514 
PKOFESSOE, A. SCHUSTER ON THE DIURNAL 
If u, V, ID Le the components of electric current, the ecjuations of induced currents 
are 
pu — — F, pv = •— G, pio = — H, 
where p denotes the specific resistance. Eliminating v, v, id by means of the relations 
V"F = — iTTip V'Gr = — Ittu, V^H = — Attw, 
we find that at all points within the sphere F, G, FI must satisfy the equations 
(V" - /r) E = 0, G = 0, H = 0, 
where 
(/F fTG _ 
dx dy d z ~ ’ 
e = ^e-i. 
The appropriate solution of these is 
F = x.(^n-(y£-2^y.. 
d d 
where r = [x^ + 2/" “h denotes a solid harmonic of degree u, and 
x.( 0-1 + r‘27r+‘3 + 2:x 
.2n + 3.2/1 -t- 5 
siiih ? 
= 3.5...2«+l.£-^j 
. + 
The total magnetic potential outside the sphere will be 
where n_„_i is the part due to the induced currents. The values of F, G, H at 
external points will then be 
F == 
G = 
11 = 
d d 
yjz-^ 
1 1 
, ,, - — 
dyj \ n + 1 n 
I '' 
d 
X — 
dz \n + 1 " 
- - O. 
X 
dy 
d 
V T. 
dx / + 1 
1 1 
- - fi . 
