302 T. H. Havelock 
accordance with the factor in (11) which involves the quantity k jl. One 
method of expressing these results is to find what height 4 of the imposed 
waves would give &’ the same numerical value as A, at each velocity, 
regardless of whether R’ is positive or negative. This is given in the last 
column of the table as h/A, the ratio of amplitude to wave-length such that 
Rk’ is numerically equal to R,. In comparing these figures with values from 
observation or experiment, it should be noted that usually the height of 
a sea wave is measured from trough to crest, and is equal to 2h of these 
calculations. The point made now is that for quite ordinary values of the 
ratio of wave-height to wave-length the additional resistance, positive or 
negative, is of the same order as the wave resistance of the model in still 
water. 
Kol cly/ (gl) R’/e?h R,/c? h/aA 
8 0-353 0-5 0-042 0-014 
7 0-378 — 0-264 0-03 0-017 
6 0-408 — 0-92 0-072 0-01 
5 0-447 — 0-78 0-1 0-013 
A 0-5 0-62 0-053 0-007 
3 0-577 1-05 0-12 0-007 
2 0-707 1-13 0-233 0-008 
5—An interesting form of the problem is the case of a model in the waves 
left by another model at a fixed distance in advance and moving at the same 
speed; it is a case for which some experimental results are available. 
Instead of (2) we now have 
$ =cut $+ Po, (12) 
where ¢, represents the disturbance due to the rear model and ¢, that due 
to the leading model. We may replace the models by source distributions 
01, O over their respective longitudinal sections, and the usual first 
approximation is taken for o in each case, namely o = (c/27) dy/0x. 
The resultant horizontal force on each model has been considered from 
this point of view in a previous paper (Havelock 1936), and a general dis- 
cussion is given there in §§4, 5. The resistance of each model consists of 
various terms: the resistance of each as if isolated, mutual actions between 
the two models which are equal and opposite and may be assigned to local 
disturbances of the fluid motion, and forces due to wave interference 
acting on the rear model only. It is easily seen, from approximate calcula- 
tions, that the mutual actions due to local effects diminish rapidly with the 
distance between the models, and we shall neglect these terms in what 
follows. 
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