## Extract

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 problems 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 form 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 calculating 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 distribution 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 4*πρmm'*/*r*^{2} 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 force on it may be taken as the vector — 4*πρmq*, where *q* is the resultant fluid velocity at that point due to all the other sources, in which the remaining internal sources may be included as their actions and reactions do not affect the final result.

## Footnotes

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- Received March 27, 1936.

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