Ogtlvte 
nent ; this effect is rather minor over most of the body surface, and 
its precise evaluation is carried out by matching the near-field and 
far-field solutions. 
In the free-surface problem, this procedure leads to an es- 
sential difficulty : In the far-field problem, the disturbance caused 
by the presence of the body appears actually to be caused by a line 
distribution of sources along the x axis, this axis lying in the plane 
of the undisturbed free surface. A concentrated source in the plane 
of the free surface is completely intolerable, because it causes 
much more than just local problems. (For example, the wave resis- 
tance of such a source is infinite.) Therefore we cannot hope to re- 
present end effects in the simple way that is sometimes so success- 
ful for bodies in an infinite fluid. In particular, we note the following 
important fact : No matter how nonlinear the local flow around the 
bow of the body may be, it cannot appear from afar as if it had been 
caused by a concentrated source. 
In fact, an even stronger statement is possible : If, in the 
far field, the disturbance appears to have been caused by a line dis- 
tribution of sources, the distribution must have a density which varies 
continuously. For the wedgelike body considered in this paper, 
slender-body theory predicts that the source density in the far-field 
expansion should have a jump at the bow. Actually, there may bea 
steep rise in the curve of source density, but there can be no jump 
in value. Otherwise the whole far-field solution has little meaning. 
The far-field solution must be less singular at the bow than one might 
expect from infinite-fluid slender-body theory. 
There is another point of view which also encourages some 
optimism for treating the free-surface problem. The local behavior 
at the nose of a body in an infinite fluid appears to be intrinsically a 
three-dimensional problem. The presence of the body must have a 
fairly significant upstream influence. However, the additional pre- 
sence of a free surface should reduce such upstream influences, 
Moreover, the isobaric property of the free surface may tend to 
smooth out variations in the longitudinal direction. Thus, one may be 
greatly encouraged to attempt to analyze the ship problem by slender- 
body theory. 
These rationalizations have come, for the most part, after 
the preceding analysis had been developed and found to compare fair- 
ly well with experiments. Originally the motivation had been more 
like that described in the Introduction, In any case, we have found 
fair agreement between the analysis and our experiments, and so we 
should proceed to investigate further the internal consistency of the 
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