# Popular Science Monthly/Volume 12/December 1877/History of the Dynamical Theory of Heat I

 HISTORY OF THE DYNAMICAL THEORY OF HEAT.[1]
By PORTER POINIER.
I.

A RECAPITULATION of the various conjectures which have been advanced in explanation of so ever-familiar a sensation as that of warmth or heat, would neither prove particularly feasible nor interesting; for doubtless during the vast period of time which has elapsed since the enunciation of atomic doctrines by the old Greek philosophers—and from their great suggestiveness—the speculations of reflective minds have wandered over wellnigh every imaginable hypothesis, and approximated with greater or less minuteness to the views which are admitted now, and which we think to be supported by experiment. Thus, as a case in point, we may refer to Galileo,[2] whose resource of observation could have scarcely been superior to Archimedes's, and who would seem to have conceived of an increase of heat as only a more elementary condition of material substance, in which the more or less considerable destruction of molecular bonds allowed the individual particles of a body to move among themselves with a more unconstrained vibration.

But very few among the countless suppositions which we might thus succeed in raking up, however curious or predictive in themselves, would have the slightest bearing on our present subject. Developed only to the extent demanded by the superiority of the scholastic mind, they would be found in general mere arbitrary, whimsical assertions; untried and unsupported by critically-devised experiments. With the reformation of philosophy does our historical sketch then properly begin, and, moreover, with Lord Bacon as its founder; for, in illustrating the proper method of establishing a philosophical doctrine, he forever identified himself with the dynamic theory, by showing that the most comprehensive explanations were afforded by considering heat to be an intestine motion of the constituent particles of a body. Systematically reviewing the known properties and effects of heat—the only practicable course open to him—he concluded in the following memorable and oft-quoted passages:[3]

"Atque hæc sit Prima Vindemiatio, sive Interpretatio inchoata de Forma Calidi, facta per Permissionem Intellectus. "Ex Vindemiatione autem ista Prima, Forma sive definitio vera Caloris (ejus qui est in ordine ad universum), non relativus tantummodo ad sensum talis est, brevi verborum complexu: Calor est motus expansitus, cohibitus, et niteus per partes minores."

We find, therefore, in older writings, the first considerable support of this doctrine attributed to Bacon; and it must be conceded that to the power and vividness with which he portrayed his conception of this agent was due in a great measure the tenacity with which it was afterward, from time to time, brought forward and upheld.

The subsequent supporters of this view, though not perhaps most numerous, comprised by far the most distinguished and profound philosophers of their time, their writings furnishing many remarkable anticipations of heat-theory as now received.

Newton,[4] quite singularly, while rejecting the wave-theory of light, gave his assent to the analogous ideas respecting heat; and, in so far as we may judge, conceived the warmth excited in a body when exposed to light or radiant heat to be due to the little shocks which luminous or radiant material might produce in it.

Huyghens, Hooke, Locke, and Cavendish, among others, were also favorably inclined to the Baconian view;[5] the works of Hooke particularly containing many and strong expositions of the vibratory notion, and his comments on the mechanical and chemical production of heat being urged often with as great clearness, and as subtile a perception of occult natural causes, as any which we now possess.[6]

But the adaptation of the known "laws of motion" to these operations, whereby heat might in many instances have been directly correlated to the energy expended in producing it, was not until long after definitely proposed; and though, in 1744, Boyle,[7] perhaps as intelligently as any one before him, had attributed the heating of a hammered body to the transfer of the "motion" of the hammer to the ultimate particles of the body struck, yet the idea of the indestructibility of energy in all cases, and of course, therefore, in the mechanical excitation of heat, would not seem to have been expressly urged before the time of Rumford and Sir Humphry Davy.

In the mean while, however, a new doctrine was brought forth, assigning to heat a material existence and chemical properties. First advocated, it is thought, by Boerhaave[8] and Lémery,[9] it received in 1787 the unrestricted name "caloric" from the French Academy.

