88 T. H. Havelock. 
Table II. 
Ay 2k. $A —2k. 8, —2k. 
65 43 120 103 
73 60 122 104 
79 74 124 104 
90 96 129 106 
96 110 130 106 
106 133 132 105 
It should also be stated that Kent has observed the wave profile for a certain 
model at two speeds, and his analysis of the waves agrees with the view that 
in that case the distance between the first regular bow crest and the first stern 
trough had increased by one-quarter of the increase of wave-length. 
Discussion of Results. 
8. We return now to the curves of fig. 2 obtained by the present calculations. 
Absolute values are not under consideration, and we notice one or two other 
respects in which the curves differ from experimental results. The interference 
effects are very greatly increased, and this is no doubt largely due to the infinite 
draught of the ship ; further, as might also have been anticipated, the oscilla- 
tions in any curve do not fall off so rapidly with increasing length of the ship 
as In practice. 
Consider now the positions of the maxima and minima. Take, for instance, 
the curve for g/c? = 0:0625, that is, for 1 = 100-5 feet. Successive maxima 
occur at 2k — 28, 128, 228; the differences are equal to the wave-length, to 
the order of approximation. This rule holds for any of the curves for moderaté 
velocities. Again, considering the actual positions, the maximum at 2k = 128 
for the same curve evidently corresponds to n = 2 in the formule (27) and (28), 
the wave-length being 100-5. In Table II we had 2k = 133 for a wave-length 
of 106. Thus, to a first approximation the actual positions are in very fair 
agreement ; more could not be expected, for the experimental results vary 
slightly according to the lines of the model, and no attempt has been made 
here to fit closely the form of any particular model. 
We have now to group corresponding maxima at different speeds. It is 
easily seen that the crests A; on fig. 2 must correspond to n = 1, A, to n = 2, 
and so on ; the troughs are given by the intermediate values n = 1, 3 
We have to follow out any one of these series and find the relation ee A 
and 2k; before doing so, we extend the calculations beyond the curves shown 
in fig. 2. 
225 
