314 
MR. G. T. WALKER OK REPULSION AND ROTATION 
x = b -j- r sin 0 cos ^ 
= b' + r sin O' cos ft 
y — r sin 0 sin <£ 
= r sin 0' sin (p' 
Thus (if b — V Ezd) 
so that 
z = r cos 6 
--- r cos O'. 
v sin O' cos <f>' = r sin 0 cos <f> d " j 
r sin O' sin ft = r sin 0 sin <£ h 
r cos O' = r cos 0 J 
r' 2 = r 2 + 2 dr sin 0 cos </> + d 2 , 
(xiii.), 
and when r — a and is less than d, 
1 _ 1 
r' ~ d 
a . n 
1 — - sm 0 cos <p . . . J > 
so that, omitting second harmonics, 
sin O’ cos </>' If 3 a . > , . a 
- - - — = — ( 1 — - sin 0 cos (p ) (a + a sin 0 cos </>) 
d 2 d* 
sin 0 cos <p -f- higher harmonics. 
sin O' sin cp' a sin 0 sin 
“d 2 = dF~ 
cos O' a eos 0 
r' 3 ~ d 3 " • ‘ ‘ 
20. Hence if the currents in the a, b surface produce upon that surface a magnetic 
| )otential 
n = (A sin 0 cos </> -j— B sin 0 sin <f> + C cos 0) cos pt 
+ (D sin 0 cos -j- E sin 0 sin (p + F cos 0) sin pt 
+ harmonics of second and higher orders, 
and if the currents in the a', b' shell produce upon itself a potential Cl', whose value is 
distinguished by dashes from the above, then the value of fi upon the tt, b shell 
will be 
