Conway — On Ihc 3Iotiou of itu I'JIci'IrijinI Sphere. 9 



In the same mannci' vvc proceed to terms involving c'; and wo dutLimini' 

 an additional term 



I ■d\\dlj d r 



and we find for the vector potential 



E^or^ - Ec-^a 4 Ec-^ I (..) - ^ I i + ^ I .s:V i) + . . . 

 \6 ^^ 2 dt r 6 dt rj 



The electrical force t at the surface of the sphere is 



-Y I /3 + c"" {2pSpa - a'-p VpaSpor) + cr' ( - 2paSp(i) + . . .', 



and the magnetic force at the surface is 



Ec-'cf^Vap. 



If the internal magnetic force is initially and afterwards zero, the 

 surface-density is simply obtained from the normal component of the 

 electric force, and this forms at each step a check on our calculations ; for 

 the total charge on the sphere must be constant. In this case we find for 

 the surface-density 



E 



- — - {1 + 2ac~'-SUocs - 2a"c~^SUofj + . . .1. 



We find from the boundary conditions the current ?'(, to be 

 4^^ [o-'VpVpcr - ac-^VpVpa^ . . .). 



Other examples easily solved by this method would be the case of 

 constant electric and magnetic force, plane waves, etc. 



v.— On Oscillatory Distributions. 



For a sphere at rest there is not only the simple distribution, but 

 also an infinite number of possible oscillatory distributions, and those can 

 be continued in the usual manner. The method can best be explained by 

 an example. For the fundamental mode take 



1 ^Ac( ^-vffl^-c- >-«-'■'• + 



n, = -c-o-a(^ 



r dt 



where a is a fixed direction in space, and we shall suppose that the sphere 



K. I. A. PKOC. VOL. XXVni., SECT. A. [2] 



