10 THEORY OF SHIP WAVES AND WAVE RESISTANCE. 
DISTRIBUTIONS OF SOURCES AND SINKS. 
Let us consider now another method of treating the wave-making 
action of a ship. It is obvious that the bow and entrance of the ship 
produce in the water an outwards horizontal velocity on either side, 
while the run and stern give rise to component velocities inwards. We 
can also see that the same sort of effect will be produced if we remove 
the ship and replace it by some apparatus which supplies water where 
the velocities are outwards and removes it where they are inwards. 
This picture suggests one of the most fruitful devices in hydrodynamics, 
the study of the motion produced in a fluid by the presence of sources 
and sinks, that is points at which fluid is introduced or withdrawn at 
a uniform rate symmetrically round each point. Just as in the 
previous section we might begin with simple cases, for example a source 
travelling at uniform speed at a constant depth below the surface and 
followed at a fixed distance by an equal sink. The wave motion 
produced by this combination can be calculated; and we can generalize 
the results, with certain limitations, for any distribution of sources 
and sinks. We need not delay over the simpler cases, but let us see 
now how we may use this idea in the ship problem. 
D 
ee 
Fie. 4. 
Consider the vertical section of the ship by the median plane 
running from bow to stern. We replace the ship by a distribution 
of sources and sinks over this vertical section, so arranged that the 
horizontal velocity outwards or inwards at each point is equal to the 
same component of the velocity of the corresponding element of the 
ship’s surface at right angles to itself. This is, of course, an approxi- 
mation; the chief limitation is that we must assume the lines of the 
ship to be fine, so that the angle between the ship’s surface and the 
vertical median plane is small. 
Without going into the details of any one problem, I shall describe 
now some results obtained from three sets of calculations made on 
these general assumptions. 
Form of Water-plane Section.—Suppose that we wish to examine 
the relative effect of making the lines at the bow finer and increasing 
the beam of the ship, the displacement being constant. We shall 
simplify the work by assuming the draught to be infinite, which means 
simply that it is large compared with the wave length at the highest 
speed; we are not concerned with absolute values of resistance, and 
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