamic units, 416 A MANUAL OF THE STEAM-ENGINE. where x and / represent the proportion of fluid in the vaporous state in the mixture and the corresponding latent heat. In gases x x' = I, and / = /' = o; and we have When the work is that of expansion, t t' is positive ; the difference of latent heats may be either positive or negative. In compression these signs are reversed. The former case is illustrated in heat-engines ; the latter in refrigerating ma- chinery. In the former, efficiency is promoted by a wide range of expansion to a minimum temperature ; in the latter, by a narrow range at maximum temperature ; the measure being, for the first, T, a - & E = and, for the second, JQ_ F - T, - T, - <2, - The choice of a working fluid, in both cases, is purely a mat- ter of extra-thermodynamic consideration, all working fluids having identical thermodynamic efficiency. Conclusions of interest and importance relative to the ther- modynamic properties of the several vapors practically most available for the operation of heat-engines, as ether, chloroform, alcohol, carbon disulphide, water, may be deduced from sim- ilar comparisons, thus :* Where the several fluids are worked between the same temperature-limits, and consequently have the same thermody- namic efficiency, considerable differences are to be observed in their tensions, at both initial and terminal temperature, ether exhibiting highest, and steam the lowest, pressures ; the one having nearly four times the tension of the other. It is ob- * Efficiency of Fluid in Vapor-engines; Van Nostrand's Magazine; 1884. Wood's Thermodynamics; 1889. THERMODYNAMICS OF THE IDEAL ENGINE. 417 served that a high tension is accompanied by a small value of the potential energy of latent heat : while great elasticity is generally an accompaniment, also, of high density ; although no direct relation is yet determined. Most interesting differences are seen in the magnitudes of work, of compression and expansion. The net effective work being the same, those vapors with which the work of expan- sion is greatest also demand the expenditure of most energy in their compression ; the difference in energy exerted and en- ergy received being constant throughout the list. The variation of the ratio of expansion among the various working fluids is, in such cases, very noticeable ; and the in- fluence of this ratio, and of the magnitude of the final volumes of the several fluids, upon the size of working cylinder required is an important practical consideration, which is well illustrated by the comparison of these quantities in the steam- and the air-engines. The fact that the familiar limiting conditions of operation of real engines may produce important practical re- sults in the modification of efficiency of fluid and of economy of working is forcibly shown by the results obtained in the other cases of comparison of vapors. On the whole, it will be found that, if we make our com- parisons within those limits of pressure found practicable with the steam-engine, the vapor of water is the most efficient of all available fluids under the conditions of use in real engines, and, since all the apparent advantages of the non-aqueous vapors may be gained by increasing pressures and, especially, of temperatures of steam, it seems probable that none of those fluids will ultimately successfully compete with steam. It is further evident that the use of air and other gases, now giving large thermodynamic efficiency, must involve comparatively low efficiency of mechanism, and that this latter disadvantage may be lessened by working a larger weight of fluid within a given volume : i.e., by working the fluid at initially greater density. Collating expressions used in the preceding study of the thermodynamics of the ideal engine, their tabulation in compact 41 8 A MANUAL OF THE STEAM-ENGINE. form will be found very convenient for reference and in doing work. The following table is thus obtained : WORKING FORMULAS OF THERMODYNAMICS. (I) dH = Qd. . (2) dH = Td$. (C)dH=dE 90- (3) log/ = a - bo? - eft*. , x Sii So"o ^vj_-' (4) A^T~ ~T~' ioo = 274 Centigrade (or 493 F.). 93- dU = pdv, THERMODYNAMICS OF THE IDEAL EXGINE. 419 pv T 95. (i) ~ = j^ = constant = R, for a perfect gas. (3) dff= (5) = KJT+fdv. (6) = (7) dH= (15) = 42O A MANUAL OF THE STEAM-ENGINE. When gas expands or contracts at constant temperature 96. H=RT l log, ^ = A"i log, ^ = A", log. r - Adiabatic expansion : 96. dH = r, Work of perfect gas at constant temperature: /Vj A*? j fc/f, J i>\ >l l U = p l v l \og e r. Work of adiabatic expansion': CHAPTER V. THERMODYNAMICS OF THE STEAM-ENGINE. WASTES OF ENERGY; EFFICIENCY. 105. The Thermodynamics of the Real Engine involves the application of the principles of science to the determina- tion of the quantities of thermal converted into mechanical energy, the proportion wasted, the efficiency of steam as the working fluid in the machine, and the weight of steam, and where the data permit that of the fuel demanded per horse- power and per hour, or other unit of power or of time, in effect- ing such transformation in an ideal, purely thermodynamic, en- gine. Since no other than thermal and the equivalent mechanical energies are taken cognizance of by this science, and no physi- cal changes or transfers are considered, all those circumstances and conditions which distinguish the real from the ideal case, in energy-transforming machinery, in the case, for example, of the heat-engines, must be treated by extra-therm odynamic methods. The study of the thermodynamics of the steam- engine comprehends, simply, the investigation of the machine so far as it is an ideal heat-engine, subject to no other than the inevitable thermodynamic wastes. The study of actual engines, however, involves the exami- nation of both physics and dynamics in their applications in such machines, and the problem is thus rendered a much more complicated one than that in thermodynamics and far less easy of exact solution. It is still generally admitted by writers on the steam-engine that, as stated by Him, it is impossible to construct a theory that shall be scientifically exact, and will accord perfectly with 422 A MANUAL OF THE STEAM-ENGINE, practical experience in even the best practice.* Nevertheless, designers and builders are required to use methods and formu- las in their preliminary computations and in preparation of their plans, not only for the computation of dimensions and proportions of parts, but also to obtain approximate estimates of the quantity and the cost of the work to be performed and of the heat, the steam, and the fuel to be demanded for its performance. In the following pages so much of applied theory and approximate methods as may be considered as practically useful, to-day, will be exhibited and illustrated. In all cases, however, the engineer is guided largely by, and his computa- tions are checked by reference to, experience with as nearly as may be similar practice. 106. The Steam-engine as a Heat-engine is a machine in which heat-energy stored in steam is converted into the dynamical form and applied to the purposes for which the en- gine has been designed. In this process, the steam, produced in the steam-boiler, is supplied to the engine at such a pres- sure and temperature as will permit a considerable range of adiabatic, or approximately adiabatic, expansion, and the con- sequent transformation of a considerable fraction of its thermal energy. This energy exists, initially, in the steam, in the form of sensible and latent heat, and is in larger proportion sensible, as has been seen, as the temperature and the pressure are more elevated. Were it practicable to use the fluid at the tempera- ture and pressure of its " critical state," all heat-energy would be in the sensible form. In any case, a fraction of the heat supplied is converted, by the cyclical action of the machine, into work ; while the other portion, usually large, is necessarily rejected at the minimum temperature reached. The larger the fraction transformed into mechanical power, the larger the efficiency of the machinery ; and its maximum possible effect is measured by the proportion, _ , Him: Thermodynamique; 1876. Sinigaglia: Machines a Vapeur; 1890. THERMODYNAMICS OF THE STEAM-ENGIXE. 423 of total heat-energy stored in the fluid at its entrance into the engine. As elsewhere shown (93, 112), the quantity of work per- formed per unit weight of working fluid is determined by the quantity of energy that may be stored as latent heat of expan- sion and vaporization. In this respect, steam is superior to other available working substances ; and the engine in which it is employed can be given smaller volume and weight than any other, the air-engine for example, in which this latent heat is less. 107. The Real and the Ideal Engines are so radically different in their conditions of action and in the nature and magnitudes of their wastes of energy that the engineer distin- guishes carefully between the two cases. The ideal engine presents a purely thermodynamic prob- lem, capable of exact and unqualified solution. It illustrates simply the transformation of thermal into dynamic energy, with no other loss than that unavoidable waste due to the operation of the second law of thermodynamics, the magnitude of which is easily and precisely computed as soon as the con- ditions of the problem are definitely given. This process of computation has been fully described and its application illus- trated. The real engine is a piece of mechanism composed of sub- stance incapable of retaining heat and permitting free transfer to and from the working fluid, wasting large quantities exter- nally by conduction and radiation, and internally by alternate storage in its own substance and restoration to the working fluid in such manner that transfer occurs without transforma- tion, in large proportion. It also wastes a large amount of the mechanical energy produced by transformation in the work of moving its own cumbersome parts. The Real and the Ideal Engines in their operation are thus distinguished by a very wide difference of efficiency, resulting from the correspondingly enormous differences of physical working conditions arising out of the thermal and 424 A MANUAL OF THE STEAM-ENGINE. mechanical operations unavoidably accompanying the thermo- dynamic phenomena. In all real engines the departure from the ideal conditions assumed is very great, not only in steam-, but even in gas- and air-engines, and so great as, in most cases, to lead to radically different results from those attained in the ideal case. Explosive and other gas engines are impelled by a mixture of hot gaseous and vaporous products of combustion, of which the latter portion is, like the working fluid in the steam- and other vapor-engines, subject to rapid and considerable changes of thermal state. Enclosed, usually, in a chamber the sides of which are kept cool by a water-jacket, enormous quantities of heat are lost as expansion proceeds, and the efficiency of the machine is correspondingly diminished, and both the efficiency and the most economical ratio of expansion are altered by the increased losses which accompany the higher ratios. Steam always condenses in the steam-cylinder in conse- quence of the conversion of a part of its heat into work, even though the expansion be perfectly adiabatic ; and, in the actual engine, this occurs to a much greater extent, unless, by superheating or by the use of an efficient jacket, consid- erable heat is supplied it before or during expansion. The first quantity is, however, insignificant in comparison with direct losses of heat ; it probably seldom approaches ten per cent of the heat supplied, and is, usually, a very much smaller figure. Initial condensation and later re-evaporation of steam in the steam-engine, and initial cooling without subsequent re- heating, in gas-engines, are the greatest sources of waste of heat, and give rise to losses that are both absolutely and relatively very great wherever the range of temperature during expansion is very considerable, and especially with low back- pressure. The steam passing out of the exhaust-ports to the con- denser or into the atmosphere is moist and heavy with the water of condensation, and is a good conductor of heat as well as a very greedy absorbent. It sweeps out of the THERMODYNAMICS OF THE STEAM-ENGINE. 425 cylinder large quantities of heat abstracted from its inner surfaces, leaving those surfaces comparatively cold and wet with a chilling dew. The entering steam meets these cold metallic and liquid masses and is condensed in sufficient quan- tity to reheat them to the temperature of prime steam. As the piston moves forward it uncovers new surfaces, and con- densation continues until, sometimes, a large fraction of the steam supplied lies in the cylinder or floats in the uncondensed steam as water and mist. Toward the end of expansion, and especially during exhaust, re-evaporation occurs, from the ex- posed surfaces and in the midst of the mixture of water and steam, at lower pressures and to a similarly serious extent. Thus heat is constantly transferred from the steam to the exhaust side, and, doing little or no work, is wasted, and the efficiency of the engine and the cost of fuel are greatly affected. This loss may be greatly reduced by superheating and steam-jacketing. Loss from this cause has been found to be so great, and to increase so rapidly with increased expansion, that it practically often sets an early limit to the economical increase of the ratio of expansion. It is thus seen that several directions of distribution and waste of energy are found in the real engine which do not exist in the ideal case, and which constitute characteristic dis- tinctions between the two. The engineer thus observes the following facts, and bases upon them his nomenclature of the various " powers" and " efficiencies." When steam enters the engine from the boiler, it is made the vehicle of heat-transfer and the medium of transformation of thermal into mechanical energy. The work performed in the cylinder and the power developed are called the "indi- cated work and power" The ratio of this work to the mechanical equivalent of heat required in a non-conducting cylinder for the same operation is the measure of thermodynamic efficiency. The ratio of this latter quantity to the actual efficiency, as measured by the ratio of mechanical energy to the total actual heat used, including 426 A MANUAL OF THE STEAM-ENGINE. heat-wastes in the metallic cylinder, may be called the efficiency of the working substance ; its efficiency for use as a medium of energy transfer and transformation. When the energy applied to the piston, as measured by the indicator, is carried onward through the machine, and finally given out at the shaft to the driven machinery, it loses an amount measured by the friction of the engine, and, this lost work being taken out of the indicated work, we have the work usefully given out as measured by the dynamometer. This is called the dynamometric power. Its ratio to the indicated power is the efficiency of the machine. Engineers usually express the quantities of power in horse- power and, in symbols, as /. H. P. and D. H. P. 108. The Wastes of the Steam-engine are comprised in three distinct classes: (i) the thermodynamic waste; (2) the physical, thermal, waste ; (3) the friction-wastes, and other dynamic, or mechanical, losses. Of these, the first is easily computed when the thermodynamic cycle of the machine is known, and can be determined with precision. The second is divided into two parts : the waste of heat directly by im- mediate conduction and radiation, the heat so wasted stream- ing steadily out to surrounding, cooler, bodies ; and the waste caused by the process described in the preceding article, that due to alternate storage of heat, without transformation, in the metal of the working cylinder, and, later, with little or no util- ization, discharged from the engine. The third kind is that produced by waste of energy previously transformed, by the thermodynamic operation, from the thermal to the dynamic form, and expended in overcoming back-pressure and the friction of rubbing parts. The sum of these wastes being deducted from the total energy supplied as heat, the remainder measures the heat- energy utilized by the engine, and delivered to the user in the form of available mechanical power. The efficiency, as already seen, of any purely thermody- namic engine depends solely on the method of heat-supply and rejection, and in no respect upon the nature of the working THERMODYNAMICS OF THE STEAM-ENGINE. 427 substance, or the structural details or arrangement of the machine. The heat-wastes of the real steam-engine, in the usual order of magnitude and importance, may thus be considered as fol- lows: (1) Thermodynamic loss. (2) Internal condensation. (3) Conduction and radiation. In detail, wastes are due to (1) Exhaust-wastes by action of the metal of the cylinder. (2) Incomplete expansion. (3) Back-pressure. (4) Clearance and restricted steam-passages. (5) Exhaust- waste, from the expansion period on. (6) Transmission of heat, externally. To which may be added, (7) Boiler and feed-water heat and other wastes. The character and the method of these various wastes of energy in the real engine remain to be studied, and their mag- nitudes to be determined by experimental investigation. . As was probably first noted by Cotterill, the wastes by the exhaust include both that due ** cylinder-condensation," initially, and that produced by condensation during expansion. The latter occurs, with production of a suspended mist, within the whole expanding mass, and its effect in robbing the metal of the cylinder of its heat is little or nothing ; while the former measures the loss by alternate storage and restoration of heat by exchanges between the steam and the metal. There is always, as shown by Him, a balance, in this case, of heat stored and heat restored, of heat-waste to the condenser and heat taken out of the entering charge. Exact computations would always require correction of estimates of energies transferred by consideration of the work of air-pump in condensing engines, and of the feed-pump in all forms ; although the latter is too small a quantity to assume importance in ordinary work. 109. The Thermodynamic Wastes include only that pro- 428 A MANUAL OF THE STEAM-ENGINE. portion of the heat supplied to the machine which is computed as waste in the ideal case ; and which is necessarily rejected from the machine at the lower limit of temperature and press- ure, during the return-stroke of the piston. In the case of those engines in which the working fluid is retained, this wasted energy is rejected as heat, by transfer to some other, cooling, substance ; the work of the engine being effected by changes of volume, temperature, pressure, and heat-content of the same unchanging mass of molecules. In other engines, the heat is rejected with the discharged working fluid, during the exhaust-period. The Sterling air-engine and the non-con- densing steam-engine are examples of the two classes of engine and the two methods of rejection. In the case of the perfect, ideal, engine working in the cycle of Carnot, the proportions of heat constituting these thermo- dynamic utilizations and wastes have been seen to be, invariably, and T = r //, ; H a -f- H b = when H a , ff b , and //, are the quantities of heat utilized and wasted, and that initially supplied. In all other cases the quantity wasted is larger, as the working cycle departs more and more from that of Carnot ; as, for example, by incomplete expansion. It can always be computed, however, when the cycle is known, either by tracing the complete cycle, noting the quantities of work done positively and negatively, taking the algebraic sum as the measure of heat transformed, and the remainder as that wasted ; or by simply measuring up the curve of energy, the " indicator-diagram " for the cycle, and taking it as the mechanical equivalent of the heat utilized by transformation, and the difference, between this quantity and the total supplied, as the waste. THERMODYNAMICS OF THE STEAM-ENGINE. 429 HO. The Physical Wastes, externally, the purely thermal external losses, due to conduction and radiation to adjacent bodies, are not usually very large in amount in the real engine: while they have no existence in the ideal case. In small gas- engines, the Author has found this loss to amount to, in some cases, ten or even fifteen per cent of the heat supplied : with single-cylinder steam-engines of 100 I. H. P., and upward, this ought not, with good coverings on external surfaces, to exceed about 5 per cent ; the compound engine is naturally subject to greater loss. The amount can be easily computed wherever the area of exposed surfaces, their character, their tempera- tures, and the nature of the covering are known. The larger the machine for a given power, the higher the steam-pressures, and the less effective the clothing and lagging of the cylinders, the greater this loss. It is also exaggerated by roughness of exposed surfaces, as of cylinder-heads, or of piston-rods and valve-rods. The internal wastes, t/iose due to " cylinder-condensation" on the other hand, are often simply enormous, as has already been stated, and are extremely variable with all the changing conditions of the every-day operation of the engine. It is well known that the magnitude of this loss is greater as the range of temperature during expansion is greater ; it is increased by slow speed of engine, by reduction of the back-pressure, by in- crease in size of engine for a given amount of work done, by increase in conductivity of the surfaces of the \vorking cylinder, and, within certain limits, probably, by wetness of steam. It is reduced by low ratios of expansion, by increasing back- pressures, by reducing initial pressures, by increasing speed of engine, and by special expedients, as steam-jacketing, super- heating, and the division of the expansion between two or more cylinders, as in " compound " or multiple-cylinder engines. Even increasing compression may reduce this loss and thus give a higher steam-line and an altered expansion-line. The waste becomes the less, when the sides of cylinders only are jacketed, the smaller their diameter ; it is lessened, when both 43O A MANUAL OF THE STEAM-ENGINE. heads and sides are jacketed, by increasing diameters, volumes being in both cases equal. The difference in back-pressure between non-condensing and condensing engines is productive of such a wide difference in the range of temperatures worked through in usual cases, that the Author has been accustomed to consider the compen- sation so complete as to justify the assumption that the value of this waste, its equivalent pressure being taken as a " virtual back-pressure," may be assumed to be independent of the mag- nitude of the actual back-pressure, and to be determined solely by other conditions above noted. This waste is found to be reduced most effectively by super- heating, and somewhat by the admixture of air with the steam, or by the free use of oil in the cylinder, as well as by any ex- pedient, in fact, which will reduce the facility of exchange of heat between the steam and the metal of the cylinder, whether by decreasing the condensing and heat-transferring power of the former, or the receiving and storing power of the latter. This internal condensation is an exceedingly rapid process ; being precisely like that occurring on the tubes of the surface- condenser, except that, instead of the difference of tempera- ture, or head producing heat-flow, being constant, the condens- ing surface immediately rises in temperature, and presently reduces the condensation to that rate at which the heat re- ceived and thus stored can be transmitted into the mass of metal behind. In Emery's experiments on the Bache and the Dallas, this rate exceeded 100 pounds per square foot per hour, and is often in excess of even that rate. It is thus found that the rate of condensation exceeds that of ordinary surface- condensation very greatly ; this greater activity of heat-transfer being very possibly due to the fact that the deposited water of condensation, which, unless artificially swept off, impedes this action greatly, in the engine is re-evaporated, at each exhaust ; thus, perhaps, giving clean surfaces at the time of initial con- densation. in. The Mechanical Wastes in the real engine are com- monly somewhat greater than the thermal wastes, externally ; THERMODYNAMICS OF THE STEAM-ENGINE. 43! but are not necessarily so ; they have been reduced, in some instances, at least, in non-condensing engines, to as low as five per cent of the total power of the engine, and, in condensing engines, below ten per cent. Probably usual values are a half higher. This loss is measured by the difference between the power shown on the indicator-diagram and that measured at the same time by the Prony brake, the absorption-dynamom- eter. Its magnitude depends on the size and proportions of the engine, and especially of its rubbing surfaces, and upon the character of the lubrication. Journals of sufficient size to pre- vent danger of overheating, and the most liberal possible con- tinuous supply of the best lubricants, are the means to be adopted in the reduction of this waste to a minimum. Flooded journals and a system of recovery and re-use of oil will be proba- bly always found advisable. The effects of clearances and of back-pressure will be studied later (Chap. VI). 112. Transformations in the Ideal Case, those of Ex- ternal Work, Energy, and of Heat, by the expansibn of steam, or any other vapor, are easily determined oy the thermody- namic processes already enunciated and illustrated. The external work done during isothermal expansion of vapors containing, or in contact with, their liquids, since their isothermal line is a line of constant pressure, is evidently, measuring from the zero line, and this amount of work demands an equivalent quantity of heat-energy for transformation into the mechanical form. A certain additional amount of heat must also, in all cyclical operations, always be transferred, without transformation, and, at the same time, " degraded " in intensity, i.e., in temperature. This latter quantity is determined by the character of the operation of which the cycle is representative. Still another quantity of heat will be required, for trans- formation in performing the internal work of separation of 432 A MANUAL OF THE STEAM-ENGINE. molecules the latent heat of expansion, the method of com- putation of which quantity has already been considered As has been seen, the amount of this heat and internal work is unimportant in cyclical operations; since equal amounts are always stored and restored during the cycle.* In isometric changes in vapors, as with gases, no work is done, and no heat is transferred, except in the production of changes of temperature ; for no space is traversed against re- sistances only to be overcome by transformed energy. In cases of expansion in real engines, in which the curve may be fairly represented by the equation pv* = constant, the amount of external work done, and the equivalent heat transformed, is thus found : When the external -work of isothermal expansion, p l v l , is added, as in the measurement of the total work done during the forward stroke of the steam-engine, * Precisely as if molecule were connected to molecule by a system of coiled springs of such tension and range as would produce the observed effects. THERMODYNAMICS OF THE STEAM-ENGINE. 433 where r is the ratio of expansion, and p m the mean total abso- lute pressure. Then, for the forward stroke, (3) When n = I, the expressions just given for U, for the external work, become indeterminate ; but, for this case, = r ; pv=v = ; and / 1W 2 (* r -*dv U = J Pl P dv = P* v J Vl = A*. l 8< r - - - (4) The form of the expression shows, and calculation verifies the conclusion, that, as the value of = r increases in geo- metrical ratio, the work of hyperbolic expansion increases in an arithmetical progression. r = 2, U= 1.693 /,?,; r= 8, U = 3.078 /,*;,; r = 4, U 2.386 /,v,; r=i6, ^7= 3-773 A^i Thus, we have a constant difference of 0.693 p l v l . Then, as before, for the forward stroke, (5) The heat demanded for transformation into external work will be the thermal equivalent of these measures of that work, and all heat supplied in excess of these amounts is waste. We now have two typical cases to examine : The exact expression for the work thus done^by saturated steam in the steam-engine is obtained thus : (i) The work of one stroke of the piston of the engine is 434 A MANUAL OF THE STEAM-ENGINE. measured on the diagram of energy by a a' b' x' O a, the work of isothermal expansion being a a' x O a, and that of adiabatic expansion a' V x' x a' . The total area is composed of these two parts, the first being equal to U l /.,,, , nearly, and the second, unity of weight being taken, by u being taken as the volume of the steam. But it has been seen ( 102) that dT and, hence, THERMODYNAMICS OF THE STEAM-ENGINE 435 and. since we have found to be the latent heat of evaporation, ^/T. . (7) Reckoned per unit of volume of steam admitted, since - = , and the density, D = , A, (8) for which densities and latent heats can be found in the stand- ard ' steam-tables." U l and U t being thus found, the total work is (9) (2) The area of the diagram may also be measured up thus : Calling // = aa'xOa, UJ ^a'b'x'xa' , and also U/ u{ _|_ u , the total work performed, u t ' = r*pdu = u; + u; -p lVl = udp + A w PPi + T-TV+P^-P^ (10) 43 6 A MANUAL OF THE STEAM-ENGINE. and, as before, there results t = /T; - T;I + log. - The work of adiabatic expansion, /,', or, as represented on the diagram, a'b'x'xa! , consists of that performed by the con- version of a part of both the sensible and the latent heat-energy of the fluid into mechanical energy. We may write out the expression (10) for this work thus : V; =JT t -JT.-jT t log, (12) Here JT t and JT, measure the work-equivalent of the sensible heat present in unity of weight of the fluid, at the beginning and at the end of expansion, respectively, reckoned from absolute zero ; p^v t and /y/ 2 are the measures of the work of isothermal expansion, or of energy due to the efforts/',, A , acting through the volumes v t and # a , and the quantity T t v t -~ has been seen to represent the latent heat of vapor- ization, H, at the temperature and pressure 7", , />, . Also, the sum of the third and fifth terms, is the measure of the latent heat of evaporation at /, , T 9 , of the fraction, , of unity of weight of steam, i.e., /, , and -. . (13) THERMODYNAMICS OF THE STEAM-ENGINE. 437 The work of adiabatic expansion is the equivalent of the sensible heat stored in the fluid at its entrance into the engine, minus the work of isothermal expansion represented by the product of the initial absolute pressure into the volume at the " point of cut-off," a ; increased by the work-equivalent of the sensible heat at the " period of exhaust," less the work represented by the product of pressure and volume at that point ; plus the latent heat at entrance, less the proportion, ~ , of the latent heat of the same weight of vapor at the terminal temperature and pressure. The fraction - , or the final volume of the fluid divided by the volume it would occupy if it were all in the state of dry and saturated steam, is the propor- tion of the initial weight of dry steam which remains unliquefied by expansion ; the remainder, - 1 -, being the part which, condensing, surrenders its latent heat for* trans- formation into work. As is readily seen, the heat-energy stored as latent heat of vaporization, in steam, is the principal source of transformed energy, or work, and the difference between such a vapor and a similar fluid taking up no latent heat, could such exist, may be realized on computing the respective quantities demanded for unit of useful power developed. Thus, the steam being used in the ideal engine and a Carnot cycle, if received at 320 F. corresponding to 75 Ibs. per square inch, by gauge and rejected into the condenser at 100 F., the efficiency would be E ^ - = 0.28, nearly. i But the sensible heat added amounts to about 80,000 foot- pounds for such a range of temperature, and the part utilized would be nearly u = 0.28 X 80,000 = 22,400 ft.-lbs. 43^ A MANUAL OF THE STEAM-ENGINE. It would therefore require the supply of about W 1,980,000 -r- 22,400 = 88 Ibs., nearly, per horse-power and per hour; while, in the actual operation of good engines at such pressures and temperatures, it is not unusual to obtain the same quantity of work with less than one fifth this weight of feed-water supply. The use of steam in a non-conducting and frictionless, the ideal, engine would similarly demand but about one tenth the above-com- puted quantity. In the case of steam-engines working, as assumed in the analysis, without compression, or where compression is neg- lected, the efficiency must evidently be less than if the com- pression be adiabatic and complete, as in the Carnot cycle. The maximum efficiency of fluid is thus reduced, in many cases, quite sensibly, and may be considerably diminished. The difference is that between the Carnot ratio and that ratio diminished by the quotient of work of adiabatic compression to whole heat supplied. For the Carnot cycles, the efficiency is and for the assumed case, , T, T, T- ~ nearly; in which latter expression // is the latent heat of evaporation. For other vapors than steam, Jc must, of course, be substi- tuted for J. In the case of steam this loss is usually very small, rarely amounting to an approximation to one per cent. THERMODYNAMICS OF THE STEAM-ENGINE. 439 Adiabatic Expansion produces the liquefaction of steam, initially dry and saturated, in the proportion, as already seen, m f = i This proportion, though small in the older types of engine, with their comparatively low pressures and small ratios of ex- pansion, becomes important in later engines with pressures ranging up toward 10 or 12 atmospheres, and ratios of expan- sion of 15 to 20 or more. Thus, comparing steam in the ideal non-conducting cylinder, at absolute pressures of 115 and of 165 pounds per square inch, as employed in modern compound and triple-expansion engines, we have, in the first case, if expand- ing to 8 pounds terminal pressure, over 14 per cent adiabatic condensation; in the latter, we have 17 per cent, nearly; one pound of the mixture giving x = 0.86 and x = 0.83, nearly, remanent steam. The heat utilized is, in these cases, respec- tively, 0.17 and 0.20, nearly a thermodynamic gain of about 1 8 per cent. Raising initial pressure to 220 pounds, as in some quadruple-expansion engines, the thermodynamic gain is an additional 10 per cent, and at 250 pounds, absolute pressure, 15 per cent. This happens to correspond closely with experience, with the real engine. The result is well shown by the illustration given on the next page, from a paper by Mr. Parker.* The diagram shows the method of expansion of steam at an absolute pressure of 140 pounds per square inch (9^ atmos.) ; (a) when kept dry and saturated ; (b) when expanding adiabatically ; and (c) as actually worked in the steam-cylinders of the S. S. " Aberdeen," de- signed by Mr. Kirk for the China trade, an example of excep- tional economy, f It is seen that the actual expansion-line was Economy of Compound Engines; Trans. Brit. Inst. N. A., 1882. Thurs- ton's Engine and Boiler Trials; p. 459. f Engines : 30 , 45-, and 7o-incb cylinders, the firs un jacketed; 4$ feet stroke of piston. Steam 125 Ibs. by gauge, in boiler; 125, 50, and 15 Ibs. in jackets. H. P. 1800; fuel per h. p. per hr., 1.28 Ibs. 440 A MANUAL OF THE STEAM-ENGINE. bounded very closely by the adiabatic line, thus showing the internal condensation to be variable in a manner similar to that in a non-conducting cylinder. The jacket-wastes, however, amounting to about 4 per cent, must be added to the quantity Dotted line shows relative pressures and volumes, steam expanding adiabatically. TABLE SHOWING AMOUNT OF CONDENSATION OF STEAM EXPANDING ADIABATICALLY FROM DRY STEAM AT 140 1.BS. PRESSURE. Temperature. Pressure. Condensation. 353 140 Ibs. O.OOO 347 130 .005 338 "5 .012 329 102 .019 320 90 .026 3H 79 034 302 69 .041 293 60 .049 284 275 11 '.ril 266 39 .070 257 34 .078 248 29 .086 239 26 093 230 21 .100 221 18 .108 212 15 .115 203 12 .123 194 IO 131 185 8.4 139 176 6.8 .147 FIG. 140. ECONOMY OF STEAM. of steam here shown. The table accompanying the diagram exhibits the computed adiabatic condensation for the full range of expansion, varying from o, at the start, to 14.7 per cent at the end. For such engines, with the progress of expansion, THERMODYNAMICS OF THE STEAM-ENGINE. 441 it would become, on this scale, about 4 per cent for steam at 70 pounds absolute pressure, 6 at 47. 7^ at 35, 10 at 23, 1 1 at 18, 12 at 14, and 14 per cent at 8; or at ratios of expansion. respectively, of 2, 3, 4, 6, 8, 10, and 15. The wastes due to action of valves, the loss in passages, and to maladjustment of the several parts of the system to each other, are seen, as in other cases to be presented, in the variation of the real diagrams from their respective portions of the ideal curve. These wastes may be reduced somewhat by improved design and construction ; but, on the whole, they increase with higher pressures and greater expansion, and thus exaggerate the difficulties of securing higher economy. All these points being considered, the gain by still higher pressure is seen to be comparatively small. As will be seen later, this condensation is cumulative in the compound engine, and can- not be reduced by arranging several cylinders in series. Insig- nificant in a single cylinder, it becomes, as just seen, quite large with the high values now usual for the total ratio of ex- pansion in such engines. For comparison with the methods of Rankine, who prefers the computation of dynamic energies, the system of Clausius, whose method preferably considers thermal quantities, may be taken, as illustrated by the following summary of the discus- sion of the ideal steam-engine cycle :* Let W the weight of fluid taken : / = ' latent heat : XtX^Xc " proportion of dry steam present ; T absolute temperature / = any temperature ; Q = quantity of heat. The " thermodynamic function" of Rankine, 0, or the measure of Clausius' " entropy," has been obtained thus : (14) *For a complete exposition of Clausius' system, consult Peabody's "Ther- modynamics of the Steam-engine;" N. Y., J. Wiley & Sons; 1889. 44 2 A MANUAL OF THE STEAM-ENGINE. when Q is the measure of heat transferred, in thermal units. When we heat water from the minimum oto any maximum temperature, /, in the steam-boiler, the only change noted is that of temperature and we have the change of entropy : but in vaporization, dt = o, O" - 7"' and the total change is measured by in adiabatic expansion, d = o, and xl . -=r = constant. f'cdt _ ) T" t/ o Then, in the four operations constituting an ideal engine cycle, we have, for the case of maximum efficiency : (A) Expansion of water into steam at constant temperature and pressure, this action occurring in the boiler ; the heat de- manded is Q I= Wl,(x b -x^ (17) (E) Adiabatic expansion to back-pressure ; no heat being gained or lost : (C) Compression at constant pressure and temperature cor- responding to the back-pressure, in which operation heat is re- jected to the amount -*<) (18) THERMODYNAMICS OF THE STEAM-ENGINE. 443 (D) Adiabatic compression : f (19) We have, from the above, ,,-,.=^,-^ whence T (20) The efficiency thus becomes, in accordance with Carnot's law: When, as usually assumed, x a = o, and x b = I, the work done is and the weight of fluid, for a given work, -i-V ...... The quantity of heat demanded is measured, in units of work, by U. ...... (23) , *i *i The weight of water required is thus W=; ....... (24) 444 A MANUAL OF THE STEAM-ENGINE. and, per horse-power and per hour, this becomes 33000X60 T t JP, T, - TV Professor Peabody computes, on the assumption J = 778, ideal-engine efficiencies as follow : WEIGHTS OF STEAM DEMANDED. IDEAL CASE. Non-condensing. Condensing. A r,- T, M 7-,- T* M (by gauge) Ti Ibs. T Ibs. 30 0.215 12.8 0.084 32.8 60 0.249 II.4 O.I24 22.9 10 0.278 10.5 0.157 18.4 150 0.303 9 .8 0.186 1 6.0 200 0.320 9-5 0.2O7 14.6 300 0.347 9.0 0.238 13-1 It can now be seen that, as already stated ( 93), the mag- nitude of the quantity Q above, which is a measure, here, of the latent heat of vaporization, determines the amount of energy which can be transformed per unit of weight, and that the best working fluid, in this respect, is that having most energy thus stored ; while the thermodynamic efficiency is en- tirely independent of Q or H and a function, solely, of tempera- ture.* 113. Dry, Saturated, Steam is often assumed to be obtain- able, and to be capable of being worked without condensation, the steam being kept at the point of saturation by heat sup- plied by a steam-jacket. The fact that dry steam, or other vapor, like gas, is a good non-conductor and non-absorber of heat makes it improbable that superheating can ever be pro- duced, to any sensible extent at least, by the use of the jacket. * See Appendix for process of transformation of Eq. 6, p. 434. THERMODYNAMICS OF THE STEAM-ENGINE. 445 For this case, we have found, following Rankine, H' V= ^ 1 dT in which the latent heat of evaporation, //', may be expressed conveniently by the expression, derived from Regnault, H* = a-bT t ....... (i) in which, in British measures, a = 1,109,550 foot-pounds, and b = 540-4. Then, for this case, b\ is as before, and {/,= / // "//= = a\og e -6(T t -TJ, .... (2) -*t and, adding O r ,=/A. . (3) - The net work done is measured by the value of /, as above, less the work of back-pressure on the opposite side of the pis- ton, resisting its advance, which work is U, = vj>,* ......... (4) when/, is the total back-pressure, and U m =U> + U m -U. ...... (5) Thus the net work done, when the expansion is adiabatic, is, per unit of weight, as has been seen, 44^ A MANUAL OF THE STEAM-ENGINE. and, as now shown, for saturated steam, in a jacketed engine, A-A); . . (6) in which expressions the pressure and corresponding tempera- tures are either known or may be obtained from the steam- tables. In all cases, the total heat demanded is that required to raise all the water, used in cylinder and jacket, from the tem- perature at which it is received into the boiler up to that of evaporation, and to produce from it steam of the temperature and pressure, J", , p t , at which its expansion in the steam-cylin- der begins. The heat transformed into mechanical work is always measured by the work performed, as shown by the in- dicator-diagram, and the difference between the total amount of heat expended and the thermal equivalent of the net work done, as thus measured by the area of the diagram exhibiting the cycle worked through, is discharged from the system as unutilized heat. In this second typical ideal case, the steam is assumed to be maintained in the dry and saturated condition by continually supplying to it, as it expands, so much heat from the jacket as will prevent that liquefaction which would take place in the course of that adiabatic expansion which would occur in a non- conducting cylinder. Since this involves the supply of heat at all temperatures intermediate between that of the "prime" steam and that of exhaust and back-pressure, the efficiency of heat so supplied must be less than that of the heat entering with the boiler-steam. This method is therefore a method of waste of steam and of heat, as will be shown, more fully, later, by computation. This introduction of a wasteful expedient will, however, be seen, in the real engine, to have for ivs purpose the reduction of a greater waste ; and the net result is usually found to be a sensible, and often an important, gain. More heat is supplied than in the first typical case, and more work is done, per pound of steam ; but the work is increased in less proportion than the heat-supply. THERMODYNAMICS OF THE STEAM-ENGINE. 447 The condensation of steam expanding adiabatically may be neglected at low ratios of expansion ; but it becomes very con- siderable, as shown elsewhere, at large ratios, and the jacket must, in such cases, supply large amounts of heat. The assumption here made as to the effective operation of the jacket may be taken to be that of nearly maximum value. In the compound engine, this condensation is cumulative, and is not reduced or affected by the action which distinguished that type and gives it its efficiency in the case of the real engine. Could the action of the jacket be made effective in the manner here assumed, and not a source of waste during the exhaust period, the ideal and the real engine would have a sensibly common efficiency. Experience indicates that a jacket of such effective action as to produce dry and saturated steam at the end ef the expansion-period actually does approximate most closely to the ideal ; but in any given case, this can only occur under very nicely adjusted and unstable conditions. 114. The Efficiency of Cyclical Operations is evidently always measured by the ratio of the net work done by the working fluid to the work-equivalent of the total heat-energy sent into the engine, and either transformed or simply trans- ferred with reduction of temperature. To determine this effi- ciency, therefore, it is only necessary to find a method of measuring the total quantity, //, of heat supplied, and the net work, U m performed by the fluid, and the efficiency is then The total heat supplied to steam, dry and saturated, per unit of weight, is given in the " steam-tables." When super- heated, additional heat of the amount H=K(T s -T,)w is demanded, T, T t being the range of temperature added by superheating. The work performed is, in practice, obtained by 44^ A MANUAL OF THE STEAM-ENGINE. the use of the " steam-engine indicator," and is measured by the area of its diagram. Dividing the work represented by the latter, as performed in the unit of time, by the mechanical equivalent of the total heat supplied to the steam passing through the engine in the same time, the efficiency is obtained. In the ideal steam-engine, this usually varies, under familiar practical conditions as to temperature and pressure, from ten to about twenty per cent, and, in real engines, from about fif- teen per cent down to five, or even less ; the difference being due to the wastes which have been described. The equations obtained on the assumption that/z'" = const., using n = 1.0646 for saturated steam, n 1.135 f r adiabatic expansion of steam initially dry, and n = 1.333 f r superheated steam, or steam gas, give fairly approximate results, as com- pared with the exact expressions just given. Assuming, as is usually approximately true, that the expan- sion is hyperbolic, we always have pv = const., and whence, as seen in the diagram, the total work of the isothermal and isopiestic compression, during the exhaust period, is equal to that of the steam-stroke up to the point of cut-off, and the net work performed is that done during expansion after cut-off, and this is substantially, as elsewhere shown, the equivalent of the latent heat of expansion ; which is thus also the measure of the useful work per stroke. Efficiency of fluid may be measured by the ratio of the quantity of heat-energy demanded in the unit of time by the ideal engine, of efficiency unity, to the quantity actually con- sumed per indicated horse-power. Per minute, therefore, 42.75 B.T.U. -Q- -; when Q is the last-mentioned quantity in B. T. 17. THERMODYNAMICS OF THE STEAM-ENGINE. 449 115. The Conditions of Maximum Efficiency of Fluid are substantially the same in all forms of heat-engines, and are. as stated as early as 1824 by Carnot for the ideal engine. maximum range of temperature, and the reception of all heat at the higher, and its rejection wholly at the lower, tempera- ture. For the real engine, another essential condition is the reduction of wastes from the exterior by conduction and radia- tion, and by initial condensation on the interior of the working cylinder, to a minimum. For vapor and for gases, alike, the maximum limit of efficiency is 800 - 6co for example for the not uncommon absolute temperatures 8oo c F. and 600 F. In the ideal steam-engine, steam is produced and isother- mally expanded, in boiler and engine, at the highest possible pressure and temperature, and is then reduced, by perfectly adiabatic expansion, to the lowest possible pressure and tem- perature, and is compressed, or is rejected isothermally. at this minimum. Where the pressure has a limit, superheating is re- sorted to to increase the temperature of the fluid and the range of temperature worked through. In real engines, the magni- tude of the losses by conduction and radiation, and especially internal wastes, modify the conditions of maximum efficiency. restricting the economical range of adiabatic expansion, and thus limiting the attainable efficiency. This subject will be considered at some length in a later portion of this work. The quantity of heat required, in doing a given amount of work, in the real engine, will be found to be almost invariably very greatly in excess of that computed for its ideal representative, and the gain by increased pressure and temperature and by expansion will be seen to be seriously diminished by the causes operating, in the manner already described, in all actual heat-engines. 450 A MANUAL OF THE STEAM-ENGINE. Maximum efficiency can only be secured, as in the ideal en- gine, by adiabatic expansion. 116. The Theory of the Efficiency of Ideal Engines applying steam or other vapor as the working fluid is simple and exact ; but the results obtained in this case differ, usually, very widely from those practically reached in the real engine of which it is the representative. These differences are consid- ered elsewhere ; in the present article the ideal case, only, is to be illustrated. The quantity of heat, H l , being received by the engine, and the amount, //,, emitted, the difference, H l ff y , is converted into work. The efficiency is, therefore, HI Following Rankine's method of treatment, we have ( 112), en re'sume', when = r ratio of expansion ; A > A i A = initial, terminal, and back pressures, absolute ; 7", , T u , T 3 , TI, T b , T 6 = temperatures of entering steam, of steam at the end of adiabatic expansion and during the return stroke, and of feed-water, of condensation, and of atmosphere, respectively ; and when the work of unity of volume is considered for the ratio of expansion ; THERMODYNAMICS OF THE STEAM-ENGINE. 45 1 the work of the fluid per cubic foot ; ^ = ,.-A=A (3) is the mean effective pressure ; which also measures the work done per unit of volume swept through by the piston ; TT TJ -J r - i =[/A(3T.-^ + Al-r, ... (4) the heat expended per unit of that volume ; and the efficiency of the fluid becomes The quantity of feed-water demanded will be measured by D, : or, per unit of volume of cylinder, W=^ (6) The heat emitted will be fia= = ' ....... < I8 > rrr Or, adopting the approximate formulas, = constant ; 09) V l A'-; ....... (21) ~ H )-/J^; ..... (22) ); .......... (23) - A . . (24) 454 A MANUAL OF THE STEAM-ENGINE. It is found that the heat demanded per pound of steam supplied is very nearly ^ = iS*M = i5ir.; .... (25) Then the efficiency E -U'-^-ii^r^- (26) -'-~ * Table III, in the Appendix, shows the values of the " cut- off," - , the ratio /, -j- rp m , of total work performed up to point of cut-off to the total work (inclusive of that below the back-pressure line) done at each stroke, the reciprocal, r Pm -=-A> f that ratio, and the ratios, L and -A for assumed f in f\ values of r, adopting the values of taken above in the approx- imate equations. 117. Examples of Application of principles and the theory to ideal cases of application of steam, illustrating the limit of efficiency which would be attainable at familiar press- ures, could all wastes by conduction, radiation, and leakage be entirely prevented by the use of a working cylinder of non- conducting material, are the following : (i) Assume one pound of steam, at an absolute pressure of 100 pounds per square inch, to expand adiabatically, in an en- gine-cylinder of perfectly non-conducting material, down to 25 pounds, and to be exhausted, on the return-stroke, into the at- mosphere, the back-pressure being 15 pounds per square inch. It is desired to find the ratio of expansion, the efficiency of the fluid, and the weight of steam and of fuel demanded, per horse- power per hour, the feed-water being supplied at I IO Fahr., and the evaporation 9 pounds per pound of coal. By the exact formulae for this case ( 112), the following figures are obtained : THERMODYNAMICS OF THE. STEAM-EXG1XE, 455 DATA. p t = 14*400 Ibs. per sq. ft.; 7", = 788^ ; PI = 100 Ibs. per sq. in.; 7", = 7 1 '7'* /,= 3,600; A-= I57.H5; />,= 25; A- 45,68o; /,= 2,160; A^ CX2305; / s = 15 ; D^ 0106256. Evaporation, 9 Ibs. water per Ib. coaL RESULTS. Ratio of Expansion : = 3-38. Work per cubic foot of Steam admitted: taking the data, as given above, = 22,547 foot Ibs. Effective Pressure : = 46.31 Ibs. per square inch. Heat expended per cubic foot of Steam admitted; = 772 x 0.2305 (788.9 - 571-2) + 157-145 = 195,884 foot-lbs. 456 A MANUAL OF THE STEAM-ENGINE. Heat per cubic foot of Cylinder and equivalent Heat-pressure : ^, 195,884 = -y-=A = "^3"8~" = 57 ' 954 foot - lbs ' ; 57)954 Ibs. P er sc l- fa- 4 2 -4 I DS - per sq. inch. Efficiency of the Steam : Feed-water per cubic foot of Cylinder per stroke : ^^. r 3-38 Volume swept through by the Piston per indicated horse- power per hour : 60*^33,000 1.980.000 / 6671 Weight of Feed-water and of Steam per I. H. P. per hour : W = a.o682 X 296.8 = 20.34 pounds. Fuel per I. H. P. per hour : W" 20.34 -r- 9 == 2.26 Ibs. (2) The same case by the approximate formulas : Ratio of Expansion and " Cut-off" : r = 3-38 ; - r = 0.296. Mean Total Pressure :* Pm p m = IOO X = 100 X 0.634 = 63.4 Ibs. per sq. inch. * See table for - , and interpolate. THERMODYNAMICS OF THE STEAM-ENGINE. 457 Mean Effective Pressure : A = Pm - A = 6 3-4 - 15 = 48-4 lbs. per sq. inch. Same by exact formula = 46.3 ; difference = 2.1. Pressure equivalent to Heat expended: 2 = lidl = 402 . ; lbs . per . inch . Same by exact formula = 402.4; difference 0.3. Efficiency : Pe E = = 0.120. A Same by exact formula = 0.115 ; difference 0.005. Feed-water and Steam per cubic foot of Cylinder, and per stroke : r 3-35 Volume swept through by piston per L H. P. per hour: . = = ft 48^ X 144 6069.6 Feed-water and dry Steam per I. H. P. per hour : W = 0.0682 X 284 = 19.37 lbs. Same by exact formula = 20.34; difference 0.97 lb., or five per cent. Fuel per I. H. P. per hour : W" = 19.37 -s- 9 = ^'S lbs - (3) Assume one pound of dry, saturated steam to expand in a jacketed cylinder, receiving just sufficient heat from the jacket to prevent condensation by doing work. To find the 458 A MANUAL OF THE STEAM-ENGINE. efficiency, etc., as before, when the data are as follows, the method being slightly different from the preceding : /, = 14,403; v t = 4.35 cu. ft. (by table) ; /> = 10 ; v^ = 37.83 cu. ft. ; / a = 1440 ; W -r- W" = 10. P,= 10 ; /.= 720; P,= 5; Ratio of Expansion : 4-35 Work per pound of Steam : U= U, - U, + v,(fi, -A); (see table for 7;) = 361,250 226,662 -j- 37-83 (1440 720) = 161,826 ft.-lbs. Mean Effective Pressure : U 161,826 A=A ,- A = - = = 4 2 77-7 Ibs. per sq. ft. = 29.7 Ibs. per sq. inch. Available Heat : 9 L= U,- U* + ff, - h, ; (see tables ;) = 361,250 226,662 + 880,756 69,522; = 945,822 ft.-lbs. Heat-pressu re ' : 945,822 ~^^ = 173.6 " " sq. inch. L 945,822 = ~ = 25 ' 502 lbs - per sq - ft Efficiency : THERMODYNAMICS OF THE STEAM-EXGIXE. 459 FfiAwater amd Steam per cubic foot traversed bj piston : w= =^= -^- = 00264 n>. rv t r 37-83 V'obtme traversed by piston per /. H. P. per hour : F= 6QX33.ooo 29-7XM4 Feed-water and Steam per I. H. P.perhonr: W = 00264 X 463 = 12.22 Ibs- Fuel per I. H. P. per konr: W" = 12.22 -=- 9 = 1.36 Ibs. (4) Same case by approximate formulas (112): . = A X 035 = ioo X 0.35 = 35 HK. per sq. inch ; /.=/. ~A= 35 - 5 = 30lbs- per sq. inch; 33.000 X 60 Cubic feet traversed per hour per I. H. P. = = 458. Fe id-water and Steam per I. H. P. per konr = 45 X 0x1264 12.09. 4&0 A MANUAL OF THE STEAM-ENGINE. Fuel per I. H. P. per hour = 12.09 -* 9 = ! -34 IDS - The differences between the two sets of results are seen to be about one per cent, only. (5) Assume the following data, from Rankine, as taken from an engine constructed for a somewhat famous ship, the Thetis, built by Rowan & Co., and the Messrs. Scott : * . Engine of 226 indicated horse-power, calculated by exact formulae : DATA. Bottom of Top of Cylinder. Cylinder. P Pressure of admission, io8i 104 144 Back-pressure, -- 3.3 4.0 144 Ratio of expansion, r 16 14 Temperature of feed-water, T t , about 122 Fahrenheit. CALCULATED RESULTS. Bottom. Top. Final volume of I Ib. of steam, v y = rv l . . 64.27 58.52 U, U t ............................... 170,151 162,726 ",(A - A)- - ........................ 21,286 19,382 Work of i Ib. steam, U' ................ 191,437 182,108 Mean effective pressure in pounds per inch. - __P - A M4 Mean of both results ................... 21.15 Mean observed result of a series of dia- grams ............................... 21.00 Difference _[_ o. 1 5 Being within the limits of errors of observation. * Steam-engine; 1859; P- 407. THERMODYNAMICS OF THE STEAM-EXGIXE 461 Bottom. Top. Heat expended per pound of steam, H' ... 9/5,301 966.524 Equivalent pressure in pounds per square inch, p h -r- 144 105 115 Mean 1 10 Efficiency, * ~ 0.196 0.188 A Mean 0.192 (6) Same case calculated by approximate formulae : DATA. Lbs. on the square inch. Mean pressure of admission, -- io6j Back-pressure, ^ 3-65 Mean cut-off. = .067 = . r 1 S RESULTS. 'Mean gross pressure, ^- = io6j X .232 = 24.6 Mean effective pressure, -"- , calculated 20.9? observed.. 2i.co Difference 0.05 Pressure equivalent to expenditure of heat = p k -r- 144 1 1 o Efficienc>', 0.19. The engine was a two-cylinder compound, and the mean 462 A MANUAL OF THE STEAM-ENGINE. effective pressure has reference to the larger cylinder, which was of four times the capacity of the smaller. At 2^ pounds of steam per hour per horse-power, for effi- ciency unity, this performance corresponds to 13 pounds, neg- lecting all wastes other than thermodynamic ; and to 1.44 pounds of fuel at an evaporation of nine pounds steam per pound of coal. These figures would probably be increased by not less than 20 per cent by the extra thermodynamic wastes ; or to 15.6 pounds of steam and 1.75 pounds of fuel, nearly. Accepting Rankine's figures, we have the following : CONDENSING STEAM-ENGINES WITH DRY SATURATED STEAM. BACK-PRESSURE, / 3 -f- 144, ASSUMED AT 4 LBS. ON THE SQUARE INCH. Examples. Ratio of Expansion, r, and Effective Cut-off, -. (l) /, -4- 144 = 20. 10. 5- 3-33 2-5 2. T -7 0.6 ol 5 t'.o 8 8 i:i AVii 1 **' 44 '.'":: 86 Q Efficiency of steam . . 095 .090 .083 075 .0625 (2) /, - 144 = 40. 16.2 26.2 2 9 .6 32.0 ,60 A -*-.i44 124 248 310 37 ucc 496 620 y (3) P\ + i44 = 60. (A, -/3)--M4 A * 144 14.8 26.3 34-9 41.4 *a 50.0 54-6 56.0 Efficiency of steam . . 159 .140 '25 .in .100 .090 073 .060 (4) /j -t- 144 = 80. (A. ->!>-- 144 21. I 36.4 47-8 56.5 63.2 68.0 74-i 76.0 Efficiency of steam. . I2 4 .170 248 .147 37 - 8 .114 620 .102 744 .091 992 .074 1240 .061 <5) /i * 144 = ioo. !)- M4 A * 144 Efficiency of steam. . 27.4 '55 '77 .15 60.8 465 71.6 620 .115 80.0 775 .103 86.0 930 .092 93-6 1240 075 96.0 1550 .062 THERMODYNAMICS OF THE STEAM-ENGINE, 463 NON-COXDEXSIXG STEAM-EXCISES WITH DRY SATURATED STEAM. KACK-PKESSTKE /i -5- 144, ASSTXED AT IS L&. OX THE SQCAKE ESCH. r. Md KffeOTC Cw-Of, 1. 4 I M I *-I I -^i I mj -4 I -5 i| - (! o. I _o 1-4 (/I-*-"4 = Taking the temperature of feed-water at such a point as will give nine pounds of water evaporated into dry steam per pound of fuel, for the condensing, and ten pounds for a non- condensing, engine a heater being assumed to be used and 2.5 pounds of steam per horse-power per hour at efficiency unity, it is easy to make a comparison of the probable ideal and the probable actual efficiencies of these various engines in terms of heat, steam, and fuel, demanded per unit of power in the unit of time. The following are efficiencies computed for the perfect, ideal, engine, by CotterilL which may afford equally interesting comparisons : * 464 A MANUAL OF THE STEAM-ENGINE. Therma! Lbs. Lbs. /, Units Steam Carbon Engine. F&. Ibs. per sq. in. I.EP. I.1TP. i.S?. r P. Efn- ciency. per min. per hour. per hour. 1 401+461 250 195 11.4 0.8o6 O.2I9 Non-condensing; J T 3 = 212 + 461 F.' 363 + 46 1 341 + 461 312 + 461 1 60 1 2O 80 233 266 329 13-8 I 5 .8 19.9 0.964 I. 10 1.36 0.183 0.161 0.130 287 + 461 55 427 26.0 J-77 O.IOO 341 + 461 120 M3 7-5 0.592 0.299 Condensing; T s = 100 + 461 F.' 324 + 461 293 + 461 250 + 461 95 60 30 150 I6 7 20 3 8.1 9.0 II. 2 0.621 0.691 0.840 0.285 0.256 O.2II 228 + 461 20 230 12.8 0.952 0.186 Binary-vapor; ( Steam and ether; '< T a 60 + 461 F. ( 341 + 461 293 + 461 120 60 122 138 6.2 7-3 0.505 o.57i 0.351 0.309 Air-engine; ( r 3 =6o + 46i F.I 660 + 461 79-8 0-33 0.536 Professor Cotterill has shown that if the heat of the feed- water could be raised to boiler-temperature, by means of a heater so constructed as to receive heat by a graded system of transfer, such that the pressures of steam at transfer could be gradually varied throughout the whole range, the steam-engine might be given the efficiency of the Carnot cycle. The heat expended would be that rejected, and the efficiency would be L is the latent heat of evaporation, supplied by the boiler. * Cotterill; 2d ed., p. 420. THERMODYNAMICS OF THE STEAM-ENGINE. 4 6 5 The following table gives the multipliers required to de- termine the mean absolute preasure of steam when the initial pressure and the ratio of expansion are known. The product of the tabulated constants, by the initial pressure. /, , is the required mean absolute pressure. CONSTANTS FOR MEAN AND TERMINAL PRESSURES. II. Dry at Tempera- III. Condensing at Cut-off. r" &l ' sr-L in. v-uuucuajnjj at Mean. Terminal. 1 Mean. Terminal. Mean. Terminal. \ .847 5 -839 -479 -833 -463 ' t -7 333 .687 .311 .678 .295 -597 25 582 .229 .571 .214 .522 .2 .506 .181 495 .167 .465 .167 449 149 437 137 .421 .143 -405 .126 393 .115 .383 .125 .369 .11 357 .099 -355 .in 339 .097 .328 .087 1 T .330 .1 314 .087 .303 .077 .309 .091 .293 .077 .282 07 I- .290 .083 275 .071 .264 -063 : 274 .077 .259 .065 .249 .058 t .26 .071 .245 .06 235 053 1 247 .067 .233 .056 .223 .049 ! 236 .062 .222 .052 .212 .046 -992 -875 .991 .868 .991 .862 I .966 75 .964 .737 .962 -726 1 -919 .025 .914 .607 .911 593 { \ -743 375 -732 -353 -723 -336 Case I is that of steam kept at the initial temperature while expanding: Case II is that of Rankine's jacketed engine; Case III is that of the non-conducting cylinder. (See also Table III, Appendix.) The fall in pressure, along the admission-line, up to the point of cut-off, in well-designed engines, having detachable cut-off valves, in the best cases, should not exceed about one pound per square for each one-tenth stroke up to that point. It is usually much more, in other types of engine. The true ratio of expansion is measured by the quotient: volume of cylinder, plus clearance, at the point of actual " cut- 466" A MANUAL OF THE STEAM-ENGINE. off," divided by volume of cylinder, plus clearance, taken at the end of expansion ; which point is seldom coincident with the end of the stroke. 118. The Limit of Actual Efficiency is now determined. From what has already been stated, in reference to the differ- ences arising between the ideal and the real steam-engine, it will be understood that the quantities of steam and of fuel above given are magnitudes representing limits which may per- haps be approached, but which can never be actually reached, in practice. The consumption of heat, steam, and fuel, by even the best types of steam-engine, exceeds these figures by from one fourth to one half ; the excess varying with circumstances, already described, affecting the physical wastes. Assuming as data the same initial and back pressures, and the same ratio of expansion, and computing the expenditure of heat, steam, and fuel for the cases of the non-conducting and the jacketed engine, it will be found that the latter has lower efficiency. In practice, however, it is found that the enclosing of the working cylinder in a steam-jacket may produce real economy; it is thus evident that the advantages attendant upon the second of the two above-described methods of working steam are due wholly to causes distinguishing the real from the ideal case. In the ideal engine, keeping the steam saturated, during expansion with reduction of pressure and temperature, is disadvantageous. Comparing the curves,/^ = const., pv 1 - 1 '^ = const., pv 1 -^ = const., for the several methods of expansion, it is seen that the curve for saturated steam lies nearer the curve of Boyle and Mariotte than does that of superheated steam ; and that, vol- ume for volume, steam kept dry and saturated does more work than even superheated steam, the initial temperature being the same. Weight for weight, however, superheated steam does most work, and has the higher efficiency; since it contains more heat than saturated, and can expend it in work more efficiently in proportion to its higher temperature and its less liability to condensation upon the surfaces of the steam-cylinder previous to the commencement of expansion. THERMODYNAMICS OF THE STEAM-EXGIXE. 467 119. The Vapor-engine Cycles, Figs. 137, 138, differ, often very greatly in form, from those familiar as illustrated by air- and gas-engines. The isothermal line being isopiestic, the first portion of the diagram, traced during expansion, instead of being an equilateral hyperbola, becomes a horizontal straight line, a line parallel with the axis of abscissas. Adiabatic expansion is represented by a line closely resembling that for gases, but one which falls somewhat more rapidly, and thus deviating also from the common hyperbola, as has been already indicated. The ideal cycles are usually composed of these curves, and often of these combined with lines of equal pressure and of equal vol- ume. In the case of real steam, or vapor, engines, the actual cycles and curves approximate more or less closely to those of the corresponding ideal engine, accordingly as the engine is more or less well designed, well constructed, and well operated : but some considerable differences almost invariably exist. The action of the metal in conducting, and in radiating, heat to and from the working substance causes changes in the form of the lines composing the diagram, and the imperfect action of the valve-gear, the mechanism controlling the introduction and discharge of the working fluid, produces considerable variations of the forms of the lines, and especially of their junctions. In the designing of engines, and in computing their probable power and efficiency, ideal diagrams are employed which are so chosen and laid down as to represent, with as close approxima- tion as possible, the actual cycle of the engine. 120. The Distribution of Energy in Real Engines is Wtly different from that thus far found, in the study of the ideal engine. The latter is a purely thermodynamic system ; while the former illustrates not only the thermodynamic trans- formations and transfers of heat-energy, but also transfers and losses by every method of conduction, convection, and radia- tion rendered possible by the nature of the material employed, and bv the structure of the machine. Of all the heat received by the engine from the boiler, and temporarily stored in the steam supplied to the engine, but a small portion is commonly transformed into useful work, even in the ideal case ; while, in 468 A MANUAL OF THE STEAM-F.NGINE. the actual engine, as has been shown, wastes occur, in addition to the unavoidable thermodynamic loss, which often result in doubling, and, in small engines, much more than doubling, the consumption of heat, steam, and fuel, and the cost of their supply. Of all these losses and wastes, that by internal, or so-called cylinder, condensation is that which offers the problem with which the engineer is now most concerned. As elsewhere re- marked by the Author, "a comparison of the quantities of steam demanded to supply an engine thermodynamically ' perfect ' with the actual quantities required by even the best of engines exhibits so wide a difference that it becomes obvious that the determination of the efficiency of an engine, and the solution of questions involving those of heat-expenditure, are not prob- kms in thermodynamics, simply. The mathematical theory of the steam-engine is not yet in so satisfactory a state and cannot be until the correct theory of this transfer of waste heat can be introduced into it that the engineer can often use it in every-day office work, with much confidence, unless checked by direct experiment." * The wastes in the actual engine are found, by examination of the results of many trials, to vary greatly in even what is considered good practice. The loss at the boiler, in ash, from the recorded weight of fuel is from about 6 per cent, with the best coals, to 10 and 15, with very good fuel, and up to 20 and 25 per cent with bad samples. The boiler should not "prime" more than 3 or 5 per cent, even if it does not produce dry steam ; but double these figures are not uncommon. In large jacketed engines using saturated steam, the jackets may, if in- efficient, condense less than five per cent of the steam made; but, if efficient, they may condense an amount which approxi- mately measures the work done by the engine 10 per cent or more or they may even, by extensive transfer of heat during * "On the Several Efficiencies of the Steam-engine, and on the Conditions of Maximum Economy." Trans. Am. Soc. of Mechanical Engineers; April 1882. Journal of the Franklin Institute; May 1882. THERMODYNAMICS OF THE STEAM-EXGI\'E. 469 the period of exhaust, or when the prime steam is wet, cause a waste of considerably larger magnitude. The use of a steam feed-pump may waste 3 to 5 per cent, and, in defective con- structions, considerably more. Independent air-pumps, now quite common, will increase the wastes 5 or 10 per cent, and, where not efficient, may make this item as much as 15 per cent. The magnitude of the waste of heat by internal alternate storage and restoration is variable, not only with the conditions of operation, but also with the character of the working fluid. It is comparatively small with gases, large with condensable vapors, and peculiarly large with saturated or wet steam. The ratio of work done per pound of the working fluid to that which it might perform in a non-conducting cylinder measures a cer- tain efficiency which we may call the Working Efficiency of the Fluid. The following tabular statement of the distribution of losses and of quantities of heat applied usefully, in a marine engine, as given by Hunt and Skeel,* corresponds to a con- sumption of 2 pounds of coal per horse-power per hour. The best engines of the present time demand two thirds this quan- tity or less. One hundred pounds of coal contain in heat-units Deduct heat-units for weight of ash Total number of heat-units in 100 pounds coal 1,200.000 Available heal 1,200,000 100 Loss of beat by the chimney MO.OOO , i6| Available to make steam 1,000,000 83$ Loss by leakage and condensation aoo.ooo 16} Available to do work on the piston Loss of heat rejected from cylinder 660,000 55 "Methods of Testing Steam-engines," etc. Journal of the Franklin ; Dec. 1874- 47 A MANUAL OF THE STEAM-ENGINE. Heat-units. per cen Transformed into work 140,000 ii Loss by frictional resistances 40,000 3$ Available to turn the screw 100,000 Si- Loss by useless resistances 20,000 i j Balance usefully applied in propulsion 80,000 6 121. The Method of Operation, in the process of distri- bution of energy, in the actual case, is the following : The supply of energy delivered to the machine is brought from its storage reservoir, the steam-boiler, by the steam which is its vehicle, in the form of heat. The engine converts a small part of this energy into the mechanical form, and applies, it to the per- formance of work ; while the remainder is wasted by transfer, untransformed, to surrounding masses, such as the atmosphere, the environing walls, and, in the case of the condensing engine, to the water by which the steam is condensed and which con- veys the heat thus acquired into the water-ways of the country. Of the work developed by conversion of heat-energy, a part is expended in driving the engine itself, and is therefore a waste; while the remainder is applied to the purpose for which the engine is designed. Of the untransformed and wasted heat, the greater part, in the very best engines, is that inevitable waste which the second law of thermodynamics indicates, and the measure of the proportion of which, in the perfect engine, must always be ~ ; the remainder is mainly transferred to the " exhaust " by the process of cylinder, or internal, waste to be more fully considered later ; in which waste conduc- tion, storage, restoration, and convection play the leading part ; while a small portion is directly conducted, or radiated, to objects immediately adjacent to the machine. Each of these wastes reduces the efficiency of the engine, and their total enormously restricts it ; making the difference between the ideal and the real case so great as to absolutely preclude the possibility of predicting the quantity of steam THERMODYNAMICS OF THE STEAM-ENGINE. tfl and of fuel required, or the cost of operation, of the actual engine, until all these losses can be closely estimated. Experi- ment and experience have supplied data on which all such estimates are now based. 122. The Methods of Waste, in all known forms of heat-engine, considered in detail, are the same in character, but are very different in their proportion in different types of engine. In the non-condensing steam-engine, the thermo- dynamic waste is greater than in the condensing engine ; the loss by conduction, internal and external, is less; the waste by friction of engine is less ; and the total of all losses may be either greater or less, accordingly as the gain by increased range of temperatures of operation in the latter is, or is not, compensated by the difference in the sum of wastes other than thermodynamic, and necessary losses of different kinds. In the hot-air engine, the great range of temperature worked through decreases the proportional necessary thermodynamic waste, while increasing the other losses ; but the resultant actual efficiency is high. The same is true of the water- jacketed gas-engines, in which the wastes by conduction of heat are enormously increased by the action of the jacket; while the thermodynamic efficiency of fluid is high, and the unavoidable thermodynamic waste correspondingly low. The efficiency of fluid and of engine has often been studied by standard authorities, but almost invariably as a problem in thermodynamics, simply; and the losses occurring in conse- quence of the working of steam in a cylinder composed of a good conductor of heat have been left unnoted, although frequently the most important of all the expenditures of heat taking place in the engine. The process of exhaust-waste which has been described is thus seen to be one of the most serious causes of loss of heat in the modern steam-engine. It is this method of waste which prevents the engineer attaining even an approximation to the estimated gain due to considerable expansion. It is this which fixes a limit practically to our expansion of steam in a single cylin- der : which limit has, as yet, in ordinary forms of engine, been 47 2 A MANUAL OF THE STEAM-ENGINE. little altered by the expedients which have been adopted to ex- tend it. It has been found by experience that with steam of 60 to 75 pounds pressure (four or five atmospheres), no gain in efficiency can usually be secured by expanding more than five or six times in the simple unjacketed engine. Passing this limit, the losses due the wasteful transfer of heat to the exhaust steam increase much more rapidly than the gain due to the increased conversion of heat into work by expansion. When the steam is so far superheated that the mass taken into the cylinder may surrender to the metal all the heat required to warm it up to the temperature due the steam- pressure, without itself falling to the temperature of saturation at that pressure, this loss is reduced to a minimum. But any such saving is always effected at the sacrifice of some thermo- dynamic efficiency. Steam-jacketing produces its well-known benefit by similarly checking the waste due to this condensa- tion and re-evaporation. The losses by the rejection of heat from the engine without transformation have thus been seen to be due to two entirely different causes : the first, thermodynamic waste and physical heat-transfer, can evidently only be saved by some as yet unknown and radical change of type of engine ; the second, which has been diminished, but has never been wholly checked by any known expedient, seems very probably to require, also, radical treatment to effect its cure. As is so well illustrated by the investigations of Dr. Kirsch, the film of metal to which the fluctuations of tempera- ture producing cylinder-condensation are mainly confined, receives alternating waves of high and low temperature, which rapidly traverse the iron, entering and leaving with the en- trance of steam and the occurrence of the exhaust ; but always, on entering, fading into the mean temperature within the mass, and always restricted, at maximum altitude, to the surface on the steam side. Their rate of alternation is that of succession of piston-strokes ; and it is thus proportional to the speed of rotation of the engine, the depth affected becoming less and THERMODYNAMICS OF THE STEAM-EXGIXE. 