py) Hydraulics of the Mississippi River. 
a function of the mean velocity of the river only. The methods 
of gauging which have been founded on the assumption of a 
simple ratio, existing between some particular observed velocity 
and the mean velocity, are therefore all erroneous. 
The ratio between the observed velocity, at any depth in any 
vertical plane, and the mean velocity, in the same vertical plane, 
is a function of three variables, which are the mean velocity of 
the stream, the depth of the river, and the force of the wind. 
There is one particular depth at which the ratio becomes inde- 
pendent of this last variable, and sensibly so of the depth of the 
river. This is the depth midway between surface and bottom. 
The simplicity of the relation, between the mid-depth velocity 
and the mean velocity in the same vertical plane, suggests a — 
method of gauging rivers, by which the labor of the process is 
atly diminished, and its accuracy promoted. A meth 
may be founded upon the observed velocity at any depth, pro- 
vided the variables which affect the ratio between that and the 
mean velocity in the same plane are duly considered. Such a 
method was employed in the measurements of the Mississippi, 
during a considerable period of the operations of the survey. 
_. The foregoing are the principal laws which govern the habi- 
tudes of water flowing uniformly in straight and regular chan- 
nels. The following relate to the relations which exist between 
the cross-section, slope, and mean velocity of the stream. 
The area of the cross-section, the wetted perimeter, the width, 
the slope, and the mean velocity of the river, are connected with 
each other by such relations, that, when the first three are ascer- 
tained by measurement, together with the discharge per second, 
the other two may be determined. For practical purposes, the — 
wetted perimeter and the width may be treated as a single — 
variable. The variables will then be four; and of these, if any 
two be given along with the discharge, unless the cross-section 
be 
and mean velocity happen to be given together, the others may — 
foun 
f asensible addition be made to the waters of the river in | 
The 
any given stage, all the variables will be increased at once. The — 
the increase of slope divided by the increase of depth be taken © 
s the abscissa, the curve to which these codrdinates correspond — 
is a parabola. The pai of this parabola is constant at the — 
different localities are different. _ 
as 
1s : 
= 
