MR. F. W. DYSON ON THE POTENTIAL OF AN ANCHOR RING.
47
are solutions of the equation
.
For putting , this equation becomes
,
that is, is a solution of Laplace's equation.
§ 2. Expansion of the Functions.—Let the plane through the axis of the ring and a point , cut the ring in the two circles whose centres are and .
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Let
;;;
and the angle
.
Also, for convenience, put
,
and
.
When is less than the above integrals may be expanded in ascending powers of or .