16 On the Determination of the Energy and Entropy of a Body. 

 T instead of y ; thus, 



e '-^(S4:-£-S- • • • m 



Applying now these expressions to equations (22) and (23), 

 and at the same time putting therein j~ =Ap-x^, we have 



, s= i.g, T+A (J.|_g.^, . . . (34) 



These expressions become particularly simple if we take for 

 the second variable so, hitherto left undetermined, the volume v, for 



we then have to make — =1, and -== =0. We thus get 

 dx dl ° 



dS=l-^dT+A±dv,. . . . (36) 



dV= d ^dr + A^dv (37) 



For the case in which the change of volume in the body takes 

 place without any partial change of its state of aggregation, the 



differential coefficient -^ which occurs in the last equations is 



simply the product of the weight of the body into its specific 

 heat at constant volume. Denoting this specific heat by c, and 

 the weight of the body by M, the equations become, for this 

 case, 



d$ = M^dT + A^dv, .... (38) 



dV=McdT + AT^dv (39) 



As will be easily understood, we might specialize the above 

 equations in various other ways, by choosing particular magni- 

 tudes as variables, or by applying the equations to particular 

 classes of bodies. I will not, however, enter further either upon 

 this point or upon the performance of the integration of the 

 complete differential equations, inasmuch as I have treated some 



