a 
198 Hydraulics of the Mississippi River. 
G=specific gravity of the water, g==measure of the force of gravity, 
s=7=slope of surface expended against ordinary resistances, 
slope expended against bends, &c. V, U, v, b=same values as 
before, 
we shall have, for the accelerating force of gravity, the expres: 
sion, Ggals, and, for the resistances at the perimeter, the ex- 
keto rss) 
U,+U, Ay as as +”) 
so ; or pew? 
If we substitute the eas of U, and U, given above, the 
equation ee itself immediately to the following : 
Rng FP $ 
pew =(0°93y—0:167(6v)*); which put —¢(z). 
Let 3 iv be denoted by r,=the radius of the entire perime- 
ter: the expression then be¢tomes ) 
78=9(-930 — 167(bv)?)=(2). 
This Webi ad equation differs from that which is usually 
assumed, in two particulars. First, the radius of the entire 
secondly o(2) is used instead of g(v), or a function of the mean — 
velocity at the perimeter, instead of a function of the mean velo A 
of the river itself. Ae 
* In stating this expression, the a 
solecism, in arbitrarily changing t 
occurrence of what the 
