ROTATION AND HORIZONTAL MOTIONS BRASCHMANN 25 



dx 



- = A +2 co sin X.y = v sin a + 2 co sin X.y. 

 dt 



dy 



■ -- = B — 2 to sin X.x = v cos a — 2 to sin /.v. 



By substituting these values in equations (2) and neglecting or 



we have 



d 2 x 



— = + 2 co v cos a sin X 



dt 2 



= — 2 co v sin a sin X 

 dt 2 



These equations determine the accelerative force 



m 



+ (f| ) 



This shows that the amount of this force is independent of th 

 direction of the current of the stream and moreover that it is 

 directed steadily toward the right-hand bank. 



If u is the angle made by this accelerative force with the axis 

 of y or the north line counting it positively around to the right, 

 then 



d 2 x -. . 



— = F sin u 

 dt 2 



d2 y Z7 



— = F cos u 

 dt 2 



but 



F = + 2 co v sin X 



hence 



sin u = + cos a 



cos u = — sin a 



u = a + 90° 



that is to say, when X is positive the direction of F is 90 farther 

 toward the right than the direction of the current. 

 When X is negative we have 



sin u — — cos a 

 cos u = + sin a 

 u= a + 270° 



