DIslrlhiitioii of the Loess. — //'/';.<;/;/. 217 
water 200 feet deep, llowing at the rate of three miles an hour, 
166 days would be required to discharge the total amount. But 
the progress of events would not be so simple as this. The wa- 
ters would begin to rise soon after the vernal equinox, and con- 
tinue so to do until the early part of August, when they would 
reach their maximum hight, and continue for a brief period of 
perhaps three or four weeks, when they would begin to subside, 
because of the diminishing suj)ply, as llic autumnal equinox 
approached. 
To make as correct a calculation as i)ossible upon the prob- 
lem presented, 1 have submitted to professor Alfred C. Lane 
a hypothetical case making the supposition that 500 cubic miles 
of water were set free in the middle portion of the ^Missouri 
valley by the melting of the sun's rays between the vernal and 
the autumnal ecjuinox while the outlet of the channel below the 
Osage river was restricted to a width of two miles and a depth, 
of 200 feet, and at the same time obstructed by high water in 
the Mississippi river, what depression at the north would be 
required to reduce the gradient sutiiciently to slacken the cur- 
rent to three miles an hour? In repl}- the following was re- 
ceived, which will shed nmch light upon the whole subject, and 
show that the movement of water which we have supposed is 
entirely within the range of mathematical probability. 
Lansing, Mich., Feb. 13, 1904I 
My dear Mr. Wright : 
In reply to your inquiry as to How and discharge of the 
glacially Hooded Missouri or Mississippi I should use Sullivan's 
fonnula \' = K R^' S-, when \' is the mean velocity (not max- 
imum velocity at the surface which will be from ^/., to V* niore). 
In a stream 2 miles broad or so and only aliout 200 feet deep 
R. which is the area of the stream divided by the wetted peri- 
meter, will be within 2'/ or 37c the same as the depth (d) and 
we may write R'^^^dH-y^d. The fourth root of d will vary quite 
slowly. For d = 200 it will be 3.76. K depends upon the 
roughness of the stream bed and varies from 19 to 75. being 
38.40 for the Mississippi at Vicksburg and 36.48 for it at Co- 
lumbus, Ky., and 37.50 for the Rhine. If we take its value for 
convenience at 37.6 we shall ,have, mean velocity = 10 (depth 
= 200) "VS. Three miles an hour would mean 4.4 feet per 
