on Rivers or Canals. 
5^5 
adly, The fpaces, run over by heavy bodies which fall 
perpendicularly by a motion uniformly accelerated, are 
in a duplicate ratio of the times and velocities refpedtively. 
3dly, Thefe fpaces, in equal times, augment in the 
fame ratio as the odd numbers in progreffion 1, 3, 5, 7, 
9, 1 r, Sec. 
4thly, Therefore, both the times and the velocities 
are in a fub-duplicate ratio of the fpaces run over. 
5thly, It is demonftrated by the principles of mecha- 
nics, that the velocity acquired by a heavy body defcend- 
ing freely upon an inclined plane, in a given time, is to 
the velocity which the body would acquire in the fame 
time, by falling perpendicularly, as the height of the in- 
clined plane is to its length. 
6thly, From whence it follows, that the velocities 
which bodies acquire in their defcent upon inclined 
planes, are in a direct ratio of the fquare roots of the quan- 
tity of inclination or declivity of the planes. 
1 1 . So that when water flows freely upon an inclined 
bed, it acquires a velocity, which is always as the fquare 
root of the quantity of declivity of the bed. 
12. In an horizontal bed, opened by fluices or other- 
wife, at one or both ends, the water flows out by its gra- 
vity alone ; and the flowing is quicker or flower in a di- 
Vo l. LXIX. 4 E reft 
