( 194 ) 



But at higher T these points of intersection exist no longer; then 



d'p dp 



the line = runs between the two branches in which — =0 



dvdx dv 



has split up, without intersecting them, at least at this place. There 



Fie. 34. 



is, however, still a point of intersection, but at much greater value 



of x, namely a point of intersection formed by the branch of 



d*p 



= which runs again to larger volumes. In this point ot inter- 



dvdx 



dp 

 section the righthand branch of — = has again minimum volume. 



dv 



dp 

 So for values of T below that of the double point of — = 0, the 



dv 



dp 

 branch of the liquid volumes of -- — has two points of intersection 



dv 



d*p 



with = 0, so a maximum and a minimum volume, and for 



dvdx 



much smaller value of x there is then a minimum volume on the 



vapour branch. If we lower T still further, maximum and minimum 



volume of the liquid branch draw nearer to each other, and they 



f da 

 coincide at the value of x for which 



dx 



2 (Pa 



- a — Then the vapour 



o dx- 



