Wave Forces on a Restratned Shtp tn Head-Sea Waves 
and letting a one-term near-field solution of the diffracted wave be the 
negative of the incident wave. So 
Ve eee (80) 
We solve (79) for o, (x) formally by letting it be an equa- 
lity for all x > - L/2. We get Abel's integral equation to solve 
(See Dettman (1965) ). The solution is 
, [20 +2 Uy im /4 
i) (x) = TW, v (x A 1/2) e€ C (81) 
The discussion that followed the expression of o, (x) for 
the zero-speed problem (see after equation (34) ) can also be applied 
for the forward-speed problem. The conclusion was that we had to 
construct a separate expansion for a region in which x+L/2 = 
0( e€”% ), (¥ some positive number) , and that o, (x) is not given 
in that region by (81). 
We wish next to find ve , but first we need to say some more 
about the far-field. 
We expect that a two-term far-field expansion is obtained by 
a line distribution of sources of density 
i (wt - vx) 
(0, +, whe (82) 
1795 
