At a great distance from the ship, the diffraction potential <J> and the 

 incident wave potential <j) satisfy the linearized free surface condition 



^\ 2 * + B ii. 



iuH-U y- I (}) + gy t =0 at z= (205) 



However, the boundary condition for <J) at z = changes near the ship as 

 was pointed out before. Instead of (j)_, we can define a function <}>' which 

 satisfies the above free surface condition even in the near field. We 

 assume that <))' coincides with (J) in the far field, while it coincides with 

 <J)' in the near field. Then in the near field, we can put 



>D + 



= K- U 5 -—-+ <\> (206) 



D w dz w 



Since the boundary condition on the hull surface is 



3n U 



the boundary condition for <J>' becomes 



^D = u? LP.^! (207) 



dn w 8n \3z / dn 



Next we assume the auxiliary functions X an< 3 ty satisfy the boundary 

 condition 



2 



3x / T ' & dz 



iw-U |- J (J) + g-P=0 atz=0 (208) 



and evaluate the integrals 



74 



