170 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



temperature of the current is colder than that of the surrounding 

 atmosphere. 



If m > m' or m = m' , f(z) increases with z and the intensity of 

 the current increases with the altitude. 



If m < m' we have f'(z) = o for a height h determined by the 



equation 



t ' _ T 



h = mm' -° — ° (11) 



g m' — m 



For this value of z, f{z) reaches a maximum and at the same time 

 we have 



T = T' 



If the altitude of the current is greater than h the virtual temper- 

 ature of the current at the surface of the earth is higher than that 

 of the surrounding calm atmosphere. 



(2) T = T '. The descending movement requires that m > m' 

 and this case includes the unstable equilibrium of the atmosphere. 



(3) ^0 > ^V I n this case f'(z) is negative up to the upper 

 stratum where the descending current must begin and consequently 

 f(z) decreases. 



If m > m' then f'(z) becomes zero for z = h, as given by equa- 

 tion (11) and f(z) attains a minimum for that value. For values 

 of z greater than h, f(z) increases and it is then possible that a descend- 

 ing current can even occur when the virtual temperature of the 

 current is higher than that of the surrounding upper layers of atmos- 

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

 virtual temperature of the descending current must increase more 

 slowly than that of the atmosphere. 



§17. Horizontal velocity produced by a vertical current 



In nature the ascending currents produce horizontal velocities 

 along the surface of the earth, which can attain very considerable 

 values and which are dangerous to the obstacles they meet in their 

 way. As to the descending currents we nearly always find that in 

 nature the resulting horizontal velocities along the surface of the 

 earth are slight, but it is probable that the horizontal velocities at 

 a certain altitude where the air enters the descending current, have 

 considerable values. 



Let us consider an ascending current and let v be the maximum 

 horizontal velocity, p Q the minimum pressure in the current at the 

 surface of the earth ; let p ' be the pressure in the calm atmosphere 



