and the same equations hold if x, y, z and x^, y-, z^ are all primed. 



It is assumed that there are incident waves which are described by 

 the velocity potential 



$- (x,y,z,t) = — e^^ cos(kx - cot) [3] 



U k 



where A is the amplitude of surface wave, 



k is 27r/wavelength = wave number, and 



CO is the circular frequency. 



In the definition of the coordinates given above, the orientation of the x- 

 and y-axes was not specified, except for the orientation of the plane which 

 they defined. Now we specify that the x-axis points in the direction of 

 propagation of the surface waves and the y-axis completes the right-hand 

 system. 



THE VELOCITY POTENTIAL 



The surface of the i spar can be specified by the equation: 



= F. (x/, y.' z.') 

 1 ^ i' ^i' 1 ' 



= [xi - Xq - P z- + y (aQ sin 9^ + y. )] 



2 



+ [yi ~ yo " y(^o "=°^ ^i + ^i) + ^^i^ 



- a^ [z. - Zq - a(ao sin 6. + y.) + (3(aQ cos 9- + x-)] 



The boundary condition on the i spar is then 



aF. 



-^+ (Vi$ -v. )F. = 9 on F. = 9 



