CURRENTS IN INFINITE PLATES AND SPHERICAL SHELLS. 
351 
and hence 
C _ A 3 ac 
C + A'~ 2n + l 
Attvicoq, 
= — (2»+l)B‘* 
(30) 
To interpret these results, let Q 0 be the value of P 0 which would result from the 
magnetism inside the shell combined with the positive image (at the surface) of the 
magnetism outside the shell, then 
Q 0 =£(A+A , )^Y +1 ^P„*.(31) 
and 
P=tC(~) 
both the foregoing results merge into the equation 
or putting 
_'i(P + Q 0 ) 
E (/</>' 
W=Pr\ © = Qo^, 
R 
(32) 
d}$ cm 
V dr 
When a=oo, and r=a+z, the above equation becomes 
dB d\%_ ( m 
dz m d<f>~~ m d<f> ‘ ' ' 
indicating the spiral trail of images obtained by Maxwell. 
P 
If in the sphere we put r=e a , we have 
(33) 
(34) 
d§_ dm 
dp 
which is analogous to Maxwell’s equation, and may be interpreted in a similar 
manner. 
