566 Mr. mann’s Treatife 
> 
re< 5 l ratio of the refpedlive heights of the water, by reafon 
of the weight of the fuperior waters upon the inferior. 
13. From hence (N° 1 x, 1 2.) it follows, firft, that as 
much as the declivity of the bed or channel of a river is 
greater, fo much alfo will the velocity of the flowing 
waters be proportionably increafed. 
2dly, As much as the water in an horizontal bed is 
deeper, fo much will the velocity of the current be in- 
creafed ; and this velocity will diminifh in proportion to 
the decreafing depths of the water in the bed. 
3dly, Abftradting from the refiftance caufed by the 
bottom and fides of the bed, as much nearer as the water 
is to the bottom, fo much will its motion be accelerated ; 
not only becaufe the inferior waters are more comprefled 
by the fuperior in proportion to their greater depth ; but 
alfo becaufe the inferior ones have a greater declivity 
than the fuperior, by reafon of their greater depth in the 
bed, where they are more depreffed with refpedl to the 
elevation of their common fource or fpring. But thefe 
different velocities of the upper and lower waters in the 
fame fection of the bed (abftradting from the fridtion of 
the bottom and fides) approximate indefinitely to each 
other in proportion to the length of the channel, but ftill 
without a poffibility of their ever becoming equal in fa 61 , 
if they met with no refiftance from the bed. 
14. There- 
