The Development of the Dynamic Theory of Heat in Early Nineteenth Century England
Masao WATANABE
Tokyo Woman's Christian College, Tokyo
. Introduction
The purpose of the present paper is to study the development of the dynamic theory of heat in early nineteenth century England. The author looks into impor tant English periodicals and the works of English scientists in question, and inquires into the arguments presented concerning the nature of heat. He particularly studies the works of three major figures, namely: Count Rumford, Humphry Davy and Thomas Young, who advocated the dynamic theory of heat in the very late eighteenth and early nineteenth centuries when the material theory of heat was predominant. The author also investigates the general historical background for the study of heat and the way in which the material theory accounted for various heat phenomena ; and he examines the points of dispute between the two opposing views of heat, the material and the dynamic, as appeared in the con temporary scientific writings in England. With these materials, he describes and analyzes the development of the dynamic theory of heat in early nineteenth century England and indicates, in conclusion, some distinctive factors whose existence caused delay of the general acceptance of the dynamic theory of heat at that time.
. The Material Theory of Heat in Early Nineteenth Century England
According to the material theory of heat in early 19th century England, "heat or caloric" was considered to be "a substance which penetrates and expands all bodies, and produces in us the sensation of heat and cold."1) It was also some times regarded as "an elastic fluid sui generis, the particles of which repel one another, but are strongly attracted, though in different degrees, by the particles of all other bodies."2) The study of heat in those days had been started in the field of chemistry and it did not have its proper position in physics as yet. So in the Natural Philosophy of John Playfair, from which the above quotations were taken, the section on heat belonged to the first half of the volume for "Aerostatics," while the second half of the same volume was on "Elastic Fluids." Likewise, in the textbook by John Robison, entitled Elements of Mechanical Philosophy,3) there 1) John Playfair, Outlines of Natural Philosophy, being Heads of Lectures delivered in the University of Edinburgh, vol. 1, 3rd ed., 1819, p. 223. 2) Ibid., p. 240. 3) John Robison, Elements of Mechanical Philosophy, being a Substance of a Course of Lectures on that Science, 1804.
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‡T‡U No. 2 The Development of the Dynamic Theory 17 was no section for heat, but heat was discussed under the section "On Steam." It was the general belief of that time that "Whenever you peceive a number of qualities always existing together, you are warranted to conclude that there is some substance which produces those qualities.... Whatever occupies space, and resists the touch, we have a right to call a material substance, whether we can see it, and weigh it, or not; thus air, which is invisible, and not very easily ponderable, is universally allowed to be a substance, and not a quality."4), This belief was called upon to support the materiality of heat, for instance, by George Adams in his Lectures on Natural and Experimental Philosophy, 1794. The elasticity of "airs and gases" was due, as Robison described, to the elasticity of fire. He likened "the elasticity of fire as the immediate cause of elasticity of vapour" to the fluidity of water as the cause of the fluidity of brine. This elasticity was also compared to the elasticity of a sponge immersed in water. He mentioned that "when air is suddenly compressed,.... the heat seems to be squeezed out as the water from the sponge."5) Thermal expansion and contraction were accounted for, in the material theory of heat, by the increase and decrease of the fluid caloric respectively and by the equilibrium of the attraction between the bodies and caloric contained in them and the repulsion of the particles of the caloric by one another.6) The different capacities of bodies for heat and the conversion of sensible into latent heat or vice versa were explained by a similar idea.6) Likewise, a change of state was considered to be a shift of equilibrium and the consequent difference of distances between the particles of the body caused by additional or reduced caloric.7) Conduction of heat took place because of the attraction between matter and the caloric and the mutual repulsion of the caloric.7)"When the temperature of a body is raised to a certain height, this last cause may operate without the former,"7) which was a statement that accounted for the phenomenon of heat radiation.
‡V. The Development of the Dynamic Theory of Heat in Early Nineteenth Century England
It was mainly Count Rumford, Humphry Davy and Thomas Young who, with experimental and supporting evidence, asserted the view that heat was a kind of internal vibration of a body.
Benjamin Thompson, Count Rumford always had a great interest in scientific study and in its application to daily life. He was especially interested in the study of heat, and performed extensive experiments on this subject although he also led a very busy life in political affairs. In relating the theory of heat to Rumford, most books on the history of science only mention his experiments on
4) George Adams, Lectures on Natural and Eperimental Philosophy, vol. 1, 1794, p. 204. 5) Robison, op. cit., pp. 17-18. 6) Playfair, op. cit., p. 240. 7) Ibid., p. 241.
-71- 18 M. WATANABE Vol. 2 the production of heat by cannon boring performed in 1798. However, his research on heat began twenty years before this exhibition, when he started a series of experiments on gunpowder. As he himself described in his historical review, these experiments gave him "occasion to make a very striking observation."8) It also seems very probable that in his early days he had already come to regard heat as internal motion of the body. In 1778, he was engaged in "investigating the force of gunpowder and the velocity of bullets discharged from fire-arms."8) As can be read in his report on this investigation,9) he observed, in successive experiments, that the velocity of the bullet in the second experiment was greater than that of the first. Therefore, he assumed that "It is very probable that the excess of the velocity of the bullet in the second experiment over that of the first was occasioned more by the heat which the barrel had acquired in the first experiment than by the position of the vent, or any other circumstance." He reasoned: "for I have since found, upon repeated trials, that the force of any given charge of powder is considerably greater when it is fired in a piece that has been previously heated by firing, or by any other means, than when the piece has not been heated." He also referred to the commonly-known fact among people acquainted with artillery that "the recoil of great guns is much more violent after the second or third discharge than it is at first" and to the practice in the navy "to lessen the quantity of powder after the first four or five rounds" to prevent dangerous accidents. He concluded that "the temperature of the piece has a considerable effect upon the force of the powder."10) Moreover, he expressed his surprise, in the same paper, when he noticed that the barrel got hotter when the gun was discharged without any bullet. This was contrary to his expectations. Then he recalled the fact that "bullets from muskets are always found to be hotter in proportion to the hardness of the body against which they are fired," and he reasoned that "It is not by the flame, therefore, that bullets are heated, but by percussion."11) "The heat acquired by guns in firing.... is not all communicated by the flame, there is but one other cause to which it can be attributed, and that is the motion and riction of the internal parts of the metal among themselves, occasioned by the sudden and violent effort of the powder upon the inside of the bore, and to this cause I imagine the heat is principally, if not almost entirely, owing."12) To support this view, he referred to the fact that "a very great degree of heat may be generated in any hard and dense body in a short time by friction, and in a still shorter time by collision."18) He also cited Boerhaave's analogy of 8) The Complete Works of Count Rumford, vol. 2, p. 189, translation from Rumford's Kleine Schriften, vol. 4. 9) "An Account of Some Experiments upon Gunpowder," read before the Royal Society, 1781; Phil. Trans., LXXI; Complete Works, vol. 1, pp. 1-97. 10) Ibid., pp. 28-31. 11) Complete Works, vol. 1, p. 34. 12) Ibid., pp. 35-36. 13) Ibid., p. 36.
