348 M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 



Laplace, and subsequently M. Poisson, have made public some very 

 remarkable theoretical researches on this subject ; but they rest upon 

 hypothetical data which appear liable to objection. It is admitted in 

 them that the ratio of the specific caloric when the volume remains con- 

 stant to the specific caloric under a constant pressure, is invariable, and 

 that the quantities of heat absorbed by gases are proportional to their 

 temperatures. 



I will finally quote among the works which have appeared on the theory 

 of heat, one by M. S. Carnot, published in 1824, under the title of Re- 

 flexions siir la Puissance Motrice du Feu. The idea taken for the basis 

 of his researches appears to me fertile and incontestible : his demon- 

 strations are founded on the absurdity which arises from admitting the 

 possibility of producing absolutely either the motive force or the heat. 



The various theorems to which this new method of reasoning con- 

 ducts us may be enunciated as follows : 



1 . Wlien a gas without change of temperature passes from a deter- 

 mined volume and pressure to aiiother volume and pressure equally 

 determined, the quantity of caloric absorbed or lost is always the same, 

 whatever be the nature of the gas subjected to experiment. 



£. The difference betioeen the specific heat under a constant pressure 

 and the specific heat at a constant volume is the same for all gases. 



3. When a gas varies in volume without change of temperature, the 

 quantities of heat absorbed or disengaged by that gas are in arithmetical 

 progression, if the increments or diminutions of volume are in geometrical 

 progression. 



This new mode of demonstration appears to me worthy of fixing the 

 attention of geometers ; it is, in my opinion, free from every objection, 

 and it has acquired additional importance since its verification by the 

 labours of M. Dulong, in which the truth of the first theorem which I 

 have recited is demonstrated by experiment. 



I think it will be of some interest to revive this theory : M. S. Carnot, 

 dispensing with mathematical analysis, arrives, by a series of delicate 

 reasonings difficult to apprehend, at results easily deducible from a more 

 general law, which I shall endeavour to establish. But before entering 

 upon the subject, it will be useful to return to the fundamental axiom 

 upon which the researches of M. Carnot are founded, and which will be 

 my starting point also. 



§11. 



It has long been remarked that heat may be employed to develop 

 motive force, and reciprocally that by motive force we may develop 

 heat. In the first case we should observe that there is always a passag( 

 of a determinate quantity of caloric from a body at a given temperatu: 

 to another bociy at a lower temperature ; thus in the steam-engine, th* 



