The pressure of water waves upon a fixed obstacle 42] 
then becomes complicated and, in practice, many other factors must be 
taken into account. The wave resistance of the ship, as calculated for 
uniform motion through still water, is probably altered; moreover, the 
motion of the ship, and in particular its pitching and other oscillations, 
must have an important influence. It may well be that interactions between 
first order effects which in themselves are purely periodic may, through 
phase differences, give rise to steady additional resistances. 
The calculations which have been made here refer to a model held at 
rest in a train of waves. The only reference to experiments of this nature 
appears to be in a paper by Kent and Cutland (1935). The model was 
No. 1255 of the National Physical Laboratory, and the dimensions were: 
length = 16 ft., beam = 1-92 ft., draft = 0-52 ft. For this model the mean 
value of sin?« was probably not more than 0-1. If we suppose the wave 
amplitude, that is half the wave height, to be 2 in. for waves, say, 5 ft. in 
length, then (43) gives as an upper limit a force of 0-17 lb. The experimental 
results were not published, no doubt because this particular experiment 
was only incidental to the main investigation; but it may be taken that the 
calculated value obtained here is of the order of one-half the measured 
value for waves of the given height and length. Here, again, although the 
model is said to be at rest, it has necessarily a certain small amount of 
freedom for oscillatory motion. While such motion might be expected to 
diminish the magnitude of the pressures we have been considering, it may 
also bring other effects into operation. Further experiments of this nature, 
with more detailed measurements, would be of great interest. 
The immediate object of the present work was to examine, in cases 
amenable to calculation, the magnitude of the mean force obtainable on 
the analogy of radiation pressure. The general conclusion is that while such 
a force exists as a contributory cause, it is insufficient to account for the 
extra resistance observed in a ship advancing through waves; in those 
circumstances the total effect is probably the result of several factors of 
approximately equal importance. 
REFERENCES 
Havelock, T.H. 19387 Proc. Roy. Soc. A, 161, 299. 
Kent, J.L. and Cutland, R.S. 1935 Trans. Instn Nav. Archit., Lond., 77, 81. 
Kreitner, J. 19389 Trans. Instn Nav. Archit., Lond., 81, 2038. 
Lamb, H. 1906 Proc. Lond. Math. Soc. 4, 190. 
— 1922 Proc. Lond. Math. Soc. 21, 359. 
Larmor, J. 1920 Cong. Inter. Math. Strasbourg (or Math. and Phys. Papers by 
Sir Joseph Larmor, vol. 2, p. 617 (Cambridge 1929)). 
Nicholson, J. W. 1912 Proc. Lond. Math. Soc. 11, 104. 
Rayleigh, Lord 1915 Proc. Roy. Soc. A, 91, 345. 
Wigley, W.C.S. 1931 Trans. N.-E. Cst Instn Engrs Shipb. 47, 153. 
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