THEORY OF SHIP WAVES AND WAVE RESISTANCE. D 
Our problem is now stated in a form in which we know, from 
general theory, that we have all the information necessary for a complete 
solution ; this solution would give us the velocity and pressure at every 
point of the water, the form of the free surface or the wave pattern, 
and moreover the resultant of the fluid pressures on the surface of the 
ship would give the wave resistance. 
It is instructive to bear in mind the general problem so stated, 
but it must be confessed at once that the direct attack leads to 
calculations which have hitherto proved far too complicated for the 
mathematical methods available. Even if we replace the ship’s surface 
by simple geometrical forms, the problem is extremely difficult; in fact 
the only direct solutions obtained so far, and they are approximate, are 
for spheres and other bodies of simple form entirely submerged at 
some distance below the surface. 
It might appear that we have not gained much from our rigorous 
formulation of the problem, and no doubt it is not often the case 
that a practical problem admits of a direct and complete theoretical 
solution. But theory is usually built up by devising and solving 
simple cases; these often give in themselves valuable suggestions, and 
we may then endeavour to approximate more and more closely to the 
actual problem. The preliminary survey is necessary to guide this 
process along lines which are likely to prove useful. 
My main task is to describe now some indirect attacks which have 
been made, and I shall consider these in two groups. In one case 
the leading idea is the pressure between the water and each element 
of the wetted surface of the ship, while in the other we fix our 
attention more upon the horizontal velocity produced in the water by 
the motion of the ship through it. 
TRAVELLING PRESSURE DISTURBANCE. 
When the ship is in steady motion there is a definite normal pressure 
at each element of the wetted surface. From a dynamical point of 
view, that is the function of the ship. We could imagine those pressures 
to be supplied by any means we please, for instance by jets of air 
properly adjusted, and the motion of the water would be exactly the 
same. We have now removed the ship and have applied to the surface 
of the water a definite distribution of pressure, definite for each 
velocity be it noted. The solution of this problem would give us the 
form taken by the surface of the water; one part of this would 
necessarily be a depression of the same form as the ship, while the 
rest would be the accompanying wave pattern. Now this is merely 
the general problem over again, with the complication that the pressure 
distribution depends upon the speed. But it suggests that we should 
study the wave patterns produced by simple distributions of pressure 
applied normally to the water surface. 
251 
