PRECIPITATION ON MOUNTAIN SLOPES POCKELS 95 



The total quantity of precipitation is computed by the formula: 



V 



G = — a C sin mx \ e F' (y) e ny dy 



and is approximately equal to 22730; this is distributed over a hor- 

 izontal strip 12000 meters in length, and therefore, for a uniform 

 distribution for a = 1 the precipitation averages 1.9 millimeters. 

 From the preceding expression for G, it is plain that for any given 

 altitude of the mountain summit G will be smaller the shorter and 

 steeper the slope becomes, that is to say, the smaller the value of k 

 is, since the exponent ny increases with diminishing values of X. 

 In the present case the horizontal velocity of the wind is given by 

 the expression: 



3 cp I f}fi 



u = ' = a I 1 + C sin m x.e~ ny 

 dx \ n 



= a(l + 0.332 sin mx.e- nj/ ); 



which attains its minimum, = 0.547a, at the bottom of the valley, 

 and its maximum, 1.283 a, at the summit of the mountain, and has 

 a for the mean value of all the horizontal planes. Above the center 

 of the valley, it increases gradually with altitude, asymptotically 

 approaching its limiting value, a; for example, at the level y — o, it 

 is equal to 0.668a, and at the level y = 2400 it is already equal 

 to 0.80a. Therefore, if the stream under consideration proceeds 

 from a point x = — A/ 4, as a purely horizontal current of air flow- 

 ing over a plain, then its velocity must diminish with the altitude 

 in the ratio e~ ny . This would, of itself, be a plausible assumption, 

 but there would then be a vortex motion for each horizontal cur- 

 rent of air, which cannot, strictly speaking, continue steadily in 

 the above assumed potential motion. 



IV 



The assumptions hitherto made by us, namely, that the distribu- 

 tion of temperature in the current of air that impinges upon the 

 mountain side already corresponds to the condition of indifferent 

 equilibrium, that is to say that it is the same as would occur in an 

 ascending current of air under adiabatic changes of condition, is in 

 general not actually fulfilled. The scientific balloon ascensions at 

 Berlin have recently given us reliable conclusions as to the real con- 

 ditions of temperature and moisture in the free atmosphere up to 



