MR. F. W. DYSON ON THE POTENTIAL OF AN ANCHOR RING. 
95 
[When the paper was read, numerical results were given for larger values of cr. 
The above method cannot, however, be employed in such cases. For, as the 
eccentricity of the cross-section increases, the expression given for the potential at 
external points will become divergent at the extremity of the minor axis of the cross- 
section. A similar result will occur if the potential of an elliptic cylinder be found at 
external points, considering it as an approximation to a circular cylinder. In this 
case it is easy to show that the eccentricity must be < 1/^/2. Assuming the same 
result for the case of a ring, it will be seen that = '2076, the value the above 
method gives for cr = ’4, gives the cross-section of too great eccentricity for the series 
to be convergent. That the series were divergent for large values of was also 
suggested by one of the Ileferees. Aug., 1892.] 
