1892.] 



The Potential of an Anchor Ring, 



449 



This fact is applied to find the potential of an anchor ring in 

 external space, the velocity potential of a ring moving in any manner 

 in an infinite fluid, the potential of a charged conductor in the form 

 of an anchor ring, and the annular form of rotating fluid. 



Fig. 1. 



2. Let a section be taken through the axis of the ring, cutting the 

 central circle at C. Let P be a point in this section, and let 



CP = R, OC = c, and OCP = x > 



When R < c, the integrals 



T ^0 and T cos d(jy ■ 



Jo a/(?" 2 + c 2 — 2 cr sin cos 0) J \/(r 2 + o 3 — 2cr sin 0cos 0) 



are expanded in ascending powers of R/c ; the expansions of the 

 integrals dl/dc, d 2 I/dc?, &c, are deduced from these. 



Fig. 2. 



