90 T. H. Havelock. 
On the scale used for fig. 2, we have 1 = 80 ft. ; from these values of x and y 
we get from (32) the values of 4 and 2k and so the results collected in Table IIT. 
Table III. 
2k. r. 3A — 2k. SA —2k. 2k. A. 3A —2k. 5\—2hk. 
0 84 126 105 171-5 201 131 81 
28 100°5 123 98 196 218-6 132 77 
66 126 123 92 244 251-3 133 70 
85 140 125 90 328 314 143 65 
125 167-5 126 84 — — — = 
From the third column we see that the wave-making length Z of the approxi- 
mate theory is not constant. There is first a small decrease, which we should 
find emphasised if we examined a higher order of crest, say, for n = 2; then 
for a short range it is practically constant, after which it increases steadily 
with the velocity. However, we see from the fourth column that the rate of 
increase is not so large as in the alternative approximate formula. 
If we had taken any other series of corresponding crests or troughs, we 
should have found similar results at moderate velocities, but with greater 
increase at high speeds where the distance between successive maxima differs 
somewhat from the wave-length. 
9. Consider now the resistance-velocity curve for any given length of ship. 
It has already been stated that the points of maximum excess or defect on 
such a curve cannot be found precisely ; however, they will be in the neigh- 
bourhood of the velocities for which dR/dk is zero for the given length of ship, 
this being, in fact, the assumption involved in the usual comparison of experi- 
mental data of the two kinds. 
We shall work out two examples. First, for a ship with no parallel middle 
body, equation (33) reduces to 
2 
(Gee+2 Ps) {2}-+ (2 Ps— Pi) {} =0. (34) 
The first seven roots and the corresponding results are shown in Table IV. 
Table IV. 
x 1-93 4-14 5-97 7-41 8-79 10-55 12-14 
A 260 121-4 83-9 67-8 57-2 47-65 Ge 
Z 130 121-4 126 135-6 142 143 mee 
V/VL 1-7 1-17 0-97 0-87 0:8 Om | OG 
227 
