1052 
MR. F. W. DYSON ON THE POTENTIAL OF AN ANCHOR RING. 
§ 8. To find the potential ofi a distribution ofi matter of density /3„ cos n^ on the 
surface of an anchor ring, at all internal points and at external ^joints near the surface 
of the ring. 
We know that for a cylinder 
and 
Let us assume for a ring 
nV; /E\» 
liV 1 
COS nx 
a 
cc\^^ 
= (r cos?zx 
I 
h 
27r/3t, \RJ 
J 
COS nx 
a /R\ 1 
4 \a, 
+ 4 Taj + 12-7^2""^ 
+ 'cos(7i-l)x +cos(n-2)x + 
a^fT.Y + ^\2n+l 1 . 
- - nx + |cos(w — 2)xj + . ■ 
...} 
4 \aj 
+ f^d(a)” l)x +jR"j cos»x+ ■ • ■ 
+ 16^' 
nij + • ■ 
+ 'oos{» + 2)x + ---} 
a j 
and 
a 
^=u; 
L»-CV“‘ / _L,^ . .rS/aV'-s r 2 »-l 
+ j(pJ (0 L«-2 
cos(n — 2) X +1 cos (n — 2) x| + 
+ I®> 
COS (w - l)x + ^ (^) COS5?.X + 
R 
...1 
+ i®MVK 
+ 1 
cos 
(n+ l)x + ^(k) cos(n + 2)x+ • • •} 
+ 16^31(1) cos0^-2)x + ... 
+ + ■■■ 
