THE PHILOSOPHY OF THE STEAM-ENGINE

The History of its Growth; Energetics and Thermo-dynamics.

“Of all the features which characterize this progressive economical movement of civilized nations, that which first excites attention, through its intimate connection with the phenomena of production, is the perpetual and, so far as human foresight can extend, the unlimited growth of man’s power over Nature. Our knowledge of the properties and laws of physical objects shows no sign of approaching its ultimate boundaries; it is advancing more rapidly, and in a greater number of directions at once, than in any previous age or generation, and affording such frequent glimpses of unexplored fields beyond as to justify the belief that our acquaintance with Nature is still almost in its infancy.”—Mill.

The growth of the philosophy of the steam-engine presents as interesting a study as that of the successive changes which have occurred in its mechanism.

In the operation of the steam-engine we find illustrated many of the most important principles and facts which constitute the physical sciences. The steam-engine is an exceedingly ingenious, but, unfortunately, still very imperfect, machine for transforming the heat-energy obtained by the chemical combination of a combustible with the supporter of combustion into mechanical energy. But the original source of all this energy is found far back of its first appearance in the steam-boiler. It had its origin at the beginning, when all Nature came into existence. After the solar system had been formed from the nebulous chaos of creation, the glowing mass which is now called the sun was the[420] depository of a vast store of heat-energy, which was thence radiated into space and showered upon the attendant worlds in inconceivable quantity and with unmeasured intensity. During the past life of the globe, the heat-energy received from the sun upon the earth’s surface was partly expended in the production of great forests, and the storage, in the trunks, branches, and leaves of the trees of which they were composed, of an immense quantity of carbon, which had previously existed in the atmosphere, combined with oxygen, as carbonic acid. The great geological changes which buried these forests under superincumbent strata of rock and earth resulted in the formation of coal-beds, and the storage, during many succeeding ages, of a vast amount of carbon, of which the affinity for oxygen remained unsatisfied until finally uncovered by the hand of man. Thus we owe to the heat and light of the sun, as was pointed out by George Stephenson, the incalculable store of potential energy upon which the human race is so dependent for life and all its necessaries, comforts, and luxuries.

This coal, thrown upon the grate in the steam-boiler, takes fire, and, uniting again with the oxygen, sets free heat in precisely 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 radiation, to the water in the steam-boiler, converts it into steam, and its mechanical effect is seen in the expansion of the liquid into vapor against the superincumbent pressure. Transferred from the boiler to the engine, the steam is there permitted 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 in the mill or to driving the locomotive or the steamboat.

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 further[421] and observe how, in each case, it is again usually re-transformed and again set free as heat-energy.

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 new science of energetics, of which the now well-grown science of thermo-dynamics is a branch. This sketch of the growth of the steam-engine may, therefore, be very properly concluded by an outline of the growth of the several sciences which together make up its philosophy, and especially of the science of thermo-dynamics, which is peculiarly the science of the steam-engine and of the other heat-engines.

These sciences, like the steam-engine itself, have an origin which antedates the commencement of the Christian era; but they grew with an almost imperceptible growth for many centuries, and finally, only a century ago, started onward suddenly and rapidly, and their progress has never since been checked. They are now fully-developed and well-established systems of natural philosophy. Yet, like that of the steam-engine and of its companion heat-engines, their growth has by no means ceased; and, while the student of science cannot do more than indicate the direction of their progress, he can readily believe that the beginning of the end is not yet reached in their movement toward completeness, either in the determination of facts or in the codification of their laws.

[422]When Hero lived at Alexandria, the great “Museum” was a most important centre, about which gathered the teachers of all then known philosophies and of all the then recognized but unformed sciences, as well as of all those technical branches of study which had already been so far developed as to be capable of being systematically taught. Astronomical observations had been made regularly and uninterruptedly by the Chaldean astrologers for two thousand years, and records extending back many centuries had been secured at Babylon by Calisthenes and given to Aristotle, the father of our modern scientific method. Ptolemy had found ready to his hand the records of Chaldean observers of eclipses extending back nearly 650 years, and marvelously accurate.[103]

A rude method of printing with an engraved roller on plastic clay, afterward baked, thus making up ceramic libraries, was practised long previous to this time; and in the alcoves in which Hero worked were many of these books of clay.

This great Library and Museum of Alexandria was founded three centuries before the birth of Christ, by Ptolemy Soter, who established as his capital that great Egyptian city when the death of his brother, the youthful but famous conqueror whose name he gave it, placed him upon the throne of the colossal successor of the then fallen Persian Empire. The city itself, embellished with every ornament and provided with every luxury that the wealth of a conquered world or the skill, taste, and ingenuity of the Greek painters, sculptors, architects, and engineers could provide, was full of wonders; it was a wonder in itself. This rich, populous, and magnificent city was the metropolis of the then civilized world. Trade, commerce, manufactures, and the fine arts were all represented in this[423] splendid exchange, and learning found its most acceptable home and noblest field within the walls of Ptolemy’s Museum; its disciples found themselves welcomed and protected by its founder and his successors, Philadelphus and the later Ptolemies.

The Alexandrian Museum was founded with the declared object of collecting all written works of authority, of promoting the study of literature and art, and of stimulating and assisting experimental and mathematical scientific investigation and research. The founders of modern libraries, colleges, and technical schools have their prototype in intelligence, public spirit, and liberality, in the first of the Ptolemies, who not only spent an immense sum in establishing this great institution, but spared no expense in sustaining it. Agents were sent out into all parts of the world, purchasing books. A large staff of scribes was maintained at the museum, whose duty it was to multiply copies of valuable works, and to copy for the library such works as could not be purchased.

The faculty of the museum was as carefully organized as was the plan of its administration. The four principal faculties of astronomy, literature, mathematics, and medicine were subdivided into sections devoted to the several branches of each department. The collections of the museum were as complete as the teachers of the undeveloped sciences of the time could make them. Lectures were given in all branches of study, and the number of students was sometimes as great as twelve or thirteen thousand. The number of books which were collected here, when the barbarian leaders of the Roman troops under Cæsar burned the greater part of it, was stated to be 700,000. Of these, 400,000 were within the museum itself, and were all destroyed; the rest were in the temple of Serapis, and, for the time, escaped destruction.