-72- No. 2 The Development of the Dynamic Theory 19 heat caused by friction to the vibration of stretched strings and of bells,14) and wrote that "in proportion to the swiftness of this vibration, and the violence of the attrition and friction, will be the heat that is produced."15) Then he discussed the phehomenon of heat caused by the blow of a hammer or by percussion and said that "the heat will be much augmented if the exertion of the force and the duration of its action are momentaneous; for in that case the fibres of the metal (if I may use the expression) that are violently stretched will return with their full force and velocity, and the swift, vibratory motion and attrition before described will be produced."16) With these facts and reasonings, he stated his explanation for the observed phenomenon concerning the force of gunpowder: ....the velocity with which the generated elastic fluid makes its escape is much greater when the powder is fired alone than when it is made to impel one or more bullets; the heat ought, therefore, to be greater in the former case than in the latter, as I found it to be by experiment
..... But if, instead of giving way with so ranch difficulty, the bullet be much lighter, so as to afford but little resistance to the elastic fluid in making its escape, or if the powder be fired without any bullet at all, then, there being little or nothing to oppose the flame in its passage through the bore, it will expand itself with an amazing velocity, and its action upon the gun will cease almost in an instant, the strained metal will restore itself with a very rapid motion, and a sharp vibration will ensue, by which the piece will be much heated.17)
Thus, it is quite evident, although the above inference is not entirely correct, that Rumford in his early days had already discovered some relation between heat and mechanical force and their mutual convertibility even with some quantitative consequence. It is also clearly seen in Rumford's writings that he already con sidered heat as a mode of motion or vibration. The same point is restated by Rumford in his historical review:
....the heating of the piece in question is not due to the combustion of the powder, but to the vibrations caused by the concussion within the barrel, and to the operation, as rapid as it is brief, of the elastic fluid generated by this combustion. No one is ignorant of the fact that a heavy blow is much more effective in producing heat in a solid body than a lighter one; and if the hypothesis be well founded that heat is nothing more than a continuous, more or less rapid, vibratory motion among the particles of solid bodies, this phenomenon is easily explained. ....On careful consideration it seems to me that this circumstance is more than sufficient to explain in a satisfactory manner the results of the experiments in question, although I am perfectly free to confess that I never could reconcile myself to the hypothesis which has been developed with regard to caloric.18
14) from Shaw's Translation of Boerhaave's Chemistry, vol. 1, p. 279, according to the foot note of Complete Works, vol. 1, p. 36. 15) Complete Works, vol. 1, p. 36. 16) Ibid., p. 37. 17) Ibid., pp. 37-39. 18) Complete Works, vol. 2, pp. 190-191, translation from Kleine Schriften.
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It may safely be inferred that his view of the nature of heat took definite shape from that time. In Rumford's next paper on the same subject,19) he made the following statement:
....M. Lavoisier, I know, imagined that the force of fired gunpowder depends in a great measure upon the expansive force of uncombined caloric supposed to be let loose in great abundance during the combustion or deflagration of the powder; but it is not dangerous to admit the action of an agent whose existence is not yet clearly demon strated, but it appears to me that this supposition is quite unnecessary, the elastic force of the heated aqueous vapour, whose existence can hardly be doubted, being quite sufficient to account for all the phenomena.20)
Then, mentioning "the amazing force of steam, when heated only to a few degrees above the boiling point," he likened a cannon to a steam-engine, saying:
....But if the force of fired gunpowder arises principally from the elastic force of heated aqueous vapour, a cannon is nothing more than a steam-engine upon a peculiar construction.21)
This statement indicates that he was ahead of the times in respect to the nature of heat; for the steam-engine, especially the mechanical work produced by it, was to be one of the most important subjects for the development of thermo dynamics and for the establishment of the law of conservation of energy. Between the dates of these two papers on the force of gunpowder, Rumford undertook "a number of successive experiments upon heat, in order to arrive at some conclusion with regard to its character, as well as to the manner of its operation."22) First of all, he made experiments on the specific heat of bodies . But before he could finish, the war interrupted them. Then, after the peace of 1783, he learned that Wilkin, in Sweden, had already carried out exactly what he had proposed to do himself, so he laid these plans aside. In 1785, Rumford began a series of investigations on the "Propagation of Heat in Various Substances."23) He "discovered that heat conld be transmitted through, or excited in, a Torricellian vaccum."24) He considered that this fact could not be reconciled with the caloric theory, which explained how the conducting power increased, in a single substance, with the compactness of the structure ; but not, so he thought, this fact of conduction through a vacuum where no attracting material particles were present. Caloricists attempted to answer this problem by attributing the above phenom-
19) "Experiments to Determine the Force of Fired Gunpowder ," read before the Royal Society, 1797; Phil. Trans., LXXXVII, pp. 98-172. 20) Complete Works, vol. 1, p. 109. 21) Ibid., p. 110. 22) Complete Works, vol. 2, p. 191, translation from Kleine Schriften . 23) Complete Works, vol. 1, pp. 401-468. 24) Complete Works, vol. 2, p. 193, translation from Kleine Schriften . -74- No. 2 The Development of the Dynamic Theory 21 enon to the self-repulsive property of the caloric fluid.25) For instance, William Henry objected to Rumford's view and singled out " one of the most marked and decisive" to point out that the phenomena of heat differ from the known and acknowledged phenomena of motion. He argued:
....Now, in the experiment of Count Rumford, before alluded to, heat passed through a torricellian vacuum, in which it need hardly be observed, nothing could be present to transport or propagate motion.26)
J.B. Emmett also pointed out the same thing concerning "the solar calorific rays" that "pass through a vacuum of nearly 95,000,000 miles in extent before they reach the earth." He wrote:
It may certainly be urged that the vibration of the solar matter excites undulations in an etherial fluid which pervades all space, and which communicates similar vibrations among the particles of which terrestrial matter is composed. This is certainly im possible; for this medium, if such exist, possesses so great rarity that its effects cannot be rendered sensible. It is, therefore, perfectly impossible for nudulations in such a medium to excite so strong vibrations in dense, solid, and liquid matter as to produce in them an expansive force which is almost infinite;....27)
If this be possible, he continued in the same paper, still another difficulty remained. For, according to the vibratory theory, the extent of vibration of the particles must be as the _??_ volume, but this was inconsistent with the fact that heat was produced when bodies were compressed. Moreover, it was in any case inconceivable for Emmett that " the particles of solids are not mutually in contact with each other" but vibrating according to the temperature, for, this system, was, for him, "highly inconsistent with the phenomena of solidity and cohesion ." Even if some motion had existed in bodies, if would have met "with great and constant re sistance" and it would thereby have diminished. So the temperature of bodies could not have been kept constant, but they would "always excite the sensation of cold; which is certainly opposite to the observed phenomena."27) Rumford also carried out "Experiments on the Temperature of Water at its Maximum Density,"28) by which de determined that water at 41•‹F was denser than water at 32•‹F. This fact that the removal of the caloric did not cause the water continuously to contract was used by him as a serious objection to the material theory of heat. Since the caloric exerted a strong attraction between matter and itself, it must necessarily have weight, namely the force between the earth and itself in a body.
