3n 



3n 



<J> 



3G 

 3n 



<<M>*> 



3x 







* 3G 

 b to 



= 



Therefore, Equation (19) becomes 



->■ -fell— j^tf) 



d S, 



4tty, 



G(P ' Q) I dx' 3x' J 



dy' 



z'=0 



4tty. 



$(x',y') G(P,Q) I dx'dy' 



■z'-O 



J 



(20) 



Since -G(P,Q) means a source at the point Q, the velocity potential is ex- 

 pressed by the distribution of sources over the hull and the still water 

 surface. The density of the hull surface sources is 



; ^ - - + ^) 



Here we take a plane parallel to x involving the normal and take a length 

 s.. along the curve of intersection of this plane and the surface S. If a 

 is the angle between the normal and the x axis, we have the relation 



3d> 3d) , . 3d) 

 ■sr- = cos a -r- 1 - + sin a if— 

 dx dn ds. 



We have assumed that 



on S, so that 



13 



