1909. | The Wave-making Resistance of Ships. 283 
of motion of the disturbance. Then the velocity of the diverging wave- 
trains normally to their crests is Vsin@. Now the same features of the 
ship are responsible for the character of both transverse and diverging 
waves; then if V’ is the velocity at which there is a point of inflection in 
the resistance curve for the transverse waves, the suggestion is that V’ sin 0 
is the corresponding velocity for the diverging waves. Taking as a first 
approximation the angle given above, viz., 19° 28’ or sin-14, we test now 
a formula of the type 
R= Ae? BV? 4 Be-a (V/V), (13) 
For the particular example already used (Froude, Ship A) we take V’ 
equal to 26 knots, and determine A, B from two values of V. We obtain 
thus 
R = 45e-3C68V? + 2976-3 26/V)?_ (14) 
With this formula we find as good an agreement as before at the higher 
velocities, and we have now at lower velocities the comparison in Table II :— 
Table II. 
In calculating from (14) we find that the two terms both increase 
continually ; at low velocities the second term is practically negligible, then 
at about 15 knots the two terms are of equal value, and after that the 
transverse wave term becomes all important. 
It must be remembered that the experimental curve was obtained from 
tank experiments, and it is possible that the width of the tank may have an 
effect on the relative values of the transverse and diverging waves. It 
would be of interest if experiments were possible with the same model 
in tanks of different widths; if the methods used in obtaining (14) form 
a legitimate approximation, the effect might be shown in the relative 
proportions of the two terms—provided always that one can make a suitable 
deduction first for the frictional resistance, and can then separate out the 
relatively small effects of the diverging waves, the eddy-making and other 
similar elements. 
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