MOTIONS IN A SPHERICAL CONDUCTOR. 
543 
same frequency, very much smaller than in copper. But the integral currents induced, 
under the same circumstances, are much more intense in an iron sphere than in a 
copper sphere of the same size. Integrating (100) with respect to r through the 
thickness of the stratum in which the currents are sensible, we find for the components 
of flow at any point of the equivalent current sheet 
d 
dy) 
d 
u=K y^r]X. 
where 
t, ' =K,sl S -a; S‘> X ' i- 
K- 2m + 1 A „ J | -.) 
~~ 2 v / 277-R D * 
( 101 ), 
( 102 ). 
The disturbance in the field, due to the presence of the sphere, is given by 
rZX, 
ap=n 
where 
ap=n Zq = &c., c x =&c. 
X_«_ x = 
dx 
2% + 1./a . 
D 
■1 
Pd 
2»+l 
zv»2»+l 
X,, . . 
• (103), 
. (104). 
The order of magnitude of the first term within [ ] depends on the relative magni¬ 
tudes of <^R and p. So long as gR, though itself large, is moderately small in comparison 
with rifi the effect is mainly due to the induced magnetization of the sphere, and is 
much the same as if the substance were destitute of electrical conductivity, although 
the distribution of the magnetization within the sphere is very different. On the 
other hand when gR is large compared with ?ip the first term in [ ] is less important, 
and the results approximate more to the form which they would assume in the case of 
infinite conductivity. The following table gives the values of D and e for iron, in the 
case n— 1, corresponding to various values of ^R. 
gR. 
10. 
50. 
100. 
1000. 
D 
412 
455 
512 
1722 
€ 
l°-,23' 
6°. 10' 
11°.16' 
35°.30' 
The relation between q and the frequency p is for iron 
q= 1 '27 \/p. 
4 A 2 
