( 628 ) 



A similar remark must be made for the curves of lower value of p. 

 The smallest value of p for gas volumes is of course p = 0; hut 

 this limit does not exist for the minimum pressure of the mixtures 

 with given value of x. For this we know that also values of/nnay 

 occur which are strongly negative. For values of p which are negative, 

 the /j-line has again divided into two disjointed portions, viz. a 

 portion lying on the left in the diagram, which is restricted to 

 volumes somewhat larger and somewhat smaller than that of the 



fdp\ 



liquid branch ot the curve f — I = 0, and a similar portion lying 



on the right in the diagram. 



Also on the locus of the points of' inflection of the isobars the 

 given diagram can throw light. So it is evident in the first place, 



fdp\ 



that between the two branches of the curve - - I = starting 



\dvj x 



from the double point, both on the left and on the right a connected 



( (/v "\ f d P\ 



series of points is found where | = 0. If the curve = 



V &x J P V l,r Jx 



itself should possess a double point, which is the case when T has 

 exactly the value of 7& minimum, this locus of the points of inflec- 

 tion of the p-lines passes through this double point, and when the 



fdp\ 



curve — =0 has split up into two separate portions, as is the 



\dvj x 



case for still higher value of T, then those points of the two portions 



dv 

 where — = oo belong to this locus. It is also apparent from the 

 dx 



diagram that two more series of points start from the double point, 

 one on the right and one on the left, as locus of the points of 

 inflection, and that these run to smaller volumes. 



An isobar with somewhat larger value of p than that of the loop- 

 shaped isobar has a tangent // to the A'-axis where it passes through 



the curve [ — ) = 0. On the right and on the left of that point it 



\dxj v 



turns its concave side to the .i'-axis, whereas at larger distance it 



must again turn its convex side to it on both sides. So there start 



/ d 2 v \ 

 from the double point four branches on which I -— - 1=0. It is 



also easy to see that the branch which moves to the right towards 



fdp\ 



smaller volumes, must pass through that point of the curve I — I = 



\clx J v 



where the tangent is // .v-axis. For an isobar which passes through 



