Dagan and Tulin 



-00 



and 



; -e j w, d^ (21) 



at second order 



2 2 I 



We determine now the first order solution by replacing the 

 body along ^ > by an unknown pressure distribution (equivalent 

 to a vortex distribution, see Stoker [ 1957] ) of strength g|(^). 

 The function k.(£,) satisfying Eq, (19) and the radiation condition 

 becomes 



k,(;) = M e'' ^'^ Ei [ i(; - V)] g (v) dv (25) 



Eq, (20) becomes now 



i^ Re e-'^^-"' Ei [ i(e - v)] g, (v) dv = - h,(e) 



(26) 



The integral Eq. (26), with a displacement kernel, may be 

 solved by the Wiener -Hopf technique. 



The Fourier transform of Eq. (27) reads 



M(MG,*(\) = -^ [ N,"(M + H;(M] (27) 



V2^ 



where M, G. , H, , and N, are the transforms of the kernel, g , h 

 and the free -surface profile, respectively. 



The kernel's transform has been factorized by Carrier et al. 



616 



