( W7) 



1 begin with pointing out that the line [ — ) = 0has an asymptote 



\dx J 



db da 

 for such a value of x for which MRT — = — , which asymptote 



dx d.v 



either exists or must be supposed to exist for a value of x which 

 is negative, and that this curve approaches the line v = b asympto- 

 tically for continually increasing values of x — at least if a^a, — 2a,, 

 is positive. I shall presently come back to this supposition, but on 



d'a 

 page 626 I have explicitly stated this supposition in the form — 



CbiC 



positive. With increase of T this line proceeds to higher value of 

 x and v. 



At lower temperatures the line ( — J = consists of two separate 



\dvj x 



T-. d ~p dv d*p 



branches. From -7^ — +-; — — = follows that the liquid branch has 

 dv dx ax dv 



, ,. d *P 



maximum volume on the line = and the vapour branch mini- 



dxdv 



mum volume on the same curve, which curve has an analogous 

 course to ( — J = 0. It has the same asymptotes, but is always con- 

 fined to greater volume. For T= minimum critical temperature the 



d % p d*p 



two branches coincide in a point for which both — and 



dv* dxdv 



d'p 



is equal to 0, so in such a point of the line = 0, for which 



dx dv 



/dp\ d*p 



[ — =0 and also — = 0. Hence in the critical point of the mixture 



\dvjx dv* 



a x 

 taken as homogenous, for which — has minimum value. At still higher 



X 

 m f d P\ 



value of T the curve — }=Q has split up into a lefthand branch 



\dvjx 



and a righthand branch, botli which branches possess tangents parallel 



'f) = 0an/- P 



dvjx dv : 



the special values of this constantly increasing value of T we must 

 mention in the first place that for which the last mentioned point 



has got on the line ( — ) = 0, the point P of fig. 31. This is the 

 \dasj v 



10* 



to the v-axis, in points for which also ( — J = and -~ = 0. Among 



