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SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



which tends toward the right-hand side in northern latitudes but 

 to the left-hand in southern latitudes: 



(2) In the determination of the amount of this pressure. 



The following is Braschmann's treatment of this problem as 

 given in his Memoir of Feb. 3, i860. 



Equations (1) [general equations of motion, here omitted] de- 

 termine also the accelerating force that the current of a river 

 exerts on its right-hand bank. 



Let M N, fig. 1, be a section of the river, b any point in this sec- 

 tion at which the average velocity of the steady stream of water 

 is v, that is to say, the uniform or steady velocity is the result of 

 all other influences combined with that of the acceleration due 

 to the rotation of the earth. Designate by x positive towards the 

 east and y positive towards the north the rectangular coordinates 

 of a point in the horizontal plane through b, neglecting the very 

 small fraction co 2 , we then obtain from equation (1) the following: 



d 2 x n . , dy 1 



— = + 2 co sin X. — 



dt 2 dt 



d 2 y . . dx 



— — = — 2 co sin /. 



dt 2 dt 



(2) 



Let a be the angle between the direction of the current and the 

 positive axes of y, then we have the following integrals 3 



3 For x = o and y = o or at the origin of coordinates, the steady velocity 

 v and therefore its projections on the x and y axes are 



dx 

 dt 



= v sin a 



dy 



^ = v cos a 



