120 



Mr. G. F. C. Searle on the 



Fk-. 1. 



Suppose that (fig. 1) is the position of q at the time t = 

 and A its position at any later time t, the velocity between 

 and A being constant and eqnal 

 to u. Let P be any point on the 

 sphere of radius r = vt, described 

 about as centre, and let the axis 

 OA cut the sphere in the pole X. 

 Then A P = R and PAX = <£, while 

 OA = ut = nr. 



Let POX = <9. Then r and 6 

 are the coordinates of P relative 

 to O, while R and <£ are its co- 

 ordinates relative to A. I£ E^ 

 along OP, we have, by (1), 



But 



_g( l-ii 3 )Rcos( 0-fl) 

 *"~ KR 3 (l-n 2 sin 2 0)f 



Reos(</>-0) = OP 

 Rsin<£ = 



A cos = r(l — n cos 0), 



r sm 



R 2 



'(1 + n* — 2ncos0) 



Hence 

 Thus 



R 2 (l-n 2 sin 2 cj>) = r\l-n cos 6)\ 



E N : 



W 



_ q(l-n 2 )r(l—ncos 6) = q(l - if) 



Kr*(l -n cos 0) 3 " Kr 2 (l -n cos Of ' 



If the particle was at rest at until £ = 0, the electric force 

 just outside the sphere r — vt is radial to and normal to the 

 sphere and has the value 



E = ?/K> 2 (5) 



At the surface of the sphere there is therefore a disconti- 

 nuity in the normal component of the electric force, and, since 

 there is no charge on the surface, this discontinuity can arise 

 only from a flux of electric displacement along the surface. 

 By symmetry this flux must be along lines of longitude. 



Let E be the tangential electric force along the lines of 

 longitude of the sphere r = vt and let 



-j* 



Ech 



(6) 



where the integral is taken over the infinitesimal thickness, 

 p, of the surface of the sphere, and dz is an element of length 

 measured along p. In other words, K^/Itt is the surface flux of 