25) Sanborn C. Brown, "Count Rumford and the Caloric Theory of Heat," Proceedings of the American Philosophical Society, vol. 93, 1949, pp. 316-325. 26) William Henry, "A Review of some Experiments, which have been supposed to Disprove the Materiality of Heat," Manchester Memoirs, 5, pp. 603-621, (1802). 27) J.B. Emmett, "Researches into Mathematical Principles of Chemical Philosophy," Annals of Philosophy, vol. 16, pp. 137-145, (1820). 28) "An Account of Some Experiments on the Temperature of Water at its Maximum Density," Nicholson's Journal, 11, 225-235; Complete Works, vol. 2, pp. 258-273.
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Rumford attempted to measure this weight of heat both in its sensible and latent form 29) after reading the record of Fordyce's experiments on the weight said to be acquired by water upon being frozen.30) Rumford was very confident of the decisiveness of his experiment. He concluded:
....I think we may very safely conclude, that ALL ATTEMPS TO DISCOVER ANY EFFECT OF HEAT UPON THE APPARENT WEIGHTS OF BODIES WILL BE FRUITLESS.
However, this did not appear to caloricists to be a conclusive experiment. The kind of objections they brought forth was more or less similar to the argument offered by Alexander Tillock, the editor of the Philosophical Magazine. He likened Rymford's measurements to the experiments of weighing things in water and suggested that Rumford might have overlooked the fact "that air may be considered as bearing the same relation to heat that water does to any substance many times lighter; that is, the air, though a rarer substance than the solid bodies weighed in it, is a denser one than heat."31) Rumford further explored the phenomena of evaporation and sublimation areas in the field of heat never convincingly discussed by the caloricists-and subsequently described them in his memoirs. He attributed the phenomenon of sublimation of ice to some of the hot particles of air (although the mean tem perature of the air might be below 32•‹F) which "accidentally come into contact with the ice."32) He also performed investigations to demonstrate the existence of particle motion in liquids at a uniform temperature.33) This "Spontaneous Mixture of Liquids" afforded one of the most direct experimental proofs of the kinetic theory, as Einstein pointed out.34) "An Expe rimental Inquiry concerning the Source of the Heat which is Excited by Friction"35) is the most often cited and disepussed aper of Rum ford's. He thought this was "a perfectly conclusive experiment" to refute the caloricists who would otherwise still object.36) The following was his idea of this experiment:
29) "An Inquiry concerning the Weight Ascribed to Heat," Phil. Trans., 84, pp. 179-194, (1799); Complete Works, vol. 2, pp. 1-22. 30) George Fordyce, "An Account of some Experiments on the Loss of Weight in Bodies on being melted or heated," Phil. Trans., 75, pp. 361-365, (1785). 31) Alexander Tillock, "An Attempt to prove that the Matter of Heat, like other Substances, possessed not only Volume but Gravity," Phil. Mag., 9, pp. 158-167, (1800). 32) "Of the Propagation of Heat in Fluids," Complete Works, vol. 1, pp. 237-400. 33) "On the Slow Progress of the Spontaneous Mixture of Liquids," 1807, Mem. de l'Inst. National de France, 8, pp. 109-115; Complete Works, vol. 2, pp. 318-323. 34) Taken from Brown's paper, op. cit., Einstein, "Uber die von der molekularkinetischen theorie der warme geforderte bewegung von in ruhen den fliissigkeiten suspendierten teilchen," Ann. der Phys., 17, pp. 549-560. 35) Read before the Royal Society, Jan., 1798; Phil. Trans., 88, pp. 80-102; Complete Works, vol. 1, pp. 469-493. 36) Complete Works, vol. 2, pp. 209-210, translation from Kleine Schriften .
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I argued that if the existence of caloric was a fact, it must be absolutely impossible for a body or for several individual bodies, which together made one whole, to com municate this substance continuously to various other bodies by which they were sur rounded, without this substance gradually being entirely exhausted. A sponge filled with water, and hung by a thread in the middle, of a room filled with dry air, communicates its moisure to the air, it is true, but soon the water evapo rates and the sponge can no longer give out moisture. On the contrary, a bell sounds without interruption when it is struck, and gives out its sound as often as we please without the slightest perceptible loss. Moisture is a substance; sound is not. It is well known that two hard bodies, is rubbed together, produce much heat. Can they continue to produce it without finally becoming exhausted? Let the result of experiment decide this question.36)
As is well known, while he was superintending the boring cannon in the military arsenal at Munich, he "was struck with the very considerable degree of Heat which a brass gun acquires in a short time in being bored, and with still more intense Heat of the metallic chips separated from it by the borer."35) So he undertook this experiment in order to thoroughly investigate the phenomenon, and to get "some reasonable conjectures respecting the existence, or non-existence, of an igneous fluid,-a subject on which the opinions of philosophers have in all ages been much divided."35) He concluded his Experiment No. 1 with the following words:
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 expenses of the latent Heat or combined caloric of the metal, I pushed my inquiries a step farther, and endeavoured to find out whether the air did, or did not, contribute anything in the generation of it.
