Falttnsen 
double pole at # = 0, with a corresponding meaning for > ae 
a modified Besselfunction of the second kind. In (41) C(+) denotes 
the half of the boundary curve of the submerged cross-section at x 
for which y > 0; Y=£(s), Z=n%(s) are the parametric equa- 
tions of the curve C(+). mu(s,k) is determined from satisfaction of 
the body boundary condition (40). It should be noted that (38), (39), 
and (40) will be satisfied for an arbitrary A, (x) in (41). A> (x) 
has to be determined by the matching procedure. 
The symbol denotes integration along a contour passing wee the 
In order to match, we need an outer expansion of (41). 
Ursell (1968 a) has done that. The result is 
A, (x) fer - yelp Lil i pis, k) og (s) ds | (43) 
C(+) 
A three-term outer expansion of the two-term near-field solution, 
Cen ae (44) 
can now be written down. It is 
gil ot = v x) = % -1/2 ae KZ pains bean 
‘= me 
C(+) (45) 
1782 
