THEORY OF SHIP WAVES AND WAVE RESISTANCE. 13 
be 80 feet; these lengths were chosen simply because they were those 
adopted by W. Froude in recording the results of his original experi- 
ments on this effect. The number marking each curve is the wave-length 
of transverse waves at the speed for that curve. 
We shall only compare these curves with experimental results in one 
respect, namely the positions of the maxima and minima, a matter 
about which there has been considerable discussion recently. There 
have been two interpretations of the experimental results put forward. 
On both of them the bow wave system is supposed to begin with a 
crest and the stern system with a trough, positive and negative systems 
as we have called them; therefore there will be a maximum on a 
resistance curve when there is an odd number of half wave-lengths 
between this crest and this trough. The difference between the two 
views is that in one case this distance between first bow crest and first 
stern trough is supposed to be constant for all speeds, while in the 
other it is said to increase with the speed in such a way that the 
increase in this distance is equal to one quarter of the increase in the 
corresponding wave-length. Let us follow some particular maximum 
on the curves of Fig. 7, say A,; on both views this corresponds to three 
half wave-lengths between the first bow crest and the first stern trough. 
On one theory the quantity 2—2k should be independent of the speed, 
while on the other it should increase at the same rate as 4A and 
therefore the quantity £’A—2k should be constant; A is the wave- 
length for a given speed and 2k is the length of parallel middle body 
at which the maximum A, occurs at that speed. Taking the values 
from Fig. 7, and adding other results obtained by further calculations, 
we get the following table :— 
Qk N 8) — 2k EN — 2k 
0 84 126 105 
28 100-5 123 98 
66 126 123 92 
85 140 125 90 
125 167°5 126 84 
171-5 201 131 81 
196 218-6 132 77 
244 251°3 133 70 
328 314 143 65 
According to this Table, neither of these quantities is constant. 
Calling $ 4 —2k the wave separation, it is interesting to notice that 
the wave separation decreases slightly at first with increasing speed ; 
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