The greatest of all the great men who lived at Alexandria at the time of the establishment of the museum was[424] Aristotle, the teacher of Alexander and the friend of Ptolemy. It is to Aristotle that we owe the systematization of the philosophical ideas of Plato and the creation of the inductive method, in which has originated all modern science. It is to the learned men of Alexandria that we are indebted for so effective an application of the Aristotelian philosophy that all the then known sciences were given form, and were so thoroughly established that the work of modern science has been purely one of development.

The inductive method, which built up all the older sciences, and which has created all those of recent development, consists, first, in the discovery and quantitative determination of facts; secondly, when a sufficient number of facts have been thus observed and defined, in the grouping of those facts, and the detection, by a study of their mutual relations, of the natural laws which give rise to or regulate them. This simple method is that—and the only—method by which science advances. By this method, and by it only, do we acquire connected and systematic knowledge of all the phenomena of Nature of which the physical sciences are cognizant. It is only by the application of this Aristotelian method and philosophy that we can hope to acquire exact scientific knowledge of existing phenomena, or to become able to anticipate the phenomena which are to distinguish the future. The Aristotelian method of observing facts, and of inductive reasoning with those facts as a basis, has taught the chemist the properties of the known elementary substances and their characteristic behavior under ascertained conditions, and has taught him the laws of combination and the effects of their union, enabling him to predict the changes and the phenomena, chemical and physical, which inevitably follow their contact under any specified set of conditions.

It is this process which has enabled the physicist to ascertain the methods of molecular motion which give us light, heat, or electricity, and the range of action and the[425] laws which govern the transfer of energy from one of these modes of motion to another. It was this method of study which enabled James Watt to detect and to remedy the defects of the Newcomen engine, and it is by the Aristotelian philosophy that the engineer of to-day is taught to construct the modern steamship, and to predict, before the keel is laid or a blow struck in the workshop or the ship-yard, what will be the weight of the vessel, its cargo-carrying capacity, the necessary size and power of its engines, the quantity of coal which they will require per day while crossing the ocean, the depth at which the great hull will float in the water, and the exact speed that the vessel will attain when the engines are exerting their thousand or their ten thousand horse-power.

It was at Alexandria that this mighty philosophy was first given a field in which to work effectively. Here Ptolemy studied astronomy and “natural philosophy;” Archimedes applied himself to the studies which attract the mathematician and engineer; Euclid taught his royal pupil those elements of geometry which have remained standard twenty-two centuries; Eratosthenes and Hipparchus studied and taught astronomy, and inaugurated the existing system of quantitative investigation, proving the spherical form of the earth; and Ctesibius and Hero studied pneumatics and experimented with the germs of the steam-engine and of less important machines.

When, seven centuries later, the destruction of this splendid institution was signalized by the death of that brilliant scholar and heathen teacher of philosophy, Hypatia, at the hands of the more heathenish fanatics who tore her in pieces at the foot of the cross, and by the dispersion of the library left by Cæsar’s soldiers in the Serapeum, a true philosophy had been created, and the inductive method was destined to live and to overcome every obstacle in the path of enlightenment and civilization. The fall of the Alexandrian Museum, sad as was the event, could not destroy the[426] new philosophical method. Its fruits ripened slowly but surely, and we are to-day gathering a plentiful harvest.

Science, literature, and the arts, all remained dormant for several centuries after the catastrophe which deprived them of the light in which they had flourished so many centuries. The armies of the caliphs made complete the shameful work of destruction begun by the armies of Cæsar, and the Alexandrian Library, partly destroyed by the Romans, was completely dispersed by the Patriarchs and their ignorant and fanatical followers; and finally all the scattered remnants were burned by the Saracens. But when the thirst for conquest had become satiated or appeased, the followers of the caliphs turned their attention to intellectual pursuits, and the ninth century of the Christian era saw once more such a collection of philosophical writings, collected at Bagdad, as could only be gathered by the power and wealth of the later conquerors of the world. Philosophy once again resumed its empire, and another race commenced the study of the mathematics of India and of Greece, the astronomy of Chaldea, and of all the sciences which originated in Greece and in Egypt. By the conquest of Spain by the Saracens, the new civilization was imported into Western Europe and libraries were gathered together under the Moorish rulers, one of which numbered more than a half-million volumes. Wherever Saracen armies had extended Mohammedan rule, schools and colleges, libraries and collections of philosophical apparatus, were scattered in strange profusion; and students, teachers, philosophers, of all—the speculative as well as the Aristotelian—schools, gathered together at these intellectual ganglia, as enthusiastic in their work as were their Alexandrian predecessors. The endowment of colleges, that truest gauge of the intelligence of the wealthy classes of any community, became as common—perhaps more so—as at the present time, and provision was made for the education of rich and poor alike. The mathematical sciences,[427] and the wonderful and beautiful phenomena which—but a thousand years later—were afterward grouped into a science and called chemistry, were especially attractive to the Arabian scholars, and technical applications of discovered facts and laws assisted in a wonderfully rapid development of arts and manufactures.

When, a thousand years after Christ, the centre of intellectual activity and of material civilization had drifted westward into Andalusia, the foundation of every modern physical science except that now just taking shape—the all-grasping science of energetics—had been laid with experimentally derived facts; and in mathematics there had been erected a symmetrical and elegant superstructure. Even that underlying principle of all the sciences, the principle of the persistence of energy, had been, perhaps unwittingly, enunciated.

Distinguished historians have shown how the progress of civilization in Europe resulted in the creation, during the middle ages, of the now great middle class, which, holding the control of political power, governs every civilized nation, and has come into power so gradually that it was only after centuries that its influence was seen and felt. This, which Buckle[104] calls the intellectual class, first became active, independently of the military and of the clergy, in the fourteenth century. In the two succeeding centuries this class gained power and influence; and in the seventeenth century we find a magnificent advance in all branches of science, literature, and art, marking the complete emancipation of the intellect from the artificial conditions which had so long repressed its every effort at advancement.

