﻿leased on Free Electrons. 

 shown by 



m 8 n fi V=€ 2 [l-H+ ^(«i 2 -«s 8 ) •••] 



„r 3nfa 2 -j 



= e- 1 — \c s + —a'a~--' * or > l largo, 



or 



_ in ■ jl , 3w ^ 2 i 



— € I 1 2 C s -t ^^ 2 ... „ „ „ 



.10815 



K23) 



according as the satellites lie outside or inside the double 

 ring, a considerable departure of r : a from 1 being 

 presumed, 



[a n a n+2 ~| 



where a„ = 



1.3...(2n-l) 



; and on this term depends the 



2 .4 ...2n 

 •fluctuation. 



For positions outside the plane we are concerned with 



X I r* + a 2 - 2ra \A -y 2 cos (</> 4 2/?tt//i) } ~ m > 

 and it may be sufficient to write the value of the mean term 



" [I -TsW-V + S (35/*«-3<y + 3) ...] 



When a/?' is widely different from 1, the field due to a 

 •double ring is given by 



XT ne{a l 2 —u 2 2 ) , 9 „ 1x ,.., 



U *= 4^ ( M } outside > 



and by 



XL = ne — T ( — 3 3 ) (3yn 2 — J ) inside. 



La, a 2 4 Vh 3 a 2 V J 



In a rough way one may say that the cone 3//, 2 =l divides 

 the Hues of approach in which an electron would be repelled 

 and its path show reflexion, from those in which the path is 

 •continued through the rings R n (0) with deviation. 



4 A 2 



