l68 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5 1 



If f(z) is positive, f(z) increases with the altitude and remains 

 larger than unity : the condition of an ascending current is then ful- 

 filled. 



We shall distinguish three cases : 



(1) T > T' . At the surface of the earth where z = o we shall 

 have f(z) positive. We conclude then that an ascending current 

 can always exist when the virtual temperature of the current is 

 greater than that of the surrounding atmosphere. 



If m < m' or m = m' then f(z) increases continuously with z 

 and the intensity of the current increases with the altitude. 



If m < m' then f(z) increases at first and reaches a maximum at 

 an altitude given by 



h = -mm' T °~ T °' (6) 



g m' — m 



and at the same time, we have 



T = V 



(2) T = Tq. It is necessary that w> m! so that f{z) can be 

 positive. This case includes the unstable equilibrium of the atmos- 

 phere. 



(3) ^0 < T' . At the surface of the earth f{z) is negative. If 

 m > m' then f'(z) = o at an altitude h determined by equation (6) 

 and f (z) becomes positive for greater altitudes. We conclude then 

 that f(z) at first decreases with the altitude and reaches a minimum 

 at the altitude h and then decreases with the altitude. It is therefore 

 possible that an ascending current can occur even when the virtual 

 temperature of the surrounding atmosphere is higher than that of 

 the current. The altitude of the current must be greater than h 

 and the virtual temperature of the current must decrease with the 

 height more slowly than that of the atmosphere. 



Descending currents 



In descending currents (fig. 13) the air enters at the height z and 

 flows outward along the surface of the earth where a barometric 

 maximum occurs. Therefore the conditions of the descending 

 motions are p' > p and p > p' . We will count the altitude z from 

 the top downward and write 



T = T + gZ and T = T ' + gZ 



a in a m 