According to these hypothetic notions, singularly cramped and superficial, as compared with the more fruitful ideas of Bacon, caloric, or the matter of heat, was thought to be a highly-elastic, imponderable fluid; which, distributed among the constituent molecules of bodies, in quantities varying with the temperature in the same, or the "capacity" in different kinds of substance, occasioned all the known phenomena of heat: the sensation, through an occult property of its own; expansion and repulsion, by the entrance of its own substance among the molecules of the bodies heated; a change of state whenever the effective action of any particular set of molecular forces should thus happen to be overcome; and in radiation passing from one body to another with vast swiftness. Being, moreover, an unchangeable material, a definite created quantity of it was considered to exist at all times in the universe.

The idea of a substance unaffected by the force of gravity did not appear so very improbable in those days, while the then frequent separation of some new or more elementary gas, and the astonishing effects directly traceable to their action, quite naturally suggested an analogous causation in thermal phenomena.

The discovery by Black, of latent heat,[10] seemed also to supply the necessary induction for its quantitative treatment; so that toward the beginning of the present century, and upon chemical considerations merely, the hypothesis of caloric had succeeded in supplanting quite effectually the ideas of Bacon.

The explanations which it gave of the mechanical excitation of heat were not so plausible, however; certain phenomena appearing utterly incongruous with the idea of an unalterable material supply of heat-substance, and its continued production of friction a phenomenon which has been since said to have furnished the key to the whole science of thermo-dynamics—serving eventually to completely overturn it. In explaining such phenomena, therefore, those who still chose the material hypothesis were compelled to overlook some very significant objections; while, still supposing it to be a vibratory motion, the additional phenomena of latent or specific heats were not at all irreconcilable or difficult of explanation.

Thus Lavoisier and Laplace, in their famous "Mémoire sur la Chaleur" of 1780, though still retaining and defending the ideas of caloric, admitted the frictional excitation of heat to be "favorable" to the dynamical hypothesis. But it is, on the other hand, to be remembered that the earlier experiments devoted to the study of this point had been by no means unmistakable in their indications, directed as they had been rather to the detection of some suspected influence of the rubbing surfaces than to the investigation of any possible relation between the heat produced and the energy expended in producing it.

The material hypothesis was, therefore, the prevailing one, when about the year 1797 Count Rumford,[11] while engaged in superintending the construction of cannon at the military arsenal at Munich, became impressed by the considerable generation of heat accompanying their boring. And as he thought upon the explanation of the phenomenon consistent with the then prevailing ideas as to the intimate nature of heat, it seemed to him impossible that an apparently unlimited supply of any substance could be separated from so inconsiderable a quantity of borings. The doubt increased when, upon making the determination, he found the specific heat of this débris to be the same, apparently, as that of the mass of metal from which it had been separated: for in some obscure manner the "capacity" for heat of any body, or the total quantity of it which it might hold in any particular state, was considered to be intimately connected with, if not entirely defined by, its specific heat.

But, though he quoted this experiment as sufficiently conclusive that the heat set free by friction could not have been produced at the expense of any caloric latent in the metal, he undertook the following more elaborate investigation to determine all the circumstances which might possibly exert an influence on its production: and it appears, both from his method of procedure and the arguments with which he supplemented his results, that he had fully comprehended the philosophical consequences of each rival theory.

In view of the preëminent importance of these first conclusive and well-understood experiments, both with respect to the establishment of the dynamic theory upon an experimental basis, and the undoubted claim of their author to be considered as its founder, we here give as detailed an account of his investigations as may be thought admissible in a work intended merely for didactic purposes; and we conceive a full statement upon this most important point to be the more desirable, from the fact that the completeness with which he then demolished the material hypothesis, and the maturity of his views respecting the dynamical nature of heat, do not of late seem to have gained the unqualified recognition which they most certainly deserve.

