$ = e ^cos(kaf^cos9■-CAJt)-2wAe ^a.cosA-sin(ka^cos9--wt) 



1^ VJ 1 X 1 Vj 1 



-rzna.' + aoa.''(Q'sin9.-(3cos9.) 

 '■ 1 1 ^ 1 "^ 1 



kz- 

 - 00 A e ^{a.-" + \ ka.) cos (kar, cos 9. - ojt)l a. log a. 



- [xQ+Pz.-Ya.Qsin9-]a.cosX-- [yQ-o^z. + Y^^nCosg-la. sinX. 



+0(a^) [10] 



Also, we note that on the surface of the i spar 



z = z.' + Zr, + 0!{3.n sin 9. + a. sin X') - (3(a„ cos 9. + a- cos X-' ) 



til 

 Thus the pressure on the i spar is 



(kz-' 

 gAe 1 sin(ka^cos9^ -cot) 



i 



kz ■'' 

 + 2 gk Ae ^ a. cos X-' cos (kaQ cos 9- - wt) 



- [z^a.' + a.^di.'' (a sin 9. - (3 cos9. ) 

 '- 1 1 1 ^ 1 



[11] 



kz' 

 - gkAe i (a.' + k ka.) sin (ka„ cos 9. - ojt)] a. log a. 



- [x„ + Qz." - va^ sin 9.]a. cos X.' - [y^, ~ cfz{ + y a.^, cos 9.] a. sin X' 

 '-O^i'O i-'i 1 -^0 1 ' i-* 1 1 



+ g fz.' + z„ + ccCa^ sin 9. + a. sin X/) - 3(a^ cos 9. + a. cos X/)]}- 

 ^'-1 ^0 1 1 i^^O 1 1 ij 



Let the force be resolved along the space-fixed axes which corre- 

 spond to the coordinates (x,y,z). In particular, designate the components 

 of hydrodynamic force on the i spar by X^, Y j , Z^. Likewise, let the com- 

 ponents of hydrodynamic moment on the i^" spar be denoted by A-, B-, R 

 which correspond to the rotations a, P, y. Note specifically that the 

 nnoments are taken with respect to the space-fixed axes at the center of 



10 



