Ogtlvte 
in the problem. If we take as the Froude number F = u/NeL » where 
U is the forward speed, L is ship length, and g is the gravitation- 
al acceleration, then the statement that F =O(1) means that there is 
a characteristic length Ug which is comparable with ship length 
and which is unrelated to the small parameter, € 
In a strict sense, this should always be the case. Suppose 
that ¢€ is a measure of ship thinness or of ship slenderness. As 
€—0, there is no reason to expect that U?/g should become either 
very large or very small ; one should certainly be able to specify the 
forward speed independently of ship thinness or slenderness, and g 
does not vary significantly in any case, 
But there are a couple of reasons sometimes not to accept 
this apparently natural assumption : a) Whe» we develop an asymp- 
totic analysis, we expect it to be more and more carly valid as the 
small parameter becomes infinitesimally smail, But we usually ob- 
tain just one or two terms in our expansions, and we try to use those 
expansions for computations when the small parameter is quite finite. 
We may actually obtain more accurate formulas if we assume an un- 
natural relationship between e¢ and the length u-7e: For example, if 
the latter is actually comparable to ship beam in the cases of practic- 
al interest, we may be better off in assuming that U*/g =O(€) when 
we formulate the boundary value problem. b) The implication about 
the ratio of inertial and gravitational forces may be locally invalid. 
That is, in some regions, one of these forces may dominate the other 
to the extent that the asymptotic solution gives grossly wrong predic- 
tions in those regions, 
The first of these two points I have discussed at length ina 
previous paper [1]”. In fact, the idea was not original there ; it was 
used many years earlier by Vossers [2] and also by Joosen [3] , 
for example. 
The second point is already implicit in slender-ship theory, 
for one assumes there that rates of change in the transverse direct- 
ions are very great compared with rates of change in the longitudinal 
direction, at least in a region near the ship. This means that accele- 
rations (and thus forces) are greater in one direction than another, 
and the ratio between them depends on e€ . Thus, to the extent that 
* Numbers in square brackets denote references listed at the end 
of the paper. 
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