This is the same form as the hull boundary condition of the radiation 

 potential for heaving, because the latter is 



" T R . 8z TT 9 f " r 



^— r = 1 CO Z ir-f - U Z -r-r 



dn g on g dn 



dz 



(196) 



Therefore, the diffraction is taken into account in the hull boundary 

 condition by replacing the vertical movement of the section by the relative 



displacement to the surface of the incident wave. This relation holds in 



1/2 

 the case of U = 0(e ) too. Then we can take up to the next term, so that 



the relation is to be modified as 



|^ = - iu { (1+Kz) |£r+u c AIt^ 



dn w dn w dn \ dz 



(197) 



Kz 

 The added term Kz comes from the exponential factor e in the incident 



wave potential and indicates the Smith correction. 



The boundary value problem for the diffraction potential is now re- 

 duced to a similar form to that for the radiation problem. The field 

 equation for the potential <J>' is the two-dimensional Laplace equation 



-0> ' + IV = 



9y 



dz' 



(198) 



with the hull boundary condition given above. The free surface condition 

 at z = is 



dz 



iil_^_ A ." - 



)z g 



when U = 0(1), 



1/2, 



w = 0(1) \ 



= when U = 0(e ' ) , to = 0(1) ' 



(199) 



71 



