,(2D) 



- a Q (l+Kz) (y+TTi) 



I *«' 



- -| (1+Kz) I aA( x ') sgn(x-x') £n(2K|x-x'|) dx' 

 "-Z 



it 



JK(1+Kz) J a (x') [H Q 



-I 



(K|x-x' |)+Y (K|x-x* |) 



+2iJ (K|x-x' |)] dx' 



(160) 



where x = +£ is the x coordinate at each end of the ship. The second term 

 on the right-hand side is added to conform to the expansion of the two- 

 dimensional solution. We can rewrite the above expression as 



-I 



> (2D) + i (1+K; n,\u; ;m(I<! ,''\) wgu(^-y') dx 1 (161) 



where 



N(u) =-y-£n2u+ 



Hq(u') du« + f Y Q (u') du' - TT i 



+ IT i 



Jq(u') du' 



(162) 



It can be shown that 



Mm N(K|x-x' |) = 

 K-*=° 



60 



