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 constant 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 Reflexions sur la Puissance Motrice du Feu. The idea taken for the basis of his researches appears to me fertile and incontestible: his demonstrations 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 conducts us may be enunciated as follows:
1. When a gas without change of temperature passes from a determined 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.
2. 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 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.
§ 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 passage of a determinate quantity of caloric from a body at a given temperature to another body at a lower temperature; thus in the steam-engine, the
