Lee 



The solution to this problem is given by Eq. (33) as 

 Fgiz) = W2(x,y) +iW*(x,y) 



00 .... .. /-»00 



= l£ h2{e)e-'''<^-^^E,(-iK(z-e))de + 2i^ ^^iw''^^^'^^ ^i 



rtOO 



+ (j-i)^ \{i)e-''''^'-^^di. (36) 



-00 



Thus Eqs. (35) and (36) finally give 



W =i W, + Wg 



Ae 



'^y iix'i-i A ^^''^^^^/;t^-'r,^ ^-'Kz 



1 rr e 



K"^- K 



jK'lxl . A r e E.(^K'z) e-"^'E.(-iK'2) 1 



- J V^^i L — kHTk — ^ IT-ric J 



+ Rej [ij°° h2(e)e-"'<^-^^E,(-iK(z-e)) d^ + 2i ^^^ h2(e)e-'''^'-^^de 



If we seek a solution to the problem described in Section 3.1 

 except the body-boundary condition, given by Sq» (21) , we can ob- 

 tain it from Eq. (33) of Case 1 of this section as 



F5(z) = W5(x,y) + LW*(x,y) 



= 1^^ h^{e)e-''*»"-*'E,(-LK5(z-4)) de +2i£°° h^(4)e-'"^"^' dg 



+ 0-i)y"h^(S)e"'"'''-^'de, (38) 



in which we let h^x) =0 in -b<x<b since the velocity potentials 

 are undefined in this line interval. In the same way, if we seek a 

 solution which satisfies all the conditions except the body-boundary 

 condition given by Eq. (26) in Section 3.2, we can obtain. U; from 

 Eq. (37) of Case 2 with the constant A replaced by age'^^ (compare 

 Eq. (30) with (34)). If we express the solution in the fornn of a com- 

 plex potential and let K' = K - K , we find that 



918 



