136 Hydrau lie Investigations . 



the motions of fluids. It is confessedly demonstrable that 

 each of two waves, crossing each other in any direction, 

 will preserve its motion and its elevation with respect to the 

 surface of the fluid affected by the other wave, in the same 

 manner as if that surface were plane : and, when the waves 

 cross each other nearly in the same direction, both the height 

 and the actual velocity of the particles being doubled, it is 

 obvious that the ascending force or impetus is also doubled, 

 since the bulk of the matter concerned is only halved, while 

 the square of the velocity is quadrupled ; and supposing the 

 double wave to be stopped by an obstacle, its magnitude, at 

 the moment of the greatest elevation, will be twice as great 

 as that of a single wave in similar circumstances, and the 

 height, as well as the quantity of matter, will be doubled, 

 so that either the actual or the potential height of the centre 

 of gravity of the fluid seems to be essentially altered, when- 

 ever such an interference of waves takes place. This diffi- 

 culty deserves the attentive consideration of those who shall 

 attempt to investigate either the most refined parts of hy- 

 draulics, or the metaphysical principles of the laws of mo- 

 tion. 



V. Of the Effect of a Contraction, advancing through & Canal. 

 If we suppose the end of a rectangular horizontal canal, 

 partly filled with water, to advance with a given velocity, 

 less than that with which a wave naturally moves on the 

 surface of the water, it may be shown that a certain portion 

 of the water will be carried forwards, with a surface nearly 

 horizontal, and that the extent of this portion will be deter- 

 mined, very nearly, by the difference of the spaces described, 

 in any given time, by a wave, moving on the surface thus 

 elevated, and by the moveable end of the canal. The form 

 of the anterior termination of this elevated portion, or wave, 

 may vary, according to the degrees by which the motion 

 may be supposed to have commenced ; but whatever this 

 form may be, it will cause an accelerative force, which is 

 sufficient to impart successively to the portions of the fluid, 

 along which it passes, a velocity equal to that of the move- 

 able end, so that the elevated surface of the parts in motion 



may 



