THE EQUILIBRIUM OF FLUIDS. 161 



8P' . 



-j- 2.3.4...2S + 1 



It now remains to find the value of the definite integral herein 



, r '2\-i 



contained. But when f 1 ) i s expanded, and the integra- 

 tions are effected by known formulae, we obtain 



f 6 / r'*\~ l ?=2 v' zt 



J I 1 "?) (J2 ~ /2) 2 '' 2<+2 *'=/. B 2r^(J 2 -r' 2 ) 2 



5' . , 



a 2 25 + 3 + w.2s + 5 + w a 4 



2 



//n\ /1\ 



r 



1.3.5 



?^-M\ l+ti.3 + w.5 + w ...... 2s 



where after the integrations have been effected, x ought to be 

 made equal to - . 



The value of the integral last found being substituted in the 

 expression immediately preceding, and the finite integral taken 

 relative to s from 5 = to s = co gives for the repulsion of the 

 inner sphere, 



11 



