PRODUCED BY ALTERNATING ELECTRIC CURRENTS. 
311 
- A 
B = 
tap 
n + 1 
4inrpa 
2n + 1 
+ cr 
_ 2n + 1 ap 4nrpa — i 2n + l<r 
n + 1 I 67 r 2 a 2 p 2 + 2?i + 1V 2 
Denoting then 
I6ir 2 a 2 p) 2 + 2n + 1 'o' 2 
by Awe shall have corresponding to 
O 0 = AY„ cos pt 
at the surface, the value 
4> = A ~“' 1 + , y '-- Y lt (4irpa cos pt -f 2?? + 1 cr sin pt), 
(n + 1) A„ v 1 1 
and corresponding to 
fl 0 = BZ ;l sin pt 
$ = BZ„ } (47r»a sin pt — Zn + 1 cr cos pt.) 
n + 1A„ v r 1 
17. If the components of magnetic induction or magnetic force along the directions 
Sr, r SO, r sin 6 S<f> 
be a, /3, y, the components of electromagnetic force in these directions will be 
04> „ 0<J> 
yv — pw, or — y ^ ^ Q ^ — p 
aw, 
or 
— av, or 
a sin 0 S<j) ^ aSO 
a SO 
04> 
a 
a 
’ sin 0 S<f) 
The couple about the axis of z will be the integral over the surface of 
— av .a sin 0, 
where in a it will be sufficient to take into account the external field (as in the case 
of the cylinder), for the shell will not exert any couple on itself. This couple is 
0 $ 
fb s -“af • 
