302 
MR. G. T. WALKER ON REPULSION AND ROTATION 
then in all we have, that on the a, 6 cylindrical surface, the momentum of the field 
that produces currents in that shell, is (to the 4th power of a, a, as will afterwards be 
explained) 
— 1 log cos pt 
2 a 
— I 75 - 5 (6 cos 0 — c sin 0) cos pt 
0“ + C“ v ' ± 
eft - 
+ I ^ /)2 + ~ ° 2 cos 20 — 2 be sin 20 ) cos pt 
, T 2a 3 - - 
+ t + (36c 2 — 6 3 cos 30 — c 3 — 36 2 c sin 30) cos pt 
4- I 2 + py (^ 4 + ° 4 ~ 66 2 c 2 cos 40 + 46c c 2 — 6 2 sin 40) cos pt 
+ 5th powers . . . 
+ M ' 0 sin pt + Q ' 0 cos pt 
+ (M\ sin pt + Q\ cos pt) a - + ^cos 0 + cos 20 . . 
+ (N\ sin pt + K x cos pt) ^sin 0 + ^ sin 20 . . )) 
a*% 
+ (Mhsin pt + Q 2 cospt) (1 + . . .) 
+ 5th and higher powers. 
9. But if D„ = 4iT 2 a 2 p° + <r 2 n 2 , an external field of momentum 
H 0 = ( V M„ cos n0 + 'N„ sin n0) sin pt fi- ('Q„ cos n0 + 'R„ sin n0) cos pt 
at the surface of the a, b shell will produce in it currents whose momentum at the 
surface is by (v.) 
H = — v [27 jap sin pt + c m cos pt] ['M* cos n0 + V N„ sin n0] 
71 
i llTCt r p 
- -p — [27ra_p cos pt — an sin pt] ['Q„ cos n0 + 'R, t sin 710]. 
Applying this to the values of H and H 0 that we have recently found, we see that 
to the 4th powers of a. a (as we shall shortly explain) 
