526 
PROFESSOR H. LAMB ON ELECTRICAL 
it appears that in all practical cases j~ ] is very large. We will therefore assume for 
the present j=0, which comes to the same thing as assuming that the velocity of 
propagation of electromagnetic effects in the dielectric medium is practically infinite. 
The equations to be satisfied in the neighbourhood of the conductors then are 
V 2 F=0, v 2 Gl = 0, v 2 H = 0 
tjF dG dfl_ 
dx ' dy + dz 
(24) 
(25) . 
Since /v 2 F+TOV 2 Cf+MV 2 H must be continuous at the surfaces of the conductors it 
appears at once that on the present assumption we shall have, at those surfaces, 
lu-\-mv-\-niv=6 
(26). 
3. Proceeding now to the special problem of this paper, viz., the case of a solid 
spherical conductor surrounded by air, let us take the origin of coordinates at the 
centre of the sphere, and let r denote the distance of any point from the origin. It 
may be shown, as in the papers on the “ Oscillations of a Viscous Spheroid,” &c., 
already referred to, that the solutions of the equations (18), (19), and (24), (25) are of 
two distinct types, which are quite independent of one another. 
First Type. We have 
In the conductor: 
F=UHyi-^~)F 
dz 
where is a solid harmonic of positive integral degree n, and the function \fj n is 
defined by 
^(C) = l- oo^ , o + o, otr.^ -R i r r &c - 
2.251 + 3 1 2.4.2«, + 3.2?t + 5 
d \» sin f 
= ( —)"3.5 . . , 2n + l. 
from either of which forms we readily deduce 
M0=' 
m, 
'K+i (0 
^( 0+^+3 ^'( 0 =^- 1(0 
25^ + 1.251 + 3 
(28), 
('29), 
(30) , 
( 31 ) , 
