21 G THE MECHANICS OF THE EARTH's ATMOSPHERE. 



pbere until it fiually, either witbiii an anti-cyclone or under the well 

 known conditions of the loehn 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 ])ortion, although it may be a very consulera- 

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



One can therefore begin the comi)ntation 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 diflterent quandties of 

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

 fore more ai)propriate to consider the unit of mass of dry air as given, 

 and the water as an ad<litional variable mixture. 



This being premised, we will now indicate by jI/^, J/j, j\J^, M^ the mas-se» 

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

 the tJri/, the rain, iliv Jidil, and the s)ioic stage, and will also attach to- 

 the other quantities similar subscri[)t letters as indices, in so far as a 

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

 putations that relate throughout to only one stage these indices maybe 

 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„ = 1 + x„ 

 or abbreviated 



jM = 1-\-x 



wliere x or .r^ 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 therelore 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 api)ie- 

 ciable intioiliu'tioii of atpieous vapor is only possible at the surface of 

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

 chan^^ed in the atmosphere between masses of air of diifereut absolute 

 humidities can certainly at first be wholly neglected. 

 {B)' — The rain stage. 



M,,=l-\-x,-\-x,' 



or, when confined to one stage as before, 



M = i -\- X + x'. 



In this Xyy indicates the mass of satuiated aqueous vapor that is con- 

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

 present. 