This question was clarified by his second experiment which was carried on without access of the external air to the inside of the bore of the cylinder, and he proved that the air of the atmosphere had no part in the generation of the heat. The process of his Experiment No. 3 was most vividly reported as he wrote:
At 2 hours 20 minutes it37) was at 200•‹; and at 2 hours 30 minutes it ACTUALLY BOILED! It would be difficult to describe the surprise and astonishment expressed in the countenances of the bystanders, on seeing so large a quantity of cold water heated, and acturally made to boil, without any fire.35) He estimated the quantity of heat produced to be "greater than that produced equably in the combustion of nine wax candles, each 3/4 of an inch in diameter, all burning together, or at the same time, with clear bright flames," and "the machinery used in this experiment could easily be carried aound by the force of one horse (though, to render the work lighter, two horses were actually employed in doing it)."35) These experiments were summerized by himself as follows:
37) The water in the box, the amount of which was 18.77 lbs.
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I found, by the experiment No. 1, how much Heat was generated when the air had free access to the metallic surface which were rubbed together. By the experiment No. 2, I found that the quantity of Heat generated was not sensibly diminished when the free access of the air was prevented; and by the result of No. 3, it appeared that the generation of the Heat was not prevented or retarded by keeping the apparatus im mersed in water.35)
He discussed the result. First of all, he showed that the heat produced did not come from any of the following:
1) the small particles of metal, detached from the larger solid masses, on their being rubbed together-because there was no change in the capacity for heat of the chips. 2) air-because the machinery was kept immersed in water and access of atmospheric air was completely prevented. 3) water-because the water was continually receiving heat from the machinery rather than giving heat to it. 4) chemical decomposition of water-because no air-bubbles were seen. 5) the machinery by way of the iron bar-because heat was continually going out of the machinary.
He further continued:
And, in reasoning on this subject, we must not forget to consider that most remark able circumstance, that the source of the Heat generated by friction, in these experi ments, appeared euidently to be inexhaustible. It is hardly necessary to add, that anything which any insulated body, a 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 these experiments, except it be MOTION.35)
Emmett criticized this argument, saying:
....The whole quantity of heat contained in the solid is doubtless diminished, but why is the capacity to be changed? ...... The greatest error appears to be the assumption that the source of the heat thus generated is inexhaustible; the quantity that can be thus excited is finite . Let the end of a thin bar of soft iron be submitted to repeated blows of the hammer , it soon becomes ignited; let the operation be continued, the heat gradually abates , and soon ceases entirely, after which it cannot be brought into an ignited state by the same process without being previously exposed to the fire. This is a process decidedly the same as that of Count Rumford in its principle, but entirely opposes the conclusions which he drew from his own experiments; he would have doubtless come to the same conclusion had his experiments been continued so long that the whole mass of metal employed had been brought to the greatest density, to which the friction used could have brought it; but since this was not the case , it is evident that the whole quantity of heat which the metal used could have furnished was not obtained .38)
38) Emmett, "Mathematical Principles of Chemical Philosophy," op . cit., pp. 142-145.
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Bertholet criticized Rumford's experiment in a similar way.", He believed that an amount of caloric was given out as a consequence of the decrease in the volume of the metal. Moreover, as for that part of Rumford's experiment to determine the specific heat of the filings of bell-metal, Bertholet made the follow ing criticism: ....But this extremely elastic metal would very naturally as soon as left to itself, and especially during the operation just mentioned, resume that state of expansion and that capacity for heat which is proper to it at a given temperature, so that the effect of the pressure to which it has been subjected partly disappears again, just as a piece of metal which has been hammered resumes its natural properties on being annealed.30) To this Rumford answered and affirmed that the source of the heat was inex haustible. He discussed:
....since the action of the force which causes the pressure is continuous, the con densation of the meta40) brought about by this force would in a short time reach its maximum; ....The rubbing surfaces, on the contrary, continue to give forth heat, and that always to the same amount.
This amount of heat would be sufficient to melt a mass of metal sixteen times heavier than that which I used in the experiment.41)
Humphry Davy was one of those few contemporaries of Rumford who held the same view concerning the nature of heat. Davy, like Faraday, was not brought up in the mathematical school of the Continent but belonged to another school of purely experimental approach. He was not more than seventeen when he formed a strong opinion opposed to the general belief in the existence of caloric, or the materiality of heat. In his first scientific paper, published in 1799, he discussed the nature of heat.42) In it he attempted to disprove the caloric theory, using "the method called by mathematicians , reductio ad absurdum." To account for the temperature rise caused by friction or percussion, the caloric theory demanded some of the following assumptions:
1) diminution of the capacities of the acting bodies induced by friction. 2) heat communicated from the decomposition of the oxygen gas-in this case, bodies must be found, after friction, to be partially or wholly oxydated. 3) communication of the caloric from the bodies in contact.
Davy demonstrated experimentally that none of these assumptions were correct. To prove his point his first experiment was as follows:
39) Bertholet, "Essai de Statique Chemique," as is introduced in Rumford's Historical Review, Complete Works, vol. 2, pp. 214-218. 40) "the condensation of the metal" in this sentence means the decrease in the volume of the metal. 41) Complete Works, vol. 2, pp. 218-221. 42) "An Essay on Heat, Light, and the Combinations of Light," Thomas Beddoes' Contri butions to Physical and Medical Knowledge, principally from the West of England, 1799; The Collected Works of Sir Humphry Davy, vol. 2, pp. 1-86.
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I produced two parallelopipedons of ice, of the temperature of 29•‹, ....By a peculiar
mechanism, their surfaces were placed in contact, and kept in a continued and violent friction for some minutes. They were almost entirely converted into water, which w ter
was collected, and its temperature ascertained to be 35•‹, after remaining in an at mosphere of a lower temperature for some minutes....according to the supposition its
capacity is diminished; but it is a well-known fact, that the capacity of water for heat is much greater than that of ice; and ice must have an absolute quantity of heat added
to it, before it can be converted into water. Friction consequently does not diminish the capacities of bodies for heat. From this experiment it is likewise evident, that the increase to temperature consequent on friction cannot arise from the decomposition of the oxygen gas in contact, for ice has not attraction for oxygen.
The possibility of the first two assumptions mentioned above was thus denied, and so was that of the third by the next experiment.