Another great social revolution thus occurred, following another period of centuries of intellectual stagnation. The Saracen invaders were driven from Europe; the Crusaders invaded Palestine, in the vain effort to recover from the hands of the infidels the Holy Sepulchre and the Holy[428] Land; and intestine broils and inter-state conflicts, as well as these greater social movements, withdrew the minds of men once more from the arts of peace and the pursuits of scholars. It is not, then, until the beginning of the seventeenth century—the time of Galileo and of Newton—that we find the nations of Europe sufficiently quiet and secure to permit general attention to intellectual vocations, although it was a half-century earlier (1543) that Copernicus left to the world that legacy which revolutionized the theories of the astronomers and established as correct the hypothesis which made the sun the centre of the solar system.

Galileo now began to overturn the speculations of the deductive philosophers, and to proclaim the still disputed principle that the book of Nature is a trustworthy commentary in the study of theological and revealed truths, so far as they affect or are affected by science; he suffered martyrdom when he proclaimed the fact that God’s laws, as they now stand, had been instituted without deference to the preconceived notions of the most ignorant of men. Bruno had a few years earlier (1600) been burned at the stake for a similar offense.

Galileo was perhaps the first, too, to combine invariably in application the idea of Plato, the philosophy of Aristotle, and the methods of modern experimentation, to form the now universal scientific method of experimental philosophy. He showed plainly how the grouping of ascertained facts, in natural sequence, leads to the revelation of the law of that sequence, and indicated the existence of a principle which is now known as the law of continuity—the law that in all the operations of Nature there is to be seen an unbroken chain of effect leading from the present back into a known or an unknown past, toward a cause which may or may not be determinable by science or known to history.

Galileo, the Italian, was worthily matched by Newton, the prince of English philosophers. The science of theoretical mechanics was hardly beginning to assume the position[429] which it was afterward given among the sciences; and the grand work of collating facts already ascertained, and of definitely stating principles which had previously been vaguely recognized, was splendidly done by Newton. The needs of physical astronomy urged this work upon him.

Da Vinci had, in the latter half of the fifteenth century, summarized as much of the statics of mechanical philosophy as had, up to his time, been given shape; he also rewrote and added very much to what was known on the subject of friction, and enunciated its laws. He had evidently a good idea of the principle of “virtual velocities,” that simple case of equivalence of work, in a connected system, which has done such excellent service since; and with his mechanical philosophy this versatile engineer and artist curiously mingled much of physical science. Then Stevinus, the “brave engineer of Bruges,” a hundred years later (1586), alternating office and field work, somewhat after the manner of the engineer of to-day, wrote a treatise on mechanics, which showed the value of practical experience and judgment in even scientific work. And thus the path had been cleared for Newton.

Meantime, also, Kepler had hit upon the true relations of the distances of the planets and their periodic times, after spending half a generation in blindly groping for them, thus furnishing those great landmarks of fact in the mechanics of astronomy; and Galileo had enunciated the laws of motion. Thus the foundation of the science of dynamics, as distinguished from statics, was laid, and the beginning was made of that later science of energetics, of which the philosophy of the steam-engine is so largely constituted.

Hooke, Huyghens, and others, had already seen some of the principal consequences of these laws; but it remained for Newton to enunciate them with the precision of a true mathematician, and to base upon them a system of dynamical laws, which, complemented by his announcement of the existence of the force of gravitation, and his statement of its laws,[430] gave a firm basis for all that the astronomer has since done in those quantitative determinations of size, weight, and distance, and of the movements of the heavenly bodies, which compel the wonder and admiration of mankind.

The Arabians and Greeks had noticed that the direction taken by a body falling under the action of gravitation was directly toward the centre of the earth, wherever its fall might occur; Galileo had shown, by his experiments at Pisa, that the velocity of fall, second after second, varied as the numbers 1, 3, 5, 7, 9, etc., and that the distances varied as the squares of the total periods of time during which the body was falling, and that it was, in British feet, very nearly sixteen times the square of that time in seconds. Kepler had proved that the movements of the heavenly bodies were just such as would occur under the action of central attractive forces and of centrifugal force.

Putting all these things together, Newton was led to believe that there existed a “force of gravity,” due to the attraction, by the great mass of the earth, of its own particles and of neighboring bodies, like the moon, of which force the influence extended as far, at least, as the latter. He calculated the motion of the earth’s satellite, on the assumption that his theory and the then accepted measurements of the earth’s dimensions were correct, and obtained a roughly approximate result. Later, in 1679, he revised his calculations, using Picard’s more accurate determination of the dimensions of the earth, and obtained a result which precisely tallied with careful measurements, made by the astronomers, of the moon’s motion.

The science of mechanics had now, with the publication of Newton’s “Principia,” become thoroughly consistent and logically complete, so far as was possible without a knowledge of the principles of energetics; and Newton’s enunciations of the laws of motion, concise and absolutely perfect as they still seem, were the basis of the whole science of dynamics, as applied to bodies moving freely under the[431] 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 compelled 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 reaction 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 will produce, acting in the unit of time on the unit of mass.

The quantitative determinations of dynamic effects of 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 feet per second, which quantity is the unit of dynamic measurement.

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 1∕64 its weight multiplied by the square of its velocity, or, which[432] 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 grandest of all physical generalizations, the doctrine of the persistence or conservation of all energy, and to its corollary declaring 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 existence in the various modes of motion of bodies and of their molecules.

Experimental physical science had hardly become acknowledged as the only and the proper method of acquiring knowledge of natural phenomena at the time of Newton; but it soon became a generally accepted principle. In physics, Gilbert 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 skillful and intelligent use of quantitative measurements, 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 have already seen how astronomy and mathematics together led philosophers to the creation and the study of what finally became the science of mechanics, when experiment and observation were finally brought to their aid. We can now see how, in all these physical sciences, four primitive ideas are comprehended: matter, force, motion, and space—which latter two terms include all relations of position.

Based on these notions, the science of mechanics comprehends 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.

Kinematics, which treats of relations of motion simply.[433]

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.

Under the latter of these 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—Thermo-dynamics. This science is simply a wider generalization of principles which, as we have seen, have been established one at a time, and by philosophers widely separated both geographically 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, as we now are beginning to see, we are slowly 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 immutable 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 created it.

