320 
MR. G. T. WALKER ON REPULSION AND ROTATION 
The Couples on two Spherical Shells, produced ly a Filament of infinite length, per¬ 
pendicular to the Line joining their Centres, and alternately Magnetised in a 
direction at right angles to its length. 
Fig. 41. 
24. Let the same axes be taken as before, and let the direction of magnetisation 
make a with the plane XOZ. The filament is equivalent to an electromagnet formed 
by currents 
K 
— cos pt, 
K 
parallel to OZ at x — 0, y = c, and 
K 
— — cos pt 
K 
at x— — k sin a, y = c — /c cos a, in the limit when k is small; the strength of 
magnetisation will then be K cos pt. 
As before, a coefficient of magnetic potential 
1 /( 6 , V, v) 
due to the current I cos pt, will become 
K 
— sin a 
fi- COS a 
06 ' 
due to the electromagnet, and if 
p cos y = h\ 
p sill y — C j 
then on reference to previous work it will be found that whereas we had for V A due 
to I cos pt, 
21 ac , , 
— —it — fourth powers, 
P' 
now we shall have 
2 Ivy 
o 
P 
[cos a -f- 2 sin y sin a — y 
