Mort-j Inui and Kajitani 



that obtained from towing test (Figure 25 and Figure 26). So the dis- 

 crepancy in amplitude functions between the present method and wave 

 pattern analysis corresponds to the discrepancy between C w obtain- 

 ed from towing test (C^.) and that given by wave pattern analysis 

 (C^). In Figures 25 and 26, A denote C^ . 



As to the causes for this discrepancy between C w and C^ , 

 we can mention first the failure of the wave pattern analysis method 

 (longitudinal cut method) itself. The value of G^ itself varies with 

 y (the distance of the parallel cut line from the center line). Second, 

 the magnitude of the discrepancy between C^ and C^ is proportion- 

 al to Fir, not to Fir , in medium speed range, this means that this 

 discrepancy is related to some characteristic of the wave height. We 

 thus mentioned the wave-breaking as one possible reason, together 

 with the non-linear wave height reduction with distance in this term. 



Of course the wake or boundary layer effect cannot be neglect- 

 ed, and should be considered in further studies. 



3. As to line integral contribution 



Our investigations made clear that the second order contri- 

 bution of the boundary condition is not so large and we reach the con' 

 elusion that the line integral contribution must be taken into account. 



From Green's theorem and free surface condition, the velo- 

 city potentiel $ at P can be given as follows 



.■if. ; ji j*(p).-|f-(p.Q)-G(p. Q )-^-#to)j <^ 



Oivi 



'--%- I j*(P).^G(P,Q) -G(P,Q)-^ *(Q)j dy (A) 



In the existing theory we take into account only the first 

 term and neglect the second term which is the so-called line integra- 

 tion. 



Figures 1 ~ 4 show the contribution of the second term 



(Ij the existing theory, namely the contribution of first term only ; 

 Ql) the contribution of line integration, namely the second term ; 

 CD CD + CD ' name ly tne l e ft hand side of Equation (\) ; 



750 