Taking the casting of a brass cannon, solid and rough as it came from the foundery, and with the cylindrical mass of metal a (Fig. 1), called the verlorner Kopf, still adhering to the muzzle, Rumford caused to he turned upon the superfluous end a smaller cylinder, b (Fig. 2),

Fig. 2.

7¾ inches in diameter and 9.8 inches long, and which remained connected to the cannon proper by the neck, e, 2.5 in diameter and 3.8 inches long.

The whole mass being then secured in the apparatus used for boring (Fig. 2), a cavity 7.2 inches long and 3.7 in diameter was bored in b, in the direction of its axis, so that a metal bottom, 2.6 inches thick, remained between the borer and the neck. In this also a small round hole, c d (Fig. 3), was radially bored for the insertion of a thermometer. The cylinder, neck, etc., are represented upon a somewhat larger scale in Fig. 3.

Fig. 3.

The borer used to create friction upon this metallic bottom was a flat piece of hardened steel, 0.63 inch in thickness, four inches long, and nearly as wide as the cylindrical bore in which it turned, 3½ inches; so that the area of contact with the bottom was about 2.33 square inches. This borer was securely held in place against the bottom of the cylinder, and kept from turning by an iron bar, m; and thus disposed for the experiment the apparatus is represented in Fig. 2.

In Rumford's first determination the borer was forced against the bottom with a pressure of about 10,000 pounds, and the cylinder was rotated at the rate of thirty-two turns in a minute, by the labor of two horses. To prevent also as far as possible any loss of heat by radiation, the exposed parts were protected by thick coverings of flannel.

At the beginning of the experiment the temperature throughout, as well as that of the surrounding air, was 60° Fahr.; at the end of thirty minutes, when 960 revolutions of the cylinder had been made, the temperature, as indicated by a thermometer introduced into the small hole, had risen to 130°.

Collecting the metallic dust—or, as he described it, scaly matter—which had been detached, he found upon a careful weighing that it amounted to but 837 grains, or 54.2 grammes. Its inadequacy to account for the large excitation of heat fully impressed him, and he exclaims:

"Is it possible that the very considerable quantity of heat that was produced in this experiment (a quantity which actually raised the temperature of above 113 pounds of gun-metal at least 70° of Fahrenheit's thermometer, and which, of course, would have been capable of melting six pounds and a half of ice, or of causing nearly five pounds of ice-cold water to boil) could have been furnished by so inconsiderable a quantity of metallic dust, and this merely in consequence of a change of its capacity for heat?

"As the weight of this dust (837 grains, Troy) amounted to no more than 1948 part of that of the cylinder, it must have lost no less than 948° of heat, to have been able to raise the temperature of the cylinder 1°; and consequently it must have given off 60,360° of heat to have produced the effects which were actually found to have been produced in the experiment!

"But without insisting on the improbability of this supposition, we have only to recollect that from the results of actual and decisive experiments, made for the express purpose of ascertaining that fact, the capacity for heat of the metal of which great guns are cast is not sensibly changed by being reduced to the form of metallic chips in the operation of boring cannon; and there does not seem to be any reason to think that it can be much changed, if it be changed at all, in being reduced to much smaller pieces by means of a borer that is less sharp.

"If the heat, or any considerable part of it, were produced in consequence of a change in the capacity for heat of a part of the metal of the cylinder, as such change would only be superficial, the cylinder would by degrees be exhausted; or the quantities of heat produced in any given short space of time would be found to diminish gradually in successive experiments. To find out if this really happened or not, I repeated the last-mentioned experiment several times with the utmost care; but I did not discover the smallest sign of exhaustion in the metal, notwithstanding the large quantities of heat actually given off.

"Finding so much reason to conclude that the heat generated in these experiments, or excited, as I would rather choose to express it, was not furnished at the expense of the latent heat, or combined caloric of the metal, I pushed my inquiries a step farther, and endeavored to find out whether the air did, or did not, contribute anything in the generation of it."

