216 THE MECHANICS OF THE EARTH -S ATMOSPHERE. 



phere until it finally, eitber within an anti-cyclone or under the well 

 known conditions of the foebn wind on the lee side of a mountain, comes 

 again to its initial level, it is not the whole mass that we again find 

 there present, but only a portion, although it may be a very considera- 

 ble fraction, since a part of the water has been lost. 



One can therefore begin the computation with the unit of mass of the 

 mixture, but must consider the loss in mass that may occur in the course 

 of the processes (a gain only occurs when the air passes over moist sur- 

 faces). But in this we have to combat the difficulty that, according to 

 the point of departure that we choose, or according to the prevailing 

 absolute humidity of the air at the point of departure, we have present, 

 not only different quantities of vapor, but also different quantities of 

 dry air, since the sum of the two must be equal to unity. It is there- 

 fore more appropriate to consider the unit of mass of dry air as given, 

 and the water as an additional variable mixture. 



This being premised, we will now indicate by M a , M b , M c , M d the masses 

 of the mixture in the four stadia so well distinguished by Hertz, namely, 

 the dry, the rain, the hail, and the snow stage, and will also attach to 

 the other quantities similar subscript letters as indices, in so far as a 

 distinction of the respective stages may be necessary. But in compu- 

 tations that relate throughout to only one stadia these indices may be 

 dropped, in order not to overburden the formula? too much. This being 

 premised, we next find for the four stages the accompanying equations 

 that may be temporarily designated as the equations of mixture. 

 {A). — The dry stage : 



M a = 1 + x a 

 or abbreviated 



M = l+x 



where x or x a designates the mass of aqueous vapor that is mixed with 

 the unit mass (one kilogram) of dry air. In this it is assumed that the 

 air is not saturated with aqueous vapor, and therefore x a indicates 

 always the mass of unsaturated (overheated) vapor that is contained 

 in the mixture. This mixture remains, in general, constant in the free 

 atmosphere, since in this stage precipitation is excluded and an appre- 

 ciable introduction of aqueous vapor is only possible at the surface of 

 the earth, and again since the quantity of aqueous vapor that is ex- 

 changed in the atmosphere between masses of air of different absolute 

 humidities can certainly at first be wholly neglected. 

 (B). — The rain stage. 



M b =1 + x h + x,,' 



or, when confined to one stage as before, 



M = 1 + x + x'. 



In this x h indicates the mass of saturated aqueous vapor that is con- 

 tained in the air, x' h is the additional mass of water liquid that is 

 present. 



