8 THEORY OF SHIP WAVES AND WAVE RESISTANCE. 
wave of translation. The waves produced by our travelling pressure 
system agree in character with this fact. Below the speed ,/(gh) the 
wave pattern is similar to that in deep water, the heights of the waves 
being increased; but at higher speeds the transverse waves have 
disappeared and the pattern is made up of diverging waves only. 
Here are some curves, in Fig. 2, which show the corresponding 
changes in the wave resistance. The numbers marking the different 
curves are the ratios of the depth of water # to the length # which 
measures the linear dimensions of the applied pressure system; each 
curve gives the variation of wave resistance with velocity for a given 
depth of water. The curve marked o is the curve for deep water 
which we have already discussed. The progressive changes in the curves 
as the depth is diminished should be noted; but consider in particular 
the curve marked 0°75. Notice the greatly increased resistance com- 
pared with deep water so long as the speed is less than a certain value, 
and the rapid fall after that point with the resistance ultimately 
becoming less than in deep water. The velocity at which the change 
Fie. 3. 
takes place in this case is, from the graph, about 0:-86./(gf); and, 
as the depth h is 0°75 ,/(gf), this velocity is practically equal to / (gh), 
the speed of the wave of translation. This result is in general agree- 
ment with various recorded experiments on the effect of shallow water 
on the wave resistance of ships. 
Interference Hffects.—Returning to the easier case of deep water, 
we can illustrate the interference of bow and stern wave systems. We 
shall call a system in which the applied pressures exceed atmospheric 
pressure a positive pressure system, and one in which they are less than 
atmospheric pressure a negative system. Let the travelling system 
consist of a positive system of the kind we have been considering 
together with an equal negative system at a fixed distance to the rear 
of the positive one. The combined wave pattern is obtained simply 
by superposing the waves due to the two systems separately, and an 
expression for the wave resistance can also be obtained (Vote 3). The 
resistance is not the sum of the resistances due to the two systems 
separately, otherwise there would be none of the so-called interference 
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