THEORY OF SHIP WAVES AND WAVE RESISTANCE. 9 
effects; the combined effect oscillates about the mean sum according 
to the positions of the crests and troughs of one wave system relative 
to those of the other system. Fig. 3 shows a graph of the wave 
resistance calculated for a certain case of this combination 3 it shows 
the typical humps and hollows, and the mean curve. 
It may be asked why we illustrate the wave-making action of bow 
and stern by positive and negative pressure systems respectively, instead 
of by two positive systems or two negative ones. The best answer to 
this question seems to be that we find that this combination gives the 
humps and hollows on the resistance curve in the same sort of sequence 
as for a ship. Another way of expressing it is this: we know from 
observation that the bow and stern produce wave patterns which are 
similar in character except that where there are crests in one pattern 
there are troughs in the same relative positions in the other pattern, 
and vice versa; the simplest combination of pressure systems which 
gives the same effect is obviously the one we have used, one system 
being positive and the other negative. 
General Pressure System.—We might now attempt similar calcula- 
tions for a continuous distribution of pressure such as would be 
essociated with the motion of a ship. So far these have only been 
carried out in certain cases of two-dimensional fluid motion, that is 
when the wave motion consists only of straight-crested transverse waves ; 
we need not consider these in detail here (Vote 4). One point should 
be mentioned to avoid possible confusion. We have already remarked 
that the action of bow and stern is similar to that of positive and 
negative pressure systems. But the actual continuous distribution of 
pressure round a ship is different; it is symmetrical fore and aft of 
the midship section as far as its general character is concerned. The 
excess pressure begins by being positive near the bow, it then decreases 
rapidly to a negative value, remains more or less constant over the 
middle length of the ship, and then increases rapidly to a positive 
value again near the stern. Now a little consideration shows that the 
places which give the main part of the wave effect of the whole system 
are not the regions where the pressure is uniform, whether it is positive 
or negative, but those places where the pressure is changing rapidly. 
Here we have near the bow a rapid change from positive to negative, 
while at the stern the change is from negative to positive; the nett 
result is that in the wave patterns arising from bow and stern respec- 
tively the relative positions of crest and trough are interchanged. 
One recognizes that the results which have been reviewed in this 
section are necessarily only illustrative of the actual ship problem. 
They are nevertheless interesting and suggestive, and students of the 
subject will be familiar with the use that has been made by various 
writers of the notion of pressure distribution in interpreting curves of 
wave resistance obtained from experiments with ship models. 
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