MOTIONS IN A SPHERICAL CONDUCTOR. 
521 
medium. If F, G, H be the components of electromagnetic momentum, u, v, w those 
of electric current, at the point ( x , y, z), we have on Maxwell’s theory 
and 
V C F = —47 TU 
V 2 G = — 477 V 
V 3 H= —47 TW 
dx'dy dz 
(1) 
( 2 ), 
where v 3 stands for dd/dx- -f- ddjdy~ -f- dd/dz 1 , These equations hold good in conductors 
and insulators alike, provided that (as we shall assume for the present) the magnetic 
permeability in neither case differs sensibly from unity. 
In the conductors we have, if p be the specific resistance, 
pu — 
pv = 
pw— 
d<f> dF 
dx dt 
d(j) dG . 
dy dt ' 
dcf> dH 
dz 
dt 
J 
( 3 ). 
The expressions on the right-hand side of (3) are the components of electromotive 
force, $ being a function which, in the case of steady motion of electricity, is known 
by the name of the “ electric potential.”* 
In the dielectric we have, if f g, h be the components of electric displacement, and 
l/v 2 the specific inductive capacity, measured (like all our quantities) on the electro¬ 
magnetic system, 
477 V Z f= 
^TTV^g — 
d±_dF 
dx dt 
d<f> dG 
dy dt 
(4). 
Anv : h— 
dxf) 
dz 
dH 
dt 
v is the velocity of propagation of electromagnetic effects in the dielectric medium. 
If this be air, v also denotes the number of electrostatic units in one electromagnetic 
unit of electricity. 
The conditions to be satisfied at the boundary of a conductor are that F, G, H and 
* In other cases, as will be seen, this name is less appropriate. 
