Mori j Inui and Kajitani 



S (0)/L =-^-sec 2 MP(0,y') sin(K i sec 0sinfy') 



where 



P 



Q 



+ Q( 0,y») cos(K /sec sin0y')> dy' (36) 



(0,y») =— Ki? sec 0/8 sin(K i sec 0x') dx" 



►'-oo 



(0,y') = -i-K £ secdj 3 2 cos(K isec0x')dx' ( 37 ) 



Figure 32 shows the first order amplitude functions, 

 C, (0)/L , S 1 (0)/L of the model M21 at the speed of K Q L = 12 

 which are calculated in three different ways. 



(a) by existing theory, or from m(£) 



(b) by wave-analyzed source m(£) 



(c) by m -correction (m= 0. 4) 



The difference between the result (a) and (b) is present- 

 ed in Figure 33 together with the second order amplitude func- 

 tions C2(0)/L , S2(0)/L wnich are calculated Equation 36. 



Figure 33 suggests that the second order correction for 

 the free -surface condition is important only for the diverging wave 

 range, where the wave -slope is predominant. 



Consequently, it appears that the remarkable discrepancy 

 which is observed in the transverse wave range cannot be explained 

 by this kind of non-linear effect. 



702 



