Ogtlvte 
as that which results from the usual slender-body theory, but itis 
still singular. It is interesting to note that the experimental data in 
Figure 6 would have a more orderly appearance if the ordinate scale 
had started at about x,,35, ~-2. In other words, the predictions in 
Figure 6 are considerably improved if we arbitrarily assume that the 
rise in water level should have been measured from a point about 2 in. 
ahead of the bow. To this extent, our linearized results follow the 
pattern mentioned above : They are approximately correct, but in the 
wrong place.”* 
The form chosen for the solution in (1) is not an essential 
part of the analysis presented in this paper. It was an easy way to 
arrive quickly at a solution for a particular case. It has already been 
mentioned that this simplification may be at least partly responsible 
for the discrepancy between analysis and experiments at the higher 
Froude numbers. Having now determined that we have found some 
general agreement between analysis and experiments, we shall next 
try to obtain more precise solutions for these and similar problems. 
For example, the body cross-section shown in Figure 1 (either (a) or 
(b)) can be mapped into an auxilliary plane in which body and free 
surface together make up the horizontal axis. The free-surface con- 
dition must be transformed, of course, and then an integro-differen- 
tial equation comparable to (3) can be obtained. This procedure can 
also be followed for bodies which are not symmetrical or for bodies 
which have an angle of attack. No solutions have been obtained yet 
except for that described by Hirata [4] for the case of a plate of zero 
thickness with an angle of attack. I hope that we shall be able to ob- 
tain solutions for several more realistic situations - for which com- 
parisons with experimental data will provide more definitive evalua- 
tions of the fundamental approach described in the present paper. 
* A more careful study of Figure 6 shows that the predicted curves 
have the correct slopes if the origin is placed on a sliding scale, with 
essentially no shift for the case of small draft, up toa shift of about 
5 in. for the maximum draft case. I do not want to try to read too 
much quantitative significance into this result, however. 
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