473 less and the waste correspondingly reduced as this speed in- creases, indefinitely. Thus, in Fig. 141, the method of heat-transfer between steam and cylinder is shown, as it takes place, stroke by stroke, in the heads of unclothed or inefficiently clothed, in well-covered and in well-jacketed engines, respectively. For example, in A we have the first and second cases, (i) When the cylinder is in operation, its mean temperature A B a T ' Tj on the inner face, ab, is XT m , and greater than on the outside, a/, where it is 07".; since heat is continuously draining into the outer air from the hot metaL With varying steam-pressures, the former temperature rises and falls, from a maximum, 7*,, at the beginning of the forward, to a minimum, T, , at the end of the return stroke of piston. The mean for the whole cycle is represented by the line T m T f ; and the extreme fluctuations by T.Ti and T m T r The area T,fT t T t measures the heat stored per unit of area ; and this, added to the waste by out- flow at T M , is the total thermal loss on the head. (2) Similarly, if fully protected against loss, externally, T m T m becomes the mean line for the whole thickness : 7> T, the fluctuation, and this loss, due to it. is T t fT,T t , substantially as before ; but to this loss is not, in this case, superadded the drain outward. This latter loss is, in the figures, much ex- aggerated. In actual work, the internal waste is usually much the greater. 474 A MANUAL OF THE STEAM-ENGINE. (3) When the engine is well-jacketed, the temperature of the interior fluctuates as before, as seen in B, where the dotted line is that of mean temperature for the preceding case, and T 3 T m is that for the jacketed engine; but the exterior is held up to the temperature, 7^, of "prime steam" or higher by contact with jacket-steam having equal or greater pressure. The result is to produce a drain of heat inward, instead of, as in the preceding cases, outward, and to restrict the minimum temperature, 7",, in its fall, and to throw the whole area, T.eT^T,, upward toward T, , and to reduce its magnitude, correspondingly decreasing internal wastes by that method. Could this process be made absolutely effective, and 7", = T lf internal or " cylinder condensation" would cease, and the only internal loss would be by transfer from the jacket to the cylin- der in the same manner as, in the preceding cases, heat passes outward. Thus, with the jacketed cylinder, there are three of these wastes : loss through the lagging, externally ; loss by interior storage and restoration of heat in and from the metal ; internal discharge by drainage from the jacket. Calling these H a , H b , H c , and the total H, and the values of the quantities vary with type and construc- tion of engine. In case I, H is largest; though // t . = o; in case 2, H is reduced by the reduction of H a to a small quan- tity, and the H H b , nearly; while in case 3, although H c is introduced, it may, by producing a larger reduction of H b , give a total value, H, in some cases, considerably less than in either of the other cases. It is here obvious that the jacket will be useful, useless, or wasteful, accordingly as it reduces H b more, an equal amount, or less than its own characteristic waste, H c . In Fig. 142 is shown the action of the metal during the movement of the engine through its cycle, and the fluctuations already alluded to. The inner face, Oa, varies in temperature from 7", to 7 a , about the mean, T m , as before, the successive THERMODYNAMICS OF THE STEAM-ENGINE. 475 isothermals taking the forms exhibited, as the waves of heat cross the metal towards X, the line OX representing the tem- perature of the outside atmosphere, and the successive lines, above, are the successive positions of the isothermals, as the flow fluctuates in the lagged but unjacketed cylinder. In the jacketed engine, the same general effect would be seen ; but the line 71,7*, would have the opposite inclination, as already seen. In quick-working engines, the action of the cylinder-walls results in producing a film of water on their surfaces, and the FIG. 142. VAR steam remaining uncondensed is but very slightly and superfi- cially affected ; it passes out still dry. In slow engines, the mass of steam may probably be rendered comparatively wet. On the other hand, the process of expansion, after cut-off, results in producing water, diffused throughout its mass, which can neither affect nor be affected by the surrounding walls. In the transfers of heat between engine and steam, the con- tact of cylinder and cooler dry steam has little effect ; but moisture on the surface of the metal and its re-evaporation has a most decided and important effect. A glance at these diagrams of heat-flow shows that, to se- cure usefully sustained temperatures on the working face of the 4/6 A MANUAL OF THE STEAM-ENGINE. cylinder-wall, the temperature and steam-pressure in the sur- rounding jacket must be higher as the thickness of that wall is greater, in order to maintain any given head and inclination of the mean temperature line. Conversely : the thinner the wall, the less the necessary head and the more effective the jacket for any given pressure and temperature of its steam, in excess of the mean temperature of the inner face of the cylinder-wall. It will be seen that the higher the speed of engine, the thinner the film of metal affected by these measurable variations of temperature and, consequently, the less useful the jacket. In other words, also, the higher the speed and the thinner this film, the higher is the temperature needed for efficient action of the jacket. Experience confirms this deduction by showing that the jacket has very slight effect, as usually applied to "high-speed" engines. To make it useful, a way must evidently be found, either to greatly reduce the thickness of the cylinder- walls as, indeed, has been proposed, many years since or to raise the temperature of jacket considerably, thus securing in- creased heat. As stated by M. Dwelshauvers-Dery, the principle of Hirn applies to all engines, thus: Between any two given successive positions of the piston, the quantity of heat transformed in the performance of external work, plus that derived from the metal of the cylinder, gives a sum equal to that of the variation of the internal heat of the steam, plus that introduced by newly entering steam, if any, or minus that lost with rejected steam, if any.* 123. The Magnitudes of Losses in the steam-engine have been ascertained with considerable accuracy, for the principal types and for engines of ordinary sizes working under familiar conditions. In general, it may be said that the actual total efficiency of engine ranges from an average of about fifteen or sixteen per cent, in the best cases, down to five for ordinarily good engines, and, often, to much lower figures. A perfect steam-engine of efficiency unity, working under the best of * Dwelshauvers-Dery: Expose, 2. THERMODYNAMICS OF THE STEAM-EXGIXE. 477 familiar conditions as to temperatures and pressures, should de- mand but about two and a quarter pounds of feed-water and steam, per horse-power and per hour. The best recorded figures are about five times as great : and twenty-five to thirty pounds are the figures commonly guaranteed for large sizes by good builders of simple engines. For small engines of ordinary con- struction, the consumption of steam and the wastes are often enormously great. The distribution of energy in evaporation in a case of ex- cellent performance of a boiler tested by Sir Frederick Bram- well and Mr. W. Anderson was as below :* B. T. U. Per ct. Evaporating the water in the wood 9557 0.32 Heating wood and air 3884 .13 Evaporating moisture in coal 8374 .29 Heating coal and air 129,321 4.44 Displacing atmosphere 53>394 T -83 Heating excess of air 130,980 ) Displacing atmosphere by ditto 535O9 ) Making steam 2,090,300 71.78 Radiation and convection 271 ,307 9.32 In ash 53,915 1.85 Balance unaccounted for 107,552 3.70 Totals. . . . '. 2,912,093 100.00 The heat received from the fuel, at the furnace, may be taken as distributed, in a good example, thus : Total heat received Waste at chimney 25 " " condenser 55 " " by radiation ... 5 Usefulwork 15 the fuel at the furnace, 100 | Total 100 * Tburston: Engine and Boiler Trials; p. 361. 478 A MANUAL OF THE STEAM-ENGINE. The " working efficiency of the fluid " is here about 73 per cent, the exhaust waste being about one half cylinder-conden- sation. In the case of an economical condensing engine, consuming one kilogram (2.2 Ibs.) of good fuel per hour per horse-power, M. Hirsch gives the following as a fair distribution of the heat produced :* Calories Calories Coeffic. expended, remaining. Heat of combustion i.oo 0.50 100.00 (1) Received from the boiler 60 40.00 60.00 (2) Thermodynamic efficiency 27 43.80 16.20 (3) Imperfection of cycle 60 6.48 9.72 (4) Efficiency of machine 77 2.22 7.50 (5) Total efficiency O-75 92.50 7.5 In a familiar form of simple non-condensing engine, doing fair work, the Author has found the following distribution of energy received from the boiler : Received. Heat-energy stored in steam, dry and saturated at the en- gine, in per cent 100 Total loo Expended. Per cent. Waste by external con- duction, etc 6 Waste by internal con- duction 33 Waste, therniodynamic 41 " by friction 8 Useful work 12 Total . . ,100 Here the working value of the fluid is 70 per cent. In the case of the best compound triple-expansion engines with steam at the same pressure (100 Ibs. ; atmos. absolute ; nearly), cylinders jacketed and expanding about 12 times, the following is a fair distribution : * Congrfes International de Mecanique appliqu6e; 1881; vol. IV. THERMODYNAMICS OF THE STEAM-ENGINE. 4/9 Received. Heat -energy stored in steam, as received from the boiler, Expended. Per cent. External wastes 10 Internal " 25 Thermodynamic wastes 36 Friction wastes 13 per cent 100 j Useful work 16 Total ioo Total 100 In this case, the working efficiency of the fluid is 70 per cent. The following are figures given by Professor Ewing, de- duced from data supplied by Mr. Main:* B.T.U. Heat supplied engine per rev 1 377 " " " by jackets 212 " total B. T. U 1589 " returned to boiler 38 " net supply 1551 " converted into work 227 " rejected 1324 Efficiency fffr = 0.146 Thermodynamic Efficiency O-335 t In all cases assuming that the expansion may be taken as hyperbolic, the work done in a cylinder of given volume will vary nearly as log, r ; but the cost of that work may vary enormously, and entirely without direct relation to the volume, f\ , of the steam at the point of cut-off. The early trials of the Owens College experimental engine elsewhere described (see frontispiece) are reported by Pro- fessor Reynolds to have given data and an account, as deduced by Mr. Cowper, as follows: J Minutes Proc. lost. C. E.; vol. LXX. Also. Thurston: Engine and Boiler Trials: p. 298. fEncy. Britannka. t Proceedings Brit. Inst. C. E.; 1889. Van Nostrand's Science Series; No. 99; 1890. 4 8o A MANUAL OF THE STEAM-ENGINE. D r . B.T.U. Percent. To steam in cylinders 14, 1 54 8 1 " " " jackets 3,325 19 17479 Cr. B.T.U. By indicated work efficiency. 3,085 " heat rejected 12,862 " " radiated 1,176 " " lost from hot-well 356 100 Per cent. 177 73-6 6.7 2.0 17,479 i oo.o The effect of back-pressure in limiting thermodynamic trans- formation and the efficiency of expansion is well exhibited by the following tables, computed by Mr. Buel : IDEAL ENGINE; NO BACK-PRESSURE. Point of Cut-off. Mean Total Pressure, pounds per square inch. Relative Area of Cylinders. Relative Amounts of Steam used. Per cent of Saving. 1 2 3 4 5 I 100. I.OO I.OOO i 96.4 1.04 .780 22. 84.7 1.18 .590 41.0 70.0 i-43 477 52.3 i 3:2 1.68 2-15 .420 358 58.0 64.2 38.5 2.60 325 67.5 T* 29.0 3-45 .288 71.2 IDEAL ENGINE; BACK-PRESSURE 17$ LBS. Point of Cut-off. Mean Effective Pressure, pounds per square inch. Relative Mean Pressure. Relative Area of Cylinders. Relative Am'ts of Steam used. Percentage of Saving. 1 2 3 4 5 6 I 82.5 I.OOO I.OO I.OOO i 78.9 959 1.04 .780 22. i 67.2 .815 1.23 .615 38.5 * 52-5 .636 i-57 523 47-7 i 42.2 512 1-95 .488 51.2 * 2Q.O 352 2.84 473 52.7 i 21.0 255 3-92 .490 51-0 T 1 * ii 5 .140 7-15 596 40.4 THERMODYNAMICS OF THE STEAM-ENGINE. 48! From this table it appears that, under the assumed condi- tions, the most economical point of cut-off is about one sixth of the stroke, since the saving is decreased, whether the cut-off is lengthened or shortened, from this point. The conditions assumed are such as accord well with modern practice. Ex- changing the initial or back pressure to suit a condensing en- gine different results will be obtained, but the table is sufficient to show the mode of application for any given data as first shown by Clark. The cause of increased back-pressure is resistance to the escape of the steam from the cylinder, by which the mean back-pressure is raised from I to 3 Ibs. on the square inch. There is as yet no satisfactory theory of that resistance, and it cannot be computed for any proposed engine by means of a general formula. The back-pressure in proposed engines can be estimated roughly from the results of experience. The following is a summary of some such results : Mean Back-pressure,/*. Lbs. on the Lbs. on the square foot. square inch. Ratio of expansion from \\ to 3. . 720 5 from 4 to 7... 64810504 4^ to 3$ from 8 to 15 . . 504. to 432 3^ to 3 The diagrams show only the effective pressures of the steam, and not the absolute pressures, which are usually left to be roughly estimated by guessing the probable atmospheric pressure.* Mr. Beer takes the back-pressure as A=A + Q-03A, for non-condensing and for condensing engines, respectively ; in which /. is the pressure of the atmosphere or in the con- denser, assuming moderate engine-speed and liberal port-areas. 482 A MANUAL OF THE STEAM-ENGINE. 124. The Thermodynamic Loss, which unavoidably takes place in all heat-engines, has been seen to have a magnitude which is absolutely definite, and easily determinable. Of all the heat subject to thermodynamic conditions, and not lost by T T conduction or radiation, one portion, never exceeding ' ', has been found to be converted into mechanical energy; while the remainder, measured by a fraction never less than ~, is, as A has been seen, necessarily and inevitably rejected untrans- formed ; this constitutes the " unavoidable thermodynamic loss," which, only, is considered by the pure science of ther- 2" T modynamics. The part utilized, - -~ ! , being divided by T T T the sum of these two parts, -= -j- = i, gives the measure, as already seen, of the maximum possible thermo- T T dynamic efficiency of the fluid, ^ The efficiency of any real engine, operated under familiar conditions, is measured by the quotient of converted heat divided by the sum of all expenditures, whether useful or wasteful. Thus the figure for efficiency, just obtained, is re- duced in proportion to the increase of the total heat-supply compelled by the aggregate of these wastes ; and the propor- tion of thermodynamic waste is at the same time correspond- ingly reduced. The latter, in many cases, thus becomes forty or fifty per cent of the total, instead of, as for the ideal case, eighty-five or ninety per cent ; the extra-thermodynamic wastes of the engine often equalling, or even exceeding, the quantity of heat, or of steam, demanded in the purely thermodynamic process of its operation. In all cases, with real engines, the quantity taken as unity, with which the useful work is compared, and on which the measure of efficiency is based, is the sum of all expenditures of heat, and not simply the heat thermodynamically demanded. THERMODYNAMICS OF THE STEAM-ENGINE. 483 125. The Conditions of Maximum Efficiency of fluid, in all real engines, other things equal, are precisely the same as with the ideal engine of thermodynamic science, viz., maximum range of temperature worked through and maximum value of p "p the expression _, -. The higher the pressures and the temperatures of the working fluid supplied, and the lower those of rejection, the higher the efficiency of operation of the actually working substance. But it does not follow that the actual total efficiency will be similarly increased. It may happen that the extra-thermodynamic wastes may also increase with increased efficiency of fluid, by this change of thermodynamic conditions, and to such an extent as to produce an actual decrease of total efficiency. This, which is a common experience, if not universal, is illustrated by the familiar fact that, for every engine of ordinary construction, a ratio of expansion may always be found, beyond which the range of temperatures and pressures being increased, an actual loss is produced by the consequent increase of internal wastes due to " cylinder-condensation." Should it be practicable, in any case, to prevent exaggera- tion of losses by wastes of heat through internal and external conduction and radiation, these same conditions lead to in- creased efficiency of heat-transformation, with the real, as with the ideal, engine. It is, in fact, in this way that all recent im- portant improvements in the economical operation of the en- gine have taken place ; the wastes having been checked, while the practicable range of expansion, and of working temperature, has been extended. 126. Heat-wastes by Conduction and Radiation have been classed as of two kinds : external losses of heat, and in- ternal heat-wastes. Of these, the first take place by conduc- tion of heat from the cylinder to the engine-frame : by radiat- ing from the heated cylinder-heads ; and from the alternately heated and cooled piston-rods and valve-rods, as they move into and out of the steam-space, and even from the carefully clothed exterior of the cylinder. 484 A MANUAL OF THE STEAM-ENGINE. An allowance of one British thermal unit per hour, per square foot, or of nearly three calories per square metre, will usually cover the losses in the ordinary engine from protected, well-lagged, surfaces. This corresponds to about o.oor pound of steam condensed by one square foot, or to nearly 0.005 kilogramme liquefied by a square metre. For any given en- gine, this loss may be assumed constant, and may often be neglected, as unimportant, in presence of so many other more serious wastes. The slight leaks of steam and of hot water about the rods will, practically, often be found much more im- portant, economically. If it be taken, in engines of moderate size and power, as five per cent, it will probably usually prove that the assumption is a safe one. Losses of heat in this manner by external conduction and radiation have, however, been rarely measured at the engine ; but the following data (p. 485) from the trials of agricultural engines at the Royal (G. B.) Society's competition, by Sir Frederick Bramwell and Mr. Anderson, will illustrate the method and extent of this waste with varying temperatures.* The total waste from engines and boilers was thus from 3^- to i6 per cent of all heat of combustion. Larger engines and boilers are less subject to this waste ; since the area of surface is less in proportion to weight and to quantity of steam and work. As, in the cases cited, the total waste, from engine and boiler, is, in the best example, reduced to 3^ per cent, it is evident that the loss from the steam-cylinder of the engine must be very slight, and, in large engines, may be made, by careful protection, insignificant. The Rate of Cooling is not uniform, but decreases as the temperatures and pressures of steam and metal fall, as shown by the line cO, in Fig. 143, and increases observably with increasing pressures, thus indicating an increasing loss which tends to set a limit to the gain otherwise attainable by this progression. The curve, c O, of waste gives the total loss in British thermal units for the given temperatures and corre- * Jour. Roy. Ag. Soc.; vol. xxiu; 1887. THERMODYNAMICS OF THE STEAM-ENGINE. 48$ X s ! * ! o o I S 5 ^- i S f ^ -r d! ^ ? S, * : ^ et T S Jco " 3. I ^ 2 3 * 5 1 1 ~ . m to Cl T KM M O x CO 1 1 ? S S a ; d i 5 E "> * t^ i-T r^ *O *?> m t r^ t- 00 i la f S ^ s^ S r^ oo - Wi ? 5 5 >o rt- o r * % - | s S S oo O in s 1 * = i? ^ 5 e" 1 3 3 R * S a i i i * 2- l< eo oo * c ? " K >-^ rC K ^ SC MM - S ~ Ml co a, CO 09 S -^ ij?iJ| i 7:tj-"5 S ^l|l ',= . =li:?^ i^jM'Ni M C* CO 4 ? : 2- - 1 - o : S -g 5 S . . o. > o 1 f^H 1 K {MMHIdf = : 15S385ils 1 :=&.* J58|J 8 5 ill|^^ i "~~ X C6 D c. o .; 486 A MANUAL OF THE STEAM-ENGINE. spending pressures. The line, cB, tangent to the curve at its upper extremity, indicates the length of time, measured by its ordinate, A B, which would have been required for cooling down to the minimum had the rate of cooling been constant, The actual time was nearly twice as great. \ FIG. 143. RATE OF COOLING OF ENGINES. The zero-point is here taken at the minimum reading. The ordinates measure the total quantities of heat at each pressure and temperature and time indicated on the curve, in excess of that remaining at the end of the period of observation (364,600 B. T. U.). It was observed, in these experiments, that the rate of cool-- ing was very variable, ranging from about 2200 up to above 10,000 units per dynamometric, or brake, horse-power, on the " ten and twenty horse engines " compared ; and that a com- pound engine wasted heat at a rate exceeding, by 28 per cent, that of its companion simple engine, similarly covered. These cases show clearly that, with small engines and ineffective lag- ging and clothing, this waste may be found, especially at high pressures, and with multiple-cylinder engines, a very observable tax upon efficiency. Wastes of from 3 to 5 pounds of steam, the ordinary range of this waste, per horse-power and per hour, THERMODYNAMICS OF THE STEAM-ENGIXE. 487 for the compound, and of 2 pounds and upward for simple engines, constitute very considerable percentages of the total consumption of steam. The waste of heat by radiation from well clothed, lagged, and felted, engine-cylinders may be taken,, as an average, at about one half a British thermal unit per square foot of surface and per degree of difference of temperature, internal and ex- ternal. About five times as much is lost from polished heads, and probably some more from that portion of the piston-rod exposed to the air and to the steam alternately. In large en- gines, well clothed, this loss often constitutes less than 2 per cent of the heat supplied. 127. The Methods of Reduction of Losses of Heat by conduction and radiation externally, as commonly practised, consist simply in carefully covering all external surfaces, where it can well be done, with hair-felt, asbestos, preparations of magnesia, or other non-conducting substances, and adding a surface-covering of painted canvas, of well-finished wooden, or Russia iron, lagging, which protects the clothing beneath it from injury. Cylinder-heads are sometimes similarly covered, but are often left bare, and are then very carefully polished, as should be all such exposed heated parts. Conduction and radiation from piston-rods and valve-rods can only be reduced by a good polish and such effective pack- ing as will insure their working dry. Conduction to the frame and other parts of the structure connected to the heated cylinder is checked by any packing or "joint" between the two members of the machine ; but it is not usual to attempt to effect such an economy by any special device. In this respect, those engines in which the cylinder is attached to the frame only by its front head probably have some advantage. A gain by improved efficiency of engine may usually be expected to give still greater gain in economy at the boiler. A reduction in steam-consumption results in the increase of the ratio of area of heating surface to weight of steam required, and this, in turn, effects an increase in the quantity of water evapo- rated per unit weight of fuel. Thus, a reported gain of 25 per 488 A MANUAL OF THE STEAM-ENGINE. cent in a small engine, by compounding, was, in a case observed by the Author, reported, also, to be accompanied by a gain of above 35 per cent in fuel required per horse-power per hour. 128. Cylinder-condensation, or loss by internal conduc- tion and radiation, is, in the best engines, next to the thermo- dynamic waste, the most serious and difficult of reduction. In ordinary cases, this is far in excess of the thermodynamic waste. Steam-engines, as already seen, are impelled by a fluid which is a vastly better receiver and transmitter of heat than the permanent gases. Steam takes up and loses heat, in the process of formation and of condensation, with extreme rapidity. The working fluid, in all steam-engines, is readily condensable, and exchanges heat with the metallic surfaces of the working cylin- der with the greatest freedom. It is usually more or less wet, and its humidity is subject to rapid and extreme variation in the course of the movement of the piston. Condensation also occurs in another way: Suppose steam to enter the steam- cylinder perfectly dry, and to expand adiabatically. As expan- sion progresses, after the closing of the steam-valve by the expansion-gear, the work done by the working fluid results in the transformation of so much heat into mechanical energy which heat can now only be obtained by drawing upon the stock contained in the steam itself that a part of the steam becomes liquefied.* This fact was shown by Rankine and by Clausius, by the study of the thermodynamics of the case ; it had, a generation earlier, been perceived by Carnot,t and by Combes as early as 1843. The liquefaction of the steam, in consequence of trans- formation of heat into work, probably aggravates this evil, although, as was stated by Rankine, not itself a waste : % * On the Ratio of Expansion at Maximum Efficiency; R. H.Thurston ; Trans. Am. Society M. E., 1881. f Reflections, etc.; Thurston's Trans.; p. 255. \ Steam-engine and other Prime Movers, 1859; pp. 395-396. THERMODYNAMICS OF THE STEAM-ENGINE. 489 " That liquefaction does not, when it first takes place, directly constitute a waste of heat or of energy; for it is accom- panied by a corresponding performance of work. It does, however, afterwards, by an indirect process, diminish the effi- ciency of the engine ; for the water which becomes liquid in the cylinder, probably in the form of mist and spray, acts as a distributor of heat, and equalizer of temperature, abstracting heat from the hot and dense steam during its admission into the cylinder, and communicating that heat to the cool and rarefied steam which is on the point of being discharged, and thus lowering the initial pressure, and increasing the final pressure, of the steam, but lowering the initial pressure much more than the final pressure is increased ; and so producing a loss of energy, which cannot be estimated theoretically." The same phenomenon is described by Professor Cotterill, thus: "When the expansion-curve drawn by an indicator is examined, it is almost always found, even when the greatest care has been taken to eliminate the disturbing causes, to show that evaporation takes place during expansion. Now these unquestionable facts can only be explained by supposing that liquefaction takes place during the admission of the steam to the cylinder, and evaporation during expansion and exhaust. This alternate liquefaction and evaporation is chiefly due to the action of the sides of the cylinder, in many cases combined with the effect of water remaining in the cylinder after exhaust is completed." The surfaces affected by this action are of varying activity and efficacy in the production of wastes. The cylinder-heads, the sides of the piston, the surfaces of the port- and steam-pas- sages, the surfaces of the clearance or " dead " spaces, often of very considerable area, and the extreme portions of the internal cylindrical surfaces, which are all exposed to the full range of temperature from boiler-steam to condenser, produce the main portion of this serious loss. Between the points of mean cut-off at the two ends of the cylinder, this range is less. It is a minimum at the middle of the cylinder ; at which point 490 A MANUAL OF THE STEAM-ENGINE. the inner surfaces are exposed to the least variation of pressure. Whatever treatment may be adopted to evade this waste will be most effective on those parts which are thus exposed to the maximum variation of temperature and pressure of the enclosed steam. Of the absolute magnitude of this waste, some idea may be obtained from the reported results of experiment ; some of which are as follows: Mr. Clark deduces from his experiments with locomotives the following figures for usual percentages of condensation at various points of cut-off in outside connected engines. Engines with inside cylinders are observably less seriously affected ; as the heat of the adjacent smoke-box and boiler, and their pro- tection against the cooling action of the passing air, exert a favorable effect.* CYLINDER-CONDENSATION IN LOCOMOTIVES. Per cent Condensation. Cut-off. Actual r. Parts of Initial Steam, Parts of Initial Steam per cent. and Water. 0.10 4 8o.O 44.0 0.15 3-40 57-0 36.0 O.2O 2.85 41.0 29.0 0.25 2.50 31-0 23-6 O.3O 2. 2O 23.0 18.7 0-35 2.OO 17-5 15.0 0.40 1.8 3 II. O 10.0 0.50 1. 60 4.5 4-3 0.70 1-25 2.75 2.7 I.OO I.OO 2.0 2.0 The results of Isherwood's investigation, as summed up by himself, give the following average data:f * Proceedings Brit. Inst. C. E., No. 1910; 1882-3. f Experimental Researches in Steam-engineering; vol. II. p. xxxiii. THERMODYNAMICS OF THE STEAM-ENGINE. CYLINDER-CONDENSATION IN MARINE ENGINE. STEAM 40 LBS. BY GAUGE. 49 * Cut-off. Actual r. Lbs. Steam per I. H. P. per hour. Relative Cost in Steam. Internal Condensation, per cent. 100 46.86 -397 10.90 90 .11 41-57 .239 12.43 80 25 37.85 .128 M-45 70 00 43 .66 35-54 34-16 059 .018 16.95 20.02 50 2.00 33-55 .000 23-94 40 2.50 33-59 .OOI 28.50 30 3-33 34-52 .029 33-56 20 5.00 36.88 .099 38.87 10 IO.OO 42.83 1.277 44.46 The figures of the last columns in each of these tables show well how rapidly internal waste increases with increasing expansion. CONDENSATION IN STEAM-CYLINDERS. Case. I. II. III. IV. V. Cut-off 0.95 0.67 0.40 0.354 O-25 Fraction condensation in Ideal Case.. 0.004 0.026 0.056 0.061 0.081 " Actual Case. 0.150 0.284 0.459 -554 0.601 Ratio of Real to Ideal 37.5 10.7 8.2 9.1 7.4 The above table presents a comparison of the actual con- densations occurring in the unjacketed engine of the U. S. S. Michigan, with the condensations, resulting from the work of expansion, which would have taken place had the work been done in a non-conducting cylinder, as computed by Professor Rankine* Hirn's experimental work furnishes some exceedingly valuable data, as may be seen in the accompanying table, abstracted from Ledieu.f The method of loss and its distri- bution are here well exhibited. * Trans. Inst. Engrs. of Scotland; Feb. 5, 1862. f Him: Theorie Mecanique de la Cbaleur; 1876. Ledieu: Machines Feu; 1882; p. 383. 492 MANUAL OF THE STEAM-ENGINE. W " OO o 1 f * CO o C/J * f Jl^l *^ C? f d d o o d g 6 i 1 W "* t 4 c? 6 3 d d d 1 d o" o S Jl 2 '1 vO 4 5? d i d 1 d 1 d 1:1 4, M 5 o o f N ju "a. o *? "c7i cc d o o d O; 8 6 1 CO " % ^ s 2 CO d M d P* d o d o o 1) "5. o "? in co o. .; S 2! c/5 co in o O 1 i i 1 : : : : . C j c" re-eva c Kind of engine Jacketed? Steam-pressure, atmospheres I. H. P Ratio of expansion Revolutions per minute Proportion of cylinderconde c c c o 1 o 1 1 c' 3 "0 o e c ^ 8 2 1 V M C 3 -a 1 1 a a o .2 '5. X ja 1 i THEKMODYXAJtICS OF THE STEAM-EXGIXE. 493 These great wastes by internal transfer of heat, without transformation into mechanical energy, are evidently due to precisely those conditions which make the steam-boiler efficient. That rapidity of conduction which causes a small area of iron in the boiler to transfer a large amount of energy, in the form of heat, for useful application, is the quality which causes a small area of iron in the engine-cylinder to store and waste a considerable part of the heat entering it. The thickness of the metallic film affected by the phe- nomenon here studied is probably slight. Mr. A. A. Wilson, in experiments on a large pumping-engine. found the mean temperature of the metal nearly equal that of the entering steam at a point as near the inner surface of the cylinder as he could safely place his thermometer-bulb; and Mr. Dixwell estimates, as a deduction from his own tests, that the mean variation of cylinder-temperature does not exceed 30" F. He thus takes, in the discussion of one of his engine-trials, a case in which 920,000 pounds of steam passed through the engine, while it made 223,000 strokes : giving 4. 12 pounds per stroke at the point of cut-off. Taking the specific heat of steam at 01475, and of iron at 0.1 14, the loss of temperature of the steam having been found to be 200 F.. 4.12 X 200 X 0475 = j: X 30 X 0.114, when JT is the weight of iron : then jr = 1 14-4 Ibs. of iron varying in temperature the specified amount, 30 F. The area of surface was 56.59 square feet; and the thickness, to weigh 1 14^ Ibs^ would be but 0.054 inch, or less than one sixteenth. In the course of experiments in the Sibley College labora- tory, Mr. W. W. Churchill being the observer, the thickness of metal of cylinder-wall was reduced to 0.2385 inch, and the temperature of its outer surface observed by means of the 494 A MANUAL OF THE STEAM-ENGINE. instantaneous action of a balanced Wheatstone bridge and a platinum-wire conductor, and without change being detected, the temperature of the entering steam being 300 F M and up- ward, the engine non-condensing, and the revolutions 308 per minute. The load was light, however, and compression heavy. The conductor indicated a constant temperature averaging six degrees lower than that of the steam at entrance. In another series, the same general results were obtained ; but the tem- perature recorded was less constant. Reducing the thickness of wall to 0.115 inch, another series of trials showed slight variation of temperature and a reduc- tion from that of the steam of about 25 degrees. Still further reducing the wall to 0.0426 inch, a fluctuation of 17 degrees became observable. These were all tentative experiments, however, and are not considered as giving reliable quantitative values. Mr. Willans, as a result of his own experience and research, concludes that a large proportion of the " missing quantity," due cylinder-condensation, must be ascribed to the action -of water in the engine, and that "water is likely to prove a more important factor than surface at such speeds as 400 revolutions per minute," and that, as in some of his own experiments, when this condensation occurs in one thirtieth of a second, the presence of a small constant weight of water in the cylinder may account for substantially all this waste, and that its generally observed variations of magnitude may be due to changing quantities of water in the engine. His engines were therefore so designed as to avoid giving opportunity for water to lodge in the cylinder ; any collecting on the piston-surface, the only place available, is swept off by the exhaust-current. A thickness of film of only about 0.008 inch of water would account for all the waste thus produced in his observed case. The diagram opposite is given by Mr. Porter, as taken from the high-service pumping-engines at Providence, R. I., now * Porter on the Indicator; p. 172. THERMODYNAMICS OF THE STEAM-ENGINE. 495 The speed of the engine was 10 revolutions per minute ; at one revolution, this action was still further, and enormously, exaggerated.* The problem of the engineer is, evidently, either to render the internal surfaces as thoroughly non-conducting, and as incapable of heat-storage, as possible, or to secure similar properties for the working fluid exposed to contact with them ; thus, by either FIG. 144. CYLINDER-WASTE. or both methods combined, reducing the condensing power of the cylinder to a minimum.t The cost of steam and power in engines of various sizes has been ascertained, by the researches of many investigators, to be largely dependent upon size of engine and power de- * The higher the speed the more superficial the action; and, at very high speeds of rotation, a limit may be approached at which the wastes by variation of temperature of the metal of cylinder become insensible. The more effective the jacket action, also, the thinner this film of varying temperature. f The Westinghouse Co., about 1885, conducted a series of experiments jto determine the possible gain in fuel economy to be realized from the use of non conducting surfaces in steam-engine cylinders, as far as possible. The non-con- ductor found to be best was porcelain. The pistons and the cylinder-heads were coated, but the difference in the fuel economy was so small as " not to be wonh consideration, commercially speaking." A device proposed by the Author consists in converting the inner surfaces into a graphitic sponge, filling it with non-conducting substances. 496 A MANUAL OF THE STEAM-ENGINE. manded. The accompanying diagrams, prepared by Mr. Emery, and the corresponding data may be taken to exhibit this cost for engines of the design.* Curves in group No. i ex- hibit the results of experiments at the Novelty Works, N. Y. City, under the joint supervision of that establishment and the U. S. Navy Department. The curves, A, B, C, D, E, refer re- spectively to steam-pressures of 25, 40, 60, 80, and 100 pounds. FIG. 145. ACTUAL WATER E FIG. 146. COMPUTED EXPENDITURES. Curve H of the series designated No. 2 represents the cal- culated quantity of water required per indicated horse-power per hour in a non-condensing engine. The calculations take into consideration the weight of steam required to fill the cylin- der to the point of cut-off and to supply the heat transmuted * Trans. Am. Soc. M. E.; 1888; No. cccxxi. THERMODYNAMICS OF THE STEAM-ENGINE. 497 into work, but make no allowance for cylinder-condensation, for losses by clearance, or for deficiency in work due to insuf- ficient area of passages, or to back-pressure. Curve G is a similar curve based on the additional condi- tion that the clearances and ports equal one twentieth of the cylinder volume. Curve Dis D in series No. I, and shows the relative extent of the losses at different points of cut-off due to cylinder-con- densation and other causes not included in the calculated re- sults for an engine of 5 horse power. The curve F was originally interpolated in the position shown from such information as was available at the time to show the probable cost of using steam at 80 pounds pressure in an engine developing about 100 horse -power. Later ex- periments show that for conditions stated the curve should more nearly approach the curve G. By means of empirical expressions conforming to the curves obtained by experiment, Mr. Emery computed probable ap- proximate values for a somewhat wide range of conditions of operation of non-condensing engines, and tabulated them as shown on page 49$. The table shows that equal economy should be secured in non-condensing engines at somewhat higher pressures than with condensing engines. It would, however, require the use of compound, triple, and quadruple expansion engines, to se- cure best results. Mr. Emery would restrict the expansion ratio in each cylinder to 2, in such engines. The parallelism of Emery's curves indicates that we are usually safe in assuming that the probable cylinder-condensation in the regular working of ordinary unjacketed non-condensing engines is sensibly constant ; and at moderate speeds Mr. Buel takes its amount as 1 5 pounds per hour on each square foot of total internal surface of the engine, including internal super- fices of cylinder, of heads, both sides of the piston, the surface of its rod, and the internal surfaces of the steam -passages. The condensation, in ordinary forms of engine, is found, on this basis of computation, to vary somewhat on both sides the as- A MANUAL OF THE STEAM-ENGINE. STEAM-CONSUMPTION. I 3 4 5 * 7 8 9 IO it POUNDS OF WATER PE R INDICATED HORSE-POWER PER HOUR. Engine of proper size to develop 100 H.-P. f= 100. Gauge Pressure. Experimental results at full stroke in small engine, ex- tended to the higher pres- sures by formula. Required to fill Cylinder. Required to supply heat for mechanical work. nder-con- miscella- 1 i a J_ 5 for N min. Required at full stroke. Required with cut-off at 0.6 stroke. Required with cut-off at 0.3 stroke. Required at most economi- cal cut-off. Approximate. J 1 M Required for cyli densation and neous losses. P 3 60 So 100 WS 150 400 500 E C, CM Ct Calc'd. C 3 + C 4 C lC=l C i c=o.4 C I- -25 -3 -35 Condensation. FIG. i 4 8.-Cc curve is just as well taken, as by Professor Cotterill, as loga- rithmic. It is, however, closely represented by the hyperbola having the equation (x + 0.12) (y -f 0.44) 0.2472 ; where x is the condensation and y the ratio of expansion ; or, referring the curve to its asymptotes, x'y' = 0.2472. At full stroke, y = I, and x = 0.12. and the condensation here becomes twelve per cent ; a result closely corresponding with THERMODYNAMICS OF THE STEAM-EXGME, JOg the earlier figures obtained by Isherwood on the U. S. S. Michigan. When we approach the limit, y = o : .r = 0.68, two thirds the steam is condensed : for these extreme cases, however, these equations cannot be expected to be accurate. In this engine, the area of internal surface exposed, up to the point of cut-off, and of which the increments are constant, with uniform variation of the cut-off, is measured by ^ = 3.96+16.5*. in square feet ; and the variation of condensation with this varying area is shown in the next figure. The equation of the curve is (* 4-77) (A - 1-0266) = 21647. Ike Author has been accustomed to assume that the curve may be taken as parabolic, and to use the more manageable ex- pression for the first case, above, = a \ ' r -VJ- 504 A MANUAL OF THE STEAM-ENGINE. in which the condensation is expressed in terms of the recipro- cal of the cut-off, = r, the ratio of expansion, a, being a co- efficient having a constant value in the same engine, the value of r only varying. From the data just given, and for this engine, when r = 6.66 -f, a 0.187; r = 4.00, a = 0.1987; r = 2.857, a = 0-1923 ; r = 2.222 -f-, a = 0.1812; r = 1.82, a = 0.174. From which it will be seen that the value of a is one fifth approximately, and the results of this investigation very closely coincide with those of earlier experiments and deduced by the Author previously to this investigation. The hyperbolic equations give the following figures : A = 13.86 ; x = cylinder-condensation = 22.01 ; error 0.39 " 12.21; " " 25.00; " 0.000 " 10.56; " " " 28.50; " 0.000 ; " 8.91; 33-50; " 2.50 " 7.26; " " 41.06 ; " 2.94 Also: y = cut-off = 0.13 ; x = cylinder-condensation = 0.499 ; error o.oor = .225; " " =0.410; " o.ooo = -33 ; " " = 0.338 ; " 0.002 = .45; " " =0.274; " +0.004 = .59; " " " =0.222; " -(-O.OO2 These equations thus so closely satisfy the record obtained by direct observation that they may be taken sensibly to represent the law of condensation, as a function of the ratio of expansion for this engine under the conditions described, and show that the weight of steam condensed is sensibly constant at all ratios of expansion within these limits. The magnitude of the coefficient, a, in the expression last given above, is obviously different with different engines, de- creasing as the size of engine and its speed increase. The value, O.2O, above found will only apply to engines similar to THERMODYNAMICS OF THE STEAM-ENGINE. $0$ that here described, in size, speed, and structure, as will be seen later, when deducing the more general expression. Taken as a function of area of surfaces producing waste, these data show the condensation to be directly proportional to that area. (2) The variation of internal condensation with varying steam-pressures, all other conditions being as usual and retained constant, was as follows, the expansion ratio being 5 : Gauge-pressure 80 pounds ; condensation 35.24 per cent. " 66.85 " " 47-83 " " 52-33 " 36-84 " " 37-0 " 41-43 " " 22.3 41.19 " The engine was here worked condensing. The equation of the curve for this case is -r = 45 0.12667; in which x is the steam-presssure and y the fraction of total steam condensed. Then y = pressure = 80.0 ; x = cylinder-condensation = 34.88 ; error .036 = 52.33; " " " =38.3*: +1-54 = 37-o ; " " =40.32; i. ii = 22.3 ; " " " =42.27; -f- 1 .08 And the equation evidently closely represents the facts for this case. It indicates that condensation would become unimpor- tant at very high pressures ; the expression giving x = o for y= 355 Ibs. by gauge. (3) The non-condensing engine appears, in this case, to have a different method of variation; for, throwing off the con- denser, the data obtained give, with the point of cut-off at 04, or a ratio of expansion r = 2.5, very much less condensation, and it is not, apparently, as before, directly variable with the variation of steam-pressure. Only three trials were made, owing to the impossibility of getting steam steadily for the 5 o6 A MANUAL OF THE STEAM-ENGINE. highest pressure attempted and the form of the curve for this case is unknown ; but the figure shows the lines for both cases: 1 .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 Condensation. FIG. 150. CONDENSATION WITH VARYING PRESSURES. (4) The effect of variation in speed of engine, or time of action of the acting surface of the cylinder, is the final subject of test. Starting with an average boiler-pressure of 19.67 pounds and a cut-off of .98 of the length of stroke and the en- gine running at an average of 33.74 revolutions per minute, three trials were made, concluding with an average speed of 62.977 revolutions per minute; the greatest variation in the point of cut-off being .05 of the stroke, and in the pressure .63 of a pound. Differences in the condensation occurring can here be attributed purely to the variation of speed. THERMODYNAMICS OF THE STEAM-EXGINE. 5OJ Difficulty was found in getting the engine to run smoothly lower than thirty-three revolutions per minute, and oppor- tunity was not given to make a fourth test at a higher speed than sixty-three revolutions, the engine being needed for its regular work. But it will be seen by reference to the figure that the three points of the curve given by these three trials are so nearly in line that a fourth test is hardly necessary. The conditions under which the trials were made were so strictly adhered to, and the results obtained varied so slightly, that an expression from these results determining the amount of condensation as a function of the speed may be taken as strictly representing the losses occurring by condensation in this engine. The greatest variation in the range of pressure for the three tests was three and one half per cent, and the greatest variation in the cut-off amounted to but one half of one per cent. The per cent of condensation was : Revolutions per minute, 62.977; per cent of condensation, 24.37 50.3; " " " " 28.75 33-74; 33.506 From which it is seen that the condensation varies in this case sensibly inversely as the speed. Algebraically expressed, jr = 45 0.33.7, and we have, as seen in Fig. 151, y = Revolutions per nain. = 62.977; * = Cjl Con. = 24.22; error - 0.15 " " " 50.3; " " 28.41; " 0.34 . * " 33.74; " " 33-86; " +0.504 Were the law as here expressed to hold good, the line con- tinuing straight to its intersection with the coordinates, the loss of steam would approach 0.45 as the speed approached the zero-limit, and would itself become zero as the engine-speed approximated to 140 revolutions per minute. 508 A MANUAL OF THE STEAM-ENGINE. Professor Cotterill's expression for this limit of speed, N = ^fv, d taken in feet, would give for zero condensation N = 400, nearly, or more than twice the former figure. Professor Marks has gone over this work to determine the \ .05 .10 .15 .ao .25 .30 .35 .40 .45 .50 .55 .6 Condensation. FIG. 151. CONDENSATION WITH VARYING SPEED. value of the so-called " condensation-constant " C, in the ex- pression for waste, W=ACt(T l - T 3 ), for this engine, under the various conditions of its operation, accepting the assumption that wastes are proportional directly to time of exposure to the exhaust steam, rather than to the square-root of that quantity. Here A, t, J", , T t , represent area of exposed surface ; time of exposure, and temperatures. The following are his results for the non-condensing engine here studied : THERMODYNAMICS OF THE STEAM-ENGINE. 509 CYLINDER-CONDENSATION. SIMPLE, NON-CONDENSING ENGINE. (Experiments of Messrs. Gately & Kletzsch, Sandy Hook, 1884.) 1 1-8 f CJ i | I 1 X u s 1 | Condensa- tion & ^J 1 i S |<5 1 1_ <2 I. " 1 . Constant. cference Number of ment. uration of Rxperimeni roke of Cylinder in fei iameter of Cylinder Ir eciprocal of True Nu Expansions. umber of Strokes per i gS 11 s 1 bsolute Pressure in poi square inch at Cut- bsolute Steam-pressur Imust at Mid. stroke, per square inch. smperature of Cylinde off (Kafir.). smpcrature of Cylinde huust. c u |j 1 *tio of Actual to I Steam at Cut-off i Ibb. of Steam. British Units of Heat. K Q m Q tt Z c < * H H w at 1 5 - k m i w 5 (9) 1.40 2.00 i -55 3.5 ;- = i-s -50.589 50.443 .50.330 136.52 Dry Sat. 6.. 54 .35.9 " " 68.34 .34.64 " " 62.10 4-aa 3-9' 4-48 294.2 [155.2 430 30.. .4:152. 15; 390.13 294.80(157.561426.35 .294 0.0,576 i 4 .ao. .371 0.01929 18.00 .5.2 0.0.909 17.31 (10) 2.00 3-3 1.50.131 137-9 " 149- 365 279.84 .49.4 530-9 .003 o-oi ^ '5.15 1-3 .5 0.208 .38.03 " " 78.80 3 24 3.i.02'.44. 58 342.2 .5440.oi544JI3.82 :: 2.00 3.5 .50.244.43.46!" " 53.21 3.24 1284.95 144.58 492.1 (?) .917 0.025631 .583 0.0.4.6, -y '14' ti 2.00 3.5! .50.2.0 2.00 3.5 .50.242 .37-82 35.85 :; :: 39-83 36. 26.74 3 46 266.741.49-02 244.261.47.2. 642.9 936.6 .7070.0.52814-16 .7000.0.37212.94 :-: ::: 3.00 3.5 .50.4.2 2.30 3.5! .5^0.420 .35-96 37-i4 :; :: 65.36 .4 7 50.42 .4.82 298..6L2 281.30 212.4 407-5 (?) .I22 ! 0.0088 4 (?) .307 0.02288 1 (?) (is 3.00 3.5! .50.466 133-04 " 28.40 .4-84 247.56212.49 886.6 (?) .376 0.04090 3 - - - (?) I) '30 (3-5 2-00 3.5 1-45 '3-5 50.938 .50.961 .50.981! 125.95 I 00.60 67-48 " " 37-38 3-'5 1245.561.46.3. 28.35 3-86 2 47-4oji5i.57 28.53 4-96 1247.811161.94 9.6.2 886.8 88t.6 .322 0.014041x2.23 .403 0.0.528 14.36 .504 0.0.449113.68 Average. Numbers 7-10 illustrate varying expansion ; 11-15, varying steam-pressures, condensing; 16-19, varying pressure, non-con- densing ; 20-22, varying speed of engine. Major English, computing the wastes in simple marine un- jacketed condensing engines, obtains just double the above- given constants ; and both sets of results correspond fairly with the experience of various other investigators.* For jacketed condensing engines he obtains nearly the mean of the two, and not far from two thirds the higher figure. * Proceedings Inst. Mech. Engrs.; 1887. 510 A MANUAL OF THE STEAM-ENGINE. Fourier's expression for heat-absorption, taking / as the symbol for time, shows that, as the period of exposure to the higher temperature diminishes, the amount of heat-absorption is reduced, and varies inversely as the square-root of the speed of engine, a conclusion independently derived by Escher * from direct experiment, and by the Author by observation of the results of various engine- trials, although not apparently confirmed by those just quoted. Professor C. A. Smith, in 1880, found a variation of 120 F. in the internal temperature of the metal in a locomotive cylin- der, the magnitude of the change varying inversely as the speed of the engine.f Escher found this waste to be propor- tional, very nearly, other things equal, to the square-root of the absolute pressure of entering steam. The rate of transfer of heat by this condensation, in en- gines of large range of expansion, is very great ; in average practice a dozen times as rapid as the transfer across the heat- ing surfaces of the steam-boiler. A flow of 6000 B. T. U. per hour in the latter case and of 60,000 units in the former are not exceptional values for transfer on an area of one square foot. This difference is accounted for by the fact that this case of the boiler, like that of a steam-jacket, is one of steady flow and affected only by conductivity of the metal and thermal resist- ance of surface ; while cylinder-condensation is a process of storage, and is a function of specific heat per unit of volume as well as of conductivity. Major English finds, as previously taken by the Author,:}: and still earlier by Professor Cotterill, that internal, or cylinder, condensation varies, at least approximately, as the square-root * Engineer; 1882. f Engineering; 1880; p. 460. \ President's Annual Address; Am. Soc. M.E.; 1880. Efficiencies of the Steam-engine; Trans. Am. Soc. M. E.; 1880. Proc. Inst. M. E.; 1871; p. 516. THERMODYNAMICS OF THE STEAM-ENGINE. $11 of the time of action, or as , where A 7 " is the number of revo- lutions per minute and s the area of surface effecting the cool- ing the entering steam.* This result has been also experi- mentally confirmed by Escher. He proposes the formula in which C is the initial condensation in British thermal units, per pound of steam, worked in an unjacketed cylinder ; W'vs> the weight of feed-water in pounds per stroke ; s, the exposed sur- face of metal at the beginning of the stroke ; and 7*, and T m are the initial temperature of steam, and the mean temperature of the cylinder-walls, at a minimum, both on the absolute scale. Pj is the density of the entering steam. A is a constant, which he finds to be, for cases studied by him, 80 in British units. For jacketed engines, he takes T t = T m and adopts in which A becomes 56, indicating a gain of about 30 per cent in the reduction of this waste, by the use of the jacket, for the cases examined. Major English finds, for re-evaporation, the following ex- pression : where the total surface exposed to the point assumed is s ; T m and T^ are the mean absolute temperatures and the final abso- lute temperature of the steam up to and at that point ; //- * Proc. Inst. M. E.; Oct. 1889. 512 A MANUAL OF THE STEAM-ENGINE. jacketed cylinders being assumed. For jacketed engines, T m is made T, , and then " Initial condensation and corresponding transfer of heat to the metal will of course go on upon each fresh surface exposed during the stroke ; but the supply of heat to effect this is drawn by re-evaporation from that stored up in the surface already exposed;" so that the effect is simply "to distribute it over a larger area." Thus the excess of re-evaporation over condensation will become, for any elementary movement of the piston, or accordingly as the unjacketed or the jacketed engine is taken ; B having the value 80 or 56, as the case may be. The net con- densation, up to any given point, becomes for unjacketed and for jacketed cylinders, respectively. The total weights of steam per stroke become W = in which A is 80 or 56, as the case may be, and X is volume swept through, to point of cut-off, in cubic feet ; c is the clear- THERMODYNAMICS OF THE STEAM-ENGINE. 513 ance-ratio to that volume ; is the ratio of cushion to total steam per stroke ; and the other quantities as already given. A comparison of these expressions with the results of test of the \Villans engine, which happens to give the needed data, shows remarkably close correspondence. It is obvious, on comparison of the data now available, and the varying conditions under which they are produced, that the precise form of the expression for this waste will be determined, as well as, probably, the magnitudes of its constants, both by the condition of the surfaces acting, and by that of the steam supplied, as well as by the variable conditions of operation of the engine itself. The indications are, as deduced from a study of representa- tive indicator-diagrams, that in about one second, were the time allowed, the process of absorption of heat would be practically, in such cases, complete ; while for shorter periods the total ab- sorption would be sufficient to condense steam in proportion to the square-root of the time of exposure ; i.e., one half as much, for example, in one-fourth second. Experiment, as shown by Hirn, proves the initial condensa- tion to be progressive, as the piston advances, up to the point of cut-off, ordinarily ; in cases cited by him, increasing from I per cent water at the beginning to 31 per cent at the end of the admission-period, and in some cases attaining very much higher proportions. Hirn has shown that, when superheated steam is used, there may exist condensation on the interior surfaces of the cylinder and superheated steam in the midst of the charge, the cylinder containing at the same time water and wet, dry, and superheated, steam. Careful discrimination should be made between the wastes produced by heat-transfer between metal and steam during the expansion-period and those occurring during the exhaust- stroke. The latter are losses of the whole quantity so trans- ferred ; while the former are the differences between the effi- ciencies of transformation with maximum range of expansion and with the lesser actual ranges for the successive decrements of heat and temperature during transfer. If possible, in all 514 A MANUAL OF THE STEAM-ENGINE. calorimetric investigations the two quantities of rejected heat should be separately recorded. The condensation at the point of cut-off is often 20 or 30 per cent; where it is reduced to 12 or 15 at the end of the expansion, and the waste by surrender of heat by the metal during the exhaust period is 10 to 20 per cent. The advantage possessed by a valve-gear and system by which separate steam and exhaust ports are provided, in reduc- tion of internal wastes, is obvious, and is practically found to be very considerable ; especially when, as is usual, the valves are so placed at each end of the cylinder as to reduce the " dead spaces " to minimum volume. Large marine engines are now designed, in some instances, with separate steam and exhaust valves and ports ; the valves being of the piston variety and double-ported. Re-evaporation taking place during expansion gives rise to a real gain of efficiency ; yet evidently a loss occurs if a com- parison is made with the case in which the same steam, instead of being initially condensed, is worked from initial, maximum pressure and temperature. While, other conditions being equal, increase of engine-speed decreases wastes, there will always be found a practical limit, if nowhere earlier, at the point at which the resulting decreased mean forward-pressure and increased back-pressure give rise to overbalancing loss. This limit is set farther away as ports are enlarged ; but, again, in a new compensation, enlarged ports increase the cost, in work, of the operation of the valves and gear. While the theory of heat-engines can only give a general knowledge of practical and of applicable principles in their design and operation, it may point the way to further improve- ment, may serve as a guide and check in novel constructions, and, coupled with experimental knowledge, may even, in some cases, enable a computation to be made of probable efficiencies that may be useful, if not substantially exact. In all cases, however, the engineer checks his work by reference to the ex- perience already had with engines of as nearly as possible sim- THERMODYNAMICS OF THE STEAM-EXGIXE. $1$ ilar kind and under similar conditions of operation. Expe- rience, after the machine has been built and set at work, finally enables him to make precise adjustment, where his preliminary estimates had given him approximations. The following table, computed by Mr. Thompson, exhibits the probable water-consumptions and the mean effective pres- sures for ideal cases, with a correction for initial condensation and leakage, the engines being assumed to be of good con- struction and of fairly large size. These allowances for internal wastes amount to about 0.12 \'r and 0.15 Vr, for non-condensing and for condensing engines respectively. The Author would allow one half greater loss in engines of common form and of one or two hundred horse-power. The figures should obviously diminish with in- creasing sizes and speeds, and should increase as the engines are smaller and speeds lower, as elsewhere shown. In conclusion : The variation of condensation, with changes of pressure and temperature, under usual conditions of prac- tice, is thus found to be very moderate, and to follow a very simple law, so far as it can be traced. The waste with varying speed of engine is found, also, to be nearly as previously indi- cated by the Author ; but the law is less exactly determined than in the case of varying expansion. Since, however, in all ordinary cases, in practice, the speed of engine and the boiler- pressure are practically constant, in the regular operation of the engine, the most important part of the investigation is that relating to the ratio of expansion. The next most im- portant matter is the determination of the variation of loss with varying speed of engine, and the results here reached are sufficiently exact to be very useful, both to the designer and the owner of engines, although the precise method of varia- tion and its exact algebraic expression still remain subjects for investigation. The last investigation, relating to variation with change of pressures, is interesting as bearing upon the future of the continually progressing advance in the direction of increasing pressures. The last two lines of research de- mand still further exploration. The results here reached must 516 A MANUAL OF THE STEAM-ENGINE. I 3T?n?9^&f^-aP?&Q " c " M fO &^VC vO* f^^oPoO* O\ 8 j-gffifsi.a^iiiaJ ffmSsS 2 'D'N I * o cj jij-a eT m m'm 5- ? S) 1 ^. aanssaaj IVU.INI THERMODYNAMICS OF THE STEAM-EXG1XE. $17 be regarded, at present, as applicable, in the theory of the steam-engine, only provisionally, and as to be accepted finally, only after repeated experiment. Collating the facts, so far as known, the Author has con- tinued to employ the expressions, based on Fourier's work and on experiment, = b in which x is the fraction of steam condensed ; a a constant to be determined for each engine, or class of engines, of similar size, speed, and stenm-pressure ; b a constant for the general expression: /IT the range of temperature worked through; d the diameter of the engine-cylinder in feet ; r the real ratio of expansion, and X the revolutions per minute. 130. The Theory of Internal Condensation and Waste is obviously one of exceeding difficulty ; and an exact and rational theory must include so many variable and mutually interacting conditions that it cannot be expected, even if fully developed, to find application, in all cases, in the engineer's, or the designer's, work. It is commonly assumed that cylinder-condensation will be proportional to the range of temperature between that of the entering steam and the exhaust ; to the time of exposure to the exhaust, or inversely as the speed of engine, and to the area of internal surface affected, up to the point of cut-off. On this basis Professor Marks has made comparisons of data derived from a considerable number of experiments, mainly on non-condensing Corliss mill-engines, and has obtained, as already seen ( 129), as a mean for ordinary work, a value of C, the number of pounds of steam condensed on the square foot of internal cylinder-surface, per hour, and per degree range of temperature, C = 0.02047. equivalent to 18.13 British thermal units.* The experiments of Messrs. Gately and Kletsch, already described, give from 0.016 to 0.019 pound, or 14.5 to * Relative Proportions of the Steam-engine ; pp. 206-7. 5l8 A MANUAL OF THE STEAM-ENGINE. 17.4 B. T. U., with ratios of expansion varying from 2 to 7, and an average of 0.0165, nearly, equivalent to 15 B. T. U. for the whole series of trials. The first-given values may probably be found sufficiently approximate for use in estimating the waste in any similar engines. The value of this constant being determined, the total cyl- inder-condensation is, approximately, in pounds of steam, per hour, W=CA(T l - T;)/; (i) where C is that constant, say 0.02, A the area of internal sur- face covered by the steam up to the point of cut-off, in square feet ; while t, the time of exposure of heat and steam observed in experiment, is generally nearly constant, at any given speed of engine, and range of pressure and temperature, irrespective of the magnitude of the varying ratio of expansion, and, as in the Sandy Hook experiments, a nearly constant product can be obtained for the product of the " cut-off " and percentage of waste. The same investigation and Professor Marks's deductions from the reported data show that it is most likely to be the time of either expansion or of exposure to the exhaust, more probably to their sum, which should be taken for / while it is not yet ascertained whether the function to be ac- cepted is the square-root of that quantity, its first power, or some intermediate function. It is probable that the several ex- pressions of Professors Cotterill and Marks and of the Author will find use, as at least approximate, each in its appropriate place. In producing an expression for the magnitude of internal heat-wastes by condensation and later evaporation, we may adopt, as already seen, either of several methods, which are more or less closely approximate. Following Fourier, we find that the quantity of heat thus stored and wastefully restored may be taken as proportional to the area of surface acting, the temperature range, or temperature head, and the square-root of the time of action. All these proposed expressions are based upon these assumptions or upon experimental data con- THERMODYNAMICS OF THE STEAM-ENGINE. 519 firming them ; except that it remains questionable whether this function of the time is of either constant form or value. That the time to be taken is not that of exposure to the entering steam, up to the point of cut-off, is certain, from the fact that the total loss is never so proportional. Experiment has indicated, however, that the waste often varies more nearly as the square-root of the time of action, and the Author has been accustomed so to take it.* It is more convenient, usually, to take this loss as a function of the ratio of expansion, as seen later, and experiment has been found to indicate this function to be the square-root, approximately, of that ratio. It has, as yet, been impossible to ascertain by ex- periment precisely how the waste varies with range of temper- ature. It seems extremely probable that the condition, the quality, of the steam from the boiler may so seriously modify the working of an engine as to make it difficult to analyze the total variation into the factors due all these constantly varying complications of physical conditions. It will often be sufficient, in the solution of special prob- lems, to assume approximate data. Thus, the Marks coeffi- cient will answer all purposes in the comparison of engines of different sizes working under otherwise similar conditions. The expression may be used in computing the probable weight of steam needed to supply cylinder-wastes ; when W^ is the weight needed, for the representative ideal case, no initial condensa- tion occurring ; a is the constant determined as already indi- cated, and which may be taken as not far from 4 for unjack- eted and 3 for well-jacketed cylinders, for average cases. D is the diameter of cylinder in inches, r is the ratio of expan- sion, and / is the time of one stroke, in seconds. In the Gately Q and Kletsch experiments, ^ = 0.2, approximately, and / = I. very nearly. * Trans. Am. Soc. M. E. ; May 1881. Jour. Franklin Inst. ; May 1881. 52O A MANUAL OF THE STEAM-ENGINE. The value of the constants a and c in the expression for waste, may, with superheating, or better thermodynamic conditions in other respects, be reduced considerably below the values here assumed as representing ordinarily good average practice. Mr. Barrus gives data from trials conducted by him in which they fall to, in some cases, two thirds, and in other seven to one half, those obtained in earlier work by the Author. The range would seem to be from, approximately, a = 2 to a = 3, c = o.io to c = 0.15 ; where steam is used without superheating, and to as low as a = i and c = 0.05, or less, with steam effectively superheated ; d being taken as the diameter of the cylinder in inches.* The assumption, in our equations, that heat-transfer, in cylinder-condensation, is sensibly proportional to the range of temperature, in ordinary cases, seems justified by experiment. This conclusion of Rankine and later engineers is confirmed, not only by the cases earlier studied by the Author, but also by later investigations. Mr. Bodmer finds this fact illustrated by the engine-trials both of Willans and of Major English. His conclusions are usually substantially in accord with those previously reached. He finds the quantity of heat transferred, and of steam condensed wastefully, proportional to the total area of the walls of the clearance and port spaces, as already seen.f In the expression, for simple engines, taken by Bod- mer, Q= C(T-t)S-i-N*, * Trans. Am. Society Mech. Engrs. ; vol. xi; 1890; pp. 170, 175; tables. f Industries; Oct. 17, 1890; p. 385. THERMODYNAMICS OF THE STEAM-ENGIXE. 521 Q is the heat transferred in B. T. U. ; T t the temperature- range ; ^' the area of clearance and port surfaces, in square feet ; and N the number of revolutions per minute. The value of C varies from about o.i B. T. U. in simple, unjacketed, engines, to 0.5 for good jacketed cylinders, and appears to be fairly constant. With well-clothed cylinders, it seems, according to the experiments of Mr. Buel, that the amount of steam unac- counted for depends mainly upon the area of internal surface ; and, in ordinary' practice, in the case of non-condensing engines, with unjacketed simple engines, but with well-clothed cylinders, the condensation per hour will be between 20 and 30 pounds per square foot of total internal surface, from 10 to 20 pounds per square foot of internal surface, for similar engines, condensing, and about these amounts for the former class with steam-jack- eted cylinders, and one half the latter figure for jacketed con- densing engines. In case it be assumed that the cylinder-con- densation is 15 pounds per hour, per square foot of internal surface, including the ports, the two sides of the piston, and the surface of the rod, supposing the interior surface to be about as follows : Ports , , 12.0 sq. ft. Sides of cylinder 3 1 .4 " " Cylinder-heads and sides of piston 12.6 " " Piston-rod 4.6 " " Total 60.6" " we have as steam unaccounted for by the indicator 60.6 x 15 = 909 pounds per hour. It would perhaps be more correct to take the areas of heads, piston and steam-passages, and a variable fraction of the cylinder-surface, and the condensations as a constant function of that total area. This total, in many marine engines, is as much as twice the combined areas of piston and cylinder heads, and all these areas are in action twice as long as the average for the cylindrical surfaces. 522 A MANUAL OF THE STEAM-ENGINE. Professor C. A. Smith concluded, after studying the work of Isherwood and other early investigators, that, as the Author has elsewhere indicated, " the whole excess of water used over that required in a non-conducting cylinder is rudely propor- tional to the difference of temperature between the incoming and outgoing steam, and to the diameter of piston ;" and such excess is nearly constant, and is independent of the ratio of expansion for ordinary cases, a conclusion which has been seen to be confirmed by both experiment and computation based on theory. There are thus available several more or less closely ap- proximate methods of computation that will answer the pur- poses of the engineer and give fairly accurate measures of these wastes. Of the several expressions on which they are based, one or another will be employed as they are found more or less suitable to the purpose and conditions of the case in hand. That the assumption of approximately constant wastes by internal cylinder-condensation, as already indicated in several ways and by reference to experiments, may be ordinarily adopted in provisional computations of efficiency and steam- consumption is also evident from .an inspection of the curves given by Mr. Emery and by the results of computation by the other methods presented in this work, notably those relating to the compound engine. Mr. Buel has computed, in great de- tail, the probable demand of steam in an engine of about 150 horse-power, having found for such engines, by experiment, a nearly constant condensation, with varying expansion, of about 15 pounds of steam per square foot of internal surface per hour.* A tabular resume of this work will be found in the appen- dix with the nomenclature, the formulas, and the results for a wide range of values of the ratio of expansion. The proportions of the cylinder affect greatly the magni- tude of this waste. Thus, * Am. Machinist; June 30, 1888. THERMODYNAMICS OF THE STEAM-ENGINE. 523 Let d = the diameter of cylinder ; / = the length of stroke ; e = the proportion of total area of surfaces of dead- spaces to those of the clearance proper ; r = ratio of expansion ; V= volumes of cylinder ; S = surfaces. Neglecting the cushion-steam, the area in contact with steam at cut-off is the volume of steam enclosed is and the ratio of S to Vis The cylinder-condensation would be proportional, all parts being equally wasteful, to the value of this ratio. The ratio of active surface to total volume of cylinder is 5, S t and the values of r and of the volume, F, , being constant, y t = \xd*l, nearly, = const., and it becomes evident that this waste is influenced greatly by changing values of d and /, increasing rapidly as the diameter 524 A MANUAL OF THE STEAM-ENGINE. is increased and the stroke diminished. With similar propor- tions and varying size of cylinder, and the waste thus varies inversely, as already elsewhere taken, inversely as the linear dimension of the cylinder, and values of the percentage of condensation obtained from any one engine by experiment must be multiplied by the inverse ratio of such dimension to obtain correct values of this proportion of waste for other sizes. The value of e, above, is given by Cotterill as from i.i in the best cases of four-valve engine, as the Corliss, to about 2 for single slide-valve engines. The time of exposure is only the same, however, for the surfaces of heads, piston, and passages, and is there a maxi- mum. As already noted, the effect of the varying exposure of the cylindrical surfaces may often probably be neglected with- out important error, and the whole loss taken as that of those parts alone. Where the ratio of expansion is not great, the presence of " entrained " water in the steam may not produce any- important ill-effect. For the ideal case of the non-conducting engine, this was long ago shown to be true, by Combes.