That matter is indestructible by finite power became admitted 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 modification 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 determination of the convertibility of heat-energy into other forms and into mechanical work, for which we are indebted to Rumford and Davy, and to the[434] determination of the quantivalence anticipated by Newton, shown and calculated approximately by Colding and Mayer, and measured with great probable accuracy by Joule.

Benjamin Thompson, Count Rumford.

The great fact of the conservation of energy was loosely stated by Newton, who asserted that the work of friction and the vis viva of the system or body arrested by friction were equivalent. In 1798, Benjamin Thompson, Count Rumford, an American who was then in the Bavarian service, presented a paper[105] to the Royal Society of Great Britain, in which he stated the results of an experiment which he had recently made, proving the immateriality of heat and the transformation of mechanical into heat energy.[435] This paper is of very great historical interest, as the now accepted doctrine of the persistence of energy is a generalization which arose out of a series of investigations, the most important of which are those which resulted in the determination of the existence of a definite quantivalent relation between these two forms of energy and a measurement of its value, now known as the “mechanical equivalent of heat.” His experiment consisted in the determination of the quantity of heat produced by the boring of a cannon at the arsenal at Munich.

Rumford, after showing that this heat could not have been derived from any of the surrounding objects, or by compression of the materials employed or acted upon, says: “It appears to me extremely difficult, if not impossible, to form any distinct idea of anything capable of being excited and communicated in the manner that heat was excited and communicated in these experiments, except it be motion.”[106] He then goes on to urge a zealous and persistent investigation of the laws which govern this motion. He estimates the heat produced by a power which he states could easily be exerted by one horse, and makes it equal to the “combustion of nine wax candles, each three-quarters of an inch in diameter,” and equivalent to the elevation of “25.68 pounds of ice-cold water” to the boiling-point, or 4,784.4 heat-units.[107] The time was stated at “150 minutes.” Taking the actual power of Rumford’s Bavarian “one horse” as the most probable figure, 25,000 pounds raised one foot high per minute,[108] this gives the “mechanical equivalent”[436] of the foot-pound as 783.8 heat-units, differing but 1.5 per cent. from the now accepted value.

Had Rumford been able to eliminate all losses of heat by evaporation, radiation, and conduction, to which losses he refers, and to measure the power exerted with accuracy, the approximation would have been still closer. Rumford thus made the experimental discovery of the real nature of heat, proving it to be a form of energy, and, publishing the fact a half-century before the now standard determinations were made, gave us a very close approximation to the value of the heat-equivalent. Rumford also observed that the heat generated was “exactly proportional to the force with which the two surfaces are pressed together, and to the rapidity of the friction,” which is a simple statement of equivalence between the quantity of work done, or energy expended, and the quantity of heat produced. This was the first great step toward the formation of a Science of Thermo-dynamics. Rumford’s work was the corner-stone of the science.

Sir Humphry Davy, a little later (1799), published the details of an experiment which conclusively confirmed these deductions from Rumford’s work. He rubbed two pieces of ice together, and found that they were melted by the friction so produced. He thereupon concluded: “It is evident that ice by friction is converted into water.... Friction, consequently, does not diminish the capacity of bodies for heat.”

Bacon and Newton, and Hooke and Boyle, seem to have anticipated—long before Rumford’s time—all later philosophers, in admitting the probable correctness of that modern dynamical, or vibratory, theory of heat which considers it a mode of motion; but Davy, in 1812, for the first[437] time, stated plainly and precisely the real nature of heat, saying: “The immediate cause of the phenomenon of heat, then, is motion, and the laws of its communication are precisely the same as the laws of the communication of motion.” The basis of this opinion was the same that had previously been noted by Rumford.

So much having been determined, it became at once evident that the determination of the exact value of the mechanical equivalent of heat was simply a matter of experiment; and during the succeeding generation this determination was made, with greater or less exactness, by several distinguished men. It was also equally evident that the laws governing the new science of thermo-dynamics could be mathematically expressed.

Fourier had, before the date last given, applied mathematical analysis in the solution of problems relating to the transfer of heat without transformation, and his “Théorie de la Chaleur” contained an exceedingly beautiful treatment of the subject. Sadi Carnot, twelve years later (1824), published his “Réflexions sur la Puissance Motrice du Feu,” in which he made a first attempt to express the principles involved in the application of heat to the production of mechanical effect. Starting with the axiom that a body which, having passed through a series of conditions modifying its temperature, is returned to “its primitive physical state as to density, temperature, and molecular constitution,” must contain the same quantity of heat which it had contained originally, he shows that the efficiency of heat-engines is to be determined by carrying the working fluid through a complete cycle, beginning and ending with the same set of conditions. Carnot had not then accepted the vibratory theory of heat, and consequently was led into some errors; but, as will be seen hereafter, the idea just expressed is one of the most important details of a theory of the steam-engine.

Seguin, who has already been mentioned as one of the[438] first to use the fire-tubular boiler for locomotive engines, published in 1839 a work, “Sur l’Influence des Chemins de Fer,” in which he gave the requisite data for a rough determination of the value of the mechanical equivalent of heat, although he does not himself deduce that value.

Dr. Julius R. Mayer, three years later (1842), published the results of a very ingenious and quite closely approximate calculation of the heat-equivalent, basing his estimate upon the work necessary to compress air, and on the specific heats of the gas, the idea being that the work of compression is the equivalent of the heat generated. Seguin had taken the converse operation, taking the loss of heat of expanding steam as the equivalent of the work done by the steam while expanding. The latter also was the first to point out the fact, afterward experimentally proved by Hirn, that the fluid exhausted from an engine should heat the water of condensation less than would the same fluid when originally taken into the engine.

A Danish engineer, Colding, at about the same time (1843), published the results of experiments made to determine the same quantity; but the best and most extended work, and that which is now almost universally accepted as standard, was done by a British investigator.

James Prescott Joule.

James Prescott Joule commenced the experimental investigations which have made him famous at some time previous to 1843, at which date he published, in the Philosophical Magazine, his earliest method. His first determination gave 770 foot-pounds. During the succeeding five or six years Joule repeated his work, adopting a considerable variety of methods, and obtaining very variable results. One method was to determine the heat produced by forcing air through tubes; another, and his usual plan, was to turn a paddle-wheel by a definite power in a known weight of water. He finally, in 1849, concluded these researches.

