MOTION'S IN A SPHERICAL CONDUCTOR. 
549 
For the first harmonic constituent we have the simple formula 
cr i 
S(xf' + yg' + zh') 
R 
(135), 
if (J, li denote the components of the electric displacement which would obtain at 
the origin if the spherical conductor were removed. 
The equation (134) expresses that so long as pp is small compared with v 1 the 
surface-density of electricity at any point will have at each instant the statical 
value corresponding to the distribution of electromotive force at that instant due to 
the external system. The arrangement of the currents in the sphere by which the 
changes in the superficial distribution are effected will however depend materially on 
the relation between the period of the changes in the field and the time of decay of 
free currents in the sphere. The discussion of this point can be conducted as in the 
case of the solutions of the first type, treated in § 5, and the results are analogous to 
those there found. When the spherical harmonics involved are zonal, tire work and 
the interpretation are much facilitated by the use of the current-function T' - , whose 
value is given by (56). 
i 
MDCCCL XXXIII. 
4 B 