In this, his Experiment No. 2, the only modification consisted in fitting the steel borer with an air-tight piston, packed with oiled leather, by which any circulation of air from without to the interior was prevented. But in the use of this device the oiled leather itself, by its friction with the sides of the borer, produced considerable heat, so that, to obviate any possible objection as to this point, Rumford had recourse to his third and most celebrated experiment.

In this, the friction cylinder was made to rotate in a water-tight box, which, being filled with water, completely submerged all the heat producing parts. Here, therefore, the only supply of caloric, if any, lay in the water, which itself was to be heated by the friction; for had any caloric been abstracted by the heated water from the ambient air, there would have necessarily been a flow of heat from a cool body to a warmer, which every one admitted to be contrary to experience. The apparatus, therefore, having been arranged, the box was filled with water at the temperature of 60° Fahr., and the machinery put in motion.

With reference to what followed, Rumford remarked:

"The result of this beautiful experiment was very striking, and the pleasure it afforded me amply repaid me for all the trouble I had had in contriving and arranging the complicated machinery used in making it.

"The cylinder, revolving at the rate of about thirty-two times in a minute, had been in motion but a short time, when I perceived, by putting my hand into the water and touching the outside of the cylinder, that heat was generated; and it was not long before the water which surrounded the cylinder began to be sensibly warm.

"At the end of one hour I found, by plunging a thermometer into the water in the box (the quantity of which fluid amounted to 18.77 pounds, avoirdupois, or two and a quarter wine-gallons), that its temperature had been raised no less than 47°; being now 107° of Fahrenheit's scale.

"When thirty minutes more had elapsed, or one hour and thirty minutes after the machinery had been put in motion, the heat of the water in the box was 142°.

"At the end of two hours, reckoning from the beginning of the experiment, the temperature of the water was found to be raised to 178°.

"At two hours twenty minutes it was at 200; and at two hours thirty minutes it actually boiled!

"The quantity of heat excited and accumulated in this experiment was very considerable; for, not only the water in the box, but also the box itself (which weighed 1514 pounds), and the hollow metallic cylinder, and that part of the iron bar which, being situated within the cavity of the box, was immersed in the water, were heated 150° Fahr., namely, from 60° (which was the temperature of the water and of the machinery at the beginning of the experiment) to 210°, the heat of boiling water at Munich."

The total quantity of heat generated may be estimated with some considerable degree of precision as follows:

 Quantity of ice-cold water which, with the given quantity of heat, might have been heated 180°, or made to boil. In avoirdupois weight. lbs. "Of the heat excited there appears to have been actually accumulated: "In the water contained in the wooden box, 1838 pounds, avoirdupois, heated 150°, namely, from 60° to 100° Fahr. 15.2 "In 113.13 pounds of gun-metal (the hollow cylinder), heated 150°; and, as the capacity for heat of this metal is to that of water as 0.1100 to 1.0000, this quantity of heat would have heated 1212 pounds of water the same number of degrees. 10.37 "In 36.75 cubic inches of iron (being that part of the iron bar to which the borer was fixed which entered the box), heated 150°; which may be reckoned equal in capacity for heat to 1.21 pound of water. 1.01 "N. B.—No estimate is here made of the heat accumulated in the wooden box, nor of that dispersed during the experiment. "Total quantity of ice-cold water which, with the heat actually generated by friction, and accumulated in two hours and thirty minutes, might have been heated 180°, or made to boil. 26.58

"As the machinery used in this experiment could easily be carried round by the force of one horse (though, to render the work lighter, two horses were actually employed in doing it), these computations show further how large a quantity of heat might be produced, by proper mechanical contrivance, merely by the strength of a horse, without either fire, light, combustion, or chemical decomposition; and, in a case of necessity, the heat thus produced might be used in cooking victuals.

"But no circumstances can be imagined in which this method of procuring heat would not be disadvantageous; for more heat might be obtained by using the fodder necessary for the support of a horse as fuel. . . .

