Assuming the body is slender, the body potential for points near 

 the body is then equal to 



(f)=9CC + wA(; expl- Kh + i K ^ cos g - icotl [16] 



plus an odd function of n . Thus, adding Equation [14], the total potential 

 on the body is 



(j) = e 5 ? + (gA/co + 2 CO A C) exp - Kh + i K C cos 3 - iwt } 



I ' [17] 



2 2 

 + 0(c , n ) 



plus an odd function of n . Here we have expanded Equation [14] in a Taylor 

 series for small values of the body transverse dimensions. Substituting 

 Equation [17] in the Bernoulli Equation [9], we find that pressure on the 

 body is 



p = -p65(;+ (ipg A + 2ia) p A?) exp | -Kh + i K C cos B - icot} 



I '[18] 



- pg c + pg ? e 



where in Equation [18] and hereafter we consistently delete the nonlinear 

 second order terms in 5 , S, and the wave amplitude A. 



The surface integral in Equation [17] can be evaluated as follows 

 from the divergence theorem: 



j/pcosc.x, dS=///|^dv=//j(i.eiE)dv 



= rrr [- p e i; - pg K A cos 6 (1 + 2KcJ exp (- Kh 



+ i KC cos 6 - icot) ] dV 



= - pg K A cos g exp (- Kh - iwt) 



J exp (iKC cos e) SiO d? [19] 



where S(C) is the cross-sectional area of the body. The volume integral 

 is over the interior of the body, and the line integral is over the body 

 length. 



