188 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



equal to ptG h; the friction between the surface of the earth and the 

 air is equal to f u and consequently we find 



or 



n ill 



(10) 



Here k denotes the coefficient of ordinary friction which we have 

 introduced in our previous problems and we have 



k = i- (ii) 



ph 



This equation shows that the coefficient of friction k is inversely 

 proportional to the depth of the current measured from the surface 

 of the earth to the stratum of maximum velocity. 



By experiments on the viscosity of the air, Clerk Maxwell found 

 the value of K at o° C. equal to 0.001878. Introducing this value 

 in equation (7) we shall have 



u = U - 0.0033 G.z 2 (12) 



Experiments on the motion of liquids show that inequalities of 

 depth produce little vortices which play an important part in the 

 law of velocity. We are led to adopt the following formula: 



«* = U 2 - 0.04 G.z I (13) 



The value 0.04 is taken from experiments on the motion of water 

 in straight channels. 



§22. Horizontal currents of air of large extent 



We shall consider a horizontal current of air that moves over 

 so large a part of the surface of the earth that we cannot neglect 

 the effect of the rotation of the earth For horizontal motion the 

 deflecting force of the rotation of the earth is normal to the trajec- 

 tory of the wind and its value is expressed by 2 w sin 8 U, where oj 

 denotes the angular velocity of the earth, 8 the latitude and U 

 the horizontal velocity of the wind. 



Assuming that the motion of the current of air is uniform, then 

 the velocity and the gradient will be constant; the acting forces 

 will be the deflecting force of the rotation of the earth, the force of 

 the gradient and the friction. In the special case where the cur- 

 rent of air moves along a surface without friction, equilibrium will 



