250 APPENDIX B. 



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 hy- 

 pothesis of the constancy of the specific heat of a 

 gas which does not change in volume an hypoth- 

 esis which has not yet been sufficiently verified by 

 experiment. Until there is fresh proof, our equa- 

 tion (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 oc- 

 cupying the volume v. Experiment having shown 

 that this heat varies little in spite of the quite con- 

 siderable 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 



Z"=0, 

 we take the integral of it, we find 



T= C, constant quantity; 

 but 



~ F't' 



whence 



_,, N N 



Ft = -?=-{? = A; 



whence we deduce finally, by a second integration, 

 Ft = At B. 



