142 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



The complete theory shows thai the value of k depends on the 

 height of the current. When the height of the current increases, 

 the value of k diminishes, which conforms with what we know of 

 the coefficient of friction of water in open channels. For very 

 broad channels the coefficient of friction is in the inverse ratio of 

 the height of the current. 



In studying the movement of a particle of air it is necessary to 

 add to the exterior forces the tangential forces and the centrifugal 

 force produced by the motion. Expressing by 5 the distance trav- 

 eled over and by R the radius of curvature of the trajectory, we 

 have 



vd v 

 the tangential force = —z — (3) 



v 2 

 the centrifugal force = — (4) 



Let us add that the horizontal currents move along the surface 

 of the earth which is normal to gravity. Consequently we neglect 

 the action of the gravity in the following problems and the acting 

 forces will be (1) the gradient force, (2) the defective force of the rota- 

 tion of the earth, (3) the force of friction, (4) the tangential force 

 of the motion and (5) the centrifugal force of the motion. 



§9. Horizontal rectilinear and uniform motion 



When the motion is uniform and rectilinear, the tangential force 

 and the centrifugal force disappear, and equilibrium is established 

 between the force of the gradient, the force of friction and the deflect- 

 ing force of the rotation of the earth. 



Expressing by a the angle between the gradient and the trajec- 

 tory and resolving the forces along the trajectory A B, fig. 2, and 

 perpendicularly to its direction we have 



fJL 



- G cos a = k v (1) 



P 



{J. 



- G sin a = 2 co sin 8 v (2) 



P 



By division we obtain 



2 oj sin 8 

 tan a = 7 (3) 



