246 APPENDIX S. 



p 



If, to abridge, we call N the quantity 1 ^ E > the 



~ 



equation would become 



^ t + 267 



P = N- ^> 



whence we deduce, according to equation (I), 



ar, 



dr = N -- dv. 



v 



Regarding t as constant, and taking the integral of 

 the two numbers, we shall have 



r = N(t + 267) log v + C. 



If we suppose r = when v = 1, we shall have 

 (7=0; whence 



r = N(t + 267) log v. . . . (2) 



This is the motive power produced by the expan- 

 sion oi the air which, under the temperature t, has 

 passed from the volume 1 to the volume v. If in- 

 stead of working at the temperature t we work in 

 precisely vtto name manner at the temperature 

 t -j- dt, the power developed will be 



r + dr = N(t + dt + 267) log v. 

 Subtracting equation (2), we have 



dr = Nlogvdt. .... (3) 



Let e be the quantity of heat employed to maintain 

 the temperature of the gas constant during its 



