jj 4>g^dS and JJ *^dS 



We have the relation which is derived by Green's identity, 



[f {% + V-^-x z i(^ w )} ds 



where £ is a vertical cylinder of large radius surrounding the ship. We 

 have omitted a line integral term which can be assumed small because of 

 the slender body assumption. Because of the boundary condition on the hull 

 surface, there is a relation 



J [ *z k (<t W ds = IT u d(^rk ds 



JJ s JJ s 



while the radiation condition satisfied by <j>' and x gives 



J/. 



3x z 3<j>' 



'D^T-Xz 8n-» dS = 



Therefore, we have the relation 



3x , , s rTQ 



JT % + V ^r dS = [f u ? w 



9n 



T~^X dS 

 9z /^z 



3x 3$ 



z 



75 



