by Terrestrial Rotation. 435 
of any particle at the bottom; let F be the deflecting force due 
to the earth’s rotation on a particle whose velocity is v. n 
F=2nv sin A where n is the angular velocity of the earth, and 
A the latitude. Let F, be the deflecting force on a particle at 
unit of volume of water. 
As in the stream now under consideration the surface veloc- 
ity is greatest, 0 will evidently be less than if the whole stream 
: ‘ F 
moved together with the velocity v,, i.e. less than tan™ oe 
Also, @ will be greater than tan™ Fy 
It seems probable that @ will not differ much from the angle 
whose tan = the sum of the deflecting forces acting on a thin 
slice between two cross-sections near together divided by the 
weight of the slice. Pas 
t is not necessary that @ should be accurately determined, 
as the following reasoning requires only that its tangent should 
be between the two values above mentioned. Suppose, there- 
nv,sin ; 
fore, @=tant——*-—*, v, being some velocity between v, and 
v,, probably not differing much from the mean velocity of the 
stream. 
tan OW, W being the weight of the cube 
he ’ oe . 
in terms of the deflecting force and gravitation, the excess of 
j 2nv, 8} oe 
hydrostatic pressure on the right face = ———--_ This 
pressure tends to move the cube from right to left across the 
Stream in opposition to the deflecting force, os the resultant 
nsin 
of the two forces is their difference, or ————— (%—¥), v 
must be urged from left to right. : Le 
In actual streams where the friction at the sides diminishes. 
