Insert the above relation in Equation (32) and put k = Y sec 9« If we 



write the relative flow velocity around the double body as u n , v„, w n , and 



2 2 2 

 put u_ + v_ = q n , after some reductions, we have the expression as 



H(y sec 2 0,0) = - ^- jj [jL {u^qg-l)} + |- (v <qj-l» ^ 



exp[iy n sec 6(x + y tan 9)] dxdy 



= fe II D(x ' 



y) exp[iy n sec 0(x + y tan 6)] dxdy (40) 



14 

 where the function D(x,y) was defined first by Baba and is written as 



D(x,y) = |^ ( ?0 u ) + |^ (C Q v ) 



(41) 



We may derive another expression from the source distribution over the 

 hull surface S given by Equation (21). Then the generalized Kochin 

 function becomes 



H( k> 0, . - J J 



a(x,y,z) exp(kz + ik(x cos + y sin 0)] dS 



U. 



a(x,y,0) exp[ik(x cos + y sin 0)] n dy 



4iTY r 



>(x,y) exp[ik(x cos + y sin 0)] dxdy (42) 



21 



