the aerodynamic case. However, for the slender floating bodies which 

 are envisaged at present (viz., a rocket vehicle or one support of a stable 

 platform), this is not expected to cause practical problems. 



The values of the potentials [13] to [ 16] on the body may be found 



by setting r = R(z) and retaining the leading terms for small R. To lead^- 



2 ? -- 



ing order, only the singular term [r + (z - z,) ] 2 contributes to the in- 

 tegrals over Zi , and the integrals may be evaluated directly since for 

 any continuous bounded function f(zi) and small values of r. 







f(zj) [r'^ + (z - z^)''] ^ dz^ = -2f(z)logr + 0(1) 

 ■H 



f(z^) i_[r2 + (z -z/]~' dzj - -Z^cose + 0(1) 

 ■H 



9x 



f(z,) -^ [r2 + (z - z,)^]"^ dz, = 2 ^ cos 20 + 0(1) 

 -H ax^ r2 



for -H < z < 0, r « H. 



Thus on the body, 



<^t = i R(z) cosO + 0(r2) [17] 



4>^ = - >]; R(z)(z - Z(3)cos0 + 0(r2) [18] 



4>. = -i R^log R+ 0(r2) [19] 



'=' dz 



= we^^ [(^ KR + 4^)R log R cos wt + R cos sin wt] + 0(r2) 

 dz 



e^^ R cos sin wt + 0(R^ log R) 



[20] 



