68 ELECTRICAL EQUILIBRIUM. 



The force, therefore, at any point of the dielectric is inversely 

 as the distance from the axis. 



If F be the force, and V the potential at any distance R, we have 



A_ _<TV 

 ~~ ~ J 



and therefore, 



Extending this integral to the volume comprised between the 

 surfaces S : and S 2 , we have 



From which is deduced for the constant A, 



V V 

 A _M _ 12 

 A-- . 



On the other hand, the electrical density o-, at the surface of 

 the inner cylinder, is expressed by 



_ _ __ _ 

 4tr * 47TRJ 47TR/ R 2 



Let S be the extent of surface comprised between the two planes 

 perpendicular to the axis ; the mass M distributed on this surface is 



(Vi-V 8 )S 

 - 



If L is the length of the cylinder, thus determined, 



S = 

 which gives, finally, 



