and 



Y 3 

 -jr — = - i 0) n_ on the body surface (9) 



n_ is the heave component of the unit vector n. The second potential of Equation (6) 



satisfies the following conditions: 



2~ 2 



31, 9 <j> 



3 + — -^- = when z < (10) 



2 2 

 3y 8z 



\ 2 . 



= on z = (11) 



and 



3z g 3 



t = m„ on the body surface (12) 



an 3 



Here m_ is given by 



m 3 = " ( n 2 h +n 3 h) 3T 1 (13) 



There are two ways to solve for the potential (})„: one is the multipole ex- 



8 9 



pansion method given by Ursell, and the other is the close-fit method by Frank. 



The solution of (j)_, using the former method, is given by 



00 



n (0) ^ ^ / cos(2m9) , K cos[ (2m-l)6] \ , ,. 



h = °3 G 2D + ^L % ( r 2m + 2^ r 2m-l J (14) 



m=l 



