Chapter 19

ThompsonBenjamin Thompson, Count Rumford.

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 thevis vivaof 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.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”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 firsttime, 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 thefirst 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.

JouleJames Prescott Joule.

James Prescott Joule.

James Prescott Joulecommenced the experimental investigations which have made him famous at some time previous to 1843, at which date he published, in thePhilosophical 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 ofheat 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 thezero of heat-motion. But the one will have absorbed but 63∕4British 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 thework 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 (weighedin vacuoat 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 metriccalorieto 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 ofenergy 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,xis 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 ofxincreases 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.

RankineProf. W. J. M. Rankine.

Prof. W. J. M. Rankine.

Prof. Rankinebegan 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 orvortices 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, andnot 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,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: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 temperatureof 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 hasshown 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 FrenchGovernment, 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,

log.p=a-bAx-cBx;

makingx= 20 +t° Cent.;a= 6.264035; log.b= 0.1397743; log.c= 0.6924351; log. A =1.9940493, and log. B =1.9983439;pis the pressure in atmospheres. Regnault, in the expression for the total heat, H = A +bt, determined on the centigrade scaleθ= 606.5 + 0.305tCent. For the Fahrenheit scale, we have the following equivalent expressions:

For latent heat, we have:

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, thusconfirming 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 conciserésuméof 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 isthe 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.

Themeasureof any given quantity of energy, whatevermay 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 expressions1∕2MV2, or WV2/2g, in which W is the weight, M is the “mass” of matter in motion, V the velocity, andgthe dynamic measure of the force of gravity, 321∕6feet, 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 explainingthe 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 asvis vivaby 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 metriccalorieequal 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 smallvariation 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,dhthe variation of total heat in the substance,kdτthe 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, andτdF 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.φis the thermo-dynamic function, andτdφmeasures 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 excessso 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.

[103]Their estimate of the length of the Saros, or cycle of eclipses—over 19 years—was “within 191∕2minutes of the truth.”—Draper.[104]“History of Civilization in England,” vol. i., p. 208. London, 1868.[105]“Philosophical Transactions,” 1798.[106]This idea was not by any means original with Rumford. Bacon seems to have had the same idea; and Locke says, explicitly enough: “Heat is a very brisk agitation of the insensible parts of the object ... so that what in our sensation is heat, in the object is nothing but motion.”[107]The British heat-unit is the quantity of heat required to heat one pound of water 1° Fahr. from the temperature of maximum density.[108]Rankine gives 25,920 foot-pounds per minute—or 432 per second—for the average draught-horse in Great Britain, which is probably too high for Bavaria. The engineer’s “horse-power”—33,000 foot-pounds per minute—is far in excess of the average power of even a good draught-horse, which latter is sometimes taken as two-thirds the former.

[103]Their estimate of the length of the Saros, or cycle of eclipses—over 19 years—was “within 191∕2minutes of the truth.”—Draper.

[104]“History of Civilization in England,” vol. i., p. 208. London, 1868.

[105]“Philosophical Transactions,” 1798.

[106]This idea was not by any means original with Rumford. Bacon seems to have had the same idea; and Locke says, explicitly enough: “Heat is a very brisk agitation of the insensible parts of the object ... so that what in our sensation is heat, in the object is nothing but motion.”

[107]The British heat-unit is the quantity of heat required to heat one pound of water 1° Fahr. from the temperature of maximum density.

[108]Rankine gives 25,920 foot-pounds per minute—or 432 per second—for the average draught-horse in Great Britain, which is probably too high for Bavaria. The engineer’s “horse-power”—33,000 foot-pounds per minute—is far in excess of the average power of even a good draught-horse, which latter is sometimes taken as two-thirds the former.

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