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Wave Resistance: the Mutual Action of Two Bodies 
By T. H. HAVELOCK, F.R.S. 
(Received March 27, 1936) 
1—Methods of calculating wave resistance which depend upon energy 
considerations are appropriate for a single body or a single system for 
which we require the total resistance. There are, however, certain prob- 
lems in which there are two or more bodies and we wish to calculate 
the resistance of each separately, or more generally the resultant force 
on each body in any required direction. For instance, the effect of the 
walls of a tank upon the resistance of a model might be calculated from 
the resistance of one model among a series of models abreast of each 
other. Another problem is suggested by experiments made by Barrillon.* 
Two or more models were towed in various relative positions and the 
resistances measured separately; the results for a model in the waves 
produced by other models in advance of it were considered to show 
interference effects due to both the transverse and the diverging waves 
from the leading models. Without attempting to deal with these actual 
problems at present, the following paper contains a method of calcu- 
lating wave resistance which seems suitable for the purpose. It depends 
upon obtaining the force on a body as the resultant of certain forces on 
the sources and sinks to which it is equivalent hydrodynamically. A 
general discussion is given first and then a simple case is worked out in 
some detail ; this may be described as two equal small spheres at the 
same depth, first with one directly behind the other, then with the two 
abreast of each other, and finally in any given relative positions. 
2—Consider a solid body held at rest in a liquid in steady irrotational 
motion. We shall suppose the motion to be due to a uniform stream 
together with given sources and sinks in the region outside the body, 
and we suppose the effect of the body to be equivalent to a certain dis- 
tribution of sources and sinks within the surface of the body; the latter 
may be called the internal sources. It is known that the resultant forces 
and couples on the body may be calculated from forces on the internal 
sources due to attractions or repulsions between the external and internal 
sources taken in pairs; the fictitious force between two sources m, m’ is 
4xemm’ /r® and is an attraction when m and m’ are of like sign. Another 
way of expressing this theorem is that if m is a typical internal source, the 
*°©C.R. Acad. Sci. Paris,’ vol. 182, p, 46 (1926). 
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