APPENDIX B. 249 



-j2 is simply the specific heat of the gas under 

 cl t 



constant volume, and our equation (1) is the an- 

 alytical expression of the law stated on page 86. 



If we suppose the specific heat constant at all 

 temperatures (hypothesis discussed above, page 92), 



ds 



the quantity '- will be independent of t', and in 

 dt 



order to satisfy equation (5) for two particular 

 values of v, it will be necessary that T' and U' be 

 independent of t; we shall then have T' = C, a 

 constant quantity. Multiplying T' and C by dt, 

 and taking the integral of both, we find 



but as T = =- , we have 



- T ~ Ct + C; 

 Multiplying both by dt and integrating, we have 



& = log (01 + C,) + C,; 



or changing arbitrary constants, and remarking 

 further that Ft is when t = 0, 



Ft 

 The nature of the function Ft would be thus 



= A log (l + |) . . . . (6) 