I procured a piece of clock-work so constructed as to be set to work in the exhausted receiver; one of the external wheels of this machine came in contact with a thin metallic plate. A considerable degree of sensible heat was produced by friction between the wheel and plate when the machine worked uninsulated from bodies capable of communi cating heat. I next procured a small piece of ice; round the superior edge of this a small canal was made and filled with water. The machine was placed on the ice, but not in contact with the water. Thus disposed, the whole was placed under the receiver, (which had been previously filled with carbonic acid,) a quantity of potash (i.e. caustic vegetable alkali) being at the same time introduced. The receiver was now exhausted. From the exhaustion, and from the attraction of the carbonic acid gas by the potash, a vacuum nearly perfect was, I believe, made. The machine was now set to work. The wax rapidly melting, proved the increase of temperature. ....In this experiment, ice was the only body in contact with the machine. Had this ice given out caloric, the water on the top of it must have been frozen. The water on the top of it was not frozen, consequently the ice did not give out caloric. The caloric could not come from the bodies in contact with the ice; for it must have passed through the ice to penetrate the machine, and an addition of caloric to the ice would have converted it into water.
Therefore, he concluded that "It has been experimentally demonstrated the caloric, or the matter of heat, does not exist," but heat was "vibration of the corpuscles of bodies," for he reasoned that "bodies become expanded by friction" and this was due to the vibration of their corpuscles caused by friction. The theory and experiments of Rumford and Davy on heat could not change overnight the contemporary concept; indeed they were criticized by the caloricists. In opposition to Rumford's paper on "Heat excited by Friction" and to Davy's mentioned above, William Henry suggested the possibility of receiving caloric from surrounding substances and from an internal source by the liberation of combined caloric .411 He continued:
43) Henry, "The Materiality of Heat," op. cit.
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Since, therefore, caloric is characterized by all the properties, except gravity, that enter into the definition of matter, we may venture to consider it as a distinct and peculiar body. Nor is its deficiency of gravity sufficient to exclude it from the class of material substances. Such nicety of arrangement might, with equal propriety, lead us to deny the materiality of light, the gravity of which has never yet been proved:....
Davy, although he conceived heat to be motion, apparently thought light to be material, and, in the same paper mentioned above, he proposed that "Oxygen gas will be proved to be a substance compounded of light and oxygen." So it was not because of the stubbornness of the caloricists that the dynamic theory of heat was not easily accepted, but because the caloric theory still worked very well in ac counting for various phenomena related to heat. In addition, there were many more new fields to be explored before the dynamic theory was to have its validity proved. The attitude of contemporary scientists is also well exemplified by the fact that Davy himself later condemned his own paper as "infant chemical specu lations," and turned away from it to experimental work, remarking that chemical knowledge was yet too incomplete to allow of generalizations. 44) When Davy gave lectures at the Royal Institution in 1802,45) he introduced two prevalent theories concerning the nature of heat; heat as "a peculiar ethereal fluid" and heat as "a specific motion of the particles of bodies." The phenomena of latent heat, of radiant heat, and of change of capacity supported, he thought, the first of these theories; while the last had been substantiated by "experiments on the excitation of heat by friction." He then went on to cite the recent experiments of Herschel, which "demonstrated that radiant heat must be con stituted by the motions of a peculiar substance," or the undulations of an elastic ethereal medium that existed in space. It was also assumed, he continued, "that certain peculiar vibratory motions of the particles of ponderable substances are capable of producing the undulations in the ethereal medium which constitute heat," and vice versa. "They are rendered more conclusive by the analogy between the laws of the motions of radiant heat, and those of sound. Any they, in some measure, reconcile the two different theories."45) In his Elements of Chemical Philosophy,46) first published in 1812, Davy again presented the caloric theory and the phenomena favorable to it. Then he turned to other facts which were not so easily reconciled to this theory, and he made the following statement:
The immediate cause of the phenomena of heat then, as Lavoisier long ago stated, is motion, and the laws of its communication are precisely the same as the laws of the communication of motion.
It seems possible to account for all the phenomena of heat, if it be supposed that in solids the particles are in a constant state of vibratory motion, the particles of the hottest bodies moving with the greatest velocity, and through the greatest space;
44) John Theodore Merz, A History of European Thought in the Ninteenth Century, vol. 2, p, 104, footnote. 45) "A Syllabus of a Course of Lectures on Chemistry," Collected Works, vol. 2, pp. 327-436. 46) Collected Works, vol. 4.
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that in fluids and elastic fluids, besides the vibratory motion, which must be conceived greatest in the last, the particles have a motion round their own axes, with different velocities, the particles of elastic fluids moving with the greatest quickness; and that in ethereal substances the particles move round their own axes, and separate from each other, penetrating in right lines through space.... If a specific fluid of heat be admitted, it must be supposed liable to most of the affections which the particles of common matter are assumed to possess, to account for the phenomena; such as losing its motion when combining with bodies, producing motion when transmitted from one body to another, and gaining projectile motion, when passing into free space: so that many hypotheses must be adopted to account for its mode of agency, which renders this view of the subject less simple than the other.
The very delicate experiments which had been made to show that bodies when heated do not increase in weight were, he continued, evidence against a specific subtle elastic fluid producing the calorific expansion; but he judged, they could not be decisive, because of the imperfection of the instruments available.
Some arguments have been raised in favour of the existence of a specific fluid of heat, from the circumstance of the communication of heat to bodies in exhausted receivers, and from the manner in which they are affected by this heat; but there are no means known in experimental science of producing a perfect vacuum; even the best Torricellian vacuum must contain elastic matter....
With the following statement, he ended the section "Of Heat, or Calorific Repulsion," from which the above quotations were also taken: The laws of the communication of heat, and the philosophy of its effects, are independent of this speculative question, which has been mentioned in this place merely with the view of guarding students against the adoption of the doctrine of a specific fluid of heat as a part of the philosophical principles of chemistry, and to show that as yet we have no decided evidence on the subject. Although he had started with the dynamic theory of heat and continued to appreciate its virtues, he did not seem to continue his enthusiasm to the extent that Rumford did. But now, as a professor of the Royal Institution, he trod the ground of sound empirical scientists, tried to present various facts and theories without partiality, and urged that no definite conclusions be drawn until further experimental grounds of proof be obtained. In these days, the relationship between light and heat began to attract the attention of the scientific world, especially when William Herschel discovered that light might not be essentially different from radiant heat.47) Light itself was
47) "Investigation of the Powers of the prismatic Colours to heat and illuminated Objects , with1800 Remarks, that prove the different Refrangibility of radiant Heat." Phil . Trans., , pp. 255-283. "Experiments of the Refrangibility of the invisible Rays of th 1800 e Sun," Phil. Trans., , pp. 284-292. "Experiments on the solar , and on the terrestrial Rays that occasion Heat, with a comparative Views of the Laws to which Light and Heat, or rather the Rays which occasion them, are subject, in order to determine whether they are the same , or different,"I Part , Phil. Trans., 1800, pp. 293-362; Part ‡U, ibid., pp. 437-538.
