22 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
restored if accidentally or artificially modified. The distribution 
of velocities within this cross-section is symmetrie, the swiftest 
threads of the current being in the center and the slowest adjacent 
to the banks. If now curvature be introduced in the course of 
the channel, centrifugal force is developed. This centrifugal force 
is measured by the square of the velocity, and is therefore much 
greater for the swift central threads of the current than for the 
slow lateral threads. The central threads, tending the more strongly 
toward the outer bank, displace the slower threads at that bank, 
and the symmetry of the distribution of velocities is thus destroyed. 
As pointed out by Thomson and others, this redistribution of velo- 
cities determines the erosion of the outer bank and the simultaneous 
deposition of detritus along the inner bank. 
It has been shown by Ferrel that the deflecting power of the 
rotation of the earth upon a body moving on the surface is equiva- 
lent to the centrifugal force which would be developed if the body 
followed a circular course with radius of curvature (p) equal to 
v 
2n cos. # | 
angular velocity of the earth’s rotation, and % the polar distance of 
the locality. 
The effect of rotation on a stream being equivalent to a centri- 
fugal force is identical in kind with the effect of curvature of 
channel,* and this identity renders a quasi-quantitative comparison 
possible. Humphreys and Abbott found during flood a mean 
velocity of the Mississippi river at Columbus of 8.4 feet per second. 
The value of p corresponding to this velocity and the polar dis- 
tance of the locality is about 20 miles. The actual bends of the 
channel in the same region, which depend for their features on the 
velocity and volume of the river at flood stage, have a radius of 
In this expression v is the velocity of the body, n the 
* The author has since seen reason to modify this statement. The two 
effects are not strictly identical in kind, because the effect of rotation varies 
with the first power of the velocity, while the effect of curvature of channel 
varies with the second power. For this reason the selective power of curva- 
ture is, for the same deflective force, double the selective power of rotation. 
The introduction of this consideration would modify the numerical results 
derived from the Mississippi river, but would not impair the qualitative 
conclusion. A modified treatment of the subject will be found"in the Ameri- 
ean Journal of Science for June, 1884; Vol. XXVII, pp. 427-482. 
