MOTIONS IN A SPHERICAL CONDUCTOR. 
539 
whilst (2) and (3) are unaltered. Hence the fundamental equations (18), (19) of our 
method retain the same form, provided 
The distribution of the induced magnetization in the conductor will be solenoidal. 
Hence if A, B, C be the components of this distribution, the corresponding' parts of 
F, G, H will be 
dN_dM rfL_<7N 
dy dz’ dz dx’ dx dy ’ 
respectively, where 
L=|| j y dxdydz, M= (j dxdydz, N— [jj- dxdydz. 
The integrations are supposed to extend throughout the magnetized substance, and r 
denotes the distance between the element dxdydz and the point for which the values 
of L, M, N are required. Hence F, G, H are continuous at the surface, but their first 
derivatives, and consequently a, b, c, w r ill be discontinuous. Let us distinguish the 
values of a, b, c just inside and just outside the conductor by the accents ' and ", 
respectively. Then the parts of a, b', c due to the induced magnetisation are 
and those of a", b". c" are 
d V dV dV 
~^dz’ ~ [X dy ’ ~ fX dz > 
dV dV dV 
dx ’ dy 3 dz 5 
where Y is the potential of free magnetism, viz.: 
V=([(ZA + mB+«C)y, 
dS denoting an element of the surface of the body, and l , m, n the direction-cosines of 
the outwardly directed normal to cZS, and the integration being taken over the surface 
of the conductor. Hence 
a"— 1 =47tZ(ZA+toB+wC), &c.; 
r 
or, since 47rpA=(ju — l)a', &c., 
a—l) l (la mb’-\-nc)=iJLa"~ 
b 1 -\-([x—l)m(la'-\-mb'-\-nc')=y.b" >. 
c J r {y — 1) n (la -f- mb' + no) —yc" ^ 
( 8 - 1 ). 
