THEORY OF SHIP WAVES AND WAVE RESISTANCE. 11 
this assumption is not likely to affect much the comparative values. 
We imagine the ship to have vertical sides and constant horizontal 
section; and we consider a series of models in which the length is 
constant, the beam and the lines altering in such a way that the area 
of the water-plane section is unaltered. Calculations have been made 
for four models in which the lines can be expressed by simple mathe- 
matical formulz so that these conditions are satisfied (Wote 5). Fig. 4 
shows a quarter of the water-plane section for the two extreme models 
of the set and the Table gives some further details. 
MopEtLs oF Constant LENGTH AND DISPLACEMENT. 
Model. Beam. Water-plane coeff. Bow and stern lines. 
A 1:0 0-667 straight 
B 1-042 0°64 straight 
Cc 1-072 0°62 Hollow 
D 1°136 0-587 Hollow 
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The calculated curves of wave resistance for these four models are 
shown in Fig. 5. 
Fie. 5. 
The ordinates are the wave resistance R on a certain scale, while 
the base is V/4/L where V is the speed in knots and L the length in 
feet. Look at the curve A, which belongs to the model of more normal 
lines. There are the typical humps and hollows due to interference, 
enormously exaggerated in value, but they occur at values of V/ /L 
which agree sufficiently well with experiment; for instance, there is a 
prominent hump at V=1:04,./L. We can trace also from the set of 
curves the general effect of putting the displacement more amidships. 
The chief point of interest is the intersection of these curves in pairs 
of values of V//L ranging from 1°12 to 1:18. Now this set of 
257 
