30 Hydraulics of the Mississippi River. 
well enough known for the purpose in hand. The numerical 
coéfficient of d,,?, in the equation of the parabola, being then 
divided by the so-assumed value of 3, will give the square root 
of the value of d which is sought. is value is found from 
equation of the trough to be a little above unity. In the equa- 
tiou employed in the previous computations, being that which | 
ad been derived from the grand mean.curve of the Mississippi, 
the numerical value of 6, as we have seen, was 071856. It 
appeared probable, therefore, that this quantity, that is, the 
parameter of the parabola of parameters, varies inversely as 
some function of the depth. For the sake of further testing the 
truth of this supposition, careful observations were made upon 
a feeder of the Chesapeake and Ohio Canal near Washington, 
having a depth of 7-1 feet and a width of 23; being, in these 
dimensions, much smaller than the. river, and much larger than 
the trough. The mean maximum velocity observed was a little 
over two feet and a half, and the mean difference between the 
computed velocities for the several points observed and the 
means of the observations themselves at those points was less 
than a quarter of an inch. The equation of the parabola de- 
duced from the observations gave a value of } equal to 0°58. 
The value of 5 (or of the parameter of the curve of parameters) — 
changes, therefore, very slowly at considerable depths; and is 
practically at its minimum value for rivers when it equals 0°1856, 
The following expression is given as representing the observa 
ons: 
5 
(D415)? 
in which D denotes the depth of the river. 
It being once established, that the curve of velocities in the . 
vertical plane parallel to the stream is a parabola, and the — 
equation of the parabola being known, the mean velocity in the — 
whole vertical curve is easily deduced. The area representing — 
the sum of all the velocities is made up of a rectangle and 2 — 
parabolic segment above the axis, and of another rectangle 4 
parabolic segment below. Dividing the sum of these areas by — 
the total depth will give the mean velocity required. But the 
dividend in this case is an expression necessarily inyolving the — 
of the axis as an element; and, although this mean depth 
had been found to be nearly constant, the actual depth is observed — 
tovary. This variation is apparently dependent on the direction — 
and force of the wind. = 
_ In the investigation of the effects of wind-force, the selected - 
observations were divided into three classes—those in which the - 
se in which it blew down-stream, an¢_ 
bs H 
