260 



THE MECHANICS OF THE EARTH S ATMOSPHERE. 



t, y, y', R, and p, the corresponding values after mixture and after 



the loss of the quantity of water that exceeds 

 the normal quantity for saturation, or also, in 

 general, any given group of the same quanti- 

 ties belonging together. 

 The pressure expressed in millimetres of mercury will as before be 

 expressed by /?; the maximum of the elastic force of the vapor will in 

 a corresponding manner be expressed by €. The pressure /i can be 

 considered ascoustaut during the process of mixing. This is allowable 

 since, where mixture actually occurs, the two masses of air must nec- 

 essarily exist under very nearly the same pressure and must also retain 

 this [in the free air] even when on account of the mixing a change oc- 

 curs in the total volume, which in general is very unimportant. 



The problem of mixture becomes extremely simple so long as no pre- 

 cipitation of water occurs, that is to say so long as the quantities ob 

 tained by the mixture are to be indicated as in the above notation by 

 the subscript3. 



In this case 



y 3 {m 1 +m 2 )=y 1 mi+y 2 m 2 



or m l (y 3 —y 1 )=m 2 {y 2 ^if 3 ) (1) 



aud further 



cinh(t s — ti)=m 2 c 2 (t 2 — 1 2 ) 



where by c t and c 2 we understand the thermal capacities of the quan. 

 tities of air to be mixed,* or since these quantities are to beconsideied 

 equal 



wi,(/ 3 -*i)=»i2(*2-* 3 ) (13) 



Jf we combine the equations (i) and (2) we obtain (the mixing ratio) 



y.-i— y\_ h— t 1 = m z 



2/2—2/s t 2 —h Ml 

 which is the well known equation that holds good for the mixture of two 



r . quantities of the fluid in question, 

 having two different temperatures. 



Since the graphic m ithod will be 

 chosen in the further development, 

 therefore first of all this simple for- 

 mula must be translated into a geo. 

 metrical form. 



To this end, in a rectangular sys- 

 tem of coordinates, Fig. 37, the tern, 

 peratures (t) are taken as abscissas, 

 the quantities of moisture (y) as ordi- 

 nates, and these are designated in the 

 ordinary manner by OT^OT, .... 



"Strictly speaking we should use mean values computed by a special formula be- 

 tween the above named Cl aud c 2 and that of the mixture v,. Since, however, the 

 values of c scarcely differ from each other for the different temperatures and pressures, 

 we. can therefore omit this rehnement. 



