The densities of sources and dipoles are determined from the inner so- 

 lution at the near field which has been discussed previously. They are 

 identical with the source term or dipole term in the solution for two- 

 dimensional cylinders in the corresponding motion of each transverse 

 section. However, the existence of the forward velocity results in a 

 slight change of the boundary condition at the hull surface. If we 

 consider the case of head seas, the oscillation of the ship is heaving and 

 pitching. The effect of surging is omitted because of the higher order. 

 Then the boundary condition on the hull surface is 



-± = (z-^-m nj - U(z -*|0 ^ ( — ) - ^ (276) 



where n' = 3z/9n', n 1 being the outward normal to the contour of the 

 transverse section. The first term comes from the relative velocity of 

 the section and the last term means the relative velocity of the orbital 

 motion of the incident wave. However, on account of the second term, the 

 boundary condition is not determined by the relative velocity of the 

 section only. If we assume U and w are both of the order of unity, the 

 inner solution is associated with the free surface condition such as 



3*! 3 2 * n 



^=-n? —^ at z = (277) 



dz w „ 2 



dz 



The source density in this case can be determined in a manner similar to 

 the radiation problem. 



m(x) = - -^ (iuH-U ^) {B(x)(zg-x^-? w )} (278) 



1/2 

 In the case of U = 0(e ) and to = 0(1), however, we have to solve the 



two-dimensional problem with the free surface condition 



9<J>- 2 3 2 A 



ar-f-*i--^ K 7? 



dz 

 97 



