[Reprinted from the PROCEEDINGS OF THE Royal Socirry, A, Vol. 131.] 
The Wave Resistance of a Spherord. 
By T. H. Havetocr, F.R.S8. 
(Received February 20, 1931.) 
1. A method which has been used to calculate the wave resistance of a 
submerged solid is to replace the solid by a distribution of sources and sinks, 
or of doublets, the distribution being the image system for the solid in a uniform 
stream. The cases which have been solved hitherto have been limited to 
those in which the image system is either a single doublet or a distribution of 
doublets lying in a vertical plane parallel to the direction of motion. It is 
shown here how to obtain the solution for an ellipsoid moving horizontally 
at given depth below the surface of the water, and with its axes in any assigned 
directions. The present paper deals specially with prolate and oblate spheroids 
moving end-on and broadside-on, the general case of an ellipsoid with unequal 
axes being left for a subsequent paper. 
In § 2 it is shown that the image system for an ellipsoid in a uniform stream 
is a certain surface distribution of parallel doublets over the elliptic focal 
conic, the direction of the doublets bemg in general inclined to the direction 
of motion ; if the motion is parallel to a principal axis, the doublets are in the 
same direction. For a spheroid the image system reduces to either a line 
distribution or to a surface distribution over a certain circle ; explicit expres- 
sions are given in §3 for prolate and oblate spheroids when moving either in 
the direction of the axis of symmetry or at right angles to that axis. 
The calculation of the wave resistance is considered in § 4. An expression 
has been given previously for the wave resistance associated with two doublets 
at any points in the liquid with their axes in any assigned directions ; this can 
be generalised to cover continuous line, surface or volume distributions of 
doublets. Incidentally, it is shown how by integration we may pass from 
a three-dimensional doublet, corresponding to a submerged sphere, to a two- 
dimensional doublet, corresponding to a circular cylinder. In § 5 expressions 
for the wave resistance are developed for the particular cases of moving 
spheroids of §3. In the final section these results are illustrated by numerical 
and graphical calculations for certain series of models. In each case the 
axis of the spheroid is supposed horizontal, and to make the calculations 
definite the depth of the axis is taken to be twice the radius of the central 
circular section. The models consist of a sphere, radius 6 ; an oblate spheroid 
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