APPENDIX 



Here the potentials cf't. 4't' . 't'j, ■ a-nd cj)., defined by Equations [l3] 

 to [l6], are shown to satisfy the boundary conditions [8] to [11], respec- 

 tively, to leading order in R. For this purpose, let us consider the po- 

 tential 



*f„°^ ="""''' ^0l^')<=^}^-l [54] 



+ TTcoK f f(zpt) e^^^"*" ^1^ jQ(Kr)dZj 



where f{z,,t) has sinusoidal time dependence with circular frequency to. 

 By appropriate choice of the function f, the potentials <j)t, cj)^ , 4",, and 

 <))a can all be obtained from i|i and 94j/9x. Thus it is sufficient to estab- 

 lish that the follow^ing conditions are satisfied on the body surface r = R: 



a^ 4j ^ cos e a 



9r 8x j^2 at 



^f{z,t) [56] 



Employing an alternative form of the source potential,^ we write ^ 

 in the form 



4^=i J ^([r2 + (^-^l)^]"^+ [r2 + (z+zi)2]"^ 

 + 2K j^" -^-^ e^^^'^^l) Jo(kr)dk\dzi 



57] 



23 



