252 Mr. J. Rose-Innes on the Theory of 



We may write this 



\di)p~ \dt/ v \dp)t' 

 Substituting this value in the differential equation we obtain 



-<tMD, — «£■ 



Multiply by _(g) ( 



\dt) v \dv/ t ~ 'dpXdvJ ' 



Again, if we put yjr for the product pv we have 



<t)r~ 



>*&).-' 



Hence 



The quantity I -^- ) may conveniently be removed to the 

 other side of the equation ; we thus obtain 



We also have 



fdyjr\ /eh/A /dp\ 

 \dv Jt \dp Jt\dv Jt 



and employing this value the differential equation becomes 



<i),---{ jK i + fiwa 



If by any method we are enabled to express the right-hand 

 side of this equation in terms of v and t, the integral of the 

 equation will give us the connexion between p and t at con- 

 stant volume without an extrapolation to infinity. In order 

 that t may be a linear function of p when v is kept constant, 

 the necessary and sufficient condition is that the right-hand 

 side of the equation should be a function of v only. 



The quantities JK^-and (j^) are both measurable for 

 several substances; in the cases of hydrogen, nitrogen, and 



