CURRENTS IN INFINITE PLATES AND SPHERICAL SHELLS. 
The components of the current are 
u = 0, v= 
d<£> dd> 
- W — 
sin delft d6' 
The equations, therefore, of the current are 
which is satisfied by 
R d<\> 
47t sin 0d<p 
(l~V d\fr 
a sin 6d<pdt a d6 
+ 
E 
a? p 
d\fr 
47 r dd a dddt a sin 9d<p' 
1 rfP 
+=°- *=i A 
Outside the sheet and within its inner surface, 
F=0, g=AL H=-A 
sm 0d<p dd 
V 2 P = 0. 
Hence 
outside 
inside 
h+ i 
P n =2A - ILe^'s* 
r \ n r 
Pi=SA(M U„<T*V; 
at the surface <f> =—^SAU„e A hP\ —— • 
a 47 t 
But we have also the further condition 
hence 
and therefore 
dl\ dV ,, 
X»=i(2n+1) 
p 0 =2:a(-)" +1 ltc-^ +1 ^ 
/r\® R 
Pi=SAf-J U*e-^ +1 W. 
This corresponds with the result obtained from the more general investigation of 
last article. 
MDUCCLXXXL 
