88 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



point x = ± A./8 up to a maximum at some very great altitude. 

 (The isolated negative value that occurs for x — X/6 and y = 500 

 is explained by the above-mentioned slight depression of the sum- 

 mit of the plateau mountain.) 



In order now, to investigate the condensation of aqueous vapor 

 that occurs in consequence of the ascending currents of air forced 

 upward by the upward slope of the ground, we first make the assump- 

 tion that the ascending mass of air experiences an adiabatic change 

 of condition and that adiabatic equilibrium prevailed already in 

 the horizontal current of air advancing toward the slope of the 

 mountain. In this case the air will be everywhere saturated at a 

 certain altitude that can be computed from the temperature and 

 humidity of the air at the surface of the valley. In a unit of time 

 the quantity of air, ve, flows in a vertical direction through a space 

 having a unit of horizontal surface and an altitude dy. If this 

 element of space lies above the lower limit of the clouds, then in 

 this quantity of air there will be as much aqueous vapor condensed 

 as the difference between what it can contain in the state of satur- 

 ation at the altitude y + dy and what it can contain at the altitude 

 y. Therefore this quantity is 



-dF 



vs. — ay, 

 dy 



where F (y) is the specific humidity of saturated air at the altitude 



y- 



Still assuming a stationary condition, we have — 



W 



V 



= - jveF' (y)dy, (14) 



as representing the total quantity of aqueous vapor condensed in a 

 unit of time in a stratum of cloud above the unit of basal area be- 

 tween the altitudes y and y' . 



This would also be equal to the quantity of precipitation falling 

 from that layer of cloud on to the unit of horizontal base in case the 

 products of condensation simply fell vertically without being car- 

 ried along by the horizontal current of air. We will make this 

 assumption, since as yet we have no clue by which to frame a com- 

 putation of the horizontal transportation of the falling particles of 

 precipitation. It is, however, easy to foresee that the horizontal 

 transportation would be of importance, especially for the slowly- 

 falling particles of water or ice in the upper strata of clouds, and 



