300 
MR. G. T. WALKER ON REPULSION AND ROTATION 
The shells are thin; let their radii be a, a, and their distances from the origin b and 
b' ; let the distance of the wire from the origin be c, and the current in it I cos pt. 
Let the position of a pt .P in space be determined by its distances r, r from the 
axes of the shells and the angles 6, 6'. 
Then if b — b' = d we have 
Hence 
therefore 
and if r < cl, 
r cos 6 = r cos 6' — d 
r sin 6 — r sin 6' 
re -w _ r ' e -ie — P . 
_1 _ 
(— d + r’e~ i6f ) n 5 
otiiO 
cos nd (—)“ 
r n d n 
, . nr' /1/ , n.n A 1 r' 2 , 
l +T c OS 0 +_ T __ C0S 2 e + ... 
sin nd ( — ) n 
cl' 1 
n' . n.n + 1 / 2 . 
n — sm 6 4- ——— ~ 2 sin 2d + . . . 
d 
2! d? 
So, too, if r < d, 
and 
r'e ie = re} 6 + d, 
cos nd' 1 
r' n d n 
sin nd' 1 
r' n ~~ d n 
\ . n r n.n + 1 r 3 . 
1 + ~d C ° S 6 + wi sm 2d + • • ‘ 
2! d 2 
r . _ , n.n + 1 r 3 . - 
-ir# sm2(l + 
7. Hue to the alternating current in the wire we have, over the a, b cylinder, 
TT T , (c — a sin 0) 2 + (& + «■ cos dY 
H 0 = — I log-^-cos pt 
where D is a constant. 