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considered by most scientists of the time to be made up of particles, according to the Newtonian concept.48) Therefore, Herschel naturally inferred that "radiant heat consists of particles of light of a certain range of momenta, and which range may extend a little farther, on each side of refrangibility, than that of light." Andrew Ure also presented the argument that Herschel's observations and the ones repeated by H. Englefield with similar results were supposed to be decisive evidence of the materiality of caloric and of light, although Ure himself did not pronounce dogmatic conclusions on the abstract nature of heat.49)
It was mainly Thomas Young who furthered the dynamic theory of heat in relation to the nature of light. Young, though he started his career as a physician, became very much interested in the study of waves and hydrodynamics. He was greatly impressed by the analogies which existed between many phenomena of sound and light, and established the undulatory theory of light. He also noticed various resemblances between the phenomena of heat, light and sound, and by these affinities, together with the experimental demonstrations already achieved by Rumford, Davy and others, he was led to the dynamic theory of heat. Actually, he was a professor of natural philosophy at the Royal Institution during the years, 1801-1803, where Rumford was the founder and secretary (1799-1802) and Davy was a lecturer (1801) and a professor (1802-1813). Young's concept of heat can be clearly seen in the lectures which he gave at the Royal Institution while he was a professor there.50) He agreed with Rumford as to the impossibility of any material theory of heat and held that heat consisted of vibrations of the particles of bodies, vibrations "larger and stronger than those of light." He mentioned, in this lecture, that the caloric theory of heat was disproved by various experiments, especially by those of production of heat by friction, and he argued:
....if it [heat] is generated out of nothing, it cannot be matter, nor even an immaterial or semimaterial substance.... If heat is not a substance, it must be a quality; and this quality can only be motion. It was Newton's opinion, that heat consists in a minute vibratory motion of the particles
48) It is very interesting to notice here that light was sometimes considered to be a peculiar chemical compound of caloric and oxygen. When light was applied to various substances, the caloric was supposed to issue from the decomposition of light in various degrees. The phenomena of colors were ascribed to the different qualities of light as containing caloric and oxygen in different proportions. The prismatic separation of light was regarded as a chemical decomposition, not a physical or mechanical division of light. The changes in the colors of different substances were due to their chemical action upon light. The absorption of light was referred to the complete resolution of this compound into its constituent parts. (See "Communication from Blackburne respecting Caloric, Light, and Colours," Phil. Mag., vol. 6, 1800, pp. 334-335.) 49) Andrew Ure, A Dictionary of Chemistry, First American Edition, 1821, vol. 1, "On Caloric," also Forth Edition, 1831, London, p. 254. 50) Thomas Young, A Course of Lectures on Natural Philosophy and the Mechanical Arts, 1807, vol. 1, pp. 654-656.
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of bodies, and that this motion is communicated through an apparent vacuum, by the undulations of an elastic medium, which is also concerned in the phenomena of light. If the arguments which have been lately advanced, in favour of the undulatory nature of light, be deemed valid, there will be still stronger reasons for admitting this doctrine respecting heat, and it will only be necessary to suppose the vibrations and undulations, principally constituting it, to be larger and stronger than those of light, while at the same time the smaller vibrations of light, and even the blackening rays, derived from still more minute vibrations, may, perhaps, when sufficiently condensed, concur in producing the effects of heat. These effects, beginning from the blackening rays, which are invisible, are a little more perceptible in the violet, which still posses but a faint power of illumination; the yellow green afford the most light; the red give less light, but much more heat, while the still larger and less frequent vibration, which have no effect on the sense of sight, may be supposed to give to rise to the least refrangible rays, and to constitute invisible heat. It is easy to imagine that such vibrations may be excited in the component parts of bodies, by percussion, by friction, or by the destruction of the equillibrium of cohesion and repulsion, and by a change of the conditions on which it may be restored, in consequence of combustion, or of any other chemical change. It is remarkable that the particles of fluids, which are incapable of any material change of temperature from mutual friction, have also very little power of communicating heat to each other by their immediate action, so that there may be some analogy, in this respect, between the communication of heat and its mechanical excitation.
.... If heat, when attached to any substance, be supposed to consist in minute vibra tions, and when propagated from one body to "another, to depend on the undulations of a medium elastic, its effects must strongly resemble those of sound, since every sounding body is in a state of vibration, and the air, or any other medium, which transmits sound, conveys its undulation to distant parts by means of its elasticity . And we shall find that the principal phenomena of heat may actually be illustrated by a comparison with those of sound....50)
Then he enumerated the similarity and the identity between these two kinds of phenomena. Some of them were correct but some were not. Young also discussed the "phenomena of the light of solar phosphori," in the general conclusion of his Barkerian Lecture for 1801,51) and said:
There are some phenomena of the light of solar phosphori, which at first sight might seem to favour the corpuscular system; for instance , its ramaining many months as if in a latent state, and its subsequent reemission by the action of heat . But, on further consideration, there is no difficulty in supposing the particles of the phosphori , which have been made to vibrate by the action of light , to have this action abruptly suspended by the intervention of cold, whether as contacting the bulk of the substance or otherwise; and again, after the restraint is removed , to proceed in their motion, as a spring would do, which had been held fast for a time , in an intermediate stage of its vibration; nor is it impossible that heat itself may, in some circumstances , become i n a similar manner latent. (Nicholson's Journal , II, 399.) But the affections of heat may, perhaps, hereafter be rendered more intelligible to us; at present , it seems highly 51) "On the Theory of Light and Colours," Phil. Trans ., 1802; Young's Lectures, ibid., vol. 2, pp. 630-631.
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probable, that light differs from heat only in the frequency of its undulations or vibrations; those undulations which are within certain limits, with respect to frequency, being capable of affecting the optic nerve, and constituting light; and those which are slower, and probably stronger, constituting heat only;....
