262 



THE MECHANICS OF THE EARTHS ATMOSPHERE. 



The investigation of the cases included in 2 can always be referred 

 to case 3, since the points Fi* and F 2 *, in which the straight line F x F 2 

 cuts the curve, JY F 2 ' play precisely the same role in the second case 

 as Fx and F 2 in the third case. 



If we consider more closely the propositions just enunciated, then we 

 shall involuntarily be led to seek certain limiting values, the knowledge 

 of which leads to the solution of the fundamental question whether, 

 under given conditions, condensation will be possible or not. 



The questions that obtrude in this connection are as follows: 



(1) Whatlimit must the relative humidity exceed for a given tempera- 

 ture of the components, or at least for one of them, in order that con- 

 densation may be possible for a properly chosen mixing-ratio ? 



(2) What limiting value must the relative humidity of one component 

 exceed when the value of the other is given, aud when also condensa- 

 tion is to become possible for a properly chosen mixing-ratio? 



The first of these two 

 questions can be expressed 

 in the following form : 

 When the limit of satura- 

 tion is to be attained for 

 an appropriate mixing ra- 

 tio, aud the relative hu- 

 midity of both components 

 is to be the same, what is 

 the minimum value of this 

 relative humidity ? 



That the knowledge of 

 this minimum value is also 

 a solution of question 1, 

 we see most easily when we more accurately examine the answer to the 

 question as last formulated. 



We obtain this latter answer very easily through the following con 

 sideration : If R { is to equal E 2 , then the straight line F x F 2 must cut 

 the axis of abscissae at the same point P Fig. 30, as does the prolonga- 

 tion of the chord F x ' F 2 '. For if this condition is fulfilled then— 



Fig. 3D. 



but now 



and 



and consequently, also 



T X F X ._T 2 F 2 



T X F,'- T 2 F 2 ' 



r I\ F x < ~ yi > 



Pl ~ 100 



T*F t y 2 B, 



T 2 F 2 '~y 2 '~ P2 -W(] 



R\ = R 2 . 



