Dr. Young's Hydraulic Investigations . 
181 
V. Of the Effect of a Contraction , advancing through a 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 determined, 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, ac- 
cording 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 suc- 
cessively to the portions of the fluid, along which it passes, a 
velocity equal to that of the moveable end, so that the ele- 
vated surface of the parts in motion may remain nearly hori- 
zontal : and this proposition will be the more accurately 
true, the smaller the velocity of the moveable end may be. 
For, calling this velocity v, the original depth a, the increas- 
ed depth x, and the velocity of the anterior part of the wave 
y, we have, on the supposition that the extent of the wave is 
already become considerable, x = p=~ v -> taking the negative 
or positive sign according to the direction of the motion 
of the end ; since the quantity of fluid, which before occu- 
pied a length expressed by y, now occupies the length 
y + v; and putting a ~ x = z, z = j~=r~ v - The direction 
