Septembbe 13, 1912] 



SCIENCE 



325 



steam at the same temperature he found 

 nearly the same value, namely, 2*"^ = 1.212. 

 Thus no advantage in point of efficiency 

 could be gained by employing the vapor 

 of alcohol in place of steam. He was also 

 able to show that the work obtainable from 

 a kilocalorie per degree fall probably di- 

 minished with rise of temperature, but his 

 data were not sufficiently exact to indicate 

 the law of the variation. 



The equation which Carnot employed in 

 deducing the numerical values of his func- 

 tion from the experimental data for steam 

 and alcohol is simply the direct expression 

 of his principle as applied to a saturated 

 vapor. It is now generally known as 

 Clapeyron's equation, because Carnot did 

 not happen to give the equation itself in 

 algebraic form, although the principle and 

 details of the calculation were most mi- 

 nutely and accurately described. In cal- 

 culating the value of his function for air, 

 Carnot made use of the known value of the 

 difference of the specific heats at constant 

 pressure and volume. He showed that this 

 difference must be the same for equal vol- 

 umes of all gases measured under the same 

 temperature and pressure, whereas it had 

 always previously been assumed that the 

 ratio (not the difference) of the specific 

 heats was the same for different gases. He 

 also gave a general expression for the heat 

 absorbed by a gas in expanding at constant 

 temperature, and showed that it must bear 

 a constant ratio to the work of expansion. 

 These results were verified experimentally 

 some years later, in part by Dulong, and 

 more completely by Joule, but Carnot 's 

 theoretical prediction has generally been 

 overlooked, although it was of the greatest 

 interest and importance. The reason of 

 this neglect is probably to be found in the 

 fact that Carnot 's expressions contained 

 the unknown function F't of the tempera- 

 ture, the form of which could not be de- 



duced without making some assumptions 

 with regard to the nature of heat and the 

 scale on which temperature should be 

 measured. 



It was my privilege to discover a few 

 years ago that Carnot himself had actually 

 given the correct solution of this funda- 

 mental problem in one of his most im- 

 portant footnotes, where it had lain buried 

 and unnoticed for more than eighty years. 

 He showed by a most direct application of 

 the caloric theory, that if temperature was 

 measured on the scale of a perfect gas 

 (which is now universally adopted) the 

 value of his function F't on the caloric 

 theory would be the same at all tempera- 

 tures, and might be represented simply by 

 a numerical constant A (our "mechanical 

 equivalent") depending on the units 

 adopted for work and heat. In other 

 words, the work W done by a quantity of 

 calorie Q in a Carnot cycle of range T to 

 Ta on the gas scale would be represented 

 by the simple equation: 



It is at once obvious that this solution, 

 obtained by Carnot from the caloric 

 theory, so far from being inconsistent with 

 the mechanical theory of heat, is a direct 

 statement of the law of conservation of 

 energy as applied to the Carnot cycle. If 

 the lower limit T^ of the cycle is taken at 

 the absolute zero of the gas thermometer, 

 we observe that the maximum quantity of 

 work obtainable from a quantity of caloric 

 ^ at a temperature T is simply AQT, 

 which represents the absolute value of the 

 energy carried by the caloric taken from 

 the source at the temperature T. The 

 energy of the caloric rejected at the tem- 

 perature To is AQTf,. The external work 

 done is equal to the difference between the 

 quantities of heat energy supplied and re- 

 jected in the cycle. 



The analogy which Carnot himself em- 



