310 
MR. G. T. WALKER ON REPULSION AND ROTATION 
If the external field have magnetic potential O 0 , and if 
1 d /T1 . 
D ° = ~ adr^ ° T ) 
(ever distinguishing quantities that refer to tire externally applied system by a zero 
suffix), then the equations connecting the components of the vector potential with 
the components of induction are satisfied by 
Tfi _ p, r\ _ 2 ^^0 TT _ _ SPo 
o ~ ’ 0 “ a sin dd<j> ’ 0 “ add 
The equations giving the currents are 
— (7 
_ d 1 g 
sin 6 dcf> dt a sin 6 dcp 
(P + Po) 
0 -v/^ 
a d6 
0<D d 
+ OTaV, = “ W 
. dd 
and are satisfied by 
Let us consider the case 
dt 
*J( p + p »> 
difr 
a sin d 0(/> 
= 0 , 
«* = |(P + P 0 ). 
n„ = A (-) Y„cK 
where a is the radius of the shell, and Y n is a spherical harmonic of degree n. 
We have 
P 0 = — A ~ eV t _ _ A -JL 
a 11 1 n + 1 n + 
- Y n e ipt at the surface. 
If due to this 
then 
<£ = B Y n e ? pl ; 
p = sTTi By A' 
at the surface, and the equation for B is 
<xB — ip 
47 ra ,. a . 1 
o-r B — r-A I 
2n + 1 1 + n 
therefore 
