200 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



whose density and specific heat have values midway between those of 

 the aqueous vapor and the air. 



We now have to compute the limit of p up to which the equation (1) 

 may be used. Hereafter let e be the pressure of the saturated aqueous 

 vapor at the temperature T; e is a function of T, but of T only. The 

 mass v of saturated aqueous vapor that is present in the volume v at 

 the temperature T amounts to 



r =wt (lc,) 



and this quantity must be greater than jx so long- as the vapor is un- 

 saturated. Therefore the limit occurs when ^ = v. If we substitute 

 for v its value from the equation of elasticity, then this latter condition 

 (ju = v) takes the form 



As soon as T and p attain values that satisfy this equation, we must 

 relinquish the use of equation (1) and pass over to the equations for 

 the second stage. 



Second stage. — The air is saturated with aqueous vapor and contains 

 also additional fluid water. We neglect the volume of the latter. We 

 can therefore here also consider the air on the one hand and the water, 

 with its vapor, on the other hand, each as though the other were not 

 present. To both are to be ascribed the same volume v and the same 

 temperature T as that of the mixture; on the other hand, the pressure 



p of the mixture is equal to the sum of the partial pressures, p 1= = 



v 



for the air and p 2 = e for the aqueous vapor. 



7? T 



The equation p = A + e 



v 



or iP—e) v = XR T 



is therefore now the equation of elasticity of the mixture. The quan- 

 tity of heat that we must communicate to the air in order to bring 

 about the changes dT and dv is as before 



On the other hand, the quantity of heat that must be communicated to 

 the water in order to bring about the change dT, and to simulta- 

 neously increase by dv the quantity v of aqueous vapor, while pressure 

 and volume change correspondingly, is 



dQz = TdQf\ + M cdT. 



