14 THEORY OF SHIP WAVES AND WAVE RESISTANCE. 
this is an effect which we find more pronounced if we follow a higher 
order of maximum such as A, or A,. After a range over which the 
wave separation is approximately constant, it ultimately increases with 
the speed but at a slower rate than that required by the quarter 
wave-length theory. Such are the results for the simplified form of 
model we have used; it is quite possible, of course, that different rates 
of variation might be obtained if the calculations could be made for 
forms more like actual ship models. A similar remark may be made 
at the same time about empirical formule derived from experimental 
results; it is not as a rule justifiable to extend these formule beyond 
the range from which they were obtained. 
-7 005 
Varying Draught.—As a last example of this set of calculations 
let us find how the resistance of model A, without parallel body, varies 
when we alter the draught (Vote 7). Hitherto we have taken the 
draught to be so large that it might be assumed infinite. We now 
cut the model off by a horizontal plane, so that it still has vertical 
sides and constant horizontal section; but we take the draught to be 
first one-tenth and then one-twentieth of the length. 
Fig. 8 shows the three curves, marked with the ratio of draught 
to length. There is little difference at low speeds until the wave-length 
becomes comparable with the draught. An interesting point is that 
the humps and hollows occur at practically the same speeds in the three 
curves; one may compare this with the observed effect that for a 
submerged model the resistance curve gives humps and hollows at the 
same speeds independently of the depth at which the model is run. 
The ratios one-twentieth and one-tenth cover roughly the ratios of 
draught to length which occur in practice. We may then compare these 
260 
