Ogtlvte 
arises only if n = 1/2, and so I make such an assumption in this paper. 
The resulting theory is still a slender-body theory, in that 
the first approximation involves a Laplace equation in the two trans- 
verse dimensions only. The rates of change in the near field are 
much greater in the transverse direction than in the longitudinal di- 
rection, but the difference in order of magnitude between them is less 
than in the usual slender-body theory. 
One can describe the theory as being valid (presumably) in 
a region just behind the bow in which x -O(e/2) , where x is mea- 
sured in units such that ship length is O(1). It will be convenient 
sometimes to speak of a ''bow near field", by which I shall mean an 
asymptotically defined region in which x =O(eV2) and r = (y2+z2)¥2 
=O(€). In the "usual near field", we assume that x =O(1) and 
r =O(€), whereas in the far field all variables are O(1) (which 
means simply that we can fix our attention on a point in the fluid and 
the point is not supposed to move as €—0 ), 
Some interesting things happen in the bow near field. We no 
longer have the rigid-wall free-surface condition which is typical of 
the usual near field. Instead, we find exactly the same linear free- 
surface conditions that are familiar from classical thin-ship theory, 
for example. But the partial differential equation is the Laplace equa- 
tion in two dimensions, as in ordinary slender-body theory. This 
means that we must solve an equation in the variables y and z, 
with boundary conditions involving derivatives with respectto x. 
The explicit solution of this problem is presented for the 
case of a thin, wedge-shaped bow. The shape of the wave along the 
side of the body has been computed, and experiments were conducted 
for comparison with the predictions. The results are in fair agree- 
ment. 
From the analysis, it can be concluded that an appropriate 
length for purposes of nondimensionalization is the geometric mean of 
two lengths, the draft and the characteristic length, Wire U 2/g x“ 
That is, we refer all lengths to (HU?/g)/* , where H is the draft 
of the forebody. The extent to which the experimental data then col- 
lapse into simple curves is quite remarkable. Even in cases of very 
low forward speed, in which the analysis fails completely, the same 
data collapse still appears to occur, 
The conditions to be satisfied in the bow near field automa- 
tically match with the conditions in the usual near field of slender- 
body theory. So it is not surprising that the solutions also match auto- 
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