where a, - a-(^) and a- = in the integrand. We adapt this type of 



= 1 



2 2 ~ 



solution to the present case as follows: (1) [R^ + (z- - ^) ] ^ is the poten- 

 tial for a source located at (0, 0, ^) in an infinite fluid. 



We replace this source potential by another source potential which, 

 in addition, satisfies the free surface condition. (2) We now impose the 

 condition that the radius a- is much smaller than the distance between 

 spars; i.e., a-Za^ « 1. Then the potential obtained by satisfying the 

 boundary condition on the i spar will produce negligible fluid velocities 

 at the other spars, and the total potential can be expressed as a sum of 

 potentials, each satisfying the conditions on one spar. The resulting total 

 potential is 



$(x, y, z, t) = e cos(kx-ojt) 



k 



N J- 

 + ^^ I -jl a. [zga.' + aQa-'la sin e. - p cos e.) 



n=l 

 -ojAe (a-' + J ka-) cos (kaQ cos 9. -ojt)] 



+ fa- [xQ + p^-^aQ sin 9^ + wAe ^ sin(kaQCOs9j^-cot)] 



7 r) 



+ i a. [yQ - a^ +yaQ cos 9.] — - 



2 



-ia. [wkAe ^cos(kaQCOs9^-wt)] — - > 



9x- J 



1 



|[Rf -f (z^ - U']'" + fj ^ e^(^i + ^) J,( vR^)dv] d^ 



N , 

 TTu^'k y I Ja- [zq a/ + aQa.'(Q' sin 9- - P cos 9-) 



[8] 