* This deduction was also found to be correct in practice, by Mon. Him. With large ratios of expansion, and especially with jacketed engines, the opposite is probably always true. The irregularities, discrepancies, and, often, apparent con- tradictions observed in the reported results of experiments on the effect of the steam-jacket, and, especially, on the extent and method of variation of cylinder-condensation and wastes are, perhaps, generally due to unnoted variations in quality of steam, and also possibly, often, to inaccurate observations. Professor Cotterill, observing that the range of temperature * Thfiorie MScanique de la Chaleur; 1863; xxxv. p. 157. THERMODYNAMICS OF THE STEAM-ENGIXE. 525 is approximately proportional to log, r, adopts, for usual ranges of expansion in a single cylinder, the expression, in which y = condensation-ratio ; r = expansion-ratio ; d = diameter of cylinder, in feet ; IV '= revolutions per minute; and finds the value of the coefficient C to average about 5 ; varying from 4 to 7 with the nature of the surfaces character- istic of the engine.* In this, as in all the preceding cases, the time-function is based on the period of action of the exhaust. It is nevertheless obvious that the time of action of the pro- FIG. 152. HKAT-TRAJ.-SFKR. gressive cooling during expansion must modify this effect. Since the total initial condensation, which is usually principally waste, is determined by the extent of the antecedent cooling, it would seem that these functions of time, which actually de- termine this waste, can be only approximately proportional to N t or to its functions as taken. The total steam demanded is obtained by multiplying the ideal quantity by I -(- y, the " liquefaction-factor." * This value for the Author's work on mill-engines is 6, nearly. 526 A MANUAL OF THE STEAM-ENGINE. Hirn's method of distinguishing the various heat and work effects, as formulated by Professor Dwelshauvers-Dery, is il- lustrated by the following : * The indicator-diagram^ Fig. 151, completed by marking on a proper scale the volume of the clearance, v, shows the quanti- ties which the diagram and the data ought to furnish. The following volumes, expressed in cubic feet, are taken directly from the engine : v, volume of the clearance space. V t , " occupied by the steam at the point of cut-off. V^ " " " " end of expansion. F 2 , " " " " " " exhaust. F 3 , " " " " " " the compression. V t , " " " " " " " stroke. V a = (F 3 v) -|- (F v} is the volume swept through during admission. V d = F, F is the volume swept through during expansion. V e = (V t FJ -f (V t F 4 ) is the volume swept through dur- ing exhaust. V e = F a F s is the volume swept through during the com- pression. Vf =. V^ v \s the volume swept through during a stroke. On the diagram the pressures are measured in Ibs. per square foot : P t , pressure at the end of admission. P t , " " " expansion. P v " " " exhaust. P % , " " the compression. T a " = area bBAab is the work in thermal units during the ad- mission before the beginning of the stroke. T^ area bBDdb is the work in thermal units during the ad- mission forward stroke. T a = T a " T a is the work in thermal units during the ad- mission. * Trans. Am. Society Mech. Engrs. ; No. CCLIX; vol. xi; 1889. THERMODYNAMICS OF THE STEAM-ENGINE. $2/ T d = area dDEed is the work in thermal units during the ex- pansion. TV = area eEFfe is the work in thermal units during the ex- haust before the end of the forward stroke. T e " = area. fFCcf is the work in thermal units during the ex- haust, backward stroke. T e = T e " 7y is the work in thermal units during the ex- haust. T, = area cCAac is the work in thermal units during the com- pression. 7} = area bBDEFfb = T a ' -f T d -f- TV is the work in ther- mal units during the forward stroke. T n = vteifFCABbf = T e " + T e + TV' is the work in ther- mal units during the backward stroke. T'= T f T n = ABDEFCA is the indicated work in ther- mal units corresponding to a stroke of the piston. The steam has also done work not indicated on the diagram, represented by the area aAKka, which is necessary to accom- plish the compression of the steam into the clearance in order to^give it a pressure equal to that of the steam entering the cylinder. Since the magnitude of this work is not known, it will be reckoned in the heat exchanged between the steam and the metal during the admission. Uncertainty exists as to the composition of the mixture of steam and water in the cylinder when exhaust ceases and com- pression begins. M. Hirn has shown that in general it may be assumed that the mixture contains only steam, all the water which covered the walls having been vaporized and expelled into the condenser during the exhaust, and hence our calcula- tion gives the weight M c pounds of steam during compression. The volume F, of steam and its pressure P t can be ascertained from the diagram, at this instant. From the tables the value of tf, is deduced, the weight in pounds per cubic foot, and Experiment must supply the weight M a pounds of steam which passes into the cylinder at each stroke of the piston and 528 A MANUAL OF THE STEAM-ENGINE. its quality x, or the weight m of pure steam contained therein at the boiler-pressure. This will be called Q thermal units. From what precedes, its value will be in which A. and q are the latent heat of the steam and the heat of the water at the given pressure. During expansion the weight of the mixture in the cylinder is, therefore, and during compression, M c . Hence if the steam is saturated, its internal heat will be as follows : During the expansion mp. During the compression U= If there is a steam-jacket, the water which comes from the condensation is weighed, and its weight ascertained per stroke of piston. Let it be called Mj pounds. This steam is con- densed under the mean pressure of the boiler. For each pound, the jacket will have furnished r thermal units. The jacket has then furnished <2' 'thermal units, and Q=Mjr. Part of the heat brought in by the jacket will have reached the steam ; another part is lost by radiation. The radiation per stroke should be evaluated experimentally. It will be called E thermal units. When the engine is condensing, the weight of water which leaves the condenser is measured, and from this is deduced the weight of cold water, M e pounds, introduced into the condenser for each stroke. Its initial temperature /, is measured and its final temperature t f . The steam-tables give the heats of the THERMODYNAMICS OF THE STEA31-EXGIXE. $29 water q t and q f which correspond. Hence the heat rejected per stroke by the cold water is ascertained by means of the equation Finally the weight Af f pounds of water comes from the con- densed steam and is at the temperature t f if the condensation is effectuated by injection, and at the temperature // if by a surface condenser. It follows that a second part of the heat re- jected into the condenser, which may be called c thermal units, will be determined by one of these two formulae, or c The heat rejected in the condenser will be the sum, or (C+c). When there is no condensation, this heat, rejected into the atmosphere, cannot be evaluated. The vapor in the cylinder carries there Q thermal units at each stroke. It receives from the jacket Q' E thermal units. It loses T thermal units to overcome the exterior work, and it carries into the condenser (C -\- c) thermal units. As the regime is reached, the sum of all these quantities of heat is zero. Hence follows the first fundamental equation : Q + &=T+(C+c) + E.. ..... (I) With condensation, all the quantities are given experiment- ally. This equation can only serve in this case as a check. If the second member should differ sensibly from the first, it would mean that the trial had been badly conducted. Without condensation this equation may serve to determine the value of the rejected heat (C -\- c\ The quantities of heat received or given up by the metal, exchanged between the metal and the steam, will be designated 53O A MANUAL OF THE STEAM-ENGINE. by R when expressed in thermal units. The subscript indicates the phase during which the exchange is measured. Hence : ^thermal units is the quantity of heat exchanged between the metal and the steam during admission ; R d thermal units is the quantity of heat exchanged between the metal and the steam during expansion ; R e thermal units is the quantity of heat exchanged between the metal and the steam during exhaust ; R c thermal units is the quantity of heat exchanged between the metal and the steam during compression. R a , R d , R c will have positive signs when the heat passes from the steam to the metal. R e , on the other hand, is positive when the heat passes from the metal to the steam. In general, R c and R a are positive, and R d is negative ; that is to say, that, generally, the steam warms the metal during the compression and admission, and the metal gives up its heat to the steam during the expansion. The exchange which takes place while the cylinder has no communication with the con- denser will be called R. It follows that The total exchange for one stroke of the piston can be called R, and R = Rf R e = R c 4- R a + R d - R e . This total would be zero if there were no heat denoted by E lost by radiation. R = E. When the jacket furnishes Q thermal units, Q' = E + ( R). The second equation can then be written as follows : R = E-Q', or R f +Q = E + R t \ or, again, R e + R a + R d = R t +(E-Q t ) ..... (II) The quantities designated by R are not given directly by experiment ; they must be computed ; which requires four new equations, in which R c , R a , R d , R e will be the unknown quanti- THERMODYNAMICS OF THE STEAM-EXGIXE. 53! ties. The equations of the expansion and the compression are easy to write, since the weight of fluid in action is constant. The fluid is enclosed in the cylinder, and cannot exchange heat except with the metal of the cylinder. When U and /, rep- resent the internal heat of the steam at the commencement and at the end of expansion, we shall have Similarly, the internal heat of the fluid at the commence- ment of compression was b\. The heat T e resulting from the work of compression is added to this, and this sum ought to preserve for the steam the heat denoted by /, , and also to give R e thermal units to the metal ; whence In the periods of admission and exhaust, the problem is complicated by the fact that the steam, in coming into the cylinder, carries thither Q thermal units, and, in leaving the cylinder, it carries out (C-\-c) thermal units to the condenser or the outer air. Whence, for the admission, U.+ Q=U.+ T.+R.- t and for the exhaust, These last equations can be written as below, and, adding those preceding, we have (I) -Q'; . . (li R*=U 9 +Q-U -T a ; ...... (Ill, R d = u.-U.-T^.. ....... (IV) R.= U t + (C+c)-U l -T.-, .... (V) R<= U.- U,+ T e ........ (VI) The quantity R a does not represent solely the exchange of heat between the vapor and the metal. There is heat given out by the steam to compress that which, under low pressure^ 53 2 A MANUAL OF THE STEAM-ENGINE. filled the waste spaces at the end of the exhaust. This heat, not shown by the indicator, is an integral part of R a , U^ has been obtained on the hypothesis that, at the commencement of compression, there the steam is dry and saturated. The object of the computations is to obtain the values of JR C , R a , R d , R e , R f , and to represent these values graphically. For this purpose the same scale is adopted for the exchange of heat as for the diagrams of pressure, and in the following man- ner: T a represents a certain number of thermal units lost by the steam while the piston is generating the volume V a cubic feet. In like manner, R a represents the thermal units lost by the steam while the piston sweeps through the same volume. The value of T a is represented on the diagram by a surface whose length, representing V a , is the base. If the pressure during admission was constant and equal to/ a , this diagram would be a horizontal line at the height which is represented by p a , and the area would be rectangular and equal \.o p a V a . l( p a is counted in pounds per square foot, then/ a F a = 772 T a \ 772T whence p a = ^77. V a Similarly, a height r a can be calculated such that r a V a whence also, in like manner, r - = -?. If the exchanges are positive that is to say, if it is the steam which furnishes heat to the metal the ordinates r will be THERMODYNAMICS OF THE STEAM-ENGINE. 533 carried above the axis in the forward stroke, and below in the backward stroke. If the exchanges are negative that is to say, if it is the metal which furnishes heat to the steam the ordi- nates r are carried below the axis for the forward, and above it for the backward stroke. In a trial, to be considered later, R a has been found positive ; R d negative ; R t negative ; and R e positive. Then the diagram of exchanges is shown in Fig. 153. FIG. 153 HEAT- EXCHANGES. The area aKLABda represents R a \ " dCDed " R d ; " eEFGHce " R e - " cljac " R c . Positive exchange is represented by hatchings from left to right ; negative transfer by hatchings from right to left. The difference of these two surfaces would be zero if there were no heat lost by external radiation, or received from a jacket. In the example there was a loss. On the diagram is a line MN, at a height such that the surface OMNfO represents R f =' 534 A MANUAL OF THE STEAM-ENGINE. R a -\-R d . This is the loss due to the action of the cylinder- walls. The straight line PQ is at such a height that, on the same scale, the surface, OPQfO, of which the contour is edged by hatchings, represents the positive work 7} of the steam. We refer all the quantities to one pound of steam em- ployed. We shall give an example of application in the chap- ter on Engine-trials ; which see. Hirn and Hallauer have shown that, in ordinary cases, at least, in the computation of the efficiencies of steam-engines, it may be safely assumed : (i) that the weight of vapor remain- ing in the clearance-spaces may be neglected ; (2) that this vapor, in compression, may be considered, if at all, as dry and saturated. It is only when the cylinder is so constructed as to hold precipitated water in its hollows that the presence of the liquid affects in this manner the economical working of the engine. The rate at which the metal surface may condense the entering steam is probably, however, greatly modified by the extent to which water adheres to it and obstructs the entrance of heat, and by the rapidity and thoroughness with which water at any time precipitated on those surfaces is removed during that or earlier stages. 131. The Restriction of Cylinder-condensation may be effected, to a limited extent, by proper precautions. This loss, as previously stated, is greater as the range of temperature during expansion is greater ; is increased by slow speed of engine, by reduction of back-pressure, by increase in size of engine for a given amount of work done, by increase in conductivity of the surfaces of the working cylinder, and by wetness of steam. It is reduced by low ratios of expansion, by increasing back-pressures, by reducing initial pressures, by increasing speed of engine, and by special expedients, as steam- jacketing, superheating, and the division of the expansion between two or more cylinders, in " compound " or multiple- cylinder engines. This waste becomes the less when the sides of the cylinders only are jacketed, the smaller their diameter; it is lessened, THERMODYNAMICS OF THE STEAM-EXGIXE. 535 when both heads and pistons are jacketed, by increasing diame- ters, volumes being in both cases equal. With superheated steam, and whenever there is little initial condensation to be anticipated, the shape of cylinder is determined by the mini- mum ratio of volume to internal superfices, Le., . = - length 2' unless as is often the case it is controlled by commercial con- siderations. The surfaces of the piston must evidently be here included, since the principal losses occur largely on those surfaces. In general, we may say that the efficiency of an engine is some function of differences of temperature, speed of engine, and areas exposed to contact with steam : but the difference of temperature is a varying function of pressures and times of exposure ; the speed determines time and exposure, and the area of surface exposed is a function of volume per unit of weight of steam, and of shape of cylinder. All these condi- tions are involved and interdependent, and simple approximate expressions will be found preferable to any exact formula. Again, there may be noted, as already stated, some com- pensations. The difference in back-pressure between non- condensing and condensing engines is productive of such a wide difference in the range of temperatures worked through as possibly often to justify the assumption that condensation may be assumed to be independent of the actual back-press- ure, and to be determined solely by other conditions above noted. In steam-jacketed engines the value of the steam- jacket is reduced by high speed; since the losses that it is designed to check are rendered less by the same cause. The internal friction of engine, due to the pressure and rubbing of the piston and its rings, produces an equivalent amount of heat, and this aids, by thus drying the steam, in reducing waste. The proper methods of prevention of such wastes are, evi- dently, those reducing: (i) the heat-transferring power of the fluid ; (2) the heat receiving and storing power of the surfaces in contact with it ; (3) the time of exposure ; and (4) the range of 536 A MANUAL OF THE STEAM-ENGINE. temperature worked through. The methods actually practised or proposed are : (1) Effectively drying the steam, as by superheating, by compression ; by steam-jacketing, and by admixture of air or gas. (2) Lining the cylinder with non-conductors, or bathing it with oil, or other non-volatile and slowly-conducting substance. (3) Increasing the speed of engine. (4) " Compounding." Superheating is found to be most effective ; but it is limited in the extent to which it may be carried ; and, practically, up to the present time, it has been found undesirable to attempt much more than to thoroughly dry the steam before its entrance into the engine. One hundred degrees Fahrenheit (55^ Cent.) is usually considered a fair and safe limit for superheating at the boiler ; and, with steam as ordinarily supplied, this merely secures dry steam at the engine, thus greatly reducing its conductivity. The chilling taking place at its entrance probably even then invariably produces more or less moisture. To carry super- heating so far as to enable the steam to be worked wholly in the superheated condition would usually compel an increase of temperature to several hundred degrees above the normal. Steam-jacketing is frequently practised with compound en- gines, and sometimes with the simple engine when intended to work at high ratios of expansion. The introduction of air, by reducing the conductivity of the fluid, has been found by Warsop, experimenting on locomo- tives,* and by others, to produce, in some cases, a gain of about ten per cent. This last is not a common practice; but the other methods are in common use, and are found to effect an economy which increases with decrease of efficiency in other respects ; an economy which may probably average, in successful practice, about twenty per cent. Lining the cylinder with a non-conductor, if practicable, * London Engineering; 1873. THERMODYNAMICS OF THE STEASf-EXGIXE. 537 would considerably reduce this form of waste. Smeaton, a century ago, so lined his cylinder-heads, using wood for the purpose, and Emery has attempted, though without permanent success, to line the whole interior with glass or porcelain,* and the Author has reduced the heat-absorbing power of such sur- faces, in experimental investigations. 40 and 60 per cent.+ The free use of oil in the cylinder has been usually found to pro- duce sensible, but costly, gain in efficiency. A well-polished internal surface, especially if bathed in oil, is hardly less effec- tive in reducing wastes than is well-dried steam. Old and carefully handled engines are apt to show a decided advantage over new, and probably for this reason. High spffds of engine, other things being equal, have been found to give very decided gains, as compared with low speeds ; and, both for this reason and on account of the gain in power also to be thus secured, speeds have been increasing steadily, since the time of Watt, from his standard maximum velocity, F= 128 I 7~. where s is the stroke of piston in feet, to several times that figure ; to more than F=8oo V~s in some cases, in locomotive engineering practice. Speeds of rotation have thus been brought up to 100, in even very large marine engines, and to 300 and upward in small stationary engines. At speeds exceeding about JT=e ~~ , those wastes become unimportant. This expedient, as affecting a good type of simple engine, has been found quite as effective, on the average, as jacketing or moderate superheating in common practice, and even to give a close competition in * Trans. Am. Soc. Mech. Engis.: iSSi. f Ibid.; 1889. See papers by Carpenter and Horse, also by the Author, in Trans. Am. Soc. C. E.; iS39-91. 538 A MANUAL OF THE STEAM-ENGINE. many cases with the compound engine operated at low speeds. Usual values of the factor first given above are about 1 50 to 200 for pumping-engines, 300 to 400 for common mill-engines, and 500 to 600 for " high-speed " engines, and equally high speeds for the fastest engines, " Compounding" or the use of two or more cylinders " in series," in which the ratio of expansion is restricted, in each, to a practically economical limit, is the now usual system, espe- cially in marine-engine construction, is becoming daily more common with stationary engines, and is also coming into use in locomotives. By the adoption of this plan, steam-pressures and total ratios of expansion for maximum economy have been increased very greatly over those admissible with the single-cylinder engine. While the latter has been found, with steam at 60 pounds pressure, by gauge, to demand, ordinarily, 3 r 3i pounds of coal, or 25 to 30 pounds of steam, per indicated horse-power per hour, the former, under similar circumstances, requires but 2 or 2^ pounds of coal, 17 to 20 pounds of feed-water, per I. H. P. per hour; and the " triple- expansion," at 150 pounds, or ten atmospheres, takes \\ to if pounds of coal, 14 to 18 pounds of steam ; while the " quad- ruple-expansion " engine, at 12 to 15 atmospheres (180 to 225 Ibs. per square inch) is said to demand only 13 to 15 pounds of feed-water, or i^ to I pounds of good fuel, figures probably never yet reached by simple engines. The ratios of expansion, which, with the simple engine, have not been usually successfully carried beyond 5 or 7, are thus increased to 8 or 10 in the "compound," to 12 or 15 with the "triple," and to 15 or 20, or even more, with the " quadruple- expansion " engine. The terminal pressure is usually between % and f atmosphere (7^ or 10 Ibs. per square inch), absolute pressure, in the best forms of engine. Compression of the exhaust as nearly to boiler-pressure as is possible, as already remarked, is decidedly advantageous and especially with the non-condensing engine not only as a means of filling the clearance and port spaces, and thus saving some steam, but also, and possibly in some cases to a still more THERMODYNAMICS OF THE STEAM-ENGINE. 539 important extent, by transforming a certain amount of energy into heat and communicating this heat to the cooled surfaces of the cylinder ; warming them up to approximately the tem- perature of the entering steam, thus checking initial condensa- tion to an extent which may much more than compensate the, apparent, added waste of power in compression. With a " link- motion" valve-gear^ an increase of the ratio of expansion is accompanied by increased compression, and thus the exaggera- tion, by increased expansion, of the evil here considered is partly checked by the coincident increase of compression. The locomotive is probably an illustration of marked gain occurring in this manner. Practical limitations of the principal methods of restricting exhaust-wastes and of enhancing efficiency are now familiar to engineers. Drying steam is always advantageous, by what- ever method practised ; but, at the pressures now common, of ten atmospheres (150 pounds per square inch) and upward, the temperature of the steam is already not far from that at which ordinary lubricants are liable to decomposition ; and any con- siderable superheat inside the engine-icylinder is therefore usually thought unsafe. Jacketing is not always considered sufficiently advantageous to compensate added cost and risks at moderate expansion- ratios, and at such speeds as are now standard ; and many engineers leave even the high-pressure cylinders of slow-mov- ing compound engines unjacketed. No practicable method of lining with non-conductors has yet been found, although the experiments of the Author seem to indicate that this is a promising direction for investigation; and speeds of engines are now but slowly, if at all, increasing. The dangers of heat- ing journals, and of breakage, introduced with excessive ve- locities, have become already appreciable. Compounding to a greater extent than now practised is only advisable with very considerable increase of steam-pres- sures, and this advance is impeded by the difficulty of obtain- ing thoroughly safe, economical, and otherwise satisfactory, steam-generators. 540 A MANUAL OF THE STEAM-ENGINE. The subjects of compounding, jacketing, and superheating are of such importance as to demand their consideration in a separate chapter. 132. The Friction of the Engine itself, the " Internal Friction ' ; of the machine, is usually a considerable quantity, and is a source of loss of energy by reduction of the efficiency of the engine as a machine. Since the efficiency of any train of mechanism, as a machine purely, is the ratio of the quantity of work delivered by it to whatever it may drive, or of work done by it upon the next element in order to the work which it receives, or the energy applied to its propulsion, the internal losses of mechanical energy become, to the engineer, subjects of real importance. As " Friction is thus the principal cause, and usually the only cause, of loss of energy and waste of work in machinery," * " a given amount of energy being expended upon a driving-point in any machine, that amount will, in ac- cordance with the principle of persistence of energy, be trans- mitted from piece to piece, from element to element, of the machine or train of mechanism, without diminution, if no per- manent distortion takes place and no friction occurs between the several elements of the train, or between those parts and the frame or adjacent parts. Temporary distortion, within the limit of perfect elasticity, causes no waste of energy ; per- manent distortion causes a loss of energy equal to the total work performed in producing it ; but permanent distortion is due to deficiency of strength, and to defective elasticity, and is never permitted, in well-designed machinery, properly oper- ated. Hence the important principle : " The only cause of lost work in mechanism which is to be anticipated in design, and calculated upon in deducing the theory of any special machine, is the friction necessarily con- sequent upon the relative motion of parts in contact and under pressure."f The compound friction of lubricated surfaces, as it may * Friction and Lost Work in Machinery and Mill-work; R. H. Thurston; N. Y., J. Wiley & Sons, 1885; p. n; 12. f Ibid., pp. II, 12. THERMODYNAMICS OF THE STEAM-ENGINE. $4! be termed, or friction due to the action of surfaces of solids partly separated by a fluid, is observed in all cases in which the rubbing surfaces are lubricated. In such instances the solids are usually not completely separated by the liquid film interposed between them, but partly rub on each other, and are partly supported by the layer of lubricant which is retained in place by adhesion and by capillary action. The rubbing together of the two solids produces wear, the amount of which is indicated by the rate at which the lubricant becomes dis- colored and charged with abraded metal. The work of friction, both of solid and of liquid, is transformed into heat and is dis- posed of as the bearing heats, principally by radiation and conduction to adjacent parts, and partly by the heating of the lubricant. In all cases some abrasion is indicated by the change produced in the lubricant, and some heating is usually perceived in the bearing. With very heavy pressures and slow speeds, the journal and bearing are forced into close contact, as is shown by their worn and often abraded wearing surfaces ; while with very light pressures and high velocities the journal floats on the film of fluid which is continually interposed between it and the bearing. In this case the friction occurs between two fluid layers, one moving with each surface. There are thus evidently two limit- ing cases between which all examples of satisfactorily lubricated surfaces fall : the one limit is that of purely solid friction, which limit being passed, and sometimes before, abrasion ensues ; the other limit is that at which the resistance is en- tirely that due to the friction of the film of fluid which sepa- rates the surfaces of the solids completely. The laws governing the friction of lubricated surfaces are evidently neither those of solid friction nor those of fluid fric- tion, but will approximate to the one or the other as the limits just described are approached. The value of the coefficient of friction varies with every change of velocity, of pressure, and of temperature, as well as with change of character of the sur- faces in contact. Where mixed friction is met with, it will usually be found 542 A MANUAL OF THE STEAM-ENGINE. that its laws approximate to those of solid friction as the jour- nal is run dry, and to those of fluid friction as it is the more effectively flooded with oil. Thus a journal or bearing surface fed with oil by an oil-cup, and where no oil-grooves are used to distribute the oil, will exhibit a total friction in some cases nearly proportional to the total pressure, the latter being varied ; while similar surfaces flooded with oil, as by the oil- bath, offer a resistance sometimes nearly independent of the pressure, and but little, if appreciably any, greater with heavy than with light loads. A perfectly lubricated bearing should follow the laws of fluid friction, and its friction should be inde- pendent of the intensity of pressure produced by the load, varying as the square of the speed of rubbing. Such perfect lubrication has never yet been attained. For perfect lubrication, assuming it practicable with com- plete separation of the surfaces, the laws of friction would be- come : (1) The coefficient is inversely as the intensity of the press- ure, and the resistance is independent of the load. (2) The friction coefficient varies as the square of the speed. (3) The resistance varies directly as the area of journal and bearing. (4) The friction is reduced as temperature rises, and as the viscosity of the lubricant is thus decreased. These laws will probably hold, even with the greases, which all become fluid when introduced between the rubbing surfaces. It is found by experiment, as stated later, that the perfec- tion of this form of lubrication depends upon the amount of fluid-pressure produced between the surfaces by forcing in the lubricant between them. This separation occurs to an impor- tant extent at high speed and less at low velocities. Hence, the friction of lubricated parts is often found to decrease at low speed with increase of velocity, while increasing at high speeds as velocity increases. The limits of pressure for lubricated surfaces are determined by the nature of the materials composing them, and by their THERMODYNAMICS OF THE STEAM-ENGINE. $43 smoothness and exactness of fit, as well as by the speed of rubbing, the character of the lubricant, and the methods of its application. A higher pressure is usually permissible on hard than on soft material ; although when the soft materials, as for example common white alloys for bearings, are well sustained by a harder metal, the heaviest pressures allowed by the lubri- cant may be carried. The more viscous the lubricating substance, and the stronger the capillary action taking it into the space between the jour- nal and the bearing, the higher the pressure safely carried. With increase of speed the maximum pressure is lessened, and it is usual to take the intensity of pressure as inversely as the velocity of rubbing. The magnitude of the waste of energy by friction is measured in horse-power by the expressions (British measure): (I) Flat surfaces, HP = (2) Cylindrical surfaces, HP= ~', when f, P, and V are the coefficient of friction, the load and the speed of rubbing in feet, and R and d are the revolutions per minute and diameter of journal in inches. The methods of reducing waste of energy by friction in mechanism are based upon very simple principles. It is evi- dent that to make the work and power so lost a minimum it is necessary to adopt the following precautions : (i) Make the coefficient of friction the least by proper choice of rubbing surfaces and by the best lubrication. To do this we should have at least one of the rubbing surfaces of a granular metal, and if possible both that one which it is easier to replace being of the softer metal. The surfaces should not be subjected to a normal pressure beyond which the lubricating matter will be expelled. For slides, a much less pressure should be taken than for journals, as they have not as free a lubrication as well-arranged cylindrical journals ; but this limit 544 A MANUAL OF THE STEAM-ENGINE. is best determined by reference to the speed of rubbing and the nature of the lubricant. (2) Make the space through which the friction is to act a minimum by reducing the diameters of all journals to the least compatible with safety under the stresses they are expected to sustain. The work done is independent of the length of the journal, except as it may modify pressures, and thus the co- efficient of friction. (3) Properly fitting the bearing surfaces, removing that por- tion of the bearing near the jaws, and transferring the bearing surface to the bottom, one sixth of the circumference of the journal may be thus removed. A journal well fitted cold is not necessarily a good fit after it becomes heated by friction, owing partly to the want of homogeneousness of the metal of the journal and bearing; a worn journal has less friction than when new. It is a question whether all journals should not be brought to a proper bearing and given a high polish before they are considered fit to perform their office. It is now usual carefully to grind all cylindrical journals, and to secure a very perfect fit in the bearing before setting the machinery at work. (4) Giving the journals such forms and such size as will allow them to convey away the heat generated, either by radiation from their surfaces or by conduction through the mass of metal, to circulating water, to lubricating matter, or to adjacent masses. (5) Securing an efficient system of supply of the lubricant. Since lubrication has for its objects both the reduction of friction and the prevention of excessive development of heat, the engineer resorts to the expedient of interposing between the rubbing surfaces a substance having the lowest possible coefficient of friction and the greatest capacity for preventing or reducing the development of heat. It is evident that in order that any substance may be efficient as a lubricating material it must possess the following characteristics : (i) Enough " body" or combined capillarity and viscosity to keep the surfaces between which it is interposed from com- ing in contact under maximum pressure. THERMODYNAMICS OF THE STEAM-ENGINE. 545 (2) The greatest fluidity consistent with the preceding re- quirements, i.e., the least fluid-friction allowable. (3) The lowest possible coefficient of friction under the conditions of actual use, i.e., the sum of the two components, solid and fluid friction, should be a minimum. (4) A maximum capacity for receiving, transmitting, stor- ing, and carrying away heat. (5) Freedom from tendency to decompose or to change in composition by gumming or otherwise, on exposure to the air or while in use. (6) Entire absence of acid or other properties liable to pro- duce injury of materials or metals with which they may be brought in contact. (7) A high temperature of vaporization and of decompo- sition, and a low temperature of solidification. (8) Special adaptation to the conditions, as to speed and pressure of rubbing surfaces, under which the unguent is to be used. (9) It must be free from grit and from all foreign matter. Oils must be used with some caution when applied to jour- nals upon which other lubricants have been employed. It sometimes happens that two oils are entirely incapable of working together, and this incompatibility may cause trouble when they are used together, or even successively. A minor good quality possessed by some lubricants in greater degree 'than others is that of being readily removed, and allowing the bearing surfaces to be easily cleansed when they have become soiled and gummed by alteration of the unguent, and by the gathering of dust and abraded metal upon them. Oils should not be liable to decomposition by heat or wear, or to separation when mixed, either in use or by long stand- ing, or by alteration of temperature. They should, if mixed, always have the same specified composition. Uniformity in this respect is as important as excellence of quality of the nor- mal mixture, and the quality of the oil is usually of more im- portance than the quantity. The adhesiveness of the oil to the metal, and the ease of flow, with minimum fluid-friction, are 546 A MANUAL OF THE STEAM-ENGINE. the essential characteristics of a good combination of materials in bearings and lubricant. Cast-iron is somewhat spongy in texture, and is therefore an exceptionally good metal for bear- ing surfaces, when of ample area. Bearing surfaces are of bronze or other alloys, of cast-iron or other metal, or of wood, according to location, intensity of pressure, velocity of rubbing, and nature of the material of the journal. Ordnance bronze wears well under heavy pressures and at high speeds if not subjected to intense localized pres- sures by the springing or misfitting of parts ; cast-iron has an advantage, if used under moderate pressures and in ample ex- tent of surface, in its porosity and absorptive power and the persistence with which oil and grease adhere to it ; wrought- iron and steel sustain heavy loads, if free from surface defects ; " mild steel " is peculiarly valuable for journals, and hard steel ground to shape and well bedded in its bearing will safely carry pressures of enormous intensity; wood is only used in special cases. Too high a polish on the harder surfaces is ob- jectionable where thin oils and heavy pressures are adopted, as the lubricant is difficult to feed between the metals in contact, or to keep there while in operation. It is nearly always advisable to make the bearing of the softer metal, since its renewal is a matter of less difficulty and expense than that of the journal, and since the journal must usually have great strength. A hard bearing cuts the softer journal, and gives rise often to serious expense. It is from this consideration that bearings are often " babbitted" or lined with the soft white alloys. The fitting of the surfaces in contact is as important a matter as the selection of the material of which they are com- posed. The theory of friction is based upon the assumption that all parts are accurately made to correct dimensions, and exactly fitted ; and the conclusions derived are therefore in- validated by any departure from such assumed conditions. Precision and stability of form stiffness of all loaded parts are essential elements of successful working. Stability of form is dependent upon extent of surface exposed to wear : if this THERMODYNAMICS OF THE STEAM-ENGINE. 547 area is ample, so that the two rubbing parts nowhere and at no time come into unrelieved metallic contact, no appreciable wear will occur, and their forms will be permanent. Surfaces of similar area and form, even when well fitted, if of different materials will wear very differently. Thus the following table shows the comparative wear of axle-bearings. Thoroughly pure bronzes, like those fluxed with phosphorus, were reported as wearing very much less than ordinary com- positions. Bearing. Composition. Cost PSL. ioo Ibs.* Miles run per Ib. Wear Per ioo miles for four bearings. Cop- per. Tin. Anti mony. 83 82 3 5 17 IS g 7 10 $28 60 28 68 32 85 32 27 13 04 28 68 25,489 27,918 22,075 24,857 22,921 2,576 200 grs.f 252 ' 3 66 ' 284 ' 308 274 ' White-metal Lead composition: lead, 84' antimony 16 Gun-metal on brake-cars. . 82 18 In many cases the excessive wear of a bearing is due to a misfit. The Hopkins bearing is a bronze bearing lined with a thin layer of lead, which, when new and unfitted, can accom- modate itself to the distorted journal and permit gradual wear to a correct fit without danger of injury, such as occurs often with the common hard, unlined " brass." In the Defreest bearing a thin bronze bearing-piece is sustained by a strong iron backing-piece, and between them is a sheet-lead filling. Journals should be fitted without the use of emery or other gritty grinding material, which may adhere to its surface and thus produce injury. Bearing surfaces of wood are, under the conditions already- described as favorable to their use, exceedingly durable, and will carry enormous loads without abrasion. Thus lignum-vitae will sustain pressures exceeding 1000 Ibs. per square inch (70 * Including melting expenses, loss, etc. These figures are constantly vary- ing. f Seven thousand grains per pound. 548 A MANUAL OF THE STEAM-ENGINE. kgs. per sq. cm.), where brass becomes rapidly abraded and de- stroyed under but little more than one fourth of that load, and will run continuously under 4000 Ibs. (281 kgs. per sq. cm.) when bronze sets fast instantly. Camwood has been subjected to pressures exceeding 8000 Ibs. per square inch (562 kgs. per sq. cm.), and has worked without injury; snakewood carries about as heavy a load as lignum-vitae. The bearing surfaces of watch-work are often made of ruby, agate, and other fine-grained and hard stones, and of gems. A comparison made by the Author between surfaces of gun-bronze, of " Babbitt"-metal, and of other soft, white alloys, all working on steel, proved all to have substantially the same friction. In other words, the coefficient of friction was deter- mined by the nature of the unguent and not by that of the rubbing surfaces, when the latter are in good order. The soft metals, however, heated more than the bronze, running at temperatures somewhat higher with equally free or even freer feed. To retain the temperature at 135 F. (57 C.), in some cases one half more oil over 300 grammes, as against 200 was needed on the white metal than on the bronze. This probably does not, however, necessarily indicate a serious de- fect, but simply deficient conductivity. Lined journals may be expected to run normally warmer than unlined bronze of good quality. The following are the results of experiment with a " Babbitt"-metal, which was compared with bronze and a sec- ond white alloy : Bronzes. White Metal. No. i. No. 2. Mean temperature, Fahr 133 152 137 Mean coefficient of friction o.oi o 0.013 o.oio Oil used per hour, ounces 7 17 12 These differences prove ordinary lubricated surfaces to have contact, since they give differences in the values of /where none could exist were the friction fluid-friction solely. Riveting, in steam-boilers and bridge-work, or other con- structions, is usually taken as having a coefficient, /= 0.333 ; but it should never be reckoned upon as an element of definite THERMODYNAMICS OF THE STEAJf-EA'ClXE. 549 value, although the enormous pressure produced by the shrink- age of heated rivets, while cooling, gives it some importance. The elastic limit of common iron is usually not far from 25,000 Ibs. per square inch (1757.5 kg 5 - P 61 " sq- cm^, and one third this amount, above 8000 Ibs. (562.4 legs.) per unit of section of rivet, is a quantity of real value as an element of safety. The friction of belts and of gearing has been often studied experimental!} 7 . Morin concluded its amount for belting to be proportional to the angle on the pulley subtended by the belt, to the logarithm of the ratio of tensions, and to be inde- pendent of the width of belt and of the linear measure of the arc embraced by it Le^ independent of the area of contact. He obtained /= 0^8 to /= 0.38, the value varying with the condition of the belt. Adopting the formula of Prony for flic difference of tension on the two parts of the belt, the values of its coefficient, t, were obtained as in the table. The maximum difference of tension allowable is The minimum tension allowable to prevent slip is taken as r.+ z; i*+ D. VALUE OF 1 IN FRONTS FORMULA. O.2O OL40 0.60 0-SO I.OO 1-50 2.00 2.30 1.9 3-5 6.6 is.3 1.8 3-3 R::* :- V 1.6 2.6 6.8 10.9 -9 3-5 6.6 23.9 ni-3 :~ *5T-4S 1-5 3-5 1:1 22.4 :-- 5 5$O A MANUAL OF THE STEAM-ENGINE. The maximum stress allowable on the leather was stated at about 350 Ibs. per square inch of cross-section. In the equations * R = T, - T t = r,(i - ef*} __ 2R ~ 2(eS - i)' /"varies from 0.15 to 0.6, the former value being found only where the belt is actually wet with -oil. Reuleaux takes f= 0.25, and the experiments of Messrs. Towne and Briggs f indicate that this value is exceeded, under ordinary working conditions, more than 60 per cent. Rubber belting has greater adhesion than leather, and values of f may be used exceeding very greatly those adopted for leather. The angle = 2nn, where n is the number of turns or part of turns taken by the belt about the pulley. Rankine gives \ the following values of the coefficient 2.72887" in the equation eS* = io 2 - 7288/ " which comes into use in the application of these formulas, as seen in Chapter II : /=o.i5 0.25 0.42 0.56 2.7288/ = 0.41 0.68 1.15 1.53 and, where 6 = n and n = , as is usual, T, (7; + FJ T,= 1.603 2.188 3.758 5.821 R = 2.66 1.84 1.36 i. 21 2R = 2.16 1.34 0.86 0.71 Usually we assume T,R; T, = 2R ; (T, + T 9 -r- 2R = 1.5 and /becomes 0.22. * Friction and Lost Work; chapter II. 31. f Journal of the Franklin Institute; 1868. J Machinery and Mill-work, p. 352. THERMODYNAMICS OF THE STEAM-ENGINE. 551 Rankine* gives / for a wire-rope running on cast-iron at 0.15 and on gutta-percha at 0.25. Rope-gearing has a value of f = 0.25 to f = 0.8, and the resistance to slipping is increased in proportion to the cosecant of the half-angle of the wedge-shaped groove of the carrying- wheel, f The method of supply of oil should be carefully looked to, and a very free " feed," with a system of collection and reap- plication of the oil leaving the bearing, will be found to give by far the greatest economy of power and cost. Experiments made for the Institution of Mechanical Engineers, in which oiling by a pad as in railway work, by a siphon lubricator or oil-cup, and by a bath, which keeps the surfaces flooded with oil, gave the following figures, showing an enormous advantage in the use of the last method : METHODS OF OILING (RAPE-SEED OIL). VELOCITY OF RUBBING, 157 FEET (46 M.) PER MINUTE. Actual Load. Coefficient of Friction. Comparative Friction. KiJogs. per sq. cm. Lbs. per sq. in. Oil-bath I8. 5 17-7 I 9 .I 263 252 272 0.00139 0.00980 0.00900 I T.o6 6.48 Pad under journal Conclusions. Specified qualities of lubricant may, by the processes here described, be secured by test. If an unguent is desired for heavy pressures, or an oil for very light work, or for high or low speeds of rubbing under known pressures, the methods of study of the available lubricants which have been described will enable the engineer or the manufacturer to select that which is best suited to the specified purpose. He may go still further, and, by repeated mixing and test gradu- ally improving the mixtures, may finally secure compounds having the best possible qualities for the various proposed * Machinery and Mill-work, p. 352. f American Machinist; November i, 1884. 552 A MANUAL OF THE STEAM-ENGINE. applications. The Author has in this manner sometimes pro- duced lubricants for manufacturers which have been found peculiarly well suited for special lines of trade. Studying the facts here stated, and the data acquired by many hundreds of other experiments, made on one or the other of these last-described machines for testing lubricants, we may recapitulate the facts and figures for ordinary use in machine- design and in estimating losses of power by friction as follows: (1) The great cause of variation with well-cared-for journals, since they must work at ordinary temperatures, is alteration of pressure and variation in methods of supply; and it is seen that the higher pressures give the lowest percentages of loss of power by friction. (2) The value of the coefficient is greatly modified by the state of the rubbing surfaces ; a single scratch has its effect in wasting power. A good journal usually has its surface as smooth and as absolutely uniform as a mirror. Every well- kept journal acquires such a surface. (3) For general purposes and for heavy work, as in the ex- periments of the Author, and at considerable speeds, the value of the coefficient varies nearly inversely as the square-root of the pressure, for pressures ranging from 50 to 500 Ibs. per square inch. (4) The coefficient for rest or starting may similarly be taken to vary nearly as the cube-root of the pressure. For closer estimates and other conditions, the tables just given can be referred to directly. (5) The coefficient for the instant of coming to rest, under the special conditions here referred to, is nearly constant, and may be taken at 0.03. (6) The resistance due to friction varies with velocity, de- creasing with increasing velocity rapidly at very low speeds, as from i to 10 feet per second, and slowly as higher speeds are reached, until the law changes and increase at ordinary tem- peratures takes place, and at a low rate throughout the whole range of usual velocities of rubbing met with in machinery. Its amount and the law vary with method of lubrication, THERMODYNAMICS OF THE STEAM-EXGIXE. 553 however. With oil-bath lubrication the value of f usually varies more nearly as the square-root of the velocity. (7) With pressure and velocity varying, we may take the coefficient as varying as the fifth root of the velocity, divided by the square-root of the pressure for such work as is repre- sented by the experiments of the Author. (8) The effect of heating journals under conditions here il- lustrated is to increase the friction above oxr or loo* F., at a speed as low as 30 to 100 feet per minute, while at higher speeds and low pressures the opposite effect is produced, and the coefficient often decreases more nearly as the square-root of the rise of temperature. 191 The temperature of minimum friction, under the con- ditions of the experiments here referred to, varies nearly as the cube-root of the velocity, for a pressure of about 200 Ibs. per square inch. no) The endurance of any lubricant should be determined by actual wear upon a good journal under the pressures and velocities proposed for its use. The economy with which it can be used will be dependent upon its natural method and rate of flow, and upon its capillary qualities, as well as upon its intrinsic wearing power and the method adopted in feeding it. Greases, therefore, are usually more economical in cost than oils, even if having less wearing capacity. (i i) The only method of learning the true value of a lubri- cant and its applicability in the arts is to place it under test, determining its friction-reducing power, and its other valuable qualities, not only at a standard pressure and velocity, and at ordinary temperatures, but measuring its friction and endurance as affected by changing temperatures, speeds, pressures, and methods of application, throughout the whole range of usual practice, and its wearing effect. (12) The true value of an oil to the consumer is not propor- tional simply to its friction-reducing power and endurance, under the conditions of his work ; but its value to him is meas- ured by the difference hi value of power expended, when using 554 A MANUAL OF THE STEAM-ENGINE. the different lubricants, less the difference in total cost of oil or grease used ; but for commercial purposes, no better method of grading prices seems practicable than that which makes their market value proportional to their endurance, divided by their coefficients of friction. The consumer will usually find it economical to use that lubricant which is shown to be the best for his special case, with little regard to price, and often finds real economy in using the better material, gaining sufficient to repay excess in the total cost very many times over. (13) To secure maximum economy, the journal should be subjected to a pressure the limit of which is determinable by either Rankine's or Thurston's formula ;* the most efficient materials should be chosen for the rubbing surfaces ; they should be reduced to the most perfect state of smoothness and perfection in form and fit ; a lubricant should be chosen which is best adapted for use under the precise conditions assumed ; the lubricant should be supplied precisely as needed, and by a method perfectly adapted to the special unguent chosen. The real problem is often, not what oil shall be used, but how to secure most effective lubrication. (14) The semi-fluid lubricants, when equally good reducers of friction, are usually the most economical for heating jour- nals, in consequence of their peculiar self-regulating flow, as the rubbing parts warm or cool while working. They are usually too viscous for economical use in ordinary work. The loss by internal friction in the steam-engine includes the wastes at the journals of the shaft, crank-pin, and cross- head-pin or " wrist-pin," and of the valve-motion ; of the sliding friction of cross-head and other guides ; of the piston-rods and valve-stems in their " stuffing-boxes," and of the rubbing of pistons and valves on the surfaces over which they glide, and the resistance of air-pumps in condensing engines. Its total is ordinarily equivalent to from one pound on the square inch of piston, in very large engines in good order, to about four or * Friction and Lost Work; 127. THERMODYNAMICS OF THE STEAM-ENGINE. 555 five pounds in small engines of 25 to 50 horse-power and be- comes very much greater when the lubricants used are ineffi- cient, the rubbing surfaces in bad shape, the stuffing-boxes too tightly packed, or the packing-rings set out too much. These figures ordinarily correspond to from five to as much as ten per cent of the total indicated power of the engine, in the best cases and to from ten per cent upward, indefinitely, in worse cases. Studying these losses in detail, it is found that the friction of the journals, when properly, uniformly, and effectively lubri- cated, is relatively less, though absolutely somewhat greater, as the pressures on them, and work transmitted across them. increase ; * that the friction of guides follows the same law ; that the work lost in the stuffing-boxes is probably independent of the work of the engine ; and that the friction of the piston and of the valve may usually be taken as also independent of the engine-load, though probably .always affected by the in- tensity of the steam-pressure. Experiments made by the Author lead to the conclusion + that the method of variation of the internal friction of the steam-engine is not usually exactly that stated by early writers on the subject. It has been customary among engineers con- versant with the operation of the steam-engine to take the " friction-card " obtained by applying the indicator to the un- loaded engine as a measure of the friction of the engine at all times, whether loaded or unloaded ; while it has been usual, in theory, to accept the formula of De Pambour, which is unques- tionably accurate in form, in which R is the total resistance, R, is that of the net work of the engine, its " useful " load, and R t is the work of friction of the parts of the machine itself, and /a coefficient of friction. * Where this is not true, the deduction follows, inevitably, that the friction is thai of solids, not, as it should be, " mediate," as Him calls it, and that the lubrication is not effective. f Trans. Am. Soc. Mech. Engineers; 1886; vol. viil. 556 A MANUAL OF THE STEAM-ENGINE. This formula is based upon the very reasonable assumption that the total friction must be a minimum in the unloaded en- gine, and that the imposition of external work upon it must, by increasing the pressure on its running parts, add to the total by the amount of friction so arising. But whether this increase of waste energy amounts to so much as to become observable, or to be practically important in the operation of the engine ; whether the engineer is right in theory, or correct in his practice, in usual cases, is not wholly certain. The friction of engine, as has been seen, consists of the resistances due to the motion of the various piston, valve, and other elements through stuffing- boxes and in guides, the friction of the piston-rings on the cylinder surface, the friction of eccentrics, and, often, of other parts which are independent of the magnitude of the load thrown upon the engine by the useful resistance, in addition to the friction of the journals transmitting the effort of the steam to the exterior resisting work, and of other parts directly and indirectly affected by its variation. It thus happens that the resistance due to the friction of the latter may be, and prob- ably often is, but a small proportion of the whole friction of engine. The total friction of engine, as has been seen, in good engines of ordinary kinds, amounts to from 5 to 10 per cent of the total power developed when fully loaded ; but the coeffi- cient of friction of any one journal, if well lubricated, has often been found by the Author, under such pressures as are usual on the main journals of the steam-engine, to fall to a low fig- ure, and the absorption of work and energy may thus be even a still lower proportion of the work of the steam as the speed of rubbing is less than that of the piston. The loss of power along the line of connection is probably always small. Again : the coefficient of friction, with really good lubrication, within the usual range of pressures on journals and guides, increases as pressures fall, and decreases when the pressures increase with variation of engine-power and load ; and this compensa- tion often occurs to such an extent that the total frictional re- sistance, on these parts even, varies slowly with variation of load ; while the friction of the other portions of the engine re- THERMODYNAMICS OF THE STEAM-ENGINE. 557 mains constant.* The resultant effect is often a practically constant friction of engine under all loads, the speed and steam-pressure being constant. In condensing engines this friction is subject to similar conditions ; but the work of the air-pump should decrease with the reduction of the load. Among the most excellent illustrations of thorough lubri- cation are those of Tower, f in which a near approach to per- fect fluid-friction was attained, the total resistance thus becom- ing nearly constant at all pressures, and, nearly, in which, as given by Kennedy,* c depends on the lubricant, and is about 0.0014 for sperm oil, 0.0015 for rapeseed, and 0.0018 for good mineral oils ; v is the speed of rubbing in feet per minute; and/ is the pressure per square inch. At i 1 = 250 and/ = 310, f = c, nearly. It will be observed that the variation of fp, which is here a constant for a given velocity, is a gauge of the efficiency of the lubrication ; since f is constant when the two solids are in actual contact. The Efficiency of Machine, as distinguished from the effi- ciency of its thermodynamic operation, the efficiency of the mechanism, is measured by the ratio of the quantity of work done at the engine-shaft, to that shown at the piston by the indicator, and is less than unity as the lost work of friction re- duces the former quantity. The value of this efficiency is, as a maximum, about 0.95 in the simplest and best constructions of non-condensing engine, and ranges from about 0.90 down to 80 or less with condensing engines ; while 0.90 is a common value of the former, and 0.85 for the latter, under usual con- ditions of operation. * Friction and Lost Work; chapter VH. f Trans. Brit. Inst. Mcch. Engrs. ; 1884. \ Mechanics of Machinery: p. 573. 558 A MANUAL OF THE STEAM-ENGINE. Increasing the number of steam-cylinders, other things equal, increases the friction of the engine. For : Let n = number of small cylinders ; d = diameter of each small cylinder ; D = " " " large cylinder; / = length of stroke ; s = area rubbing surface of small cylinder ; S= " " " " large " Then s = nrtdl ; 5 = n D I = >fnndl\ and the friction increases as the square-root of the number of cylinders, where all the small cylinders are of equal size. This friction in a double engine would thus exceed by 40 per cent that of a simple engine. 133. Investigations of Internal Engine-friction were made, within a few years, to determine its nature, extent, and method of variation, and the conclusions reached have been sustained by still later experiment. Of these investigations, the first, made under the supervision of the Author, was con- ducted by Messrs. Aldrich and Mitchell,* with the following results : Number of Card. Revolutions. Steam-pres- sure. Brake H. P. Indicator H. P. Diff. Friction per cent. I 232 5 4.06 7.41 3-35 45 3 230 63 6.00 IO.OO 4.00 40 5 230 73 8.10 11-75 3-65 32 7 230 75 IO.OO 14.02 4.02 28 9 230 80 12. OO 15-17 3-17 21 ii 230 75 14,00 16.86 2.86 17 13 231 72 20.1 22.07 2.06 9 IS 22 9 60 29-55 33-04 3-i6 9-5 17 22 9 70 39-85 43-04 3-19 7-4 19 230 90 5O.OO 52.60 2.60 4-9 This engine was rated at 30 I. H. P., 8 inches in diameter of cylinder, 14 inches stroke of piston, having a rod 44 inches * Trans. Am. Soc. Mech. Engrs.; 1886; vol. vm; No. ccxxviii. THERMODYNAMICS OF THE STEAM-ENGIXE. 559 long between centres, a balanced valve with stroke of 2 to 4 inches, according to position or governor and eccentric, a fly- wheel 50 inches in diameter, weighing 2300 pounds, the steam and exhaust pipes having diameters of 2^ and 4 inches, re- spectively, and the whole machine weighing 2\ tons. The space occupied by the engine was 9 feet 4 inches in length, by 4 feet 8 inches in width, and 3 feet 10 inches in height. Examining the above table of powers, it is seen that the difference between indicated and dynamometric power, the friction of the engine, varies somewhat, with varying steam- pressures and varying total power ; but in such manner as to indicate the controlling cause to be irregular in action, and possibly to some extent due to errors of observation and to accident ; and we are probably justified in taking it as approxi- mately constant under all ordinary variations of load. The repetition of the experiment upon an engine of another make, having a cylinder 9 inches in diameter and a stroke of piston of 12 inches, which would naturally give a somewhat in- creased percentage of friction, in consequence of the propor- tionally smaller stroke, at 20, 30, 50, and 65 horse-power, by brake, and running free, revolutions 300 per minute a speed which may also have caused some increase in frictional resist- ance, not only in rubbing parts, but by increasing back-pres- sure gave a friction of engine measuring from 2.66 horse- power unloaded, to 4 horse-power at 2O to 30 horse-power, 4.8 horse-power at 50, and 5.3 at 65 horse-power, the total friction increasing perceptibly, as assumed by De Pambour, but de- creasing in percentage of load, from 16 to 7.5, between 20 and 65 horse-power. It is very nearly constant throughout the whole range of power that the engine would be worked under ordinary circumstances, and may be so taken without serious error. At their rated powers these two engines thus exhibit efficiencies of mechanism of about 94 and 90 per cent, re- spectively. Another series of experiments was made by Messrs. Day and Riley during the year 1886, confirming the deductions already given. The engine taken for test was built for pur- 5 6o A 'MANUAL OF THE STEAM-ENGINE. poses of experimental investigation. It was 12 inches stroke, and 6 inches in diameter. The conclusion already reached is thus again confirmed. The following are the data obtained : 1 2 3 4 5 6 7 8 No. of Card. Rev. per Minute. Steam- pressure. Brake Power. H. P. Ind. H. P.P.I, per card. Diff. Frict. H. P. Mean F. Pres. Frict. per cent. I 282 19 2.26 2.26 3-70 IOO 3 286 66 7 .6l 10.95 3-33 5-25 30 5 285 71 I3.IO 15-99 2.61 4-25 18 7 284 74 18.55 20.73 2.65 4.18 12 9 279 65 23.61 25-95 2-33 3-73 9 ii 280 72 29.03 32.22 3-i9 5-15 IO These experiments lead to the discovery of the fact that the engine-friction varied, at constant load and speed, with varia- tion of steam-pressure. In order to determine whether this hitherto unobserved fact were true, the following data were obtained : No. of Card. Rev. Steam- pressure. I. H. P. Mean Pressure. Mean F. Press. Per cent. Frict. I 250 25 6.01 10.84 i-95 18 1 3 285 42 7-17 "35 3.63 32 Ten 5 271 58 6.81 11.28 3-i6 28 } pounds on 7 286 68 7-77 12.25 4.90 40 the brake. 9 2 9 6 82 7.87 12. OO 4.68 39 J ii 279 66^ 1.995 3-22 3-22 IOO 1 13 275 35 1.71 2.80 2.80 " 1 No load on 15 272 25 i . 876 3.11 3-" " 1 fthe brakes. 17 270 15 1.712 i 2.86 2.86 " J In the first set of experiments, here numbered i to 9, in- clusive, the weight on the brake-arm was kept constant at ten pounds ; in the remaining experiments all weight was removed. In both cases, the same general effect is seen. As the steam- pressure rises, the speed being the same and the resistance the same, the friction of the engine increases ; from 2 pounds, at 25 pounds' pressure in the steam-chest, to nearly five pounds per square inch of piston at the maximum, 82 pounds steam in the valve-chest. As the steam-pressure fell from this point to THR&MODYNAMKS OF THE STEAM-EXGIXE. 5 6l 15 pounds, in iments 9 to 17, the load being thrown off entirely, and the speed being nearly constant, the mean pressure measuring the friction of engine falls again below 3 pounds per square inch of piston. The accompanying figure illustrates graphically the method of variation of the internal resistance,, in per cent of power de- veloped, with variation of work done by the engine, as illus- trated in the first series of trials. The curve is. evidently, at least approximately hyperbolic. Similar experiments conducted, for the Author, by Professor R. C Carpenter, exhibited the same facts where the method of steam-distribution was changed from the "* automatic ** system of regulation and adjustment of the ratio of expansion to the "throttling" system. A series of trials made to determine the effect of variation 5^2 A MANUAL OF THE STEAM-ENGINE. of speed of engine showed a general tendency to increase of friction-resistance as the speed increased, and these and the ex- periments and data already obtained serve to give the law of variation with a very satisfactory degree of accuracy. The line most closely corresponding with the data which have been found most reliable has very exactly the equation y o.ooS-r ; and the internal friction of this engine in horse-power was about O.8 per cent of the number of revolutions per minute. Referring to the results obtained by the Author, Mr. D. K. Clark remarks: "The degree of nearness to uniformity of fric- tional resistance for various powers of the same engine, at the same speed, is probably dependent upon the degree of nearness by which the momentum of the reciprocating parts is balanced by the pressure of the steam."* Earlier experiments have incidentally supplied some data relating to this form of waste of energy, thus : A Porter-Allen engine, 16 inches diameter of cylinder and 30 inches stroke of piston, in trials by the American Institute in 1871 gave : I. H. P 27 56 84 109 142 Friction H. P 9.1 9.5 8.5 8.7 12.7 A pair of Westinghouse single-acting engines 12 inches di- ameter and 1 1 inches stroke gave the following,f at 300 revolu- tions : I. H. P., loaded 84 Friction H. P 7 " light 10 " " 10 A "Buckeye" engine, 7X14 inches, at 280 revolutions, gave : I. H. P., loaded 23.0 Friction H. P 5.0 " light 5.1 " " 5.1 *The Steam-engine; vol. u. p. 619. f Trans. Am. Soc. Mech. Engrs. ; 1887. THERMODYNAMICS OF THE STEAM-ENGINE. $63 MM. Him and Hallauer give the following for compounded engines,* condensing : I. H. P., loaded 347 181 Friction 44 19 reduced I'd.. 185 137 " 4025 Indicating, as would be anticipated, lessened waste energy with lessened load and correspondingly reduced air-pump work. The experiments of M. Walther-Meunier on engines of a wide range of power show an average of efficiency of machine of 0.8815 for the compound and 0.9115 for the simple engine, the difference of 3 per cent being in favor of the latter. The former had the advantage, on the other hand, of 8 per cent in con- sumption of steam a small gain, however.f The internal friction of condensing engines has been the subject of an investigation by MM. Walther-Meunier and Lud- wig,* a compound engine of some 300 indicated horse-power being used, with the following results : (l) ENGINE WORKING COMPOUND. I. H. P. D. H. P. Frict. H. P. Efficiency. 28845 248.97 39.48 0.863 222.73 188.68 34.05 0.847 136.07 108.28 2 7-79 0.795 (2) H. P. CYLINDER WITH CONDENSATION. 153.12 128.38 24.74 0.839 108.96 88.19 20.77 0.809 55-19 37-94 i7- 2 5 0.689 (3) SAME WITHOUT CONDENSATION. 145.87 128.38 1749 0-880 103.93 88.19 15.74 0.848 51-34 37-94 U-40 0-738 * Alsatian Experiments; 1876. t Congres International de Mecanique appliquee; 1889; vol. II. p. 133. \ Bull, de la Soc. Ind. de Mulhouse; 1887; p. 140. Proc. Inst. C. E.; xc; 1886-7: part iv. p. 524. 564 A MANUAL OF THE STEAM-ENGINE. With a range of work from about 150 to nearly 300 horse- power, the friction-waste was thus, as expressed by the formula of De Pambour, P f =P + o.07$P e , nearly ; while, when the high-pressure engine only was at work, giving 55 to 150 H. P., P f =P -\-o.iiP t with condenser in action, and P f = P + o.o6P e working, non-condensing, at about the same power, measured by indicator. The air-pump demanded 7.25 to 7.5 horse-power. Earlier issues of the journal in which these data are re- corded give, from various sources, the following figures : Date. Engine. Builder. Best H. P. Max. Effic. 1864 Beam, simple. G. A. Him. II5.OO 90.8 1867 " Woolf. Koechlin. 191.44 89.6 1876 Horizontal, Woolf. Alsatian Soc. 174.46 89.1 1878 Corliss. Berger-Andre. 144.82 9!-5 1879 Horizontal, comp'd. Weyher & Richmond. 6o.OO 87.5 1884 Collman. Burghart Bros. 22.26 87.8 1884 1885 Hor. portable. " compound. Quid & Co. Alsatian Soc. 23-97 59.26 86.3 89.1 !2 cyls. and condens. ) 248.97 86.3 1886 icyl. " " I Bitschweiler-Thaun. 128.38 83-9 i " " " i 128.38 88.0 The data here collated show plainly the increase in efficiency of machine as the power demanded increases; but the last table also shows that, where equally well proportioned to their work, small engines may have practically equal efficiency, as machines, with large engines ; and that horizontal and beam engines may be substantially equal in this respect. Single-cylinder engines but slightly excel good compound engines ; and the triple- expansion engine with three equidistant cranks is still more satisfactory in its operation. THERMODYNAMICS OF THE STEAM-ENGINE. 565 134. The Methods of Variation and of Distribution of Internal Friction of Engine are, so far as deducible from these data, and from those of other investigators, evidently as follows : (1) The friction of the non-condensing engine, of the better class as here described, is sensibly constant, at any given speed, at all loads; and at different speeds, is independent of the magnitude of the load. (2) The friction of such engines is variable with variation of speed of engine ; increasing as speed increases, in some ratio as yet not fully determined, but probably differing with every engine, and, for the same engine, with every change of conditions of operation. Generally, we may write (3) The friction of engines increases with increase of steam- pressure, in such cases, in a probably similarly variable manner with that observed with alteration of speed ; neither method of variation being ordinarily capable of representation by any convenient algebraic expression. (4) The total resistance measured at the piston of the engine is composed of two parts, the one sensibly constant at the working speed, the other variable with external load, and may be, for practical purposes, at least, represented by the expres- sion in which R is the total resistance, as shown on the indicator diagram, R t the resistance due to the external load e.g., as measured by a Prony brake, and R. the resistance of the un- loaded engine. Here/ = o hi the cases taken in 133. (5) In engines of this class, the internal friction varies di- rectly with the speed, or sensibly so, other things being equal ; 566 A MANUAL OF THE STEAM-ENGINE. is directly proportional to the power exerted, and may be taken as a constant part thereof, whenever other conditions remain unchanged with varying speed. (6) We usually find confirmation of the fact, well known to engineers of experience, that the operation of a well-cared-for engine will continuously, and for a long time, appreciably re- duce the internal friction of the machine. In Distribution, experiment shows the total friction of engine to be composed, in most cases, mainly of main shaft, piston, and valve-gear resistances, in the non-condensing engine, and of air-pump and load in condensing engines. Investigations made for the Author by Messrs. Carpenter and Preston give the following for a fast-running engine with unbalanced valve and " automatic " valve-gear ; the total amounts to ten per cent of the rated power of the engine 20 I. H. P. Friction H. P. Friction per cent. Main shaft and eccentrics 0.867 42.4 Three-ported valve 0.560 27.4 Piston and rod 0.328 16. 1 Cross-head and pin 0.174 8.5 Crank-pin 0.115 5.6 Total 2.044 100.0 The following distribution was found for a similar case with a balanced valve, the total being about 7^ per cent of the rated power : Friction H. P. Friction per cent Main shaft, etc 0.867 56.9 Valve 0.038 2.6 Piston and rod 0.328 21.6 Cross-head and pin 0.174 11.5 Crank-pin o. 1 1 5 7.4 Total 1.522 100.0 THERMODYNAMICS OF THE STEAM-ENGINE. 567 The coefficient of friction can be deduced with certainty only for the main journals of the engine; since there is a variation in pressure of piston-rings, stuffing boxes, and in other quantities, which is, to a great extent, unknown. If we call f the coefficient of friction,/ the pressure on the bearings in pounds for engines light, and plus mean pressure on piston for engines loaded, c the circumference of the bear- ings in feet, n the number of revolutions per minute, fpcn will thus equal the "lost work" of friction; which has been determined in the previous experiments, and is expressed as horse-power ; this is indicated to foot-pounds by multiplying by 33>ooa Hence fpcn = 33,000 H. P. 33,000 H. P. pen. The following shows the value of this coefficient for several engines, and the next table is a summary of results. COEFFICIENT OF FRICTION FOR THE MAIN BEARINGS OF STEAM-ENGINES. Engine. F. H. P. due to Main journals. Weight on Journals in pounds. u 1 Coefficient of Fric- tion, engine loaded. Iw g to Rcvolutionn of Jour- nal per nvinutc. 0.85 3-70 0.68 3-30 1500 2DOO 500 4OOO u is 5* -04 * This engine was new, and gave an excessive amount of friction as com- pared with older engines of the same class. These main-journal frictions seem to the Author large; especially numbers 2 and 3. 568 A MANUAL OF THE STEAM-ENGINE. DISTRIBUTION OF FRICTION. SUMMARY OF RESULTS. Pans of Engine. Percentage of Total Friction. VO " e- 51 31 u .y" 11 bi 1 4; > t, cfl o P VO y II 7 " x ID" Trac comotive Va & *1 ^ C - OQ 21" x 20" Con Balanced V 47.0 35-4 35-o 4 i.6 46.0 32.9 25.0 21. 