44 APPLICATION OF THE PRECEDING RESULTS 



p and p being the densities of the electric fluid - at the surfaces 

 A and B respectively. Permitting ourselves, in what follows, 

 to neglect quantities of the order 0* compared with those re- 

 tained, it is clear that we may write 6 for /? and hence by 

 substitution 



where V and p are quantities of the order 7=; $ and /3 being 



the order $ or unity. The only thing which now remains to 



d*V 



be determined, is the value of -=- for any point on the sur- 



dw* 



face A. 



Throughout the substance of the glass, the potential func- 

 tion V will satisfy the equation = B F, and therefore at a point 

 on the surface of A, where of necessity w, w' and w" are each 

 equal to zero, we have 



dw 2 dw* dw" z 



the horizontal mark over w, w and w" being, for simplicity, 

 omitted. Then since w = 0, 



and as V is constant and equal to ft at the surface A, there 

 hence arises 



w* dV 



R being the radius of curvature at the surface A, in the plane 

 (w, w f }. Substituting these values in the expression imme- 

 diately preceding, we get 



w'* ~ E dw 



