96 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



altitudes of 8000 meters. The mean values of the temperature 

 and moisture at successive levels, 500 meters apart, which von 

 Bezold has deduced 7 from the observations of Berson and Suring 

 show that the mean vertical diminution of temperature is slower 

 than the adiabatic, and that, in general, the moisture does not attain 

 the saturation value. In a horizontal current of air, in which these 

 average conditions prevail, the air will, therefore, never be satu- 

 rated, and, consequently, our assumption of the existence of a con- 

 stant lower limit to the clouds is not allowable. Moreover, it is no 

 longer the vertical component alone that controls the condensation 

 that shall occur at any given point in the current of air ascending 

 above the mountain slope, as was assumed in the derivation of 

 formula (14). We must rather, in the computation of W, consider 

 that the quantity of water condensed in a unit of space under steady 

 stationary conditions is equal to the excess of the quantity of water 

 vapor flowing into the space above that simultaneously flowing out. 

 For one cubic meter and one second this excess is: 



d (euF) d (ev F) 

 d x dy 



or since because of the equation of continuity we have approxi- 

 mately 



therefore, 8 



and hence, 



de u de v _ 



o , 

 d x d y 



8F dF 



— e ( u - + v 



d x dy 



W = - C s (u dF -+v d —) dy (17) 



J \ dx dy J 



2/° 



where y° and y' indicate the altitudes of the limits of the clouds 

 above the point under consideration. The evaluation of the inte- 

 gral still demands not only a complete knowledge of the stream, but 



7 W. von Bezold: Theoretische^ Betrachtungen, etc. Theoretical consid- 

 erations relative to the results of the scientific balloon ascensions of the 

 German Association for the Promotion of Aeronautics at Berlin. Brunswick, 

 1900, pp. 18-21. (See No. XIV of this present collection). 



8 In so far, namely, as the quantity of the aqueous vapor condensed in a 

 unit of volume is inappreciably small in comparison with the total quantity 

 of moist air flowing through this space. 