49.1 21.8 6.8 5-4 2.5 5-3 5-1 4.1 13-0 Valve and rod 26.4 4.0 22. 9-3 21.0 9-0 12.0 Total IOO.O IOO.O IOO.O IOO.O IOO.O The friction-waste of a very small engine, tested by Pro- fessor Jacobus, as computed on the assumption of a constant coefficient of 8.5 per cent, is as below. The engine developed 0.944 D. H. P. at 100 revolutions per minute, with a mean pressure of 53 pounds; its size being 3^ inches diameter and 5 inches stroke, with link-motion and unbalanced slide-valve. FRICTION OF ENGINE. D. H. P. Valve 0.0240 Piston 0.0030 Packing 0.0020 Eccentrics 0.0097 D. H. P. Pins at cross-head. . 0.0068 Guides 0.0079 Crank-pin 0.0985 Shaft and wheel. . . 0.0230 Total o. 1 749 Actual by experiment 0.175 H. P. Or 18.5 per cent. Efficiency of engine 0.815 THERMODYNAMICS OF THE STEAM-ENGINE. 569 Shaft a H. 6x 12 230 rev. 12 H. P. P. 7X 10 200 rev. 15 H. P. Crank-pin. . Wrist-pin . . Guides. Valve . 0.30 . O.O6 0.13 O I7 d 0.38 0.08 0.12 0.68 Eccentrics. Piston J ' 1 / . 0.08 o 16 048 on Packings. . . . o.oo e j ' * o 0.2O The assumption of a coefficient of friction constant, at 10 per cent, gives the following, for 30 Ibs. mean effective pres- sure :* Remarks. "Including thrust of piston rod. b Weight = 500 Ibs. c =1500 " d Valve balanced. e No packing or rod; using Sweet's me- tallic sleeve. Total 1.83 2.64 Actual 1.64 2.86 Studying the data, it is seen that, in the engines here rep- resented, the friction of the shaft and eccentrics is the princi- pal item ; that the friction of the valve and its stem is the next most serious item in the case in which it is tested under pressure unbalanced, but becomes only a fraction as great when well balanced, and is then comparatively unimportant ; that the friction of the piston may be a heavy item, and that of the crank-pin is a very small proportion of the total. Since the sliding friction of the cross-head is known to be consider' able, it is at once evident, on comparing that item with the last, that the friction of the cross-head-pin must be a very small, and probably an insignificant, part of the total. This is also to be inferred when the fact is considered that, although it is subject to the same pressure as the crank-pin, the extent of rubbing motion during a revolution of the engine is there very much less than on the latter. Stevens Indicator; Oct. 1890; p. 351. 57 A MANUAL OF THE STEAM-ENGINE. The conclusions relative to the opportunity for, and the methods of, reducing this waste of energy are, evidently, (i) that it is advisable to secure a minimum shaft-friction, by care- ful selection of material and proportioning and finishing of journals ; (2) to make piston-friction a minimum by securing the least possible pressure of rings and piston on the internal surface of the cylinder ; (3) to adopt a good balanced valve an essential desideratum, also, of all automatic regulation and (4) especially to secure the most efficient possible lubri- cation. In condensing engines, the wasted energy, in addition to the above, consists of that expended in taking the water from the condenser and expelling it from the system ; the power required to move the air-pump valves and the bucket in the pump-barrel, the resistances of the circulating pump, when a surface condenser is employed, and the frictions of the pump mechanism. Of these quantities, the first, as a minimum, is approximately proportional to the quantity of steam to be condensed ; the other quantities are nearly constant. The expedients to be adopted to reduce these wastes are the same as in the non-condensing engine, and also, by careful design and proportions of the pump-system, the reduction to the least possible amount of the friction of flow of the water used through its various channels. 135. The Conditions of Maximum Efficiency of Ma- chine, from what has preceded, are seen to be simply the conditions of minimum lost work by friction. Journals and all other rubbing parts must be of carefully adjusted size, well made, of proper material, and, above all, well lubricated. Pis- ton-rings, if expanded by springs, should bear against the cylinder as lightly as possible, should be made of material giving minimum friction at the temperature of their operation, and under all the other peculiar physical conditions to which they are subjected. Stuffing-boxes, if used, should be deep, well filled, and lightly packed ; and the whole system, includ- ing valve-gear and all connections, should be arranged to offer the least possible resistance. The machine, as a whole, should THERMODYNAMICS OF THE STEAM-EXGIXE. 5/1 be loaded to the maximum, consistent with economy of fuel and steam, and operated in such manner and at such speed as will give highest total efficiency. The lubricating apparatus should, if possible, be so designed as to flood the journals constantly, and to utilize the lubricant fully, by a constant circulation. This system not only reduces the sliding friction of the machinery to a minimum, but also usually gives rise to minimum risk from failure of lubrication. 136. The Conditions of Maximum Total Efficiency, in the engine, are easily stated generally, but are not so easy of exact determination for a specified instance, or of complete realization in any case. In some directions, one element of efficiency is only promoted at the expense of another; and maximum total efficiency is always the resultant of compro- mises effected among conflicting conditions. Thus: increas- ing speed of engine usually diminishes exhaust-wastes, while increasing friction-losses; and, at the best velocity, any change of speed will increase aggregate loss, while diminishing some one or more of its elements. Increase of velocity giv- ing rise to greater loss by friction than is compensated by decreased cylinder-condensation ; a decrease in speed ex- aggerates total loss by producing waste at the exhaust in excess of the gain by decreased engine-friction. Similarly : a high ratio of expansion gives high thermodynamic efficiency: but it exaggerates condensation, and with considerable rapidity; the best ratio, from this point of view, is that at which this resultant efficiency is a maximum. It is this which limits the ratio of expansion practically allowable, often, in the condensing engine, a small fraction of that which the thermo- dynaraic theory of the case would dictate. The final test of total engine-efficiency, and of satisfactory design, construction, and operation, is the measure of the ex- penditure of steam or of fuel in the production of the required net, useful, work, the dynamometric power of the engine, as shown by a Prony brake or other apparatus. The test of ultimate value, to the purchaser and user, is a still different one : it is the money-cost of the power supplied, and of useful 572 A MANUAL OF THE STEAM-ENGINE. work done, as measured by the total expense-account on the treasurer's books. 137. Actual Efficiencies and Economy of proposed steam-engines may be approximately computed, when operated under conditions similar to those of the experiments from which the available data are derived. As has been seen, all the expenditures of heat in the engine are now recognized ; their magnitudes have been measured ; the laws governing their variation with all the usual conditions have been, in some cases closely, in other instances roughly, determined ; and it is practicable to make estimates that shall be, in many cases and for standard conditions and usual construction and methods of operation, fairly approximate, and which may also serve to guide the designer, the builder, and the user, in making esti- mates for proposed constructions. The total expenditure of steam has been seen to be com- posed of: (i) that demanded for the thermodynamic cycle proposed for the engine ; which can be computed with perfect accuracy ; (2) that required to furnish the heat wasted by the engine otherwise than thermodynamically. This latter quan- tity is divided into two parts : (a) that needed to supply the heat wasted externally ; (ft) that wasted by internal transfer, by cylinder-condensation, without useful transformation. All these quantities are now easily computed, in most cases, with some degree of approximation ; and the total probable heat and steam-supply may thus be obtained in the usual measures of heat and steam demanded per horse-power and per hour, and, when the efficiency of the boiler is known, in fuel, both per horse-power per hour, and as a total. Examples of such computations have already been given for the ideal case. It is obvious that the computed expenditures for the ideal case must be increased in the proportion to which wastes occur, and that all the figures which have been thus tabulated must be increased from ten per cent upward to obtain probable values of weight demanded of steam and fuel in the actual case. THERMODYNAMICS OF THE STEA3/-EXGIXE. S73 The following are selected illustrations of the ideal case for otherwise common practice, at the several pressures and ratio of expansion given ; i.e., for the ideal _ase in which the steam IDEAL EFFICIENCIES OF ENGINE. rl. H. P. per - - : _ - - 20 2 40 2 e . . . 3. . . . ! 6 3 3 O 125 4 So 4 o {%> 2 iS s. . . . .... IOO 5.0 o 1=0 . . - ;- g 60 - - -; So 3-33 0.091 27 78 - -- s MIOO c o - - , - - . I2O 10 1 60 5 O l"*~ iS 90 is either worked in a non-conducting cylinder or in an other- wise perfect engine, the steam being kept in the dry and satu- rated state by adding heat during expansion in just the quan- tity needed to prevent its partial condensation in consequence of the conversion of its heat into work. Adding to the above computed quantities of steam and of fuel those demanded to supply the wastes invariably met with in greater or less amount in all actual engines, we may obtain figures of approximate, perhaps closely approximate, values, for every-day practice. To determine the probable real efficiency of fluid, allowing for transfer without transformation, by internal wastes other than thermodynamic. assume the engines to be of moderate size and operated under familiar conditions, such as those which were met with in experiments conducted by the Author, in which the wastes were very exactly measured by the expres- sion c = j^^ r = - 2 * / *' f r th e non-condensing unjacketed en- gine, and take the losses of the jacketed engine at a common 574 A MANUAL OF THE STEAM-ENGINE. proportion, three fourths that amount, c = o.i5 V ' r for engines which we will take as of usual proportions, and will assume D = 20 inches diameter of cylinder. The speed of engine may be taken as about 500 feet per minute, that at which our data were secured, in these cases, a = 4, nearly ( 130). Adding this proportion to the previously computed amounts for the ideal case, we obtain for the actual engine figures, assuming other losses too small to be here considered, which agree fairly with common experience. Further, assume that it is practicable, in each case, to make the mechanical efficiency of the non-condensing machine 0.90 and the condensing engine 0.85, usual figures for the two classes. Then we obtain the following for indicated and for dynamometric power : ACTUAL EFFICIENCIES OF ENGINE. Ste am. Fi el. I. H. P. D. H. P. I. H. P. D.H.P. I 20 2 0.069 36.2 42.6 4.0 4 7 2 40 2-5 0.085 29.2 34-4 3-2 3-8 3 60 3-3 0.098 25-5 30.0 2.8 3-3 4 80 4.0 O.IOO 25.0 29.2 2.8 3-2 5 IOO 5-0 0.109 22.9 26.9 2.5 3-0 6 60 2-5 0.050 44-9 50.0 4.5 5-o 7 80 3-3 o 067 37 - 40. 1 3 7 8 IOO 5.0 0.073 34-2 38.0 3 4 Q 8 9 120 5-0 0.080 31-3 34-8 3-i 3-5 160 5 o 087 28 7 32 o Drier or superheated steam, higher piston-speed, larger powers of engine, efficient jacketing, will increase these effi- ciencies by reducing wastes ; the opposite conditions will de- crease them. Condensing engines are here found to promise about twenty per cent better performance than non-condensing, a promised fulfilled in good practice. The differences between the steam-consumption figures of THERMODYNAMICS OF THE STEAM-ENGINE. 575 the ideal and the real case represent those internal wastes \\ hich may be largely reduced by compounding ; they amount to a nearly constant quantity, six pounds of steam for the con- densing and ten pounds for the non-condensing engines.* Similar computations, assuming, as before, that clearances may be neglected, and that the ideal case is first taken, then the corrections introduced for wastes, give the following results for an engine working steam at 500 pounds total absolute ini- tial pressure, subject to 16 pounds back-pressure for the non- condensing and 5 pounds for the condensing machine, and taking the evaporation at 10 pounds for the former and 9 for the latter; the ratios of expansion ranging from 2 to 160. The condensation-waste is taken for the simple engine as the same as obtained in the Sandy Hook experiments, c = o.2 V*r; i.e., corresponding to the simple engine of good construction and moderate speed, having about 20 inches diameter of cylin- der. The feed-water is taken at the same temperature in all cases, 200 F. ; since, at such pressures, a high temperature is advisable and is obtained by the use of heaters, in the one case taking heat from the exhaust-steam, in the other through jacket and receiver wastes. Buel's tables are here used ; but Porter's or Peabody's will give similar results. The data and results are as tabulated below : HIGH (CONSTANT) PRESSURE, r, VARIABLE. v = 0.942; /, = 46y.42 F.; H '= 1224.54 B.T. U.; ffi= 815,650 ft.-lbs. IDEAL CASE, 8 10 13 16 2O 25 30 . . 178 .0 151.5 124.0 105.5 88.5 74.O 63.5 . 162 .0 135.5 108.0 89-5 72.5 58.0 47-5 u i?5 ,792 182,805 191,452 194,241 196,692 196,692 193,301 Efficiency. . . Steam o n .216 .32 0.223 10.80 0.235 10.34 0.238 IO.2O O.242 10.06 O.242 10.06 0.237 10.24 Fuel i 13 i.oS 1.03 1.02 1. 01 i. or i. 02 * The constancy of this waste, as thus computed, as already noted, accords singularly with the results of experiment. 57 6 A MANUAL OF THE STEAM-ENGINE. Condensing. 20 30 40 50 60 80 88.5 63.5 50.0 41.5 35-5 28.0 23 o u 83.5 58.5 45-0 36.5 30-5 23.0 226 535 238,066 344,170 247,561 248,240 249,596 18.0 Efficiency. . . . Steam 0.278 0.292 0.299 0.304 0.304 0.306 8 75 8.32 8. i i 7.99 7.98 7.93 0.299 8 ii Fuel 0.97 0.92 0.90 0.89 0.89 o788 REAL CASE, Non-condensing ; Simple Engine. 0.90 16 I+.2f9... Efficiency . . . Steam Fuel .... 1.4242 1.4899 1.5658 1.6325 1.7211 0.1287 0.1356 0.1376 0.1365 0.1364 18.95 17-87 17-73 17-54 17-81 i. 89 i-79 i-77 * 75 1.78 1.800 0.132 18.36 1.84 Condensing, Simple Engine. 5 8 10 15 25 30 i+24/;.... Efficiency ... Steam Fuel . . 1.447 1-5658 1.6325 1.7746 2.000 0.1400 0.1486 0.1523 0.1481 0.1434 17.40 16.54 15-9 l6 -47 16.94 i. qi 1.84 1.77 1.83 1.88 2-095 0.0139 17-43 I.Q3 Studying the above figures, it is seen at a glance that, in such a case as is taken, the best work is done by the ideal en- gine, non-condensing, at about r = 20 and condensing at r = about 80; while there is no great advantage, even in the ideal engine, in going beyond r = 10 expansions in the one or 20 in the other. Even these figures are reduced, in the case taken as actual, to r = 6 and r = 10. By the adoption of the expedient of dividing the wastes by compounding the engine, these best ratios can be increased and the expenditure of steam and of fuel decreased very greatly, as seen elsewhere (Chapter VI, 149), and it is evident from this study of the case and on comparison with cases of engines worked at lower pressures, that such high steam should not be used except in multiple-cylinder engines of three or four in series. We neglect the effects of clearance and compression, in all these cases, assuming that, in all cases, they are made minima, the clearance being not only reduced to the least possible vol- THERMODYNAMICS OF THE STEAM-ENGINE. S77 ume, but that the cushion-steam is expanded and compressed substantially in equal proportions, and that, for this reason, its action may be neglected. Him and Hallauer have shown that, in practice, the cushion-steam has not sensible effect, either theoretically or actually, in enhancing waste by cylinder-con- densation ; and many experiments conducted under the super- vision of the Author have similarly shown the cushion-steam to be so absolutely dry, in even small engines, as to fully justify Hirn's conclusions.* The Influence of Size of Engine may be very important as affecting wastes and the efficiencies of the engine. In all of the examples taken, it has been assumed that the engines were of fair size for factory engines, and of moderate speed of piston ; at least, such that the rate of condensation found by experi- ment might be fairly assumed to apply to them. It will be in- teresting to endeavor to obtain some idea of the effect of vari- ation of size of engine upon performance. That this is not necessarily serious, with even quite small engines, when proper precautions are taken to make the waste a minimum, is seen in the results of the trials of agricultural engines, where engines of ten and twenty horse power are reported giving as high ef- ficiency as the average of fairly good engines of the same work- ing pressures at sea, both simple and compound being com- pared. It is evident that the greater extent of surface exposed, per unit weight of working fluid subject to condensation, must, other circumstances being equal, give the larger engine the ad- vantage. But the heat-storing power of the unit of surface is less as the size of engine is less ; since, if we follow Fourier, the rate of absorption varies, for a given temperature-head, nearly as the square-root of the total quantity of heat presented, and since, also, the water-flooded surface of the small engine is less effec- tive, because of its reduced absorptive power, than the com- paratively dry surface of the larger cylinder. Experience also * In making such computations, for real cases, as are here illustrated, pre- liminary to designing engines, good average conditions are to be usually as- sumed; and when in doubt, less rather than more favorable conditions. 578 A MANUAL OF THE STEAM-ENGINE. seems to indicate a less rapid rate of variation of internal waste than is indicated by the factor . To make this comparison, it is necessary to ascertain the waste per unit area of surface exposed, per unit of time of ex- posure, and per unit range of temperature within the cylinder. The computations of Professor Marks* give for this quantity, assuming it for present purposes a constant, a value never far from c = 0.02047, which is here taken as the value affecting the cases assumed. Let the process of computation already illus- trated be adopted, and let the data be as follows : Data : Engine, single-acting compound. Clearance, 20 per cent. Boiler pressure, 165 Ibs. per sq. in., 23,660 per sq. ft. Back pressure, 18 Ibs. per in., 2592 per sq. ft. Ratio of expansion in H. P. cylinder, 2.5. Ratio of low- to high-pressure cylinder, 2.78 to I. Piston-speed, 600 feet per minute. Initial volume, v lt 2.8 feet ; final, v,, 7 feet ; /, = 8690. Results : Weight of steam in low-pressure clearance, 0.554 Ib. Compression begins at 0.047 ! M - E - p -> m H. P. cylinder, 6400 Ibs. Ditto in L. P. cylinder, 1940 Ibs. per ft. Weight of steam in L. P. cylinder, 1054 Ibs. Energy of steam per Ib., 138,860 ft.-lbs. Efficiency of the steam, E = 0.1413. Water per H. P. per hour, Ibs., 17.56. Fuel at 10 Ibs. per Ib., 1.76. Heat, at usual equivalent, per I. H. P. per hour, 19,766 B. T. U. The above figures show what the ideal engine would do under the given conditions, and what would be the performance * Proportions of Steam-engine; 3d ed., p. 257. THERMODYNAMICS OF THE STEAM-ENGINE. 579 of the real engine, irrespective of size, were there no wastes. With varying sizes, the volumes, v, worked at any given ratio of expansion, the stroke of piston being made variable with the diameter of the cylinder, will vary as the cubes of the diameters; while the surfaces, s, exposed will vary as the squares. The wastes occurring internally will thus vary as the quantity s -t- z; or inversely as the diameter with cylinders of similar proportions. If the stroke be kept unchanged, the diameters varying, the wastes will vary as above, with the variations of surfaces and volumes, but less rapidly than hi the first case with a given variation of power. In illustration, take three engines of the assumed type, having dimensions as below : (1) 1 8" and 30" X 16" stroke; (2) 9" and 15" X 9"; (3) 3" and 5" X 3" Taking the internal wastes, as already proposed, using the coefficient c = 0.02047, and computing the loss on the areas of the piston, the clearance, and port passages and interior of cylinder up to point of cut-off, we obtain the following results : VARIATION* OF EFFICIENCY WITH SIZE OF ENGINE. Fuel and Wa tor per H. P. ^^ _ \rea i LHP Friction. LH. P. D. H. P. perLH.P. Ideal. 1 1.76 17.6 o.o No. i 1 10. 16 220.7 1-3 23 2-4: 34 5-4 5p.c. " 2 i 2.66 30.37 2.8 27.9 3-1; 30-7 10.30 10 p. c. ' 3 0.294 I.I32 4.8 48-25 5-4: 45-2 30-7 15 p. c. The enormous effect of this method of waste in small engines, and the very considerable influence of size upon its magnitude in the smaller classes of engines, are thus well ex- hibited. In the above instance, the interior wastes increase from 5.4 pounds to 10 and to 30 pounds per I. H. P., as size decreases, and the consumption of steam thus rises from 17.6 58O A MANUAL OF THE STEAM-ENGINE. in the ideal case, to 28 and 48 pounds for the smaller engines. The modifying effects of the various expedients for reducing wastes and approximating more closely in real engines to the ideal case of pure thermodynamics will be illustrated in the chapter on compound engines ; superheating and steam-jacket- ing ; in which computations will be presented exemplifying those effects. Computing the thermodynamic problem for the compound engines of the steamer City of Fall River from the data reported to the Author by Messrs. Adger and Sague, the observers, we may profitably compare the results with the actual performance.* This computation gives figures as below. The difference, 22 per cent, between the ideal and the real engine, being, in fact, probably, mainly the waste in one cylinder, as explained elsewhere, gives a measure of the extent to which cylinder-condensation affects the most wasteful of the two cylinders. The steam was, in this case, dry ; the engines large (44" and 68" diameters of cylinder; 8' and 12' stroke of piston) and the efficiency of boiler high. The engine had an efficiency of mechanism of 83 per cent, the paddles 80 per cent, 66 combined, and the whole machine was of excellent design. The lengths of trials ranged between eleven and twelve hours. The following are the data and results : /, = absolute pressure of admission = 11,808 Ibs. per sq. ft. pi = absolute pressure of release = 1363.68 " " / s = mean absolute back-pressure = 704.16 " " t< = absolute temperature of feed-water = 558. 36 Fahr. The corresponding temperatures, densities, and latent heats are designated by the same subscripts: A = 774-5o Fahr. ; /, = 652. 32 ; Z,, = 131841.14; Z a = 19000.39; Z>, = .1909 ; D^ .02606. 'Engine and Boiler Trials; R. H. Thurston; pp. 388-393. THERMODYNAMICS OF THE STEAM-EXCIXE. $8l From these data the following results were arrived at by considering the cylinders as non-conducting and the engine perfect : * The ratio of expansion r = 6.7167. Energy per cubic foot of steam admitted, UD t = 27183.43 foot-lbs. Heat expended per cubic foot of steam admitted, //,/?, = 163716.507 foot-lbs. Mean effective pressure, or energy per cubic foot swept through by piston. UD l - = 4047.5 Ibs. per sq. ft. Heat expended per cubic foot swept through by the piston, TT rt = 24,377 Ibs. on square foot = pressure equivalent to heat expended. UD U Efficiency of steam = n = -77 = .166. -T7,//, -T7, Net feed-water per cubic foot swept through by piston D = = .0284. Cubic feet to be swept through by piston for each indicated 1980000 horse-power per hour = M E p _ 4Q . , c = 489-2 cubic feet. Feed-water per I. H. P. per hour = 489.2 X .0284 = 13.89 Ibs. Actual feed-water = 17.00 Ibs^ nearly. 13.89 Difference, 3.11 Ibs. = 22 per cent * Steam-engine Trials; pp. 388, 389. 582 A MANUAL OF THE STEAM-ENGINE. due to cylinder-condensation and leakage-waste and other wastes. The average locomotive of the old, simple, type demands about 6 pounds of good coal and 40 pounds of steam per horse-power per hour. Mr. Clark found the water-consumption of the "Great Britain " locomotive to be, approximately, w = i6-j-o.i-j-o.ooi4 a ; where w was the weight in pounds per indicated horse-power per hour, and a the fraction of the stroke at which cut-off took place. The following are common figures for usual performance of stationary engines in 1890 : GENERAL COMMERCIAL ECONOMY OF ENGINES IN ELEC- TRICAL WORK. High-speed, single cylinder 35 to 40 Ibs. water. " " compound, non-condensing 25 "27 " " " " " condensing 19 " 21 " " " " triple, " 16 " 17 " " Corliss single, non-condensing : 27 "29 " " " compound, condensing 15 " 16 " " " triple, " If the available energy of combustion in the pound of coal be taken as U c , the coal consumed will be, per horse-power per hour, U7- U C E if the efficiency, E, be that of the engine as computed on the basis of the given power. Thus, if E = o. 1 5 and U c = 10,000,000 foot-pounds, 1,980,000 W - =1.6; Ibs. 10,000,000 X 0.12 THERMODYNAMICS OF THE STEAM-ENGINE. 383 Assuming the heat obtainable for conversion into work to be 10,000,000 foot-pounds for each pound of fuel burned in the boiler-furnace, we have the quantities of fuel needed, at various total efficiencies, per indicated horse-power per hour, as below: WORK AND FUEL AT VARIOUS EFFICIENCIES. Ft--lbs. of Los. per I. H. P. Efficiency. Work per Ib. per boor. i 10,000.000 a 198 0.80 8,000,000 0.25 0.60 6,000,000 0.33 0140 4,000,000 0^95 0.30 3,000,000 0.66 0.25 2,500,000 0.79 0.20 2,000,000 0.99 o.i 8 1.500.000 1. 10 ai6 1,600,000 1.24 0.15 1,500,000 1.32 0.14 1,400,000 1.414 0.13 1,300,000 1.523 0.12 1,200,000 1.650 an 1,100,000 1.800 aio 1,000,000 1.980 CHAPTER VI. THE COMPOUND OR MULTIPLE-CYLINDER ENGINE; STEAM-JACKETING AND SUPERHEATING. 138. The General Theory and the Construction of the multiple-cylinder engine are equally simple ; and their correct forms may be readily and very exactly deduced from the prin- ciples and the facts already revealed by current practice and experience with the simple engine. As has been seen, the great source of avoidable wastes in the single cylinder is that alternate heating and cooling, and that consequent wasteful condensation and re-evaporation of steam, which is due to the exposure of the internal surfaces of the cylinder to the alter- nate heating action of entering steam and cooling effect of ex- pansion and condensation. Any expedient which will reduce this waste by preventing that transfer of heat from the steam to the exhaust side of the engine without transformation in proper proportion, into work, will reduce this loss and increase the economical value of the machine. In " compound " en- gines, this is done by effecting a limited expansion and partial transformation of heat into work, submitting, so far as may be necessary to cylinder-condensation and re-evaporation, but then transferring the working steam, both the uncondensed and the re-evaporated, to a second cylinder in which the latter portion is enabled either to do some work or to balance its waste more or less fully. Any number of successive expan- sions may be thus practised ; but experience indicates that not more than two is desirable at ordinary moderate pressures, three at from eight to ten atmospheres, or four with twelve to fifteen atmospheres pressure. Experience, as well as the study of the distribution of 584 THE COMPOUND OR MULTIPLE-CYLINDER EXGIXE. $83 wasted work in the machine, also indicates that a well-designed multiple-cylinder engine may exhibit higher efficiency of machine, Le., less loss by friction, than ordinary simple engines arranged in pairs ; thus giving still greater advantage when employed for marine work or wherever coupled engines are needed. The multiple-cylinder engine is, therefore, any engine in which steam is used as the means of transformation of heat- energy into work, through a succession of expansions in cylin- ders placed ** in series." In construction, this succession of steam-cylinders may be obtained, either by using structurally independent engines, or by making them parts of a single structure. The former system is sometimes seen, in stationary engine practice ; the latter is usual in marine engines. The question of adoption of the compound engine, or either form of multiple-cylinder engine, for the usual work of the locomotive or in any case in which the speed, pressure, or load, either or all, is expected to be variable, is complicated by the fact that, under such variable conditions, it is impracti- cable to find proportions of cylinders suitable, and permanently so. Whenever the load and speed maybe expected to be reasonably constant, a suitable design may be produced. Hence the success of the marine engine in these forms and the less completely satisfactory results with other cases in which less uniform conditions are maintained, as in the locomotive. All the conditions affecting the choice and use of engines of differing type are those of practice, and quite apart from the thermodynamic problem. In practice, the multiple-cylinder engine exhibits several advantages, and we may make a fairly-complete summary thus: (1) Reduction of expansion in a single cylinder. (2) Great restriction of internal waste. (3) Ability to adopt large ratios of expansion, with light loads, without " wire-drawing." (4) Reduced leakage in engine. (5) Reduction of depreciation of boiler. 586 A MANUAL OF THE STEAM-ENGINE. (6) Lighter blast ; smoother draught ; less waste, annoy- ance, and danger from sparks and cinder ejected from locomo- tives. (7) Elevated limit of speed and power. (8) Reduced loss by tender and fuel haulage. (9) Greater uniformity of crank-moments. (10) Larger efficiency of the machine. 139. The Wastes of the Engine are similar in kind, in all cases, to those of the simple engine.* Were it possible to construct a steam-engine of which the theory should be purely thermodynamic, an engine in which the only waste of energy should be that known as the necessary thermodynamic loss, its theory, as has been seen, would be most simple and most satis- factory. The efficiency of the engine and the quantities of heat, steam, and fuel demanded for its operation at a given power would be simple functions of the physical properties of the steam and of its ratio of expansion. The engineer, in con- structing its theory, would only concern himself with the quan- tity of heat imported into the machine, the temperatures of the initial and terminal portions of the expansion-line, and the relation of initial to back pressures. The essential facts are the magnitudes of the pressures and volumes of the steam and the extent of adiabatic expansion, and it matters not whether the engine be one of a single cylinder or a multi-cylinder en- gine of indefinitely extended complexity. For this, the ideal case, the indicator-diagram represents precisely the amount of transformation of heat-energy into mechanical work, and the ratio of its measure in units of work to the mechanical equiva- lent of the total quantity of heat-energy supplied to the en- gine, while doing that work, is the measure of the efficiency of the engine ; as it is of the thermodynamic efficiency of the working fluid. The thermodynamic efficiency, the dynamic efficiency of the machine, and the total efficiency of the engine are here identical. * This portion of this chapter was presented, in part, at the Twentieth Meeting of the American Society of Mechanical Engineers. See Trans. 1889. THE COMPOUND OR MULTIPLE-CYLINDER EXCIXE. 587 To ascertain how much heat, steam, and fuel are demanded by such an engine for the performance of work, it is only neces- sary to measure the quantity of work done by the steam upon the piston, as shown by the indicator, and to divide this quan- tity by the energy received by the engine from the boiler ; the quotient is the efficiency of the engine. As the operation of the engine approaches more nearly the conditions of best effect, the magnitude of this measure of efficiency approaches a limit which is expressed by the quotient of the range of tem- perature worked through to the absolute temperature of the working fluid at entrance into the engine. The excess of the actual consumption of fuel, in the best engines, above the for- mer figure measures the sum of all wastes in real engines due to imperfections other than of thermodynamic cycle. Thus, the best work of the Corliss compound mill-engine being taken as about sixteen pounds of steam per horse-power and per hour, where the thermodynamic efficiency is about twenty-five per cent, the ideal case demands about ten pounds, under similar conditions otherwise, and the wastes amount, in this case, therefore, to about six pounds per horse-power and per hour, or sixty per cent of the ideal consumption. This com- parison is easily made by the method already presented, which enables the thermodynamic efficiency to be easily computed for any given case. The wastes of the steam-engine have been shown to com- prehend two principal classes : the external and the internal wastes ; and these latter are of two distinct kinds. We may classify such losses thus : (1) External wastes ; consisting of those losses of untrans- formed heat which are produced by the conductivity and the radiating power of the materials of which the heated parts of the engine are composed. Five per cent should probably rep- resent as large a percentage as is to be reasonably expected in good practice with engines of moderate or large size. (2) Internal wastes ; consisting of two parts : (a) Thermodynamic, unavoidable, losses of heat rejected at the lower limit of temperature of the working fluid ; 588 A MANUAL OF THE STEAM-ENGINE. (b} Wastes by internal conduction and storage of heat, fol- lowed by later rejection with the exhaust-steam. To these are to be added : (3) Wastes of mechanical energy. Of the internal losses, the first, (a), is, for any given set of initial and final temperatures of working fluid, a fixed quan- tity, and one which measures the defect of efficiency of the perfect engine working between the given temperatures. The second, (ft), is a quantity of variable amount, capable of ameli- oration by one or all of several known expedients, and reduci- ble from the enormous proportion observed in small and ill- designed or badly constructed engines to a very moderate amount in large engines of good type. The last item, (3), is one which is seldom large in good constructions, and may in some cases, by careful design, good construction, and skilful management, be brought down to less than five per cent in non-condensing and to perhaps ten per cent of the total energy in condensing engines of simple forms and high mean working pressures. The unavoidable thermodynamic waste is rarely less than seventy-five or eighty per cent of the total thermo- dynamic demand, and the internal wastes by conduction and storage with subsequent rejection, by cylinder or internal con- densation, as it is customarily called, and by leakage, range from ten per cent, as a minimum, perhaps, to twenty-five or thirty per cent of the heat received from the boiler, in good engines, to fifty per cent, in many cases, and even to much more than the latter proportion in exceptional cases. It is this which has now been found to constitute, ordinarily, the great source of loss and inefficiency of the real, as distinguished from the ideal, engine. Leakage, in well-built engines, may be neg- lected as unimportant ; but internal condensation is usually both serious in amount and extremely difficult to check ef- fectively. Since it is easy to prevent serious losses by external trans- fers of heat, by leakage, or by friction of engine, and since, as is well understood, the thermodynamic waste is unavoidable, and for any given case unalterable by the engineer, it is ob- THE COMPOUND OR MULTIPLE-CYLINDER ENGINE. 589 vious that the direction in which he must look in his endeavor to further improve the economical performance of the engine, is that which leads towards the reduction of internal wastes by cylinder-condensation. This is the direction which coming inventions must take. In comparing the simple with the compounded engine, in average practice, it will be found that the former excels, in the best types, in the small clearance practicable in a single cylinder ; in the adaptability to that type of an effective ex- pansion-gear, as illustrated in the Corliss type; in its giving a dynamic cycle which is represented by an indicator-diagram, of which the area is very nearly that of the ideal case : and, finally, in its lesser total area of exposed, radiating, and heat- wasting surfaces, exterior and interior. On the other hand, the compounded type excels in the fact of its utilizing the wastes occurring in the full cycle, step by step, as they take place, more and more perfectly as the number of cylinders and of successive stages of expansion are increased, thus permitting an increase of the practically economical ratio of expansion. It also excels, in the marine type, in which two or three engines are found to be desirable in order to secure a good distribution of turning stresses and moments, by giving a more uniform pressure on the crank- pin and smoother and more nearly frictionless rotation of the shaft. The advantage may lie on the one side or the other, in special cases : and it has usually been found practicable to attain substantially the same efficiency of working fluid in the one type as in the other by exercising sufficient care in provi- sion against wastes. The simple engine must probably be largely dependent upon either jacketing or superheating for high efficiency ; while the compounded types are more nearly independent of these expedients. Comparing the ideal with the real engine, we may take in illustration the following from available data of engine-opera- tion, computing the ideal case and comparing the results with those actually obtained : 590 A MANUAL OF THE STEAM-ENGINE. DATA AND RESULTS. Engines Compound. Standard. Cases I. II. /i (Ibs. persq. in.) 155 13 r 4 2 A 20 20 Temperature of feed-water 60 F. 60 F. Efficiency of steam 0.1445 0.1197 " " furnace (Rankine's Eq.) 0.664 0.60 The fuel used on trial was reported as 4.1 and 4.7 pounds per D. H. P. per hour, respectively. Coal per D. H. P. per hour 4.iolbs. 4.7 Ibs. " " I. H. P. " " at 20 p. c. friction 3.28 " 3.6 " " " " " " ideal 2.01 " 2.35 " Wastes, extra-thermpdynamic, per cent 30 . 9 37.6 Value of a (c = a ^r ) 0.22* 0.26 A gain of 7 per cent is made by reduction of waste, by compounding, in this instance, which represents an actual case in locomotive practice. 140. The Amelioration of Wastes thus becomes an important matter. The efficiency and economy of operation of the single cylinder, the " simple " engine, is at all times limited by internal waste, and the question which all engineers endeavor to solve is : In what manner may we best proceed to eliminate or ameliorate this loss? The three methods which have been found advantageous, and, in special cases, effective, have been seen to be : (1) Superheating; (2) Steam-jacketing; (3) " Compounding." Superheating is a well-known but not a common method. It is evident that, if the steam can be introduced into the engine at such a temperature that the cooling action of the metal of the cylinder will not cause its condensation initially, and the stroke may be performed without condensation in * Closely corresponding with the Author's deduction for engines of quite nearly equal volume, and earlier reported. THE COMPOUND OR MULTIPLE-CYLINDER ENGINE. 9 1 consequence of doing work, no loss of heat from the cylinder can take place by re-evaporation ; and if no such loss occurs, the waste of heat at entrance, in turn, by initial cooling, will be reduced. Superheated steam, also, is a good non-conductor and a non-absorbent of heat, like the permanent gases. It is thus, also, less liable to this waste. But it is found in practice that superheating beyond a very moderate degree, perhaps 100 F., is inadvisable on account of risks of injury to engines and cost of repairs to superheater, which more than com- pensate its advantages. It has come to be regarded as an auxiliary in economizing, not as a complete remedy for in- terior wastes. This method of augmenting efficiency will be more fully discussed later. Steam-jacketing is a common partial remedy for this waste. By surrounding the steam-cylinder with the steam-jacket, it is possible to produce, in part, the effect of superheating ; that is, to secure drier steam in the engine throughout the stroke. The amount of re-evaporation, during the period succeeding cut- off and up to the closure of the exhaust-valve, and the quantity of heat of which the cylinder is thus robbed, measures closely the amount of initial condensation and waste and the weight of steam which must be supplied in excess of the thermo- dynamic demand to compensate that loss. The effect of the addition of a steam-jacket depends upon the conditions of operation of the engines, largely, and may be productive of marked advantage or, under unfavorable conditions, of no important useful effect. With steam initially dry, the jacket is probably usually helpful ; but, with wet steam, or with super- heated steam, it is of comparatively little value, even if not sometimes a positively wasteful adjunct. Steam-jacketing will be made the subject of a later article. Of the several available methods of checking cylinder- wastes of heat, it is evident that only the plan of securing a non- conducting interior surface is purely economical in method. To superheat the entering steam is to reduce a great loss by sub- mitting to a small one ; and even permanent superheat, as in the conversion of the fluid into a gas, still leaves this loss only 592 A MANUAL OF THE STEAM-ENGINE. ameliorated, not completely destroyed. In a single unjacketed cylinder, heat carried out by the exhaust is a pure waste ; in the jacketed engine, this remains true, though in less degree, not only of the heat lost by initial condensation and later re- evaporation, but also of that heat which may have been em- ployed in reducing its amount, either by drying the prime steam, or by the normal action of the jacket. In multi-cyl- inder engines, the heat employed in raising the temperature and reducing the initial condensation of the steam in the first cylinder is utilized in the second by there securing a better quality of steam, as well as by directly checking this waste. All the heat swept out of the last cylinder into the condenser is wasted. Utilization of the added heat, in either system, is obviously, at best, incomplete. With wet steam, the jacket may even exaggerate, rather than reduce, the loss ; as it may, with considerable expansion, increase exhaust-wastes in greater amount than it decreases cylinder-condensation. The same remarks, to a less extent, apply to the systems of compounding where excessive expansion is adopted. Superheated, or at least dry, steam must be provided by the boiler to insure economy, either with or without these special constructions, and to enable the ratio of expansion to be economically in- creased. " Compounding" or the use of the multiple-cylinder engine, in which the steam exhausted from one cylinder is again worked in a succeeding one, is now the most familiar of devices for ex- tending the economical range of expansion and increasing the efficiency of the engine. The limit to useful increase of the ratio of expansion of steam in a single cylinder is found to be determined by the magnitude of the wastes incurred in the operation of an engine of which the working cylinder is a good conducting material. Any method of reducing this waste of heat internally will enable the efficiency of the engine to be increased by further profitable extension of the ratio of expansion. 141. The Problems in Compounding are now readily stated. Assuming it to be possible to divide the waste by THE COMPOUND OR MULTIPLE-CYLINDER ENGINE. 593 cylinder-condensation and leakage by two or more, it is evident that the limit to economical expansion and transformation of heat into work will be set correspondingly farther away. This is done by the multiple-cyclinder engine : the internal wastes are reduced approximately to those of one of its cylinders, and the gross percentage of waste is made less in the proportion of this division. The heat and steam rejected as waste by inter- nal transfer without transformation from the first cylinder is utilized in the second nearly as effectively as if it were received directly from a boiler at the pressure of rejection from the first cylinder. Insomuch, therefore, as the pressure can be in- creased and the increase utilized by the addition of another cylinder, gain is secured. Common experience shows that the best results are ordina- rily obtained, in each class of multiple-cylinder engine, when, the engine being properly designed for its work, the terminal pressure for the system can be economically made something above the sum of back-pressure in the low-pressure cylinder, plus friction of engine. This total may be usually taken, probably, at about eight or ten pounds above a vacuum. The latter figure will be here assumed. 142. The Three Fundamental Principles are: (1) Economical expansion in a single cylinder has a limit, due to increasing internal wastes ; which limit is found at a comparatively low ratio of expansion. (2) The method of expansion may be, for practical pur- poses, and such as are here in view, taken to be approximately hyperbolic ; the best terminal pressure being something above that which corresponds to the sum of all useless resistances, and which may be here taken as, for example, about ten pounds per square inch above a vacuum.* The division of the initial tension by this terminal pressure will thus give an * Mr. H. A. B. Cole finds the value of the index , in ordinarily good engines of the triple-expansion type, to be approximately 1.2, varying but little with the range of expansion adopted. (Converting Compound into Triple-expansion En- gines; Trans. Brit. Inst. N. A.; 1886.) 594 4 MANUAL OF THE STEAM-ENGINE. approximate measure of the desirable ratio of total expansion for the best existing engines. (3) All steam entering any one cylinder will be rejected, as steam, into the succeeding cylinder, external wastes being neg- lected, and ultimately into the condenser ; and the full amount of steam liquefied at entrance by absorption of heat by the interior surfaces of the cylinder will be re-evaporated later, and will pass into the condenser or into the next cylinder. Heat transferred in the one direction, in the one process, will be transferred in precisely equal amount in the opposite direction, in the other. This last point is important, and is easily established : The cylinder, when in steady operation, is neither permanently heated nor permanently cooled ; no progressive heating can go on, as it would, in that case, become heated above the tem- perature of the steam and become a super-heater ; no progres- sive cooling can occur, since, in that case, the cylinder would become a condenser of indefinite capacity. It must, therefore, transfer to the next element of the system all the heat which it thus receives ; assuming that external radiation and conduc- tion may be neglected, and that the Rankine and Clausius phenomenon of liquefaction of steam by transformation of heat into work is ignored.* It also further follows that the introduction of one or of many cylinders between the terminal element and the oiler does not, through cylinder-condensa- tion, affect the operation of the final cylinder, however great that condensation may be ; provided the introduction of the added elements is effected by raising the steam-pressures commensurately, leaving to the final element of the series the same initial pressure as at first. The Rankine and Clausius phe- nomenon, it should however be noted, insignificant in amount and effect, in any one cylinder, with its customarily low ratio of expansion, produces a cumulative condensation in the series, *This the Author would denominate Hirn's principle. See a paper by M. Dwelshauvers-Dery in the Bulletin de la Societ6 Industrielle de Mulhouse, October 1888, on the theory of simple engines. A mathematical proof may be found in De Freminville's Cour de Machines a Vapeur; 1862; p. 121. THE COMPOUND OR MULTIPLE-CYLINDER ENGINE. 595 which, at high total ratios, has already been seen to be impor- tant, amounting to something between 1 5 and 20 per cent of the steam thermodynamically demanded. This condensation is not at all affected by the principle of " compounding," as the heat thus surrendered by the steam is transformed into work and thus taken out of the system instead of being temporarily stored. The total waste by this form of loss is thus evidently meas- ured, in the case of the multiple-cylinder engine, by the maxi- mum waste in one cylinder. If all are equally subject to this loss, the rejected steam of re-evaporation from any one cylinder, as the high-pressure cylinder, supplies precisely what is needed to meet the waste by initial condensation in the next ; and so on through the series. Thus the use of a series of cylinders, in this manner, divides the total waste for a single cylinder, ap- proximately, at least, by the number of cylinders ; and it is in this manner, largely, that the " compound " system gives its re- markable increase of efficiency. The three principles which have been enunciated give a means of constructing a philosophy of the multiple-cylinder engine, which will meet all essential needs of the engineer. The first principle shows that, a limit existing to economical expan- sion in a single cylinder, the advisable number of cylinders in series may probably be determined, when that limit is ascer- tained for any case, either by experiment, by general experience, or by rational theory and computation. The second principle shows that we may find an approximate measure, at least, of the desirable total ratio of expansion for maximum efficiency, when the best terminal pressure for the chosen type of engine is settled upon. This total range of expansion is divided by the maximum admissible range for a single cylinder to deter- mine the minimum desirable number of cylinders. Otherwise stated : The total ratio is a quantity which should approxi- mately equal the admissible ratio for a single cylinder raised to a power denoted by the number of cylinders. Combining thus the two considerations referred to, we may obtain a de- termination, probably fairly approximate, of the proper mini- 5 A MANUAL OF THE STEAM-ENGINE. mum number of cylinders in series. The third principle enables an estimate to be made of the total internal wastes of the series, and the probable expenditure of heat and of steam, and permits a solution of all problems of efficiency for the com- pound engine, of whatever type. 143. The First Step in designing the "Compound" En- gine is the determination of the best ratio of expansion, under the assumed conditions of operation and for the given type of engine, for a single cylinder ; then the best ratio of expansion for the series ; this study being made largely from the financial stand- point. It is not the thermodynamic, nor the fluid, nor even the engine, efficiency, which must be finally allowed to fix the best ratio of expansion ; but this must be the ratio of ex- pansion at maximum commercial efficiency ; that which will make the cost of operation at the desired power a minimum for the probable life of the system. The total ratio being settled upon, and that allowable, as a maximum, for the single cylinder, it becomes easy to determine the best number of cyl- inders in series. The first-mentioned ratio is that of maxi- mum commercial efficiency, as just stated ; but the second must be taken as that which gives highest efficiency of engine, the back-pressure in that cylinder and its friction, taken singly, being considered, together with its proper proportion of the friction of the engine as a whole. Studying the method of distribution of wastes among the several cylinders of the multiple-cylinder engine, it will be ob- served that, since the pressures increase more rapidly than the temperatures, the range of temperature in the high-pressure cylinder is greatest ; while, the same weight of steam passing through the whole series, the low-pressure cylinder presents the largest area of condensing surface in proportion to quantity of steam used.* * In Professor Schroter's tests of the Augsburg triple-expansion engine, in 1889, the condensation in the cylinders ranged from an average of 14.4 per cent, in the small cylinder, to 33.7 and 51.9 per cent, in the intermediate and low-pressure cylinders, respectively; the total amounting to from 16 to 20 percent of the whole steam-supply. Otherwise stated, these interior wastes THE COMPOUND OR MULTIPLE-CYLINDER ENGINE. S97 144. The Extent of Economical Expansion in a single cylinder will vary with the working range of temperature and pressure, and with the physical condition of the working fluid : but it may be taken, as determined by experience, as perhaps not above two and a half expansions for unjacketed engines with wet steam, or not over three or four for good practice with the better classes of engines. The total expansion-ratio thus becomes, for the several types of multiple-cylinder engines, as below : MULTIPLE-CYLINDER ENGINES. No. cyls. 123 4 r 2.5 to 3 6.25 to 9 16 to 27 40 to 81 /, 25 tosolbs. 6oto loolbs. I2oto3oolbs. ssotoSoolbs. The result of this sharing of the wastes in the multiple-cyl- inder engine is that, in the triple-expansion engine, as an illus- tration, the total cylinder-condensation may be reduced from about 30 per cent, as in the parallel case of simple engine, to 10 or 12 per cent. This assumes good design and dry steam i.e., steam containing less than three per cent water. In such case, the area of the combined indicator-diagram should ap- proximate 80 per cent that of the ideal case. The compound engine should approximate 70 per cent. In common practice with 1 50 pounds steam, the temperature being equalized in the triple-expansion engine, the ratios of cylinder-volumes are about i : 2.5 : 7.5, or, equalizing work, not far from i : 2.8 : 7.1. Thus a triple-expansion engine should do best work up to a pressure above 200 pounds, and the four-cylinder engine should be adopted from that point up to the highest pressures likely to be employed in the steam-engine ; the common double- expansion compound serving its purpose well below the lowest figures assigned to the triple engine. Any type of engine may amounted, each, to from 2^ to 10 per cent of the total steam made; being, for example, in one trial, 2.6, 6.0, and 9.7 per cent in the three cylinders, respect- ively; the minima being 2.2, 5.4. and 7.3; and the maxima 2.9, 6.4, and 10.7; while the totals ranged from 16. 1 to 20 per cent. 59^ A MANUAL OF THE STEAM-ENGINE. ' be made to overlap the range assigned it by suitably providing against wastes occurring within the engine ; as by increased speed; by superheating; by any expedients giving higher effectiveness to the jackets, or by any other method of im- orovement. Any system which increases the efficiency of the simple engine will improve the efficiency of the compound, and will correspondingly increase the range of pressure through which it will give satisfactory gain as compared with the former. 145. The Influence of Economical Expedients recog- nized as useful in other forms of engine, as superheating, jack- eting, and increasing speed of engine, may readily be perceived when the method of operation of the multiple-cylinder engine is understood in its relations to heat-transfer and heat-trans- formation. We may consider them in their order : (i) Superheating the steam transferred from boiler to engine results in the supply of a fluid which may surrender to the metal of the working cylinder a certain portion of heat meas- ured by the product of its specific heat as a gas into the range of superheating and into its weight without the production of initial liquefaction. If this quantity of heat is equal to or greater than the loss during expansion and exhaust, there will be no initial condensation ; and the waste from the high-pres- sure cylinder will be nearly that due the passage of a gas through it under similar conditions of temperature and expan- sion ; a comparatively small quantity, since any substance in the gaseous state possesses low conductivity and slight power of absorption and storage of heat. Should the superheating be in excess of this amount, the steam will not begin to con- dense until a later period, perhaps not at all ; the only require- ment to prevent liquefaction being now for heat to supply the amount required to keep the steam dry and saturated while expanding and doing work. If the superheating be less than the first-mentioned quantity, initial condensation will be re- duced but not entirely prevented. It is probably never the fact that it is practicable to secure, safely and economically, so much superheating as is needed to keep the steam dry through- SUPERHEATING AND STEAM-JACKETIXG. 599 out the stroke.* In any case, the quantity represented by the superheating will be a gauge of the amelioration of wastes by internal transfer of heat in every cylinder of the series. The steam leaving the high-pressure cylinder will be to that extent drier; and this will be true of the succeeding cylinder or cylinders. Were there no other disappearance of heat than that due to cylinder-condensation, superheating at the first element of the series would give superheating at each of the others. In so far as condensation, such as was pointed out by Rankine and Clausius as the result of conversion of heat into work, takes effect, and so far as other wastes by transfer without transformation occur, to that extent will the gain, as observed in successive passages from cylinder to cylinder, be reduced ; though the improvement of the working conditions above as- serted will be none the less reaL Each cylinder will have wet- ter steam than the preceding, in proportion as the condensa- tion doing work and the losses by conduction and radiation increase, as a total, cylinder by cylinder. Superheating at the high-pressure cylinder will produce a favorable effect all through the series, including the low-pressure cylinder. Cylinder-conden- sation will, nevertheless, cumulatively increase throughout the series, in consequence of the fact that the wetter the steam enter- ing any one cylinder the more the condensation, and the wetter that leaving it, both by this initial increase of humidity and heat-storing power and by the additional moisture coming from the Rankine and Clausius phenomenon, and from the loss by transfer to surrounding bodies. This last action will, however, be the less observable and the less important in its effect as the moisture of the entering steam and the magnitude of the waste by initial condensation become greater. The more nearly the total proportion of water in the mixture approaches one half, the more nearly does this phenomenon become a * In one case reported to the Author an initial superheating of 500* F. was required togire 50' F. superheating at exhaust; 100* F. has usually been con- sidered a practical maximum superheat. 600 A MANUAL OF THE STEAM-ENGINE. vanishing quantity. It may probably be neglected entirely in the computation of efficiencies for a large proportion of the engines in use, without introducing sensible error, and very probably may be neglected in all cases without invalidating conclusions reached ignoring it. On the other hand, super- heating is not likely ever to produce much effect upon this action. (2) Steam-jacketing, the expedient devised by Watt for the purpose of reducing internal wastes, is a method of approxi- mately " keeping the cylinder as hot as the steam which enters it," as Watt states it, in order that no such chilling of the en- tering steam may occur. Authorities disagree as to what ex- tent and in what manner the jacket is advantageous in the multiple-cylinder engine. It is sometimes advised to jacket only the high-pressure cylinder ; sometimes only the low-pres- sure, and sometimes the whole series, whether one, two or three cylinders, or more. The philosophy of the engine would indicate that, to secure maximum good effect, assuming the jacket on the whole desirable at all, the best system is the lat- ter ; and that, since the waste of the engine is most nearly measured by the losses of its most inefficient member, to omit the jacket from any one cylinder insures that the aggregate loss of heat in the whole engine will be increased by just the amount by which waste is increased in that one cylinder by such omission. The question which actually arises in practice, for the de- signing engineer, is whether it will pay to jacket at all, or not. It can be readily seen that it is not as important, in a financial sense, that the multiple-cylinder engine be jacketed as it is to jacket a simple engine of similar total range of expansion. The value of the waste due to omission of the jacket is less, ordinarily, as the number of cylinders, in series, is the greater. It is also seen that those conditions which may make it un- necessary to jacket the simple cylinder make it still less im- portant in the multiple-cylinder engine. As piston-speeds are increased, for example, the necessity of the jacket decreases, and the limit at which it will pay here to dispense with it is SUPERHEATING AND STEAM-JACKETING. 6oi sooner reached than in the single-cylinder engine. It is this principle which justifies the not uncommon practice of omit- ting jackets from engines which are driven up to 200 or 300 revolutions or to 1000 feet a minute, or more, of piston-speed ; while pumping-engines, for example, in which the speed is low, must usually be jacketed, if high duty is demanded. (3) High engine-speed, a device for reducing internal wastes, as well as decreasing cost of construction and weight, is evi- dently a matter of less serious importance as the number of cylinders is increased ; yet it is equally evident that, to secure maximum efficiency, it is essential that the time of exposure to the action of the wasteful influences in each cylinder be made a minimum. At modern and customary speeds of piston and of rotation, the value of these several expedients for improving performance is much less than formerly ; but all are to be adopted where it is hoped to secure such high efficiency as is coming to be demanded of the designing and the constructing engineer. So long as the advantages of further gain in this direction are safely attainable for the simple engine, they are still desirable, and may prove attainable, in the multiple-cylin- der machine. Non-conducting cylinders, such as were partly secured by Smeaton by the use of his wood-lined pistons and heads, and such as have since been sought by Emery and others ; such as were shown to be needed by Watt, and later more conclusively by Rankine and his successors, would do away with the neces- sity of compounding on the ground of thermodynamic gain ; but would leave the advantages of the multiple-cylinder en- gine, on the score of better division of stresses and work, un- affected. Clearances are usually greater in the multiple-cylinder than in the simple engine ; but it is also seen that the loss by clear- ance, and the rejected steam thus unutilized, in any one cylin- der, goes to fill the clearances of the next ; and thus the loss by this method of waste is divided approximately, also, by the number of cylinders, as in the case of other losses. It remains advisable to reduce the " dead-spaces" as much as is practi- 602 A MANUAL OF THE STEAM-ENGINE. cable; but the importance of this matter is less than in the case of the simple engine. Thus the adoption of the multiple-cylinder engine reduces wastes of every kind, except those coming of increased radia- tion from the exterior, where the total area is, commonly, in- creased, and the loss due to the friction of the engine when the number of cylinders is in excess. These are, however, minor wastes. 146. The Number of Cylinders to be introduced in series is finally settled by financial considerations. The fact that the loss by internal wastes is measured by that of one of the cylin- ders only indicates that, as a matter of economy of heat, simply, there is no natural limit to the number ; except that the losses by external conduction and radiation may finally more than compensate the gain by further complication. This principle is easily shown, thus: The work performed is proportional to the quantity I -j- log r, and the cost of that work is proportional to the quantity I -j- ar>*, since the expansion in one cylinder is the nth root of the total ratio of expansion for the series ; ;;/ being taken as the index determined by the rate and method of variation of the cylinder-condensation with variation of the ratio of expansion, and which is not far from m 2 ; and a is a constant coefficient, not far from 0.2. The cost of power, measured in terms of steam expended thermodynamically and by internal wastes, is a minimum when the quotient of the two expressions, i + log r i -f- ar mn above is a maximum ; this is a maximum when the denomi- nator is a minimum ; and this is a minimum when the value of n increases, without limit. Assuming, in illustration, as the result of general experience in good practice, that, under the best customary conditions of operation, a good simple engine, working at high pressure, SUPERHEATING AND STEAM-JACKETING. 603 condensing, and at the best ratio of expansion for maximum engine-efficiency, may be fairly expected to give as good a result as two pounds of fuel of satisfactory quality per horse- power and per hour. Under similarly favorable conditions, we may also, with equal likelihood, anticipate a probability that we may obtain better work with multiple-cylinder engines in some- where about the following proportion : Con- Gain, Gain, Engine. sumption. TotaL Difference. Simple, one cylinder 2 Ibs. Compound (double-expansion). . . 1.6 20 p. c, 20 p. c. Triple-expansion 1.4 30 10 Quadruple-expansion 1.25 40 10 Quintuple-expansion i.i 50 10 The figures in the first three cases are based upon what is probably ample experience ; the others are obtained by infer- ence from the rate of progression thus established, and upon the principle, above enunciated, that the waste is reduced in proportion, approximately, to the number of cylinders in series. The probable first cost and running expense of adding one and another cylinder to any given type is easily ascertained by the engineer; and he can then, in such cases, readily determine whether the gain fairly to be anticipated is sufficient to com- pensate the cost of its acquirement, and to give a fair margin of profit. Another important inference from what has preceded is that the question of use of one or another type of multiple- cylinder engine is not primarily settled by the magnitude of the steam-pressure to be adopted ; although it may be taken as settled by experience and by the financial aspect of the question, as just indicated, that it will not usually pay to com- pound a machine working at very low pressures ; nor to adopt a third cylinder until the pressure approaches some four or five atmospheres; the advisability of adding cylinder after cylinder being, in part, determined by the rise in pressure, at the rate of perhaps not more than one cylinder for each four O04 A MANUAL OF THE STEAM-ENGINE. or five atmospheres of pressure. Whatever the pressure, how- ever, compounding will divide the total internal thermal loss, approximately, by the number of cylinders in series ; but it does not at all follow that the efficiency of engine, or the com- mercial efficiency, will be reduced in similar ratio. On the contrary, as will be seen later, it will never pay to carry the complication as far as the study of the case from this point of view would dictate. The discrepancy will be found to be the greater as the real engine more closely approaches ideal perfec- tion ; the simple engine becoming the more desirable type as the efficiency of it, and of each of the several elements of the compound engine, becomes greater. 147. As respects Size of Engine, it is now easily seen that the gain by compounding is, so far as the considerations here studied are concerned, at least, likely to prove even more marked with small than with large engines. As the wastes are invariably, under similar working conditions, greater as size decreases, the desirability of reducing those losses would seem likely, ordinarily, to be also greater. In the case of the adapta- tion of this system to small engines, the effect of cylinder- condensation remains, in each cylinder, well marked, ordi- narily, as is seen in the hitherto unnoticed effect observable where such small engines are constructed of the Wolff type, and the first effect of the cooling action of the metal upon the entering steam is shown by the sudden drop of pressure be- tween the two cylinders, at the moment of opening communi- cation ; the fall being like that seen when exhaust occurs into the atmosphere from a high terminal expansion, and amount- ing, often, to several pounds.* 148. Problems relating to the relative efficiency of the various classes of multiple-cylinder engine may now be readily solved, the needed data being obtainable, by assuming the above enunciated principles to be applicable, and first computing the efficiency of the representative ideal engine, and then ascertain- *This has been noticed and provided for by the designers of a familiar type of single-acting compound engine. SUPERHEATING AND STEAM-JACKETING. 605 ing the probable wastes of heat, of power and of work, of the several cylinders, and of the engine as a whole. Obviously, the computation for the ideal engine is the same, whether the system is simple or complex. The wastes, however, vary with each type, and with every size and proportion of engine. If, as is now often possible, we may ascertain the approximate measure of waste for each cylinder and for each engine, what- ever its type, it becomes perfectly practicable to determine the relative merits of each, and the probable efficiency and con- sumption of heat, of steam, and of fuel, also, if the efficiency of the boiler is given or can be computed. The difference of efficiency among the several types or examples indicates the relative standing of those various examples, and furnishes the basis for computation of all the efficiencies. The following are illustrations of approximate solutions of such problems, as arising in common practice or as illustrated in the experiences of the engineer seeking to ascertain which of all available designs is the best for the special purposes in view: The differences between the steam-consumption figures of the two tables given in the preceding chapter for the ideal and the actual efficiencies of simple engines have been seen to be the measure of those wastes which may be largely reduced by compounding ; a nearly constant quantity, 6 pounds of steam for the condensing and 10 pounds for each form for the non- condensing engines. A two-cylinder compound engine should reduce these wastes to approximately 3 and 5 pounds, a triple-expansion to 2 and to 3.3 pounds. Case No. 5, in the last table, using 23 pounds of steam per hour per horse- power, would, as a compound engine, demand 20 pounds, as a triple-expansion 19 pounds, and as a quadruple-expansion engine about 18.2. A familiar type of tandem compound high-speed engine is usually operated at a pressure of about 1 10 pounds by gauge, at a ratio of expansion of 9 and with cylinders having the ratio of 2.3 to I. The following is the result of investigation 606 A MANUAL OF THE STEAM-ENGINE. of this case, thermodynamically. It is first assumed that tl;c engine is supplied with steam of variable pressure, next that the pressure is constant at the figure intended by its builders and the ratio of expansion varied. The deductions from these studies of efficiency are that both the boiler-pressure and the ratio of expansion assumed by the builders are very nearly ideally right for best economy with that form of engine. Fur- ther gain could be better secured, however, in this case, by an increase of the expansion than by that of the steam-pressure at the given ratio of expansion. It is here assumed that the friction of engine is 10 per cent, the efficiency of machine being 90 per cent, and that jacket-wastes are 8 per cent, and external radiation 5 per cent ; the net "efficiency of engine" thus becoming about 77 per cent the thermodynamic " efficiency of steam." The pressure in the valve-chest is taken as 0.97 that in the boiler. It must be borne in mind, however, that the investigation represents the ideal, not the actual, case, and that the consump- tion of steam and fuel and the real efficiencies will be some- what different ; possibly varying from the computed figures 10 to 15 per cent, and correspondingly reducing the ratio of ex- pansion and the pressure for best effect. HIGH-SPEED ENGINE. Variation of Pressure, f, = 4 ; r = Ki X K* - 9. Boiler pressure ft 50 75 IOO no 120 140 160 1 80 Engine " Pi 48.5 72.8 97.0 107 116 125 155 175 Receiver " A 20. 8 29.0 37-2 40.5 43-8 50.3 50.9 63-4 Mean total" Pm 9.15 12.8 16.4 17.8 19-3 22.1 25-3 27-9 Meaneff. " A 5-15 8.76 12.4 13.8 15-3 18.1 21.0 23.9 " Heat-pressure". . . A 50.8 69.0 87.2 94-5 1 02 116 131 155 Effic. of Steam Et O.IO .127 .142 .146 .150 .156 .l6l .163 Effic. of Engine . 0.08 .099 .in .114 .117 .122 .126 .127 "Water-rate" w 17-3 13-8 12.5 12.0 ii. 8 II. 2 IO.g 10.8 SUPERHEATING AtTD STEAM-JACK ETIXG. 6o/ * = 106.7. Ezpansioa ratio ---- r 6 8 10 12 15 iS 21 Receirer pressure . . f, 4* 4* 39 39 37 35 34 Total mean 4 .. /. 22.4 17.9 14- 5 "-3 9-9 6-94 5-34 MeancffectiTe" ../ 18.4 13.9 10.5 8.29 6.42 4.94 3.86 "Heai-preasore'.../^ 206 134 92 7 48 36 27 Efl&c, oi Steam ..... , 0.09 .102 .113 .120 .129 .134 .138 "Engine ---- , 0.07 .000 .089 .094 .102 .105 .109 " Waier-raie" ...... W 14.2 12.3 n.i 10.5 9.65 9.35 9.0 The actual efficiencies will be reduced by the wastes to considerably smaller figures, as hereafter shown, and the water- rate thermodynamically computed will be increased, in such engines, ordinarily, by ten pounds, more or less, according to size and speed of engine, clearances, and other variable condi- tions affected by design, construction, and operation. With compound engines, the added quantity may be taken, for en- gines of considerable power, as about 6 pounds for compounds, 4 for triple-expansion, and 3 for quadruple-expansion. The compound non-condensing engine is often employed, especially where it is difficult to secure a good and unfailing supply of condensing water. The following are the results of the investigation of this case, taking the total absolute press- ure, and the back-pressure constant, as below, and assuming a variable ratio of expansion within the limits r = 2 and r = 20. The Rankine exact method and formulas are employed as before. Let/, = 180 Ibs. per sq. in., absolute ; /, = 16; r = var- iable. Assume the available heat of the fuel at 10.000.000 ft.-lbs.. and the evaporation to be 10 pounds of steam per pound of coal, as representing best practice, with a good feed-water heater and dry steam supplied at the steam-chest. Steam used, unity; v t = 2.315. Then we obtain, in the mariner already indicated : 608 A MANUAL OF THE STEAM-ENGINE. NON-CONDENSING ENGINE. IDEAL CASE. U 404,330; /i = 180; /> a - 16; ^ = 140 F.; 7*4=600 F.; ^,=2.315; /&4 = 83,459. 4.6-? " J 5-79 j'jjj 7.72 3 11.58 23.15 a 30.87 46 1O / Q*VJ[ 94.07 74.12 54.57 35.70 17.00 14.50 H*-' 1 j*-> 8.12 77, 357,280 342,595 323,977 298,282 255,838 2A7 T AA 21 c 2S& H t 911,263 907,385 902,646 896,456 886,867 *<\ 19 x *t*f 885,006 ^1 D>^0 878,462 U' 47,407 62,071 80,6^0 106,176 148,515 157,140 188,707 h . . . 874,849 885,661 899,540 918.945 952,830 958,733 984,075 M. E. P... 71.1 74-5 72.6 63-7 44-5 34-8 28.3 h (rej.)- - 827,442 823,590 818,890 812,861 804,315 801,593 795,308 Effic. St. p. c.. 5-42 7.01 8.96 "5 15-4 16.4 19.2 Fuel per H. P. per hour 3.65 2.81 2.21 1.72 1.28 1. 