MOVEMENTS OF ATMOSPHERE — GULDBERG AND MOHN 189 



exist between the deflecting force of the rotation of the earth and 

 the force of the gradient; consequently the two forces must be oppo- 

 site and their directions must be along the same straight line. 

 We shall then have 



- G = 2 oj £7 sin 6 (1) 



P 



The deflecting force of the rotation of the earth being normal to 

 the path of the wind, we conclude that in the case where the friction 

 is zero, the current is normal to the gradient, that is to say, the wind 

 moves along the isobar. The ratio between the velocity of the wind 

 and the gradient is expressed by 



^ = / 2 oj sin 8 (2) 



Let the pressure be 76o mm , the temperature o° C, and the tension 

 of the vapor of water o, we shall have 



50° 60° 70° 



8.31 7.31 6.77 



We have supposed that the force of friction, at the surface of the 

 earth, is opposite to the motion of the particle of air. In this case 

 its path will form an acute angle with the direction of the gradient. 

 Since friction has its greatest value at the surface of the earth and 

 diminishes with altitude, the velocity of the air and at the same time 

 the angle of inclination </> in §i i must increase with the height, which 

 observations also show to be the case. 



In the stratum that separates the lower current from the higher 

 current, (in the systems of wind that we considered in the preceding 

 chapter) the gradient must be zero and consequently the velocity 

 of the air nothing. Thus the velocity of the air increases with the 

 altitude in the part near the earth while.it diminishes toward zero 

 in the region near the stratum that is intermediate between the 

 two currents. The velocity of the air must consequently attain its 

 maximum at a certain height. 



