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SCIENCE 



[N. S. Vol. XXXVI. No. 924 



ployed in the interpretation of this equa- 

 tion was the oft-quoted analogy of the 

 waterfall. Calorie might be regarded as 

 possessing motive power or energy in virtue 

 of elevation of temperature just as water 

 may be said to possess motive power in 

 virtue of its head or pressure. The limit 

 of motive power obtainable by a reversible 

 motor in either case would be directly pro- 

 portional to the head or fall measured on a 

 suitable scale. Caloric itself was not mo- 

 tive power, but must be regarded simply 

 as the vehicle or carrier of energy, the pro- 

 duction of motive power from caloric de- 

 pending essentially (as Carnot puts it) not 

 on the actual consumption of caloric, but 

 on the fall of temperature available. The 

 measure of a quantity of calorie is the 

 work done' per degree fall, which corre- 

 sponds with the measure of a quantity of 

 water by weight, i. e., in kilogrammeters 

 per meter fall. 



That Carnot did not pursue the analogy 

 further, and deduce the whole mechanical 

 theory of heat from the caloric theory, is 

 hardly to be wondered at if we remember 

 that no applications of the energy prin- 

 ciple had then been made in any depart- 

 ment of physics. He appears, indeed, at a 

 later date to have caught a glimpse of the 

 general principle when he states that ' ' mo- 

 tive power [his equivalent for work or 

 energy] changes its form but is never an- 

 nihilated." It is clear from the post- 

 humous notes of his projected experimental 

 work that he realized how much remained 

 to be done on the experimental side, espe- 

 cially in relation to the generation of 

 caloric by friction, and the waste of motive 

 power by conduction of heat, which ap- 

 peared to him (in 1824) "almost inex- 

 plicable 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 propor- 

 tional 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 inconsistent with 

 the general opinion prevalent at the time, 

 and with one solitary experiment by Dela- 

 roche and Berard, 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 favor 

 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 inde- 

 pendent of the pressure. 



Another point which troiibled Carnot 

 was that, according to his calculations, the 

 motive power obtainable from a kilocalorie 

 of heat per degree fall appeared to dimin- 

 ish with rise of temperature, instead of re- 

 maining constant. This might have been 

 due to experimental errors, since the data 

 were most uncertain. 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 kilogrammeters per kilo- 

 calorie, subsequently found by Joule, he 

 could hardly have failed to notice that this 

 was the same (within the limits of experi- 

 mental error) as the maximum work AQT 

 obtainable from the kilocalorie according 

 to his equation. (This is seen to be the 

 case when the values calculated by Carnot 

 per degree fall at different temperatures 

 were multiplied by the absolute tempera- 

 ture in each case. E. g., 1.212 kilogram- 

 meter per degree fall with steam at 79° C. 

 or 352° Abs. 1.212X352 = 426 kilogram- 



