534 
PROFESSOR H. LAMB ON ELECTRICAL 
The values of the functions X ?i are to be found as follows. It is easily seen that if 
a 0 , b 0 , c Q be the components of the magnetic field due to the inducing system alone, the 
expression xa 0 -\-yb 0 -\-zc 0 must satisfy the equation 
V*(xa 0 +yb 0 +zc Q )=0 
at all points outside the inducing system, and vanish at the origin. Hence it must 
admit of expansion in a series of solid harmonics of positive integral degrees, say 
xa Q +yb Q -\-zCu=t™®n .(61). 
But it appears from (35) that we must have 
xa 0 -\-yb Q -\-zc 0 = —'£™n.n-\- l.X„ 
(62). 
Comparing with (Gl) we find 
X, 
n.n +1 
(h) 
For instance, let the magnetic field due to the inducing system be sensibly uniform 
in the neighbourhood of the sphere, say 
We find 
«o=I, k 0 =°> c o—0- 
X] =— ^Ix ; Xo=X 3 =&c. = 0. 
The formulae (33) for the currents in the sphere then become 
u— 0 
v— —Di p^krj.z j>.(63), 
w— D xp^Jcrj.y 
where 
1J = 
m 
S7J"v^ 0 (CR.) 
. (6i); 
and the disturbance (cq, b v c L ) in the magnetic field, due to these currents, is given 
