471 Wave Resistance 
On the other hand, there are such effects for the other sphere if tan? « > 8, 
that is, if 5 — «< 19° 28’ approximately. Thus the interference effects 
occur if this sphere lies within the wave pattern left by the leading sphere; 
and the two prominent terms in the evaluation of the integral correspond 
respectively to the transverse waves and the diverging waves of the pattern. 
SUMMARY 
A new method is given for calculating wave resistance directly from the 
source distribution equivalent to the body producing the waves. The 
method can be applied to two source systems representing two distinct 
bodies in any relative positions, giving the resistance of each separately. 
It can also be used to obtain the resultant force in any direction, or the 
resultant couples. 
Results are obtained for a simple case representing two small spheres in 
various relative positions. With the two spheres in the line of motion, 
the resistances differ by certain forces of action and reaction and also by 
the wave-interference effects, which are assigned entirely to the following 
sphere. 
Taking the two spheres abreast, the results are interpreted as showing 
the effect of a vertical wall upon the resistance of a sphere; the expressions 
are given in terms of Bessel functions and curves show the magnitude of 
the influence of the wall for various distances and velocities. An expres- 
sion is also given for the force towards the wall. 
Finally, with the spheres in any relative positions, it is shown that 
effects of wave interference occur when the following sphere lies within 
the wave pattern produced by the leading sphere, and arise from both 
the transverse waves and the diverging waves. 
Reprinted from ‘ Proceedings of the Royal Society of London’ 
Series A No. 886 vol. 155 pp. 460-471 July 1936 
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