360 Prof. T. H. Havelock. Wave Resistance: Some 
the surface elevation is the same as the second part of (24); hence the same 
supply of energy is needed, and is obtained in this case from the work of the 
applied pressure. Thus we may assuine that the wave resistance is the same 
in the two problems. 
From (19) and (25) we have 
R = 4 oP gpf—Fabade— 9? Wy, 1 («), (26) 
which agrees with the value for the sphere given in the previous paper. The 
connection between the wave patterns of a submerged body and of a certain 
surface pressure has been pointed out by Dr, G. Green in a recent paper,* in 
which the correspondence is developed from a different point of view. In the 
following analysis we deal only with combinetions of simple pressure systems 
(12), and the corresponding submerged body can be found from a similar 
combination of doublets, as in the preceding case. 
6. The foregoing results can be generalised for other symmetrical forms of 
local pressure distribution, provided transformations such as are used in (4) 
and (14) are applicable. Assuming this, it appears, from the analysis of § 3 
and § 4, that fora pressure system p = F (w) we have 
R = (4rr/gp) Ki [see 6 Fle sec? ) }2 dd, (27) 
where f(x) is given by (3). 
7. Some points of interest in the theory of wave resistance can be 
illustrated by combinations of the simple type (12). We consider first two 
equal systems, at a distance 2/ apart, and advancing in the direction of the 
line of centres; that is, 
P= Aff (P+ av)? + Af[(f? + o27)?, (28) 
where oi” = (e—A)?+7? and wo = (a +h)? +y?. 
Writing, for the moment, p; and ps for the two component systems, and 
G, & for the surface elevations which would be caused by these systems 
acting separately, the waves due to the combination are given by &+ 2, since 
we neglect, as usual, the squares of the fluid velocities. It follows from the 
definition in (7) that the wave resistance is the sum of four parts, Ry, Re, Rio, 
and Ry. Here R; is the resistance due to the pressure ; acting on the waves 
produced by ji, Riz is that due to p; operating on the waves caused by po, and 
similarly for Ry and Ray. 
It follows from § 4, that 
1/2 
R, — Ro — (47 g A293 sec? 7 2xaf sec? > cf, y 29 
p ; ( 
* G. Green, ‘ Phil. Mag.,’ vol. 36, p. 48 (1918). 
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