the motion variables. Neglecting now second-order terms in a- and a-', 

 we find the condition on $,: 



1 1 



kz- ^ 



+ coAe ^ sin(kaQ cos 9--cot)f- cosX^ 



+ i Yq - az- + Y aQ cos 9- V sin X- 



+ -<-|- ka-toAe ^ cos (kaQ cos9-- wt)!- cos 2Xj 



- "I Zq a-' + aQ a^ (a sin 9^^ - P cos 9- ) [7] 



kz- "^ 



- (a' + ^ka. )wAe ^ cos (kag cos 9. - u^t) > 



We note that the boundary condition is now applied at the surface of the 

 undisturbed spar, and the right-hand side is evaluated in the space-fixed 

 (x-, y • , z) coordinate system. 



If this i spar were located alone in an infinite fluid with the above 

 boundary condition valid for — H < z- < 9, the solutions for $, by slender 

 body theory would be 



■* = ■{ 2 ^i t ^9 3-i' + 3.Qa((a sin 9- - p cos 9-) 



- to A e (a.^ + J ka^) cos (ka^ cos 9^^ - oot)] 

 + J a^ [xQ+p^-"yaQsin9-+GoAe sin(kaQCOs9--cjt)] 



+ i a. [yQ - a^ + y aQ cos 9.] -^ 



- I af [ookAe^^ cos (kag cos 9- - cot )] -i--|[R? + (z- - ^)^]"' d^ 



9x. J 