In this lecture "On Collision,"52) Young stated that "the sum of the momenta of all the bodies of the system,.... is the same," and that "When the bodies are perfectly elastic,....the sum of their energies or ascending forces, in their respective directions, remains also unaltered," where the term "energy" was defined by him as "the product of the mass or weight of a body, into the square of the number expressing its velocity." He also noticed that:
In almost all cases of the forces employed in practical mechanics, the labour expended in producing any motion, is proportional, not to the momentum, but to the energy which is obtained;....52)
Thus he had a clear idea of the conservation of mechanical energy. He even applied this idea to various sorts of mechanical operations, such as cutting, turning, boring, digging, polishing, etc. in another lecture, "On Modes of Changing the Forms of Bodies."53) But he never related mechanical energies to other sorts of energies, such as heat, electricity, etc. For him, heat was "generated out of nothing" when heat was produced by friction, and this was why heat could not be a substance but a quality, or vibratory motion.
It was Robert Mayer who first clearly stated that mechanical force and heat were mutually convertible with their quantitative relations. In 1842 he published his foundings in a paper entitled "Bemerkungen fiber die Krafte der unbelebten Natur." In the following year, appeared James Prescott Joule's paper, "On the Calorific Effects of Magneto-electricity, and on the Mechanical Value of Heat," in which the author reported on the mechanical equivalent of heat as determined by his experiments. Joule himself regarded heat as motion,54) and he also clearly pointed out the relationship of heat and mechanical work in steam-engines; he corrected the error of Carnot and Clapeyron, as may be seen in the following statement:
....the steam, while expanding in the cylinder, loses heat in quantity exactly proportional to the mechanical force which it communicates by means of the piston, and that on the condensation of the steam the heat thus converted into power is not given back. Supposing no loss of heat by radiation &c., the theory here advanced demands that the heat given out in the condenser shall be less than that communicated to the boiler from the furnace, in exact proportion to the equivalent of mechanical power developed.55)
52) Young's Lectures, op. cit., vol. 1, pp. 75-82. 53) Young's Lectures, ibid., vol. 1, pp. 220-235. 54) For instance, see the Appendix of his paper, "On the Heat evolved during the Elect rolysis of Water," Memoirs of the Manchester Lit. & Phil. Soc., 2nd ser., vol. 7. 55) "On the Changes of Temperature Produced by the Rarefaction and Condensation of Air," Phil. Mag., ser. 3, 1845.
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The new discovery of Mayer and Joule opened a way to the theoretical acceptance of the dynamic theory of heat. But neither their discovery nor the dynamic theory of heat was easily adopted. Nor was Count Rumford able, as be hoped, to "live a sufficient long time to have the satisfaction of seeing caloric interred with phlogiston in the same tomb."56) But as late as 1856, the caloric theory of heat still prevailed over the dynamic theory as can be seen in the article "Heat" in the Encyclopaedia Britannica (8th edition).
‡Y. Conclusion
Thus far, the author has presented a brief account of the caloric theory, together with the caloricists' explanations of the phenomena of heat, has described the development of the dynamic theory of heat and the debates between these two opposing views, and has indicated some difficulty in the general acceptance of the dynamic theory. The study of heat entered into a new phase in the late 18th century. But it was pursued mainly from the chemical standpoint. Moreover, the study of chemis try was the major subject of interest among English scientists. When the editor of the Annals of Philosophy, Thomas Thomson, contributed an article in 1816, entitled "Account of the Improvements in Physical Science during the year 1815," out of an article of 70 pages he devoted 44 pages to chemistry but only sixteen to physics and astronomy. In the same article he used only one third of a page on behalf of mathemetics. Similar disposition can be seen in another article of his for the year 1813. Since he himself was a chemist, one may suspect that he had partiality toward chemistry. However, that was not the case because one meets with the same tendency in other leading English scientific journals of the time. If one takes, for instance, the two volumes of the Philosophical Magazine for the year 1800, he will see that nearly half the contents of these volumes include articles on chemistry; the next largest section is biology including the medical sciences, while topics on physics are few and there is not a single paper on mathematics. This sketch may illustrate the nature and the proportion of the various fields of science of the time. There, the study of heat was relegated to a minor place as may be seen in the above-mentioned article by Thomson. He devoted in this article but two pages to this study out of 44 pages devoted to chemistry. Thus, the newly discovered properties and phenomena of heat were pursued mainly from the chemical aspect, and it was naturally considered as a kind of material. Moreover, as Lilley pointed out,57) the caloric as an elastic fluid was, for Lavoisier, the key-stone of anti-phlogistic chemistry, and as scientists became converted to the new chemical theory, so also they accepted the caloric. Further more, the material theory of heat not only had "the advantage of offering an
56) Rumford's letter to Marc Auguste Pictet of Geneva, written in 1804. 57) S. Lilley, "Attitude to the Nature of Heat about the beginning of the 19th Century," Archives Internationales D'Histoire des Sciences, I2, 1948, pp. 630-639 .
-86- No. 2 The Development of the Dynamic Theory 33 easily intelligible explanation of the phenomena of heat," as Lardner mentioned already in 1833,58) but also it proved workable and satisfactory in the state of knowledge at that time, and particularly when the chemical phenomena of heat were the most important topics. The caloric theory could even give good quanti tative relations, for instance, to explain the phenomena of specific heat and latent heat. And those phenomena had many analogies with chemical combinations. Thus, the caloric theory continued to be generally accepted. On the other hand, the dynamic theory of heat was not so easily comprehen sible nor applicable except for the phenomenon of heat produced by friction. This theory also remained vague and non-quantitative, or, according to Lardner, it was "involved in the difficulty of requiring more acute powers of mind to apprehend its force, or even to understand any of its applications"; and "it would scarcely admit of full exposition without the use of the language and symbols of the higher mathematics."58) Therefore, experiments performed by Rumford and Davy did not appear to others to be conclusive, but the caloric theory seemed to most scientists far more comprehensive than the other and they preferred this theory. The general acceptance of the dynamic theory of heat was delayed until various other phenomena of heat, especially irreversible ones, were further studied; until the identification of heat with light was more generally recognized, especially in consequence of the wave theory of light; until the nature of gases in relation to heat was investigated; until the correlation of heat and mechanical work was perceived; and until the great synthesis of various fields of natural science, such as mechanics, heat, electricity, chemistry, etc., was achieved by the establishment of the law of conservation of energy.
