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 sur 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. When a gas without change of temperature passes from a deter- — 
mined volume and pressure to another 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. 
g. The difference between 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 eee 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. 
i § II. 
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 passa 
_of a determinate quantity of caloric from a body at a given temperature | 
to another body at a lower temperature ; thus in the ai ine: the | 
