THE LATERAL EROSION OF STREAMS 439 



Effect of F^ on Objects Moving in Fixed Courses 



Obviously, if the object were not free to move as these forces 

 would direct it, but were constrained to move in a fixed channel, the 

 deflecting force would cause it to press against the side of the channel. 

 Now, if the channel were along a meridian, only one component of 

 the deflecting force would be active, or, if along a parallel, the other 

 alone. But if the channel were in any other direction, the movement of 

 the object would have both a north-and-south and an east-and-west 

 component of motion, and both components of the deflecting force 

 would operate proportionately to the components of relative motion 

 from which they arise. And since, according to Ferrel,' the amount 

 of the deflecting force arising from an east-and-west relative motion 

 is exactly equal to the amount due to a north-and-south relative 

 motion under similar conditions, it follows that at any given latitude 

 for the same rate of relative motion, the deflecting force is constant, 

 regardless of the direction of the relative motion. 



Measurement of F^ 



The amount of this deflecting force varies with the rate of relative 

 motion and the latitude. 



Using Ferrel's formula,^ — = ^—^ — ( A/' = gyratory velocity 



of the earth in terms of the radius; 5 = rate of relative motion; sin 

 Z = sin. of the angle of lat.; ^=accelerative force of gravity), and 

 adopting arbitrarily a definite rate of relative motion of 2 meters per 

 second, or 4^ miles per hour, the expression of the deflecting force 

 in terms of the force of gravity for each fifth degree of latitude is 

 given in column 2 of Table I. 



Taking the amount of the deflecting force at the fifth degree 

 of latitude as a unit of measurement, the amount active at each 

 fifth degree of latitude is given in round numbers in the third 

 column of Table I. 



For comparison with the more familiar eft'ect of F^ as developed 

 on curves, radii of curvature have been computed which would 



1 Ferrel, Popular Treatise on the Winds, 42-8S. 



2 Ferrel, loc. cit. 