The above work was carried on at Harvard University while the author was in receipt of a grant from the Harvard-Yenching Institute, which is gratefully acknowledged. The author also wishes to acknowledge his indebtedness to Professor Thomas Kuhn for valuable suggestions and helpful advice.
Bibliography
1. Books for general reference. McKie, Douglas & Heathcote, Niels H. de V., The Discovery of Specific and Latent Heats, London, 1935. Merz, John Theodore, A History of European Thought in the Nineteenth Century, Edin burgh & London, Vol. 1, 1923, & Vol. 2, 1928. Nash, Leonard K., The Atomic-Molecular Theory, Harvard University Press, 1950. Roller, Duane, The Early Development of the Concepts of Temperature and Heat, Harvard University Press, 1950.
2. Articles for general reference. Boas, Marie, "Establishment of the Mechanical Philosophy," Osiris, Vol. 10, 1952, pp. 412-541.
58) Dionysius Lardner, Treatise on Heat, London, 1833, op. cit., p. 398.
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Brown, Sanborn C., "Count Rumford and the Calorie Theory of Heat," Proceedings of the American Philosophical Society, XCIII, 316-325. -, "The Caloric Theory of Heat," American Journal of Physics, XVIII, No. 6, 367-373. - , "Count Rumford's Concept of Heat," American Journal of Physics, XX, 331-334. - , "The Discovery of Convection Currents by Benjamin Thompson, Count of Rumford," American Journal of Physics, XV, 273-274. Lilley, S., "Attitudes to the Nature of Heat about the Beginning of the Nineteenth Century," Archives Internationales d'Histoire des Sciences, Tome 27, 1948, pp. 730-639.
3. Books for particular reference. Adams, George, Lectures on Natural and Experimental Philosophy, in 5 vols., London, 1794. Boerhaave, Hermann, A New Method of Chemistry (translated from the original Latin, Elementa Chemise, 1732), 2nd ed., London, 1741. Dalton, John, New System of Chemical Philosophy, Part 1, Manchester, 1808. The Collected Works of Sir Humphry Davy, London, 1839-1840. Paris, John Ayrton, The Life of Sir Humphry Davy, London, 1831. Kelland, Philip, Theory of Heat, Cambridge, 1837. Lardner, Rev. Dionysius, A Treatise on Heat, London, 1833. -, Hand-Books of Natural Philosophy and Astronomy, 2nd course, Philadelphia, 1853. Pl ayfair, John, Outlines of Natural Philosophy, vol. 1, 3rd ed., Edinburgh, 1819. Robison, John, Elements of Mechanical Philosophy, Edinburgh, 1804. The Complete Works of Count Rumford, in 4 vols., Boston, 1870-1875. Rumford, Count, Benjamin Thompson, Essays, Political, Econompcal, and Philosophical, in 3 vols., 5th ed., London, 1800-1802. Ellis, George Edward, Memoir of Sir Benjamin Thompson, Count Rumford, Boston, 1871. Tait, P. G., Lectures on some Recent Advances in Physical Science, London, 1876. Tyndall, John, Heat as a Mode of Motion (American ed.), New York, 1869. Thomson, Thomas, An Outline of the Sciences of Heat and Electricity, Edinburgh, 1830. Ure, Andrew, A Dictionary of Chemistry, 1st American ed., 1821, and 4th ed., London, 1831. Young, Thomas, A Course of Lectures on Natural Philosophy and the Mechanical Arts, in 2 vols., London, 1807. Peacock, George, Life of Thomas Young, London, 1855. Wood, Alexander, Thomas Young, Natral Philosopher, Cambridge UP, 1954. 4. Articles for particular reference. "Communication from Dr . Blackburne respecting Caloric, Light, and Colours," Phil. Mag ., VI, 334-335, (1800). Carnot, Sadi, "Reflections on the Motive Power of Heat" (1824), Magie, W. F., The Second Law of Thermodynamics, New York & London, 1899, pp. 1-60. Emmett, J. B., "Researches into Mathematical Principles of Chemical Philosophy," Annals of Philosophy, XVI, 137-145, 180-188, & 351-358. Fordyce, George, "An Account of some Experiments on the Loss of Weight in Bodies on being melted or heated," Phil. Trans., LXXV, 361-365, (1785). "Heat ," The Encyclopaedia Britannica, 8th ed., 1856, XI, 260-276. Henry, William, "A Review of some Experiments, which have been supposed to Disprove
the Materiality of Heat," Manchester Memoirs, V, 603-621; Nicholson's Journal , ‡V, 197-207, (1802). Herschel, William, "Investigation of the Powers of the prismatic Colours to Heat and
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illuminated Objects, with Remarks, that prove the different Refrangibility of radiant Heat," Phil. Trans., 1800, pp. 255-283. -, "Experiments of the Refrangibility of the invisible Rays of the Sun ," ibid., 284-292. "-, "Experiments on the solar , and on the terrestrial Rays that occasion Heat, with a comparative Views of the Laws to which Light and Heat, or rather the Rays which occasion them, are subject, in order to determine whether they are the same, or different," ibid., 293-362, & 437-538.
Joule, James Prescott, "On the Heat evolved during the Electrolysis of Water," read 1843; Manchester Memoirs, 2nd ser., ‡Z, 87; Joule's Scientific Papers, I, 109-123. -, "On the Changes of Temperature produced by the Rarefaction and Condensation of
Air," Phil. Mag., 3rd ser., ‡]‡]‡Y, 369-383, (1845); Joule's Scientific Papers, I, 171-189.
Powell, Baden, "On Light and Heat from Terrestrial Sources," Quarterly Journal of Science,
‡]?, 45-61, & 213-216, (1825). Thomson, Thomas, "A Biographical Account of Sir Benjamin Thompson, Knt. Count Rum
ford," Annals of Philosophy, V. 241-250, (1815). -, "Sketch of the Imprevements in Science made during the Year 1813," ibid., ‡V, 1-32,
(1814). -, "Account of the Improvement in Physical Science during the Year 1815 ," ibid.,‡Z, 1-71, (1816).
Tillock, Alexander, "An Attempt to prove that the Matter of Heat, like other Substances,
possessed not only Volume but Gravity," Phil. Mag., ‡\, 158-167, (1800). Watanabe, Masao, "Count Rumford's First Exposition of the Dynamic Aspect of Heat,"
Isis, Vol. 50, Part 2, No. 160, 1959, pp. 141-144.
(March, 1957)
(Received Mar. 15, 1959)
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