The method of calculating the mechanical equivalent of[439] heat which was adopted by Dr. Mayer, of Heilbronn, is as beautiful as it is ingenious: Conceive two equal portions of atmospheric air to be inclosed, at the same temperature—as at the freezing-point—in vessels each capable of containing one cubic foot; communicate heat to both, retaining the one portion at the original volume, and permitting the other to expand under a constant pressure equal to that of the atmosphere. In each vessel there will be inclosed 0.08073 pound, or 1.29 ounce, of air. When, at the same temperature, the one has doubled its pressure and the other has doubled its volume, each will be at a temperature of 525.2° Fahr., or 274° C, and each will have double the original temperature, as measured on the absolute scale from the[440] zero of heat-motion. But the one will have absorbed but 63∕4 British thermal units, while the other will have absorbed 91∕2. In the first case, all of this heat will have been employed in simply increasing the temperature of the air; in the second case, the temperature of the air will have been equally increased, and, besides, a certain amount of work—2,116.3 foot-pounds—must have been done in overcoming the resistance of the air; it is to this latter action that we must debit the additional heat which has disappeared. Now, (2,116.3/23∕4) = 770 foot-pounds per heat-unit—almost precisely the value derived from Joule’s experiments. Had Mayer’s measurement been absolutely accurate, the result of his calculation would have been an exact determination of the heat-equivalent, provided no heat is, in this case, lost by internal work.

Joule’s most probably accurate measure was obtained by the use of a paddle-wheel revolving in water or other fluid. A copper vessel contained a carefully weighed portion of the fluid, and at the bottom was a step, on which stood a vertical spindle carrying the paddle-wheel. This wheel was turned by cords passing over nicely-balanced grooved wheels, the axles of which were carried on friction-rollers. Weights hung at the ends of these cords were the moving forces. Falling to the ground, they exerted an easily and accurately determinable amount of work, W × H, which turned the paddle-wheel a definite number of revolutions, warming the water by the production of an amount of heat exactly equivalent to the amount of work done. After the weight had been raised and this operation repeated a sufficient number of times, the quantity of heat communicated to the water was carefully determined and compared with the amount of work expended in its development. Joule also used a pair of disks of iron rubbing against each other in a vessel of mercury, and measured the heat thus developed by friction, comparing it with the[441] work done. The average of forty experiments with water gave the equivalent 772.692 foot-pounds; fifty with mercury gave 774.083; twenty with cast-iron gave 774.987—the temperature of the apparatus being from 55° to 60° Fahr.

Joule also determined, by experiment, the fact that the expansion of air or other gas without doing work produces no change of temperature, which fact is predicable from the now known principles of thermo-dynamics. He stated the results of his researches relating to the mechanical equivalent of heat as follows:

1. The heat produced by the friction of bodies, whether solid or liquid, is always proportional to the quantity of work expended.

2. The quantity required to increase the temperature of a pound of water (weighed in vacuo at 55° to 60° Fahr.) by one degree requires for its production the expenditure of a force measured by the fall of 772 pounds from a height of one foot. This quantity is now generally called “Joule’s equivalent.”

During this series of experiments, Joule also deduced the position of the “absolute zero,” the point at which heat-motion ceases, and stated it to be about 480° Fahr. below the freezing-point of water, which is not very far from the probably true value,-493.2° Fahr. (-273° C.), as deduced afterward from more precise data.

The result of these, and of the later experiments of Hirn and others, has been the admission of the following principle:

Heat-energy and mechanical energy are mutually convertible and have a definite equivalence, the British thermal unit being equivalent to 772 foot-pounds of work, and the metric calorie to 423.55, or, as usually taken, 424 kilogrammetres. The exact measure is not fully determined, however.

It has now become generally admitted that all forms of[442] energy due to physical forces are mutually convertible with a definite quantivalence; and it is not yet determined that even vital and mental energy do not fall within the same great generalization. This quantivalence is the sole basis of the science of Energetics.

The study of this science has been, up to the present time, principally confined to that portion which comprehends the relations of heat and mechanical energy. In the study of this department of the science, thermo-dynamics, Rankine, Clausius, Thompson, Hirn, and others have acquired great distinction. In the investigations which have been made by these authorities, the methods of transfer of heat and of modification of physical state in gases and vapors, when a change occurs in the form of the energy considered, have been the subjects of especial study.

According to the law of Boyle and Marriotte, the expansion of such fluids follows a law expressed graphically by the hyperbola, and algebraically by the expression PVx = A, in which, with unchanging temperature, x is equal to 1. One of the first and most evident deductions from the principles of the equivalence of the several forms of energy is that the value of x must increase as the energy expended in expansion increases. This change is very marked with a vapor like steam—which, expanded without doing work, has an exponent less than unity, and which, when doing work by expanding behind a piston, partially condenses, the value of x increases to, in the case of steam, 1.111 according to Rankine, or, probably more correctly, to 1.135 or more, according to Zeuner and Grashof. This fact has an important bearing upon the theory of the steam-engine, and we are indebted to Rankine for the first complete treatise on that theory as thus modified.

Prof. W. J. M. Rankine.

Prof. Rankine began his investigations as early as 1849, at which time he proposed his theory of the molecular constitution of matter, now well known as the theory of molecular vortices. He supposes a system of whirling rings or[443] vortices of heat-motion, and bases his philosophy upon that hypothesis, supposing sensible heat to be employed in changing the velocity of the particles, latent heat to be the work of altering the dimensions of the orbits, and considering the effort of each vortex to enlarge its boundaries to be due to centrifugal force. He distinguished between real and apparent specific heat, and showed that the two methods of absorption of heat, in the case of the heating of a fluid, that due to simple increase of temperature and that due to increase of volume, should be distinguished; he proposed, for the latter quantity, the term heat-potential, and for the sum of the two, the name of thermo-dynamic function.