20 IO.2 Steam per H. P. per hour. 36.5 28.1 22.1 17.2 12.8 12.0 1.02 REAL CASE. Assume steam-wastes approximately constant at 6 Ibs. ; engine-friction to demand 3 Ibs. steam in excess of that com- puted. Indicated Power. Steam . . . 42.5 J.*t* fc 7 34.1 28.1 23.2 18.8 18.0 16.2 Dynamometric Power. Fuel 4.52 3.71 3-H 2.62 2.18 2.10 1.92 . 45.2 37.1 31. 1 26.2 21.8 21. IQ.2 As another interesting case, assume a boiler-pressure, />! = 250, absolute, and back-pressures of 16 and 5 pounds, respectively, for the non-condensing and the condensing en- gine, feed-water temperatures 203 and 104 F., jacketed engines of such size and speed as to give internal wastes approximating 0.075 \/r, due to the action of the exhaust- SUPERHEATING AND STEAM-JACKETING. 609 period. Take Rankine's system of computation for the jack- eted engine as the probably best approximation. Take the evaporation at 10 and 9 pounds for the two cases, respectively. Determine the variation of efficiency with varying expansion. In this case, it will be seen that the variation of coal-con- sumption will differ from that of steam, in consequence of the fact that a part of the heat supplied the engine enters by way of the jacket, and, when condensed, this portion of the steam simply flows back to the boiler if the drain-pipes are properly arranged and does not enter into the measure of feed-water supply ; though the heat which it conveys comes from the fuel, as really as does that transferred by the steam entering the cyl- inder. The fuel may thus be divided into two parts : that sup- plying heat to the entering steam ; and that giving heat to the jacket. The measure of the heat supplied by the jacket may be obtained by deducting from the total computed heat-supply that required to furnish the steam entering the cylinder with its initial store. This gives us The weight of water and of steam worked in the cylinder is. per H. P. per hour, W= 1,980,000-=- If ', where V is the work performed by one pound of steam. The division of this quantity by the rate of evaporation gives the weight of fuel. It will be observed, on examining the tabu- lated results of such computations, that the minimum water- rate does not correspond, precisely, to the maximum efficiency; a consequence of the steady circulation of the jacket-steam and water. The minimum coal-consumption, on the other hand, does correspond exactly with the best efficiency; as it should. The following are the data and results of com- putation : 6lO A MANUAL OF THE STEAM-ENGINE. STEAM-ENGINE EFFICIENCY: IDEAL AND ACTUAL. NON-CONDENSING ENGINE. /i =250; vi ... 5 = 1.84; / 8 3 = 16; Ui Ideal Case. 10 = 420,280; 15 * = 132, 20 g.2 14.7 18.4 27.6 36.8 ff . . 875 141 897,647 908,357 927,296 940,694 Ay.. Ef 77,890 o 1671 100,396 .1794 111,106 .1821 130,045 .1793 143,443 .1-20 W.. 13-54 1.35 12.29 1.23 11.96 i. 20 11.91 1.19 12.24 1.22 Ft o. 14 0.16 0.17 0.19 0.22 p 1.39 1.37 1.38 1.44 5 8 Real Case. 10 15 20 i+< E e t fr.. 1.17 . ... 0.143 1. 21 .148 1.24 .147 1.29 .139 1-34 .129 W it 82 14 90 14 80 15.37 16.34 F... 1.74 1.68 1.69 1.78 1-93 CONDENSING ENGINE. / = 250; v, = 1.84; /a = 5; U\ = 420,280; A 4 = 55,612. Ideal Case. r. . v*. . , 5 9.20 . . 951 889 IO 18.40 985 105 20 36.8 1,017,442 30 55-2 1,036, 144 40 73-6 1,049 J 8 50 92.0 i 059 080 hi 143 443 162 145 185 081 Ef . W 0.169 12 32 .198 .216 .221 8 66 .220 8 =H .216 8 fa F, . Ff 1-37 12 I.OO 17 .96 _95 .96 F , 1.27 I 17 I 13 5 Real Case. 20 E e .. W .. F... tV~r.. I- 17 145 H.38 . 1.74 1.24 .160 12.58 1.57 1-34 .162 12.01 1.41 .156 12.36 i. 60 1.47 .149 12.66 i. 60 1-52 .141 13.24 1.70 The above corresponds to the case of an engine of perhaps one thousand horse-power, working under favorable conditions ; SUPERHEATING AND STEAM-JACKETING. 6l I a simple engine, well jacketed, and supplied with dry or slightl} superheated steam. With effective superheating and at the best expansion ratios, the wastes have been actually brought down, as reported on trials made by engineers of reputation, to an additional four pounds of steam and half pound of fuel, and with considerably lower pressures ; or, for the best cases to- date, the performance has been made to approximate within thirty or forty per cent of the ideal minimum. All these cases, however, fail to represent modern practice ; since they do not assume a sufficient expansion to give best results when compounded. The benefits of the multiple-cyl- inder type are best seen with extreme ratios of expansion, where internal wastes would prove excessive in the simple engine. 149. As Examples of coming problems, and as better illus- trations of advanced practice, take a quadruple, compared with a triple-expansion, engine at a pressure of 200 pounds per square inch, absolute, with a back-pressure of 8 pounds and a total ratio of expansion of 16, or of 2.5* in the one case and of 2* in the other. The condenser is worked at a temperature of 1 50 F., in both cases, the feed being at 145 F. The friction of engine is taken in both at 15 per cent, the efficiency of machine being 0.85. The boiler evaporates nine pounds of water per pound of coal. The engines are jacketed efficiently, and of such proportions that the waste may be fairly taken to be probably measured approximately by the factor c = -~ V~r = 0.15 V~r = 0.15 l 7 ^ for the one case and c = 0.15 ^~2 in the other, or 24 and 21 per cent, for the three- and the four- cylinder engines, respectively. For a single engine, of similar character, in this respect, it would be = 0.15 VT6 = 0.60, nearly. Adopting the method and formulas already employed, we obtain the following results : For the ideal case, which would give the same figures for both engines, we find the following, the slight discrepancies 6l2 A MANUAL OF THE STEAM-ENGINE. being due to the corresponding difference in total expansion, taking the one to work at a ratio of 2.5 for each cylinder, and the other at 2 : IDEAL MULTIPLE-CYLINDER ENGINE EFFICIENCIES. Engine. No. Cylinder. E. B. T. H. per I. H. P. Water per I. H. P. Coal per I. H. P. 1 Triple Total I 2 3 .0811 .0730 .0779 .231 11761 10.85 I.-JC Quadruple. Total i 2 3 4 .0637 .0598 .0580 .0598 2414 11577 10.68 The consumption of water and of fuel is thus seen to be ex- extremely low, as compared with the actual performance of the preceding cases of simple engines at lower pressures. Adding the prescribed allowances for internal wastes, we have : EFFICIENCIES OF REAL ENGINES. Engine. Water per I. H. P. Coal per I. H. P. Ideal Simple Triple I* 4 r 3 ! I 4 Had these engines been unjacketed, assuming waste greater by one third in the actual and unchanged in the ideal case, we might probably have obtained the following : UNJACKETED REAL ENGINES. Engine. Water per I. H. P. Coal per I. H. P. Ideal .... I 2 Simple 2 2 1.6 13 8 1.5 SUPERHEATING AND STEAM-JACKETING. 613 The gain by increasing complication thus decreases as the number of cylinders increases, whatever the rate of internal waste. Going into higher and unaccustomed pressures, it may be interesting to endeavor to compute the probable performance of a well-designed quintuple-expansion engine, working at a pressure of 500 pounds per square inch. The ratio of expan- sion is taken at r = 2.3* = 64.4, the back-pressure at five pounds. These results may be compared profitably with the case of the simple engine discussed in Chapter V, 137, in which somewhat similar data are taken. Assume data thus: QUINTUPLE-EXPANSION ENGINE. Data: pi 500 X 144 = 7!>ooo Ibs. per sq. ft. A = 5 X 144 = 720. r = 2.3 s = 64.4. Results : /, = 862.2 Ibs. per sq. ft., 6 Ibs. per sq. in. Heat expended per lb., H 27,324 ft. Ibs. = 1898 B. T. U. 77- p t = -jf = 4464 Ibs. per sq. ft., 31 Ibs. per sq. in. '* p h = 17,330 Ibs. per sq. ft, 120.3 Ibs. per sq. in. Efficiency of fluid, E =%= 0.2576. Pk B. T. U. per I. H. P. per hr. = 10,189. Steam per I. H. P. per hr., at 1 100 units per lb., = 9.32 Ibs. Coal per I. H. P. per hr., at 9 Ibs. evap., = 1.03 ; say i lb. For this case, therefore, the weights of steam and of fuel, for unity efficiency, would be approximately 2.4 pounds, and about 0.3 pound per horse-power per hour. Were the internal wastes to be taken as in the first part of this discussion, as indi- cated by experiments the rereferred to, we should have the fol- lowing, assuming the losses to be reduced in proportion to the number of cylinders employed, and the efficiency of mechan- 6i 4 A MANUAL OF THE STEAM-ENGINE. ism to be 0.95 for the simple engine ; 0.90, 0.90, 0.85, and o.8s for the compounded engine in the five cases given, respectively : EFFICIENCIES OF MULTIPLE-CYLINDER ENGINE. Engine. Water per I. H. P . Fuel per I. H. P. E. E. Water per D.P.H. Fuel per D. H. P. Pounds. 9.32 Pounds. I I Pounds. 9.32 Po nds. Simple jacketed Double-expansion 20.5 14.9 13.0 2.2 1.6 95 90 GO 21.4 16.5 15.0 -4 .8 .7 euadruple-expansion . . uintuple-expansion . . 12. 1 II. 6 1-34 1.24 ss 85 14.4 13-6 .6 5 The above is sufficient to give a fair idea, assuming the figures satisfactorily approximate for the conditions assumed, of the advances to be anticipated through the use of higher pressures and ratios of expansion, and with saturated steam. These figures may be further decreased by increasing boiler- efHciency, by superheating the steam, and by other methods of improvement. 150. The General Results of Experience and of experi- ment accord, very satisfactorily, in cases of good design and construction and of good management, with the deductions and computations which have now been presented. Differences of type produce differences of performance, however, that sometimes modify the general conclusions which have been stated, to an observable extent. Thus the conclu- sions of Hallauer, after comparing the performance of the simple Corliss engine, with its efficient valve-gear and small clearance-spaces, with the ordinary Woolf compound, both working at about 5 atmospheres pressure, were that the one was substantially equal to the other ; although the ratio of ex- pansion of the latter was comparatively large, and both at their best working ratios.* This fact is probably quite as much due to the comparatively small port-spaces and clearances, and the separated steam and exhaust ports of the Corliss engine, as to any other cause. Trans. Soc. Indust. de Mulhouse; 1878. SUPERHEATING AND STEAM-JACKETING. 615 A notable difference between the conditions dictating the design and construction of the locomotive and the marine en- gine is observed in these facts : the former must be proper, tioned and built to meet a great range of resistance and speed ; as it must, on a level, haul at high velocity against low resist- ance ; on a steep gradient, it must pull heavily at low speed. It may at one time haul light passenger trains, at another handle a heavy and slow merchandise traffic. The latter, on the other hand, has a steady load and practically constant speed, under ordinary conditions of operation. The locomotive is given large cylinders to meet the exigencies of heavy loads, and a link valve-gear to give high expansion and compression ratios under the opposite conditions. This is not as essential with the marine engine; with which, since the power demanded varies as the cube of the speed, the variation of velocity is usu- ally moderate. These differences favor the use of the multiple- cylinder engine at sea more than on land, notwithstanding the fact that it is less affected than the older type by variations from the normal load. The necessity of proportioning the locomotive for its maximum pull and the comparatively con- stant liability to enormous variations of load and speed, its short periods of working and frequent stops, and its exposed cylinders and exaggerated wastes, are all conditions telling against this engine. Experience at sea indicates that a good double-cylinder, compound, engine, with steam at 100 pounds by gauge (7 at- mos., nearly) should not demand more than 2.2 pounds (l kg.) of fuel of good quality per horse-power per hour; a triple- expansion engine 1.8 pounds (0.8 kg.) ; and a quadruple-expan- sion engine 1.5 pounds (0.7 kg.); the steam-pressures and ratios of expansion adopted being appropriate to each. The very considerable economy to be noted in such com- parisons is not usually wholly attributable to differences in de- sign and construction of engine. The greater steam-pressure and resultant higher ratio of expansion adopted with the later engines is generally, in part, the cause of the observed gain. But the simple engine could not be economically worked with 610 A MANUAL OF THE STEAM-ENGINE. as high a ratio of expansion at such pressures as the compound engine, and the latter thus possesses a decided advantage ; which advantage is, as is now known, due to its better ar- rangement for checking exhaust-wastes. Trials of agricultural engines, made by Sir Frederick Bram- well and Mr. Anderson,* indicate that the efficiency of machine may be as high in compound as in simple engines, and give for the value of this factor from 0.75 to 0.94, the common values approximating 0.85, the steam consumed being about 33 pounds per dynamometric horse-power and per hour in the best simple engines, and 22 in the better class of small com- pound engines; the corresponding coal-consumption being nearly 3 and 2 pounds, respectively. The total friction of en- gine was thus about 15 per cent of the total power, or 3 Ho P. on a 2O-H. P. engine. On the steamer Suez, the replacement of two-cylinder com- pound by quadruple-expansion engines was reported, "with the same kind of coal, the same revolutions, the same speed of ship, and the same propeller," to have reduced the fuel-con- sumption 34 per cent. The steam-pressure was raised, how- ever, to above 150 pounds.f An experience extending over three years, according to Mr. R. Wylie, with steamers having compound and triple- expansion engines gave a marked difference in favor of the latter, the former using nearly 14 tons a day, the latter loj; the former averaging 2.16 pounds of fuel per horse-power and per hour, the latter 1.414 The quadruple-expansion engines of the steamship Singa- pore were reported, in 1890, to have demanded but 1.122 pounds of best navigation coals per hour, per I. H. P. The compound pumping-engine designed by Mr. Corliss, in 1879, f r tne Pawtucket (R. I.) water-works, a small engine of but 15 and 30 inches diameter of cylinders and 30 inches stroke * Jour. Royal Agricult. Soc. of England; vol. xnu 1887. f London Engineer; Feb. 24, 1888; p. 162, t Trans. Brit. Inst. M. E.; 1886. SUPERHEATING AXD STEAM-JACKETING. 6l/ of piston, was reported, in the year 1889, to nave given, for the year, an average duty of 124,500,000 foot-pounds for 100 pounds of fuel consumed, on an evaporation of approximately 9 pounds of water per pound of fuel, or 13.7 pounds of steam and of feed-water, and 1.5 pounds of coal, per horse-power per hour for the whole year.* This extraordinary, probably unexampled, result is presumably due to the high steam-pressure (125 pounds by gauge) : the choice of the most economical ratio of expan- sion (18) for that case ; continuous steady work against a high head ; unusually high speed for a pumping-engine (50 revolu- tions per minute), and remarkably good proportions and con- struction. In this engine, heads as well as sides of both engines are jacketed ; but with apparently small practical advantage, either because of its speed, its employment of superheated steam or of an actual defect in jacketing. An examination of records of trials of 60 engines in various parts of the world, and under a great variety of conditions, and for periods averaging about five months, gives an average gain of 1 8 per cent, in comparing the compound locomotive with the simple engine.f Trials in the United States, on the E. Tennessee, Va., and Ga. Railway, resulted in the reporting of a gain of 1.6 pounds fuel per train-mile, or of 19 per cent, for standard engines, and of 4 pounds per mile, or 31 per cent, for lo-wheel engines by compounding.* Mr. Urquhart reports a gain of i8 per cent in liquid fuel during the year 1890 and on a million of miles run. The economy of the multiple-cylinder engine is thus seen to be mainly due to the cascade-like action of the machine, in its disposition of the heat-wastes in such manner that, with a given total range of expansion, the total internal waste is re- duced approximately in proportion to the number in series : but it also is, in part, a consequence of the fact that the total condensing power is, or may be, less than that of the single * Annual Report. \ Compound Locomotives; A. T. Woods; Jour. Assoc. Eng. Societies; Maj 1890. \ Railway Review; 1890. 6l8 A MANUAL OF THE STEAM-ENGINE. cylinder that might displace it. Comparing the condensing power of a triple-expansion and of a compound engine, for example, with that of the corresponding simple engine, as measured by the product of range of temperature in each cylinder by its cooling surface, it will be found, as shown by M. Demoulin,* that the ratios of the sums of these products for each engine is not far from 65, 75, and 100, respectively, for usual practice; the reciprocals of which ratios, 1.3, 1.33, and i, nearly, measure rather closely the commonly stated ratios of relative economy. Assuming a steam-pressure of approximately 127 pounds per square inch by gauge, a ratio of expansion of 10 and a back-pressure of 4 pounds, M. Demoulin* compares, in this re- spect, the simple, the two-cylinder compound, and the " triple- expansion" engines. These have diameters, respectively, of I metre, of o m .75 and i m .5, and of o m .6i, o m .g6, and i m .5 ; and lengths of stroke, of i m .5 for the first and I metre for the others. Multiplying the ranges of temperature in each cylinder by the total areas of cylinder exposed to steam, their products are compared and the triple-expansion engine shown thus to pos- sess an advantage of 15 per cent over the double and 34 per cent over the simple engine.f The work of the compound engine illustrates a feature of the more economical types of that engine which is especially valuable when the load is not fixed and appropriate to the machine. Thus, in the figure, we have the method of variation of economy with varying ratios of expansion with three types of single-acting engine. It is seen that the efficiency of the compound is comparatively unaffected within any usual range of variation of load. In the figure the upper curve represents the efficiency of the non-compound engine under variable loads. Many tests have * Machines a Vapeur; Paris, 1890; p. 6. f Etude sur les Machines Compound a Triple Expansion; Paris, Baudry & Cie.; 1885. SUPERHEATING AND STEAM-JACKETING. 619 determined the two corresponding curves for the compound engine, both with and without vacuum. This peculiarity of the more economical type of engine makes it the more desirable where varying resistance is to be encountered. As a general result of experience, it may be concluded that, for the average case, with good engines of the several classes : (i) The volume of steam shown by the indicator, when superheated, or thoroughly dry, steam is used in well-jacketed compound engines, of moderate size, is nearly the same as FIG. 155. ECOK computed for a similar ideal engine, both at cut-off and at the end of stroke. The actual excess may be taken as not above fifteen per cent by weight at the first and ten per cent at the second point, if we follow Hirn, in such cases as were studied by him. (2) Ordinary, nearly dry, steam i.e., not containing five per cent moisture worked in jacketed simple engines, may usually be expected to exhibit an excess at least one half greater than in the preceding cases, for good average practice. (3) Moderately wet steam in any jacketed engine, or dry 02O A MANUAL OF THE STEAM-ENGINE. steam in an unjacketed engine of any considerable size, may be expected to exhibit a waste of the kind here considered increas- ing rapidly with the ratio of expansion, and often double in amount that observed in the first case, above, in even good practice. (4) Wet steam, in small and unjacketed engines, especially if worked at low speeds, may be expected to be condensed to such an extent as to give rise to expenditures of heat, steam, and fuel enormously in excess of, often several times greater than, those computed for the similar ideal case. (5) The advantages of thus placing cylinders in series is less as wastes are less in the simple engines, as costs are less, and, in more detail, as the steam is drier, expansion less, speeds of engine higher, and as power demanded is greater ; and the number in series is less for best effect, in all cases, as the performance of the actual engine approaches more nearly that computed for the ideal. 151. The Balance of Forces at the main shaft, in the multiple-cylinder engine, may often prove a matter >>f real con- sequence. Mr. John Elder, in 1866, stated that it was perfectly possible that a saving of 10 per cent and more of the indicated power might be wasted in an engine by avoidable friction at the shaft.* He ascribed much of the advantage of "compounding" to the division of the work of the engine and to the better con- sequent adjustment of pressures on the shaft and pins. A three-cylinder engine, with its cranks at angles of 120, may be made to work with almost a balance of thrusts and pulls at the shaft. A double-cylinder compound engine, with cranks set opposite, is also thus advantageous; and, in both, the maximum pressures become a fraction of those in the simple engine. The comparison of three similar British naval vessels, the Arethusa, the Octavia, and the Constance, fitted, respectively, with a pair of simple, trunk, engines, with cranks at 45, a set of three single cylinders with cranks at 120, and a three-cylin- der "compound " engine, in 1865, running from Plymouth to Rankine's Life of Elder; 1871. SUPERHEATING AND STEAM-JACKETING. 021 Funchal, resulted in giving, as the fuel-consumption, 3.64, 3.17, and 2.51 pounds per horse-power per hour; while the last two ships are reported to have shown a relative efficiency of mech- anism of 100 to 127; or of 79 to 100.* This difference was slightly lessened as speeds and power increased. The last- described disposition of the engine also conduces to smooth- ness of motion and to regularity in crank-pin pressures and turning moments. Variations of pressure on the running parts of the engine, due to extreme ranges of expansion, in the simple engine, may sometimes, and especially in marine engines, prove objection- able, and thus to constitute another argument in favor of the use of the multiple-cylinder engine. The steamers Polynesia and Circassian, of the Allan Line, were originally fitted out, the one with compound, the other with simple, engines. In all other respects they were alike. They were so designed that the same expansion could be adopted in both. The result was that the simple engine was badly shaken and injured, the ma- chinery was removed, and engines similar to those of the Poly- nesia were put in, with thoroughly satisfactory results.f The extent to which the stresses and strains due to high- pressure steam are relieved by " compounding " the engine may be readily seen by computing these quantities for parallel cases. It will be found that the simple engine is subject to double stress when expanding 10 to 12 times, as when working at a ratio of expansion of 3! to 4, and must be correspondingly heavier and stronger. In multiple-cylinder engines, the total stresses may be made substantially equal in each, and the range of pressure reduced, and the strains as well, in similar propor- tion. A condensing triple-expansion engine, at ten atmospheres pressure (150 Ibs.) by gauge, would be subject to about one fifth the stresses, on each piston and its connections, that would come upon the piston of its large cylinder, if all the work were done within it, or in a simple engine of the same size. * Rankine's Life of Elder; p. 44- f King: Report on European Ships of War; 1877. 622 A MANUAL OF THE STEAM-ENGINE. This reduction of loads is so considerable that it is actually possible, at high pressures, to save weight of engine by com- pounding. At very low pressure the simple engine has the ad- vantage, both in weight and efficiency. From the constructors' point of view, "compounding" the steam-engine often becomes, with the now usual boiler-press- ures, a matter of vital importance ; since it would be imprac- ticable to successfully work the simple engine under those pressures, and with the enormous variations of pressure due to a high ratio of expansion. To do so would compel the adop- tion of such size and weight of parts, and such special propor- tions of journals, as would make the engine excessively heavy and costly, while at the same time causing great loss of engine- power through the friction of its own parts. 152. Steam-jackets on Engines, whether simple or other, have one and the same main purpose, in every case and on every type the reduction of internal wastes due to initial con- densation. In the older Worthington direct-acting type, and perhaps in other pumping-engines, the use of the jacket may bring an incidental advantage of some practical value, enabling, as it does in this case, the stroke to be completed at a higher ratio of expansion than it could otherwise be, a result of the higher terminal pressures produced by it, and of prevention of water in the cylinders. A special reason for the use of the jacket on engines liable, as is the Cornish pumping-engine, or to a certain extent in marine engines, for example, to be stopped occasionally for in- tervals of greater or less length and to be started up again at a moment's notice, is that the cylinder can be kept heated, the engine "warmed up," however long the stop, and thus kept in condition for immediate starting, without danger or delay. The jacket also, incidentally, is useful in keeping the bore of the cylinder unstrained, if properly constructed. This is con- sidered so important that, in some cases, the "liner" is inserted only after the engine is set up in place. As is well known, the use of the steam-jacket was original with Watt, who remarks, in a letter to Professor Jardine, that. SUPERHEATING AND STEAM-JACKETING. 623 after his experiments on the Newcomen model, his next, and an easy, step was " to inquire what was the cause of the great consumption of fuel. This, too, was readily- suggested: viz., the waste of fuel which was necessary to bring the whole cylinder, piston, and adjacent parts, from the coldness of water to the heat of the steam no fewer than 15 or 20 times a minute." * He invented, first the separate condenser, then the st^.-jn- jacket, in order " to keep the steam-cylinder as hot as the steam which entered it." The cause of the great internal waste detected by Watt is now well known and has been de- scribed as cylinder, or internal, or initial condensation. Combes, in papers presented to and published by the Aca- demic des Sciences, was probably the first to introduce into the theory of the steam-engine the consideration of that phenome- non, discovered by Watt, to check the wasteful effects of which the latter invented the steam-jacket.f That author gradually gave shape to his ideas, as time went on, publishing them in 1845.* and, later, in i863~67. He says in his first paper, just mentioned : " The utility of the jacket, or rather that of heat- ing the cylinders of steam-engines from the outside, ... is rendered unquestionable, both by direct experiment and by detailed observation of the phenomena characterizing the action of steam in the cylinder, and the logical discussion of these ob- servations." " Jackets have not for their main result the main- tenance of the temperature of the steam during expansion ; their use consists in the prevention of refrigeration of the walls of the cylinder while in communication with the condenser :" probably the first exact statement of this effect ever printed. [ Mr. Gill, as early as 1844, says : " If the cylinder be supplied with dry steam, and no heat is dissipated by radiation, there will still be a loss of heat in the cylinder occasioned by the sudden expansion of the steam when the communication with * History of the Steam-engine; Thorston; p. S3. t Comptes Rendos; 1843. Traitfe d'exploration des Mines. Priocipes de .'a Tbeorie Mecankme de la Cbalenr. | Memoirs of 1*43; P- *45- 624 A MANUAL OF THE STEAM-ENGINE. the condenser is opened. ... As the heat for evaporation is furnished by the hot metal of the cylinder, piston, etc., such heat must be returned to them by the condensation of steam during the succeeding stroke, such condensation and evapora- tion going on until an equilibrium is established." He sug- gests superheating as the best remedy.* Hirn published his Mtf moire sur /' Utility des Enveloppes it Vapeur in 1855.! This memorable paper gives us the first analysis of experiments showing the quantitative measures of the thermal action of the walls of the steam-cylinder. He concludes : " (i) There is a capital difference between the thermal phe- nomena characterizing two types of engine : In the simple en- gine, the cylinder-walls always yield heat to the steam during expansion ; though the amount is less when the jacket is work- ing than when shut off. In the Wolff engine, the surfaces of the cylinder take heat from the steam, even during the expan- sion, and lose it again during the exhaust." " (2) With the simple engine the walls of the cylinder give to the steam the same amount of heat with as without the jacket ; but, in the former case, the heat is given up during the expansion, and thus, without cost, adds considerably to the amount of work done ; while, without the jacket, this heat is all lost by being thrown into the condenser without doing any work, uselessly evaporating the condensed water, mainly after the exhaust-valve has opened." As explained by many recent writers, the benefit of the jacket comes of the facts that it not only reduces initial con- densation but insures that a part, at least, of such heat-waste as does take place shall occur through condensation within the jacket, where it does no additional harm, instead of in the cyl- inder, where it would produce, indirectly, wastes out of all pro- portion to its own amount. It is by allowing the surfaces of the cylinder exposed to the entering steam to become as hot, ap- proximately, as the steam itself, and nearly or quite dry, so as * Improvements of the steam-engine; Weale's paper; Jan. 1844. f Bulletin de la Societe Industrielle de Mulhouse; t. xxvn. pp. 105-206. SUPERHEATING AND STEAM-JACKETIXG. 625 to largely check, if not to prevent, initial condensation, that the steam-jacket gives its economic advantage. As has been well stated by Holmes : * A jacket operates in two ways, in keeping the temperature of the cylinder-walls constant : first, by keeping the working steam comparatively dry, it reduces the power of the sides of receiving heat from, and of giving it out to, the former, and thus deprives the sides of the power of taking up the extremes of temperature which would otherwise be possible ; and, second, whatever differences of temperature would actually occur are further greatly re- duced by the flow of the heat from the jacket-steam to the inner walls of the cylinder. It is only the heat supplied in the latter process which costs the jacket-steam anything. The great gain due to the rendering of the working steam non-con- ducting and non-radiating costs nothing whatever ; seeing that it is an indirect effect of keeping the sides hot. Thus, the steam-jacket, though for half the time warming the exhaust, has proven in the majority of cases to be an undoubted source of economy." * The operation of the jacket may thus be defined to be that of improving the working fluid, converting a defective into an efficient, changing a heat-absorbing into a non-absorbing ma- terial, a wet into a dry vapor, or into a gas, more or less com- pletely. Thus the quantity of heat and steam lost in the jacket is not, as often assumed and stated, precisely the equivalent of the amount which would, without it, be wasted inside the cylin- der. The real effect of the jacket is to present a compara- tively hot and dry internal surface to the entering working steam, and thus to prevent any condensation of that steam at its admission, and corresponding re-evaporation during exhaust. The transfer of heat by internal conduction is thus made to take effect between dry surfaces and through a comparatively dry medium with the result of greatly reducing the quantity so transferred and, to the extent of that reduction, adding to * The Steam-engine; 1887; p. 451. 626 A MANUAL OF THE STEAM-ENGINE. the efficiency of the engine. The jacket wastes, if it is one of high efficiency, only the quantity of heat needed to preserve the working steam in the " dry and saturated " condition. The jacket thus acts usefully in two distinct ways : (i) by preventing exchange of heat between the steam and the cylin- der-walls, by keeping the steam more nearly gaseous ; (2) by reduction of the range of temperature occurring within those metallic masses, and of their tendency to initiate and continue the waste. Throughout the whole cycle of the engine, however, the jacket is either transferring heat through the sides of the cylinder to the steam, or is compensating a previous loss by storing heat in the metal composing the inner layers of cylin- der, piston, and heads ; constantly draining heat into the engine from the boiler, and all the time wasting it ; either by transfer without transformation, or by transformation within a smaller range of temperature than the maximum. It is a wasteful device for preventing or ameliorating a greater waste. When this latter is a larger loss than that due to the jacket itself, a gain occurs; when the internal wastes are otherwise reduced to the magnitude of minimum jacket-waste, that accessory has no value; whenever, as by superheating, or other device or combination of expedients, the interior wastes are made less than the normal waste due the jacket itself, the latter can have no useful effect ; and finally, an inefficient, or an exceptionally wasteful, jacket may possibly prove absolutely hurtful. This has been observed, for example, in some re ported cases of locomotive performance, and in cases which, perhaps, the heat wasted from it during the terminal portion of the expansion-period and during the exhaust-stage is more than the equivalent of the earlier gain by reduced initial con- densation and during expansion. This last effect may be a consequence of excessive wetness of steam, causing the pres- ence of water in its mass up to and beyond the termination of the expansion-line. The action of an effective jacket, notwithstanding its pro- duction of a drain of heat into the cylinder, results in greatly SUPERHEATING AND STEAM-JACKETING. 62J accelerating the re-evaporation, and in its completion at so early a period in the stroke as to accomplish two results : (i) the conversion of the water from this condensation into effec- tive working fluid ; (2) the drying and warming of the walls of the cylinder so completely, before the succeeding admission, as to make the heat-absorption and the consequent initial con- densation minima. The net result is usually a gain by reduc- tion of interior wastes ; and the exterior losses, although exaggerated by the increased areas of surface exposed, remain insignificant when the cylinder is properly clothed. 153. The Action of the Jacket, in Detail, is probably not complicated ; but it is obscure because of the facts that it is so far out of reach of the investigator that the variations of temperature and in heat-storage and transfer affect variable quantities of metal and fluid which the engineer cannot easily measure, and are subject to intricate and uncertain physical changes of condition and quality of the mixture of steam and water, or possibly, at times, of dry and superheated steam, similarly difficult of determination. We will examine several typical cases (see 122, Fig. 140, P-473): (i) Jacket and cylinder receive gaseous steam; i.e., the fluid is highly superheated and behaves like a gas. In this case the action of the jacket tends to keep the inner walls of the cylinder up to its own temperature. Assume this possible. The gaseous steam enters the cylinder at maximum temperature, expands, doing work, constantly losing both heat and temperature, down to a minimum, at exhaust, and is finally discharged, it may be assumed, dry but saturated. Each entering charge finds the inner surface of the cylinder slightly cooler than itself, before expansion begins, but absorbs its heat continually, once expansion has begun, up to the close of the exhaust-period. This heat is partly utilized by conver- sion into work, but within a reduced range of temperature and with reduced efficiency, and is in part discharged as pure waste. But the total quantity so absorbed will be small, since the fluid has small specific heat, large specific volume, and insensible conductivity. 628 A MANUAL OF THE STEAM-ENGINE. Precisely what the internal waste would be under such con- ditions is not precisely known; but experience with gas-engines and with superheated steam would indicate that it would not usually be ten per cent in large engines, and probably not be less than five for what might be taken as fair examples. We may perhaps call eight per cent the normal waste due to the action of the jacket, and the minimum to be anticipated with the best possible jacketing. The gain by the use of a jacket is approximately the difference between this and the waste of the same cylinder without the jacket. Experience indicates this to be, usually, in such cases, a very small quantity, and often inappreciable. (2) Jackets and cylinders receive dry steam. In this case, the jacket readily keeps the external surface of the cylinder-walls at maximum temperature, that of the steam itself, and due its pressure. The slightest reduction of temperature at once pro- duces condensation in the jacket, and the temperature of the cylinder-surface next the jacket is restored by absorption and storage of the latent heat of the jacket-steam so condensed. This process of transfer by condensation is known to be one of such great rapidity that we are justified in assuming that the surface of the cylinder which is exposed to jacket-steam is kept up fully to the temperature of the latter throughout the whole cycle. Consider the four phases of the engine-cycle : (i) induction; (2) expansion ; (3) exhaust ; (4) compression. During the first, the steam has the same temperature and pressure on both in- terior and exterior of the cylinder-walls ; during the second period, differences of temperature and pressure on the two sur- faces are observed, progressively increasing to the end of the expansion and the establishment of the back-pressure ; during the exhaust, this difference remains nearly constant and a maximum; while the compression-period sees this difference once more reduced, we will assume, to zero. Thus both "prime" steam and jacket-steam at first unite in restoring to the metal heat lost during the preceding cycle, and none passes from the jacket into the interior of the cylinder. Jacket-heat SUPERHEATING AND STEAM-JACKETING. 629 flows into the engine throughout the remainder of the cycle, and is partly converted into work, partly transferred and wasted as heat ; and the proportion of these two quantities, the partial waste by inefficient transformation and the pure waste, is de- termined both by the extent to which expansion is carried and by the quality of the working fluid.* If the steam be dry or nearly so, at the close of the first period, and if the second, the expansion-period, is sufficiently prolonged, the action of the jacket and the heat-storing prop- erty of the metal of the cylinder promptly results in superheat- ing the expanding steam and so checking further waste of heat from jacket, and from cylinder-walls, during the terminal period of expansion and during the exhaust, and thus allows the jacket to raise the temperature of the cylinder promptly and fully to that of the entering steam. This being accomplished, initial condensation is, in turn, reduced to an unimportant quantity ; the total waste is mainly jacket-waste, and is a minimum. On the other hand, if the amount of water produced, either by initial condensation or by the work of expansion, or both, is so great that it cannot be all re-evaporated early in the stroke, and if the cooling of the cylinder-walls is thus continued, the jacket-waste becomes increased, the waste which it is intended to check may remain serious, and the result may be a consider- able net loss and but little or no advantage from the jacket. This must be the result, probably, to a greater or less ex- tent, whenever the drying of the cylinder and steam is not nearly or quite completed at the opening of the exhaust-valve, as when the jacket is defective or the steam too wet. It would seem possible that intermediate conditions might prove to be those of best jacket-action. The process is here, probably, one in which the first effect of the jacket, during expansion, is to dry the steam which con- tains, always, if not superheated, suspended within its mass, more or less of the water of initial condensation ; next the * The resistance to transfer of heat from the metal into a gas is 30 or 40 times as great as to water. 630 A MANUAL OF THE STEAM-ENGINE. checking of condensation due to the work of expansion, and finally the superheating of the steam, if the earlier stages are completed early enough, and existing conditions permit. The first portion of this process gives a gain of work by adding steam to that existing, as such, at the beginning of expansion ; the latter portion by giving the steam larger work-power. The whole operation is a waste of a smaller, to gain by reducing the waste of a larger, quantity of heat-energy. During the exhaust-period there is a pure waste of heat with a compensating gain by drying and heating the interior surfaces of the cylinder preparatory to the entrance of the next charge of steam. Compression has a similar effect, as a result of the conversion of the work of compression into heat. During the engine-cycle, the metal is first drenched by the water of condensation, which gives it heat from the entering steam, then cooled by evaporation and lowering of tempera- ture during expansion, and then it is dried off, and is finally warmed up, more or less nearly to the temperature of the prime steam, by the combined action of the jacket and com- pression. (3) Wet steam is supplied. In this case, the jacket, on its side, acts precisely as before. The water in the steam in the jacket drains out or is trapped off, and is returned to the boiler, leaving the steam practically dry, as before. But the interior of the engine is placed under quite different conditions : In addition to the heat demanded of the jacket to keep the working steam dry, and to first dry off and then warm up the interior surfaces of the cylinder, a quantity of heat, which, within limits, will be larger as the steam is initially wetter, and which may be often very great, is drawn from the metal and from the jacket, throughout substantially the whole cycle, to evaporate all or a part of the entrained water, and to then, if possible, dry off the metal and to heat it up again to the maxi- mum temperature. Not only is this amount of heat increased with increase in quantity of water entering with the steam ; but the proportion of heat drained off wastefully in the terminal portion of the expansion, and throughout the exhaust-period, SUPERHEATING AND STEAM-JACKETING. 631 is continually increased as the quantity of water to be evapo rated is greater ; so that it may readily be believed that the interior of the cylinder, drenched and flooded with water at the opening of the steam-valve, may continue to act as a waste-producing boiler quite through the cycle ; thus causing an enormous loss during the exhaust-period, when, the differ- ence of temperature being a maximum, the heat which the jacket is capable of thus wasting becomes itself a maximum and both absolutely and relatively very large. If the water of initial condensation is not, in any instance, all re-evaporated during the expansion-period, it will be re- converted into steam during the exhaust-period. It is thus obvious that the quality of the boiler-steam is a vitally important matter ; and it may be easily seen that dry steam is an essential element of successful action of the jacket. It may perhaps even be possible, under specially unfavorable conditions in this respect, that a jacket may do more harm by loss of heat during this wasteful period than it can save by its legitimate action earlier in the cycle. It is as unquestionably the fact that dry steam is essential to the best action of the jacket, as that superheated steam, as shown later, may render the jacket unnecessary and useless. It is uncertainty as to the condition of the steam supplied, and the probability that it may have been both wet and vari- able in its humidity, that makes it difficult to secure safe and jeliable deductions from many experiments hitherto made on jacketed engines. It is impossible to base on data obtained in such cases any useful computations. M. Him concludes, from observations made by him on en- gines with and without jackets, that the action of the walls of the cylinder can only affect the working mixture of steam and water either in actual contact or in close juxtaposition with them. This conclusion is confirmed by the computations and experiments of Cotterill and of Dixwell, and of many other authorities. Under ordinarily favorable circumstances, and in ordinary practice, as M. Dwelshauvers-Dery remarks: "If the jacket be 632 A MANUAL OF THE STEAM-ENGINE. applied to a single cylinder, it gives up little heat, although the effect produced is very considerable ; for the larger part of the heat given up by the walls, and employed in useful work during expansion, is that already imparted by the steam to the metal during admission. In a compound engine, on the other hand, the heat given up by the steam in the jacket increases the work performed during expansion."* We find, thus, that the jacket may produce economy by simply preventing external losses from the working barrel, giv- ing absolutely no heat to the steam, but simply preventing its losing as much as it otherwise would, at the critical instants, by transfer to the metal of the cylinder. It is easy to see that the use of the jacket is ordinarily advantageous by preventing transfer of heat to the metal of the cylinder during admission, and that the function of the jacket is usually substantially completed at the close of this period, and, consequently, that the engine of large diameter and small stroke, a given volume being assumed, and with jacketed heads, has, ideally at least, an advantage. In general, the greater the area of wetted sur- faces, and the wetter those surfaces, the greater is the waste and the more is a jacket needed ; but, possibly, also, the nearer may be the limit beyond which the jacket ceases to be advan- tageous. 154. Jacket-wastes and Cylinder-wastes, in the sense in which the latter term has come to be understood, must evi- dently be carefully distinguished. In an engine without the jacket, it is obvious that the latter form of loss has no limit, up to that set by the complete raising of the whole mass of metal exposed to prime steam up to the temperature of the latter, with subsequent equally complete rejection and waste of this store of energy, down to the temperature of exhaust and back- pressure ; except as the limit is determined by conductivity of metal and fluid and by restriction of the period of action. Ex- perience proves, however, that high speed of engine, by reduc- ing the time allowed for alternate absorption and rejection of * Lond. Eng'g; Dec. 13, 1889; p. 692. SUPERHEATING AND STEAM-JACKETING. 633 heat by the metal, and by making the quantity of steam passed through the engine greater relatively to this waste, may, in large engines, especially, reduce it, as a percentage of heat sup- plied, to a comparatively small amount. Jacket-wastes, on the other hand, are determined by the mean difference of temperature between jacket and cylinder and by the quality of the working fluid. In the same engine, they may be great with large expansion and small with late cut- off ; or large with wet steam and insignificant with effective superheating. But they can never become zero ; nor can a jacketed engine ever be entirely free from waste internally by complete suppression of these two forms ; both will always have sensible value, and probably considerable magnitude. The economy of steam-jacketing is evidently the difference between the total intrinsic cylinder-wastes without the jacket and those wastes with it, reduced by the amount of the jacket- waste proper. Since no heat can pass from jacket to cylinder- steam during the steam-stroke, up to the point of cut-off, and since all heat supplied later is either partly or wholly wasted, it is obvious that the net loss is a minimum, and the gain by the use of the jacket is a maximum, when, later, it dries off and brings the temperature of the interior of the cylinder up to that of initial steam with most promptness, completeness, and cer- tainty. The total jacket-waste is easily determined, and is, for many cases, well known, being obtained simply by measuring the water draining from the jacket, and deducting from the total heat which it represents that wasted externally by conduction and radiation, a quantity of small amount and easy of approxi- mate computation, if not determinable by direct experiment. It is obvious that a steam-jacket will be useful or injurious, more or less, accordingly as it wastes less or more heat by the drain constantly going on, into, and through the engine, to the condenser or the atmosphere than it saves by reducing the normal internal wastes of the unjacketed engine. It may, at one or another period, in the cycle of the engine, thus effect a net saving or a net loss ; or it may produce no sensible effect ; 634 A MANUAL OF THE STEAM-ENGINE, and the total net result may be either a positive, a negative, or a doubtful gain. Any case in which, through the use in it of exhaust steam or steam of too low pressure, or in consequence of malconstruction or misuse, the jacket, on the whole, acts as a refrigerator, will give a negative and wasteful net result. Could a perfectly efficient jacket be made, in the sense of being capable of instantly and fully supplying any demand, however sudden or great, for heat needed at the beginning of the stroke, on the interior of the engine, and could the steam be supplied perfectly dry initially, the vapor would remain per- fectly dry throughout the stroke ; none would be condensed at the beginning, to be re-evaporated later, at the expense of heat from the jacket ; and the cost would be only that of the com- paratively small normal heat-waste of a dry gas ; while a saving would be effected of substantially all the initial condensation that would otherwise have occurred, and at insignificant ex- pense. Under such conditions, the more readily the jacket surren- ders heat, the less the amount it is called upon to yield, and to waste. This was first seen and proved by Hirn. The weight of steam condensed in the jackets is a very variable quantity. It obviously may be taken as a measure of the efficiency of jacket-action ; but it may nevertheless be the fact that highest efficiency of jacket-action may not insure maximum efficiency of engine, as it may, especially with wet steam, induce excessive wastes during the exhaust-period. The amount of this condensation is variable between very wide limits. The Pawtucket Pumping-engine gives but five per cent. In Professor Unwin's report on the Worthington " High- duty" Engine he gives the jacket-water as 15 to 20 per cent of the total ;* in the Lawrence and Lynn engines of Mr. Leavitt's design, it amounted to about 16 per cent ; f in Donkin & Co.'s engine at the Eichburg paper-mill it was 10 per cent,:}: and * Lond. Eng'g; Dec. 7, 1888; p. 566. f Eng'g and Mining Jour.; Nov. 25, 1871. \ Zeitschrift des Vereins Deutscher Ing. ; Apr. 1869. SUPERHEATING AND STEAM-JACKETING. 635 about the same on the London Gas Works,* on expenditures for these several engines of 17, 14.4, 16.8, 22.2, and 25 pounds of water per horse-power per hour. The minimum jacket-drainage reported by investigators is below ten per cent and its lowest value may be perhaps safely assumed at about five per cent ; which may be taken as the jacket-waste proper. With perfectly dry steam, it has been known to be less than five per cent. By the expenditure of five to fifteen per cent in this direction, therefore, a reduction of cylinder-condensation from twenty to forty per cent down to perhaps ten or less may be sometimes effected ; and this net gain of ten to twenty-five per cent then constitutes the advan- tage of jacketing in such cases as the above. With the introduction of other methods of reduction of the second form of loss, the relative value of the jacket, and the return for its expenditure and waste become less, and, with high engine-speed and compounding, or superheating, the gain may become insignificant ; a deduction amply confirmed by experience. In the development of the thermodynamic theory of the steam-engine (1859), Rankine assumes "that the steam in the cylinder, while expanding, receives just enough of heat from the steam in the jacket to prevent any appreciable part of it from con- densing, without superheating it." This assumption is founded on the fact that dry steam is a bad conductor of heat as com- pared with liquid water, or with cloudy steam, and that after cloudy steam has received enough of heat to make it dry, or nearly dry, it will receive additional heat very slowly. The assumption is justified by the fact that its results are confirmed by experiment.t Rankine's assumption, as is now well under- stood, involves the further assumption that the jacket is pre- liminarily effective in preventing initial condensation. His theory of the jacketed engine thus becomes the theory of a dry, saturated, steam engine. * Lond. Eng'g; Feb. i, 1878. f Steam-engine; 287, p. 396. 636 A MANUAL OF THE STEAM-ENGINE. 155. Computations of Efficiency of jacketed engines and of jacket-waste may be made which are fairly approximate for good examples of actual practice. From what has preceded, it is seen that the ideal engine with non-conducting cylinder, free> as it is, from internal wastes, must have higher efficiency than the ideal jacketed engine which is subject to pure jacket-waste, but not to the second method of internal loss ; while the real engine, with its combined jacket- and cylinder-wastes, reduced by the jacket, as the latter are, to a minimum amount, is more wasteful than either of the preceding, but is more efficient than the same real engine would be without a jacket. In the ideal cases, jacketing results in loss ; in actual cases, it commonly produces gain. Could we approximate in real engines to the ideal conditions, we might lose, rather than gain, by the action of the jacket; should the jacket actually waste during exhaust more than it saves on the steam-stroke, it might also, in ineffi- cient engines, even, produce loss. It gives maximum gain under intermediate conditions and when its own waste is a minimum, while its activity in reducing other loss is a maximum. The following results of computation illustrate these deduc- tions. The methods and formulas adopted are the same as those previously presented. In all cases, the real, not the ap- parent, ratio of expansion, is assumed, and no allowance is made for compression. COMPARISON OF THE EFFICIENCY OF IDEAL JACKETED AND UNJACKETED CYLINDERS. The approximate formulas are here used, having been proved sufficiently accurate for present purposes. ASSUMPTIONS : Ideal non-condensing engines. DATA: /, = 60, 80, 100, 1 20 Ibs. per sq. in. (absolute). -=0.15 ; 0.2; 0.25 ; 0.3; 0.4; 0.5. / 3 = 1 8 Ibs. per sq. in. (absolute). T<= 110 F. SUPERHEATING AND STEAM-JACKETING. 637 RESULTS: (a) Pressures Unjacketed Non-conducting Cylinders. 0.15 0.2 0.25 0.3 0.4 0.5 pi A? A .407 .496 .572 .639 -748 .533 60: /. 24.42 29.76 34.32 3S.34 44-83 49.95 A 6.42 11.76 16.32 20.34 26.83 31.98 80: pm 32.56 39.68 45-76 51-12 59.84 66.64 A 14.56 21.68 27.76 33.12 41.84 48.64 100: pm 40.70 49.60 57-20 63-00 74-8o 83 30 A 22.70 31.60 39.20 45-90 56.80 65-30 120: p n 48.84 59.52 68.64 76.63 89.76 99 96 A 30.84 41.50 50.64 58.68 71.76 81.96 #,A = i3iA + 4,ooo A = lbs. persq. in 144 144 60 827.8 80 1094-4 100 1361.1 120 1627.8 = rp t p t Ibs. per sq. in. 144 ^A 144 i r 0.15 0.2 0.25 0.3 0.4 0.5 >,= 60 42.8 58-8 65.28 67.8 67.2 63.06 >,= 80 97 108.4 111.04 110.4 104.6 97.28 01 = IOO 151.1 158 156.8 150.3 142 130.6 i = I2O 205.6 207.6 202.56 195.6 179.4 163.9 638 A MANUAL OF THE STEAM-ENGINE. (b) Pressures Jacketed Cylinders. A 0.15 o .2 0.25 o-3 0.4 0-5 r PjH_ .417 .505 .582 .648 -756 .840 Pi 25.02 30. 30 34-92 38.88 45-36 50.40 pe 7.02 12 .30 16.92 20.88 27-36 32.40 pi = 80: pm 33.36 40 .40 46.56 51.84 60.48 67.20 Pe I5-36 22. 40 28.56 33-84 42.48 49.20 pi = ioo: pm 41.70 50.50 58.20 64.80 75.60 84.00 Pe 23.70 32. 50 40.20 46.80 57.60 66.00 /l = 1 20: p m 50.04 60. 60 . ,69.84 77.76 90.72 100.80 Pe 32.04 42. 60 51.84 59-76 72.72 82.80 I5-5A P * r \ o. 15 O.2 0.25 0.3 0.4 o-5 p for pi = 60 139 >5 186 232-5 279 372 465 ph for/ t = 80 186 248 310 372 496 620 p for pi = ioo 232 5 ' 310 387-5 465 620 775 ph for /i = 120 279 372 465 558 744 930 UD, (c) Efficiencies-, (a) For the unjacketed cylinders , = (V) For the jacketed cylinders E, = ^. A- F t *,-- 0.15 42.8_ = - 5 = II! 1361 232-5 ~' 205.6 - 1361 = .116 =.105 310 207.6 I627T 8 = - 15 16.92 1094.4 28^56 lj *r- 1361 40 2 387.5 202 . 56 827.8 "t- 1094.4 372~ " I50_3_ = 1361 46,8 __ 465 '95.6 . 1627.8" 27.36 T^T 66 627.8 82.8 SUPERHEATING AND STEAM-JACKETING. 639 (a) For Maximum Efficiency of Fluid. /, 60 80 100 120 0.3 0.25 o^ Ot2 E t jo82 .101 .116 .128 /:, JO75 .092 .105 .114 .914 .911 .905 -899 It will be observed that maximum efficiency of fluid in- creases as/, increases, and the value of r for maximum efficiency also increases as/, increases ; but the value of -j? decreases as /, increases that is, the loss due to the jacket increases, in these ideal cases, with increase of initial pressure. (>) Fuel-amstimptwn. Assume an effective evaporative power of 9 to I ; then the available heat per Ib. of coal = 6,700,000 ft. Ibs. 60 X 33*000 0.295 r vx f- = ~- = Ibs. of coal per H. P. per hour. E X 6,700,000 E IDEAL ENGINE. FUEL-CONSUMPTION. /,... 60 8O IOO I2O Lbs. coal per H. P. per hr. Unjacketed. 3.6 2.85 2.55 2.3 . Jacketed.... 3.9 3^ 2.8 2.5 The fact that the steam-jacket, as employed on the steam- engine, of whatever form and arrangement, is intrinsically a wasteful element, and that its use only gives, in certain cases, an economical advantage by its repression of wastes of larger magnitude, is also shown by the following illustrations, com- puted with and without jacket for various ratios of expansion. The results, as given in the following tables and as illustrated in the curves plotted from them, show clearly that the jacketed engine is always more wasteful than the ideal un- jacketed engine.* * Jomal Franklin Institute ; April 1891. " On a Maximum EfiaeacyI~ Steam-jacket ;" R. H. Tlmisum. 640 A MANUAL OF THE STEAM-ENGINE. Making the computations by the methods already employed and tabulating the results, we have, for/, = 115 Ibs. absolute, *i = 799 F - and A = 4: EFFICIENCIES OF WORKING FLUID. Steam-engine, Jacketed and Unjacketed. Cut-off. 0.05 .10 15 .25 35 45 55 75 1. 00 Ratio Exp. 2O.OO IO.OO 6.66 4.00 2.85 2.22 1.82 i-33 1. 00 Eff. without. 0.2073 1795 .1566 .1358 .1237 .1119 .0898 .0707 Eff. with Jacket. 0.1930 .I808 .1665 .1442 .1302 .1209 .1087 .0812 .0707 Ratio of expansion. FIG. 156. EFFECT OF JAGKEI SUPERHEATING AXD STEAM-JACKETIXG. 641 An examination of the tables, of the curves still better, wfll show clearly the wasteful influence of the steam-jacket, as an element considered by itself. Within the useful range of prac- tice, from about five or six to fifteen or twenty expansions, under the assumed conditions of initial pressure and cut-off, it it is seen that the loss by its application is fairly constant at something over one per cent, in these cases ; rapidly falling to zero as the ratio of expansion falls from the lower figures to unity. The consumption of steam, in pounds per horse-power per hour, may be computed very approximately by dividing 2.3 by the computed efficiencies. The cases assumed are for con- densing engines, and the evaporation always taken at nine pound? of steam per pound of fuel, the fuel expenditure may be gauged by dividing the weight of steam computed by 9. This gives, for example, about 12.06 and 12.95 pounds for the unjacketed and for the jacketed engine, respectively, at a ratio of 20, in steam demanded; and of about 1.33 and 1.44 pounds of fueL For a ratio of expansion of 4, the figures becoine about 1 6 and 17.3, respectively, for the steam and 1.75 and 1.85 pounds of fueL At full stroke, the figures become 35 pounds of steam and of feed-water, and 4 pounds of fuel per horse- power and per hour, for both engines. The consumption of fuel by the ideal jacketed engine is thus found to exceed that of the ideal unjacketed engine. To determine what such engines would actually demand, we must know their size, speed, and such other data as will enable us to estimate the probable cylinder-wastes. Assuming that they are of such size and character as to give wastes for the unjack- eted and jacketed engines, respectively, of 0.2 ifr and of o.i V7, they would consume : Actual Consumption of FueL p^ 60 80 100 120 (a) Unjacketed 4-8 4-O 3-2 2.8 (0) Jacketed. 4-2 3-8 3-O 2 -7 The ratio of expansion would usually be larger at these higher pressures and the actual gain by the jacket greater. 642 A MANUAL OF THE STEAM-ENGINE. But the assumption made in these computations that the steam is kept by the steam-jacket just dry and saturated during expansion is probably never true except with initially dry and perhaps superheated steam. The fact is, more likely, that waste usually goes on during the whole exhaust-period, and that the total jacket-waste is thus seldom less than, and may often even exceed, ten per cent. A maximum efficiency of jacket is always found in practice between full stroke, where the cylinder-waste is a minimum, and extreme expansion, where jacket-waste is a maximum, extending through the exhaust-period. Fortunately, this maximum rises as pressure increases, precisely as required for best results. It is obvious that, in the computation of probable efficiency, and of steam-consumption, in the case of the engines efficiently jacketed, in the manner here assumed, the volume of steam at the opening of the exhaust-valve, measures the amount used and requires no correction. A table will be found in the Appendix, computed by Mr. Buel, exhibiting, concisely, the nomenclature, data, formulas, and results for this case. The following table* represents the results of computations of probable efficiency and performance, on the assumption that the initial pressure is 250 pounds per square inch, absolute, the internal wastes as found in experimental work already referred to, and measured by the expression I -f- O-O/5 Vr, the engine being a jacketed tandem-compound engine, and these wastes assumed to be those due a single jacketed cylinder of moderate size and under usual conditions of operation.f Back- pressures are taken as 5 pounds condensing, and 16 non-con- densing, feed-temperatures as 104 F. and 203 F., respectively, and the evaporations as 10 to 11 respectively. Rankine's assumption as to effectiveness of jacket is accepted, the wastes above referred to being taken as those of the exhaust-period. * Trans. Am. Soc. M. E.; ccccli; vol. xii; 1891. f Mon. Haton de la Goupilliere coincides with Sinigaglia; who says that this function was first proposed by the Author, and subsequently confirmed by direct experiment at Sandy Hook and elsewhere. Cours des Machines; vol. u. SUPERHEATING AXD STEAM-JACKETLXG. COMPOUND STEAM-EXGINE JACKETED. NON-COXDEXSIXG. 643 : ::.-: ' CONDBXSIK 3 ., 9- K> 1 I2.AO W " 36-8 30 * ,: 55.1 ,| ^ - 9Z.o 5-9 - i _:,-,; - ^ ^ = ^ - :::.. XOX^TOXDEXSIXG. IHHU ; - - 1 * ! Is - 1 I :Bl5 S-^i H COXDEKSIXC. 873999 TAP I -i"9 a: W ,., -M4* "4-3JJ -t -*?* -, ->597 ^ 573 .JTij ..335' .rf, 008 1.563 .ndl -4ii3 .isfi* a-jfc: -6oi 36>oo OML per sq. ft. ^ >9> Per sq. in. 644 A MANUAL OF THE STEAM-ENGINE. It will be seen that the efficiencies range from 16.7 to 18.2 per cent in the case of the non-condensing, and from 16.9 to 22 per cent for the condensing engine, the maximum being found at a ratio of expansion, in the first case, of about 10, and in the second of about 30. Beyond these ratios the terminal pressure falls below the back-pressure, and a waste follows, instead of gain, by further expansion. These results are still better exhibited by the curves (Figs. 157 and 158) plotted from the numerical values ; the ideal case, in both sets, being represented by dotted lines, and the real engine giving the widely different curves in full line. The great difference between the condensing and the non-condens- ing engine, for the ideal case, is well shown, not only as to consumption of fuel at similar ratios of expansion, but also as affected by changing values of that ratio. The gain by expan- sion in the former case continues far beyond that at which the latter finds a limit ; while the point of maximum effect is far more sharply defined with the non-condensing engine. Varia- tion from the best ratio for the latter causes much more marked loss than with the condensing engine. The numerical values obtained are presumably those which we should obtain if we were to find a way of building engines with working cylinders having non-conducting inner surfaces. The points of maximum efficiency and those for minimum consumption of steam and of fuel are coincident in these cases, and also that for minimum supply of feed-water. As will be seen presently, this last is not the case for jacketed engines, in either the ideal or the real case, in consequence of the fact that a part of the working fluid circulates continuously between jacket and boiler and makes no demand upon the source of supply for replenishment. The efficiencies of the real engine range from 13 to about 15 per cent, and from 14 to 16 per cent, in the two engines, respectively ; while the best results are now given at a ratio of expansion of not far from 8 and 20 in the two cases, respec- tively. The water-consumption has increased from 12 to 14.8 pounds, and from 8 to 12 pounds, and the fuel account has risen from 1.36 to 1.68 and from 1.13 to 1.55 pounds per horse- SUPERHEATING AND STEAM JACKETIXG. 645 - - - : :::;- : COMPOUND JACKETED ENGINE. "7 J_ \ 646 A MANUAL OF THE STEAM-ENGINE. FIG. 158. FUEL AND WATER CONSUMPTION. SUPERHEATING AND STEAM-JACKET1XG. 647 power and per hour for non-condensing and for condensing engines. These changes are best seen on the curves ; the lower sets being those for the real engine, and the differences being best exhibited by the shaded areas separating the pairs on the second plate. It will be seen that the effect of this introduction of wastes in the ideal, as in the real, engine is to greatly reduce that ratio of expansion, which gives maximum efficiency, and to make variation from that ratio of maximum efficiency more seriously' productive of loss : while at the same time making the differences between the several cases less than in the ideal engine. The following are the values of the ratios for maxi- mum efficiency and for minimum steam and water consumption for the cases taken : COMPOUND JACKETED ENGINE, /i = 250; p% = 5 and 16; r variable. CASK. r for maximum efficiency n 8.5 ;: 17 Water-rate j 12 14.75 8.5 12 Fuel-rate \ 1.35 ] 1.68 i.i ] 1.55 The real measure of the useful power of an engine is the dynamometric power at the point at which the engine delivers its energy to the machinery of transmission. A well-built non- condensing engine should have an efficiency of machine as high 3592.5 per cent. An equally well-built condensing engine should approximate 90 per cent efficiency of machine. Tak- ing these values, the last table becomes modified thus : COMPOUND JACKETED ENGINE. (Data as above.) Ideal. Real. IdeaL ReaL II 8.5 : - 17 Water per D H P 13 16 8-5 13-5 Fad ner D. H. P. . . 1-5 i.S 1.2 1-7 648 A MANUAL OF THE STEAM-ENGINE. 156. Limitations of Jacket-action have been noted, in many cases ; and, while the precise methods of operation of their various causes have not always been fully revealed, we are perfectly familiar with their general action and effects. It has been found that the use of superheated steam, the com- pounding of the steam-engine, or the increase of speed of pis- ton and of rotation in fact, any circumstance independently promoting economy reduces the value of the jacket, and sets a limit beyond which it would presumably have no useful ef- fect. That this limit is sometimes reached is unquestionable. Him first detected such limitation in the application of super- heated steam to a compound engine. Later experience has very often illustrated the fact that the jacket may be of little service, especially on compounded high-speed engines ; and it is sufficiently obvious that any conditions which tend to make the net jacket-waste and the net cylinder-waste equal, either by exaggerating the former or by reducing the latter, will tend to bring about this result ; as will any defect in the design, construction, or operation of the jacket which renders it ineffi- cient in its working. Precisely where the limit is reached in any class of engines is not easy to determine. A clue to the solution of such prob- lems is found in the measurement of the condensation in the jacket ; the quantity of water trapped off being a measure of the total heat-supply to the cylinder, dry steam being received from the boiler. Mon. Dwelshauvers Dery, analyzing the data supplied by test of the Whitworth Laboratory experimental engine, obtains the following : Let Q = heat supplied by the boiler, directly ; <2, = that supplied by the jacket ; T = total indicated work ; E = rejected heat externally ; C~\-c = that sent to the condenser. Then __ Q+Q, SUPERHEATIXG AXD STEAAf-JACKETIXG. 649 Referring to six tests in three of which the jackets were all in use, and in three of which they were on the reservoirs, only, and were shut off on the cylinders, the following table is ob- tained : * HEAT-DISTRIBUTION. Number of trial Heat of the direct steam. Hear of fh iarket *r 0.749 - o.Si6 0.869 0.893 0.904 Work , - :. T 0.16^ - Radiated waste E o 127 o oqi o 060 Q + Qi Heat utilized by jacket, Q-E 1 /I o, 720 0.035 10.519 v; T vr Thus, deducting the quantities of heat wasted by external radiation, the jackets supply an almost perfectly uniform quan- tity of heat, the figures being 12.4, 12, and 12.4 per cent in the first three trials ; the cause of the greater variation in the last three cases is indeterminate from the available data. Mon. Dwelshauvers concludes from his somewhat extended observations, and experimental researches, that, other things equal, and under usual working conditions, the jacket has little value at a low ratio of expansion ; and that, to enable it to be of much service, that ratio must exceed at least 5. He has observed an economy, in his own trials, of 1 5 per cent at a ratio of 5, of 3 to 4 per cent at ratios approximating 3.3. In compound engines, when the expansion in the high-pressure cylinder is small, he sees little advantage in the use of the jacket ; while he considers it indispensable on the large cyl- inder. Heat wasted in the smaller cylinder may be utilized * Correspondence. 6$O A MANUAL OF THE STEAM-ENGINE. in the larger ; but waste from the latter cannot be compen- sated. Could the conditions assumed for the ideal case, as illus- trated in the cases of jacketed engine and dry saturated steam, elsewhere computed, be actually secured, the exhaust deliver- ing dry steam to the condenser, it is probable that the waste of heat from the cylinder during that period would be slight and the efficiency of the engine in actual operation thus made to approximate a maximum. Were the jacket made so effective as, for example, in the case of Donkin's gas-heated jacket as to superheat the steam exhausted ; or were it so ineffective, as is probably usual, as to permit the exhaust-steam to be sent to the condenser wet, it is probable that the resultant, total, efficiency would be less. This consideration justifies an apothegm of Dwelshauvers-Dery : the waste by the cylinder- walls is measured by the heat demanded to evaporate the water in the exhaust-steam at the end of the expansion-period. In all cases where the cylinders are provided with steam- jackets, if practicable, steam should be introduced into the cylinder-heads ; and non-conducting coverings should be ap- plied to the heads as well as to the cylinders, proper. The jacket-steam should not be allowed to become either stagnant or charged with air ; and it should not pass into the cylinders. The jacket should be neither too greatly nor too slightly ener- getic ; its action should be sufficient to insure dryness of the surfaces of the cylinder at the close of the exhaust, so as to prevent initial condensation ; but it should not superheat the steam during expansion or exhaust.* Such efficiency of the jacket must apparently be secured, first, by proper construction of the jacket and cylinder and, secondly, and especially, by in- suring reasonably dry or slightly superheated steam. It would seem, from all that has preceded, that where a high ratio of expansion is proposed in any one cylinder, and when the steam supplied it is initially dry, or fairly dry, the steam-jacket may be confidently expected to give an unmis- * See Ledieu: Machines a Feu; 1882; p. 714. SUPERHEATING AND STEAM-JACKETING. 6jl takable and very desirable economy, even from the final com- mercial point of view from which all costs, direct and inci- dental, are noted ; but when the expansion is restricted, the range of temperature in the cylinder slight, the steam super- heated, or, on the other hand, when it is so wet that the jacket connot completely dry and thoroughly reheat the metal of the cylinder before it is again exposed to the entering steam, the value of the steam-jacket may become questionable, or null, or even negative. A good jacket covers all active condensing areas, permits neither water nor air to remain in it, returns all water of con- densation immediately to the boiler, and is itself well covered by non-conductors. In 1886, a " Research Committee" was appointed by the British Institution of Mechanical Engineers, to investigate the action of the steam-jacket.* A very extensive collection of data pertaining to the efficiency of the jacket was secured, and from these the following figures were collated and results de- duced :f The first case is a single-cylinder non-condensing Corliss engine, 21.65X43.31 inches, the body only jacketed. The jackets were supplied by a small pipe from the main steam- pipe and were automatically drained. The second case is a single-cylinder condensing engine (Corliss), cylinder dimensions as before, body only jacketed ; experiments carried on at the same place, in the same manner. The third case is a horizontal compound condensing tandem engine, the body of the cylinders only being jacketed. The whole steam-supply to the cylinders passed through the jackets, which were drained by trap ; and when not in use the jackets were open to the air. The last trials were carried on at a constant boiler-pressure * Proceedings. 1890. f journal Franklin Institute; Apr. 1891. " On a Maximum Efficiency of Steam-jacket;" R. H. Thurston. 6 5 2 A MANUAL OF THE STEAM-ENGINE. of 42 pounds above the atmosphere and a piston-speed of 196 feet per minute. VARYING JACKET-EFFICIENCIES. Ratio of Exp. 2 6.2 I 6 < 5 Eff. of Jacket. Per Cent. 21-33 20.6 1 15-79 Elatio of Exp. 8 10 7 1 6 * 5 4 Eff. of Jacket, Per Cent. 7-38 5-94 4-67 3-6 1.64 5-5 13 15 f 12 i 4 9 3 j 9 .6 .63 -38 10 i I ^ g 5 7-45 6.28 3-84 3-o8 2.03 a 4 J 3 < 2 7.64 7 3-93 12 " H IO ! rated heated Diner- Q ^ dif- Steam. Steam. ence. ference. .65 3-71 2-99 -72 24-1 .60 3.07 2-74 33 12. 1 .58 31-4 26.1 5-3 20.3 .50 32.7 25.1 7.6 30.3 -: 3-38 2.91 -47 16.2 35 2-73 2-33 .40 17.2 .32 30.6 28.4 2.2 7-8 68o A MANUAL OF 7 HE STEAM-ENGINE. The next table is given for the case of condensing engines by Mr. Buel ; and the following cases are from Bourne :* GAIN BY USE OF SUPERHEATED STEAM IN MARINE ENGINES. Total Coal Pounds. Vessel. Saturated Steam. Super- heated Steam, Differ- ence. Per cent of difference. Alhambra, Southampton to Lisbon and re- turn Colombo, Southampton to Alexandria and 405,440 275,520 129,920 47.2 return 2,287,280 613,520 26.8 Norman, Southampton to Cape of Good Hope and return Ceylon, Southampton to Alexandria and 1,189,440 365,120 3-7 return 3,364,480 2,201,520 1,072,960 46.8 Since these dates, however, the increasing pressures, ad- vances in general efficiency and especially high temperatures and wide range of expansion, which have become common, have greatly reduced the margin for gain by superheating. In multiple-cylinder engines, especially, the adoption of re-heating methods, between cylinders, by jackets and even by " live," boiler, steam, afford gains of important amount, and without the disadvantages, costs, and risks of direct superheating. It is evident that, as long since observed by Professor Hirsch, a most serious obstacle to the employment of super- heated steam exists in the difficulty of regulating the quantity of added temperature. It is also obvious that, to secure every desired favorable condition, a method must be found of appor- tioning the degree of superheating to the varying demands of the engine, as determined by variation of the ratio of expan- sion, from time to time, and by the quality of steam entering the superheater. 170. Experience and Testimony derived from many ex- periments prove the value of moderate superheating. Mons. Hirn reports, as the results of trials in which he was aided by * Treatise on the Steam-engine, by John Bourne; 1859. SUPERHEATING AND STEAM-JACKETING. 68 1 Messrs. Dwelshauvers-Dery, Grossteste, and Hallauer, the fol- lowing figures, checked by Cotterill : SUPERHEATING. Extent. /, r Steam superheated 157 F. 61 4 o 54 4 95 56 7 o 55 7 Per cent of waste. 7-8 I 5 .6 I2. 4 21.8 The engines built, in 1832, for H.M.S. Dee demanded 3.9 pounds of coal per I. H. P. per hour with saturated steam, but only 2.74 pounds at a temperature exceeding that of satu- ration by 1 88, the pressure being but 9 pounds. The Ceylon in 1860 gained over 25 per cent by superheating about 100 F.; the Alhambra gained over 25 per cent ; the Nepaul about 50 per cent.* The following table, compiled by Mr. Dixwell from the ex- periments of Isherwood, Emery, and Loring, shows well the advantages of superheating steam within the safe limit and at moderate pressure. It thus appears, as remarked by Mr. Dix- Boiler- Pounds pressure of Coal Name of Steamer. Kind of Engine Kind of Steam used. above Atmos- Actual Cut-off. consumed net horse- Lbs per power sq. in. per hour. Michigan. . . Simple Saturated 21 29 4-5 Mackinaw. . " " 35 43 3-49 Eutaw .... " " 27 54 3-84 Dexter .... " " 67 .29 3-4 Dallas " " 32 31 3-8 Bache j Compound ) M 80 .20 2.66 ( Jacketed f Rush ' " 69 .16 2.71 Georgeanna. Simple Superheated 33 .31 2.58 Adelaide " " 34 39 2.45 Mackinaw.. . c * " 39 2 9 2.48 Eutaw 28 54 2.99 Proc. Brit. Inst. C. E.; vol. xix. p. 473. 682 A MANUAL OF THE STEAM-ENGINE. well, that the Georgeana, Adelaide, Mackinaw, and Eutaw, working with superheated steam at moderate pressures and without jackets, surpassed the performances of jacketed com- pound engines working with much higher pressures and much greater expansion. Conclusions relative to superheating may evidently be arrived at, and without question, favorable to the moderate use of superheating. It is certain that, as long since pointed out by Him, this method is more thorough in its reduction of cyl- inder-wastes than jacketing, or even, if it can be carried suffi- ciently far with safety in the simple engine, than " compound- ing." It gives dry steam initially, and throughout the expan- sion-period, and is not productive of loss during the exhaust- period, a phase in the engine-cycle during which wastes by the jacket are especially active where it has not left the steam and the walls of the cylinder dry at the end of expansion. The jacket keeps these surfaces approximately at the boiler tem- perature, even during this last most wasteful part of the whole revolution ; while superheated steam produces its effects just when and where they are needed, and does not thus exaggerate losses during exhaust. Where the superheating is effected by the saving of heat which would otherwise have passed up the chimney, as is often, perhaps usually, the case, the gain at the engine is a real gain. When, however, the superheater simply produces dry and superheated steam where it would otherwise have been wet, and by the application of heat that might otherwise have been employed in the boiler in the production of saturated steam, the apparent gain must be reduced by this expenditure and the net and real saving is correspondingly lessened. This net sav- ing is to be measured in fuel, rather than steam, consumption. A net gain amounting to from 50 to 75 per cent the apparent saving has been attained in practice, in such cases, by a reduction of cylinder-wastes to a very small quantity, as to five per cent, or even less. There exists, for every engine, a set of conditions, and especially a quality of steam, which make the jacket most SUPERHEATING AND STEAM-JACKETING. 683 effective. With sufficiently superheated steam, the jacket is not needed at all : it would add nothing to the efficiency of the engine ; with wet steam it might be possible that the loss from the jacket during the terminal portion of the expansion-period, and throughout the exhaust, might exceed the gain in the earlier part of the active period of jacket-action, and during the compression. With intermediate conditions, a maximum gain by the jacket-action might be observed. This maximum may be expected to be found when the steam is at least fairly dry and the ratio of expansion considerable. Once the surfaces become dry, they can yield but little heat to the enclosed vapor, and the jacket can then promptly bring them up to approximate the temperature of the entering steam. This action is that desired of the jacket, in fact, and the more completely it is effected and the less the waste of heat in the process the better. 171. Compression and Clearances have rather definite relations ; nevertheless they are not related by purely kinematic principle ; even if the usual treatment, by such a process, have any really important bearing. Were there no exchange of heat to be anticipated, between the working fluid and the walls of the cylinder, the proper treatment would be to secure such compression as would just fill the "dead-spaces'* to initial pressure. But not only does this transfer occur and thus modify the case : but the purely dynamic exigencies of operation may enter as important factors in determining these relations. The " clearance" in the steam-engine is the small space nec- essarily left between the piston and head, at the end of stroke, to evade danger of their being brought into actual contact, through wear, accident, or carelessness in adjustment of length in taking up wear on the connecting-rod " brasses," or in other bearings " in series" with it. The " dead-spaces" include this clearance and the port-spaces ; which latter are often large. The total varies from below 2 per cent up to 6, 8, or even 10 per cent of the volume of the cylinder. Since these spaces must be filled with steam at every stroke, they constitute a 684 A MANUAL OF THE STEAM-ENGINE. source of waste ; except they are filled from the back-pressure steam by compression. Thus the waste due to clearance maybe reduced and in some cases made zero by suitable compression. Where expansion is incomplete, it will be found that, dynamically, the best result is secured when the compression is somewhat in excess of the expansion-ratio, and, under usual conditions, not far from 50 per cent higher.* The thermal effect in reduction of internal wastes is sufficiently important, however, to make it advisable to aim at compressing, in most cases, probably, well up toward boiler-pressure, regardless of this aspect of the problem. The dynamic loss, in engines with large clearance, as 6 to 10 per cent, may be as much as 10 and 15 per cent without compression, and but one third these figures with best adjustment. Zeuner's principle, affecting the action of the clearance and port spaces, is the following : In any case, complete compression, if practised, annuls the wasteful effect of those spaces with complete expansion. Complete expansion occurs when the pressure at its end is equal to the back-pressure ; complete compression is that which carries the final pressure of compression up to the initial pressure of admission. Assuming that the law of com- pression is the same as that of expansion, and also assuming the law of Mariotte : Let v l = the volume of steam entering at the initial press- ure /, ; v =. the volume of the dead-space ; P O the back-pressure. The expansion will be complete when the pressure at the end of expansion is equal to / , which requires that the vol- ume at that point shall be greater than at the beginning of * See Cotterill; p. 258. SUPERHEATING AND STEAM-JACKETING. 685 expansion in the proportion -'. In a cylinder having no clearance, the work per stroke of piston is, in such case. When there exists a dead-space, r, the initial volume of p steam, i\ , first fills a portion, v v,ol this space, and then drives the piston through a volume, t\ v -f- v , during ft admission. The work at full pressure is //+ A* The total volume of steam at the end of the admission is v, - '^ ; while the work of expansion is measured by log j (A*'. + A*0- The volume of steam at the commencement of the exhaust is Ai the volume at the beginning of the compression is, in order that it shall be complete, evidently v -'. A The work of the back-pressure is then ^ " ~~ V ~ V = ** Vl ~ P ~ P * V ' 686 A MANUAL OF THE STEAM-ENGINE. and the work of the compression will be A* log*. The net amount of work done is thus, finally, ^-r-A^ + iA^i+A*') ~~ Pi v \ Pi v P

