( 241 ) 



As soon as T descends below Ti , the quantity v'—v can become 

 very great; this happens, however, between such values of r, as lie 

 within the border curve, and which therefore cannot be realized. 



If for the two substances, of which the mixture is to be composed, 

 such curves are construed, whoso dimension and form will depend 



on b and — , a point of the mapping of (1— .?) (r/— I'l) + '«(f/— '■'a) 



b 



may be found by connecting two points of those curves by a 

 straight line, and by dividing that straight lino into parts which 

 are in inverse ratio to .» and 1 — .v. The two points chosen must 

 always belong to values of vi and v-z , which occur under the same 

 pressure. The curve obtained in this way will approach I'l' — v^ the 

 nearer, the smaller *• is, and may to some extent be considered as 

 a mean curve. "When v'—v has been construed, Lu may be found 

 bv taking the difference of the ordinate of the resulting curve of 

 the two first mentioned and of the last mentioned, always for such 

 values of v, as occur at given }). 



Though it is true that the course of A» does not follow in parti- 

 culars from this way of construing, yet some general rules may be 

 derived from it. As has been observed before, we find for u =: qo 

 again the former value, viz. « (1 — .«) \Aa — Ah]- For the limiting 

 value on the other side we find: 



— Av = bi (1— .r) + bo x-b^ = X {\—x) Ah , 



SO a contraction. In all these cases, in which An— Ah is positive, 

 a pressure must exist, under which mixture without variation of 

 volume takes place. It the volumes are very great so that ^i' — I'j, 

 fj' — V.2 and v' — V remain invariable, Ay too will not vary much in 

 absolute value. The variation may however be considerable relative 

 to the limiting value. But it appears at any rate, that if none of 

 the three substances, viz. the components and the mixture, remain 

 considerably below the critical temperature '), the absolute value of 

 Ao remains within finite limits throughout the course of the iso- 

 thermal. 



If we try to calculate (A^,)' directly, viz. the increase of pressure 

 on the mixture, in order to keep the volume equal to the sum of 



') By the criliciil temperatiire of u iiiixtui-e is iiiulerstood (luit temperature wliicli 

 is c.ilculated from «, and Li in the same way as for a simple substance. 



