574 Mr. mann’s TreatiSe 
When the fum of refiftances and caufes of retardation 
is greater than the fum of accelerating caufes, the velo- 
city of the river is diminilhed in proportion to the excefs. 
23. The percujfion of the waters of a river againft an 
obftacle which is oppofed to their motion, is the a< 5 tion of 
the waters linking againft that obftacle; and the prin- 
ciples for calculating the quantity of this percuflion, or 
the effects which any obftacles whatever produce in the 
motion of rivers, by known forces, and in determinate 
times, are as follows : 
ill, The percuflion of the water of a river againft any 
obftacle whatever is univerfally in a compound ratio of 
the quantity of the plane or planes which the obftacle 
oppofes to the current of water, of the fine of the angle 
of incidence which the direction of the current makes 
with thefe planes, and of the fquare of the velocity of 
the faid current. 
odly,, The refiftance, therefore, which the bed of a 
river oppofes to its current from any particular obftacles 
in it, is in a compound ratio of the magnitude and fitua- 
tion of the planes of thefe obftacles, together with the 
fquare of the current’s velocity in the place where thofe 
obftacles are found. 
3dly, The accelerating force of a river, or that 
by which it furmounts the refiftance of its bed in any one 
7 place,- 