d r^-T Oco oc< mM in In in In in In in In in . "^ d >So (in co T M co >O mo inO O 00 00 00 o" O 00 q co c> co oo e T in co in co in aa " 8 ! 1 SUPERHEATING AND STEAM-JACKETIXG. 689 F II 11 1 1 1 1 I IS d f M II 1 1 II -. if ! 5* I 1 1 II II II if = 3 IS od ~ II II 1 ! i n -~ C- 1 1 I < H f 1 1 1 1 S SK SI. SS d do od do- do o S I S s i : : : ~ 5f S I f I i 1 |S 25 SS = : = : : : = : : : : : = : : d do do d d = =" do" = d d o" s? ?^ ^ ^^ 5^ 5^ ?s~ : T f 'i 'i =' :' t d d ~'z'z : * = 1" o II z z z z z oo ~^ 5^ 55 55 55 55 55 d = d d = do do do d d d d J f I II II M M M M II II II 690 A MANUAL OF THE STEAM-ENGINE. The main value of high compression, as is seen in some types of engine, certainly, is not to secure that nice adjustment which would prevent a slight waste of power due to maladjust- ment of the ratios of expansion and compression, but to secure a smooth-running engine by " cushioning," in such manner as to take up, by the spring thus produced, that impact and jar, that " pound," otherwise liable to occur with annoying, if not dangerous, consequences, every time the crank swings past the centre. In high-speed engines the designer carefully adjusts the volume of clearance to be adopted, with this end in view, making the " dead-space " comparatively large to insure that the work of compression shall furnish the needed means of absorption of the energy of retardation. Still another and, in respect to efficiency, even more influ- ential factor in the determination of the magnitude of the ratio of compression is the fact that the heat of compression tends to check cylinder-condensation, and that it may be made really effective. This would dictate that compression should be carried fully up to boiler-pressure, in order that the surfaces which are productive of interior waste may be heated as nearly as possible to such a temperature as will reduce that loss to a minimum. From this point of view no computation is required, or is yet possible, that shall exactly determine the magnitude of these effects. It is, however, obvious that compression to boiler-pressure is always desirable, and that the volume of dead- spaces should be such as will make the work of compression approximately equal to so much of the stored energy of the reciprocating parts as is required to be absorbed.* * Leloutre remarks: "I can easily demonstrate, by an immense number of diagrams and of calorimetric observations made on a large scale, that the law of Mariotte is radically false in its application to the steam-engine. This law is expressed by the equation *= - ^. Rankine was the first, I think, Pn / Vm\ lfl1 to propose the expression = IT^/ More recently MM. Him and Cazin, in the courses of thoroughly scientific investigations, have found the SUPERHEATING AND STEAM-JACKETING. 69! It is evident, further, that compression is a necessary and an effective adjunct to all other methods of economizing; although the magnitude of the dead-spaces and the waste by clearance is a matter of less importance with the multiple- cylinder engines. So essential is the use of compression to insure smooth action in high-speed engines with their large inertia-effects that their usually large clearances are sometimes even purposely exaggerated to obtain ample cushioning. In such makes of engine the clearances are carefully proportioned with this pur- pose in view. Thus Messrs. H. VVestinghouse and Rites intro- duce a " clearance-chamber of carefully determined proportions between the two cylinders of the single-acting compound en- gine, which space is constantly open to the small cylinder, in order that the initial and compression pressures may be made equal. The action of the engine is that characteristic of the Woolf or receiyerless engine, and the result of this arrange- ment is that the compression in the small cylinder is made independent of the load, but variable with the steam-pressure, this compression always beginning when the low-pressure expansion begins, producing the distribution shown in Fig. 159, the diagram being that used in designing the engine. In this diagram three variations of load are shown, respec- tively, by the heavy, light, and light-dotted lines, the compression value, for superheated steam, *- = -^' Butin "^e application of these last formulas to cur industrial motors they will be found even more incorrect than the law of Mariotte. Through numberless researches I have reached the following conclusion: There is no fixed taw of expansion in these engines; or, rather, the general law, if one can be established, varies in its effects from one stroke of the piston to another. ... I have already demonstrated, in a report on the superheated-steam-engine of Mons. Him, that the succession of press- ures during the expansion is represented very exactly by the general formula ** = I -I f in which the index a is generally less than i, and, consequently, pm * V' that the machine has slightly more power than the constructors consider them- selves able to guarantee." (Bulletin de la Societe Industrielle de Mulhouse; 1873.) 692 A MANUAL OF THE STEAM-ENGINE of each commencing at c, b, and a, respectively, but following the same curve, and terminating in each case at the same initial pressure, M, In like manner, with the steam-pressure raised to N, we get the heavy-dotted diagram, in which cut-off having taken place earlier, compression would commence earlier at d, but terminating at the new initial pressure, TV. Whatever be the exhaust-pressure at the commencement of compression in the small cylinder, due to changes of load or of boiler-pressure, it is automatically compensated by shifting the point of com- FIG. 159. FULL COMPRESSION. pression itself to such a position as will insure final pressure equal to that of the admitted steam. Expansion in the large cylinder should commence coincidently with compression in the small cylinder. This result is arrived at by the simple combination of cor- rect valve-travel and proportion, with a specific and constant clearance-volume in the small cylinder. In this case, also, the clearance and compression are ad- justed to compensate that loss of pressure between the cylin- ders due to cylinder-condensation in the initial stage in the low-pressure engine. SUPERHEATING AND STEAM-JACKETING. 693 Where the two pistons are secured on the same rod, as in most tandem compound engines, the smooth running of the engine is facilitated by the aid given in the cushioning of the steam in the high-pressure cylinder, -wheiv. as. in condensing engines, large compression in the low-pressure cylinder becomes difficult. Compression was not used by Mr. Corliss in his engines, whatever their speed. Mr. Henthorn advises, for Corliss en- gines, a compression not to exceed the terminal pressure on the expansion line for condensing engines, and an excess over this pressure of about five pounds for non-condensing engines.* The loss of work by the clearance and the cushion-steam is readily computed as a purely dynamic quantity ; but the real loss by clearance and the thermodynamic gain by high com- pression are not, as yet, capable of computation with accu- racy. If the pressure and volume of the steam at exhaust are/,, v , , the back-pressure /, , and the volume of the clearance-space v t , the pressure and volume of the cushion-steam at the begin- ning and end of compression, and the ratio of compression, re- spectively, /,^, , pp t , and r c , the work of compression is, very nearly, U e = /,?'j ( i -f- log, r c ) + *>*$ : hyperbolic expansion being assumed. The work of expansion of the cushion-steam is * The Corliss Engine: Henthorn and Thurber; N- Y., E. P. Watson. i8gi. 694 A MANUAL OF THE STEAM-ENGINE. The difference in work lost by incomplete expansion of the cushion-steam is When, to insure best thermal action or effective cushioning, the compression is made complete and/ 4 =/,, t - U c ' = /,*, (log, 4 - log, 4) ; With complete expansion, r c = r ; with clearance reduced to zero, v t = o ; in either case U c UJ = o. The effect of clearance in producing a difference between the real and the apparent ratio of expansion is exhibited by the following diagram and tables which were prepared by Mr. Buel.* Perfect Vacuum 1 2 3 45 6 T 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 FIG. 160. EXPANSION-CURVES. A clearance of 5 per cent is assumed. For the effect of clear- ance on the cut-off and ratio of expansion, see Appendix. * Am. Machinist; Apr. 14, 1888, p. 2. SUPERHEATING AND STEAM-JACKETIXG. 695 Fig. 160 is a diagram showing the expansion of steam in hyperbolic curves, at the points of cut-off noted, the initial pressure being 100 pounds per square inch : (1) In a cylinder with 5 per cent clearance (curves in full lines). (2) In a cylinder with no clearance-spaces ('curves in broken lines). In the following table the numbers in column 4 are mean pressures, corrected for back-pressure, for stroke plus clearance, and the numbers in column 5 are the mean effective pressures in column 4, corrected. Compression to initial pressure reduces the mean effective pressure, but the steam in the clearance- space is saved. This case is illustrated in the diagram by the curve KA, the clearance being AG. THEORETICAL RESULTS OF Uasc STEAM ExrxsarELT CORRECTED FOR BACK CLEARANCE AXD Ccsmox. :: Btalfai Costtooo* to 3 efeanam sgwcet 82.5 1.000. 1.00 1.050 .762 S7.0 79.5 78.5 .952 1.051 jMf .524 86.2 68.7 67.1 .813 1.23 J , .365 73.3 55.8 53.6 , .650 1.54 .590 |J8f 64.4 1 46.9 ' 44.2 .5361.87 .561 La06 53.2 35.7 i 32.5 .394 2.54 .550 I JOTI 46.5 29.0*25.5 .309 3.24 .567 .!:: 38.8 :: s ::.4 ::: 74 = r a a |j:=c ^ .-. 20.( .645 35.5 .562 43.S .534 46.6 .524 47.6 .540 46.0 1.00 1.05 -- " 77.9' 1.000 73.9 .949 62.5 .802*1.25 49.0 1 .629 1.59 39.6 j .508 '1.97 27.9 j .358 iW 20.9 .969 3.T3 ItAI .164 6.10 .5*) .-_- .465 .466 I? II 21.2 37.5 47.0 50.7 53.5 '-: I Another method of treatment is the following : The quan- tity of steam, q. entering the cushion-spaces is the difference between that required to fill them at boiler-pressure,/,, and that compressed into them, reduced to the same pressure ; Le^ if f, is the " dead-space," q = r e v, . 696 A MANUAL OF THE STEAM-ENGINE. But, assuming hyperbolic expansion, which value becomes o when the compression is complete, and v c v,. The total steam admitted up to the point of cut-off is The larger the ratio of expansion and the greater the vol. ume v c , the more serious is the loss due to incomplete expan- sion of the cushion-steam and, the clearance being given, the useful effect of increasing pressure becomes less and less as the pressure rises. The greater the back-pressure, the less the ratio needed or desirable, either to effect complete compression or to annul the waste by cooling. Non-condensing engines are given in- significant ratios of compression as compared with those re- quired for complete compression in condensing engines. Other things equal, the higher the initial pressure, the less should be the clearance. Large port and clearance spaces increase the cost of the engine, as they decrease the net useful work of the machine, both by actual reduction of the indicated work and by increasing the waste-work due to friction. SUPERHEATING AtfJ) STEAM-JACKETING. 697 EXPANSION OF STEAM. offl. Initial Mean total Quantity Per cent r pressure, pi. pressure, /. of steam. saving. I IOO IOO IOOO 1 u 96.4 780 22.0 i M 84-7 590 41.0 i U 70.0 477 52.3 M 59-7 420 58.0 i U 46.5 358 64.2 i M 38.5 325 67.5 rS tt 29.0 288 71.2 Same, allowing 17^ Ibs. back-pressure : A i 100 82.5 1000 " 78.9 780 22 i " 67.2 615 38.5 i 52-5 523 47-7 | " 42.2 488 51.2 * " 29.0 473 52.7 i " 21.0 490 51.0 r ? " 11.5 596 40.0 172. The Binary-vapor System is a method of what may be termed " compounding " engines with transfer of heat and without transfer of working fluid from the high- to the low- pressure element of the series. The general principles are thus, in the main, the same as in the usual form of multiple- cylinder engine ; but with important differences of result due to practical differences of physical conditions of environment and of operation. While the principle of Carnot, asserting that, thermodynami- cally, all working substances have the same value of efficiency of fluid when working through the same range of temperature in adiabatic expansion, in the ideal engine, it happens to be the fact that it is often practically impossible to obtain the ideal conditions of maximum efficiency in all cases. Some fluids are more liable to loss of heat in actual working 698 A MANUAL OF THE STEAM-ENGINE. through internal and external conduction and radiation, than others ; and the pressures of the various possible working sub- stances at any temperatures vary enormously ; vapors of ether and chloroform, for example, having much higher pressures than steam. A defect in the action of steam, as commonly used, is that, at high temperature, it has, if saturated, dangerously and even uncontrollably high pressures ; while, at low temperatures, its pressure falls below that of the atmosphere and compels the use of an expensive and cumbersome system of condensa- tion if we seek to transform low-temperature heat into work. The binary-vapor system is one in which this latter difficulty is sought to be remedied by using a volatile fluid as the con- densing medium, so that the latter may be vaporized at a good working pressure by the condensation of the former and may then, in turn, be used in a supplementary engine, transforming a new and sometimes large quantity of thermal into dynamic energy. Thus a kind of " compounding " results in the substitu- tion of a second engine, " in series " with the first, for a con- densing apparatus. This added machine must necessarily also be made a surface-condensing engine in order that its always costly and sometimes dangerous working fluid may be saved and used over and over again. By the use of such a system, the gain due to decreased cylinder-condensation and increased range of expansion, combined, may prove to be considerable, when compared with the economy of the ordinary steam-engine. The following, adopting Rankine's methods, is the theory of this case : * Let/, be the absolute pressure of the steam at its admis- sion; ?>j , the volume of i Ib. of it when admitted ; rv^ , the volume to which it expands. Let //, denote the available heat expended, in foot-lbs. per Ib. of steam ; U, the energy exerted on the piston by I Ib. of steam. * Rankine ; p. 145. SUPERHEATING AND STEAM-JACKETING. 699 Then the heat rejected by each Ib. of steam, and given up to the ether, is H 9 = H t -U. ....... (i) To find what volume will be filled with ether-vapor, the ex- penditure of heat per cubic foot of ether-vapor, at the pressure under which it is evaporated,//, is necessarily lower than the temperature at which the steam is condensed : T"^ ..... (2) where j.i L = T' -j^r; is the latent heat of evaporation of one cubic foot of ether-vapor under the given pressure ; Jc 1 = 399.1 foot-lbs. per degree Fahrenheit, is the specific heat of liquid ether : iy is the weight of one cubic foot of ether- vapor; T' is the temperature at which the ether is evaporated, and T'" that at which it is condensed. The initial volume of the ether evaporated, per Ib. of steam condensed, is Let ft' denote the intended final pressure of the ether- vapor, and p'" its mean back-pressure ; about 5 Ibs. on the square inch. Then by means of the formulae for steam, already given, substituting the constants which apply to ether, we may obtain : The ratio of expansion, r / , and the final volume, r'u f , of the ether evaporated per Ib. of steam ; the energy exerted by that ether, /"', and the ratio rV is that of the volume of the ether-cylinder to that of the steam- cylinder. In practice, those cylinders are usually of equal size, or the ether-cylinder somewhat larger. 700 A MANUAL OF THE STEAM-ENGINE. The heat per Ib. of steam, abstracted by the cold water in the ether-condenser, is H.-U-U' ........ (4) The mean effective pressures in the steam and ether cylinders are U U' and -,. ....... (5) rv l rti But the amount of energy obtained by the addition of the ether-engine to the steam-engine might be obtained by con- tinuing the expansion of the steam. The following are means, computed from results given in the report of M. Gouin, on the performance of the steam and ether engines of the Bre'sil : Pressures in Pounds on the Square Inch. In Boiler or Back- Mean Evaporator. pressure. Effective. Steam ............ 43.2 7.6 n.6 Ether ............. 31.2 5.3 7.1 Total M. E. P. reduced to the area of one piston, the areas and strokes of the pistons having been the same . . . ............... . ...... 18.7 It appears that the proportions of the power obtained in the cylinders, respectively, were : 11.6 Steam ......................... = = .62 18.7 Ether The gain of power by the addition of the ether-engine is not so great as this shows ; because, had the steam-cylinder been used alone, the back-pressure would have been in all probability about 4.6 instead of 7.6 ; so that the mean effective pressure in the steam-cylinder would have been 14.6 instead of SUPERHEATING AND STEAM-JACKETING. 7OI 1 1.6 ; and the proportion of the power of the steam-engine to that of the binary engine would have been 14.6 _ leaving 1.00-77 = . 23 of the power of the binary engine, as the gain due to the ether- engine. The consumption of fuel was either 2.8 or 2.44 Ibs. of coal per indicated horse-power per hour, according as certain ex- periments made under peculiarly adverse circumstances were included or excluded. Rankine adds : " The binary engine is not more economical than steam- engines designed with due regard to economy of fuel ; but by the addition of an ether-engine, a wasteful steam-engine may be converted into an economical binary engine" a conclu- sion which is sufficiently obvious from the fact that such figures are considered rather high for the ordinary compound steam-engine. A binary-vapor engine, tested by Mr. Haswell, in which the auxiliary fluid was carbon disulphide, gave the following re- sults in a trial in which the operation of the engine was con- tinued five hours, which, as that period involved the cleaning of the fire, was held to afford time for a test.* The reported data are as below : Pressure, steam boiler 75.8 pounds " shell.. 15.3 " " vapor engine 76 " " " mean, by indicator. . 31.35 " Water evaporated 571 cubic feet Revolutions per minute IOO Vacuum 9.85 pounds Coal consumed 600 Horse-power indicated 86.64 * Trans. Am. Soc. C. E.; 1887; also Steam-engine and Boiler Trials: p. 454. 7O2 A MANUAL OF THE STEAM-ENGINE. From which it appears that steam at a pressure of 75.8 pounds per square inch passed through the automatic regulat- ing valve to the shell surrounding the generator at the reduced pressure of 15.3 pounds, due to a temperature of 250.4 degrees, produced a vapor in the generator of 76 pounds. The consumption of coal was thus reported as 1.385 pounds per indicated horse-power per hour. These results confirm the indications of thermodynamic science, that substantially as good work may be done with other vapors as with steam ; but the steam-engine has actually given as good economical results as those here reported, and has many practical points of superiority. This trial was, how- ever, too short to be taken as fully satisfactory, and the history of these devices, so far as known, does not seem to encourage an expectation of the displacement of the steam-engine by their introduction. The data and results obtained by Mr. Barrus, by three tests of a Campbell ammonia-engine and boiler, as reported to the Campbell Engine Co., April 1887, were as follow : DIMENSIONS OF BOILER AND ENGINE. Boiler One horizontal-return tubular, set in brick-work. Diameter of shell 42 in. Length of shell 10 ft. Inside diameter of tubes 1.75 in. Area of water-heating surface 369.3 sq. ft. Area of steam-heating surface 318.8 " Area of grate-surface . . . , 9.17 " Collective area for draught through 67 tubes 1.12 " Ratio of water-heating surface to grate-surface 40.3 to I Ratio of steam-heating surface to grate-surface 33.6 to I Height of smoke-stack above grate 30 ft. Engine Porter-Allen automatic cut-off, single cylinder. Diameter of cylinder 1 1.5 in. Stroke of piston 20 " SUPERHEATING AND STEAM-JACKETING. 703 DATA AND RESULTS OF TESTS. Date 1887, March 8, March 9, April 16. Duration of test hrs. 8 10 7.45 Percentage of ashes, etc.... per cent 9.9 8.2 Coal per hour per sq. ft. of grate Ibs. 19.09 15.27 16.07 Boiler-pressure above at- mosphere 100 95.5 86.6 Temp, of feed-liquid en- tering boiler deg. F. 167.6 167 Temp, of gases entering stack " 390 394 Vacuum in feed-well inches 1 1.5 n Revolutions of engine per minute revolu. 205.2 204.5 201.5 Indicated horse-power de- veloped by engine H. P. 61.80 57-53 54 Proportion of stroke com- pleted at cut-off .189 .211 Proportion of stroke com- pleted at release .773 .791 Proportion of return stroke uncompleted at compres- sion .307 .342 Coal consumed per indi- cated horse-power per hour Ibs. 2.832 2.433 2.729 All the fluids which have been proposed or employed as substitutes, wholly or in part, for steam, have been seriously objectionable on the score of either cost or danger and usually both. None has yet been found satisfactory in these re- spects. Comparison of results of experience, as illustrated by the pre- ceding facts and figures, leads to such final conclusions as fol- low: 704 A MANUAL OF THE STEAM-ENGINE.-. (1) Experiment, experience, and the philosophy of the steam-engine combine to indicate that the limit of possible advance in their economical application is now so nearly ap- proached that further progress must be expected to be both slow and toilsome. (2) That the range left for such further improvement upon the best and most efficient of existing engines is probably small, and the difficulties arising in the attempt to reduce it are increasing in a higher ratio than progress in its reduction. (3) That, while wasteful engines may be improved by vari- ous expedients, including the substitution of other working fluids than steam, either wholly or partly, no other vapor has yet been found to give an economical performance exceeding, on the whole, or even equalling, that obtained with the best steam-engines. CHAPTER VII. THE MAXIMUM EFFICIENCIES OF THE STEAM-EN'GIXE. 173. The Mathematical Theory of Efficiencies has been comparatively little studied. The thermod ynamic theory, and the efficiency of the ideal engine free from all other than thermodynamic wastes, has been fully developed by Clausius and Rankine and their successors : but neglect of experimental and mathematical investigation of the physics of the case, and consequent ignoring of the practically important conditions distinguishing the real from the ideal case, has often led to seri- ous misconceptions, and to enormous losses of money, in the attempt to realize in practice the advantages indicated as attainable by the pure thermodynamic treatment. In the estab- lishment of a correct and practically applicable theory of effi- ciencies, it is not only essential that the physical, as well as the purely thermodynamic, conditions of working should be taken into the account : but, also, that the several efficiencies should be very carefully distinguished, and that the finance of prac- tical operation should be no less carefully studied. The latter division of the subject, in fact, includes, and depends upon, all the preceding, and, to the user of the engine, presents the con- trolling considerations and the essential problem. 174. The Several Efficiencies of the Steam-engine.* In the design of the steam-engine the engineer has frequent occasion to solve certain problems relating to its economical performance, to determine what proportions of engine and boiler are best adapted to give maximum economy of fuel or of money under certain conditions precisely defined in advance. * Trans. Am. Soc. M. E. ; 1882. 70S 7O6 A MANUAL OF THE STEAM-ENGINE. Such problems may usually be solved by the determination of the ratio of expansion producing maximum economy under the given conditions. Several problems of this character may be classed together, all of which relate to one or another of the " Several Efficien- cies of the Steam-engine," as the Author has called them. These are : (1) Tliermodynamic Efficiency of Fluid. This is measured by the ratio of work done by the working substance to the mechanical equivalent of the heat expended on it to do that work. In the perfect engine-cycle this efficiency is measured by the quantity -; the range of temperature worked through, divided by the maximum, initial, absolute temperature of the fluid entering the cylinder of the engine. To obtain a measure of the thermodynamic efficiency of the working substance, as has already been seen, it is only necessary to measure the work done, as by the measurement of the indicator-diagram, and compare its amount with the mechanical equivalent of the heat expended in its perform- ance. In the case of the steam-engine, this requires the deter- mination of the volume of steam and its weight, at the point of cut-off, the determination, by computation or from the tables, of the quantity of heat required in its production from the feed-water, and, finally, the division of the work shown in the diagram by this quantity. This is substantially the method adopted by Rankine, in the first construction of the thermo- dynamic theory of the heat-engines. In real engines great losses occur by incomplete expansion and by direct transfer of heat from induction to exhaust with- out production of work. (2) Actual Efficiency of Working Substance. This is here considered to be that observed in the actual operation of the engine as the ratio of heat conveyed into the engine by the working fluid, and acting purely thermodynamically, to the total heat entering the system. Various working fluids have different values in this respect. MAXIMUM EFFICIENCIES OF THE STEAM-EA'CIXE. JO? Thus a gas has little conducting or radiating power, can sur- render but little heat and can absorb but little, in its contact with the parts of the machine in which it is employed, while a saturated vapor like steam may take it up with comparative freedom when in contact with hotter substances, and can reject it with enormous rapidity if brought in juxtaposition with a cold body. The latter is a less efficient vehicle of heat for thermodynamic purposes than the former, and, in this respect, a much less satisfactory working substance. The " actual efficiency of the working substance " is lower with saturated than with superheated steam, and with steam than with gas. It varies with every known working substance. (3) Efficiency of the Machine. This is measured by the ratio of the quantity of work yielded to the " machinery of transmission " to that done upon the piston by the working fluid. This is the ratio of the " dynamometric power" to the indi- cated power, and is less as the waste in engine-friction is greater. (4) Efficiency of the Engine. In some cases the product of the total efficiency of the fluid by the efficiency of the machine is called the Efficiency of the Engine or Efficiency of the System. It measures the ratio of the work performed by the engine, externally, to the work-equivalent of the heat supplied it. (5) The Efficiency of the Furnace is the ratio of quantity of heat transferred to the working substance to that developed by combustion of the fuel. (6) The Efficiency of Combustion, or ratio of heat produced by combustion to that latent in the fuel. (7) The Total Efficiency of the Apparatus, or of Plant, as the Author would term it, is the product of these several par- tial efficiencies, and is the fraction of the total calorific power of the fuel which is delivered to the machinery of transmission as mechanical energy. It is a maximum when each of its fac- tors is a maximum. (8) The Efficiency of Capital, or the Commercial Efficiency of Steam Machinery, is measured by the amount of capital re- 70S A MANUAL OF THE STEAM-ENGINE. quired, or the total running expenses, per unit of time, for a given power required and obtained ; i.e., it determines how small a sum will provide a given amount of power, and ivhat size of engine must be selected for the given work, a problem first enunciated by Rankine.* Each of the above efficiencies is made a maximum by a set of conditions the determination of which constitutes an im- portant problem in the science of engineering. Each must be solved, and in a certain definite order, in the application of steam-power to any given case. The determination of the effi- ciency of fluid is included in the problem relating to efficiency of engine, and this and all other efficiencies are included in the last, the efficiency of capital, which cannot be exactly deter- mined unless they are first ascertained. (9) In addition to the above, another problem may present itself to the user of power, although seldom to the designer, or to any one proposing to purchase a steam-engine ; viz., the determination of the maximum economy of a given plant ; i.e., how the most work may be obtained for the unit of cost from a given engine already constructed. This is entirely a different problem from the preceding ; its solution leads to very differ- ent results, and does not usually, if ever, determine maximum commercial efficiency. This problem relates to what may be called the " Maximum Commercial Efficiency of a Given Plant" (10) It may, finally, be necessary to determine still another question : " What is the Maximum Amount of poiver that can be profitably obtained from a Given Plant?" This is a more commonly familiar problem than the last, and in most cases of more direct and practical importance. The solution of all these problems in the case of the real engine and for the purposes of the designing engineer, of the builder, or of the proprietor, is complicated by the presence among the data to be introduced of the varying thermal inter- nal wastes. As has already been stated, however, and as will * Trans. Royal Society of Edinburgh; 1851; vol. xxi. Rankine's Miscel- laneous Papers ; No. xvi. p. 295. Shipbuilding, Appendix ; p. 292. MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. 709 be again shown later, the engineer is always able to say, in ad- vance, how these variations of wastes will affect the problem, and can say in advance, with some degree of approximation, what will be the probable size of the engine, and the slight un- certainty arising from a first approximation based on data ob- tained in this manner becomes insensible with a second ap- proximation obtained by repeating the process of computation or graphical construction, as presently described and illus- trated. 175. Maximum Thermodynamic Efficiency, or the effi- ciency of the working fluid operating under, purely thermody- namic conditions, is, as has been seen, entirely independent of the nature of the fluid selected, and is dependent simply on the limits of temperature adopted and the character of the cycle employed. With the cycle of maximum efficiency, as T T the Carnot cycle, the measure is invariably ' -; with other methods of operation this efficiency is measured by the ratio of work done by the fluid, and of heat thermodynamically transformed in its performance, to the quantity of heat sup- plied from the source during the same period : this period being that of a cycle or of some stated number of complete cycles. The processes by which this ratio is calculated have been already given and examples presented, illustrating their use and practical application. 176. Estimates of Heat, Steam, and Fuel are easily made. Were it possible to utilize all heat stored in the steam supplied to the engine, under the usual conditions of practice, there would be demanded but about 2| pounds (about one kilogram) of feed-water, or of dry steam, per horse-power per hour. The horse-power is the equivalent of 1,980,000 foot- pounds (or in metric H. P. 270,000 kilogram-metres per hour, equal to 2565.5 B. T. U. per hour or 43 units, nearly, per min- ute (metric : 637 calories per hour, or 10.6 per minute). Assum- ing the total available heat to be 1 1 50 B. T. U. per pound as a maximum, the steam of ordinary pressure demanded in a perfect engine of efficiency unity would thus be between 2.2 7IO A MANUAL OF THE STEAM-ENGINE. and 2.25 pounds (one kilog., nearly) per horse-power per hour. Dividing the quantity 2.2 pounds (i kilog.) by the thermody- namic efficiency of fluid will give the weight of steam de- manded at that efficiency, and, assuming a maximum pract\- cally attainable evaporation of 9 or 10 to I, the weight of coal required is obtained by dividing this weight of steam by 9 or 10 for condensing or for non-condensing engines, respectively. Thus : a steam-engine receiving steam at a pressure 100 pounds above vacuum, and condensing it at a temperature corresponding to 4 pounds, the ratio of expansion being 5, has a thermodynamic efficiency of 0.15, nearly ; it would demand about 15 pounds of feed-water per horse-power per hour, and about 1.7 pounds of coal. A non-condensing engine similarly operated would have an efficiency of fluid o.io, nearly, would use about 22 pounds of steam and 2.2 pounds of fuel, the engine being, as before, ther- modynamically perfect. If, in the latter case, the steam-pres- sure were ten atmospheres, this efficiency would become 0.125, nearly, and the steam and fuel consumption 18 pounds and 1.8 pounds, respectively. With larger ratios of expansion the efficiencies would be increased and the expenditure of steam and fuel correspond- ingly reduced. The Gain by Expansion, in an engine free from the wastes which characterize the steam-engine as actually used or for an ideally perfect case, is seen in the table on p. 711, which assumes hyperbolic expansion. Thus it is found that the gross or " absolute" work done by a pound of steam, or, as assumed in the table, by that giving loo units of power, at full stroke, increases enormously with its use expansively, doubling at one-third stroke ; and becoming three times the initial amount at r = 8, and four times at r 20. But, as will be seen when studying the losses of the actual engine, these gains are rarely even approximately real- ized. The extent and the nature and effect of the losses in real engines have been already fully indicated. MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. Jll GAIN BY EXPANSION. Point of Cut-off. :: Efr Work and Power. !, .. J 2*S 6 . --V 5 i 3 X 9 7 H I ? V* " 16 ^77 2 M 18 i " ** The values in the last column of the table are evidently proportional to the quantity, _/.('+ log.*) /.- - - The true, net, work of the engine would be proportional to -A; where p b is the mean back-pressure. Were it possible to expand steam in a non-conducting cylinder, the adiabatic curve would differ slightly from the hyperbola, and the relative work of the steam would corre- spondingly differ, giving figures as follow, for ideal non-con- densing engines : WORK OF ADIABATIC F-XPANSION. Point of Cnt-off Value of U per pound Steam per H.P. per hour. . * 285 1-459 I-667 [23-8 21.4 1l8. 115 ! 107 ', 96 I 1.905 16.4 9i 2.278 2.85 15.4 :: 61 23 712 A MANUAL OF THE STEAM-ENGINE. 177. The Actual Efficiency of Working Substances has been seen to be very greatly less than the thermodynamic efficiency, in any real engines ; the difference being mainly due to wastes of heat by internal storage, conduction, and radia- tion. As shown by experimental investigations, such as have been already described, the magnitudes of these wastes vary with the area of the confining walls of the working cylinder, and the differences of temperatures produced, and probably nearly as the square roots of the times of exposure of the working fluid to refrigerating influences. It is becoming practicable to determine, approximately, the amount of waste to be anticipated when the size of engine arid the conditions of its operation are known. This quantity being added to that demanded by the thermodynamic action of the engine, the total weight of steam required is obtained, and the quotient of the work done, or its heat-equivalent, by the work-equivalent, or the total heat supplied, as just indicated, is the measure of the actual efficiency of working substance in the real, as distinguished from the ideal, engine. Thus: in the cases considered in the preceding section, the ideal condensing engine has a thermodynamic efficiency of about 0.15, and requires about 14.7 pounds of steam, or 1.47 of coal, per hour and per horse-power ; but its exhaust-wastes, due to internal conduction and loss, may amount to one third of all steam entering the engine, fifty per cent of the thermo- dynamic requirement, or to about ten pounds of steam and one pound of coal, making the total 25 pounds of steam and 2.5 of fuel, nearly ; which are very common figures for good engines of moderate size. Similarly, the non-condensing engine, requiring, thermodynamically, 18 pounds of steam, or 1.8 pounds of fuel, if subject to similar losses, would actually demand 32 and 3.2 pounds. The actual efficiency thus be- comes, for the condensing engine o.io, and for the non-con- densing engine 0.065, instead of 0.15 and o.io, as for the ideal case. Relative Actual Efficiency is the efficiency actually attained, as compared with the computed ideal efficiency. It is here MAXIMUM EFFICIENCIES OF THE STEAM-EXG1XE. ?I3 0.667 for the one, and -^ = 0.65, for the second of these two examples. 178. Estimating Consumption of heat, of steam, and of fuel, for the actual case, becomes a very simple matter, approx- imations such as may be based upon the researches already described being accepted. The engineer may desire either to estimate the probable total absolute weight of steam condensed in the cylinder : or he may, for purposes to be presently de- tailed at some length, find it desirable to estimate this waste as percentage or as a function of the ratio of expansion, simply, where all other conditions are constant, and the expansion-ratio is the only variable : thus making two cases. The weight of steam condensed may be estimated as a function of range of temperature, or pressure, of area of in- ternal surfaces, and of time of exposure, or speed of engine. It may also be reckoned as a fraction of the thermodynamic consumption of steam, and in terms of the ratio of expansion. The Relative Actual Efficiency of the working fluid is thus from 0.90 to 0.75 for these cases, The quantity of heat, of steam, or of fuel, being estimated thermodynamically, as already indicated in the preceding sec- tion and the last chapter, the quotient of the quantities so ob- tained by a known relative actual efficiency of a working sub- stance gives the amount of heat, of steam, or of fuel, to be ac- tually consumed. Thus, if the efficiency, calculated from the thermodynamic conditions, be 0.15 : the heat demanded being ^-p = 285 2566 British thermal units per horse-power per minute or 2.2 = 17,107 per hour; the steam called for amounting to = O.22 = 14.7 pounds per hour ; and the fuel amounting to = 1.5 pounds, the product of these quantities by the reciprocal of the 714 A MANUAL OF THE STEAM-ENGINE. relative actual efficiency, -- = i.ni, gives for the real de- mand per indicated horse-power 18,817 thermal units; 15.1 pounds of steam; and 1.67 pounds of coal figures often at- tained by modern engines. The net efficiency of the fluid is thus found to be, for this case, the " indicated power" being considered, E 0.15 X 0.90 = 0.167. It should be remembered that this efficiency of the fluid employed as the medium of energy-transformation is deter- mined both by the physical properties of the substance and by the conditions of its employment in the engine. 179. The Efficiency of the Engine, as a Machine, and be- low unity, as has been seen, is less as the friction of its moving parts is greater. It has been further seen that this friction may probably be usually taken as sensibly constant for all loads, and, for any given, or for the rated, load, as a determ in- able fraction of the resistance or power. In its absolute amount, it may be taken as equal to the product of a nearly constant friction-pressure, as it may be termed, into the area and speed of piston ; and the work of friction is the product of that intensity of pressure, p f , into the volume ASN traversed by the piston in the given time. This pressure being taken as /y, we have U f =p f AS as the work of friction per stroke of piston, and the efficiency of the machine as This efficiency usually varies from E m = 0.80, in small en- gines, to above E m = 0.90, in large engines of the best con- struction. The smaller values are the more common. The total efficiency of the engine is the continued product MAXIMUM EFFICIENCIES OF THE STEAM-EA'CIXE. ^5 of the thermodynamic efficiency, the relative actual efficiency. and the efficiency of the machine. For the case last con- sidered, this becomes E t = E t X E r X E f = 0.15 X 0.90 X 0.95 = 0.129. For a more common case, in which these values are much less, E t = 0.08 X 0.75 X 0.90 = 0.054 ; and only about one eighteenth the energy supplied by the steam-boiler is here converted into useful work ; such as is measured by the absorbing dynamometer and known as the " dynamometric power," the D. H. P., as often symbolized when given in horse-power. T/tf Actual Demand of the engine, as measured in heat, steam, and fuel, is thus known to be often much greater than the quantity computed for the ideal engine, and is, as already seen, readily estimated by multiplying the values for the ideal case by the reciprocal of total, final, efficiency. Thus, for the last example, we have 2566 Heat per horse-power per hour - = 49>37<> ; Steam " " " ^ = 4 - 4: And, for the case next preceding, Heat - jfl = '9.89.B.T.U, Steam, - = 17,054 Ibs.: 7l6 A MANUAL OF THE STEAM-ENGINE. In the best of modern engines, the thermodynamic effi- ciency is about 0.20; the wastes are reduced to about one tenth the total thermodynamic expenditure, making the rela- tive actual efficiency 0.90 ; the efficiency of the machine is not far from 0.95, and the total real efficiency of the system is thus E t 0.20 X 0.90 X 0.95 =0.17, and the actual consumption is Heat, -^ - 1 5,094 B. T. U.; Steam, - = 12.94 Ibs.; Fuel, 222. = 1.29 Ibs* The common non-condensing mill-engine has often, as ac- tually operated, a total efficiency of about E e = o.io X 0.75 X 0.90 = 0.068, and the expenditures are, per H. P. per hour, Heat, ||| = 38,030 B. T. U.; Steam 'bS = 32-35 Ibs.; Fue1 ' = 3-24 Ibs. The efficiency of boiler here assumed is rarely attained, however, and taking the steam evaporated at nine times the weight of fuel, instead of ten, the three cases would give, re- spectively, 2.99, 1.45, and 3.6 pounds of coal per horse-power of work done and per hour ; which are figures now familiar to the experienced engineer. * This is the figure actually attained, since the above was written, by a large Corliss engine designed by Mr. Reynolds. MAXIMUM EFFICIENCIES OF THE STEAM-EXGIXE. ^\^ Accepting Rowland's value of the mechanical equivalent of heat as 778, the quantities above computed become Heat per H. P. per hour, '- = 47.056 ; steam " " S =4o: Coal - - - -' 8 and Heat, - = Steam, i!j=,. 68 Ibs.; Fuel - 57itr M3lbs - : for the first two cases, respectively : and Heat, ~~= 14,941 B.T.U.; Fue1 ' and Heat - = 37,367 B.T.U.; -j 18 Steam, = 29 Ibs. ; 0.068 0.218 Fue1 ' = 2 - for the second pair. 71 8 A MANUAL OF THE STEAM-ENGINE. 180. Thermal Lines and " Curves of Efficiency," as the Author has called the latter, may be now studied for the case of the actual engine.* It has been shown that friction and often to a vastly greater extent cylinder-condensation, due to expansion of a heated fluid in a working cylinder made of a material of high conducting power, modify the methods of expansion and of expenditure of heat so greatly that the ratio of expansion for maximum efficiency, in unjacketed engines, is small, although its value would otherwise be, often, several times greater than it actually is. It was also shown that these modifying con- ditions very differently affect different kinds of steam-engine and different engines and also individual engines, at various pressures and piston-speeds. It has become evident that in no case, in steam-engines as to-day constructed, can the expansion, line or the curve of mean pressures for varying ratios of expan- sion be such as would be obtained in a non-conducting cylinder. Steam must always be more or less condensed at the beginning, and must always carry away heat by its re-evaporization at the end of the stroke. The steam-jacket checks the first operation, but accelerates the last, and, with wet steam, may possibly even increase the evil that it is designed to prevent. The actual expansion-line is not only modified in position and in form by the conductivity of the cylinder, but, also, although perhaps less seriously, by the quantity of water con- tained in the mass of fluid at the instant of closing the expan- sion-valve. The expansion-curve may be often closely represented by a regular curve of the hyperbolic class, p^v* = pv n , the ex- ponent n varying with the proportions of steam and water in the mixture at the commencement of the expansion, which is assumed to take place in a non-conducting cylinder. Table * On the Ratio of Expansion at Maximum Efficiency in Steam-engines; Trans. Am. Soc. Mech. Engrs., 1881; Jour. Franklin Institute, May 1881. On the Behavior of Steam in the Steam-engine, and on Curves of Efficiency; Jour. Franklin Institute, Feb. 1882. MAXIMUM EFFICIENCIES OF THE STEAM EXGIXE. 719 1 1 1, appended, gives the values of the ratio of mean pressure to initial pressure, ^, for various mixtures from steam 1.00, water o, to steam 0.50, water 0.50, assuming the formula to be prac- tically accurate within that range. With these are given the adiabatics for superheated steam, n = 1.333. Table III also gives the values of ~- for steam-expansion in a jacketed metal cylinder, in which it is kept just dry and saturated by heat from the jacketed sides and ends ; the values for wet air com- pressed in air-compressors, in which n is frequently found to be 1.2 ; and for peculiar cases in actual steam-engines in which leakage or re-evaporation, or both, raise the terminal pressures greatly, giving n = 0.50, n = 0.75. Table IV, similarly, gives the ratios . A It is, as yet, impossible to predict which of these curves will be found, in any case, and the engineer is compelled to rely entirely upon the " indicator" for information of this character. The greatest possible variety of curves are found to occur in such cases.* but they approach the adiabatic more nearly, as the steam is drier and as the speed of piston is increased, rarely departing far from the common hyperbola in good engines. Perfectly dry or superheated steam, in fast-running engines, gives a curve most closely approaching the adiabatic ; but the deviation is more marked as the speed of engine is decreased, and as the amount of moisture in the steam, initially, increases. The Emit may be taken as pv / t r, , on the one side, and to p?% = PJP& on the other : the latter being the rare case some- times met with of an unjacketed engine working at a piston- speed below 50 feet per minute (under 15 metres), and with a * An indicator-diagram lying before the Author gives n = i.ooi at the begin- ning of the stroke, = 0.94 at the middle, and m = 0.89 at the end. The com- pression-line starts with *= 1.52 and varies thus, * = i.2o. 9=90.6 to the end. where =O-77, showing that the mean temperature of the surfaces in contact with steam is above that of the vapor during the first half of the period of com- pression, and below that of the fluid during the second half. 720 A MANUAL OF THE STEAM-ENGINE. high ratio of expansion ; while the former is a very usual limit- ing value with well-constructed jacketed engines at good speed. '"Hi kill 1 Where the steam contains much :::: actual engines often, especially -- occurs, lies entirely above the -- curve of Mariotte, the value of n r cases, the line may fall under I . V V \ V . >1 _ _ . 1 K Ijjijijjjjijiijjljjljji <0p^--- IjEJj ^ but rise far above it toward the curve more nearly parabolic in ^ . 1 iN. i i i i ! i ! i i Mil j | i i i gft : W=g%Tf :::::! --- ;: 4j : .30 jl| -L- JyitirllJIIIIIIIIIjlllljllllJ :::::::::::::!: 1|:S:=::^SS; :: :::::::::::::: ::::::::: :::: ::::: 1 15 FIG. 161. CUF MEAN PRESSURE. MAXIMUM EFFICIEXCIES OF THE STEAM-EXGI\E. /2I appearance, and also with a mean value of a less than unity. The values of r ~ giv< P\ I in the tables are plotted in Figs, 161 and 162. These curves of mean pres- sure are valueless, usually, for direct application, but the en- gineer will find them useful in the construction of probable mean-pressure curves for pro- posed engines; and by properly applying them he may obtain practically valuable curves of efficiency for any given class of engines. Referring to Fig. 163, sop- pose a pound, a cylinderful, or other unit of quantity of stecm and water to be drawn from "^ ^ - 3 ^ 722 A MANUAL OF THE STEAM-ENGINE. the boiler, carrying 10 per cent its total weight of water, 90 per cent being saturated steam, and to have a pressure which may be called i.oo. When separated from the boiler and carried into the cylinder it will retain the pressure i.oo and, worked at full stroke, will do the work i.oo. If supplied with additional heat until completely dry, the work becomes i.n at full stroke and, if worked at different ratios of expansion, such steam will give a series of mean pressures represented by the curve of effi- ciency, A lt Fig. 163, as obtained from the expansion-curves whose equation is/^ 1 - 135 = constant, provided expansion occurs in a non-conducting cylinder where no condensation can occur except such as is due to performance of work. Expanded wet, , as drawn from the boiler, the mean pressures of curve B from pv 1 - 12 * = constant, which is deduced by Zeuner for x = go are proportional to the work done by the mixture if worked with- out change of proportion other than occurs by production of work. If, again, the same weight were drawn from the boiler at the pressure assumed and in the same proportions steam 90, water 10 and if, on entering the cylinder, initial condensa- tion should double the quantity of water present, the work at full stroke would be .90 and the mixture would, at other ratios of expansion, the proportion remaining unchanged, give rela- tive quantities of work measured by the ordinates of curve C: pv* = constant. It now contains steam 81, water 19. Simi- larly, the proportion of water present being increased by initial condensation from the original amount carried out of the boiler, so as to reduce the work of unity of weight to .80, .70, .60, .50, etc., at full stroke, the curves of efficiency become as shown in Fig. 163, curves D, E, F, etc., successively, down to the base- line where condensation has become complete and the work of expansion of the water may be neglected. (See, also, 187.) Such are the curves of efficiency, of work, and of mean pressures to be obtained where steam is expanded in a non- conducting cylinder. They are easily deduced and easily con- structed, and, by reference to Zeuner's formula, the engineer can determine them with a satisfactory degree of accuracy for all cases which are likely to arise in his practice. Studying the I FIG. 163. CURVES OF EFFICIENCY. MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. ?2$ behavior of steam in a metallic cylinder, we find vitally differ- ent conditions and results ; but given the law of variation of composition of the mixture with change of point of cut-off, or of ratio of expansion, it is, nevertheless, practicable to deter- mine curves of efficiency, and to deduce values of the best ratio of expansion for any given case, as illustrated in the suc- ceeding section. In the actual engine, steam entering from the boiler at the instant of starting the piston forward consists of a mixture of steam and water, of which the proportions are determined by the character of the boiler-steam and the amount of initial condensation. As the piston moves forward, this proportion becomes independent of all external conditions at the instant of the closing of the steam-valve. From this point on, the interchange of heat between the steam and the sur- rounding walls of the cylinder produces a continuous change of proportion until the exhaust-valve opens. Thus, assuming steam to enter at a pressure of i.oo, and to contain 10 per cent water, its curve of efficiency * starts on curve B and gradually shifts from curve to curve as seen on the plate, curves K, L, and J7 more or less rapidly, as cylinder- condensation takes place to a greater or less extent, the real curve of efficiency usually crossing C, D, E, etc., and taking the general form indicated by lines K, L, O, and P. With con- siderable expansion and wet steam, the expansion-line may again rise during any one stroke, by re-evaporation, toward the end of the stroke to such an extent as to somewhat increase the mean pressures, but this case is, apparently, not a very common one. The amount of that condensation is, evidently, some function of the ratio of expansion in every engine, aqd the Author has been accustomed to take it as varying approxi- mately as some power of r. Lines K, Z, and M, which are pre- sented simply in illustration, represent, respectively, the curves of efficiency when the total loss by cylinder-condensation, k c , varies approximately as Vr, and when A e = o.i i r, h e 0.2 tV, * The curve of efficiency and of mean pressures must not be confounded with the expansion-line representing the varying relations of pressure and volume during the stroke. 724 A MANUAL OF THE STEAM-ENGINE. h c = 0.3 Vr, nearly ; values in per cent of total steam demanded not uncommon in engineering practice. The abscissas of the curves are, as before, measures of weights of steam used. If, in any case, condensation were so to vary that no gain should be derived from expansion and such cases are, within a limited range of expansion, sometimes nearly approximated to the curve of efficiency would become a straight line, N, the " line of constant efficiency," Fig. 163. The curves O and P are obtained by altering the vertical scales of L and M, so as to give them a common initial point with B and K at / = 100, and thus enabling the reader to compare the differences of form of the several lines, and of the two kinds of curve more satisfactorily. It will be seen, later, on comparing the second of the two kinds of curve with those derived from experiment on working engines, and to be presented later, that the curve of efficiency here obtained by induction is of precisely the same character as that given by direct experiment. Referring once more to the set of curves of efficiency, Fig. 163, we may deduce the same conclusions from graphical construction, and obtain results far more easily and rapidly. Pb Selecting values of such as are often obtained with non-con- p. densing and with condensing engines^ respectively, = .20; - = .10, we may determine ratios for maximum efficiency of engine thus: From the points .20 and .10 on the axis of ordi- nates on the scale measuring total work per stroke, draw lines tangent to the several curves, as RT, RV, SV, SW, etc., etc. The points of tangency being found, the values of their abscissas measure the quantities of steam to be used per stroke to give maximum engine efficiency, since the ordinate of any point divided by the abscissa is a measure of the ratio of work done to steam expended in doing it, and, for the assumed back- pressures, the net amount of work per unit's weight of steam is a maximum at the points just identified.* * This principle was pointed out by Rankine. See his Miscellaneous Papers, p. 295, and Shipbuilding, Appendix. MAXIMUM EFFICIENCIES OF THE STEAAf-EXGIXE. 725 On making the construction it will be found that these maxima are found for very nearly the same values of abscissa and, therefore, for the same ratio of expansion, nearly, what- ever the dryness-fraction of the steam used in the non-conduct- ing cylinder. But, drawing tangents RK, RY, SX. SZ. etc., to curves K, C, and J/, to determine the best ratios for the metallic steam-cylinder, values are formed for r far removed from those just obtained for the non-conducting cylinder, and also differ- ing among themselves greatly with the proportion of water present. In the cases shown on the plate, the ratio for the non-condensing engine is decreased to two thirds, and for the condensing engines to less than half that found best for the non-conducting cylinder. It is to be remembered that the quantity of steam used per stroke, although in direct propor- tion to the distances " followed " by the steam up to point of cut-off in the non-conducting cylinder, may be in widely differ- ent proportion with the metal cylinder. In the latter it varies from nearly an equal proportion at full stroke to. often, a double proportion at high ratios of expansion. iSi. The Ratio of Expansion at Maximum Efficiency. In all heat-engines the method of transformation of heat-ener- gy into useful mechanical work has been seen to be the fol- lowing : * A certain mass of the working fluid is heated from a tem- perature which is usually not far from that of the atmosphere up to some higher temperature. This is accompanied by a definite increase of volume, or of pressure, or of both, and in the case of -liquids by a change of physical state after passing a certain point which is variable, but definite for each press- ure ; this latter temperature is the boiling point, and the change is that known as vaporization. Evaporation being complete, the mass is expanded in the working cylinder of the engine until it has attained a certain larger volume, z- t , the magnitude of which is r times that of the initial volume, , , with which expansion began. We thus have the "ratio of * See Journal Franklin Institute ; May 1881. 726 A MANUAL OF THE STEAM-ENGINE. expansion" r = . When expansion is complete, the whole volume, v t , of steam or gas at the pressure/., is rejected from the cylinder into a condenser or into the atmosphere, and the piston which it has impelled through the total volume, z> a f returns to the starting-point, resisted by the " af-pressure," /, of the condenser or of the atmosphere. During the latter operation all heat which has not been transformed into work is rejected, and an additional amount is expended, which is equivalent to the work done by the piston upon the fluid dur- ing its expulsion. This operation is that which has already been more than once described. This process is thus graphically represented : In Fig. 164, the fluid, initially in the state measured by the pressure a or a'E' and volume Oa or Oa', is heated, sometimes at constant volume, as Oa, and sometimes with compression, as from Oa' to a higher temperature, the pressure and volume varying as shown by EA or by E'A. Heated next at constant pressure or at constant temperature, the mass expands, doing work, to B or to B'. At this point, v l , p l , the supply of heat ceases and the fluid expands " adiabatically," transforming into mechani- cal energy all the heat demanded as equivalent to the work measured by the area bBcC, and drawing upon its own stock of heat to supply this demand. At the end of this stage the fluid has a lower temperature and a pressure and a volume, cC, Oc (Pii ^a>) determined by that temperature and the value of r = -, and which are indicated by the location of the point V 1 C. Rejecting heat at constant volume, v t , pressure falls to D, / 3 , and then rejection of heat continuing at constant pressure, / 8 , the volume is reduced to that with which it started. The total or gross work done is, in gas-engines, measured by the area ABCcaA, in steam and vapor engines by this area increased by a very considerable amount the measure of internal, of molecular, work which cannot appear on the indi- cator-diagram. The net work done is measured by the area included in the MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. 727 indicator-diagram ABCDEA. This work is the equivalent of all heat transformed into mechanical work or energy. Ttu efficiency of the fluid is the ratio of net work done to total heat received by the fluid, and is a maximum when the area ABCDE is a maximum, assuming the ratio of expansion alone to vary. It is evident that this maximum is determined, there- fore, by the conditions which make the area bBcC a maxi- mum, which conditions are very simple in the hot-air engine, and are easily expressed, while in the steam and in vapor engines they are very difficult of determination and expression in consequence of their extreme variability. But the efficien- cy of the fluid is but one factor Y in the determination of the ratio of expansion for maximum econ- omy. The heat in the fluid is compelled to do its work, not simply through that fluid as a transmitting mechanism, but also through a machine which, as an \Q a. a 7 " apparatus intended tO imprison F 'S- 164. INDICATOR DIAGRAM WORK OF and direct so subtle and elusive a form of energy as heat, is extremely imperfect, and which has the additional and very serious defect of being itself cumbersome and difficult to start and to keep in motion without considerable loss of power within itself. The useful work of the machine is that which it transmits beyond its own boundaries to other mechanisms, and this is a maximum at that ratio of expansion which gives energy to the machinery of transmission beyond the engine at least cost in heat expended. This efficiency of the system is therefore the product of the factors, total efficiency of the fluid and actual efficiency of the engine considered as a piece of mechanism. Taking first the purely ideal case in which the mechanism is assumed to be perfect and the ratio of expansion the only variable element, we may by examining Fig. 165 see at once what should be the value of that ratio. It is obvious that the ratio of expansion simply determines 7 28 A MANUAL OF THE STEAM-ENGINE. how far the transformation of stored heat-energy existing at B shall be continued by transformation into work during the expansion of the working fluid. It is equally obvious that this expansion should continue until the gain of work by further expansion is more than balanced by losses avoidable by ter- mination of that process. Where the only loss is due to a fixed back-pressure, FD = p s , it is seen that, were expansion to cease at C, the work which would have been done had the expansion-line BC extended to the right beyond C, is lost, and that the counterwork of FIG. 165. ENGINE CYCLES. back-pressure beyond that point is gained ; but the former exceeds the latter, and the net result is a loss by incomplete expansion. On the other hand, were the ratio of expansion increased so that the expansion-line becomes B" , the back- pressure line is reached at D' ; and, beyond this point, we note a gain of work done usefully, which is measured by the area D'EFF'D ', while a loss accrues by back-pressure measured by D'DFF'D'. We thus again meet with a net loss which is represented by D'DED', and expansion has evidently been carried too far. Making the value of r= such that expan- sion reaches the back-pressure line at D and/ 2 becomes equal to / , we meet with neither kind of loss, and it follows that MAXIMUM EFFICIENCIES OF THE STEAM-EXGINE. J2$ expansion should in this ideal case be continued until the expansion-line meets the back-pressure line. This may be readily shown by other methods : It was shown, nearly two generations ago, by Sadi Carnot, that max- imum efficiency of fluid is attained when expanding between the widest possible limits of temperature. It is now well known, and it is shown by every elementary treatise on physics, or mechanics, or thermodynamics, and on heat-engines, that the efficiency of the fluid in any heat-engine is measured by the expression l ^ *, in which 7*, and 7", are the temperatures of reception and rejection of heat measured from the " abso- lute " zero. But this maximum range of temperature corre- sponds to the maximum attainable range of pressure, and, the upper limit being fixed, this range is determined by the value of r and is a maximum when p^ = /, and expansion continues to the back-pressure line. A general analytical demonstration is obtained in the following manner : Problem : Given/,, v lt v * > P* > to find the value of the ratio of expansion, r, which will make the net work done a maximum for the Ideal Case. This work, ABODE, figure, is measured by -pf>** .... (I) and is a maximum when the variable part / ' pdv /,z>, is a maximum. The method of variation of / with variation of v is deter- mined by various conditions which do not affect the analysis. Let this relation be such that we may write, as experiment in- dicates that we may with practically close approximation, *V=A*V = const. ; = r. 73 A MANUAL OF THE STEAM-ENGINE. Thus we have or, for hyperbolic expansion, where n i, W H =fl l v 1 (i -f- log* r) / 3 z' 2 (3) Determining the maximum for the first and usual case, we get j-^ = af I ^ v. -4-^- LJ ^-^ Prv. ) . ,- = O : alir X^ 1 n i ^ 3 V V whence Hence and the ratio of expansion for maximum efficiency of fluid is that which makes the terminal direct pressure equal to the pressure resisting the motion of the piston, and irrespective of the method of variation of/ with v, or of the value of n. This analysis must be modified when the expansion-line is taken as an equilateral hyperbola ; in which case we have n = i and/,^, =A 7 V This case is often assumed in the theory of gas and air engines, as it is in those cases that of isothermal expansion ; but it is probably rarely observed in actual prac- tice, and perhaps never occurs in steam and vapor engines. In simple computations of work, however, the assumption does not lead to serious error, and, so expanding the working fluid, the energy exerted by it, up to the point of cut-off, is equal to the lost work due to back-pressure ; the net work done is measured by the total area under the expansion-line of the MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. 