284 
MR. G. T. WALKER ON REPULSION AND ROTATION 
The results obtained in the preceding analysis are applied to the case of two thin 
spherical shells in the presence of an alternating current in a straight infinite wire. 
Fig. 7. 
If the line joining the centres of the spheres be taken as OX, and the axis OY be 
the shortest distance between OX and the wire W (the last two lines being taken 
perpendicular to one another), then calling the distances of the centres of the 
spheres from the origin b, b', and their radii a, a' (as with the cylinders), we have as 
the first terms of the couples upon the a, b and the a', b' shells— 
and 
where 
1 cfia'^c 
pV 2 d s Aj A' x 
(2b + b') l\ 
1 (d^a^c 
p“p'~ d s A t Aj 
(6 + 2b') V, 
A„ — 1677 ' 2 ay 2 + (2 n + l) 3 o- 2 , 
and I cos pt, or, cb, c, and d hav^e the same meanings as before. 
If we write h for \ (b + b'), the couples are 
7 27T 2 p 2 crer / «% /4 C 
P y*<p\ Aj 
(Gh ± d) I 3 . 
Hence 
(a.) If cr, a or c vanish, the couples vanish, as might be expected. 
()3 .) The signs of the couples fall into three cases : — 
