[ 364 ] 
XXXY. Mutual Induction. By Prof. D. N. Mallik *. 
IF M be the potential energy between any two shells r 
ty, -^r' the magnetic strengths of these shells, and co the 
solid angle subtended at any point of one of the shells by the 
other, and dn an element of outward drawn normal and ds 
an element of surface of the first, then we know that 
¥° ds. 
=^'jl: 
Again, let ds' be the element of surface at any point of the 
second surface and 
p = distance between the points, 
dn' = element of outward drawn normal of the second 
surface. 
Ex. 1. Two circular wires in any relative position to each 
other, carrying currents i, i'. 
Let c l5 c 2 be the radii of the spheres of which they are 
circular sections, the origin being the centre of both 
spheres. 
Then 
M = -ii' {[^ . A ._ ds . ds' 
J J OCi dc 2 y/c^ + c 2 2 — 2c 1 c 2 cos r 
= -*' [*T • 5T- ["-* ( -T Pn(cosr) . c?dpc 2 uA dW 
== ii' 2 I n 
c n + l 
(n 4- 1) -^- P« (cos r) dfi dfjJ dcf> d<j>' ; 
c 2 
where c ± > c a , 
r= /.between any two radii of the two circles, and 
fju, </> have their usual meanings. 
But 
PJcosr) = P^)P n cos(r')42T:(^)Tr(cos/)cosm(^-f') 
and 
P w (cos r') =P w ^0P„(cos 6) + 2T:V)TJr(cos 0) cos m(f -0"'X 
* Communicated by the Author. 
