276 



THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



The quantity y 3 that still remains liquid will uow dissolve, in so far 

 as the mixture is not saturated, or so much of it will dissolve as is 

 needed for saturation. This of course can only occur in that the mix- 

 ture itself cools, and that too by 2°.6 or 2 C .9 for each grain that is evap- 

 orated, since we exclude the cases where heat is communicated from 



without. 



The final temperature T is therefore 



found by passing upward in Fig. 43 from 

 F 3 toward the left, parallel to the guide- 

 line F x F 2 , until at F we reach the same 

 height as F 3 . or at least until we reach the 

 curve F'i F' 2 , in case the line 1\ F' so 

 drawn would need to cross over the curve 

 F, F> 2 . 



In this latter case, which is represented 

 in Fig. 44, all the water is not dissolved 

 but only a portion {y'—y 3 ) as is represented 

 in Fig. 44 by the distance F 3 P. 



The first of these two cases can be easily 

 handled numerically, since under these 



conditions we have 



t=t 3 — Ky 3 



= t 3 — E^ 



nu 



m x -f m 2 



niitx + m 2 t 2 

 m A 4- m 2 



-Kh 



Wo 



mi -r «*2 



nijti 4 - m 2 i 2 — Ky x m 2 

 w'i 4- m 2 



But the computation is as simple as this only when all the water is 

 really evaporated; in tbe second case where mechanical supersaturation 

 still continues it is better to apply the graphic method. An especial 

 interest; pertains here again to the investigation of the limiting cases 

 for which in general there can occur a complete dissolution of the water 

 originally present as liquid in one of the components. Of such extreme 

 eases there is an extraordinary variety according as we are at liberty 

 to assume arbitrarily either the mixing-ratio or the humidity of one or 

 the other of the components. 



At present we shall consider only the question, what is the initial 

 limit of the mixing-ratio for given components in order that complete 

 dissolution must always follow. This limit is evidently obtained when 

 F' Fn lie at the same altitude above the axis of abscissas, that is to say, 

 when ii = y'=y Z) or when F and F' coincide. In this case F is the 



