The Initial Wave Resistance of « Moving Surface Pressure. 244 
Begin with a case in which there is no ambiguity, namely, when the waves 
are produced by a rigid body moving horizontally through the liquid. We 
can apply the general hydrodynamical principle that the rate of increase of 
total energy of the fluid is equal to the activity of the pressure taken over all 
the bounding surfaces. If we equate the rate of increase of energy to the 
product of a force R and the velocity of the rigid body, it follows that R is 
simply the total fluid pressure on the moving body resolved horizontally. This 
result can easily be verified by direct caleulation for the steady state, whether 
the waves are produced by the motion of a rigid body or by the motion of an 
assigned surface pressure ; in fact, the two cases are identical in the steady 
state, for we can imagine the surface pressure to be applied by a rigid cover 
which fits the water surface everywhere. 
Consider now the problem before the steady state has been established. If 
the waves are caused by a moving rigid body, we can use either definition for 
the wave resistance; we can calculate it from the rate of increase of fluid 
energy or from the total horizontal pressure on the body. We are not 
discussing this case, simply because so far the analysis has proved too 
complicated to allow of suitable reduction. We replace this problem by that 
of the motion of an assigned surface pressure. Now we can calculate the rate 
of increase of the total energy of the fluid when the pressure system is in 
motion. But it would not be satisfactory to divide this quantity by the 
velocity of the pressure system and define the quotient as the wave resistance, 
for part of the increase of fluid energy is independent of the motion of the 
pressure system. For instance, if a stationary pressure system is suddenly 
established and maintained steady, the activity of the surface pressure is not zero 
immediately after the initial instant; there is a subsequent flow of energy, 
whose rate ultimately subsides to zero. From these considerations it seems 
that we should get results more comparable with the wave resistance of a 
rigid body by adopting the alternative method of calculation. In what 
follows we shall therefore calculate for any instant the total horizontal 
component of the surface pressure regarded as applied normally to the surface 
of the water; and we shall define this to be the wave resistance. 
With the usual limitation that the slope of the surface is everywhere 
small, we have from this definition 
R== * Fo) Shas. (11) 
We can verify that this gives the same result (10) for the steady state. 
For instance, taking the expressions in (8), the part which is symmetrical 
with respect to the origin gives no contribution to R, and we obtain 
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