SOME ASPECTS OF THE THEORY OF SHIP 
WAVES AND WAVE RESISTANCE 
By PROF. T. H. HAVELOCK, F.RB.S. 
The Paper gives a general survey without detailed calculations, of 
attempts made during recent years to develop the mathematical theory 
of wave resistance. The first section is a short statement of the general 
problem from the theoretical point of view, while the two remaining 
sections describe some results which have been obtained by indirect 
attacks. It is shown first how calculations with travelling pressure 
disturbances illustrate such problems as the variation of wave resistance 
with speed, the interference of bow and stern waves, and the effect of 
shallow water. In the last section the ship is regarded as equivalent 
to a certain distribution of sources and sinks in the fluid; problems 
discussed briefly im this section are the effect of the form of the water- 
plane section, of the length of parallel middle body, and of varying 
draught. Cwrves are reproduced which show the results of these 
calculations, and some mathematical notes and further references are 
gwen in an appendix. 
EARLY forty years ago Lord Kelvin delivered to the Institution 
N of Mechanical Engineers a lecture on ship waves which is 
familiar to all students of this subject. I may venture to appropriate a 
paragraph from that lecture and to quote it now in addressing this 
society: ‘I must premise that, when I was asked by the Council to 
give this lecture, I made it a condition that no practical results were 
to be expected from it. I explained that I could not say one word 
to enlighten you on practical subjects, and that I could not add one 
jot or tittle to what had been done by Scott Russell, by Rankine, and 
by the Froudes, father and son, and by practical men like the Dennys, 
W. H. White, and others; who have taken up the science and worked 
it out in practice.’’ 
My object is to discuss the wave resistance of ships as a problem 
in hydrodynamics. It is, of course, impossible to do so adequately 
without the use of mathematical analysis which would be unsuitable 
for a general lecture. I must therefore be content to give a mere 
outline sketch, aiming at giving some idea of the theoretical point of 
view and of the sort of contribution which mathematical theory can 
make to the scientific discussion of our problem. Such an outline suffers 
inevitably from two drawbacks: on the one hand we can only glance 
at the various practical problems which are suggested, and on the 
other we are not able to do justice to the mathematical interest of 
the theoretical treatment. It may, however, serve in some measure 
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