532 
PROFESSOR H. LAMB ON ELECTRICAL 
£2 re 
T-——.n.«+1 .rxjjjkr) at,, sin 0(7# 
47T 7 J a 
7j 2 
= —— ^(ytr)^ 
d<p, t 
dd 
(56). 
Here 9 denotes the colatitude (viz., ra-=rsin 0), and is supposed expressed in 
terms of r, 0. The integration is effected by means of the differential equation of 
zonal harmonics. The most interesting case is when n— 1. Writing &> 1 =r cos 6, we 
have 
The forms of the lines of flow (' V F= const.) corresponding to a series of equidistant 
values of T are shown in the figure. The different systems of lines of flow are 
separated by the spheres for which xjj 1 {kr) = 0. The drawing includes the first two of 
these. In the most persistent mode the inner sphere must be taken to represent the 
boundary of the conductor; in the next mode the second sphere must be taken; and 
so on. 
It appears from (44) that the currents in the sphere exercise no magnetic action in 
the external space. Conversely no motions of the present type can be originated by 
any electromagnetic operations outside the sphere. It will be shown further on that 
both these statements require qualification when we take account of the finite value 
of v. 
By combining in the proper way solutions of the two types we can represent the 
