MOTIONS IN A SPHERICAL CONDUCTOR. 
525 
On the above assumption, (2) become 
pu=— ( ~ —\F, See., See, 
(17), 
whence eliminating u, v, w by means of (1) we obtain as the equations to be satisfied 
in the interior of a conductor 
^+OF = -ff 
and 
where 
(v*+F)G=-|g ^ 
(v*+OH=-fg 
dx+cly + dz ~~ 
In the dielectric we have 
df 
47tX 
V 3 F=—47t ‘ = — AnXf, Sec., &c. 
Cl o 
Eliminating/, g, h we obtain 
477 ^/=— XF, &c., &c. 
Ctt/j 
(V s +/)F = --'^' 
(v=+i s )G 
X dx 
__ _/ //> 
X dy 
with 
where 
(vH/)H=-ff 
/G ffl_ 
dx ' dy + dz ~ 1 
X 2 
d v 2 
(18) 
(19) , 
( 20 ) . 
( 21 ), 
( 22 ), 
(23). 
So far our equations are exact. But it appears from various physical analogies 
(more especially in Acoustics), and it will be verified in the course of this paper, that 
when the dimensions of the conductors are small compared with j~ l the phenomena 
are sensibly the same as if j were =0. Now, in air, v=3 X 10 10 [C.G.S.], whence 
1 1 = v/iX = 3 x 10 10 /iX. Since X is proportional to the rapidity of the electrical motions 
mdccclxxxiit. 3 Y 
