316 
MR. G. T. WALKER OK REPULSION AND ROTATION 
Now we have shown (xi ) that a field 
produces a current function 
n 0 = Y J*. 
The P of this is 
2 n + 1 ap . . - . „ . 
* = (n+l)A. ^ Pa ~ *' 2 " + 1 ^ Y ^‘ 
47 rci /«\* H 
2n + 1 ' ' [rj ’ 
and its magnetic potential at the surface 
47rn 
-<t>. 
(2 n + 1 ) 
Hence the magnetic potential of the currents induced in the a, b shell by the system 
It 0 = ('A sin 9 cos (f> -j- 'B sin 9 sin <£ -J- 'C cos 9) pt 
+ ('D sin 9 cos </>-}- 'E sin 9 sin (j> fi- F cos 9) sinpZ 
will be 
n = 
‘Inrpci 
[('A sin 9 cos <]> + 'B sin 9 sin (f> + 'C cos 0) (4 77 -pa cos pt + 3cr sinpZ) 
+ {'D sin 9 cos <f) + 'E sin 9 sin rf> + 'F cos 9) ( 47 rpa sin pt — 3cr cospZ)]. 
Comparing this with 
(A sin 9 cos <£ + B sin 9 sin <f> + C cos 9) cos pt 
-fi (D sin 9 cos <^» -J- E sin 9 sin <f> -f- F cos 9) sin pt, 
we have, on giving 'A . their values, 
A =- 
cirpa 
■2Iac 
4 77 -pa — — 
O to 
la a - 
A' 
B - 
C = 
D = 
E 
jirpa 
"aT 
Inrpa 
a7 
/ 2IaZ> aa' 2 ^.A 
4 ^ a (- 7 + ^ b )- 3 , 
/<m' 2 , N ,\ „ aa' 2 " 
c )~ 3ct #- F . 
an 
- E' 
2irpa r 
A, 
J7T/. 
A, 
2Iac 
OCT - , - 
2««' 2 
p - fZ 3 
21c5 «a' 2 
A') + 477-pa ( - D' 
2aa 
n l \ P' 
F =T[ 3<r (> c ') +4 ^^ F ■ 
B') + 47rpa (^ E' 
aa 
'2 \ “I 