Carnot had stated, a quarter of a century earlier, that the efficiency of a heat-engine is a function of the two limits of temperature between which the machine is worked, and[444] not of the nature of the working substance—an assertion which is quite true where the material does not change its physical state while working. Rankine now deduced that “general equation of thermo-dynamics” which expresses algebraically the relations between heat and mechanical energy, when energy is changing from the one state to the other, in which equation is given, for any assumed change of the fluids, the quantity of heat transformed. He showed that steam in the engine must be partially liquefied by the process of expanding against a resistance, and proved that the total heat of a perfect gas must increase with rise of temperature at a rate proportional to its specific heat under constant pressure.

Rankine, in 1850, showed the inaccuracy of the then accepted value, 0.2669, of the specific heat of air under constant pressure, and calculated its value as 0.24. Three years later, the experiments of Regnault gave the value 0.2379, and Rankine, recalculating it, made it 0.2377. In 1851, Rankine continued his discussion of the subject, and, by his own theory, corroborated Thompson’s law giving the efficiency of a perfect heat-engine as the quotient of the range of working temperature to the temperature of the upper limit, measured from the absolute zero.

During this period, Clausius, the German physicist, was working on the same subject, taking quite a different method, studying the mechanical effects of heat in gases, and deducing, almost simultaneously with Rankine (1850), the general equation which lies at the beginning of the theory of the equivalence of heat and mechanical energy. He found that the probable zero of heat-motion is at such a point that the Carnot function must be approximately the reciprocal of the “absolute” temperature, as measured with the air thermometer, or, stated exactly, that quantity as determined by a perfect gas thermometer. He confirmed Rankine’s conclusion relative to the liquefaction of saturated vapors when expanding against resistance, and, in 1854,[445] adapted Carnot’s principle to the new theory, and showed that his idea of the reversible engine and of the performance of a cycle in testing the changes produced still held good, notwithstanding Carnot’s ignorance of the true nature of heat. Clausius also gave us the extremely important principle: It is impossible for a self-acting machine, unaided, to transfer heat from one body at a low temperature to another having a higher temperature.

Simultaneously with Rankine and Clausius, Prof. William Thomson was engaged in researches in thermo-dynamics (1850). He was the first to express the principle of Carnot as adapted to the modern theory by Clausius in the now generally quoted propositions:[109]

1. When equal mechanical effects are produced by purely thermal action, equal quantities of heat are produced or disappear by transformation of energy.

2. If, in any engine, a reversal effects complete inversion of all the physical and mechanical details of its operation, it is a perfect engine, and produces maximum effect with any given quantity of heat and with any fixed limits of range of temperature.

William Thomson and James Thompson showed, among the earliest of their deductions from these principles, the fact, afterward confirmed by experiment, that the melting-point of ice should be lowered by pressure 0.0135° Fahr, for each atmosphere, and that a body which contracts while being heated will always have its temperature decreased by sudden compression. Thomson applied the principles of energetics in extended investigations in the department of electricity, while Helmholtz carried some of the same methods into his favorite study of acoustics.

The application of now well-settled principles to the physics of gases led to many interesting and important deductions:[446] Clausius explained the relations between the volume, density, temperature, and pressure of gases, and their modifications; Maxwell reëstablished the experimentally determined law of Dalton and Charles, known also as that of Gay-Lussac (1801), which asserts that all masses of equal pressure, volume, and temperature, contain equal numbers of molecules. On the Continent of Europe, also, Hirn, Zeuner, Grashof, Tresca, Laboulaye, and others have, during the same period and since, continued and greatly extended these theoretical researches.

During all this time, a vast amount of experimental work has also been done, resulting in the determination of important data without which all the preceding labor would have been fruitless. Of those who have engaged in such work, Cagniard de la Tour, Andrews, Regnault, Hirn, Fairbairn and Tate, Laboulaye, Tresca, and a few others have directed their researches in this most important direction with the special object of aiding in the advancement of the new-born sciences. By the middle of the present century, the time which we are now studying, this set of data was tolerably complete. Boyle had, two hundred years before, discovered and published the law, which is now known by his name[110] and by that of Marriotte,[111] that the pressure of a gas varies inversely as its volume and directly as its density; Dr. Black and James Watt discovered, a hundred years later (1760), the latent heat of vapors, and Watt determined the method of expansion of steam; Dalton, in England, and Gay-Lussac, in France, showed, at the beginning of the nineteenth century, that all gaseous fluids are expanded by equal fractions of their volume by equal increments of temperature; Watt and Robison had given tables of the elastic force of steam, and Gren had shown that, at the temperature[447] of boiling water, the pressure of steam was equal to that of the atmosphere; Dalton, Ure, and others proved (1800-1818) that the law connecting temperatures and pressures of steam was expressed by a geometrical ratio; and Biot had already given an approximate formula, when Southern introduced another, which is still in use.

The French Government established a commission in 1823 to experiment with a view to the institution of legislation regulating the working of steam-engines and boilers; and this commission, MM. de Prony, Arago, Girard, and Dulong, determined quite accurately the temperatures of steam under pressures running up to twenty-four atmospheres, giving a formula for the calculation of the one quantity, the other being known. Ten years later, the Government of the United States instituted similar experiments under the direction of the Franklin Institute.

The marked distinction between gases, like oxygen and hydrogen, and condensible vapors, like steam and carbonic acid, had been, at this time, shown by Cagniard de la Tour, who, in 1822, studied their behavior at high temperatures and under very great pressures. He found that, when a vapor was confined in a glass tube in presence of the same substance in the liquid state, as where steam and water were confined together, if the temperature was increased to a certain definite point, the whole mass suddenly became of uniform character, and the previously existing line of demarkation vanished, the whole mass of fluid becoming, as he inferred, gaseous. It was at about this time that Faraday made known his then novel experiments, in which gases which had been before supposed permanent were liquefied, simply by subjecting them to enormous pressures. He then also first stated that, above certain temperatures, liquefaction of vapors was impossible, however great the pressure.

