1909. ] The Wave-making Resistance of Ships. 279 
discussed, and one is given in illustration of the wave-making resistance of 
an entirely submerged vessel. 
§2. Pressure System travelling over Deep Water. 
It is known that a line pressure-disturbance travelling over the surface 
of water with uniform velocity v at right angles to its length gives rise to a 
regular wave-train in its rear of equal wave-velocity.* Take the axis of z 
in the direction of motion and let the pressure system be symmetrical with 
respect to the origin and given by p= f(x); suppose that f(x) vanishes 
for all but small values of x, for which it becomes infinite so that 
| J (v)dz=P. The regular part of the surface depression » due to this 
integral pressure P practically concentrated on a line is given by 
wr Vv? 
gE stn, (4) 
The part of the surface effect which is neglected in this expression consists 
of a local disturbance symmetrical with respect to the origin and practically 
confined to its neighbourhood. 
If we suppose P constant, the amplitude in the regular wave-train and 
the consequent drain of energy due to its maintenance diminish with the 
velocity. 
To obtain results in any way comparable with practical conditions it is 
necessary to suppose the pressure system diffused over a strip which is not 
infinitely narrow. 
An illustration is afforded by taking 
p=fa)= (5) 
where # is small compared with the distances at which the regular surface 
effects are estimated. This type of pressure distribution is shown in fig. 1. 
Rane 
om aaa 
Tw a24+ 2? 
P 
Fic. 1 
* For a discussion of the wave pattern, see Lamb, ‘Hydrodynamics,’ § 241 et seq. ; or 
Havelock, ‘Roy. Soc. Proc.,’ A, vol. 81, p. 398, 1908. 
37 
