2i8 The American Geologist. a^"''' "04. 
second, 4.4 = 2000 "VS. S = (.0022) ^ = .0000048 = .0253 
feet per mile. This is considerably less than the slope of the 
Mississippi at present. The amount delivered in a day would 
be the velocity times the area = 3 X 24 (=72 miles per day) 
X 2 (miles broad) X ("''V5080) miles deep = 5.3 cubic miles 
per day. It would take some 96 days to carry off the amount 
of 500 cubic miles of water which you mention. 
We may write the formula, discharge = K X width X 
depth'/^ X slope^/2, and it is apparent that the discharge will vary 
pretty nearly as the square of the depth or the square root of the 
slope, being much more sensitive to changes in depth than to 
changes in slope. I m.ay say that K is less, the rougher the 
channel is, and I should imagine that in a flood it would be less 
rather than more than 37.6, and the velocity and discharge for 
a given slope less. Moreover you will remember that the ex- 
pression for the slope applies only so long as the section is of 
the shape you mention, and for the same discharge and depth 
but greater width the slope will drop rapidly being inversely 
as the square of the width. 
It is perfectly obvious that differential depressions only of 
the same order as the uplifts Gilbert finds to be now going on, 
might give flood sections of the breadth and depth you mention 
if the amount of water to be discharged were as great as you 
mention. If the discharge may be assumed to vary from the 
spring to the fall equinox in a simple harmonic ratio then the 
mean discharge would be -~ (-z^) of the maximum. This, if 
the former is 5.3 cubic miles a day, X 182 days {— ^2 year) 
would be about 620 cubic miles per annum. But it is probable 
that the exceptional flood is in a greater ratio to the mean dis- 
charge than 7:11. For to take a random instance from the 
measurements of the U. S. Geological Survey Water Supply 
Paper No. 84, p. 19, the mean discharge of the Niobrara river 
at Valentine, Nebraska for March to August inclusive was 
844 second feet, which at the ratio 7:11 would imply a max- 
imum of 1330 second feet or according to their rating table 
1.9 feet gage hight. Whereas they had a number of days a 
little above this, and one flood up to 2.05 feet. 
Very truly yours, 
Alfred C. Lane, State Geologist. 