Faraday’s conclusion was justified by the researches of Dr. Andrews, who has since most successfully extended the investigation commenced by Cagniard de la Tour, and who has[448] shown that, at a certain point, which he calls the “critical point,” the properties of the two states of the fluid fade into each other, and that, at that point, the two become continuous. With carbonic acid, this occurs at 75 atmospheres, about 1,125 pounds per square inch, a pressure which would counterbalance a column of mercury 60 yards, or nearly as many metres, high. The temperature at this point is about 90° Fahr., or 31° Cent. For ether, the temperature is 370° Fahr., and the pressure 38 atmospheres; for alcohol, they are 498° Fahr., and 120 atmospheres; and for bisulphide of carbon, 505° Fahr., and 67 atmospheres. For water, the pressure is too high to be determined; but the temperature is about 775° Fahr., or 413° Cent.

Donny and Dufour have shown that these normal properties of vapors and liquids are subject to modification by certain conditions, as previously (1818) noted by Gay-Lussac, and have pointed out the bearing of this fact upon the safety of steam-boilers. It was discovered that the boiling-point of water could be elevated far above its ordinary temperature of ebullition by expedients which deprive the liquid of the air usually condensed within its mass, and which prevent contact with rough or metallic surfaces. By suspension in a mixture of oils which is of nearly the same density, Dufour raised drops of water under atmospheric pressure to a temperature of 356° Fahr.—180° Cent.—the temperature of steam of about 150 pounds per square inch. Prof. James Thompson has, on theoretical grounds, indicated that a somewhat similar action may enable vapor, under some conditions, to be cooled below the normal temperature of condensation, without liquefaction.

Fairbairn and Tate repeated the attempt to determine the volume and temperature of water at pressures extending beyond those in use in the steam-engine, and incomplete determinations have also been made by others.

Regnault is the standard authority on these data. His experiments (1847) were made at the expense of the French[449] Government, and under the direction of the French Academy. They were wonderfully accurate, and extended through a very wide range of temperatures and pressures. The results remain standard after the lapse of a quarter of a century, and are regarded as models of precise physical work.[112]

Regnault found that the total heat of steam is not constant, but that the latent heat varies, and that the sum of the latent and sensible heats, or the total heat, increases 0.305 of a degree for each degree of increase in the sensible heat, making 0.305 the specific heat of saturated steam. He found the specific heat of superheated steam to be 0.4805.

Regnault promptly detected the fact that steam was not subject to Boyle’s law, and showed that the difference is very marked. In expressing his results, he not only tabulated them but also laid them down graphically; he further determined exact constants for Biot’s algebraic expression,

Since Regnault’s time, nothing of importance has been done in this direction. There still remains much work to be done in the extension of the research to higher pressures, and under conditions which obtain in the operation of the steam-engine. The volumes and densities of steam require further study, and the behavior of steam in the engine is still but little known, otherwise than theoretically. Even the true value of Joule’s equivalent is not undisputed.

Some of the most recent experimental work bearing directly upon the philosophy of the steam-engine is that of Hirn, whose determination of the value of the mechanical equivalent was less than two per cent. below that of Joule. Hirn tested by experiment, in 1853, and repeatedly up to 1876, the analytical work of Rankine, which led to the conclusion that steam doing work by expansion must become gradually liquefied. Constructing a glass steam-engine cylinder, he was enabled to see plainly the clouds of mist which were produced by the expansion of steam behind the piston, where Regnault’s experiments prove that the steam should become drier and superheated, were no heat transformed into mechanical energy. As will be seen hereafter, this great discovery of Rankine is more important in its bearing upon the theory of the steam-engine than any made during the century. Hirn’s confirmation stands, in value, beside the original discovery. In 1858 Hirn confirmed the work of Mayer and Joule by determining the work done and the carbonic acid produced, as well as the increased temperature due to their presence, where men were set at work in a treadmill; he found the elevation of temperature to be much greater in proportion to gas produced when the men were resting than when they were at work. He thus proved conclusively the conversion of heat-energy into mechanical work. It was from these experiments that Helmholtz deduced the “modulus of efficiency” of the human machine at one-fifth, and concluded that the heart works with eight times the efficiency of a locomotive-engine, thus[451] confirming a statement of Rumford, who asserted the higher efficiency of the animal.

Hirn’s most important experiments in this department were made upon steam-engines of considerable size, including simple and compound engines, and using steam sometimes saturated and sometimes superheated to temperatures as high, on some occasions, as 340° Cent. He determined the work done, the quantity of heat entering, and the amount rejected from, the steam-cylinder, and thus obtained a coarse approximation to the value of the heat-equivalent. His figure varied from 296 to 337 kilogrammetres. But, in all cases, the loss of heat due to work done was marked, and, while these researches could not, in the nature of the case, give accurate quantitative results, they are of great value as qualitatively confirming Mayer and Joule, and proving the transformation of energy.

Thus, as we have seen, experimental investigation and analytical research have together created a new science, and the philosophy of the steam-engine has at last been given a complete and well-defined form, enabling the intelligent engineer to comprehend the operation of the machine, to perceive the conditions of efficiency, and to look forward in a well-settled direction for further advances in its improvement and in the increase of its efficiency.

A very concise résumé of the principal facts and laws bearing upon the philosophy of the steam-engine will form a fitting conclusion to this historical sketch.

The term “energy” was first used by Dr. Young as the equivalent of the work of a moving body, in his hardly yet obsolete “Lectures on Natural Philosophy.”

Energy is the capacity of a moving body to overcome resistance offered to its motion; it is measured either by the product of the mean resistance into the space through which it is overcome, or by the half-product of the mass of the body into the square of its velocity. Kinetic energy is the actual energy of a moving body; potential energy is[452] the measure of the work which a body is capable of doing under certain conditions which, without expending energy, may be made to affect it, as by the breaking of a cord by which a weight is suspended, or by firing a mass of explosive material. The British measure of energy is the foot-pound; the metric measure is the kilogrammetre.

Energy, whether kinetic or potential, may be observable and due to mass-motion; or it may be invisible and due to molecular movements. The energy of a heavenly body or of a cannon-shot, and that of heat or of electrical action, are illustrations of the two classes. In Nature we find utilizable potential energy in fuel, in food, in any available head of water, and in available chemical affinities. We find kinetic energy in the motion of the winds and the flow of running water, in the heat-motion of the sun’s rays, in heat-currents on the earth, and in many intermittent movements of bodies acted on by applied forces, natural or artificial. The potential energy of fuel and of food has already been seen to have been derived, at an earlier period, from the kinetic energy of the sun’s rays, the fuel or the food being thus made a storehouse or reservoir of energy. It is also seen that the animal system is simply a “mechanism of transmission” for energy, and does not create but simply diverts it to any desired direction of application.

