166 PROBLEMS IN THREE DIMENSIONS. [CHAP. V 



113. The investigations of this chapter relate almost entirely 

 to the case of spherical or ellipsoidal boundaries. It will be under- 

 stood that solutions of the equation V 2 </> = can be carried out, on 

 lines more or less similar, which are appropriate to other forms of 

 boundary. The surface which comes next in interest, from the 

 point of view of the present subject, is that of an anchor-ring, 

 or ' torus ' ; this problem has been very ably treated, by distinct 

 methods, by Hicks*, and Dyson f. We may also refer to the 

 analytically remarkable problem of the spherical bowl, which has 

 been investigated by Basset J. 



* "On Toroidal Functions," Phil. Trans., 1881. 

 t " On the Potential of an Anchor-Ring," Phil. Trans., 1893. 

 J " On the Potential of an Electrified Spherical Bowl, &c.," Proc. Loud. Math. 

 Soc., t. xvi. (1885). 