731 indicator-diagram, and the efficiency is proportional to the hyperbolic logarithm of r. Thus we have w * = A", (i + log, r) - whence we again find A -A- The following are values of n for various cases commonly taken in these discussions : VALUES OF n IN p~S = CONSTANT. Air, isothermal expansion i.o " adiabatic " 1 .4 " wet and adiabatic 1.2 Gases generally, isothermal i.o adiabatic 1.4 in explosive gas-engines, Steam, dry and saturated . adiabatic, Steam, 0.76 ; water, 0.24. superheated .6 .046 135 .in 333 Steam and water generally 1.035 H But in all real engines we have a resistance to the motion produced by the expanding fluid, which is composed of two parts : an actual back-pressure on the piston, p b = /,, as in the ideal case above, and a resistance due to friction of engine, including pumps and all attachments. It is evident that, as this latter resistance,//, like the back-pressure, p b , is a constant 73 2 A MANUAL OF THE STEAM-ENGINE. source of lost work, we must terminate the expansion as soon as it produces a greater loss of power or of work than is gained by further expansion. In fact : given a certain value for the sum of these resistances, p b -}-//, we may consider the whole as back-pressure, if we choose ; and it is a matter of indiffer- ence, so far as the determination of the ratio of expansion is concerned, what are their individual magnitudes. To determine /&+//, the sum of resistances due to back- pressure,^, and to the frictional and other resistances as of pumps, etc. denoted by//, take an indicator-card from the engine unloaded. Its mean pressure measures the friction,//, of the unloaded engine, and this, sometimes, probably, increased by a fraction of the pressure added by the load, is the value of //. Or, still better, determine the indicated and the dynamo- metric power of the engine simultaneously ; their difference is lost work, and the value of //, corresponding to that work, is that required. Hence, for actual engines, where no other cause of loss exists of any appreciable magnitude, we may write (6) and, by the process already outlined, we obtain a maximum and deduce Hence : Where the lost energy and work is that due to back- pressure and to friction of engine, the ratio of expansion should be such as to carry the expansion-line down to the mean-pressure line of the engine-diagram taken without load. The useful work is, as before, the gross work done during expansion ; and, thus adjusted, the net useful work and the efficiency are nearly proportional to log* r. This conclusion is obviously true, whatever the value of n or the character of the expansion-line. Thus, as stated by Rankine, " the greatest useful work is obtained by making the expansion cease when the forward- MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. 733 pressure is just equal to the back-pressure, added to a pressure equivalent to the friction of the engine." * For all actual steam and other engines still further and still greater modification is necessary, since in such engines the departure from the ideal conditions first assumed is so great as, in most cases, to lead to radically different ratios of expansion. Even in the gas-engines, the action of the working fluid, as assumed above, is very greatly modified by such variations from the ideal conditions as are here referred to. For any given engine, there is always a certain ratio of ex- pansion appropriate to every steam-pressure, and which gives, on the whole, the most economical performance. Every engine must therefore be most carefully proportioned to the usual conditions of its operation. The best ratio of expansion, kinematically, when the ex- pansion-curve is defined by the expression p m if t = const., is and, for engine-efficiency, friction being considered, r/(-Jf. The defining equation usually takes the form/'V + I = const.; when we have It may evidently be concluded from what has preceded : (i) That the work done in a non-conducting cylinder, the fluid expanding adiabatically, varies so little with the propor- tion of water present that this variation may be neglected by the engineer, and he may assume the performance of work to * Life of John Elder; 1871; p. 16. 734 A MANUAL OF THE STEAM-ENGINE. be such as would come of hyperbolic expansion ; while the heat thus expended may be computed, as in the thermc- dynamic case, from the quantity of work, when the latter is known. (2) That, in cylinders of metal, the work done at any given point of cut-off is nearly the same as in the non-conducting cylinders; but that the quantity of heat and of steam ex pended in doing it are increased, and usually very greatly increased, by cylinder-condensation, if ordinary nearly dry steam is used, or by other methods of storage and transfer of heat to the exhaust, and consequent waste, if superheated steam or other gaseous working fluid is employed. (3) That the ratio of expansion at maximum efficiency of fluid would be but slightly changed by ordinary variations in the proportion of water entrained by the steam, if it were worked in a non-conducting cylinder, and the value of that P ratio, r e , is very nearly -+ , the quotient of initial pressure by the sum of the cylinder back-pressure and other wasteful re- sistances. (4) That the ratio of expansion at maximum efficiency of fluid, when steam expands in a metallic cylinder, is affected by the introduction of water entrained by the steam ; and this difference is increased and usually is made a serious one by the occurrence of cylinder-condensation, or other method of transfer of heat to the exhaust. This ratio becomes, in this case, much less, usually, than r e = ^ . Pb (5) That the quantity of fluid used per stroke, in the non- conducting cylinder, is in direct and exact proportion with the volume of the cylinder open to the supply-pipe at the instant of closing the expansion-valve, and is measured by -, the re- ciprocal of the ratio of expansion. (6) That the volume of steam worked per stroke, in the metal cylinder, is not in direct proportion to volume of cylinder open to steam at the point of cut-off ; but that it is often very MAXIMUM EFFICIENCIES OF THE STEAM-ENGIXE. 73$ greatly in excess of the latter quantity, and is in greater excess, as the ratio of expansion is increased, indefinitely. (7) That the ratio of expansion is not a gauge of the volume of steam demanded from the boiler, and paid for by the proprietor of the apparatus, when the metal cylinder is employed ; but that the volume of steam used, and quantity of heat demanded, must always exceed the proportion in real engines. (8) The Curve of Variation of Efficiency of which the ab- scissas measure varying quantities of steam used in a given steam-cylinder, while the ordinates are proportional to the quantities of work done by those amounts of steam is a curve of entirely different character and form, and often widely dif- ferent in location, with the actual engine, from the curve of adiabatic mean pressures, or other curve of mean pressures exhibiting the work done by various quantities of steam ex- panding in a non-conducting vessel. (91 That no predetermination of the efficiency of any pro- posed engine, whether of fluid, of machine, or of capital, can be made unless the elements of the true curve of efficiency can be obtained for the assumed case (10) That the most certain and the most satisfactory solu- tion of any problem of efficiency will be that obtained by first securing the data for the curve of efficiency, from actual en- gines, operated in the manner proposed for the case taken. (n) That, having obtained, by experiment upon any en- gine, the true " Curve of Efficiency," as defined by the Author, the efficiency of fluid, of engine, and of capital expended to do a given amount of work, and the quantity of work to be ob- tained most cheaply from a given engine, may all be obtained for any given set of conditions : and the ratio of expansion at maximum efficiency, of fluid, of engine, and of capital, and the ratio of expansion which, with a given " plant," gives most work for a dollar of total expense of operation, may all be de- termined with a degree of exactness only limited by the mag- nitude of the errors of observation. 73^ A MANUAL OF THE STEAM-ENGINE. To construct the theory of cases of non-adiabatic expansion, the Author has taken the following method:* We may take two distinct cases: (i) That in which, as when the cylinder is unjacketed and unprotected against radiation and the ratio of expansion small, so little re-evaporation occurs that it may be neglected ; (2) That in which, as in most cases familiar to the engineer, and especially in jacketed cylinders with considerable expansion, nearly all condensation occurs before the point of cut-off is reached, and re-evaporation takes place throughout the remainder of the stroke. Case i. It has been seen that the form of the adiabatic expansion-line may be obtained from approximate expressions of the form pv n = p 1 i> 1 n ; p^ = p l r~ n . Since loss of pressure occurs in the metallic cylinder by a transfer of heat, taking place by initial condensation and later re-evaporation, and since the amount of this loss is determined, in any given cylinder, by the magnitude of the ratio of expan- sion, we may write The values as well as the form of this function of r, f(r) above, are not yet exactly ascertained. The Author has found that for the ordinary values of the ratio of expansion we may assume, as an approximation, f(r) = ar m ; m being taken con- stant. In this expression a, for any engine, has a value which is de- termined by the condition of the steam at entrance into the cy- linder, and is connected with the exponent n by some definite, though as yet unascertained, relation. The value of m is de- pendent upon the character of the engine and the method of its operation, so far as they determine the variation of the proportions of steam and water during expansion. Given the values of n and of a, m becomes determinable. We have * On the Behavior of Steam in the Steam-engine, etc. Trans. N. Y. Acad. Sci., 1882 ; Jour. Franklin Inst., Feb. 1882. MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. 737 where A is the terminal pressure, a quantity always known when either it or r is obtained by experiment. The equation for the expansion-line, the working substance being enclosed in a metallic cylinder, is then The work done by expansion is The net work is in which / 4 is the back-pressure plus friction and useless re- sistance. The terminal pressure is given above. Making r = i, we obtain from that equation A = A(* a ) = A' showing that A is not the initial cylinder-pressure, A '> but the pressure which the same weight of steam would have given if working at the same volume and without condensation in the same cylinder : A exceeds A' in the ratio I : I a ; which ratio measures the relative working values of the same mass of steam with and witnout cylinder-condensation.* Integrating the expression for net work done during ex- pansion, * If x is the " dryness-fraction" of the steam when worked to the end of stroke, it having been dry when drawn from the boiler, /,' = /, x ; jr t = . 73^ A MANUAL OF THE STEAM-ENGINE. we obtain while the total useful work per stroke is F M W e -f- AX- In this analysis the work-effect of re-evaporation is neglected as unimportant. The equation of these curves of efficiency for adiabatic expansion is n The equation for the present case is 3- _ i ar m -"+ l a . nea y< The mean pressure is then and the mean effective pressure is p,r 2 '" p,r~ l ap.r" 1 '* ap.r" 1 , p t - -- -- r- 1 -- h A r~* Pi- i n m n-{- i The mean effective pressure and the work of the engine are maxima, r varying and the back-pressure, p b , being fixed, when * In fact, however, re-evaporation the effect of which is not in such cases usually found to be important in increasing efficiency usually prevents the fall of terminal pressure to the value / 3 =/* MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. 739 provided, as assumed, re-evaporation may be neglected. Then r--r~ =A A The Ratio of Expansion for Maximum Efficiency of Fluid is, however, that which makes a maximum. The A 27 . " cut-off," or fraction of stroke completed at the instant of closing the steam-valve, is = c, and its value for maximum work is that which gives * ac*~ m = . The following cases, illustrating the results of this method of treatment, as applied to several selected examples, such as are met with in ordinary practice, are given as exhibiting a very usual range of values of the quantities involved in the preced- ing equations: Character of Engine. /, pb a m n r t I. Non-condensing engine 100 20 0.2 1.5 1.115 4-5 II. Condensing, un jacketed 40 5 O.2 0.5 1.115 2.5 III. compound, jacketed 60 6 0.1 i.i 1.125 - IV. " " too 5 o.i o.o 1.135 10.0 In the first three of the above cases, the steam is taken from the boiler nearly dry ; in the last, it is so far superheated that it expands as practically dry steam, cylinder-condensation being negligible. Case 2. The second assumed case is probably that usually met with in practice, initial condensation ceasing with the closing of the expansion-valve, and re-evaporation occurs throughout substantially the whole period of expansion. Then, taking b = I a, b thus measures the proportion of actual work done at full stroke to that which the same steam, with- out cylinder-condensation, would do; while r* is a factor pro- portional to the wastes at other ratios of expansion. We may write, for fhe net power delivered : 74^ A MANUAL OF THE STEAM-ENGINE. Here p l v l measures, as before, the work obtainable from the same weight of dry steam, up to the given point of cut-off, when working at the same ratio of expansion, and when, therefore, bp l v l =/>/z/ 1 = (i #)/,?', , as taken in the first case. The above expression, r varying, becomes a maximum when qn ' bqn p l ' The mean effective pressure is n r l ~ A = b 1 * 'A n i A ' and the equation of the curve of efficiency is, for this case of non-adiabatic expansion, y = n i For the case of nearly hyperbolic expansion, which is a common one for this class of engines, W n = bp,v,(\ + log,r)r -A^,, nearly ; which is a maximum when "*// The mean effective pressure is A bp^i -\- log,, r]r q ~ l p b . The value of q varies from o, nearly, to 0.5 ; being greatest with most efficient engines. The ratios of expansion for maximum efficiency are those which satisfy the above equations. The following are corresponding values of a, b, and n: a o.oo .10 .20 .30 b i. oo .90 .80 .70 n 1.135 1.125 1.115 1-105 MAXIMUM EFFICIENCIES OF THE STEAM-EXGIXE. 741 The consumption of steam and cost of power in these cases is measured by the volume actually introduced at the initial pressure, as with the non-conducting cylinder. The values of a and b are very widely variable, as has al- ready been seen (Chap. \j, with variation of working conditions, size and construction of engine ; the engine can easily obtain a fairly approximate figure for either, taking that found by ex- perience to be usually characteristic of similar engines of nearly the size of that which his judgment commonly leads him to anticipate will be approximately that of the engine to be de- signed. Where the commercial and other problems to be here discussed relate to an engine actually in use. these quantities may sometimes be directly determined. Professor Marks has solved this problem, incorporating in his expressions for efficiency the Rankine function of conden- sation-waste.* These expressions thus become somewhat complicated, and graphical methods are commonly preferred by the engineer, in solving all problems of this class. 182. The Efficiency of Capital is the final and the most vitally important of the problems of maximum efficiency. It determines, when solved, the best ratio of expansion, all things considered. But since the quantity of work to be performed and the power of the engine are the magnitudes usually given, and since the size of engine needed to do a given amount of work varies, other conditions being the same, with the extent to which expansion is carried, the solution of the problem giv- ing the ratio of expansion at maximum commercial efficiency, or efficiency of capital, is, really, the determination of the proper size of engine for the case taken. The solution of this problem evidently involves a study of all the conditions affecting either first cost or expenses of operation, immediate or remote, direct or indirect, during the life of the apparatus. Of these items of cost, some are constant for the case assumed : some vary with the size of engine ; and * Steam-engine ; 3d ed., p. 191. 742 A MANUAL OF THE STEAM-ENGINE. others are variable with the size of boiler and quantity of steam demanded.* In Case 8, 174, making the sum of both items of variable annual expense those variable with size of engine and those variable with quantity of steam demanded a minimum, the sum of these items and of all invariable expenses, i.e., of the total running expense, becomes a minimum, and the problem is solved when the ratio of that sum to the quantity of work is thus made a minimum. A knowledge of these conditions and of all other expenses, constant as well as variable, is also es- sential to the treatment of Case Q.f Since economy of fuel and steam demands the use of a large engine, working steam with considerable expansion, and gives reduced size and weight of boiler, it is evident that the first of the two problems, Case 8, 174, is to be solved by de- termining what proportion of engine and boiler will be cheap- est when summed up at the end of the life of the plant ; this is settled when the ratio of expansion at maximum commer- cial efficiency is known, since the mean pressure is thus fixed, and the best size of engine and boiler is thus settled. The work will then be done less economically either by a larger engine and a smaller boiler, or by a smaller engine supplied with more steam by larger boilers. The last enunciated problem, Case 9, is solved by determin- ing what degree of expansion and resulting mean pressure and work will give the power, from an engine and boiler already installed, at least total cost per horse-power. The first of these problems contains, as elements, all items of cost variable with change of proportions of engines and boilers capable of doing the same given quantity of work ; the second considers every item of expense, while the amount of power is the variable quantity. Both problems require the study of all the costs of steam-power, the determination of the way in which each is * The Several Efficiencies of the Steam-engine ; R. H. Thurston. f First treated, so far as the writer is aware, by Messrs. Wolff and Denton. Trans. Am. Society Mech. Engrs., 1881 ; American Engineer, 1881. MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. 743 related to total expense, and the manner in which each varies with variation of the variable quantities in either case. The first of these is the designer's problem, the second the owner's or the user's, as the Author has customarily designated them. If we have given a certain annual invariable expense of operation, certain additional expenses variable with size of engine, and therefore with the ratio of expansion adopted, and certain other additional expenses variable with quantity of steam demanded and with size of boiler needed, and thus also dependent upon the ratio of expansion at which that steam is used, we may call the two latter quantities, respect ively./~"(r) and/"(f), while the constant part maybe called C. Then the total annual expense is f\r)-\-f"(r)-t-C r which is a minimum when the variable part, f\r)-\-f "(r)=j\r) is a minimum, and this is a minimum when its ratio to work done, F(r), is a min- imum, Le., when ^^ is a minimum, or d^\ -s-dr = o. The value of r which satisfies this condition determines the required mean pressure, and gives Maximum Commercial Efficiency. The determination of the value of r which makes p a minimum gives the solution of Case 9. Case 10 is solved by determining at what ratio of expansion the cost of power becomes equal to the market value of the power, less a stated paying profit. The Annual Cost of Steam Power thus consists : (1) Of certain expenses which are invariable, whether the work is done by a large engine with high ratio of expansion and small boilers, or with a smaller engine working at a low ratio of expansion and with necessarily larger boilers. These expenses are, usually : rent of building or interest on cost ; taxes, repairs, etc., etc., on structure and cost of location : the " engineer's" salary, and sometimes all, sometimes part, of the fireman's or "stoker's" wages; also sundry minor expenses, or a part of each of other expenses, which as a whole are variable. (2) The interest on first cost of engine, in place ; the cost 744 A MANUAL OF THE STEAM-ENGINE. of maintenance and repairs ; and a sum which measures the depreciation in value of the machine due to its natural wear, or to its decreasing value in presence of changes that finally compel the substitution for it of an improved engine. Oil, waste, and other engineer's stores fall under this head. All these items are variable with size of engine. (3) The expenses of supplying the engine with steam. These are : (a) The cost, on fuel account, of the steam supplied ; and which includes also the cost of steam condensed en route to the engine, and that wasted by " cylinder-condensation " and by leakage, as well as that actually utilized. This total quan- tity of steam greatly exceeds that actually used in the produc- tion of power by simple transformation of heat energy. This item varies with the efficiency of engine, and deter- mines the size of boiler demanded. . (b) The interest on cost of boilers in place, and their appur- tenances; rent of boiler-room, or interest on its cost ; deprecia- tion, taxes, repairs and insurance, wholly chargeable to boilers. This item is variable with size of boiler. (c) Cost of attendance in excess of the costs included in the constant quantity of item (i) and variable with size of boiler or quantity of steam demanded. The pay of the engineer in charge is usually not chargeable to either engine or boiler alone : his position is one of super- vision over the whole apparatus, and a good engineer usually keeps the closest watch over the boilers. With small engines, the engineer is also the fireman. With large engines, the num- ber of additional firemen may be taken as proportional to the quantity of steam demanded ; and, with very large marine engines, a similar remark may apply to engine-room attendance. In working up this account, it w.ill be most convenient to refer all costs to volumes of cylinder, and to so express variable quantities that they may enter the equations in terms of the ratio of expansion, which ratio is to be taken, as hereafter shown, as an independent variable upon which all other vari- able quantities are made dependent. We will enter all con- MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. 745 slant quantities as so many dollars of annual expense ; the total, invariable expense being denoted by A, which includes all such expenses, whether chargeable to engines or boilers, or both. The first cost of an engine varies according to no defi- nite rule, and differs greatly with type of engine, kind of valve- gear, character of work, and value of material and labor, both at the manufactory and at the place of installatioa With standard forms 01 engine, nowever, it is found that the cost may be reckoned, for ordinary variations of size, as approxi- mately proportional to volume of steam-cylinder; and prices may be fixed on that basis. The cost of transportation, other things being equal, may often be similarly estimated ; as may expenditures for repairs, engineer's supplies, etc.; although these items are less exactly determinable. For present purposes, it may be assumed that interest on cost of engine in place, depreciation, repairs, and all other ex- penses varying with size of engine, may be reckoned per cubic foot of cylinder. The cost of steam supplied to the engine, exclusive of the constant quantity entered in (i) may be reckoned as a certain number of dollars per pound, or per cubic foot of steam worked in the cylinder. The weight of steam supplied for the performance of work when the weight per cubic foot of steam at the given pressure, /, is w ; and its total volume is v^ = v t -f- r, where r is the " real " iw ratio of expansion is wv^ = ; its cost per cubic foot of CWV CIV steam-cylinder is f = , and its total cost per year is 2Rcwv l = 2Rc -, where R is the number of revolutions made by the engine per annum. To this [weight is to be added steam wasted by cylinder, condensation, by leakage, and by conduction and radiation from engine and boiler. This may be allowed for by multiplying the last item by a factor greater than unity, determined as elsewhere shown. 746 A MANUAL OF THE STEAM-ENGINE. 183. Theory of Efficiencies of the Ideal Engine. When the cylinder-condensation and other wastes, and their variation with variation of the ratio of expansion, may be neglected, the " Equation of Ideal Steam-engine Efficiencies" may be writ- ten : 2RW n Where Fmay be called the counter-efficiency, and E"' is the ratio of work done to variable costs, and therefore, in the sense here adopted, the efficiency. This quantity becomes a mini- mum, and the best ratio of expansion and the corresponding mean pressure are obtained when, r being made the indepen- dent variable, n nr l ~ .- A ) = o; r -._*_ Here r has become r"'. A is the total annual charge per cubic foot of cylinder on engine account, B is the annual cost of steam per cubic foot filled each stroke, and is measured by 2Rwc, when R is the number of revolutions of engine per an- num, iv the weight of a cubic foot of steam at the pressure/,, and c its cost per pound, including all running expenses, in the boiler-room, and M = -~ More explicitly : since this problem demands minimum cost of a known power, and the ratio of expansion at Maximum Commercial Efficiency, we have ptrv, = Constant = W. i n i The variable cost will be, as before P= MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. 747 which is to be made a minimum. But from the equation of condition, just given, W Thence du and the minimum is found, as above, when = o ; Le., when The construction of this equation shows that, under the as- sumed conditions, this ratio for maximum commercial economy is not dependent simply on the size of engine or ratio of ex- pansion : but in the real engine small cylinders have a higher value of / than large e ngines, are more subject to wastes, internally and externally, and have greater friction. They therefore require to be worked, under .similar external condi- tions, with less expansion than large engines. Thus the solution of the problem determining the ratio of expansion r/" and the mean pressure at " Maximum Commer- cial Efficiency, or Efficiency of Capital," Case 8, fixes the size of that engine which, doing the required work, will do it at least cost. The sum of all variable expenses being here made a minimum, the total running expense, which includes all in- variable charges, also becomes the least possible, and the pre- scribed work is done at least total annual cost. To find the ratio of expansion at which any given engine, already constructed and in place, Case 9, will give the largest amount of work for the unit of running expense, i.e., to deter- mine the " Ratio of Expansion. r, l , at Maximum Efficiency. of a Given Plant," we may use the same general equation. In 74$ A MANUAL OF THE STEAM-ENGINE. this case, the size of the engine being fixed, the whole annual " cost of engine" becomes constant, and we write the equation in precisely the same form as before, V - I A' ~ 2RW n ' but making the symbol A' cover all annual expenses of the en- gine-room, estimated per cubic foot of cylinder, and including all constant charges of attendance in the boiler-room as well ; while B now only includes those costs which are still variable with the steam-supply ; V thus measures the ratio of total an- nual expenses of operation to work done. We now obtain, by the same process as before, such a ratio of expansion that when TV is a modification of M, such that it represents the ratio of the total expenses classed with engine-cost to the " cost of full steam," as already taken, and r has become r^. Again : making A and M or N equal zero in the general equation, and making p b the sum of useless resistances ex- pressed as the intensity of pressure on the piston, A and r r" , the ratio of expansion at " Maximum Efficiency of Engine." Similarly, if / 3 is the actual back-pressure in the steam-cyl- inder, and we have the ratio of expansion at " maximum efficiency of fluid," r = rj. To solve this problem, therefore, we are to determine the costs of steam, assuming the engine to work at full stroke, in- MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. 74Q eluding all incidentals dependent upon its quantity ; make this the scale of measurement ; find the total costs of engine in the same manner and on the same scale ; ascertain the total con- stant annual or hourly expenses; introduce these quantities into our general equation, or our graphical construction, and solve for the required ratio of expansion. This determined, we are to find what size of engine, working at this ratio, will give the demanded power, and the problem is completely solved. Should the size so determined be far different from that assumed in the estimates of costs and losses, a second approxi- mation, based upon the new estimates of these quantities, will give a satisfactory solution. In each of these several cases the expression obtained is de- rived, it will be noted, by making r the independent variable, and determined by the magnitude of the ratio of the two cost- items, and is the result, under the given conditions, indepen- dent of the actual size of the engine. Thus we determine, in each case, the ratio of efficiency which is correct, under the as- sumed conditions, for all engines of the class upon which our estimates are based. We thus are able now to tabulate the proper size of engine for assumed quantities of work, and the powers at which each engine, once set at work, will operate with maximum efficiency, commercial or other. Finally, com- paring costs, it can be determined in any known case just when a change of engine will be financially advisable. But this simple method of treatment cannot be applied where cylinder-condensation becomes a serious item ; in fact, therefore, it is comparatively valueless for very many cases in engineering practice. 184. Rankine's Diagram of Efficiency. For the ideal case, or any fair physical approximation, Rankine's graphical treatment of the problem here studied is conveniently applica- ble, and by its use the engineer may easily solve such problems by a simple construction on his drawing-board. In illustration : Suppose an engine, of one cubic foot ca- pacity, to be in operation, expanding steam adiabatically, its 750 A MANUAL OF THE STEAM-ENGINE. cylinder and piston being impervious to heat, and the engine having an adjustable expansion-gear. When following full- stroke it uses one cubic foot of steam per stroke, at initial pressure; when "cutting off "at half-stroke, one half cubic ~EE|E~E~EEEEEEEEEE;EEEEEE =^^^i :::::::~z:* ^ ' --~-~ 72 - - ^ f 7/K --/- -A-- . - 7 . . LL / f ,, _ Z_^__ - - f ^/ _ . . _ j ^ _ _ y ".'. __ t j - - Z ~1 . _ J B -L i /+ -dw.K-.Macgo ern De ---R-H^h^tonDei- O ._!__ . .2 .3 .4 -'13. 5. 3.:', 2.5 .5 .6 .1 .8 ..9 2. 1.7 1.4 1.3 1.1 I FIG. 166. RANKINE'S EFFICIENCY-DIAGRAM. foot, and at a cut-off of one quarter, one fourth of a foot, are used, the quantity used always being inversely as the ratio of expansion. To determine the best ratio of expansion : Con- struct a curve, OA, Fig. 166, of which the abscissas are pro- portional to the amount of steam used, while the ordinates are MAXIMUM EFFICIENCIES OF THE STEAM ENGINE. 751 proportional to the mean absolute pressure for that degree of expansion, and the " total work" of the steam so measured off. Drawing a line, BC, parallel to the base, and at a height pro- portional to the back-pressure in the engine-cylinder, the ordi- nate from any point in the curve down to this line will measure the corresponding " mean-effective pressure" shown by the in- dicator for that degree of expansion, and will be proportional to the " indicated power" of the engine. Again : Drawing a line, DE, at the height measuring the sum of all useless resist- ances, the " net" or " dynamometric" power of the engine, as transmitted to the machinery of transmission, is measured by ordinates between the curve and this line. Finally, extending this second line toward the left, and measuring off upon it a distance proportional to the cost of operation so far as it de- pends upon the plant, and measured on the same scale as that used in laying off DG on the base-line in terms of cost of steam, the sum of the two costs, as /% measures the total expense of obtaining the power ; while the height of ordinate GH, measured from the last drawn line, is proportional to the net amount of power obtained. For any one amount of con- stant expense, as determined by the location of the point, F, the line FH, drawn tangent to the curve, touches the latter at a point marking the ratio of expansion at maximum commer- cial economy, or if drawn from the axis OY, as DK, it identi- fies the ratio for maximum "efficiency of engine." To solve this problem of maximum efficiency : Draw the mean-pressure curve OA, making the base-line, OX, a measure of all costs, " at full steam," variable with quantity of steam demanded by the engine, and the ordinates proportional to the mean pressure, corresponding to the cut-off. Draw a line parallel to the base, as BC or DE, at a height corresponding to the back-pressure plus useless resistances of engine.* Take DF equal to the unvarying costs, independent of steam-sup- ply, on the same scale on which DE measures costs of full * I.e., back-pressure plus mean-effective pressure as found on the "friction- diagram." 75 2 A MANUAL OF THE STEAM-ENGINE. steam. Draw a tangent, Fff, to the curve OH A and let fall a perpendicular from H to the base-line. The point thus identified on OX will indicate the proper ratio of expansion for highest total commercial efficiency. This simple and beautiful construction is correct and ex- act, when cylinder-condensation and other wastes of the real engine, as leakage, may be neglected. For other cases this construction may lead to widely inaccurate results. It is ob- vious that any accurate and reliable method must take account of all losses of heat, and must thus distinguish between effi- cient and inefficient classes of heat-engines. 185. Theory of Efficiencies of Real Engines. The di- rect process of analytical treatment of this general problem for real engines, adopted by the Author, is the following : Let it be known what style of engine is to be adopted, for any case, and what kind of boilers and attachments are to be used in supplying steam. Let the costs of attendance and all other expenses be ascertainable. Then, to adopt Rankine's terms, ascertain A, the annual variable "cost of engine" of the selected type, per cubic foot of steam-cylinder, and , the an- nual variable " cost of boiler," per cubic foot of steam-cylinder supplied without expansion and without allowance for cylinder- condensation or leakage ; ascertain all other costs, invariable with change of size of either engine or boiler within the range of the problem, and call their total C. The " cost of engine" will be, as before, Av t = Arv l ; the "cost of boiler" will be Bv^ and the constant charges C. Make 4 = M. z> The work done per stroke may be called W M , and work per annum becomes 2RW n . The ratio of the total of annual variable costs of power to work done by the engine is 2RW n ' r" . which is a minimum when - TJ - is a minimum. MAXIMUM EFFICIENCIES OF THE STEAM-EXCISE. 753 The value of W u may here be obtained by multiplying the value of W, for adiabatic expansion, such as would be obtained in a non-conducting cylinder, by a factor variable with the ratio of expansion, as already shown, which shall measure the ratio of actual work done in the metallic cylinder to that performed with adiabatic expansion. Thus : Let b represent the proportion of steam present in the working cylinder when r = i , as reduced by the cylinder-con- densation ; let r 1 represent the rate of variation of losses with increase of ratio of expansion ; and let n be the index for the expansion-line of the mixture. / nr~* r~ m \ Then we shall have : W m = 2R\bp^ r* pp\. \ ft I j The " General Equation of all Steam-engine Efficiencies" therefore, now becomes which becomes a minimum and makes the Commercial Effi- ciency of an Engine, for the required work, a maximum when, to obtain r/", we have made + q-m+i _ -T A ~Mn( 3 -if -- When the ratio of expansion, r** 9 at " Maximum Efficiency of a Fixed Plant" is required, Av t is constant, and we may make ' * = N, and the equation for Efficiency of Plant becomes " . (C) 754 A MANUAL OF THE STEAM-ENGINE. and this gives, similarly, for r iv and a maximum, ^ + -J^-^~ l - '(?-!) &. -I) Nn(q-l) n I A To obtain r" for Maximum Efficiency of Engine, we make N = o, and have 9 ^-: ^-n+i _ n-i p, q-l n(q-l) ~nb(q-i)p; and to obtain Maximum Efficiency of Fluid, p b becomes/,, and in which r/ satisfies the equation. When ^ = i and q = o, we have the ^/ case considered in 5, and the equation (B) for r,'" becomes, as before, for the perfect engine, for Maximum Commercial Efficiency ; and we again obtain for the ideal case of Maximum Economy of a Given Plant, for r e lv , (H) For Maximum Efficiency of Engine we now again obtain a value of r e ", such that and finally for ideal Maximum Efficiency of Fluid we find a value of r e ' such that ' .-"-.- r-.j ----- ,.. . . . (J) precisely as already stated. MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. /$$ By making the assumption considered allowable by Mr. Buel and by Professor C. A. Smith, and apparently justified by the experiments of Emery and the work of the Author, as already remarked (Chapter V), the equations for the ideal engine and the Rankine diagram may sometimes be made to yield substantially accurate and satisfactory results. In such cases the internal wastes are taken as sensibly invariable for all ratios of expansion and can be reckoned as a part of the con- stant charge in A ; and thus the value of FD, Fig. 166. or of J/, is increased proportionally. As seen later, this value is usually 2 or 3 per cent in the exact case. J/ may become, by the addition of internal wastes, 12 or 15 per cent for un jacketed mill-engines, 8 or 10 per cent for jacketed simple engines, as low as 5 to 7 per cent for compound engines, and still less for the higher types. N will be thus increased to a figure 2 or 3 per cent larger than J/, for non-condensing engines, in ordinary work, assuming the engines of at least two or three hundred horse-power, and 6 or 8 per cent greater for condensing engines, as seen later, in the tables. The constants in the formulas should be carefully deter- mined, if possible, by experiment on the class and the size and speed of engine to be designed ; but, in the absence of better data, are taken by the Author with moderately large engines, at usual speeds, as follows, for good practice : * t I. Cylinders jacketed, steam superheated at boiler 0.90 o. 1.06 II. Cylinders jacketed, steam saturated, but dry at boiler 0.85 0.25 1.06 III. Cylinders unjacketed, steam saturated, but dry at boiler 0.85 0.3 0.98 IV. Cylinders unjacketed, steam slightly moist 0.80 0.5 O-95 Case I is illustrated by the best work of well-known and successful builders. The value of b is obtained by comparing 75 A MANUAL OF THE STEAM-ENGINE. the actual results of test with the figures for the perfect engine to determine the waste ; that of n is obtained by assuming these engines effectively jacketed, the steam being retained dry and saturated throughout the stroke ; and q is taken to be o, since the rate of transfer of heat to exhaust seems to be nearly constant for such engines, as well as, for the usual ratios of expansion, of minimum amount. The second case is obtained by examining scattered records of somewhat less efficient engines. The values of b and q for III are obtained by studying the performance of good unjacketed engines \ while the last, IV, came originally from the results of test of the U. S. S. Michigan, with an allowance of 10 per cent for the unrecorded waste concealed by re-evaporation. In all cases the variations in value, as determined by conditions already fully described (Chapter V) should be considered where the experimental data are taken from engines of a different class or size. 186. Curves of Efficiency for Real Engines. The correct curve for the diagram, for actual engines, has not yet been expressed by any exact equation. It is very variable in location, in form, and in dimensions, and, as yet, can only be exactly determined by experiment. In the diagram above given, as is evident, the quantities of steam laid down in arithmetical progression on the base-line cannot now correspond with the ratios of expansion there taken; since in actual engines those values are not in exact, or in constant, inverse proportion. The quantity of steam drawn from the boiler is not measured by the volume of cylinder open to steam up to the point of cut-off ; nor is the mean pressure obtained with any given weight of steam drawn from the boiler at each stroke, even approximately, equal to that given by expansion in a non-conducting cylinder. Both these causes operate to depress and flatten the curve of efficiency, and thus, often, to reduce the ratio of economical expansion far below that predicted when the former and impossible con- ditions were assumed. The vertical scale of pressures and the horizontal scale of ratios of expansion have become altered in MAXIMUM EFFICIENCIES OF THE STEAM-EXCISE. 757 relative magnitude, and the latter becomes for usual cases a variable scale. To obtain a solution of the actual problem as presented daily to the designing engineer, a new method of procedure must be adopted. The Author has proposed the following : 187. Thurston's Diagrams and Curves of Real Effi- ciency. It has become evident that the best ratio of expan- sion or proper " point of cut-off," and the mean effective pressure to be assumed in designing a proposed engine, for any actual case, is determined, not by the percentage of loss sus- tained at that point simply, or by the cylinder-condensation there taking place, but by the method of variation of such loss all along the curve of efficiency and at other ratios of expan- sion ; since, in the metallic cylinder, the proportion of the water present in the working fluid is constantly varying with change of volume, and the loss of pressure and of work is con- stantly and proportionally varying, producing a curve of effi- ciency differing greatly in character, form, and location from that given by a non-conducting cylinder. It is obtained thus : Assume for the unit of measure so much steam as is drawn from the boiler at one stroke of the piston, without expansion. Draw, Fig. 167, OX, and divide it, as unity of volume or of weight, into a scale of equal fractional parts. Erect at X a perpendicular, XAB, and divide it into any convenient number, say 100, of equal parts. Were there no condensation-wastes, the fluid being worked in a vessel of non-conducting material, instead of an iron steam-cylinder, the mean pressure at full stroke and the work done per cubic foot or per pound of boiler-steam would be measured by XB, and the curve of mean total pressures, or of steam used per " total " horse-power per hour, would be OWE. Condensation reduces the work at full stroke, and it is actually measured by XA. Were the condensation in con- stant proportion for all values of the real ratio of expansion, the ordinates of the true curve would be proportional to those of O WB, and the values of would remain proportional to the 758 A MANUAL OF THE STEAM-ENGINE. expenditure of steam, as in adiabatic expansion. But the amount of condensation usually increases, and often very rapidly, with increasing expansion, and at one half, one quarter, or one eighth cut-off more, and sometimes much more, than FIG. 167. THURSTON'S REAI, CURVES OF EFFICIENCY. one half, one quarter, or one eighth as much steam is used as at full stroke. The scale of ratios, , is thus not only shifted, but is made a scale of unequal parts, of which the successive values must be located by determining the amount of steam used at each point of cut-off, and placing the value - opposite the value of the corresponding amount of steam expended, as has been done in Fig. 166. MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. 759 It may be remarked here that if, as is sometimes under special circumstances nearly true, the losses by condensation and leakage, or both, are so great as to annul the benefit derived from expansion, the curve flattens down to a straight line, OA. In every engine a point is reached by increasing r, at which the amount of steam used per hour per total horse- power is as great as at full stroke ; in every case, therefore, the true curve crosses the line OA, as at C. The line OCE is thus representative of the class of mean-pressure or efficiency curves given be actual engines. Could the variation of expen- diture of heat be exactly expressed by an algebraic equation, this equation would be that of the line ACE, and the problem would be capable of exact solution by algebraic methods. It will be seen that the employment of this curve for the real case by the method previously applied to the ideal case, in the solution of the actual problem, as practically meeting the engineer, results, primarily, in the determination of that quantity of steam per stroke, as a fraction of the conventional unit taken, which will yield the demanded power at minimum cost. The identification of the corresponding, required, ratio of expansion for maximum efficiency is effected after the solu- tion of this problem is completed. The problem solved might have been thus stated : Required, the quantity of steam, taken as a fraction of that used at full stroke, without either expansion or condensation, which should be worked per stroke to insure minimum total cost of the prescribed power. This becoming known, the corresponding point of cut-off is at once determinable. 188. Solution of Problems for Actual Engines. Draw HG at a height above OX, Fig. 167, equal to the back-pressure, p 3 then the tangent line HK identifies a point K, which gives the ratio of expansion and the mean pressure at maximum efficiency of fluid since the ordinate GK measures the work done by the steam HG drawn from the boiler and the ratio (*K *= becomes a maximum at G. Drawing ML to represent HG 760 A MANUAL OF THE STEAM-ENGINE. the pressure demanded to overcome all useless resistance, /=/ 3 +//, a similar construction identifies D as the point corresponding to the ratio of expansion and the mean pressure at maximum efficiency of engine. Finally, extending this line to Fand making VM proportional to cost of all running ex- penses, stated in terms of costs of engine and accessories per A cubic foot of cylinder, VM ' = -%- M for the case of engine working at full stroke, the tangent line VZ meets the curve at a point, D', which gives the ratio of expansion and the mean pressure at maximum commercial efficiency. Comparing these values of r with those given by the tangents, HR, MP, VW, drawn to the curve OWB, for dry saturated steam expanded adiabatically, it is seen that the best ratio of expansion, and the mean pressure to be chosen, must be, in each actual ex- ample, less than in the hypothetical case, and may even become unity for each kind of efficiency, with very slow piston-speeds, where, were no loss of heat to occur in the manner here con- sidered, considerable expansion would be desirable. These differences all become greater as the back-pressures and current expenditures become less. Making the value of VM a measure, in the case of an engine in use, of the total current expenses, including the constant as well as variable items of cost, as of attendance, of rent, insurance, etc., which do not depend on size of engine, A' VM = ~7T N, and a value of r will be obtained which is that n real ratio of expansion at which maximum work is done for a given expenditure, per hour or per annum, on a plant actually established. This problem is less frequently presented to the engineer than those already given, and is not the problem of maximum commercial efficiency ; since, this ratio and the corresponding power of engine being determined, it will be found, on solv- ing for maximum commercial efficiency, the " designer's prob- lem" as the Author has called it, that another proportion of engine with higher ratio of expansion will supply the power Ji/AXIJ/UM EFFICIENCIES OF THE STEAAl-EJCGIXE. j6l now demanded at still lower cost. To this new engine the last problem again applies, and the practical conclusion to be drawn from the solution of the interminable succession of problems of this last character which thus follow the first is that the largest amount of power possible should be en- trusted to a single engineer, or " engineer's crew," and placed under one roof, etc. In this last case, all items become con- stant except those dependent upon the quantity of fuel burned. Finally, the last of these problems may be solved. To ascertain what ratio of expansion, what mean pressure should be adopted, and what amount of work, as a maximum, can be profitably obtained from an established plant : Compute the net power obtainable from the engine without expansion, and the market value, or otherwise real value to the proprietor, of that power, and estimate the cost of fuel and all items of cost variable therewith. Divide the price of power by this cost. .Then lay off, on the base-line appropriate to the given engine, the distance 5F, produced, equal to the quotient, tak- ing the distance MS as unity, and from the extremity of this prolonged base-line draw a straight line, TA f to the point A, at the altitude AS equal to the measure of the net power just calculated. Finally draw a line, UA, parallel to this hypothe- nuse of the triangle so described, and tangent, as at Z\ to the curve of efficiency- The point of tangency Z' wfll identify the minimum profitable ratio of expansion* and thus determine the maximum amount of work obtainable from this engine with profit. For, at this point of tangency the ratio of total cost of power to the price obtainable for it, or to its actual value, is that already given as the greatest permitting a fair profit, while the ratio of expansion so determined is that giving that power at that rate of cost. The value of the Ratio of Expansion at Maximum Profitable Power is evidently, in all actual examples, less, and the work done is greater, than in either of the preceding cases, and is dependent upon the market value of that power. In all cases, the ratio of expansion computed or determined is the real ratio ; the apparent ratio is the former, decreased by 762 A MANUAL OF THE STEAM-ENGINE. clearance, and increased, often considerably, by the wire-draw- ing which occurs just before the valve is seated. It is evident that loss of steam by leakage modifies the curve of efficiency in the same general way as does loss of heat by cylinder-condensation. For cases in which it is allowable to take the weight of steam condensed as constant at all ratios of expansion, the problem may be greatly simplified, and the change of the form of the graphical construction from that adopted originally by Rankine is then but slight. Thus, in Fig. 166, 184, set off DF equal to the "cost of engine" plus that proportional cost which measures the assumed or actual constant value of steam wasted by internal condensa- tion and otherwise ; giving a total cost, GF, which will include not only the " cost of engine" and " cost of steam," but also the wastes of the real engine. This correction obviously throws the point /''farther toward the left, and thus, by carry- ing the point of tangency, //, in the opposite direction, gives an approximately correct measure of the best ratio of expan- sion for the case taken. It is probable that, in very many cases, this simple modification of Rankine's ideal curve and original construction will be found to give perfectly satisfactory results. Another and equally .simple, though less correct, method of approximation is to raise the base-line EDF such a proportion of the abscissa of the point A as will measure the percentage of wastes at a ratio r = I, and make the construction other- wise as before. 189. Construction of Diagrams of Actual Efficiencies. By the application of this method, as proposed by the writer, we may thus determine, from the results of experiment, a set of data and a graphical representation of those results which may serve as a standard for the class to which the engine ex- amined belongs. It is further evident that, the ratio of expan- sion at maximum efficiency being determined by experiment, and with precision by this graphical method, it becomes easy to ascertain with exactness the value of the ratio of expansion Tofaccfag, 763. Fig. sition s the maxi- y ex- sum jiving ngine ies of >rking jnted. is the of no msion is the steam 2 line .m in- ad by B is oa 8 8 6 S 60 4.2 4 XIV 3 5 1 04 II 8 7 4i XX i *> OS IO II 8 6 So 5-6 5* XV 3 5i .04 14 g 8 6 XXI 05 13 14 10 7 100 7-0 6* XVI 3 6 .04 17 10 9 7 XXII $\ .05(18 16 12 8 120 8.4 8 XVII 3 6 04 20 II IO 8 XXIII | 5i 05 33 20 ij Q 150 10.5 IO XVIII 3 6 .04 25 13 10 9 XXIV 3 6 05 7 r s l 10 The value of ^4 being thus obtained, in terms of power, mean pressure, and velocity of piston, the diameter of piston and length of stroke are readily settled. Further investigation will, undoubtedly, sooner or later, establish the curves of efficiency for all standard types of en gine and for those special cases for which the engineer can MAXIMUM EFFICIENCIES OF THE STEAM-EXGIXE. 77 1 day only obtain them approximately. Meantime, the plate exhibits a range of variation of curve which extends completely across the field of every-day practice; and an experienced engineer can trust his judgment in the interpolation of the curve of efficiency for any special case arising in his own practice. For example : Cases of best practice in which the engine is worked at higher speed, and with a warmer condenser, and having less friction, will, when corrected for any differences of size, speed, and range of expansion or temperature, give a curve for the class from which B was obtained which will fall be- tAveen B and C. The values given of are interesting in comparison with Pt the values of r t , as exhibiting the enormous difference between the best ratio of expansion in actual work and the ratio giving maximum efficiency in the ideal case, and also as strikingly presenting to the mind how far we are still, in actual practice, from even an approximation to the conditions exhibited in the perfect, ideal, engine. TABLE II. RATIOS OF EXPANSION GIVING MAXIMUM WORK AT MINI- MUM COST FOR A GIVEN PLANT OF KNOWN PROPORTIONS. CLASS I. CLASS II. Cases. i ii m IT v TI TH vm ix x xi xii N 04 .04 .04 .04 .04 .04 .IO -IO .IO .IO .IO .IO r* I* 2* 2f 3* 3^ 4 if 2* 3 3* 3 4 CLASS IIL CLASS IV. Cases xm xiv xv xn xvn xnii xix xx xxi xxiixxjnxxiv *V-.... .IO .IO .IO .IO .IO .IO .12 .12 .12 .12 .12 .12 r,*V . .... 2i 3 i 4} 4* 4i 4f 4 4* 4| 5 5 5i Table II gives values, similarly obtained for the cases taken, of that ratio of expansion which gives a maximum quantity of work for the unit of value with a fixed arrange- ment of plant. These values are seen to be very much 77 2 A MANUAL OF THE STEAM-ENGINE. smaller than the ratios for maximum commercial efficiency ; and, although they may give more work for such unit than the higher ratios just determined, they do not give maximum efficiency of capital. For : Assume the engine working at this closely adjusted ratio for the now given power, still more work will be given for the unit of cost if the value of r be increased by replacing the given engine by a larger one, in many cases, or in any case by speed- ing up the engine, or otherwise doing the larger amount of work with a new and higher ratio of expansion. The Author has sometimes accomplished this latter result by both speeding up the engine and carrying higher steam, with an automatic adjustment of expansion. The real limit to this increase of work done by the given engine is determined by quite other considerations than those abo've noted. It is determined by the money value of the power obtained, and this increase of power finds a limit, as has been seen, only when either the limit of safety in working engine or boiler is reached, or when the money made by the use of additional power is insufficient to pay a fair profit on the additional expense incurred ; which latter limit may be obtained at a value of r iv either equal to or less than r e . The radical distinction between the problem of maximum efficiency of capital (8) and maximum commercial efficiency of a given plant (9), 174, is here well brought out by this differ- ence of results. Comparing Nos. 7, 12, 13, and 18 of Table I with the same in Table II, it is seen that, instead of ratios of 2, 5, 3, and 9, we have 1.75, 4, 2.5, and 4! ; results which, while absurd as solving the " designer's problem" (8), are perfectly satisfactory as a solution of the " owner's problem" (9). 193. Relation of Costs and Profits. Table III exhibits the effect of variation of actual value of the power in deter- mining the maximum amount profitably obtainable from any engine. For example : Suppose the cost of a horse-power to be, as is frequently the case, about equal to the cost of fuel (in the furnace) producing that power without expansion ; then calling MAXIMUM EFFICIENCIES OF THE STEAM ENGINE. 773 this value p m and this cost p c , the base-line of the diagram will be extended until it measures fc = i = N\ twice the length of OX, and the angle made by the line from its extremity to A, Fig. 1 68, makes an angle = 45 with OX. On the large- scale drawing, set the triangle against the edge of the T-square, and adjust it to the line here given ; find by shifting it along the blade that point on the selected curve of efficiency at which a parallel tangent can be drawn, and then the ratio of expansion, r v , answering to this case, is found If an engine, IV of Class I, is selected, it is found to be r v = 2 : if No. VII of Class II, r v = 2, etc, etc., as in Table III. It is particularly interesting and instructive to observe how the importance of waste, as of cylinder-condensation, in its in- fluence on the best ratio of expansion, here diminishes with decreasing expansion, and that, finally, the most economical and the least efficient give nearly identical figures when the point of cut-off approaches half-stroke. TABLE III. Effect of Variation of Ratio of Market Value to Cost of Power, Maximum Limiting Values of r v . N 1 0.40 0.50 0.60 0.70 0.80 i. oo 2* 2 2 2* 2* 2* 2* 22 27 31 35 39 45 Taking the cost of fuel, in the furnace, for the engine work- ing without expansion, at $50 per annum per horse-power, the above table gives the ratio of expansion below which a loss II VII j " II " X " III xv .... 7 5 4 3 " III " XVII .... 7 5 4 3 IV " XXI 9 7 6 4 3 " IV " XXIV 10 7 6 4 3 774 A MANUAL OF THE STEAM-ENGINE. will accrue when the cash value of the horse-power is 20, 25, 3> 35> 4> and 50 dollars. At these ratios of expansion, all that is received for power above these sums is profit. For other costs, the prices obtained must be correspond- ingly varied to secure a profit. 194. Profits at any Fixed Expansion. Other problems, the converse of the last, may be solved by this construction : " What is the maximum price which can be paid for power without loss at any given mean pressure or ratio of expansion ?" " What profit is obtainable at a given cost ?" " What total cost makes any given ratio of expansion the most economical ?" To solve these problems, draw an ordinate to the line of mean pressures, or the curve of efficiency, at the assumed ratio of expansion ; then the abscissa measures the cost, in terms of full steam, of the power measured by the ordinate, above which loss will accrue, when M = o. The difference be- tween the total cost and the higher price measures the profit obtained if the power is sold at the larger figure. Table IV exhibits the variation of the relative maximum allowable cost of power, with variation of the ratio of expan- sion ; actual cost of expenses variable with fuel, with ratio unity being taken as the unit. TABLE IV. Maximum Limit of Relative Allowable Cost. Most Economical Ratio of Expansion assumed as r. Cost of Frill Steam = Unity. M or N = o. I . Class I No. IV . " II " VII . " II X .1 III XV . " III " XVII . " IV " XXI . " IV " XXIV . 80 .75 -75 -85 .85 .80 .85 i.i ... 75 -80 .95 .75 .70 .70 .75 .80 .90 i.i .75 .70 .70 .70 .70 .75 .90 .75 .70 .90 .65 .70 .75 .90 .75 .70 .65 .65 .55 .55 .65 MAXIMUM EFFICIEXCIES OF THE STEAM-EXGINE. 77$ 195. Cost of Engine as affecting the Best Ratio of Ex- pansion. The effect of variation in cost of engine now be- comes of interest, and indeed a matter of real importance to the designer. Studying cases arising in practice, he will prob- ably find the value of J/or J\"to fall between .02 and .15, as in those selected above, but it will probably rarely, if ever, exceed 0.20. The curve being established correctly for any given engine, it becomes the easiest possible matter to determine the effect of variation of this ratio. Table V gives such results as seem most instructive, from the cases here studied. TABLE V. Effect of Variation of "Exgimt-cost Ratio" Best Values of r f '" orr?. J/ar& .02 .04 .06 .08 ao .15 .20 Class I Example IV 3i 3l 3 2f 2f 2* 2 "II - VII .. 2 2 if if if i \ "II - X .. 4 3f 3* 31 2f 2i " HI - XV .. 6 5 4i 4 3* 3 - Ill - XVII ..8 6 4 | 44 3l 34 - IV - XXI .. 6J 6 5i 4l 3f 3i - IV - XXIV - 9 7 6 5 4 3i These differences in the value of the mean pressure and ratio of expansion at maximum commercial efficiency are least where the exhaust wastes are greatest, and as their absolute values become smaller. Cases IV, X, XVII, and XXIV have the same initial steam-pressure and are seen to approximate toward the same value of r t as the value of M or JV becomes greater, becoming, for the first two, and for the last two, nearly equal to the maximum value here taken. It is obvious that the value r t becomes a good gauge of the economical value of the engine and of its type, and that the greater these values, other things equal, and the nearer r/', r t "" t r,' T approach each other, in any given engine, the better the design. 77$ A MANUAL OF THE STEAM-ENGINE. It is now seen that we have here a method of determining the effect of variations of single variable quantities, while re- taining all others constant a method very greatly needed, but hitherto unknown. The case just taken is an illustration of its application. The following is another instance of no less importance : 196. Back-pressure as Modifying Economy. The Effect of Variation in Back-pressure may be studied, by means of this method of investigation, with the same facility. Table VI exhibits this effect for a wide range of cases. TABLE V. Effect of Variation of Initial Pressure and of Back-pressure. Best Values of r e '. ^ * i t t i A A A Class I No. ' IV 2f 3 i si 3 i II VII I* If If If 2i 2i .. .. " II " X if 2i 2i 3 4 " III " XVI 4i 6 7 9 ii " IV " XXII 6 6 8 12 15 These differences in value of r e are obtained on the assump- tion that cylinder-condensation and all other conditions re- main unchanged while variation occurs in the back-pressure. In all actual cases, the differences would be reduced by the fact that increased condenser-pressure and the reduction of chilling effect which comes with increase of back-pressure so check exhaust waste that the ratio for maximum efficiency be- comes somewhat increased and these differences of ratio are thus lessened. The gain from this and other causes becomes sufficient at high pressures to justify the use of the simpler and less expensive non-condensing engine ; it will be best appreci- ated after comparison of Class I with Class II. An indepen- dent solution of every actual problem is always desirable. 197. Deductions. In illustration of the use of this method and of the application of the results, we may observe as in MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. 7/7 Table I values of the ratio of expansion for maximum effi- ( ciency for any standard type of engine. Thus . Case III is that of an ordinary, standard, non-condensing, drop cut-off en- gine, steam 65 pounds (5^ atmospheres) by gauge, and the cut- off occurs, properly, at a little inside \ stroke , Case V is the same with steam at 105 by gauge (8 atmospheres), and its valve should close a little inside \ stroke. For maximum commercial efficiency those engines should " cut off " at about and i re- spectively. In the second class, Case VII is that of the old naval or modern very low-pressure river-boat engine carrying 25 pounds of steam by gauge (2$ atmospheres). The valve should drop so as to completely shut off steam at about half- stroke to give minimum expenditure for coal, and a little later to give minimum cost on total account,* a result already reached by the builders of such engines. Case VIII is that of some of our old Hudson River steamboats (steam 45 by gauge), and these two ratios are found to be a little greater and a little less than 3. The irregularity of wheel which a short cut-off produces, however, makes it inadvisable to expand as much as this, even. Case IX is often seen in mill-engines ; its valve closes at and for the cases taken. Above this pressure, a comparison of Class I with Class II shows that in the cases taken the non-condensing engine is about as economical as the other a conclusion justified by Isherwood's comparison of Corliss engines f but comparing values of r t '" it is seen that the condenser may probably be exchanged for the heater with Classes III and IV only at some very high pressure not yet at- tained with jacketed engines of good design, while the ten per cent gain obtained at the boiler by the higher temperature of feed given by the heater of the non-condensing engine, to- gether with the differences in size of cylinder, brings down the pressure at which total efficiency becomes a minimum to some * Engines of this class by good builders, having the " Stevens valve-gear," close the valve at 6 feet on a 10 feet stroke, which, allowing for a little throt- tling, gives exactly this figure. Those fitted with the "Sickles cut-off "drop the valve as near half-stroke as possible; they cannot " follow" further. f journal Franklin Institute; Sept. 1881. 7/8 A MANUAL OF THE STEAM-ENGINE lower figure which may be determined, by the method here given, for any given case. Cases XV and XVI are often illustrated on transatlantic steamers and by good compound pumping-engines. The cut- off takes effect at or \ for maximum efficiency of engine and fuel, and at \ or \ for most economical expenditure of money,* figures already settled upon by the most successful builders. Cases XXII and XXIII represent the most advanced practice in the use of high steam pressure, superheated steam, and re- heating at the intermediate receiver, as is done in the pumping- engines of Cowper, Corliss, and Leavitt. The best ratios of expansion are 12 and 15, if measured by duty attained and fuel saved, simply, and two thirds those values give maximum efficiency of capital. Case XXIV represents most nearly that of Corliss* best pumping-engine, which lies between XXIII and XXIV ; its best ratio of expansion lies between 9 and 10, if the curve of efficiency here taken for Class IV suits that case. If nine is the real ratio, the apparent cut-off will be nearly at one tenth, while for maximum efficiency of engine and maximum " duty" the valve should drop at about one- sixteenth stroke. It should be kept in mind that the measure of cost, in all problems relating to expense, as here treated, is the total cost per annum, without expansion, of all items of Class 3, i.e., variable with variation of steam-supply. The problem illustrated by the cases taken up in Table III is of rare occurrence. The following are two such cases : (i) Where the proprietor of an engine can rent power from an engine already set up, having boiler-power sufficient to sup- ply an ample amount of steam, he will obtain the best return from his invested capital by delivering so much power at remunerative prices as will give the values r e ' v , found in Table II. Cases IV, V, and VI are among the most usual, the best point of cut-off averaging about -J stroke. Had this quantity of power to be demanded been originally * Vide Clark's Manual for Mechanical Engineers, pp. 888, 890. MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. 77$ known, however, the proprietor would have done better to have ordered, at the first, a larger or a faster running engine with a higher ratio of expansion, and would usually find it economical to alter the engine here assumed to be used in the manner already described if possible, so as to deliver the maximum power, working at the shorter cut-off. (2) The second is that of a naval engine intended to work with maximum efficiency at low power, or on long runs, and only requiring high power for short periods of time. It has sometimes been customary to design such engines to .work with high ratios of expansion while cruising, and to develop full power with less expansion when in action, supplying a fan- blast for the latter occasion. For such cases the best ratio at low power would be r e ", and it might be well to make the ex- pansion variable through as wide a range as from r" to rj*, taken with extreme values of M and N. As already stated, in all ordinary work, the ratio of expansion at maximum com- mercial efficiency is the ratio of expansion to be adopted for any engine. The values here given for M and N are based on cost of fuel taken at $5 per ton. The value of the ratios of expansion at maximum efficiency will be less at lower prices and greater at higher costs, the expenses of maintenance of plant being constant, since the values of cost of steam will be directly, and of M inversely, as the price of fuel. With coal at ten dollars per ton, M will be practically one half the figures given above, and the least ratio of expansion correspondingly increased as per Table VI. Table III may be consulted by the owner of steam-power for cases which, as is usual, fall within the given limits. For exceptional cases he, or his consulting engineer, can, when data are obtainable, always make his own curve of efficiency and obtain a practically exact solution of the case presented. The curve, B, in the last group of efficiency-curves, may be taken as fairly approximate for simple locomotives ; which fall into the class of simple, unjacketed engines. This deduction is confirmed by comparing independently produced curves. 780 A MANUAL OF THE STRAM-ENGINE. Mr. H. J. Hotchkiss has collated for the Author a consider- able amount of data from reports on the practice of railways in the United States, for the purpose of solving these problems.* Taking the value of engine as $8000, of which 45 per cent, $3600, is charged to boiler and tender, yearly mileage 33,000, life locomotive, 25 years, evaporation 7 to i, the engine costs per mile $4.50, boiler charges at "full steam" $4.00, coal per mile 10.5 cents, labor 7.4 cents, M 0.32, and the problem of the designer being solved, the ratio of expansion at maximum commercial efficiency should be r e = 0.2, nearly, and the engine should be given such size and proportions that it may do its ordinary and average work at that point of cut-off. Once constructed, however, it may be employed, with gradually in- creasing loads, under similar conditions as to costs until its steam is " following" as far as 0.7 stroke and continuously pay better and better, but yet never as well as an engine precisely adopted by the designer for the heavier work. A very similar case gives : Cut-off for maximum efficiency of fluid , 0.40 " " " " " engine 0.48 " " " commercial efficiency 0.63 " " " work and " 0.75 the values of the coefficients being M = 0.27 ; N = 0.89. The assumed conditions may be taken as representing a common set for their data, in the United States and Canada. The following are figures obtained in 1891 in securing the required data for the solution of the "designer's problem" of Chap. VII, Part I. Three types of engine were proposed for driving the electric machinery of a street railway : (I) simple non-condensing ; (II) simple condensing; (III) compound condensing. Their power, market value, etc., were, respectively, as in the table : * For much of most valuable data, Wellington's Railway Location has been referred to. MAXIMUM EFFICIENCIES OF THE STEAM-ENGINE. 781 COSTS AND POWER OF ENGINES. Type I II HI I. H. P., rated. 105 105 112 D -H.P, " 95 95 96 Cost per I. H. P., in place $24 $28 $39 " " " transmission 2 2 2 Total cost $26 $30 $41 Cost of boilers, set, per H. P $14.00 $12.00 $9.00 " " chimney, etc 7.00 6.50 6.00 Total cost $21.00 $18.50 $15.00 Total cost of engine $2560 $3040 $3990 " " "boilers , 1995 1710 1425 " outfi t $4555 $4750 $5415 Coal per I. H. P. per hour 3.5 2.75 2.1 The annual costs, allowing 1.5 per cent tax on a two-thirds valuation, interest 5 per cent, repairs 2 per cent, depreciation of engine 4 per cent, boilers 10 per cent, oil, waste, etc., at 0.0002 per I. H. P. per hour, fuel at $3.00 per ton, amount to about as below : I II III Annual costs 1 $4500 $57/o $3168 and about $500 per annum could be saved by adopting the compound condensing engine, or the interest on $10,000. Taking curve EE on the last figure, Chap. VII, Part I, as satisfactorily approximate for this case, making/, = 100, p b = 3, = 0.033, M = 0.07, the designer finds that he should plan A his engine, for its average power, at r = 7.5, nearly. Maximum efficiency, as determined by the solution of the "owner's problem," is obtained when r 5, nearly. 782 A MANUAL OF THE STEAM-ENGINE. We may compare the preceding with the case of a simple " automatic" non-condensing engine of about 75 I. H. P., of such good construction and such high speed as will make its curve substantially the same as the last, the curve E on the plate. This engine gives the following data : FIRST COSTS. Power, I. H. P 75 D. H. P 67.5 Cost, per I. H. P., engine $25 " " shafting 5 " " " total $30 " " " boilers, set $12 " " " chimney, etc 8 " " " total $20 " total, engine $2250 " " boilers 1500 " plant $3750 Weight, water per I. H. P., per hour, Ibs 25 coal " " " " " 4 The engine is to work 12 hours a day, 313 days in the year. Water costs nothing. ANNUAL COSTS. (i) Invariable : Building and land $7000 Assessment on 4000 Annual taxes @ 1.5 % $60 Interest @ 5.4 % 378 Engine-driver's pay 1000 Fireman's " 700 Total '. $2138 MAXIMUM EFFICIENCIES OF THE STEAM ENGINE. 783 (2) Variable with engine : Interest on cost @ 5.63 % $126.55 Repairs @ 2 % 45.00 Depreciation @ 4 90.00 Taxes @ 1.5 , on f valuation 24.75 Oil, waste, etc., @ 94 cents per I. H. P 70.50 Total $356.80 (3) Variable with boiler : Fuel @ $2 per ton, 563^ $1126.80 Interest @ 5.63 % 84.38 Depreciation and repairs @ 155* 225.00 Insurance @ 0.5 on \ cost 20.00 Taxes @ i.i % on cost 16.50 Total $1472.68 Total of all annual variable costs (2) and (3). . $1829^48 Making use of curve , we find, for p b = 18, /, = 95, = 0.19, and M = 0.85. The results, obtained as before, are : Ratio of expansion for maximum efficiency of fluid 4.35 Ditto for efficiency of engine 3.64 " capital 2.94 And the engine should be designed to do its work at cut-off of about 0.3, but will give highest duty when r = 3.6, nearly. 198. Variation of Cylinder-condensation. One other among the numerous problems capable of solution by this method promises to prove both interesting and important : " Given the method of variation of efficiency with varying ratios of expansion or proportions of steam used, to determine the method of cylinder-condensation with varying values of ." To solve this problem, construct the curve of efficiency, as 784 A MANUAL OF THE STEAM-ENGINE. A, D, , Fig. 167, and draw the curves of adiabatic mean pressures for various values of x, as in dotted lines in that figure. The points of intersection of these curves with the curve of efficiency identify the ratios of expansion at which the total condensation amounts to the proportion due to the adia- batic line so cut. In all problems of maxima or minima solved by the con- struction here given it will be observed that the item of quan- tity of expenditure made the independent variable is that de- pendent upon the quantity of steam or of fuel demanded by the engine. 