90 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



influence on the value of W, since both — F'(y) and ve rapidly 

 diminish with the altitude. 



For the numerical computation of W, it is advantageous to first 

 bring the expression (14) by partial integration into the following 

 form: 



v' 



W{x) =| veFiy) P + P F (y)—cty (14a) 



Vo 



In this expression v is given by equation (13) as a function of y 

 and x. F(y), or the saturation value of the specific moisture at the 

 altitude y, as well as the corresponding values of the pressure and 

 temperature necessary for the computation of e are most easily 

 obtained with the help of the graphic diagram for the adiabatic 

 changes of condition of moist air first given by H. Hertz, since 

 a simple analytical expression for these quantities cannot be given. 

 In using the Hertzian table 3 we have to remember that y is not the 

 absolute altitude but the altitude above the axis of x in our system 

 of coordinates, therefore, in order to obtain the altitude above sea 



level, it is still to be increased by the quantity — >jl x = — "7 ) and 



also by the altitude of the valley above the sea. The integral in 

 equation (14a) can be evaluated with sufficient accuracy by divid- 

 ing the integral from y Q to y' into parts y 9 ...y v y^—y^ y^-i ■•■■ v h 

 (where y h = y'), and for each of these introducing an average 

 value F mk whereby we obtain equation (15). 



Vh h 



Vo 



(ev) k - M*-i 



(15) 



In order to execute the complete computation of W for a special 

 example, we will assume that the current of air which strikes the 

 mountain having the profile shown in fig. 1 has a pressure of 760 

 millimeters, temperature 20 , and specific humidity, 9.0, 4 at the 

 bottom of the valley. Hence, according to our assumption of adia- 

 batic equilibrium it follows that the lower limit of the clouds will 

 lie at an altitude of 950 meters above the bottom of the valley, and, 

 therefore, 50 meters above the center of the mountain, if v = 500; 



3 H. Hertz: Met. Zeit., Vol. I, pp. 421-431, 1884, or the preceding collec- 

 tion of translations, 1891, p. 198. 



4 That is, 9.0 grams of water per kilogram of air. 



