where 



w « (a-x j cos 6 + (y-y ) »1« • 5 



5^ - (x-x ) cos 8 - (y-y ) sin G 



(36) 



J - \z + 2 | 



«o a k o 8ec 9 



The notetion under two of the Integrals 1c Equation (35), namely, L. or L , 



represents the Integral paths shown in Figure 4. To derive the derivatives of 



7 

 the first two terms of Equation (35), the as&thod which Rasa end Ssith developed 



s 

 for unbounded flow can be used. Kong and Paulling have applied this method for 



the computation of motions of a body in wavea, and their paper can be examined 



for the details. Since Reference 3 can be exaained for these details, we will 



present here the derivation of the last two teras of Equation (35). 



We write Equation (35) as follows 



G-i-i+G, (37) 



r r. 3 



"3 



, ■> ~ =2u, iiiL.u . iw_u> 



1 t l , a ( t e (a ' + a ) . 



- J u d9 { J * du 



u — u. 



(*-!> (38) 



-ZU, -IWaU . iW_Uv 



(e + + e ) 



6 



+ r s _ — __ du] 



a,) 



We now change the variable for the integral path, L, , as follows: 

 v»(u-u )(7-i£5) with GS » S+ or GS_; 



!! 



