G. K. Gilbert—The Deflection of Streams. 429 
‘The conditions of symmetry in the profile of the cross-section 
are thus destroyed. The outer bank 1s eroded; a deposit is 
accumulated on the inner bank. Moreover there is no com- 
pensating tendency to restore an equilibrium, for the erosion 
of the outer bank increases the sinuosity of the channel instead 
of rectifying it. 
' Curvature of course thus causes a stream to shift its channel 
laterally, and in this manner enlarge its valley. It is the mos 
Important condition of lateral corrasion. 
s shown by Ferrel, the deflective force due to terrestrial 
ith the velocity of the stream. It 
Let F=deflective force, per unit of mass, due to rotation. 
n=angular velocity of the earth’s rotation. 
v=velocity of stream. 
A=latitude of the locality. 
-p=radius of a curvature of the stream’s course. 
f=the centrifugal force, per unit of mass, developed by 
such curvature. 
2 
Then f= = - - - : (1) 
cand, from Ferrel, 
F==2vn sin A - - : : (2)* 
Let v,=velocity of a rapid-flowing thread of the current, 
Bem oe ae slow ce o oe oe 
Represent by F,, F,, 4, and f, the corresponding deflective 
forces due to rotation and curvature, 
then F,—F,=(v,—v,) X 2n sin A - - (3) 
y2—y? 
RN fj fee te - . : - (4) 
I . | 
F,—F, evidently expresses the selective power due to curva- 
ture; f.—f similarly expresses the relative power due to rota- 
'_ * This Journal, IT, xxxi, 29, equation (5). _Ferrel’s expression is modified above 
“by the substitution of the sine of the latitude for the cosine of the polar distance. 
