TRANSACTIONS OF SECTION A. 61' 



respectively contribute Qi, Q.,, Q^ unit-tubes ; and if a con- 

 ductor be at pressure V (every part of a conductor must be at 

 the same pressure, of course, as the aether in it is weightless 

 and under no molecular forces), each tube that leaves the con- 

 ductor must meet V surfaces of equal pressure before it comes 

 to a region of no pressure at all. 



So the total number of cells is 5Q . V ; and energy of 

 system = -I 2Q .V. 



4, As a particular case, consider the energy of strain of a 

 charge Q on a sphere of radius a. 



E Q 



The pressure at the surface = -j ... (^2.) 



E Q2 



•'• Energy ^ ^■-^^—' 



Also the energy of strain of the medium between a sphere 

 of radius a and a concentric conductor of radius a' is, for 

 similar reasons, 



i.EiQ^_Q:| (,2) 



^ 4:ir(a a') ^' ^ 



5. Next consider the strain due to charges Qi andQo on tvv'o 

 spheres of radii Vi and r., placed at a distance b from each other, 

 b being large compared with Ti and r.,. 



The pressure at any point is the sum of the pressures due 

 to the two charges. Thus the pressure at a point on the sur- 

 face of the 1st sphere is very nearly — j— j_ -^-, for r^ is so 



47r [ 7\ b I 



small compared with b that , , may be taken as equal to 



1 



F 



Similarly the pressure at any point on the second sphere 



Hence, by end of § 3, 



Energy of strain of medium 



_ 1 EQi (Qi,Q.1 ,1 EQ, (0,0;, 



~ ' 47r i ri 6 I "^ - 47r U "^ r, 



-1 E (Q,2 2Q,.Q, Q,2) 



~ - 4t 1 r, b "*" r, ) ■ 



Thus the energy depends upon b — i.e., the distance apart of 

 the two spheres. The force of separation may be obtained by 

 differentiating the expression for the energy with respect to b. 

 This gives — 



