Thus we add to Equations [I4c], [l4d], and [I4e], respectively, the addi- 

 tional force and moments 



. ** 



- 2 TT p \/ 



«0 a.(z. ) b.(z. ) r _ -| 



.H ' c.(z|) cos[p(z,)-v(z.) + ^J 



(zq + aQ Q- sin 6- - aQ (3 cos 6.)dz- 



JO a-(z- ) b.( z- ) r -. T 



'' '' '' '' sin p(Zi)-v(z.).li 

 -H '^Cj(z^) L ^ ^ 4 J 



(zq + a^ a sin 6. - a.^^ (3 cos 9.)dz. > 



A** = aQ sin 6. zf* 

 B^'^ = - aQ cos e. Z?''* 



If these additional quantities are inserted into the equations of mo- 

 tion, we can still obtain solutions by the same method used previously. 



Although the viscous forces thus obtained are linear in the veloci- 

 ties, they do not fit properly into the perturbation scheme in terms of 

 small radius. The modified Bessel functions encountered have singulari- 

 ties vi^hen the argument approaches zero. In fact, 



b 1 



— '^ — :; ; as a — 0. 



a a log a 



Thus, as the slenderness of the spars is accentuated, the viscous forces 

 increase. This is in contrast to the potential flow forces, which become 

 smaller and smaller. No general conclusion can be drawn concerning the 

 relative importance of the viscous and nonviscous damping forces as far 

 as dependence on radius is concerned. Calculations should be made in 

 individual cases. 



28 