"By meditating on the results of all these experiments, we are naturally brought to that great question which has so often been the subject of speculation among philosophers, namely:

"What is heat? Is there any such thing as an igneous fluid? Is there anything that can with propriety be called caloric?

"We have seen that a very considerable quantity of heat may be excited in the friction of two metallic surfaces, and given off in a constant stream or flux in all directions without interruption or intermission, and without any signs of diminution or exhaustion.

"Whence came the heat which was continually given off in this manner in the foregoing experiments? Was it furnished by the small particles of metal, detached from the larger solid masses, on their being rubbed together? This, as we have already seen, could not possibly have been the case.

"Was it furnished by the air? This could not have been the case; for, in three of the experiments, the machinery being kept immersed in water, the access of the air of the atmosphere was completely prevented.

"Was it furnished by the water which surrounded the machinery? That this could not have been the case is evident: 1. Because this water was continually receiving heat from the machinery, and could not at the same time be giving to and receiving heat from the same body; and, 2. Because there was no chemical decomposition of any part of this water. Had any such decomposition taken place (which, indeed, could not reasonably have been expected), one of its component elastic fluids (most probably inflammable air) must at the same time have been set at liberty, and, in making its escape into the atmosphere, would have been detected; but, though I frequently examined the water to see if any air-bubbles rose up through it, and had even made preparations for catching them, in order to examine them, if any should appear, I could perceive none; nor was there any sign of decomposition of any kind whatever, or other chemical process, going on in the water.

"Is it possible that the heat could have been supplied by means of the iron bar, to the end of which the blunt steel borer was fixed, or by the small neck of gun-metal by which the hollow cylinder was united to the cannon? These suppositions appear more improbable even than either of those before mentioned; for heat was continually going off, or out of the machinery, by both these passages, during the whole time the experiment lasted.

"And, in reasoning on this subject, we must not forget to consider that most remarkable circumstance, that the source of the heat generated by friction, in these experiments, appeared evidently to be inexhaustible.

"It is hardly necessary to add that anything which any insulated body, or system of bodies, can continue to furnish without limitation, cannot possibly be a material substance; and it appears to me to be extremely difficult, if not quite impossible, to form any distinct idea of anything capable of being excited and communicated in the manner the heat was excited and communicated in these experiments, except it be motion."

From this quotation we see, then, that Rumford, with a sagacity indeed consummate, had seized upon the most notable circumstance presented by these experiments, against the materiality of heat. Italicizing the word inexhaustible—a far more significant proceeding than the use of any acids would have been—he showed most incontestably that, to still further reconcile the doctrine of caloric with experience, it would be necessary to admit the creation of it—a substance—in the production of heat by friction. But, even against so absurd a proposition, he proceeded to prepare, when he subjected to a comparative investigation the quantities of energy expended and heat produced in such an operation.

In his "Experiment No. 3" he made, as may have been already noticed, nearly all the observations and corrections necessary for an entirely trustworthy estimate of the "mechanical equivalent of heat;"[12] and, although never literally employing such a term, he subsequently stated, in reviewing still other experiments undertaken at about this period,[13]that the heat so generated "is exactly proportional to the force with which the two surfaces are pressed together, and to the rapidity of the friction:" in other words, that the production of heat is "exactly proportional" to the work expended in producing it.

First drawing attention to the absurdity of an apparatus containing or creating an indefinite supply of a material substance; then proving by experiment that the quantities of heat excited in a given time were proportional to the expenditures of an entirely different magnitude—work: he must be credited not only with the first conclusive, but with the most weighty argument initially available, against the existence of caloric, or in favor of the dynamic origin of heat.