199. Problems Solved by Inspection of the Diagrams. An important class of problems of simple character may be solved with ease and rapidity by the use of the curve of effi- ciency for the class of engine studied in any case, e.g. : (1) To determine the gain or decrease of power obtainable by change of ratio of expansion or point of cut-off, measure the ordinates of the curve at the present and at the proposed ratio of expansion. Their relative magnitude will be a meas- ure of the relative power of the engine at the two points of cut-off, using the quantity of steam measured by the abscissas. (2) To determine the quantity of fuel or of steam, per hour per horse-power, to be gained or lost by change of the ratio of expansion, compare the value of ratios of abscissa to ordinate at the existing and proposed points of cut-off ; their relation will be that of cost of power in steam or in fuel. (3) To determine the absolute amount of fuel or of steam, consumed per horse-power per hour, at any assumed rates of expansion, first compute the consumption for the given engine as a thermodynamic problem simply, and multiply by the ratio, V , of the mean pressure in the perfect engine at the given expansion to that shown by the true curve of efficiency for the engine studied. Or, compute the consumption for the engine working without expansion and without waste, and multiply MAXIMUM EFFICIEXCIES OF THE STEAM-EXG1XE. 785 p by the ratio, L - , obtaining y and p m from the diagram A", the given cut-off, and remembering that /, measures the mean pressure at full stroke of the given steam used dry. 2OO. Conclusions. In view of what has preceded, it be- comes obvious that the engineer purposing to write a speci- fication for steam machinery on which bids are to be made with guarantee of performance should first determine the probable curve of efficiency for the type and design of engine called for, and should solve all the several problems relating to its economy. He should prescribe the size of engine, then the mean pressure, or the ratio of expansion at which maxi- mum "duty" is to be obtained, as well as fix the duty expected in regular work ; at which ratio the work done will be less than the regular working power of the machine. He must also indicate at what mean pressure, or what degree of expansion, the engine will be required to do its ordinary work at maxi- mum commercial efficiency, and should state what limit of economy at that rate of work will be accepted. Finally, it should be prescribed that the engine should be capable, if its work should be increased, of attaining at least its maximum 4 * efficiency of plant" with safety, and with a specified economy which should be reasonably high. Thus : fixing the mean pressure and the ratio of expansion for the duty-trial, the builder is able to give an intelligently estimated guarantee of performance at highest efficiency; fixing it for maximum commercial efficiency in regular work fixes at the same time the proper size of engine; and the last specification secures ample strength of parts. The cases which have been here investigated must be taken simply as illustrative and not as affording results to be accepted in any specified case coming up in the practice of the engineer. Every such case should be independently and thoroughly in- vestigated. A considerable amount of data and some further illustrations of the principles which have been here enunciated will be found in the concluding chapter of the second part of this work. 786 A MANUAL OF THE STEAM-ENGINE, 201. Absolute Limits to Expansion. It has been gener- ally assumed, hitherto, that the best ratio of expansion, whether for maximum efficiency of fluid, of engine, of capital, or of plant, increases with increase of steam-pressure without limit, and that such ratio may be indefinitely increased with decrease of the ratio of back-pressure for any one kind of engine, not- withstanding the fact that the value of the ratio of expansion is modified by variation of the conditions of working, even where the ratio ~ is the same. But it may be seen that, in every engine operated under the conditions of real work and of usual practice, there exists a limiting value, for any one of these " ratios of maximum efficiency," beyond which it cannot be economically raised, even with a greatly, perhaps infinitely, ele- vated boiler-pressure. It will be further seen that this " abso- lute limit " may be readily, and probably often is, passed in every-day practice; that, in the usual forms of steam-engine, an absolute limit exists, within, or not far beyond, the customary working range of expansion, beyond which expansion cannot be carried with economy, however high the steam-pressure adopted; in other words, with infinite pressure, the economical value of the ratio of expansion will be found often not merely finite, but sometimes probably even within the limits of familiar practice. The designing engineer keeps these facts and all the pseviously described conditions in mind and bases his deter- minations of the character and the principal dimensions of the engine, upon them. These investigations all have for their pur- pose the solutions of the main problem in finance. Studying the equations, it will be found that, in all except those relating to efficiency of engine or of fluid, it is possible to find finite values of r such that their left-hand members shall reduce to zero ; since n nearly always approximates unity; q varies from q O to q = 0.3 in good practice, and b usually ranges between b 0.8 and b 0.9 ; M or N usually has a value between 0.02 and 0.15. Thus the form of the function is such that the first member may always be made to disappear for some finite value of r, and MAXIMUM EFFICIENCIES OF THE STEAU-EXGINE. 7*7 the value of r, at which this condition is obtained, constitutes an " absolute limit," for the case taken, beyond which expan- sion cannot be carried economically, even with steam increased to infinite tension : beyond this point becomes negative, in- dicating the assumption of impossible conditions. Examining equations relating to the purely thermodynamic problem, we find no such limit ; the sign of the first member remains positive for all values of r y and can never become zero for a finite value of that quantity. Thus an important differ- ence here evidently exists between the idtal engine, with its non-conducting cylinder, and the real engine working steam in a metallic cylinder, as well as between the case of maximum efficiency' of engine and that of maximum efficiency of capital. In the case of maximum efficiency of fluid for the ideal perfect engine only, is it true that indefinite increase of steam-pressure permits indefinitely increased expansion. In all other cases an absolute limit exists, fixed for each case, beyond which expan- sion cannot be economically carried. For the U. S. steamers Michigan, Georgiana, and Bache. for which three cases the real curves have been obtained, these curves remaining unchanged by increase of pressure, it is im- possible economically to increase the ratio of expansion in such engines beyond three, five, and ten, respectively, even with un- limited steam-pressure : Le., even when ~f = O- P\ We conclude : (1) That in all real engines there exists an "absolute limit to the economical expansion of steam," whether considered with reference to efficiency of fluid, of engine, or of capital : which limit cannot be passed, whatever pressure of steam may- be carried up to the point of cut-off. (2) That this limit is found at higher ratios of expansion as the type of engine is more efficient, but that the limit is indefi- nitely removed only in the ideal engine, and then only as af- fecting the ratios of expansion at maximum efficiency of fluid and engine. 788 A MANUAL OF THE STEAM-ENGINE. (3) That this limit is found at a small value of the ratio of expansion in ordinary and inefficient engines, and maybe read- ily passed in every-day practice. (4) It is evident that these general propositions are true of all heat-engines having fluid working substances, whether vapors or gases, worked in metallic cylinders. APPENDIX. TABLES. PACK I. NUMERICAL CONSTANTS: CIRCLES; AREAS; ETC 790 II. LOGARITHMS, COMMON AND NATURAL.. 803 III. MEAN PRESSURE RATIOS 806 IV. TERMINAL PRESSURES 809 V. HEAT TRANSFER AND TRANSFORMATION 810 VI. COMPARISON OF THERMOMETERS 812 VII. VOLUMES OF WATER; DENSITIES. 814 VIII. METRIC STEAM TABLE 815 IX. METRIC STEAM AND WORK TABLE. 818 X. STEAM TABLE; BRITISH UNITS 820 XI. STORED ENERGY ix STEAM AND WATER 827 XII. FORMULAS FOR PROPERTIES OF STEAM 829 XIII. FACTORS OF EVAPORATION 831 XIV. COMPOSITION OF FUELS. 832 XV. HORSE-POWER CONSTANTS 834 XVI. REAL RATIOS OF EXPANSION 835 XVII. LOGS AND FORMS FOR BLANKS 836 XVIII. ELECTRICAL HORSE-POWER 840 XIX. WATER COMPUTATION TABLE. 841 XX. HIRN'S ANALYSIS BLANKS. 843 XXI. HEAT AND POWER UTILIZATION; NON-CONDENSING ENGINE 845 XXII. NOTE TO 112 856 - 789 790 A MANUAL OF THE STEAM-ENGINE. I. NUMERICAL CONSTANTS. JZ n-n " 4 * 3 Vi fc I.O 3.142 0.7854 .000 I.OOO .0000 .0000 I.I 3-456 0.9503 .210 1.331 .0488 .0323 1.2 3-770 I.I3IO .440 1.728 0955 .0627 1-3 4.084 I 3273 .690 2.197 .1402 .0914 1.4 4.398 1-5394 .960 2.744 .1832 .1:87 1.5 4.712 1.7672 2.250 3-375 .2247 .1447 1.6 5-027 2.0106 2.560 4.096 2649 .1696 1-7 5-341 2.2698 2.890 4-9I3 3038 J 935 1.8 5-655 2-5447 3.240 5-832 .3416 .2164 1.9 5-969 2-8353 3.610 6.859 .3784 .2386 2.0 6.283 3-1416 4.000 8.000 .4142 2599 2.1 6-597 3-4636 4.410 9.261 .4491 .2806 2.2 6.912 3-8013 4.840 10.648 .4832 .3006 2-3 7.226 4.1543 5-290 12. 167 .5166 .3200 2.4 7.540 4-5239 5.760 I3-824 5492 .3389 2.=: 7-854 4.9087 6.2SO 15.625 -5811 3572 26 8.168 5-3093 6.760 17.576 .6125 3751 2.7 8.482 5-7256 7.290 19.683 .6432 3925 2.8 8.797 6.1575 7.840 21.952 6733 4095 2. 9 Q.III 6.6052 8.410 24.389 .7029 .4260 3.0 9.425 7.0686 9.00 27.000 7321 .4422 3-i 9-739 7-5477 9.61 29.7QI 7607 .4581 3-2 10.053 8.0425 10.24 32.768 .7889 .4736 3-3 10.367 8.5530- 10.89 35-937 .8166 .4888 3-4 10.681 9.0792 11.56 39-304 8439 5037 3-5 10.996 9.6211 12.25 42-875 .8708 0183 3-6 11.310 10.179 12.96 46.656 -8974 .5326 3-7 11.624 10.752 13.69 50.653 9235 5467 3-8 11-938 11.341 14 44 54-872 9494 5605 3-9 12.252 11.946 15-21 59-3I9 .9748 5741 4.0 12.566 12.566 16.00 64.000 .0000 5874 4.1 12.881 *3-203 16.81 68.921 .0249 .6005 4.2 I3-I95 13-854 17.64 74.088 .0494 6134 4-3 13 5<>9 14-522 18.49 79-507 .0736 .6261 4-4 13-823 15.205 19.36 85.184 .0976 .6386 4-5 14.137 15.904 20.25 91.125 -1213 .6510 4.6 14.451 16.619 21. l6 97.336 .1448 .6631 4-7 M.765 17-349 22.09 103-823 .1680 6 7 5f APPENDIX. CONSTANTS Continued. 791 - - ,? m* m* ? $3 26.0 81.681 530.93 676.00 17576.000 5.0990 2.9624 26.1 81.996 535-02 681.21 I7779-58I 5.1088 2.9662 26.2 82.310 539-13 686.44 17984.728 i 5.1185 2.9701 26.3 82.624 543-25 691.69 18191.447 5.1283 2-9738 26.4 82.938 547-39 696.96 18399.744 5.1380 2.9776 26.5 83.252 551-55 702.25 18609.625 1 5.1478 2.9814 26.6 83.566 555-72 707-56 18821.096 ! 5.1575 , 2.9851 26.7 83.881 559.90 712.89 19034.163 5.1672 2.9888 26.8 84.195 564-10 718.24 19248.832 5.1768 2.9926 26.9 84.509 568.32 723-61 19465.109 5-1865 2.9963 27.0 84-823 572.56 729.00 19683.000 5.1962 3.0000 27.1 35.137 576.80 734-41 19902.511 5-2057 3.0037 27.2 85-45r 581.07 739-84 20123.648 : 5-2153 3-0074 27-3 85-765 585.35 745-29 20346.417 5.2249 ! 3-OIII 27.4 86.080 589.65 750.76 20570.824 5.2345 3.0147 27-5 86.394 593-96 756.25 20796.875 5.2440 3-0184 27.6 86.708 598.29 761.76 21024.576 i 5.2555 3-0221 27.7 87.022 602.63 767.29 21253.933 5-2630 3.0257 27.8 87-336 606.99 772.84 21484.952 5-2/25 3.0293 27.9 87.650 611.36 778.41 21717.639 5.2820 3-0330 28.0 87.965 6I5-75 784.00 21952.000 5.29I5 3.0366 28.1 88.279 620. 16 789.61 22188.041 5.3009 3.0402 28.2 88.593 624.58 795-24 22425 . 768 5-3103 3-0438 28.3 88.907 629.02 800.89 22665. 187 5-3197 3-0474 28.4 89.221 633.47 806.56 22906.304 5-329I 3-0510 28.5 89.535 637-94 812.25 23149.125 5.3385 3-0546 28.6 89.850 642.42 817.96 23393-656 5-3478 3-0581 28.7 go 164 646.93 823.69 23639.903 1 5-3572 3-0617 28.8 90.478 651.44 829.44 23887-872 5.3665 3-0652 28.9 90.792 655-97 835-21 24137.569 5-3758 3.0688 29.0 91.106" 660.52 841.00 24389.000 5.3852 3.0723 29.1 91.420 .665.08 846.81 24642.171 5 3944 3-0758 29.2 91-735 669.66 852.64 24897.088 5-4037 3-0794 29-3 92.049 674.26 858.49 25153.757 5-4129 3.0829 29.4 92.363 678.87 864.36 25412.184 5-4221 3.0864 29.5 92.677 683.49 870.25 25672.375 5-4313 3-0899 29.6 92.991 688.13 876.16 25934.336 5-4405 3-0934 29.7 93.305 692.79 882.09 26198.073 5-4497 3.0968 29.8 93-619 697.47 888.04 26463.592 5.4589 3-1003 29.9 93-934 702.15 894.01 26730.899 5.4680 3.1038 30.0 94.248 706.86 900.00 27000.000 5-4772 3.1072 30.1 94-562 711.58 906.01 2727O.9OI 5.4863 3-1107 30.2 1 94-876 716.32 912.04 27543.608 5.4954 3-1141 APPEXDIX. CONSTANTS Continued. '97 m trm - * 4 " *; fc 30.3 95.190 721.07 918.09 27818.127 5-5045 3-1176 30-4 95 505 725.83 924.16 28094.464 5-5136 3.1210 30-5 95.819 730.62 930.25 28372.625 5.5220 3.1244 30.6 96.133 735-42 936.36 28652.616 5-5317 3.1278 30-7 96-447 740.23 942.49 28934.443 5-5407 3-1312 30.8 96.761 745.06 948.64 29218.112 5-5497 3.1346 30.9 97-075 749-9 1 954-81 29503.629 5-:!=7 3-13*0 31 o 97-3S9 754-77 961-00 29701.000 5-5678 3.1414 3i-i 97.704 : 759.65 967.21 30080.231 5o767 3-I448 31.2 98.018 764.54 973-44 30371.328 5-5S57 3.1481 3i-3 93.332 769.45 979-69 30664.297 5-5946 3-I5I5 31-4 98.646 774-37 985-96 30959.144 5.6035 3.1548 31-5 31.6 98.960 779-31 992-25 99.274 784-27 998.56 31255.875 31554.496 5-6124 5-6213 3.1582 3.1615 3i-7 99.588 789-24 1004-89 31855.013 5-6302 3.1648 31- 3 99-903 , 794-23 1011.24 32157.432 5-639I 3-i65i 31-9 100.22 799 23 1017.61 32461.759 5-6480 3.I7I5 32-0 100.53 804.25 1024.00 32768.000 5.6569 3-1748 32.1 100.85 809.28 1030.41 33076.161 5-6656 3.1781 32.2 101.16 814.33 1036.84 33386.248 ! 5.6745 3.1814 32-3 32.4 101.47 101.79 819.40 824.48 1043.29 1049.76 33698.267 34012.224 5.6833 5.6921 3.1847 3.1880 32-5 IO2.IO 829.58 1056.25 34328.125 . 5-7008 3-19*3 32.6 102.42 834-69 1062.76 34645.976 5.7096 3-^945 32-7 102.73 839.82 1069.29 34965-783 5-7183 3-1978 32.8 103.04 844-96 1075.84 35287.552 5.7271 3.2010 32.9 103.36 850.12 1082.41 35611.289 5-7358 3.2043 33-0 103.67 855.30 1089.00 35937.000 5.7446 3-2075 33-1 103-99 860.49 1095.61 36264.691 5-7532 3.2108 33-2 104.30 865.70 1102.24 36594 368 5.7619 3.2140 33-3 IO4.62 870.92 1108.89 36926.037 5-7706 3-2172 33-4 104.93 876.16 1115.56 37259.704 5-7792 3.2204 33-5 105.24 881.41 1122.25 37595-375 5-7879 3.2237 33-6 105.56 886.68 1128.96 37933-056 5-7965 3.2269 33-7 105.87 891.97 1135.69 38272.753 5-8051 3-2301 33 -8 IO6.I9 897-27 1142.44 38614.472 5-8I37 3-2-532 33-9 106.50 902.59 1149.21 38958.219 5.8223 3-2364 34-o 106.81 907.92 1156.00 39304.000 5-8310 3.2396 34-1 107.13 913.27 1162.81 39651.821 5-8395 3.2428 34-2 107.44 918.63 1169.64 40001.688 5.8480 3-2460 34-3 34-4 107.76 108.07 924.01 929.41 1176.49 1183.36 40353.607 40707.584 5-8566 5.8651 3-2491 3-2522 798 A MANUAL OF THE STEAM-ENGINE. CONSTANTS Continued. n - 4 n" ^n h 34-5 108.38 934-82 1190.25 41063.625 ; 5.8736 3.2554 34-6 108.70 940.25 1197.16 41421.736 5.8821 3.2586 34-7 109.01 945.69 1204.09 41781.923 5.8906 ! 3.2617 34-8 109.33 95I-I5 1 2 1 1 . 04 42144.192 5-8991 3.2648 34-9 109.64 956.62 I2I8.OI 42508.549 5-90/6 3-2679 35-o 109.96 962.11 1225.00 42875.000 5.9I6I 3.2710 35-i 110.27 967.62 I232.OI 43243.551 5-9245 3-2742 35-2 110.58 973-14 1239.04 43614.208 5.9329 3-2773 35-3 110.90 Q78.68 1246.09 43986.977 5 9413 3-2804 35-4 III. 21 984.23 1253.16 44361.864 5-9497 3-2835 35-5 "I- 53 989.80 1260.25 44738-875 5-958r 3.2866 35-6 111.84 995.38 1267.36 45118.016 5.9665 3-2897 35-7 112.15 lOOO.gS 1274.49 45499.293 5-9749 3-2927 35-8 112.47 I006.6O 1281.64 45882.712 5.9833 3-2958 35-9 112.78 1012.23 I28S.8I 46268.279 5.9916 3.2989 36.0 113.10 1017.88 I296.0O 46656.000 6.0000 3.3019 36.1 113.41 1023.54 1303.21 47045.881 6.0083 3-3050 36.2 "3-73 IO29.22 1310.44 47437-928 6.0166 3-3080 36-3 114.04 1034.91 1317.69 47832.147 6.0249 3-3III 36.4 "4-35 IO4O.62 I324-96 48228.544 | 6.0332 3.3I4I 39-5 114.67 1046.35 1332.25 48627.125 6.0415 3.3I7I 36.6 114.98 1052.09 I339-56 49027.896 6.0497 3.3202 36 7 "5-30 1057.84 1346.89 49430.863 ! 6.0580 3-3232 36.8 115.61 1063.62 1354.24 49836.032 6.0663 3-3262 36.9 115.92 1069.41 I36l.6l 50243.409 6.0745 3.3292 37-o 116.24 1075-21 1369.00 5O653.00O 6.0827 3-3322 37-1 "6-55 108 i . 03 1376.41 51064.811 6.0909 3-33=2 37-2 116.87 1086.87 I383.84 51478.848 6.0991 3.3382 37-3 117.18 1092.72 1391.29 5I895.II7 6.1073 3-3412 37-4 117.50 1098.58 1398.76 52313.624 6.1155 3-3442 37-5 117.81 1104.47 1406.25 52734-375 6.1237 3-3472 37-6 118.12 1110.36 1413.76 53I57-376 6.1318 3-3501 37-7 118.44 1116.28 1421.29 53582.633 6.1400 3-3531 37-8 118.75 1122.21 1428.84 54010.152 6.1481 3.3561 37-9 119.07 1128.15 1436.41 54439-939 6.1563 3-3590 38.0 119-38 II34-" 1444.00 54872.000 6.1644 3-3620 38.1 119.69 1140.09 I45I.6I 55306.341 6.1725 3-3649 38.2 I2O.OI 1146.08 1459.24 55742.968 6.1806 3-3b79 38.3 120.32 1152.09 1466.89 56181.887 6.1887 3-3708 38-4 I2O.64 1158.12 1474.56 56623.104 6.1967 3-3737 38-5 120.95 1164.16 1482.25 57066.625 6.2048 3-3/67 38.6 121.27 1170.21 1489.96 57512.456 6.2129 3.3796 38.7 121. *S 1176.28 1497.69 57960.603 6.2209 3-3825 APPENDIX. CONSTANTS Continued. 799 - -; ft* - t^ h 38.8 121.89 1182.37 1505.44 58411.072 6.2289 3-3854 38.9 122.21 1188.47 1513-21 58863.809 6.2370 3-3883 39-0 122.52 1194.59 1521.00 59319.000 6.2450 3.3912 39-i 122.84 1200.72 1528.81 59776.471 6.2530 3-3941 39-2 123.15 1206.87 1536.64 60236.288 6.2610 3-3970 39-3 123.46 1213.04 1544.49 60698.457 6.2689 3-3999 39-4 123.78 ! 1219.22 1552.36 61162.984 6.2769 3-4028 39-5 124.09 1225.42 1560.25 61629.875 6.2849 3.4056 39-6 124.41 1231.63 I568.I6 62O99.I36 6.2928 3.4085 39-7 124.72 1237.86 1576.09 62570.773 6.3008 3-4"4 39-8 125.04 1244-10 1584.04 63044.792 6.3087 3-4I42 39-9 125.35 1250.36 1592.01 63521.199 6.3166 3.4I7I 40.0 125.66 1256.04 1600.00 64000.000 6-3245 3-4200 40.1 125.98 1262.93 1608. 01 64481.201 1 6.3325 3-4228 40.2 126.29 1269.23 1616.04 64964.808 6.3404 3-4256 40-3 126.61 1275.56 1624.09 65450.827 6.3482 3-4285 40.4 126.92 1281.90 1632.16 65939.264 6.3561 3.43I3 40.5 127.23 1288.25 1640.25 66430.125 6.3639 3-4341 40.6 127.55 1294.62 1648.36 66923.416 6.3718 3-4370 40.7 127.86 1301.00 1656.49 i 67419.143 6.3796 3-4398 40. S 128.18 1307.41 1664.64 67911.312 6.3875 3-4426 40.9 128.49 1313-82 1672.81 68417.929 6-3953 3-4454 41-0 128.81 1320.25 1681.00 68921.000 6.4031 3.4482 41.1 129.12 1326.70 1689.21 69426.531 6.4109 3-45io 41-2 .129.43 1333.17 1697.44 69934.528 6.4187 3-4538 41-3 129.75 1339.65 1705.69 70444.997 6.4265 3.4566 41-4 130.06 1346.14 1713-96 70957.944 6-4343 3-4594 41-5 130.38 1352.65 1722.25 7I473.375 6.4421 3-4622 41.6 130.69 1359-18 1730.56 71991.296 6.4498 3-4650 41-7 131.00 1 1365.72 1738.89 72511.713 6.4575 3-4677 41.8 131.32 1372.28 1747-24 73034.632 6.4653 3-4705 41.9 131.63 1378.85 1755-61 73560.059 6.4730 3-4733 42.0 131-95 1385.44 1764.00 74088.000 6.4807 3.4760 42.1 132.26 1392.05 1772.41 74618.461 6.4884 3-4788 42.2 132.58 1398.67 1780 84 75151.448 6.4961 3-4815 42.3 132.89 1405.31 1789.29 75686.967 6.5038 3-4843 42.4 133.20 1411.96 1797.76 76225.024 6.5115 3.4870 42.5 133-52 1418.63 1806.25 76765.625 6.5192 3-4898 Ja.6 133-83 1425.31 1814-76 77308.776 6.5268 3-4925 42.7 42.8 134.15 134.46 1432.01 1438.72 1823.29 1831.84 77854.483 78102.752 6-5345 6.5422 3-4952 3-4080 42.9 134-77 1445-45 1840.41 78953.589 6.5498 3-5007 800 A MANUAL OF THE STEAM-ENGINE. CONSTANTS Continued. 43-o JT -i V h I35-09 1452.20 1849.00 79507.000 6-5574 3 5034 43-1 135-40 1458.96 1857.61 80062.991 6.5651 3-5o6i 43-2 135-72 1465.74 1866.24 80621.568 6-5727 3-5088 43-3 136.03 1472.54 1874.89 81 182.737 6.5803 3.5II5 43-4 136.35 1479-34 1883.56 81746.504 6-5879 3-5I42 43-5 136.66 1486.17 1892.25 82312.875 6-5954 3-5169 43-6 136.97 1493-01 1900.96 82881.856 6 . 6030 3-5196 43-7 137.29 1499.87 1909.69 83453-453 6.6ic6 3-5223 43-8 137.60 1506.74 1918.44 84027.672 6.6182 3-5250 43-9 137.92 1513-63 1927.21 84604.519 6.6257 3-5277 44-0 138.23 1520.53 1936.00 85184.000 6.6333 3-5303 44-i 138.54 I527-45 1944.81 85766.121 6.6408 3-5330 44-2 138.86 1534-39 1953 64 86350.888 6.6483 3-5357 44-3 139-17 I54L34 1962.49 86938.307 6.6558 3-5384 44-4 139-49 1548-30 1971.36 87528.384 6.6633 3 54-^c. 44-5 I39-80 I555-28 1980.25 88121.125 6.6708 3-5437 44-6 I4O. 12 1562.28 1989.16 88716.536 6.6783 3-5463 44-7 140.43 1569-30 1998.09 89314.623 6.6858 3.5490 44.8 140.74 1576.33 2007.04 899I5-392 6.6933 3-55i6 44-9 I4I.O6 I583-37 2016.01 90518.849 6.7007 3-5543 45-0 I4L37 I590-43 2025.00 91125.000 6.7082 3-5569 45-1 141.69 I597-5I 2034.01 9I733-85I 6.7156 3-5595 45-2 142.00 1604.60 2043.04 92345.408 6.7231 3-5621 45-3 142.31 1611.71 2052.09 i 92959.677 6./305 3-5648 45-4 142.63 1618.83 2061.16 ' 93576.664 6-7379 3-5674 45-5 142.94 1625.97 2070.25 94196.375 6-7454 3-5700 45-6 143.26 1633.13 2079.36 94818.816 6.7528 3-5726 45-7 143-57 1640.30 2088.49 95443-993 6.7602 3-5752 45-8 143.88 1647.48 2097.64 96071.912 6.7676 3-5778 45-9 144.20 1654.68 2106.81 96702.579 6-7749 3-5805 46.0 I44.5I 1661.90 2116.00 97336.000 6.7823 3-5830 46.1 144.83 1669.14 2125.21 97972.181 6.7897 3-5856 4 6.2 145-14 1676.39 2134-44 98611.128 6.7971 3-5882 46-3 145.46 1683.65 2143.69 99252.847 6.8044 3 5908 4 6. 4 145-77 1690.93 2152.96 99897.344 6.8117 3 5934 46.5 146.08 1698.23 2162.25 100544.625 6. 8191 3-5960 46.6 146.40 1 75 -54 2171.56 101194.696 6.8264 46-7 146.71 1712.87 2180.89 101847.563 6-8337 3.6011 46.8 M7.03 1720.21 2190.24 102503.232 6.8410 3-6037 46.9 147-34 I727-57 2199.61 103161.709 6.8484 3-6063 47-o I47.65 1734-94 2209.00 103823.000 6.8556 3.6088 47-1 147-97 1742.34 2218.41 104487.111 , 6.8629 3-6114 47-2 148.28 1749.74 2227.84 105154.048 6.8702 3.6i39 APPENDIX. fn ri~T- Cimfimmtf 801 . 4 IT. h 47 3 148.60 1757.16 2237.29 105823.817 ", - " " - 3-6165 47-4 i : _ : . : : 1764.60 2246.76 106496.424 -- "- : 36190 47-5 149-23 1772.05 2256.25 I07I7I.875 6.8920 3.6216 47-6 149-54 1779.52 2265.76 107850.176 6-8993 3 .6241 47-7 j :- -: 1787.01 2275.29 108531.333 6.9065 : 47-8 ; 150.17 1794 51 2284.84 109215.352 6.9137 : -:- 47-9 1802.03 2294.41 109902.239 6.9209 3.6317 48-0' I: - 1809.56 2304.00 110592.000 6.9282 3.6342 i : 151.11 lSl7.II ! 23I3.6I 111284.641 6-9354 3-6368 48.2 151.42 151-74 1824.67 ' 2323.24 111980.168 :-:; :: 2332.89 112678 587 6.9426 3.6393 6.9498 3.6418 48.4 152.05 1839.84 j 2342.56 113379.904 6-9570 3-6443 48.5 152.37 1847-45 2352-25 114064-125 6.9642 .- --'- 48.6 :=: : r 1855.08 2361.96 114791.256 6-97M 3-6493 --.- 153.00 1802.72 2371.69 115501.303 6-97S5 3-6518 153-31 1870.38 2381.44 116214.272 3.6*43 153.62 1878.05 2391.21 116930.169 6.9928 3.6568 49-0 153-94 18*5.74 2401.00 117649.000 .7.0000 3-6593 49 I 49-2 49-3 154-25 154-57 :-_ -- 1803.45 2410.81 1901.17 2420.64 1908.90 2430-49 118370.771 119095-488 119823-157 7-0071 7-0143 7.0214 m 49-4 155.19 1916.65 2440.36 120553.784 7-0285 | 3-669* 49-5 49-6 ::: -.: : '- 1924.42 2450-25 1932.21 2460.16 :;::-- --: 122023.936 7-0356 3-6717 3-6742 49-7 156.14 1940.00 :_-. :. 122763.473 7.0498 3-6767 156.45 1947-82 2480.04 123505.992 7.0569 , .... 49-9 156.77 1955.65 i 2490.01 124251.409 7.0640 3.6816 50.0 51.0 157.08 160.22 1963.50 : _: -: 2500.00 2601.00 125000.000 132651.000 7.0711 7-I4I4 : '.-''- 52.0 163-36 2123.72 2704-00 140605.000 7-2IH 3.7325 53-0 166.50 2206.19 2809.00 148877.000 7.2801 54-0 169.64 2290.22 2916.00 157464.000 .; gj 55-0 172.78 - -. - : - : 3025.00 166375.000 f.iloi 56.0 57-0 175-93 179.07 M63.01 3136-00 3249-00 175616.000 185193-000 7-4*33 3-8259 7.5498 3-8485 :T : 182.21 : ; _:.:- 5364 x 195112.000 7-6158 3-8709 59-O 185.35 2733-97 IfBl 205379.000 7.6811 3-8930 60.0 188.49 :-:- ^ 3600.00 216000.000 7.7460 3.9149 61.0 191.63 2022-47 3721-00 226981.000 : 7.8102 3-9365 62.0 194-77 3019.07 .--- : 238328.000 1 7-8740 3-9579 63.0 64.0 197.92 201.06 3117.25 3216.99 3969.00 4096.00 250047-000 i 7-9373 3-9791 262144-000 ; 8.0000 4.0000 65.0 66.0 204.20 33I8.3I 3421.20 4225.00 4356-00 274625.000 287496 ooo 8.0623 4.0207 8.1240 40412 802 A MANUAL OF THE STEAM-ENGINE. CONSTANTS Continued. n nit "'I 3 v* *' 67.0 210.48 3525-66 4489.00 300763.000 8.1854 4.0615 68.0 213-63 363I-69 4624.OO 314432.000 8.2462 4.0817 69.0 216.77 3739-29 476I.OO 328509.000 8.3066 4.1016 70.0 219.91 3848-46 4QOO.OO 343000.000 8.3666 4.1213 71.0 223.05 3959.20 5041.00 357911.000 8.4261 4.1408 72.0 226.19 4071.51 5184.00 373248.000 8.4853 4.1602 73-0 229.33 4185.39 5329.00 389017.000 8.5440 4-J793 74-o 232.47 4300.85 5476.00 405224.000 8.6023 4.1983 75-o 235-62 4417.87 5625.00 421875.000 8.6603 4.2172 76.0 238.76 4536-47 5776.00 438976.000 8.7178 4.2358 77.0 241.90 4656.63 59 2 9 oo 456533.000 8.7750 4-2543 78.0 245.04 4778.37 6084 . oo 474552.000 8.8318 4.2727 79.0 248.18 4901.68 6241.00 493039.000 8.8882 4.2908 80.0 25L32 5026.56 6400.00 512000.000 8.9443 4-3089 81.0 254-47 5153.01 6561.00 531441.000 9.0000 4.3267 82.0 257.61 5281.03 6724.00 551368.000 9-0554 4-3445 83.0 260.75 54IO.62 6889.00 571787.000 9.1104 4-3621 84.0 263.89 554L78 7056.00 592704.000 9.1652 4-3795 85.0 267.03 5674.50 7225.00 614125.000 9.2195 4-3968 86.0 270.17 5808.81 7396.00 636056 . ooo 9.2736 4.4140 87.0 273-32 5944-69 7569.00 658503.000 9.3274 4.4310 88.0 276.46. 6082.13 7744.00 681472.000 9.3808 4.4480 89.0 279.60 6221.13 7921.00 704969.000 9.4340 4.4647 90.0 282.74 . 6361.74 8100.00 729000.000 9.4868 4.4814 91.0 285.88 6503-89 8281.00 753571.000 9-5394 4-4979 92.0 289.02 6647.62 8464.00 778688.000 9-59I7 4-5144 93-0 292.17 6792.92 8649.00 804357.000 9-6437 4-5307 94.0 295-3I 6939.78 8836.00 830584.000 9.6954 4-5468 95-0 298.45 7088.23 9025.00 857375-000 9.7468 4.5629 96.0 301-59 7238.24 9216.00 884736.000 9.7980 4-5789 97.0 304-73 7389.83 9409.00 912673.000 9.8489 4-5947 98.0 307.87 7542.98 9604 . oo 941192.000 9-8905 4.6104 99.0 311.02 -697.68 9801.00 970299.000 9.9499 4.6261 IOO.O 3I4-I6 7854-00 lOOOO.OO lOOOOOO.OOO IO.OOOO 4.6416 APPENDIX. 803 II. LOGARITHMS. HYPERBOLIC LOGARITHMS. Log. Log. N. Log. N. Log. Log. *a : : r - - r '- - :g .65 1 70 :E| .85 .05 3365 .3716 4055 4383 .4700 .5008 .5306 35 40 45 3.60 3-65 3-70 3-75 3.80 3-85 3-90 3-95 10 5 30 35 40 - : " io 85 5892 6.40 6.70 6.80 6.90 7-00 7-20 7-40 7.60 8'ot I' 25 8.50 8-75 9.00 9.25 9-50 9-75 10.00 it. oo 13.00 13.00 I4.OO .8871 .902. .9169 -93'5 -9459 974* .0015 .0281 .0541 0794 .1102 : :Z5 .2513 33 .77*6 COMMON LOGARITHMS: 10-1200. S 804 A MANUAL OF THE STEAM-ENGINE. COMMON LOGARITHMS Continued. 8 9 Oiff N. 1 2 30 47712 47857 4800, 48144 48287 48430 48572 48714 48855 48996 40 3 1 49136 49276 49415 49554 49693 49831 49969 50,06 50243 50379 36 3 2 50515 50651 50786 50920 51055 5"88 5,322 51455 5,587 51720 32 33 51851 51983 52244 52375 52504 52634 52763 52892 53020 8 34 53275 53403 53529 53656 53782 53908 54033 54158 54283 4 35 54407 55630 54531 55751 54654 55871 54777 5599' 54900 56,10 55023 56229 55*45 56348 55267 56467 55388 55509 56585 56703 7 1 57978 56937 58092 57054 58206 57I7I 58320 57287 58433 57403 S75I9 58659 57634 58771 57749 57864 58883 58995 4 i 39 59106 592,8 59329 59439 59550 59660 59770 59879 59988 60097 09 40 60206 60314 60423 6053, 60638 60746 60853 60959 61066 6,172 06 41 61278 61384 6,490 6,595 61700 61805 61909 62014 62118 6222, 04 4 2 62325 62428 6253, 62634 62737 62839 62941 63043 63,44 63246 43 44 63347 64345 63448 64444 63548 64542 63649 64640 63749 64738 63849 64836 63949 64933 64048 65031 64147 64246 65128 1 65225 99 97 45 65321 65418 655M 656,0 65706 65801 65896 65992 66087 i 66,8, 95 46 66276 66370 66464 66558 66652 66745 66839 66932 67025 67117 93 47 672,0 67302 67394 67486 67578 67669 67761 67852 67943 68034 90 48 49 68*24 69O2O 682,5 69,08 68305 69,97 68395 69285 68485 69373 68574 69461 68664 69548 68753 69636 68842 68931 69723 ; 69810 89 87 5 69897 69984 70070 70157 70243 70329 70415 70501 70586 70672 86 5' 5 2 70757 71600 70842 7,684 70927 7,767 71012 71850 7,096 7'933 71181 72016 7,265 72099 71349 72181 7M33 1 7I5I7 72263 72346 84 83 53 72428 72509 72591 72673 72754 72835 72916 72997 73078 73159 81 54 73239 73320 73400 73480 7356o 7364 73719 73799 73878 73957 80 55 74036 74"5 74194 74273 74351 74429 74507 74586 74663 74741 78 56 57 74819 75587 74896 75664 74974 75740 75051 758,5 75,28 75891 75205 75282 76042 76^8 75435 755" 76193 76268 76 58 76343 764,8 76492 76567 76641 767,6 76790 76864 76938 770,2 74 59 77085 77159 77232 77305 77379 77452 77525 77597 77670 77743 73 60 77815 77887 77960 78032 78,04 78,76 78247 78319 78390 78462 7 2 61 78533 78604 78675 78746 788,7 78888 79029 79099 79169 7 62 79239 79309 79379 79449 79518 79588 79657 79727 79796 79865 69 63 79934 80003 80072 80140 80209 80277 80346 804,4 80482 80550 68 64 80618 80686 80754 80821 80889 80956 81023 8,090 81158 81224 67 65 8,291 8,358 8,425 81491 81558 8,624 81690 8,757 8,823 8,889 66 66 81954 82020 82086 82,5, 822,7 82282 82347 824,3 82478 82543 65 67 82607 82672 82737 82802 82930 83059 83-23 83,87 64 68 83251 833,5 83378 83442 83506 83569 83632 83696 83759 83822 63 69 83885 83948 840,1 84073 84.36 84,98 8426, 84323 84386 84448 63 7 845,0 85126 86 84634 85248 84696 85309 84757 85370 848,9 85431 84880 84942 85552 85003 85065 856,2 85673 62 61 72 85733 85794 85854 859,4 85974 86034 86094 86,53 862,3 86273 60 73 86332 86392 8645, 865,0 86570 86629 86688 86747 86806 86864 59 74 86923 86982 87040 87099 87157 872,6 87274 87332 87390 87448 58 75 87506 87564 87622 87679 87737 87795 87852 879,0 87967 88024 58 70 88,38 88,95 88252 88309 88366 88423 88480 88536 88593 57 77 88649 88705 88762 88818 88874 88930 88986 89042 89098 89154 56 78 89209 89265 89321 89376 89432 89487 89542 89597 89653 89708 55 79 89763 89818 89873 89927 89982 90037 90091 90146 90200 90255 55 80 90309 90363 904,7 96472 90526 90580 90634 90687- 90741 90795 54 8, 90849 90902 90956 9,009 9,062 91,16 91,69 91222 91275 91328 53 82 91381 9 1 434 9,487 91540 91593 91645 9,698 91803 91855 52 83 9,908 9,960 920,2 92065 921,7 92,69 92221 92273 92324 92376 52 84 92428 92480 9 2 53' 92583 92634 92686 92737 92788 92840 92891 85 92942 92993 93044 93095 93*46 93IQ7 93247 93298 93349 93399 51 Be 93450 93500 9355 i 9360, 93651 93702 93752 93802 93852 93902 50 87 93952 94002 94052 94101 94I5 1 94201 94250 94300 94349 94399 50 APPENDIX. COMMON LOGARITHMS Centimud. 80S ;;.' ;;; s ;;; | ..:-- 01384 01326 0*703 OI 745 o 033432 05383 03743 osTifa 04139 ! 04179 04532 . 0457. 0493* 04961 05308 05346 95569 97405 t 97451 9905 1 ::-:- 3 06145 zs sg sS 03060 03100 58 32 oSS o^ 93fc **3^7/ ^ ss .a-ss 693g ^6^67 OTaoB 07335 07664 07700 97543 :.:^ 04717 05115 I;:; 1 ; 95*3* 1 33 n: DM. 35 :-::: ::;;; 3 of Xapemn IoeriUis. 11 = . - :: 0-434*945 9-6377*43 -* 806 A MANUAL OF THE STEAM-ENGINE. III. MEAN PRESSURES FOR VARIOUS METHODS OF EXPANSION. Values of . Adiabatic Expansion of Steam. Ratio of Expansion. Hi k $ u PERCENTAGE OF STEAM AND VALUB OF n. 100 I-I35 90 1.125 80 1.115 76 I. Ill 70 1.105 60 1.095 5 1.085 100 1-333 2 i .829 .831 833 .834 835 .836 837 .810 2* 1 .785 .787 .788 .789 .790 .791 793 754 2* t 744 .746 747 .748 749 750 751 .714 at T 4 T .707 .708 .710 .711 .712 713 .714 675 3 i 675 .676 677 .678 .679 .681 .683 639 3i A .644 .645 .647 .648 .649 .650 .652 .606 9i A 633 .635 636 .637 639 .641 643 .600 31 1 .616 .618 .619 .620 .622 .62 4 .626 576 3* TV 591 592 593 594 59b .596 598 552 4 i .567 .568 570 572 573 574 576 523 4 1 .525 527 528 530 531 533 534 .486 5 i .488 .491 493 494 .496 .498 .500 447 51 A 458 .460 .462 463 465 .467 .470 .417 6 i 432 434 435 437 439 .441 443 390 6| A .409 .410 .411 413 .415 .417 .420 369 7 1 .387 39 392 394 .400 403 405 345 8 i 355 356 357 358 360 361 363 .312 10 iV .298 300 .302 303 304 305 .308 .263 20 A .170 173 175 177 .178 .180 .182 .144 50 A .080 .082 .083 .084 .084 .085 .086 .063 100 riff .044 045 045 .046 .046 047 048 034 APPENDIX. .807 III. (Continual.) MEAN PRESSURES FOR VARIOUS METHODS OF EXPANSION. Values of &L f or Steam, Air. Gas, and Mixtures. Rutio of l'.|uir i. '. Point of cut-off, r Slruin I'.M'.>'I>K, Dry nnd Siiluruted, M, l.04<. Mol Air In Com- preiHorn, N, i.sio. Steam and Leak- age, Aetna! En- gines. GM and Vapor In Own engine, *, 1.60. Gases. Isother- mal,-, 1 .00. Adiabat- *., l-4. ,H nreais jo ADuapiyg jad papuadxa WH qi jad is jsnBqxg aq} JJO paiJJBD JB3H jo "q| Jad pajBDip -UI J3MOJ aAllOJ\[ O1UI P31J3AUOD }B3H HJBajc jo 'qi jad papuadxa }Baf *>o in t- m o o E3J S jo -qi jBdxg3ui -g niBajs jo -q[ jad jap -uijX^ Suiaa}ua jcaj jaMod-asjoH pajBD -ipujjad -anon J3d J3MOd-3SJOH pajBDipui jad juaraaDBidsiQ uoistj jo -qi jsd idsici uojsij 00000000 S.S^ C 0-080. q. q q. MIIIII iWSfS Ifliiflt - S) S fc^C0>0 > g> ajnssajd [e i 'bs jad ajnssajd -8583 APPENDIX. BB8WR*a &? KISS'S 811 nil . o.q.. . o.o.o. move qo - o d-oJ oo" ti ti\d " ! ..Ifel **, 0.0 jag.** i s VOLUME. -.uisuap mnoiixEUi jo ajniEjadmai IE jaieM panps;p jo tqSiaM isnba jo amhioA 01 tnEsjs jo aoiniOA jo oiiE'y f m o moo o O ?SH 1 | [ * g !|| - IIS I III - llflllll!! g? B, 72.274 S rt - OCXO -*--*fON"p4 - O 11 I f 1 11} & S ? &% ^? In^^o fJ "^ O T T S j 1 '~ - iifiiemi 53 11 1 r "w 5- Svo ^-^.TO oo S H - spunod ui 'ronnDBA B aAoqE ajnssajj - ""*-* **[* r 4- VM APPENDIX. 821 , MS a&a \m\ - - - - o p o ?? lllilH bill S82- s-s? r t i. roo oo *55^BWfrff 5prSi?;r nnnnn ncicinnnciac i^^iiiifi ^^^iiffi . \m 822 A MANUAL OF THE STEAM-ENGINE. tpui a-iunbs J3G pnnod ui 'umnDBA v 3Aoqe aanssajj .uisuap ainuiixBui jo 3jmBJ3dtU31 IB J3JEM p3[|USIp jo i jSiaM i^nbs jo auihioA OJ IQE3JS JO OUin|OA JO OlIE- 133J oiqno ui TOB35S jo punod B JQ spnnod UI 'UJB37S JO }OOJ D(qnD B JO .l^fHI K8 5 *o. > t^b w -1- vo o ~ (^ n ^jodBAa jo sitan ui ' O ze UOIJBJodBA3 J Jr8 ?ras^,3-?^-?!?,S ^^^^R * I** li spnnod ui 'mntiDBA B aAoqe sjnssojj li APPENDIX. 82 3 5*?**wf2 =5?=r! = ^m;~: -- ----- S3. 5-S mssus ;.-.- - 553 lliflll i ^. e R ~<< Isasll* m tn **- T m mo O I f^- r r^ao oo o> ^ c> O O | ,: .: : ; : ^ 1 :- :': .' ^ irivo 00 > - cT^l ^.^O r^ C < iri tt o N Vvo CO O ? 1^. a- M r^ ir t^ o t tJ-^^tgOOODM^^o;! Sg-O.^O.'?^; noijEjodBAa jo sunn ni ' O z 3Aoqe uo;)ejodeA9 j SB |t SieLl j " a * il iigfb S33j3sp jisqnajqr j 'aanjEjadcaax $ ?S,8,! qoai 3.renbs aad spnnod ui 'omnroA v aAoqe ajnssAij i _. I rrs-rrr?! -~- | APPENDIX. ssm-tsml 82 5 r. rx -. ~ 30 -. ~ c 3: ^El?f2??S ----rc-r:-: IlilFlllliJUS lllflHIII Is&H nil ssi ^RSSft:^?. H ,25 :??r = > SI a = 383. ,,, msi .! ss 8 ?- 2 5- iHH ilU 826 A MANUAL OF THE STEAM-ENGINE. The column headed " U" in the table cf the properties of saturated steam is useful for reducing the performance of differ- ent boilers to a common standard this standard being that most generally accepted by engineers : the equivalent evapora- tion at atmospheric pressure and the temperature of boiling water, or, as it is frequently called, the evaporation from and at 212. In the table it is assumed that the temperature of the feed-water is 32, and an auxiliary table is added, giving corrections for any temperature of feed from 32 to 2 12. CORRECTION FOR TOTAL HEAT IN UNITS OF EVAPORATION. Tempera- ture of feed, Fah- renheit degrees. I Tempera- ture of feed. Fah- renheit degrees. . Correction. Tempera- ture of feed, Fah- renheit degrees. Correction. Tempera- ture of feed, Fah- renheit degrees. Correction. Tempera- feed.Fah- renheit degrees. Correction. 33 .001 69 .0383 105 .0756 141 .1129 177 .1504 34 .002 70 393 106 .0766 142 .1140 178 .1514 35 .003 71 .0404 107 .0777 M3 .1150 179 -1525 36 .004 72 .0414 108 .0787 144 .1160 1 80 '535 .005 73 .0424 109 .0797 145 .1171 181 1545 38 .006 74 435 .0808 146 .1181 jS-2 155 39 40 .007 .008 9 0445 45 i i I 2 .0818 .0829 \% .1192 . 1202 J|3 .1566 '577 4 1 .009 77 .0466 1 3 .0839 149 .1213 185 .1587 42 . 78 .0476 1 4 .0849 150 186 .1598 43 79 .0487 ; i 5 .0860 '5 1 2 33 187 .1608 44 2 80 0497 i i 6 .0870 244 188 .1618 9 35 45 81 82 .0507 .0518 ! 11 .0880 .0891 J53 '54 190 .1629 .1639 47 48 : ii 11 .0528 .0538 1 119 .0901 .0911 '55 156 - 2 7S . 285 192 .1650 .1660 49 . 76 85 .0549 1 121 .0922 157 296 iQ3 .1670 5 . 86 86 0559 122 .0932 158 194 .1681 5' 97 87 .0569 123 0943 159 . 3l6 1691 52 .0207 88 .0580 i 124 -0953 160 327 196 .1702 S3 .0217 89 .0590 125 .0963 161 337 197 .1712 54 .0228 90 .0601 126 .0974 162 . 348 i 9 8 X 7 2 3 1 23 92 .0611 .0621 3 .0084 .0994 163 164 199 200 '733 .0259 93 .0632 129 .1005 165 ' 379 201 '754 58 .0269 94 .0642 ! 1 66 389 202 .1764 59 .0279 95 .0652 J 3* . IO25 167 . 400 20 3 1775 60 .0290 96 .0663 132 . IO^6 168 410 204 1785 61 .0300 97 .0673 133 . 046 ,69 420 205 .1796 62 .031 98 .0683 '34 57 170 43 1 206 .1806 63 .032 99 .0694 135 . 067 171 44' 207 1817 64 33 100 .0704 136 77 172 452 65 034 101 .0714 *37 . 088 173 . 462 209 1837 66 035 102 .0725 138 . 098 174 473 210 .1848 67 .0362 103 0735 139 . 109 175 . 483 211 .1858 68 .0372 104 .0746 140 . 119 176 493 212 .1869 APPENDIX. 827 mm . -- - - : ? 5 - ~ - 2?H* <---=*='* Ail HtH rl2os! ^ .:--.-;. -^--- i z5-E|=-| s o. ill &S85R.a8 J 8-S8 f r S ? H Hii r ? . 828 A MANUAL OF THE STEAM-ENGINE. C^ J. ~ OO f~.OO '-'OOOtx'VCt'* ; TOO g-r^-O Q is.r^ -^-o ^ :*& tt 2 ft. g ri 5> -acjvSoo O^M^rnmrn ' ^vfi %o Ln < Frslfflllllllfllitiliilfl ill HP U g* E 3 u"5 i i---cag^o^' n ^"w w > " , 00 ^ r". m g< S> ? C S'. tt m RcM 1 m o- fnc O r^r^. -s-t>>rjf, per cubic f< a c oT :ubic feet. equal weig imum dens ii ii I! - g" C. c "o rt r . S 8 5 5 11 b'l jj & n latent heat of evapo: Of a cubic foot of ic foot of distilled wat< Of a pound of ste r olume of steam to vol water at temperature 'olume of distilled wat jual weight at tempers | "3 "o^ "5 1 1 1 f 1 1 1 > APPENDIX. 831 m \ ih ?i :l^]v**** ^ * 2 el ?ls = 5g 8fv! 1^^- Jr? ?= = ?s 1f?f 1 1 ? srr 1 ?? 'i.^s^j; iL^ss^^n? gr2?s I x ' ** I * S - - - - - _ _ _ - ___'_ S 3T S 'i I I s.,'?n.5? !H*.H???? ??-??= ==??f HnifirHI i |T?i < = y 5 . a_ t. I -^ > "3 SX i^ ~ ^ * I! ? L ! = =i?i?|Kif ??f?5 5n= 2i?y nm fifti i B .,,.,,, ..HRmimn ~l , = IffSf ifSfl ????? r = S = ? fffff f Stfl III?? ? |J s: |nsfH*??f??????1 = = = |SfK i - - 1 1 8??5 5 IFs^fl _!: K ( - E= : 8 3 2 A MANUAL OF THE STEAM-ENGINE. XIV. COMPOSITION OF VARIOUS FUELS OF THE UNITED STATES. C. H. 0. N. S. Mois- ture. Ash. Spec. Grav. Pennsylvania Anthracite Rhode Island " 78.6 85.8 2.5 1.7 ,0.5 0.8 3-7 ... 14.8 !-45 2 61 7 8 2.0 .78 Welsh " 8 4 .2 Maryland Semi-bituminous 80.5 !-7 8-3 33 .i 4( *9-4 38.8 .8 i 24 Illinois Bituminous .Y.Y.T~""II " (Block) Bituminous 52.0 62.6 58.2 39-o 35 5 37-i Vd 6 9 27 3 Kentucky (Cannel) Bituminous Tennessee Bituminous 48.4 71.0 48.8 17.0 56 5 .8 25 45 Alabama *" 42 6 o I ^ Virginia " * 18.6 California and Oregon Lignite 50.1 3-9 '3-7 0.9 i-5 16.7 13.2 1.32 THEORETIC AL VALUE. STATE. COAL. KIND OF COAL. Per Cent, of Ash. In Heat Units. In Pounds of Water Evaporated. Pennsylvania . Anthracite 3-49 6.13 14,199 3,535 14.70 14.01 i ' ;; ! Connelsville Semi-bituminous Stone's Gas Youghiogheny. .. 6.50 10.77 is M& 3.'55 4.021 4.265 3:8 3S Kentucky Caking Cannel a. 75 4-39 s 108 ^89 16 76 M '384 Illinois...;'.'.'.! Lignite Bureau County 7.00 5.20 5 60 9,3 2 6 13.025 9.65 13-48 13 5 8 1C Indiana Block Caking 5*11 13,588 ll'll i Cannel Maryland Arkansas Colorado Cumberland Lignite 13.98 S.oo 9.25 2,226 9,2'5 3.562 3866 12.65 9-54 14.04 Texas it so tt 3 lo II QO Pennsylvania . Petroleum 20,746 21.47 APPENDIX. 833 ANALYSES OF ASH. Specific Grav. Color of Ash. Silica Alum- ina. Oxide Iron. Lime. at Loss. 0.48 0.40 Acids S.&P. Pennsylvania Anthracite Bituminous Welsh Anthracite Scotch Bituminous 559 .373 Reddish Buff. Gray. 45-6 76.0 40.0 37-6 42.75 44-8 9-43 2.60 5*8 1-4* 3-7 -33 trace 26 2.97 5-0 33-8 7 3 3 7 834 A MANUAL OF THE STEAM-ENGINE. XV. HORSE-POWER PER POUND MEAN PRESSURE. SPEED OF PISTON IN FEET PER MINUTE j3U 100 240 300 350 400 450 500 550 600 650 750 4 .038 .091 .114 133 152 .171 .19 .209 .228 247 .285 4i .048 .115 .144 .168 .192 .216 -24 .264 .288 .312 .360 .06 .144 .18 .21 '288 27 '36 33 6 36 450 6 .086 .205 .256 .299 -342 .324 385 & 471 -43 2 555 64 6} O2 .245 37 .391 .409 464 .512 563 .614 .698 .800 7 ; 16 .279 348 .408 .466 524 583 699 .756 874 7i 34 .321 .401 .468 534 .602 .669 .802 .869 1.002 8 - 52 .365 456 532 .608 .685 .761 .912 .989 1. 121 84 7 2 4'3 .516 .602 .688 774 .86 .. .118 1.200 9 92 .462 .674 .770 .866 963 059 J 54 251 1.444 '5 5'5 .644 751 859 .966 1.074 .181 .288 395 10 . 38 57' .714 .831 952 1.071 1.190 39 .428 547 I . 785 .262 -63 787 .919 1.050 1.181 444 575 .706 1 1.969 22 .288 .691 .864 I.OOS 1.152 1.296 1.44 584 .728 .872 '2.160 IlJ. .314 754 943 I.I 1.257 1.414 1-572 729 .886 .043 i 2.357 12 342 1.025 1. 195 i . 366 1.540 1.708 .880 .050 2.222 . 2.564 J 3 .402 ^64 1.206 i. 608 1.809 ; 2.01 .211 2.412 2.613 ; 3.015 *4 .466 1.119 1.398 I.63I 1.864 2.097 ' 2-33' 564 797 3.029 3.495 15 535 1.285 i. 606 1.873 2.131 2.409 2-677 945 .212 3.479 1 4.004 16 .609 1.461 1.827 2.131 2.436 2.741 3.045 349 654 3.958 4.567 17 .685 1.643 2.054 2-739 3.o8l 3-424 .766 4-450 5.135 18 77' 1.849 2.312 2.697 3-083 3.468 3-854 239 :e 4 5.009 i 5.780 '9 859 2.061 2-577 3.006 3-436 3.865 4-295 .724 154 5.583 6.442 20 952 2.292 2.855 3-331 3-807 4.28S 4-759 234 5-731 6.186 7.138 21 1.049 8.518 3.148 3.672 4- I 97 4.722 5.247 5.771 6.296 6.820 i 7.869 22 2 3 1.152 1.259 2-764 3.021 3-455 3-776 4.031 4-405 4.607 5-035 5.183 ' 5.759 6.334 5.664 6.294 6.923 6.911 7-552 7.486 8.638 8.181 i 9.44 2 4 1.370 3.289 4. HI 4-797 5-482 6.167 ' 6.853 7.538 8.223 8.908 10.279 2 5 1.487 4.461 5-105 5-948 6.692 7.436 8.179 8.923 9.566 11.053 26 1.609 3.861 4.826 5.630 6-435 7.239 8.044 8.848 9.652 27 !-733 4-159 5.199 6.066 6.932 7.799 ; 8.666 9-532 10.399 1.26 12.998 28 1.865 4-477 5.596 6.529 7.462 8.395 9.328 10.261 11.193 2.12 I3-99I 29 2.002 4.805 6.006 7.007 8.008 9.009 10.01 ' I. OH 12.012 3-01 15.015 30 2.142 5.141 6.426 7-497 8.568 9.639 I0. 7 I i 1.781 12.852 3.92 16.065 3 1 2.288 5.486 6.865 8.001 9.144 10.287 11-43 j 2.573 13.716 4.86 17.145 3 33 2.436 2 590 5.846 6.216 7.308 7.770 8.526 9.065 9-744 0.360 10.962 12. 18 3.398 1.655 12-959 4-245 4.616 5-54 is! a? 1 9 '.425 34 2.746 6-59 8.238 9 .6n 0.984 2-357 '3-73 5->3 i 6.476 7.84 20 595 P 2.914 3.084 6-993 7.401 8.742 9.252 10.199 10.794 1.656 2.336 3.113 14.57 6.027 7.484 3.878 15.42 6.962 8.504 8-94 =1855 0.04 23.130 P 3-253 3-436 7.8.9 8.246 9-774 0.308 11.403 12.026 3-032 3-744 4.861 16.29 7.919 9.548 5.462 17.18 8.898 20.616 1.17 24 435 2-33 25 770 39 3.620 8.648 0.86 2.67 4-48 6.29 18.1 ; 9-91 21.62 3-53 27.150 40 3.808 9.139 1.424 3.328 5-232 7.136 19.04 0-944 22.848 24-75 128.560 41 4.002 9.604 2.006 4.007 6.008 8.009 20.00 26.01 130 015 4 2 0.065 2-594 4-693 6.792 8.901 20.99 3.089 25.188 27.287 31.485 43 '44 4.40 4.606 0.56 1.046 3-20 3-818 3:!,, 7-6 8.424 9.8 0.727 22.00 23.03 4.2 25-333 26.4 27.636 28.6 29-939 33.00 34-545 45 4.818 1.563 4-454 6.863 9.272 1.681 24.09 26.399 28.908 3 I -3 I 7 36.135 46 47 5.043 5.256 2.o86| 5.128 2.614' 5-768 7.626 8.396 0.144 2.662 3.652 25.18 26.28 27.698 28.908 30.216 32-754 34.164 37-770 39 420 48 5.482 2.846: 6.446 9.187 4.669 27.41 30-151 3'- 1 52 35-633 4i-"5 49 5-7I4 2.913 7.142 9-999 5-713 28.57 34.284 37 -H 1 42.855 5 5-950 4.28 7-85 20.825 3-8 26.775 29-75 32-725 35-7 38-675 44-625 6.180 4.832 8-54 1.665 4-76 27-855 30.95 34.045 37.08 40-205 46-425 52 6.432 5-437 19.296 2.512 5.728 28.944 32.16 35-376 38.592 i. 808 53 6.684 6.041 20.052 3-394 6-736 30.078 33-42 36.762 40.104 3-446 50.130 54 6.940 6.656 20.82 4.29 7-76 31-23 34-7 38-17 41.64 52.05 55 7.198 7-275 21-594 5-193 8.792 32. 39 1 35-99 39-589 43-188 '.787 53.985 56 7.462 7.909 22.386 26.117 9 848 33-579 37-31 41.041 44.772 j 8.503 55 965 57 7-732 8-557 23-196 27.062 ! 30.928 34-794 38.66 42 . 526 46.392 | 50.258 57-99 58 8.006 9 214 24.018 28.021 j 32.024 36-027 44-033 48.036 | 52.039 60.045 59 8.284 9.902! 24.852 28.964 | 33.136 37.278 41.42 45 562 48.704 53.846 62. .3 60 8.566 20.558' 25.698 64.24J APPENDIX. 835 11" 2 S 2 8 5-i: iill ft I fill isss S|&Sl -"I--" -"-- "-""I Sjrs*ki*lEi jo naaa 1 now o M 2 IT aaj . . . . = ?! I o?o?| o"ooo i ^o o o i 'o'S'o'S j 836 A MANUAL OF THE STEAM-ENGINE. LOG OF TRIAL BY MECHANICAL LABORATORY, DEPARTMENT OF ENGINEERING. TVstmaHpAt U - tvk \ - b ! i i li I \ f j d REMARKS. PRIMING TESTS. i I i ' ! "",H " r is WJ g -saajSaa /f WEIGHTS. *l ar o^ui unj ujeaic; i| ,t - r = v I J - = ft I i U I n = y x/ J3J3UIUO[E3 01 II HEAT-UNITS PER POUND FROM BOILER. ^ tnE 31S iM i RIMETER. TEMPERATURE. | li 1* E^ 1 s " 1 PRESSURES. li CALO WEIGHTS. ||. (7 1 Condensing Water. W Si u i H sasnssaHH I 1 AffENDIX. 837 313 1 - nonjodojj | g. unoq aad soepns -bs ja Mnoq d 3JEJ9 jo 100; 1 5 S XDVJH.1S -OXU.V3H Oi jo uojjaas SSOJ3 jsea-j g" nsli" 3uijBa H | x ! -max 1 nuux of Heat require utr unc <e JB PUB - -niBais reniDB JB OUB ' IB PUB '4 oil luaiPAinbg poB mojj oiBajs rBnioB JB PUB jaiEM-paaj jo ajni Bjadmaj [EnjaB uioaj 838 MANUAL OF CHE STEAM-ENGINE. I ra T 4 ~ i s II! "3 - n J 3 NI ff QNV V J K g! Ill unoq ns-3ui ; -bs ja siqusnqino-) jo'punojiaj APPENDIX. 8 39 3UUdS JO 3IK>S M d -H 'a * 1 pn 1 iwox d -H I ^? Z 'd 'K - I ^s, x - - 'd H 'I ! : d '3 K i jaxM-ooimCn! i S * JWW.-PW* ^ : OIC31S p3SlpU03 S t; 1 5 s - 5J|1 jspayiAj ill! B . ns3 D m I I | J31Bil-33jBa3Sin i j^B^-aonoatu! 09 -r Hi; H -,,,^-p^ are^s P3 su 3p uo 3 |lff J-s mooj-3ai3ug j !V l*Bia - u ^ ^. 1 1 JB S se E > ^5 ^ 2 S" -; 5 ' . i -isnBqxg V I o -adid-nre^s 3 : ^ 8 fc --"Iiofl JS : 1 It uo^pu^s 11 5- ft* -D W 3- O c c i II! amix i : i ? jaqtnnx G a S JS 840 A MANUAL OF THE STEAM-ENGINE. VOLTS DR AMPERES. -i w a v-J V) ^ H 2g n et co moo 01 o M m 1010 t-.oo 01 o ^S S- 8 io J 5- 8 8 < - 8 2 I o g * I I S- N ^R ?"S o-S S- 2"o >0 %2 o? 1 ?! Sj^ tS M ^- o -^-00 eo fnt^tN^o -^OIH >oo IAO * M w-d-io"ooO"r^ ^.vo r^ ox <^ ^^O oo O\ 000000->-",.r-NSNNMN 2 ? : j 1 ^ M ^ " co^ ^-^ ^2 xS r^^-oT &^ O 'o 2" N t 1 N ^-O OO O N <*-^O 00 O N -*^O 00 O fc fr D H I 1 ! " n r>i^-^5 ^0 Oi M ro ^- tr.^C f| M 8 8 31 i s M N 88888 8 8 ? IM et mi-uvo t^oo 010 cj ^^-^^ g 1 ] g ^S < W fcS-' * S o o^g "I Mil pill K 'S 7 1 - : ? - e S 31 r| %- g ig Ss o | 3 0. * J 5 5 * rt i i3 [2 *" 5 2 s * o>& ?l is 1! li APPENDIX. ~ d d d CO I in Cr^ w 00 t^ O r^C^r^** co O co - C O O O O r^ T co ;> T O n O T=o n co -co =000 OO - co m r^ =- r^ m co sssss^sssssRsteH OOrv t ^d-rr ; -0 > e moo 6 co mco ~ ci TO i2?l!OS' f - < ""'* ""-co ci inco - inos - T i O r^l^r^ooaoco c* o s n z o dl XD Pu S I ^5^R$8SR^SR%884ilR5 r-C*inc*Ococim f^o TOO -i TTcoci O i co i^. O T r^ TOO - ^f-j-J ^ Cnoo - S^.cc'^ TCO 2"*T S w N w cococOTTTr^T-'r^c*oaoOcicoei d oo T ^* T O* coco O O cot^-O Tf^O CI moo coo oo O co in r^ O* coo O co t^ O T r^ - TOO - TOO - TOO ~ T r>. ~ -tt^O T r- C c-.O -. d d d coeocOTt-^-Tinrn mo O O r^ r t-co oooo C-C>J>O OO O Ocor^ NO>fe C^co O C^r^c~.ooooinH o 1-O co ~ - 1~~ O moo O^ t~* r^oo O ^ s co co - mo C"QO *-*-oO't'OO"TcoOt' * t^ 'Too O co co I- & C>0 co n r>.eo co 1-1 mo O Too oo w o r^o coo ^ I^ C> CO in T C- N T m co S> in 5 T in T T O N r^no ** in^ coo O T r^ C coO ^ "^ T r^ C* w TO QO O ct cT o J-coO ?^r^ O cor>.5 T r- O T r- O co r^ O coo O coo O coo ~WWCOCOCOTT Tminino OO l r^ t^oo coco <*&<>O O m O C CO m q m co ^) q* o c rc? 1 q - o S d t^. - "d d c r : i-i r^ c^.oo Tco cor^dO o^cor^O Tf^O co mco -* coo co *- co m r^ & M rnOdO ocoo CcooOcor^Ocor-0 coo O o<> "3* J^b O> JJ jp M - d d d cocOTTT>nininooo r^r^. t^-co oococo CT> O> CT- O O goooooogoo oo 0^00080230^008580 coco r^ ci in T O TO r^ m M oo co r^ C- S>oo oco Ooi^O>'"comT r^-co^inO >n6 -**> NO 6 cor>-d coo O mco O co in r^ 6 t-O - inco 00 C>?--= CM-.O O coo O coo O COO C7> COO 5> M O C-c; in _ M M ci CI cococOTTmminOOOO l^t^ l^co oo CO C^ CT> C^ O O co <* mO I>-CO C> O * w co f nO t^oo C> O co T >"O r^oo O O MMMMMMI-IMMndCldddCICIdddCOCO 842 A MANUAL OF THE STEAM-ENGINE. a I N TtvO OO CO CO CO.CO CO CO COCO O T N OcOO TN OcOO r^cOOmw 1^ mi-^ t^ in moo wTr-O comTmoo co Ooo ON r^coN COTOO f^OO M Ooo in T N OO -* o Omt-*o O TO co O O Oco O CO O *-" N co N N CO TOO Nco TO co in r-^ O i-i CO i O N in i^co Ooo r^mr^OO " N -< Too NO TTTTTTT inco O OO O TOO N o O Oco r~ co N i-i co TO Too \C rcc O^O "-< w to-i-u-jr^QO ^ - -t f^ O -^- r^ O cno o w moo \oO i O r^.t^.r^.oocoooao c^OC^ Oooo *t *1- f -* *fr t -to co O w Tj-o co O w -to c in' ^oco -^fOO wco -to r^'-iO cow cor^M OCXD miocoooo r^innn t^*-. u^oo NO O co mo r^o m - 1 ; OOOOcococococococoOOOOOOOOOOOOcocococococ in M r^ 5 OO coOt^-t'-iONOCMOOcJONOOc-icoocO't Oc N C N f^"co O co'R S" co T m m co O N T m r^oo' O 6 >-> f^co O ^-Tr^ OOO NO O Tr^r^r^r^r^r*. r^o NCO TOO ^NOO TO r^N TO co o N T T co O O Ooo t-O in TO O m co co Too coi-i~NOcofiOcoOO O Oco in co M OO N I^M inN r^NO Ow COTTCO^ O co ino O O I-- O comr^co 6 N co mo co O " N co mo t-^-co O O >-' N co T mo ONO ON inco N inco -* TI^O Tr^O coo ON inooi inco Tf^ i-, _ w N o) N cococoTTTinininoooO r^r^r^cococo OOO cOTNOMtH*HMMWMOTOOO>-. r O C i >-< N co ON m ON moo wTcoi-i-tr^OcooOcooONmcoi-iTcoTr-~ oTNJ^r^r^t^r^r^r^OPJTOrr NTOcoONOcot^inO TTN M N cOTinO rococo inTu"jOT*H o w tnO NCD r^--< N Tm r^c co N inoo T t^ T r^ O co N coTmO r^co OO M *-< co T m r^co O O O -' N T ino r^ c<-o O N mco n moo T r^ p^ coo ~co O O w N co T >nO r^oo O ( APPENDIX. 843 XX. HIRN'S ANALYSIS. DATA AND RESULTS. Test of Steam-engine made by at. Kind of engine . . .Diam. cylinder Length stroke Diam. piston-rod Vol. cylinder, crank end Vol. head end Vol. clearance, cu. ft., head Clearance in per cent of stroke " " " crank " " " Boiler-pressure by gauge Barometer Boiler-pressure absolute Boiling temp., atmos. pressure Revolutions per hour Steam used during run, Ibs Quality of steam in steam pipe Quality of steam in steam-chest Quality of steam in compression Quality of steam in exhaust Weight of condensed steam per hour Pounds of wet steam per stroke Head Crank. . . Temperatures condensed steam Temperatures condensing water, cold Hot Pounds of condensing water, per hour Per stroke SYMBOLS. To denote different portions of the stroke, the following subscripts are used : Admission (a); expansion (6); exhaust (c)\ compression ( -c r oo Q U B US u < > > z D S < w Q U x < x g H < CO > CJ C w 1 w o g oo | O U 2 O z 5> ? 2|Ss, ?! ^.g^ ? ?' -. i ?? M * 8 ? s " " i a o o 5 - - sL|-as s- 1 j % I S, 8 A S 1 s ? a ^ ; OOfN. h 5 - o n otn *** * t^ n mmx^-oKnK V - jsa-s* j -s E 5 ? a g ? - 4lflU;^ - a.s.r- : t : : s o o-c 3 B : a - -.-'~=a-^ > s --= = 5 a " = ix = S :g| i|~a& "Hi -S i o 2 a So "~ m, * o c a > g ^ S i- a i - i- c ^ _- >-T O. -- i_ t u v w o- O u iS < = 2 8 4 6 A MANUAL OF THE STEAM-ENGINE. 3.0U3JSJ3H I JQJ jaqmnjjl 8, & :!? * > * *O M in oo '3- S 8. < I -l|i ? i.i- 2 ?Ir ^ APPENDIX. 847 wniaini joj Jaqnmx s, s r ?* sf * * % i 5 ? 5 e H R i 1: 1* i :- S : 1 4 = I ~ I 5 **l*s i - . ! J => 1 ^ * Ml 5 5 if 52* i ! = 1 1 1 I I 5l |s| i O f |* -> n - { S.i 5f!-:?Jltf5 -.-----__'--'- _.-_ - nS u UN - u P- > 8 4 8 A MANUAL OF THE STEAM-ENGINE. ao?"^nN ^ ;? $. 3 a a s in i'i lo ^ S < | g ? f f 1 | fo ? : ' . 'i s I ~ ! ' i i i i S 2 S ? H. 1 i ; ? i $ % S> K ^ ] O ^ vo ^ g W 00 vo ) 5 m * S * S " 3- h O H ! i S ? ! & * "S * i c 1 H,, OH 1 1 ^ 1 f * & m fy i, f 1 " gj m M S> g * t^ VO ID S < " M 0. . N g 5 = 1 R. - i : i ': ': >n s ^ " : : : : : 00 ^ * x r x N O -)- N-)_ 2 ^ s. ^1 ^- - J> P 3 9 "5 | , | M + X 1 cs,j -"=!^ fid e ^ * xx-v ^.1 ""' ox x . x ; 5- X ~ g + x S, joqoiXs o- b ^ - S S K 3 Si [ : ! : : : : : i ill \ t ! 2 is'LH ! lit I ** 1111 I s^^ 3 J a'sg 1 "a "8 *" > *l i< ili* * d>s " g g S^jf ^j ff -s jj'i c" SMJ, u w rt "B S 9-S c !IIllH IS! ^IflfUllli- ||li ill ||.|| ill, (2 s ":S U4 ' 5"j & " Thickness of piston, inches, to 1 nearest half-inch. ) Internal condensing surface, 1 square feet. f ' " Probably condensation hourly, on 1 internal surfaces, pounds. ( Probable consumption ) V Per eff J I h | 1 APPENDIX. 849 850 MANUAL OF THE STEAM-ENGINE. 3 2 T X X "-" co O ir>co ^f 1-1 O ^H'-t^OO WM- r^. CO Tf r-.H'-*? l N' O sO ^_^ 5 o __., g;co cowN > ?~ 1 "cONconei r^inj co cO co i-t IT'S JIT'S 2" - 3 ?. coco'co P^'co n ^i- fcC - ^ -- ^^. ^ .oqtuAs Es e ^j "0 k, ^ ,__ >^ C ^ i * i^ ^1- s c 5 |sl :| i| II s . I M ~ Z = " V 8^1 | J ~ ||i 14 il II*- Is j i r7= :|| 1 = . 7 5 Jl^~ 5 ? ^ : ill ^ll i = i r j.- -r Ed t/5 E s " _- ~ = -. = _ r^ = E 3 ? i i 2 - c - O imp] = Hi 7i ~ -^" Hilliii 852 A MANUAL OF THE STEAM-ENGINE. jJSqwni "' S vg , 2 f R.IA I? 00 O> t-- O oo ... oo c^ Ot O j * f ? : M 1 : ? ? 1 01 ^ o oo" j* * I?, ; - ~ - d ?s " r^ !f ^* I D " O - C* > v? -, ! n '! " * *| ' V * ^ : ^ ^ > " " ? f -e' s : E " ~ ; " 1 a, B J ^ | 5 ^ q fj fjssl? ? ? f 1 % f * f s " I d 1. - C 1 o f-. d o* 8 . - t^ SJIOJIS - - i - ? - i ! &5 1 1 ; I 1 , J "*""* ^ ^ ^.T l^- * ^ fl 'HI 8 >< | | d^ 1 ' ^ ^^1^ " ^ d^ ' ' + + < = E (i. x < x - ! 1- > S o 5 * ^ ^ - ? < Q - 1 * ^ B I |T ||p r ; J- M ^ l| -M 1 -i I = ___, ir" zr"~ ,B : Sj I|SS g | - ^_ ? aS |'5 "= S & S g ? 3 |1 |i|'^ . E | |1 2 1 ll l^=, s| 1 2 S j || J||SI i||| :| |l ! i SITlJHl if I >lute pressure at .95 stroke, unds per square inch, ght in pounds of a cubic fo steam at pressure B. ght in pounds of a cubic fo steam at pressure L. I ! 8S< 'SS'" | 2 a | ^ | PfF APFEXD2X. 354 A MANUAL OF THE STEAM-ENGINE. APPENDIX. XXI. ( Continued. ) 855 NON-CONDENSING ENGINES, UNJACKETED CYLINDERS, STEAM SUPERHEATED SUFFICIENTLY TO PREVENT CONDENSATION. (/} POINT OF CUT-OFF. H 17 ; - Full Str'ke % '5'-5 5539 366 M '47 5 3494 23 -7 M % M A 150.1 3925 26.1 Probable effective horse-power. Pounds of steam used ! p ta y hourly, calculated by \ *}" "' p.ston-displacement. ! f ,! ct ' ve l^ ri . r . . 9 .; 150-6 5851 38.8 148.8 3963 26.6 150.6 33^8 22.1 148 8 149.8 32 | 3627 22 I 24.2 Pounds of steam Point of Cut-off. Pounds of steam hourly. Effective horse-power. hourly, per effective hcrse-power. Full stroke. 5883 '77 33.2 94 5582 178.9 31.2 $2 434 180.2 22.4 iZ 36,1 1 88 93 3506 202.3 7-3 r? 369 228.6 5-9 3 44^ 257-3 321.9 57 3-9 XXII. NOTE TO 112. The transformation of the first of the equations of Rankine into the second may be thus effected : /"^' C* 1 i T dp\ udp = dpd^(J log, _' + P, ^J - ,' // dT T, T, > T; (r, - r a ) -/(r, log, r, - T; log, , - r, + 7 1 ,) = / [r t - T, + T, (log, T; - log, 7,) + ', INDEX. Absolute Limits to Expansion m 201 786 Action of the Jacket 153 627 Actual Cases, Construction of Efficiency-diagrams 189 762 . Unavoidable Thermodynamic Waste in 124 482 Actual Efficiencies and Economy of Proposed Steam-engine 137 572 Actual Engine Efficiency, Limit of n3 466 Actual Engines, Method of Waste in 122 471 Actual Thermodynamic Lines and - Carres of Efficiency". 180 718 Adiabaiic Condensation 112 431 Agricultural Engines 38 179 Algebraic Expressions in Energetics 79 307 Amelioration of Wastes by Jacketing 140 590 by Superheating 140 590 Application of Computations, Ideal Engine Efficiencies 117 454 Back-pressure arts. 123,171, pp. 477, 683 and Clearance in 430 as modifying Economy 196 776 in Actual Engines 123 476 Balance of Forces 151 620 Binary-vapor Engines. 172 697 Boiling and Fusing Points 89 322 Calonmetry ...92 333 Capital, Efficiency of 182 741 Carnot's Work 58 2=5 Character ot Energy. Transformations, Sources, etc 47 245 Chemical Principles involved in Transformations of Energy 48 245 Clansins' Work 59 2fel Clearance and Back-pressure i 43 and Compression 171 683 Compound and Single Engines 34 93 Compound Engine, Waste of the 139 58 , Early .- 19 27 . Screw Engines 42 217 857 858 INDEX. ART. Compounding, First Step in 143 596 , Problems of 141 592 , Three Fundamental Principles of 142 593 Compression and Clearances 171 603 Computation of Efficiency and Economy of Real Engines 137 572 , Examples of. 137 572 Latent and Total Heat of Steam 93 336 Efficiency, Examples of 149 611 Ideal Engine Efficiencies, Examples of Applications of "7 454 Conclusions relative to Maximum Efficiency 200 785 Condensation, Adiabatic 112 431 , Cylinder 65-70 271-281 , Magnitude of 128 488 , Restriction of 131 534 , Status of Theory of, in 1850 68 217 , Variation of 198 783 Condensation, Internal, and Waste, Theory of 130 517 , Laws governing Loss by 129 499 Condition of Internal Surfaces of Engine 161 659 Maximum Efficiency .115 449 of Fluids 125 483 Conduction and Radiation, Heat-wastes by 126 483 , Methods of Reduction of Losses by 127 487 Constitution of Matter and Thermodynamics 88 326 Construction, General Principles of 31 86 Construction of Thermodynamic Lines 103 400 Consumption of Steam , 1 28 488 Corliss and Greene Engines, Simple and Compound Forms 34 95 Costs and Profits, Relation of 193 772 , Deduction from the Investigation of 197 776 , Estimation of 191 766 Cotterill's Work 67 275 Critical Physical Condition and Temperature of Steam 94 350 Curves of Efficiency for Real Engines 186 756 Real Efficiency, Thurston's 187 757 Cycles of Real Engines , 119 467 Cyclical Operations, Efficiency of 114 447 Thermodynamic Operations 104 410 Cylinder-condensation 65 271 , Clark's Researches on .. 65 271 , Hirn's Investigations on. . . . , . . 66 274 , Magnitude of 128 488 , Restriction ol 131 531 , Status of Theory of, in 1850 68 277 INDEX. 859 ART. PACE Cylinder-condensation, Three Periods of Philosophy of 69 279 , Variation of . . igS 783 , Work to be done on 70 281 Cylinder-wastes vs. Jacket-wastes 154 532 Cylinders in Series, Numbers of 146 602 De Pambour's Problem 58 258 Design, Principles of 30 85 Designer's Aim 30 85 Details of Action of the Jacket 153 627 Diagram of Ideal Efficiency, Rankine's 184 749 , Construction of Efficiency, for Actual Cases 189 762 , Method of Use of Efficiency 190 765 Distribution and Magnitude of Losses in Actual Engines 123 475 Variation of Internal Engine Friction 134 . 565 Distribution of Energy in Real Steam-engines 120 467 Pressures and Efficiency of Mechanism 151 620 Double-acting Engine, Watt's 17 23 Dwelshauvers-Dery, Work of 66 274 Dynamic Wastes, Mechanical or ill 430 Economical Expansion, Extent of 144 597 Economy, Back-pressure as modifying 196 776 and Efficiency of Real Engines, Computation of. 137 572 , Examples of 187 757 , Computation of .187 757 and Efficiencies. Actual, of Proposed Steam-engines 137 570 Efficiency, Actual, of the Working Substance 177 712 , Conditions of Maximum, of Fluids .... 125 483 .Curvesof 180 718 , for Real Engines 186 756 Diagrams, Construction of, for Actual Cases 189 762 , Method of Use of 190 765 , Examples of Computations of 149 6n , Ideal, Rankine's Diagram of 184 749 , Limit of Actual Engine. . 118 466 Problems, solved by Inspection 199 784 , Real Maximum, of Engine; Conditions of ...135 57O , Real, Thurston's Curves of ..187 757 , Solution of Practical Problems of ........... . SS 759 , Thermodynamic 1/5 709 and Economy of Real Engines, Computation of... . .137 5Q2 Examples of 187 757 and Jacket-waste, Computation of 155 636 , Maximum, Conditions of 115 449 , of Jacket-action 156 648 86O INDEX. Efficiency of Capital 182 of Cyclical Operations 114 447 of Engine and the Jacket 106 66S of Ideal Engines, Th?ory of 1 16 450 of Mechanism 151 620 of Steam, Conditions of Maximum Total 136 571 of the Machine and Engine Friction 132 540 and the Engine 179 683 Efficiencies, Application of Computations of, for Real Engines 117 455 , Computations of, in Ideal Engines 117 454 for Real Engines, Theories of 185 752 , Mathematical Treatment of Engine 173 705 , Maximum, Conclusions relative to 200 785 of the Engine, The Several 174 705 of the Ideal Engine 183 741 , Ratios of Expansion at Maximum. 181 725 and Economy, Actual, of Proposed Steam-engines 137 572 Energetics and Thermodynamics 51 249 Algebraic Expressions in 79 307 denned and discussed 75 298 Fundamental Law of 75 298 Laws of 77 304 Newton 's Laws and 78 305 , Thermodynamics a Restricted Case of 80 309 , Thermodynamics as a Branch of 74 297 Energy 76 299 , Character, Source, and Transformation of 47 24; Chemical Principles of Transformation of 48 245 , Distribution of, in Real Steam-engines 120 367 , Mechanical Principles of Transformation of. ....... 50 247 , Physical Principles of Transformation of . 49 246 , stored, in Steam 100 383 , Thermodynamics of Work and .. 97 365 , Transformation, General Methods of 2 i Engine, Compound, Waste of the 139 586 .Screw 42 217 , Conditions of Real Maximum Efficiency of ... .135 570 , Cost of, as effecting Best Ratio of Expansion 195 775 Efficiency, Actual, Limit of nS 466 and the Jacket . 166 668 of the Machine and the. 179 714 Efficiencies, Mathematical Treatment of . . 173 705 ri ction and Efficiency of the Machine 132 540 , Internal, Investigation of 133 558 . Variation and Distribution of 134 565 INDEX. 86 1 ART. PAGE Engine Heat-, Purpose of the , , , The Steam-engine as a 1O 5 ^ 22 .Hero's 6 , Ideal, distinguished from the Real 107 423 , Efficiencies of the 1 g 3 - 40 , Ideal and Real 52 - o Progress of the Philosophy of the 54 251 , Influence of Size of 147 50, , Marquis of Worcester's g g , Newcomen's 12 12 , its Merits and Demerits 13 jfc , Performance of Savery's u jj , Real, distinguished from the Ideal 107 423 , Several Efficiencies of the Steam 174 705 - speed, Influence of 145 ggg , Steam, Actual, Efficiencies of proposed 137 572 , as a Heat-engine 106 422 , Origin of the 5 3 , Peculiar Types of 44 331 , Philosophical Study of Development of 26 77 , Process of Development of 25 73 , Structure and Use of 27 82 , Thermodynamics of 105 42 1 , Superheated Steam and the Steam- i6S 671 , The Locomotive- 21 34 , The Mill- or Factory- 34 95 , The Stationary 20 33 Older Forms of 33 87 , Thermodynamics of the Steam- 72 296 , Watt's Double-acting 17 23 , Watt's Single-acting 16 22 with Jackets, Proportions of 163 661 Engines, Actual, Methods of Waste in 122 471 , Classification of, into Types 28 82 , Corliss and Greene, Simple and Compound Forms 34 95 , Distribution of Energy in Real 120 467 , Early Compound 19 72 , Experimental 44 231 , Heat-, Classified . 3 2 , High-speed, Jackets on 159 656 , Simple and Compound Forms 35 116 , Ideal, Computations of Efficiencies of 117 454 , Theory of Efficiency of. . 116 449 , Jackets on Multiple-cylinder 157 654 .Jacketed 113 444 862 INDEX. ART. P^ GK Engines, Low-speed, Simple and Compound Forms 35 116 , Marine 41 211 .Early 22 45 -Later 23 57 , Standard Forms 42 217 , Multiple-cylinder, Recent Use of 24 68 , Portable 38 179 .Pumping 37 163 .Later 18 25 , Real, and their Cycles 116 467 , Computations of Efficiency and Economy of 137 572 , Curves of Efficiency for 186 756 , Examples of Computations of Economy and Effi- ciency of 137 572 , Theory of Efficiencies for.. 185 752 , Single-acting and H igh-speed 36 150 , Size of 182 741 , Steam-, Classed 29 83 .Defined 4 2 .Steam Fire- ... 21 34 , Steam-jackets on Multiple-cylinder 152 622 on Simple Cylinder. 152 622 , The Locomotive 40 103 , The Scope of the Philosophy of the Heat- 45 243 , Theory of, General 57 257 , Theory of Multiple-cylinder, General 138 584 Equations, General Fundamental Thermodynamic. 86 319 Equivalent, Mechanical, of Heat. .. 82 312 Estimate of Costs 191 766 of Fuel ,., 178 713 of Heat 178 713 of Steam... 178 713 Evaporation, Factors of 89 332 , Tables of Factors of . 99 376 Examples of Computations of Efficiencies 149 61 1 Expansion, Absolute Limits to 201 786 , Best Ratio of 64 271 , Cost of Engine as affecting 195 775 , Extent of Economical 144 597 , Profits at a fixed 194 774 , Ratios of, at Maximum Efficiencies 181 725 , Thermal Lines of, for Steam 102 394 , for Vapors 102 394 Experiment, General Results of ,. 150 614 Experimental Engines 44 2-" INDEX. 863 AJTT. FACE Experimental Results. Experience with Jackets , 165 664 External and Internal Work 99 ygf Factory or Mill Engine 34 95 Fire-engine. Sarerys ,o n Fire-engines, Steam 2I 34 First Law of Thermodynamics 82 312 Fluid, Superheated Steam as a Working 167 671 Fluids, Conditions of Maximum Efficiency of 125 453 Force 76 299 Forces, Balance of 151 620 Friction, Internal Engine. Investigation of 133 55$ , Variation and Distribution of 134 565 Friction of Engine, and Efficiency of the Machine 132 540 Fuel, Heat, Steam, Estimates of 178 713 , Thermodynamk Demand for 176 709 Function, Thermodynamic 101 319 Fundamental Principles of Compounding. 142 595 Thermodynamic Equations, General 86 319 Fusing and Boiling Points 89 322 Gas, Definition of Perfect 95 354 Equation for the Perfect 95 354 Thermodynamics of the Perfect 96 355 Gases 89 322 and Vapors, Thermodynamics of the Imperfect 95 373 Greene and Corliss Engines, Simple and Compound Forms 34 95 Heads and Piston, Jacketing the 162 661 Heat and Temperature. Absolute Scale 91 328 , Mechanical Equivalent of 82 312 , Mechanical Theory, Origin and Form of 55 253 of Steam, Computation of Latent and Total 93 336 . Quantities of .....92 333 , Steam, Fuel, Estimates of .*. . ..178 713 , Thermodynamic Demand for 176 709 Heal. Transformed 112 431 Heats, Specific. Latent and Total 93 336 Heat-engine, Purpose of I I . The Steam-engine as a 106 422 H rat -engines, Classification of. 3 2 .First Law of 83 515 . The Scope of the Philosophy of 45 243 Heat-wastes by Conduction and Radiation 126 483 Hero's Engine 6 3 High-speed and the Steam-engine 131 534 and Single-acting Engines 36 150 Engines, Jackets on 159 656 804 INDEX. ART. PAGE Hirn's Investigations on Cylinder-condensation 66 274 Ideal Efficiency, Rankine's Diagram of 184 749 Thermodynamic Cases 112 431 , Special. 113 444 Ideal Engine distinguished from Real 94 350 , Efficiencies of 183 746 Ideal Engines and Real 52 250 , Progress of Philosophy of 54 251 , Scientific Problem of 53 251 Ideal Engines, Application of Computation of Efficiencies of 117 454 , Computation of Efficiencies of 117 454 Theory of Efficiency of 116 450 Imperfect Gases and Vapors, Thermodynamics of 98 375 Internal Condensation and Waste, Theory of 130 5 1 7 , Laws governing loss by 129 499 Internal Engine-friction, Investigation of 133 558 , Variation and Distribution of 134 565 Internal Work 90 327 Investigation of Costs, Deductions from 197 776 Ishenvood's Work 67 275 Jacket, Action of the, in Detail 153 627 and Engine Efficiency 166 668 Jacket-action, Limitations of 156 648 , Maximum Efficiency of 156 648 Jacket-waste, Computation of Efficiency and 155 636 Jacket-wastes v. Cylinder-wastes , 154 632 Jackets, Air in 164 663 , Experimental Results of Experience with, 165 664 , on High-speed Engines 159 650 on Multiple-cylinder Engines 157 654 , Temperatures and Pressures in 160 658 , Proportions of Engine with 163 661 Jackets, Steam 131 534 , on Simple and Multiple-cylinder Engines . . 152 622 Jacketed Engines 113 444 Jacketing, Amelioration of Wastes by 140 590 , Conclusions relative to 166 668 , Defective 164 663 .Influence of 145 598 the Heads and Piston ,.162 661 and Superheating 158 656 Kinetic Theory of Gases < 89 322 Latent Heat of Steam, Computation of r 93 336 Heats, Specific, Total and 73 291 Law, First, of Heat-engines 83 315 INDEX. -C: XKT. PAG* Law, First, of Thermodynamics. ............". 82 312 , Fundamental, of Energetics. 75 ,98 *4 315 and the Steam-engine 85 319 Laws and Basis of Thermodynamics 8l 310 governing Loss by Internal Condensation 129 409 , Newton's, and Energetics 78 305 of Energetics. 77 304 of Thermodynamics, Relation of the two 87 321 Limit of Actual Engine Efficiency 118 466 in Superheating.. 169 675 Limits, Absolute, to Expansion .201 787 Limitations of Jacket-action.. 136 648 of Thermodynamic Theory 62 267 Lines, Actual Tbermodynamk, and Corves of Efficiency 180 718 Liquids 89 322 21 34 40 193 Locomotives, Road- - 39 187 Loss by Internal Condensation, Laws governing 129 499 Losses by Conduction and Radiation, Methods of Reduction by.... 127 487 in Actual Engines. Magnitude and Distribution of 122 4?! Machine, Efficiency of the Engine as a . 179 714 . Friction of the Engine and Efficiency of the 132 540 Magnhnde of Cylinder-condensers 128 488 and Distribution of Losses in Actual Engines 123 476 Marine Engines 41 211 .Early 22 45 .Later 23 57 , Standard Forms of 42 217 Mathematical Treatment of Engine Efficiencies 173 705 Matter 76 299 , Thermodynamics and Constitution of SS 326 Efficiency, Conclusions relative to 200 788 , Conditions of 115 449 of Engine. Conditions of Real 135 570 of Fluids, Conditions of 125 483 of Jacket-action .156 627 Efficiencies, Ratio of Expansion at 181 725 Total Efficiency of Steam, Conditions of. 136 571 il Equivalent of'rleat 82 3" or Dynamic Wastes in 430 Theory of Heat, Origin and Form of 55 253 , Efficiency of 151 620 Methods of Operation of Real Engines 121 470 866 INDEX, ART. PAGE Methods of Waste in Actual Engines 122 471 Mill or Factory Engine 34 95 Model, The Newcomen 15 19 Multiple-cylinder and Simple Engines, Jackets on 152 622 Multiple-cylinder Engines, General Theory of 138 584 , Jackets on 157 654 , Recent Use of 24 . 68 Newcomen Engine, The 12 12 , its Merits and Demerits 13 16 Newcomen Model 15 19 Newton's Laws and Energetics 78 305 Operations, Efficiency of Cyclical 114 447 , of Real Engines, Methods of 121 470 Origin and Form of Mechanical Theory of Heat 55 253 Perfect Gas, Definition of 95 354 , Equation of 95 354 , Thermodynamics of the 96 355 Performance of Engine, Solution of Problems relating to 148 604 Philosophy of Cylinder-condensation, Three ^tiods of 69 279 Heat-engines, Scope of the 45 243 Ideal and Real Engines, Progress of 54 25 1 Physical Condition, Critical, and Temperature of Steam 94 350 or Thermal Wastes no 429 Principles of Transformation of Energy 49 246 Piston, jacketing the Heads and 162 661 Points, Fusing and Boiling 89 322 Portable Engines 38 179 Pressure, Back- 171 683 , as modifying Economy 196 776 , and Clearance in 430 Pressure, Steam, Adaptation of Structure to Increasing 43 229 Pressures, Distribution of ... 151 620 and Temperatures in Jackets 160 658 Princip''.s of Construction, General 31 86 of Design 30 85 of Transformation of Energy, Chemical 48 245 .Mechanical 50 247 .Physical 49 246 Three Fundamental, of Compounding 142 593 Problem, Scientific, of Real and Ideal Engines 53 251 Problems, Efficiency, solved by Inspection 199 784 of Compounding 141 592 , Practical Solution for Efficiency 188 759 relating to Performance, Solution of 148 604 Processes, Nature of the Thermal 46 243 INDEX. 867 ART. J-AGE Profits and Costs, Relation of 103 j-j 2 at a Fixed Expansion IQ ^ -74 Progress of Philosophy of Ideal and Real Engines 54 251 Pumping-engines 37 ,63 .Later X S 25 Quality of Steam in Steam-jackets 161 659 Radiation and Conduction, Heat- wastes by 126 483 , Method of Reduction of Losses by 127 487 Rankine's Work 60 263 Diagram of Ideal Efficiency 184 750 Ratio of Expansion, Best 64 271 Ratios of Expansion at Maximum Efficiencies 181 725 Cost of Engine as affecting 195 775 Real Efficiency, Thurston's Curves of 187 757 Real Engine distinguished from Ideal 04 350 and Ideal 52 250 , Progress of Philosophy of 54 251 , Scientific Problem of 52 250 Real Engines and their Cycles 119 467 , Computation of Economy and Efficiency of 137 572 , Curves of Efficiency for 186 7^6 , Distribution of Energy in 120 467 , Examples of Computation of Economy and Efficiency of 137 , Methods of Operation of 121 471 , Theory of Efficiencies for 185 752 Real Maximum Efficiency of Engine, Conditions of 135 570 Reduction of Losses by Conduction and Radiation, Methods of 127 487 Results of Experiment, General 150 614 , Statement of 192 768 Road Locomotives and Rollers 39 187 Rollers, Steam 39 i:~ Rollers, Steam Road 39 187 Savery's Engine, Performance of n n "Fire-engine" 10 Science of Thermodynamics 46 243 Scientific Problem of Real and Ideal Engines 53 251 Screw-engine, Compound... 42 217 Second Law of Thermodynamics 84 315 and the Steam-engine 85 319 Several Efficiencies of the Steam-engine 174 705 Simple and Compound Forms, Corliss and Greene Engines 34 95 Multiple-cylinder Engines, Steam-jackets on 152 622 Single-acting Engine, Watt's 16 22 Engines and High-speed Engines 36 150 868 INDEX. ART. PAGE Size of Engine, Influence of. , 147 604 Smeaton's and Watt's Discoveries 63 268 Solids 09 326 Solution of Practical Problems of Efficiency 188 759 Problems relating to Performance 148 604 Source of Energy, Transformations, Character of, and 47 245 Special Ideal Thermodynamic Cases 113 444 Speed, High 131 534 Stationary Engine, The 20 33 , Older Forms of 33 87 Status of Theory of Cylinder-condensation in 1850 68 277 Steam, Conditions of Maximum Total Efficiency of 136 571 , Consumption of 128 488 , Critical Physical Conditions and Temperature of 94 350 , Early Knowledge of 7 5 , General Thermodynamic Equation for 101 389 , Thermodynamic Demand for 176 709 in the Middle Ages 8 5 -power 100 383 -pressure, Adaptation of Structure to increasing 43 229 , Quality of 161 659 Road Rollers 39 187 , Saturated, Use of 113 444 , Stored Energy in 100 383 , Superheated, and the Steam-engine 168 671 , Superheated, as a Working Fluid 167 671 , Thermal Lines for Expansion of 102 394 Steam-engine as a Heat-engine 106 422 , Peculiar Types of the 44 231 , Philosophical Study of Development of the 26 77 , Process of Development of the 25 73 , Structure and Uses of the , 27 82 , Thermodynamics of the 105 421 , Wastes of the 108 426 Steam-engines, Actual Efficiencies 01 Proposed 137 572 classed 29 83 defined 4 2 , Economy of Proposed 137 572 , General Theory of 57 257 , Origin of 5 3 , Real, Distribution of Energy in 120 467 , Thermodynamics of 72 296 Steam Fire-engine 21 34 Steam-jackets 131 534 on Multiple-cylinder Engines 152 622 INDEX. 869 ART. PACE Steam-jackets on Single-cylinder Engines 152 622 Stored Energy in Steam 100 383 Structure, Adaptation of, to increasing Steam-pressure. 43 229 Superheated Steam and the Steam-engine 168 671 as a Working-fluid 167 671 Superheating 131 534 and Jacketing 158 656 , Amelioration of Wastes by 140 590 , Conclusions relative to 170 680 , Experience and Testimony 170 6So , Influence of 145 598 , Limit in 169 675 Surfaces, Condition of 161 659 Tables of Factors of Evaporation 99 376 Temperature and Critical Physical Condition of Steam 94 350 and Heat, Absolute Scale 91 320 Temperatures and Pressures in Jackets 60 263 Testimony and Experience in Superheating 170 680 Theory, General, of Multiple-cylinder Engines 138 584 , of Steam-engines 57 217 , Kinetic, of Gases 89 322 of Cylinder-condensation, Status of, in 1850 68 277 Efficiency of Ideal Engines 116 450 for Real Engines 185 752 Heat, Mechanical, Origin and Form of 55 253 Internal Condensation and Waste 130 517 Thermodynamics, Limitations of 62 262 Thermal Lines, Actual 180 718 , Construction of 103 400 for Expansion of Steam 102 394 Vapors 102 394 Processes, Nature of the 46 243 Wastes, Physical or no 429 Thermodynamic Cases, Ideal 112 431 Demand for Heat 176 709 Steam 176 709 Fuel 176 709 Efficiency 175 709 Equation, General Fundamental 86 319 , General, for Steam 100 383 Thermodynamic Function 101 389 Operations, Cyclical 104 410 Theory, Limitations of 62 267 Wastes 109 427 , Unavoidable, in Actual Cases 124 482 8/0 INDEX. ART. PAGE Thermodynamics , 49 246 and Energetics 45 243 and the Constitution of Matter 88 322 as a Branch of Energetics. . -'A 74 2 9? , Basis and Laws of Si 310 , Definition of 73~8o 291-309 , First Law of 82 3-2 of Imperfect Gases 98 373 Vapors 98 373 of Steam 99 376 of To-day 61 267 Work and Energy 97 365 the Steam-engine 72-105 296-421 Perfect Gas 96 355 , Relation of the Two Laws of 87 321 , Restricted Case of Energetics So 309 , Science of 56 256 , Second Law of 84 315 Total Efficiency of Steam, Conditions of Maximum 135 570 Total and Latent Heat of Steam, Computations of 93 336 Total, Latent and Specific Heats 93 336 Transformations of Energy, Character, Source, and 47 245 , Chemical Principles of 48 245 , Mechanical Principles of 50 247 , Physical Principles of 49 246 Types, Classification of Engines into 28 82 , Peculiar, of Steam-engines 44 217 Vapor System, Binary 172 697 Vapors and Gases, Theory of Imperfect 98 373 , Thermal Lines for Expansion of 102 394 Variation and Distribution "of Internal Engine-friction 134 565 Waste and Internal Condensation, Theory of 130 517 , Computation of, in Actual Engines 122 491 , Unavoidable, in Thermodynamic Cases 124 482 Wastes, Amelioration of 140 590 , by Jacketing 140 590 , by Superheating 140 590 , Mechanical or Dynamic in 430 Wastes of Heat, by Conduction and Radiation 126 ^83 Jacket vs. Wastes of Cylinder 154 632 the Compound Engine . 139 586 Steam-engine 108 426 Wastes, Physical or Thermal ito 429 , Thermodynamic 109 427 Watt, James 14 18 INDEX. Watt's and Smeaton's Discoveries 63 266 Double-acting Engine 17 223 Single-acting Engine 16 22 Worcester's Engine, Marquis of 9 5 Work 76 209 and Energy, Thermodynamics of 97 365 External and Internal 90 327 RegnanU's. loo 383 Working Fluid, Superheated Steam as a 167 671 Substance, Actual Efficiency of the 177 712 END OF PART L IHIflll I 1306205