= 
36 Hydraulics of the Mississippi River. 
If any value could be assigned to d in this expression, which 
should reduce the fraction in brackets to zero, it would follow 
that the depth m (which would then be d) is inde oe of the 
=r agape of the river, v. This cannot one; but if d 
de =4D, the ratio is greatly simplified, and the equation 
Teste 
— Vin 
Vartre(be)t 
Since both D and d, fies from this expression, the ratio 
of the mid-depth velocity is independent both of the depth of 
the river and of the force of the win f the velocities in the 
mean of all vertical planes parallel to the current be represented 
by U instead of V, we shall have 
pene ane 
Ua ae (ov) 4 
-98u, the coéificient remaining cay. constant. ” abetentiad 
this ‘value, the authors of the report have tested the formula, by 
_ computing the ratio, 
“93v 
930-L-A-(bv)” 
for every even foot of velocity from 1 to 8, and employing the 
results in the computation of mean velocities from many mid- 
depth velocities actually observed. The observations include 4 
number the Mississippi and - outlet bayous, in fees 
stages of “the water, and also those made, as before mentioned, 
on the feeder of the Chesapeake a ef Ohio "iaaal, together with 
others by Messrs. Hennoeque and Defontaine on ‘the Rhine, @ 
finally those by Mr. Boileau on his experimental wooden trough. 
he position of the axis, among these data, varied from the 
surface to a point below. mid- -depth, and the mean velocities 
varied from a foot and a half to more than four feet. The dif 
ferences between the observed and computed values of vi | 
however, were, for the most part, practically insensible, and in — 
the few eases in which this was not true they amounted to but 
two or three per cent. | 
The near approach to constancy, and equality of the ratio be 
tween the mid-depth velocity and the mean velocity, is is easily — 
intelligible when the fact is once detected e resistances to — 
motion proceed from the perimeter; that is, “from the bottom and — 
the surface. The discharge remaining sensibly constant, ear in 
a a uniform channel, the cross-section also, whatever vo 
at 
