Dagan 
region -7 +é<arg(f - ih+ l)<7 
The far free waves associated with w, (44) or w (48) 
are given by z, (37) as 
(49) 
it/F* nies is/F* <t (ee 
Zz =Aje =[4ie if t(s)e dsle 
-1 
and the coefficient of wave resistance is 
2 ae JA,| ° / 8F° (50) 
Again, these well known expressions continue to exist if 
F-0, in virtue of (48). 
III .4 - The Naive Small Froude Number Expansion 
We turn now to (36), valid for a body of finite thickness 
moving at low speeds. Substituting (36) into (32) and (33) we obtain 
ae 226 (vy = 0) (51) 
ihe Sa igs way (52) 
1 I. 40 0\4 # 
ima. ws, = Ter ) ( ¥ =0) (53) 
ee (¢— - ) (54) 
a is therefore the solution of uniform flow at infinity past 
the actual body beneath a rigid wallat w=0, briefly ''the rigid 
wall solution". wi’! described a flow generated by a source distri- 
bution along ¥=0, (53) being a standard Neumann condition. It can 
be shown that the higher order approximations satisfy the same type 
of free-surface conditions (53). Moreover, it has been shown (Dagan 
and Tulin, 1972) that the total flux of the sources in (53) and higher 
order approximations is zero such that w?, w’ , ... are 0(1/ |£7| ) 
as |£| — oc for a closed body (in the absence of circulation). In parti- 
cular no free=waves are present and the wave resistance is identical- 
ly zero. 
We can now consider a thin body limit of wo i6 dee.) an 
expansion of the type 
LTk2 