All the available forms of energy can be readily traced back to a common origin in the potential energy of a universe of nebulous substance (chaos), consisting of infinitely diffused matter of immeasurably slight density, whose “energy of position” had been, since the creation, gradually going through a process of transformation into the several forms of kinetic and potential energy above specified, through intermediate methods of action which are usually still in operation, such as the potential energy of chemical affinity, and the kinetic forms of energy seen in solar radiation, the rotation of the earth, and the heat of its interior.

The measure of any given quantity of energy, whatever[453] may be its form, is the product of the resistance which it is capable of overcoming into the space through which it can move against that resistance, i. e., by the product RS. Or it is measured by the equivalent expressions 1∕2MV2, or WV2/2g, in which W is the weight, M is the “mass” of matter in motion, V the velocity, and g the dynamic measure of the force of gravity, 321∕6 feet, or 9.8 metres, per second.

There are three great laws of energetics:

1. The sum total of the energy of the universe is invariable.

2. The several forms of energy are interconvertible, and possess an exact quantitative equivalence.

3. The tendency of all forms of kinetic energy is continually toward reduction to forms of molecular motion, and to their final dissipation uniformly throughout space.

The history of the first two of these laws has already been traced. The latter was first enunciated by Prof. Sir William Thomson in 1853. Undissipated energy is called “Entrophy.”

The science of thermo-dynamics is, as has been stated, a branch of the science of energetics, and is the only branch of that science in the domain of the physicist which has been very much studied. This branch of science, which is restricted to the consideration of the relations of heat-energy to mechanical energy, is based upon the great fact determined by Rumford and Joule, and considers the behavior of those fluids which are used in heat-engines as the media through which energy is transferred from the one form to the other. As now accepted, it assumes the correctness of the hypothesis of the dynamic theory of fluids, which supposes their expansive force to be due to the motion of their molecules.

This idea is as old as Lucretius, and was distinctly expressed by Bernouilli, Le Sage and Prévost, and Herapath. Joule recalled attention to this idea, in 1848, as explaining[454] the pressure of gases by the impact of their molecules upon the sides of the containing vessels. Helmholtz, ten years later, beautifully developed the mathematics of media composed of moving, frictionless particles, and Clausius has carried on the work still further.

The general conception of a gas, as held to-day, including the vortex-atom theory of Thomson and Rankine, supposes all bodies to consist of small particles called molecules, each of which is a chemical aggregation of its ultimate parts or atoms. These molecules are in a state of continual agitation, which is known as heat-motion. The higher the temperature, the more violent this agitation; the total quantity of motion is measured as vis viva by the half-product of the mass into the square of the velocity of molecular movement, or in heat-units by the same product divided by Joule’s equivalent. In solids, the range of motion is circumscribed, and change of form cannot take place. In fluids, the motion of the molecules has become sufficiently violent to enable them to break out of this range, and their motion is then no longer definitely restricted.

The laws of thermo-dynamics are, according to Rankine:

1. Heat-energy and mechanical energy are mutually convertible, one British thermal unit being the equivalent in heat-energy of 772 foot-pounds of mechanical energy, and one metric calorie equal to 423.55 kilogrammetres of work.

2. The energy due to the heat of each of the several equal parts into which a uniformly hot substance may be divided is the same; and the total heat-energy of the mass is equal to the sum of the energies of its parts.[113]

It follows that the work performed by the transformation of the energy of heat, during any indefinitely small[455] variation of the state of a substance as respects temperature, is measured by the product of the absolute temperature into the variation of a “function,” which function is the rate of variation of the work so done with temperature. This function is the quantity called by Rankine the “heat-potential” of the substance for the given kind of work. A similar function, which comprehends the total heat-variation, including both heat transformed and heat needed to effect accompanying physical changes, is called the “thermo-dynamic function.” Rankine’s expression for the general equation of thermo-dynamics includes the latter, and is given by him as follows:

Jdh = dH = kdτ + τdF = τdφ,

in which J is Joule’s equivalent, dh the variation of total heat in the substance, kdτ the product of the “dynamic specific heat” into the variation of temperature, or the total heat demanded to produce other changes than a transformation of energy, and τdF is the work done by the transformation of heat-energy, or the product of the absolute temperature, τ, into the differential of the heat-potential. φ is the thermo-dynamic function, and τdφ measures the whole heat needed to produce, simultaneously, a certain amount of work or of mechanical energy, and, at the same time, to change the temperature of the working substance.

Studying the behavior of gases and vapors, it is found that the work done when they are used, like steam, in heat-engines, consists of three parts:

(a.) The change effected in the total actual heat-motion of the fluid.

(b.) That heat which is expended in the production of internal work.

(c.) That heat which is expended in doing the external work of expansion.

In any case in which the total heat expended exceeds that due the production of work on external bodies, the excess[456] so supplied is so much added to the intrinsic energy of the substance absorbing it.

The application of these laws to the working of steam in the engine is a comparatively recent step in the philosophy of the steam-engine, and we are indebted to Rankine for the first, and as yet only, extended and in any respect complete treatise embodying these now accepted principles.

It was fifteen years after the publication of the first logical theory of the steam-engine, by Pambour,[114] before Rankine, in 1859, issued the most valuable of all his works, “The Steam-Engine and other Prime Movers.” The work is far too abstruse for the general reader, and is even difficult reading for many accomplished engineers. It is excellent beyond praise, however, as a treatise on the thermo-dynamics of heat-engines. It will be for his successors the work of years to extend the application of the laws which he has worked out, and to place the results of his labors before students in a readily comprehended form.

William J. Macquorn Rankine, the Scotch engineer and philosopher, will always be remembered as the author of the modern philosophy of the steam-engine, and as the greatest among the founders of the science of thermo-dynamics. His death, while still occupying the chair of engineering at the University of Glasgow, December 24, 1872, at the early age of fifty-two, was one of the greatest losses to science and to the profession which have occurred during the century.