112 Mr. E. F. J. Love on the 



whence (|&--M' + n-'- K -)£}' 



where it is to be noted that J- is not a partial differential 

 coefficient. v ■, 



To evaluate this quantity we must determine -~ ; and to 



do this we must assume some form for the gas-equation. It 

 does not much matter which we take — as we shall see 

 presently — for an approximation is all that is required ; 



anything further is rendered needless by the fact that I ^— ) 



/dU\ \oo/r 



is always small compared with I =-^ ) • 



We will employ van der Waals's formula ; then 



ET a 







r v-b v" 



■'■ 



dp 



dv 



R o 7 T RT ±a 



v — b dv (v — b) 2 v 3 ' 



but dH _ 

 dv 



e 



IT 



dp RT a 



. -j-, and j =p + - 



do v — b <r 



therefore 



r) 



w 



"R \ 9n P + ^ 



?. e. 



dv 



rfy \ LI v — b) ~ v* v — b 



5 \v* v-b\\ liv-b) . 

 Substituting this value of -j- in the equation 



we obtain 



a 



2a 



P + ^z 



U^ T = r + n • J • M ,.jJL " p -' 



n u-& 



Since — 2 is in general small compared with ^j, and & and 



