300 The Wave-making Resistance of Ships. 
Hence the amplitude of the regular wave-trains formed on deep water in 
the rear of this disturbance is proportional to «?Ae-**, and the effective 
wave-making resistance is proportional to «*A%c~***, We make the same 
assumption as before, viz., A proportional to v®, and write « = g/v?; then the 
resistance is given by 
1 = Oo ao- ae, (31) 
We use this expression to show how R varies with the constant h of the 
pressure system. Let v = 10 ft./sec.,and let R = 1 for h = 0; then we find 
the following relative values : 
R decreases very rapidly as # is increased. We have chosen this example 
for the following reason. Consider the motion of a thin infinite cylinder in 
an infinite perfect fluid; if we consider a plane parallel to the direction of 
motion and to the cylinder and at a distance % from it, we find that the 
distribution of excess or defect of pressure due to the motion is of the above 
type. Now, this is not the same as a cylinder moving in deep water at 
a depth h below the free surface, but it is suggested that as a first approxi- 
mation the wave-forming effect is that of an equivalent diffused pressure 
system. The illustration shows how rapidly the wave-making resistance 
diminishes with the amount of diffusion, that is, with the depth 4; this, of 
course, agrees with the experiments on the resistance to motion of submerged 
bodies, and, in fact, with the resistance of submarine vessels. 
In the preceding work no attempt has been made to connect theoretically 
the constants in the pressure formula with those of the model; since the 
theory rests chiefly on the consideration of transverse waves only, this would 
presumably bring into question the length of entrance, run, and so forth. The 
consideration of any “transverse” constants, such as the beam, would need 
a fuller treatment of a diffused pressure system in two dimensions on the 
surface so as to give a more detailed investigation of both transverse and 
diverging wave systems. 
Harrison AnD Sons, Printers in Ordinary to His Majesty, St. Martin’s Lane 
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