« 
200 Hydraulics of the Mississippi River. 
195ast t 
z==(195r,s ft =(-F ste) i 
From this are deduced values for each of the variables in 
terms of the rest (regarding p+ W as a single variable), viz: 
__((p+W)z?\? 
meres 7 TO fe 
a PEW? 
ct eee ie 
pws — 
Instead of p-+W, may be as oe ee error, for 
rivers, 2°015 W. Resuming the value 
5s das bitte At 
and solving with respect to of, we obtain 
ot = —4/0-00815-+-(2257, s*)3-L.0-008%, 
2 
and v=(-470-00818-+4 (225°, s)? 40-0908 
The negative value of the radical is that which it is necessary 
to take, in order to fulfil the condition that v shall become zero 
when s is zero. 
For rivers, the value of }, as heretofore given, is 0°1856. The 
term containing it under the radical will have only the value 
‘0015, and may ordinarily be neglected. The expressions for 
the ever] variables will then become 
r=(oanen— (etn) }e= (onan (2) 
ooo 
(v? — 0-0388)4 ts (f= 0:0388)*\? * 
225s8t ag: 225r, | 
If Q represent the amount of discharge per second, then 
v=—, and a=-. 
a v 
If Q be given, along with any two of the foregoing variables, 
the rest may be computed by the help pts this equation, unless 
the two given at the same Pe are v 
In estimating the effect of a the authors found the — 2 
* In the last two formule, the second t erm of the sccmnggd has the nogat 
e two form 
involves 
at t all in the 
PE ee, Se Se ee a Dw te es 
