6 THEORY OF SHIP WAVES AND WAVE RESISTANCE. 
Localized Pressure.—To begin with the simplest type we may picture 
a fine jet of air impinging on the water surface; we could call this 
in the extreme case a point pressure system, or more generally a 
distribution of surface pressure symmetrical round a vertical axis. 
We may imagine the jet to move horizontally with constant speed, or 
we may study the equivalent problem of a stationary jet of air directed 
down on to the surface of a uniform stream. Everyone is familiar 
with the simple and beautiful wave pattern produced in this way, and 
we are encouraged to proceed with this line of attack by the fact that 
the pattern is so similar in its main features to the waves produced 
by a ship. 
The mathematical solution of this problem can be obtained com- 
pletely, provided the surface waves are not too large; the wave pattern 
shows the well-known transverse and diverging waves contained within 
lines making angles of about 19° 28/ on either side of the line of 
motion of the system. Leaving on one side the discussion of the wave 
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Fie. 1. 
system let us consider what is perhaps less familiar, the corresponding 
wave resistance. We are considering a pressure system applied to 
the water surface and moving horizontally with constant velocity ; 
accompanying the system there is a steady wave pattern. Suppose 
now that we place over the whole surface of the water a smooth rigid 
cover exactly fitting the surface at every point, and let this cover move 
horizontally with the same velocity. We could now remove the jet, or 
other means by which we applied the pressure system, for this function 
will now be performed by the rigid cover; and the fluid motion will 
be exactly the same as before. Moreover, at all those outlying parts 
where the surface pressure is the same as atmospheric pressure, the 
cover could obviously be cut away; and we are left with what corres- 
ponds to the ship in this problem. Let me repeat that in the actual 
ship problem we are given an assigned depression in the water surface, 
namely, the surface of the ship; we have replaced this by a problem 
in which the pressure distribution is assigned and the ship is, so to 
speak, made to fit the surface disturbance. The reason for doing this 
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