MOTIONS IN A SPHERICAL CONDUCTOR. 
541 
7T \ 7T 
(91). 
In iron we have /x=403 (Thal^n), p=9827 C. G. S. The lowest root of (89), in the 
case n=l, is then AR=l*42687r, and the corresponding value of r is 
t=-0256R 3 . 
The duration of the free currents is very much greater than in a non-magnetizable 
sphere of the same size and of equal conductivity. For an iron ball one foot in 
diameter the above value of r is six seconds. For an iron globe of the size of the 
earth it would be 330,000,000 years. 
The magnetic susceptibility of the substance has the effect of modifying the 
character, as well as the duration, of the natural modes of decay. Inside the sphere 
we have 
lct+mb+nc= _ ”•” + 
Since, by (89), this is almost zero at the surface, the lines of magnetic induction 
inside the sphere are for the most part closed curves. Their forms, in the first two 
modes of the class n= 1, are given by the figure of § 4. The surface of the conductor 
is not, however, in these two respective modes, now represented by the two spherical 
surfaces there shown, but rather by two concentric spherical surfaces of radii smaller 
(for the case of iron) by about the four hundredth part. 
For the free currents of the second type we have, by (88), 
^ n {JcR) = 0 
(92). 
The natural modes of decay are exactly the same as when /a= 1, but the persistency is 
in each case greater in the ratio of /x : 1 ; viz., the values of r corresponding to the 
various roots of (92) are given by (91). 
10. In the case of induced currents caused by a periodic variation in the magnetic 
field the value of X„ is to be found in the same manner as in § 5; and X_„_ x are 
then determined by (86) and (87). If p be the frequency, 
A= (1 — i)q 
where now 
<2 2 =47 r'fip/p .(93). 
Let us examine first the case where Add is small. We then have, at the surface, 
X*— -;-TT X 
n,fjL + n +1 
4 A 
(94), 
MDCCCLXXXIir. 