1. Introduction to an unpublished work on Thermo-Dynamics.
2. "Opere di Galileo Galilei," tom. ii., p. 505, et seq.
3. "Novum Organum," lib. sec., aphorism 20. Spedding and Ellis's translation, vol. iv., p. 154.
4. Newton's "Optice," queries at the end of treatise, especially Nos. 6, 8, 12, 18, 23 and 31.
5. The ideas of Huyghens on this point would seem to have resembled somewhat those of Galileo, already quoted. See "Exposé de la Situation de la Mécanique Appliquée," par Combes, etc., p. 200. Paris, 1867. And Locke quite uniformly made use of Bacon's hypothesis. See particularly his essay on the "Conduct of the Human Understanding Elements of Natural Philosophy," chap, xi., where he says:
"Heat is a very brisk agitation of the insensible parts of the object which produces in us that sensation whence we denominate the object hot; so what in our sensation is heat, in the object is nothing but motion. . . .
"On the other side, the utmost degree of cold is the cessation of that motion of the insensible particles which to our touch is heat."
6. Hooke's "Micrographia," obs. xvi., 12th particular. "Posthumous Works," p. 49. "Lectures on Light," p. 116.
7. "And now I speak of striking an iron with a hammer, I am put in mind of an operation that seems to contradict, but does indeed confirm our theory: namely, that if a somewhat longer nail be driven by a hammer into a plank or piece of wood, it will receive divers strokes on the head before it grow hot; but when it is driven to the head, so that it can go no further, a few strokes will suffice to give it a considerable heat; for while at every blow of the hammer the nail enters further and further into the wood, the motion that is produced is chiefly progressive, and is of the whole nail tending one way; whereas, when that motion is stopped, then the impulse given by the stroke being unable either to drive the nail further on or destroy its entireness, must be spent in making a various, vehement, and intestine commotion of the parts among themselves, and in such an one we formerly observed the nature of heat to consist."—(Boyle, "On the Mechanical Origin of Heat and Cold," "Complete Works," vol. iv., p. 236, et seq., exp. vi.)
8. "De Igne, Elementa Chemiæ," i., 116.
9. "Sur la Matiére du Feu," "Histoire et Mémoires de l'Ac. Par.," 1709, pp. 6, 400.
10. We know, however, that these discoveries did not fail to be correctly interpreted at the time, for Cavendish, in a foot-note to some "Observations on Mr. Hutchinson's Experiments," etc., "Philosophical Transactions," 1783, p. 312, remarked:
"I am informed that Dr. Black explains the above-mentioned phenomena in the same manner; only instead of using the expression, 'heat is generated or produced,' he says, 'latent heat is evolved or set free;' but as this expression relates to an hypothesis depending on the supposition that the heat of bodies is owing to their containing more or less of a substance called the matter of heat, and as I think Sir Isaac Newton's opinion, that heat consists in the internal motion of the particles of bodies, much the most probable, I choose to use the expression 'heat is generated.' "
11. "Inquiry concerning the Source of the Heat which is excited by Friction," "Philosophical Transactions," 1798, p. 80. "Complete Works," Am. Ac. ed., p. 400.
12. Its value from the data given may be calculated as follows:
Considering the shape of the borer, and its contact with the bottom of the cylinder, we see that the moment of friction may be represented by the expression—

${\displaystyle \scriptstyle 4fp\int r^{2}sin^{-1}{\tfrac {a}{r}}dr}$,

where f denotes the coefficient of friction, p the total pressure between the rubbing surfaces,r the variable distance from the axis, of any rubbing particle, and a the half-width of the borer: when, moreover, the superior value of r alone is substituted.

The integral indicated is—

${\displaystyle \scriptstyle 4fp{\big \{}{\frac {r^{3}}{3}}sin^{-1}{\frac {a}{r}}+{\frac {ar}{6}}{\sqrt {(}}{r^{2}-a^{2}})+{\frac {a^{3}}{6}}log{\frac {r+{\sqrt {(a^{2}-a^{2})}}}{a}}{\big \}}}$,

13. "Kleine Schriften," 1805, vol. iv., p. 41. "Complete Works," Am. Ac. ed., vol. ii., p. 209.