II ' 



Figure 2 - Limits of Integration 



By substitution of Equation (70) into Equation (87), the diffraction force is given 

 by 



h. = -p (icon.+m.) [ ^^^Kc^(<t> +(|) ) ] dS 

 J JJ 3 2 //ss 



(92) 



We first substitute Equations (48) and (49) for n. and m., and apply Green's second 



(s) -' -^ 



theorem to the term containing f ^ . The diffraction force can be written 



h. = 



3 



-P JJ -^ ((p.-(t>pdS-p J J (iojn +m )C^((j)^+(j)^) dS 



(93) 



(s) 

 where C^ is given by Equation (77) and (f) is the symmetric part of i/?^ that sat- 

 isfies the two-dimensional Laplace equation and the boundary condition. Equation 

 (72). By substitution of Equation (71) for ifi , the diffraction heave force is 

 expressed by 



h^e 



/ r iK^x r 



= I i2pa) Ale dx J 



K z 



e dx J e n cos K y-n sin 3 • sin Kyi (({)-(})) di 



2' 2 



K3 T3. 



- 2p C,(x) dx (iajn_+m„) Re[d) ] d£ 



/ J J J s 



(94) 



23 



