[ 43 J 
II. Tlie Potential of an Anchor Ring. 
By F. W. Dyson, B.A., Fellow of Trinity College, Cambridge. 
Communicated, by Professor J. J. Thomson, F.R.S. 
Received Marcli 19,—Read May 5, 1892. 
Introduction. 
In this Paper I have developed a method of dealing with questions connected with 
Anchor Pings. 
If r, 6, (j) be the coordinates of any point outside an anchor ring, whose central 
circle is of radius c, then 
_ d4 _ 
- 0 v /+ d — 2cr sin 6 cos f) 
is a solution of Laplace’s equation, finite at all external points and vanishing at 
infinity. Let this be called I. Then cTLjdz is another solution ; and two sets of 
solutions may be found by differentiating I and dljdz any number of times with 
respect to c. These solutions are symmetrical with respect to the axis of the ring. 
In the first set « is involved only in even powers ; in the second set in odd powers. 
Take a section through the axis Oz of the ring and the point P, (r, 9) cutting the 
central circle of the ring in C. 
Z 
Let CP = P and Z OOP = y. 
When R is less than c, the integral 
_ d4 _ 
0 \/{ d + c“ — 2ci‘ sin 6 cos (/>) 
G 2 
21J.y3 
