Ogtlvte 
too surprising, since the body boundary condition was satisfied by 
distributing sources over the underwater part of the centerplane, to 
which we added a distribution of opposite sinks on the abovewater 
image of the centerplane. These two distributions alone would certain- 
ly lead to the dipole-like behavior far off to both sides. Apparently, 
the third term in the expression for @ , as given in [1] , has negli- 
gible influence in this sideways limit. 
Actually, we guaranteed such a result by choosing the com- 
plementary solution as we did in [7] . Effectively, we have implied 
that there are no waves upstream of the bow, even in the bow near 
field. In the final section, we shall return to this point ; it requires 
much more study in the future. 
The transform of the wave deformation function can be ex- 
pressed 
U 
Gal) = (== "Go 
g x 
and, from (9), this quantity has the following behavior near L=0 
% a = L| i 
(xt) = E l-e Hl sin VK |f£] x (10) 
Nxt ( ) 5 i 
zat fi ee 6 et 
2 6 
The inverse transform then must have the behavior 
2 
H K 
(Gy) > = ae E + 7 [o.. as pe 
It can be shown that the potential itself drops off inversely 
with y? ,» but this does not seem to provide any special insight into 
the results. 
Behavior as x-+e%o , This is an important limit; for it pro- 
vides the connection to the usual slender-body solution. Let us recall 
that x =O(e 1/2 ) in the bow near field region. Our solution, when we 
let x -—co, should match the solution of the usual slender-body pro- 
blem if we let x —0 in the latter. 
1498 
