3 
PROFESSOR C. NIVEN ON THE INDUCTION OF ELECTRIC 
P = — cor sin 6./3 — 
'J\jr 
~dr 
(l^r 
Q=+ojv sin 6.a—^ e }» 
( 19 ) 
K= 
d\jr 
r sill deity 
Since, with the present notation, we have U = 0, Y=0, W =cor sin 6, we shall choose 
the same forms for the vector potentials and current-functions as in § 8, viz. :— 
A.=|(Por).F.=0,G 0 =-^,H 0 =^. 
dQ 
F=0, G= 
dV tfP 
sin 6d<fi’ ~ dff 
The magnetic force a. /3, y is clue to both potentials, and thus (see § 3 B, c), 
a — 
1 d 
sin 6 dO 
—. sin 6 
d? + P 0 1 d> P + P 0 
cW 'sin 2 6 c /</> 2 J’ P 
1 ^.F + P 0 
r circle 
r- 
1 cZ 3 .P + P n .r 
r sin 9 clrd 
The currents will be denoted by 
where 
observing that 
d<£> d<$> 
u — 0 , v-- - vj= a , 
sm 6cl(j) cie 
47r<E>=— V 2 P 
v 2 P 0 =o. 
( 20 ) 
Substituting for P, Q, R in terms of u, v, w by Ohms’ Law, the last of equations (19) 
becomes 
cZ<l> city 
This is satisfied by taking 
c/0 r sin 9d(f) 
■ • (21,) 
• ■ (21,) 
and the first of equations (19) becomes 
. n d 2 P + P 0 .r . /.vr 
OJ SU1 0——~rz -cr Sill 0—,., = 0, 
circle circle 
or 
cry= co. (P + P () ).(21 3 ) 
