306 
MR. G. T. WALKER ON REPULSION AND ROTATION 
changes sign if it be applied to the a, b' shell instead of the a, b ; the direction of 
rotation is negative when b — b' is positive, i.e., is as indicated in the figure, and is 
d priori likely, since the repulsion is likelier to be stronger where the currents and 
Fig. 31. 
X 
Y 
field are stronger, i.e., on the side nearest the wire of the shell to the left and on the 
unshielded side of that to the right. The couple changes sign with c as it should, and 
vanishes if cr or a vanish. The term of the eighth degree vanishes when p = d, i.e., 
QQ' = Q'W. 
The Effects on two parallel Thin Infinite Circular Cylindrical Shells of a Thin 
Filament parallel to them, and alternately Magnetised in a direction perpendicular 
to its Length. 
14. Let the same axes and coordinates be taken as before ; the filament may be 
regarded as an electromagnet consisting of a current 
•A 
— cos pt (where k is small), 
K 
parallel to OZ at x = 0, y = c, and a current 
A 
-cos pt, 
K _ 
parallel to OZ at x — — k sin a, y — c — k cos a. 
The direction of magnetisation will then make an angle of a with OX, and the 
strength will be A cos pt per unit length. 
If L . f (b, b ', c, cl) were a coefficient in the expansion of the electromagnetic 
momentum in the case of a current Icos£>£ at x — 0, y = c, then, with the electro¬ 
magnet, that coefficient will be the limit of 
o 7 
A A 
- f (b, b', c , cl) — — f (b + k sin a, b' + k sin a, c — k cos a, d), 
i.e., 
A 
