MOVEMENTS OF ATMOSPHERE OHLDBERO AND MOHN 



18' 



The vertical motion being zero, the vertical gradient H will dis 

 appear and consequently the pressure is independent of the alti- 

 tude z. We conclude therefore that the horizontal gradient G is 

 independent of z and constant. Integrating equation (5) we shall 

 find 



K 



du 

 dz 



C — ji G z 



(6) 



XT 



»w- 



In order to determine the constant C we notice that the internal 

 friction disappears at a certain value of z which we will denote by 



h; at the same time the velocity has its 

 maximum value U. It is evident that 

 the friction is equal to zero in the stra-~ 

 turn whose velocity is a maximum be- 

 cause the velocity decreases equally on 

 each side of this stratum and conse- 

 quently the difference between the ve- 

 locities of the two strata located sym- 

 metrically is equal to zero. By choosing the origin of coordinates 

 at this distance h from the surface of the earth (see fig. 21) we 

 shall have the constant C equal to zero and by integrating equa- 

 tion (6) we shall find 



zc< 



fig. 21 



2K 



(7) 



Let the velocity of the air at the surface of the earth be u , then for 

 z = h we shall have 



u n = U — 



2 K 



k- 



(8) 



The upper limit of a free horizontal current is found by placing u = o 

 and let the corresponding value of z be H, we have 



= U - 



2 K 



W 



(9) 



From equation (6) we conclude that the friction at the distance z, 

 is equal to ^ G z; at the surface of the earth the internal friction is 



