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PROFESSOR C. NIVEN ON THE INDUCTION OF ELECTRIC 
(1.) Within the conductor 
c OT _, (IF d\Ir 
V ~T : -- — 
47r dt dx 
dC r 
dt 
di]r 
~dy 
a 
47 T 
6=0, V~l//=0. 
ddf 
dz 
(2.) Outside the conductor C'=0, and K' may be neglected ; therefore 
V 2 F' = 0, v 2 G'=0, V 2 H' = 0, 
e // = 0, V 2 xJj'= 0, 
(e" = electric density outside). 
(3.) At the surface of the conductor 
dF dF' 
F —F' n 
’ dN~dFr ® c * 
d -£+Z= 0 ’ ^=ZF+mG+«H, ^=f 
47r(e / ) 
_dj/ 
dN 
d-yfr 
dN' 
(4.) When £=0, v//=0, xfj'= 0, e'=0, and the currents are confined to the 
conductor. 
When the conducting substance is moving in any manner, the equations of electro¬ 
motive force are (Maxwell, Yol. II., Art. 598) 
P=w-*-f 
Q=“-^- f 
B,=0x—ay—-^ 
dyjr 
dx 
d-yfr 
dy 
dyfr 
dh 
If we differentiate these with respect to x, y, z and add, putting for 
its electrostatic value 477 (e), we find 
dF rfQ rfK 
dx' dy dz 
4i7T 
(ux+vy -f mb) + 2 (aw, + ^cuj+y<u 3 ) — V 2 i/( 
( 12 ) 
