Yim 



where H is the Struve function and Y is the Bessel function of the second kind. 

 If we use the relation from the pressure condition on the free surface 



^1 



and the Green's function represented on the free surface 



G^(^,0,0,x,0,0) 



Re 



\[ 



ik sec 9 e 



_ ^ -'q k - k^ sec 6^ - i^t sec 



dkd^ 



2 d 



- 477k^^ — Y,(t) + 7Tk ^ Th (t) - Y (t)1 



t=kjx-^) 



we can evaluate the line integral (50) at large x and y = O neglecting higher or- 

 der terms, 



^1. 



2 tan a 



0(k^x-t) ^ Y,(t) 



l<„(x-a) 



a r- 



+ 4 tanak^l ^ ^ ^^ Yj(t) 



t = k„(x-f) 



d^. 



If we take only the lower limit of the above equation, it can be considered from 

 the equation for the surface wave to represent a regular wave starting from the 

 bow due to the influence of the free surface. From here Yim (1964) calculated 

 the amplitude and the phase of the regular bow wave Cj^ far behind the ship on 

 y = due to the line integral, 



^1. -P ^in (l<o'' 'J'f")- 



It is easy to see from Havelock's result that the regular bow wave r_^ from 

 the first order theory is, 



^ ^ Q sin (k^x + ^j 



477 " 



^ k V l^77k x 

 or o 



In Fig. 10 are shown the phase difference /3 and 



1090 



