G2 
MR. F. W. DYSON ON THE POTENTIAL OF AN ANCHOR RING. 
Hence 
ciU 
d(j) 
= 4 
d 
2cr .sin 6 cos cf^ + c~} c dc \R + 
If R + R, 4F ,^1 
= ’''“li + n,™"'sj- 
Difterentiating again we shall find 
2c2 
IHh 
F 
4r 
0(i: +lh) ^ cos l// - COS' xjj- 4 C0S3 xfj - COR 'Ixjj 
Therefore, at any external point, 
V = 
4F 
h + Ih 
i A COS'' ^ 
+ &c. 
7 t > 8 ^,4 
, E (R. + Ih) [ , 
10 2 ^4 
4^2 
5 + 8 cos rp — COS' xjj — 4 COS'”’' xfj — cos 2xfj 
lillj 
2cr 
2 COS' xp ~ 4 cos xjj + cos ‘Zip 
It 1 11 
+ &c. k 
where xp is the angle between K and and the modnlns of the elliptic functions is 
ip - Ji 
r7f h ' 
I have calculated the value of V, retaining only the terms 
4F 
R + R, 
1 — 
1 a2 o^l-l , E (R + Rda^ 
+ —ni:— 
for the values 
^ c 2c 3c 4c 
“ = 6- 6’ '5 
’ r;’ C, 
