112 



Trans. Acad. Sci. of St. Louis. 



We will apply equation (8) to determine the energy of a 

 system consisting of two charged spheres having radii i\ and 

 r 2 , and having charges Q x and — Q 2 . We will assume that 

 the spheres are in air, so that //=1, and that Q x > Q 2 

 numerically. 



The potentials of the spheres will be 



V, 



Qi 



v.=_a 



In the figure, the smaller sphere is assumed to have the 

 charge — Q 2 . All of the lines proceeding to it come from 

 the larger sphere. They are all within a surface of revolu- 

 tion generated by revolving any critical line P M a around 

 the principal axis of figure of the system. 



The point P is the position of unstable equilibrium, where the 

 attraction of — Q 2 balances the repulsion due to Q v This 

 critical surface intersects the charge Q x in a circle, and pro- 

 ceeding to P it continues either in the line P b or P b v 

 The lines of force external to this surface, proceed from the 

 larger sphere to an infinite distance. We have here two tubes 

 of force separated from each other by the critical surface, 

 a MP . 



In the external tube of force there are 4^ (Q x — Q 2 ) lines. 



