But the swifter the velocity of the water, the greater is the height, from whence it has descended:
Consequently the obstacles, which contract the chanel, cause the water to rise against them.
But the rise will cease, when the water can run off as fast as it comes:
And this must happen, when, by the fall between the obstacles, the water will acquire a velocity in a reciprocal proportion to that in the open chanel as the breadth of the open chanel is to the breadth of the narrow passages.
VII. The quantity of the fall caused by an obstacle in a running stream is measured by the difference between the heights fallen from to acquire the velocities in the narrow passages and open chanel.
For just above the fall, the velocity of the stream is such, as would be acquired by a body falling from a height higher than the surface of the water:
And at the fall, the velocity of the stream is such, as would be acquired by the fall of a body from a height more elevated than the top of the falling stream; and consequently the real fall is less than this height.
Now as the stream comes to the fall with a velocity belonging to a fall above its surface;
Consequently the height belonging to the velocity at the fall must be diminished by the height belonging to the velocity, with which the stream arrives at the fall.