[Reprinted from the PROCEEDINGS OF THE Roya Society, A. Vol. 93] 
The Initial Wave Resistance of a Moving Surface Pressure. 
By T. H. Havetock, F.R.S., Professor of Applied Mathematics 
in the University of Durham. 
(Received January 18, 1917.) 
1. The study of the water waves produced by the motion of an assigned 
pressure distribution over the surface has hitherto been limited to the steady 
state attained when the system has been moving with uniform velocity for a 
very long time. In his latest series of papers on water waves, Lord Kelvin* 
made an elaborate graphical and numerical study of cognate problems, and 
expressed the hope of applying his methods to calculate the initiation and 
continued growth of canal ship-waves due to the sudden commencement and 
continued application of a moving, steady surface pressure. 
In the following paper, I have not attempted any analysis of the surface 
elevation itself, but I have proceeded directly to the calculation of the corre- 
sponding wave resistance. At present the wave resistance is known only 
for the steady state for certain localised pressure systems in uniform motion, 
and it seems desirable to attempt some estimate of the time taken to attain 
this state when we take into account the beginnings of the motion. One 
might examine the effect of initial acceleration, but I have limited the 
problem by considering only the case of a system which is suddenly 
established, and is at the same instant set in motion with uniform velocity. 
* Kelvin, ‘Math. and Phys. Papers,’ vol. 4, p. 456 (1906). 
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