the boundary condition can be written as 



n . ML + n . |i = _ k c h n' e Kz (230) 



y dy z dz z 



It is known that the above condition can be satisfied by putting 



lp = e iKx X (231) 



and the density of the wave source is determined by such a simple equation 

 as 



^K e- ±1T/4 J £iSI d? + c h = (232) 



-h ^ 



This is Abel's integral equation, the solution of which is 



/2tt"K(x+£) 



a(x) = c h e (233) 



33 



This approximation was actually given by Faltinsen who calculated the 



pressure and force acting on a body with semicircular cross section. 

 However, the solution shows the density of the source being infinite at 

 the forward end of the body which results in an infinite pressure there. 

 Such things never happen in actual phenomena. In order to eliminate this 

 difficulty, one has to retain other terms in the expression of ty other 

 than the lowest order. In this case, the function tJj is expressed by a 

 linear combination of X an< ^ ^ as 



+ a(x) ( V i f e Kz + £ P n \) (234) 



n=l 

 82 



