PRECIPITATION ON MOUNTAIN SLOPES POCKELS 85 



uniform horizontal current of air. A profile curve of this kind, 

 which rises steadily between the values x greater than — — 'and 



X 



less than + — - and falls also with uniform gradient between the 

 \£ 



limits x = 5/12A and x= 7/1 2a, and in the intermediate region 



describes a horizontal straight line at the distance + H from the 



axis of Xij is obtained by means of the Fourier series 



24# ^-a 1 . hn . 2hit 



7] = > h — Sln • Sln X, 



1 ^ ^ h? 6 X 



where h has all positive uneven numbers. In order to represent a 

 profile curve of the given form approximately, we take the first 

 three terms of the series, and therefore have 



7? = C { % sin m l x + j sin 3 m x x + ^ sin 5 m t x\ . . . (10) 

 The numerical values of the parameters are: 



X =60000 meters, hence m^ - — = . 1047 X 10 ~ s 



A 



and 



C = 1100 meters. 



The coefficients b h , in the expressions (8) and (9) therefore, have 

 the following values : 



b, = 881, 63 = 148.3, b s = 24.8 



The profile given by equation (10) is shown in fig. 1, where the 

 vertical scale is magnified five times. We perceive that the ascend- 

 ing gradient is nearly all confined to the interval between 



x greater than — and less than + — 

 12 12 



where, moreover, it is quite uniform, and further that the surface 

 of the valley is raised a little in the center, and the surface of the 

 plateau mountain is depressed by the same amount. The differ- 

 ence in altitude between the center of the valley and the center of 

 the mountain, which according to the adopted numerical values 

 should be 900 meters, is, therefore, not the absolute maximum 

 difference but is about 18 meters less. The profile curve here con- 



