2 
results and to extend them to the region where more accurate 
data are needed. 
General Theory.._We obtain a clearer view of the problem 
to be solved if we pass over the idea of resistance and fix our 
attention directly upon the transformations of energy which 
accompany the motion of a ship. Imagine a ship which is 
moving at constant speed and whose engines are developing 
energy effectively at a certain rate. None of the energy 
supplied goes into the motion of the ship, for its speed re- 
mains the same; clearly all the energy goes into the water. 
If we could calculate completely the motion of the water we 
should know the rate at which energy must be supplied from 
the ship and consequently the effective horsepower necessary 
to maintain a given speed. Naturally the problem has 
proved too difficult to solve as a whole. All that can be done 
is to classify the motions of the water into groups which seem 
more or less independent; the results of the separate calcula- 
tions are then added together and the sum compared with 
the total effect in actual experiments. Fora first attempt we 
consider the following groups of motions:—surface waves; 
wake and large eddies; smaller eddies of turbulent motion ; 
rotations and heat-motions of the particles of water. Since 
the rate of supply of energy is equivalent to some resistance 
multiplied by the speed of the ship, we may express the 
results of calculations in terms of effective resistance obtained 
in this way. The latter groups in the above scheme are 
usually taken together, and their effect is expressed as a 
frictional resistance calculated from an empirical formula 
based on experiment. It has been found that a suitable ex- 
pression is SV", where V is the speed and S is the area of the 
wetted surface of the ship; the numerical values of f and n are 
taken from tables of experimental results. After this part has 
been deducted from the total effective resistance, the re- 
mainder is called the residuary resistance; following the 
usual custom, we assume that this is associated almost en- 
tirely with the surface waves, and we proceed to estimate 
the rate at which energy goes into the wave motion. 
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