MOVEMENTS OF ATMOSPHERE — GULDBERG AND MOHN 209 



then the air flowing into a stationary cyclone changes its physical 

 state and becomes colder and dryer, the horizontal barometric 

 depression diminishes little by littte and the cyclone is destroyed 

 after a certain time. 



§28. Instantaneous systems of wind 



Let us consider a column of air of the height / that has been heated 

 so that the pressure p at the upper end (see fig. 29) exceeds the 

 pressure p' of the surrounding air. The air commences to leave 

 , the upper end of the column and at the same 

 4, \ r f r time air enters at the lower end, but the density 

 of the supplementary air filling the column up 

 to the height z has a value p different from the 

 value p' of the air of the calm atmosphere and 

 consequently the weight of the column dimin- 

 ishes so that the pressure p at the surface of 

 the earth decreases and produces a depression 

 I J ! ^ p ' — p Q . The pressure p diminishes at the 



p p ' same time that the vertical velocity w of the 

 current increases up to a limit that corresponds 



Fir* 20 



to the maximum value of the vertical velocity, 

 and after this moment the steady motion goes on. As an approx- 

 imation we can neglect the variation of density due to gravity and 

 consider the force that maintains the ascending motion as equal to 

 Po ~ P 



1 



% 



The equation of motion assumes the form 



I (1) 



pi 



dw p - P 



dt pi & 



The difference p Q — p is equal to the weight of the column of air z 

 having the density p and of the column I — z having the density 

 p'; consequently we have 



Po ~ P = g P z + g P' ( l - z ) 

 Introducing this value in eq. (1) we have 



dw (p' — p) I 



dt s ' p I 



(2) 



From equation (1) we conclude that the vertical velocity increases 

 up to the moment when the pressure has attained the value 



Po = P + g P l 



