MOTIONS IN A SPHERICAL CONDUCTOR, 
527 
The equations (27) constitute the complete solution (of the first type) of (18) and (19) 
subject to the condition of finiteness at the origin. In the absence of this restriction 
we should have to add to the right-hand sides similar terms in which n is replaced 
by —n—1* 
In the space surrounding the conductor we have 
G =(4-4)( X '+ X -"-i> >•.(32), 
H =(4-4)< x “ +x -b 
where X„, X_ w-1 are solid harmonics of the algebraical degrees indicated by the 
suffixes. 
Since the values (27) of F, G, H make (v 2 +& 2 ) F=0, &c., &c., it follows by (1) that 
the components of current inside the sphere are 
(33). 
The flow of electricity is everywhere perpendicular to the radius vector, and hence 
(j)= const., inside and outside the sphere. 
From (27) and (32) we derive :— 
Inside the sphere : 
{(»+l 
Zrr 2 «+ 3 
V) 
Zn 
+ 1.2%+3 
7cV“ +3 
2 n+ 1.2+i + 3 
7V 2n+3 
11 - 
2%+1.2% + 3 
'I'n + i(kr)j z x, l r- 2n - 1 j 
h . 
( 34 )+ 
* These terms would be required in treating the case of a hollow spherical shell, 
t These formulae make 
•xa + yb + zc= — n.n +1 .ty a (kr) 
