Page:Reflections on the Motive Power of Heat.djvu/274

250 determined, and we would thus be able to estimate the motive power developed by any fall of heat. But this latter conclusion is founded on the hypothesis of the constancy of the specific heat of a gas which does not change in volume—an hypothesis which has not yet been sufficiently verified by experiment. Until there is fresh proof, our equation (6) can be admitted only throughout a limited portion of the thermometric scale.

In equation (5), the first member represents, as we have remarked, the specific heat of the air occupying the volume v. Experiment having shown that this heat varies little in spite of the quite considerable changes of volume, it is necessary that the coefficient T' of log v should be a very small quantity. If we consider it nothing, and, after having multiplied by dt the equation

$$T' = 0,$$

we take the integral of it, we find

$$T = C,$$ &emsp; constant quantity;

but

$$T = \frac{N}{F't},$$

whence

$$F't = \frac{N}{T} = \frac{N}{C} = A;$$

whence we deduce finally, by a second integration,

$$Ft = At + B. $$