[Reprinted from the PROCEEDINGS OF THE Royat Soctery, A, Vol. 118.] 
Wave Resistance. 
By T. H. Havetocr, F.R.S. 
(Received December 15, 1927.) 
Introduction. 
1. The object of this paper is to give more direct proofs of certain expressions 
for wave resistance which have been used in previous calculations ; further, 
in view of other possible applications, the expressions are generalised so that one 
can obtain the wave resistance for any set of doublets in any positions or 
directions in a uniform stream, or for any continuous distribution of doublets 
or equivalent sources and sinks. The only limitation is the usual one that the 
additional velocities at the surface are small compared with the velocity of the 
stream. One might take a simple source as the unit, but to avoid certain 
minor difficulties it would be necessary to assume an equal sink at some other 
point. The possible applications are to bodies either wholly, or with certain 
limitations partially, submerged. The image system in such a case consists of 
a distribution of sources and sinks of zero aggregate strength, and so may be 
replaced by an equivalent distribution of doublets. Hence it is simpler to 
use the doublet as the unit from the beginning. 
The wave resistance of a submerged sphere was obtained previously both by 
direct calculation of pressures on the sphere and by an analogy with the effect 
of a certain surface distribution of pressure. The latter method was then 
generalised to give the wave resistance of any distribution of horizontal doublets 
in a vertical plane parallel to the direction of the stream. In a recent paper 
Lamb* has supplied a method for calculating wave resistance which avoids the 
* H. Lamb, ‘ Roy. Soc. Proc.,’ A, vol. 111], p. 14 (1926). 
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