CURRENTS IN INFINITE PLATES AND SPHERICAL SHELLS. 
345 
d? 
On the two faces of the plate P and — are to change continuously on crossing the 
faces. 
The final result of the calculation gives 
a (/c 3 - /P)(^-<r^) 
• • (16) 
wl 
hen b is indefinitely small, we treat R,= p as finite, and therefore while k is finite /x 
47 rmt 
is infinitely great, but jx~b is finite and equal to -——— .i. To find C, we have then 
it 
C _/P — fj? — 
C + A 2 K k( 0^ — e~^) + fjb + c - ' 1 '') 
(k~— fj,~)b 
07 0 
1+A+ 
(3 
i+^+eJ+^4 
J U 
27rwra 
If Q he the value (due to a positive image of P 0 ) on the positive side of the plate, 
and P the value of P due to the currents, 
Q=^Ae'HJ /l ,(K P )e +K: , P= tCe^'hj J K p)r-^ 
then, putting 
27TO) 
(17) 
cl? cl? _ dQ 
clz ~ m dcj> 
(18) 
This corresponds with Maxwell’s result; see also equation (34). 
Spherical shell and sphere. 
§ 18. We shall now treat the case of a spherical shell, whose outer and inner 
radii we shall take to be b, a. . 
The expressions for the electromotive force are (taking dx, dj, dz to correspond 
respectively with dr, rdd, r sin ddcft). 
