September 5, 1912] 



NATURE 



23 



That Carnot did not pursue the analogy further, 

 and deduce the whole mechanical theory of heat Irom 

 the caloric theory, is scarcely to be wondered at if we 

 remember that no applications of the energy principle 

 had then been made in any department of physics. 

 He appears, indeed, at a later date to have caught a 

 glimpse of the general principle when he states that 

 "motive-power [his equivalent for work or energy] 

 changes its form but is never annihilated." It is 

 clear from the posthumous notes of his projected ex- 

 perimental work that he realised how much remained 

 to be done on the experimental side, especially in rela- 

 tion to the generation of caloric by friction, and the 

 waste of motive-power by conduction of heat, which 

 appeared to him (in 1S24) "almost inexplicable in the 

 present state of the theory of heat." 



One of the points which troubled him most in the 

 application of the theoretical result that the work 

 obtainable from a quantity of caloric was simply pro- 

 portional to the fall of temperature available, was 

 that it required that the specific heat of a perfect gas 

 should be independent of the pressure. This was in- 

 consistent with the general opinion prevalent at the 

 time, and with one solitary experiment by Delaroche 

 and B^rard, which appeared to show that the specific 

 heat of a gas diminished with increase of pressure, 

 and which had been explained by Laplace as a natural 

 consequence of the caloric theory. Carnot showed 

 that this result did not necessarily follow from the 

 caloric theory, but the point was not finally decided 

 in his favour until the experiments of Regnault, first 

 published in 1852, established the correct values of 

 the specific heat of gases, and proved that they were 

 practically independent of the pressure. 



Another point which troubled Carnot was that, ac- 

 cording to his calculations, the motive-power obtain- 

 able from a kilocaloiie of heat per degree fall appeared 

 to diminish with rise of temperature, instead of 

 remaining constant. This might have been due to 

 experimental errors, since the data were most uncer- 

 tain. But, if he had lived to carry out his projected 

 experiments on the quantity of motive-power required 

 to produce one unit of heat, and had obtained the 

 result, 424 kilogrammetres per kilocalorie, subse- 

 quently found by Joule, he could scarcely have failed 

 to notice that this was the same (within the limits 

 of experimental error) as the maximum work AQT 

 obtainable from the kilocalorie according to his equa- 

 tion. (This is seen to be the case when the values 

 calculated by Carnot per degree fall at different tem- 

 peratures were multiplied by the absolute temperature 

 in each case. E.g. i'2i2 kilogrammetres per degree 

 fall with steam at 79° C. or 352° .'\bs. i'2i2 X352 = 426 

 kilogrammetres.) The origin of the apparent dis- 

 crepancy between theory and experiment lay in 

 the tacit assumption that the quantity of 

 caloric in a kilocalorie was the same at dif- 

 ferent temperatures. There were no experirrients 

 at that time available to demonstrate that the caloric 

 measure of heat as work per degree fall, implied in 

 Carnot 's principle, or more explicitlv stated in his 

 equation, was not the same as the calorimetric 

 measure obtained by mixing substances at different 

 temperatures. Even when the energy principle was 

 established its exponents failed to perceive exactly 

 where the discrepancy between the two theories lay. 

 In reality both were correct, if fairly interpreted in 

 accordance with experiment, but they depended on 

 different methods of measuring a quantity of heat, 

 which, so far from being inconsistent, were mutually 

 complementary. 



The same misconception, in a more subtle and in- 

 sidious form, is still prevalent in such common phrases 

 as the following: "We now know that heat is a 

 form of energy and not a material fluid." The experi- 

 NO. 2236, VOL. 90] 



mental fact underlying this statement is that our 

 ordinary methods of measuring quantities of heat in 

 reality measure quantities of thermal energy. When 

 two substances at different temperatures are mixed, 

 the quantity remaining constant, provided that due 

 allowance is made for external work done and for 

 external loss of heat, is the total quantity of energy. 

 Heat is a form of energy merely because the thing we 

 measure and call heat is really a quantity of energy. 

 Apart from considerations of practical convenience, we 

 might equally well have agreed to measure a quantity 

 of heat in accordance with Carnot 's principle, by the 

 e.xternal work done in a cycle per degree fall. Heat 

 would then not be a form of energy, but would possess 

 all the properties postulated for caloric. The caloric 

 measure of heat follows directly from Carnot 's prin- 

 ciple, just as the energy measure follows from the law 

 of conservation of energy. But the term heat has 

 become so closely associated with the energy measure 

 that it is necessary to employ a different term, caloric, 

 to denote the simple measure of a quantity of heat as 

 opposed to a quantity of heat energy. The measure- 

 ment of heat as caloric is precisely analogous to the 

 measure of electricity as a quantity of electric fluid. 

 In the case of electricity, the quantity measure is more 

 familiar than the energy measure, because it is 

 generally simpler to measure electricity by its chemical 

 and magnetic effects as a quantity of fluid than as a 

 quantity of energy. The units for which we pay by 

 electric meter, however, are units of energy, because 

 the energy supplied is the chief factor in determining 

 the cost of production, although the actual quantity 

 of fluid supplied has a good deal to do with the cost 

 of distribution. Both methods of measurement are 

 just as important in the theory of heat, and it seems 

 a great pity that the natural measure of heat quantity 

 is obscured in the elementary stages of exposition by 

 regarding heat simply as so much energy. The in- 

 adequacy of such treatment makes itself severely felt 

 in the later stages. 



Since Carnot 's principle was adopted without 

 material modification into the mechanical theory of 

 heat, it was inevitable that Carnot's caloric, and his 

 solution for the work done in a finite cycle, should 

 sooner or later be rediscovered. Caloric reappeared 

 first as the "thermodynamic function" of Rankine, 

 and as the "equivalence-value of a transformation" 

 in the equations of Clausius ; but it was regarded 

 rather as the quotient of heat energy bv temperature 

 than as possessing any special physical significance. 

 At a later date, when its importance was more fully 

 recognised, Clausius gave it the name of entropy, and 

 estalDlished the important property that its total quan- 

 tity remained constant in reversible heat exchanges, 

 but always increased in an irreversible process. _ Any 

 process involving a decrease in the total quantity of 

 entropy was impossible. Equivalent propositions with 

 regard to the possibilitv or impossibility of transforma- 

 tions had previously been stated by Lord Kelvin in 

 terms of the dissipation of available energy. But, 

 since Carnot's solution had been overlooked, no one at 

 the time seems to have realised that entropy was 

 simply Carnot's caloric under another name, that heat 

 could be measured otherwise than as energy, and that 

 the increase of entropy in any irreversible process was 

 the most appropriate measure of the quantity of heat 

 generated. Energy so far as we know must always 

 be associated with something of a material nature 

 acting as carrier, and there is no reason to believe that 

 heat energy is an exception to this rule. The tendency 

 of the kinetic theory has always been to regard entropy 

 as a purely abstract mathematical function, relating to 

 the distribution of the energy, but having no physical 

 existence. Thus it is not a quantitv of anything in 

 the kinetic theory of gases, but merely the logarithm 



