278 Thermodynamic Theorems of Carnot 



ent types of working substances and points out how far the efficiency of steam 

 engines actually in operation in his day falls short of the theoretical maximum. 



Of these three parts of the Reflexions, the third is a contribution primarily 

 to technology, while the first and second contain Carnot's contributions to 

 science. Of these contributions to science, in turn, by far the most important 

 are contained in the first part of the Reflexions: Carnot's cycle and Carnot's 

 theorem on reversible engines are the ideas which in the minds of Clausius 

 (1850) and of William Thomson (1851) gave birth to the second law of thermo- 

 dynamics. It is moreover only this outstanding part of his achievement by 

 virtue of which Carnot lives in the consciousness of scholars today; the exist- 

 ence of the second part of the Reflexions appears to have been completely 

 forgotten. 



Our object in this article is to show that Carnot's forgotten theorems deserve 

 some attention both from historians of science and from scientists of the 

 present. 



II. Critical Summary of the Forgotten Thermodynamic Theorems 



These theorems, quoted from Ma in the order of their enunciation and num- 

 bered by us in that order, are as follows: 



1. When a gas passes without change of temperature from one definite vol- 

 ume and pressure to another, the quantity of caloric absorbed or emitted is 

 always the same, irrespective of the nature of the gas chosen as the subject of 

 the experiment. 



2. [At a given pressure] the difference between the specific heat [referred to 

 unit volume] under constant pressure and the specific heat at cojistant volume 

 is the same for all gases. 



3. When a gas changes in volume without change of temperature the quanti- 

 ties of heat which it absorbs or gives up are in arithmetical progression ichen 

 the increments or reductions of volume are in geometrical progression. 



4. When the volume of a gas increases in geometrical progression its specific 

 heat [referred to unit zveight] increases in arithmetical progressioji. 



5. [For a given gas at a given temperature] the difference betiueen the specific 

 heat under constant pressure and that at constant volume is always the same, 

 whatever the density of the gas, provided the quantity of gas by iveight remaijis 

 the same. 



6. The quantity of heat due to the change in volume of a gas [at constant 

 temperature] becomes greater as its temperature is raised. 



7. The descent of caloric produces more motive power at loiver degrees of 

 temperature than at higher. 



Comments. (1) Gases are assumed throughout to obey the laws of Boyle and 

 Gay-Lussac, that is, to be perfect. (2) All the proofs given in the text proper 

 are of the synthetic quasi-Euclidean type, but in a long footnote (beginning 

 on Ca p. 73, Ma p. 39) Carnot gives alternative analytic proofs of theorems 



