§ = (q,£ 2 ,£ 3 ), = (e r e 2 ,e 3 ) 



r = (x-x G ,y-y G z-z G ) 



(308) 



the fluid velocity at the moving hull surface is expressed by 



V = y Q + [(§+0xr)V] V (309) 



Substituting Equation (301) for <$>,<$>,§ in Equation (306) and making use 

 of Equation (309) together with the boundary condition for $„ given by 



n^. + n„<J>- + n_<J). + n. = (310) 



l r 0x 2 Y 0y 3 r 0z 1 



and the irrotationality condition 



u=v, v=w, w=u (311) 



y x z y x z 



we obtain eventually 



^l n l + ^2 n 2 + ^3 n 3 + 9 1 ^y"y G )n 3"^ z ~ Z G^ n 2^ 



+ 9 2 {(z-z G )n 1 -(x-x (; )n 3 } + 6 3 { (x-x^n^y-y^n.^ 



- E, 8u/3n - E„ 8v/8n - E, 8w/9n 



- 8 X |^ {(y-y G )w-(z-z G )v} - 2 |^ { (z-z G )u-(x-x G )w} 



- 9 3 i ((x - x G )v -^G )u}= ^ (312) 



This is the boundary condition for the periodical potential tf> 1 . Then the 

 periodical potential is constituted by 12 components such as 



\ 4*1 72*2 ^3 3 14 2 5 3 6 



+ E^ 1 + E 2 i> 2 + Ejl> 3 + 0^ 4 + 6^ + 6 3 ^ 6 (313) 



109 



