PRODUCED BY ALTERNATING ELECTRIC CURRENTS. 
301 
On putting 
we get when a < p, 
b = p cos y 
c = p sin y 
TT T i P 2 + cos 7 + 6 + a 2 
H 0 = - I. log -- — -cos pt 
= — cos pt 
21 cos pt 
- cos 0 + y — COS 20 + y + — cos 30 + y 
IP 
On substituting for 
p cos 6, p sin 20, he., 
we get to the fourth power of ajp, 
- —cos46 + y. . . 
H 0 = + I cos pt 
— log 
+ 
+ 
+ 
b 2 + <? 
D 2 “ 
a? 
(6 s + c 2 ) 2 
2a 2 
(¥ + c 2 ) 2 
2 a 
b 2 + & 
(b cos 6 — c sin 6) 
(— c 3 + b 2 cos 20 — 2 be sin 20) 
(3 bo 2 — b 3 cos 30 — c 3 — 3b 2 c sin 30) 
2 (b 2 + c 2 ) 4 
(6 4 + c 4 — 6& 2 c 3 cos 40 — 46c b 2 — c 2 sin 40) + .. 
8. The currents set up in both cylinders will clearly be parallel to their axes, and 
if those in the a, b shell produce at points on itself the momentum 
H = M 0 sin pt + Q 0 cos pt 
+ (M x cos 6 + N : sin 6) sin pt + (Q 2 cos 0 -f Rj sin 0) cos pt 
+ (Mo cos 20 No sin 20) sin pt + (Q 3 cos 20 + R 3 sin 20) cos pt 
+ higher harmonics, 
and if the currents in the a, b' shell produce on itself a momentum, distinguished 
from the above by the dashing of the letters 
H = M' 0 sinp£ + Q' 0 cos pt 
+ (M\ cos 0 + . . .) sinpt +(...) cos pt 
+ (M' a cos 20 + . . .) sin pt + . . . 
4- higher terms, 
