MR. F. W. DYSON ON THE POTENTIAL OF AN ANCHOR RING.
45
Section I.—Preliminary Analysis.
§ 1. Take a fine ring in the plane of , , centre at the origin, and consisting of attracting matter of density , where is the azimuth of any point.
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The potential of this ring at a point , whose coordinates are , is
.
Put , then the potential
as the second integral vanishes between the limits.