MOTION'S IN A SPHERICAL CONDUCTOR, 
provided 
2 ItoW I 
( 66 ). 
For the full interpretation of our formulae it would be necessary to disentangle the 
real and the imaginary parts, and to discard one or the other. The results would be 
very complicated, even for the simplest harmonic constituent (n=l). There are 
certain cases, however, in which we can use methods of approximation, and so 
deduce the results of interest without much difficulty. 
Thus, in the first place, let us suppose that the changes in the field are comparatively 
slow; more precisely, let the frequency p be very small compared with p/ It 3 . Since 
JcR is then a small quantity, the expressions for the currents in the sphere are 
approximately, 
2 Trip i 
> d 
ydz 
P ' 
2irip i 
f _ d 
P 
\ dx 
2nripi 
f d 
P 
K X dy 
d 
~ Z dy. 
-4) x » >■ 
(67). 
This is the result which we should have obtained by neglecting ab initio the mutual 
influence of the currents in the sphere. The disturbance in the field due to these 
currents is given by 
ai =j£x„r-^' 
b l= J^X„r-^ >■.(68) 
where 
y_— d>ir~inpTi~’ l+?> 
2n+1.2n-\-?>.p 
For spheres of the same size the disturbance is cater is paribus proportional to the 
specific conductivity. 
Next let us examine the other extreme case, where the frequency p is large com¬ 
pared with p/It 3 , and consequently /It is a large number. When £ is large, the 
formula (28) becomes, approximately, 
sin (f+ttw) 
«£) = (-)*•3-5 • • • 2n+l. V„ +1 V . 
3 z 2 
