( 157 ) 



Tf wo had discussed the third of the equations, the values of m 

 would have been found still, higher. According to the first of the 

 equations of course smaller. 



Let us finally examine the course of the line — — in the 



\dxj v 



fdp\ 

 cases that there can be no contact with the line I — , or only on 



\dvj x 



the side of the liquid volumes. We saw already above, that then the 



locus of the points of intersection of the two curves mentioned (cf. 7) 



runs to greater volumes, if x is made to increase. Then at given T, 



fdp\ 

 only that part of the line — = exists, for which this line runs 



\dxj o 



to greater volume. The lefthand part, for which this curve may 



reach infinitely large volume lies in the common case at a value of x 



db 

 MRT~ 

 do da v — 6 / dx 



to be calculated from MRT — = — . Then 



d,v dx v I / da 



dx 



and the first part of this equation is then equal to the unity, because 



v v — b 



= oo. But can also be equal to 1 in another case, viz. : if 



b v 



b should be = 0. This can only occur, when extrapolating we also 

 admit negative values of x, and moreover choose for b such a func- 

 tion of x that it can become equal to for negative value of x. This 

 is the case for a linear function, but putting b = b i (l — x)-\-b 2 x is 

 only an approximation. Whether this can also be the case with a 

 more exact shape of b = ƒ(#), must be left undecided. Moreover it 

 is necessary, if we choose always greater negative value of x, that 



da 

 we first find b = 0, before finding — = 0. But then the shape of 



dx 



the p-lines must also be modified. I shall however not enter into a 



discussion of this, for one reason because Dr. Kohnstamm informed 



me, that he had already been engaged in the study of the modified 



course of the isobars, and that he had also come to the conclusion 



that the relative situation of the values of x, for which b = and 



da 



— = 0, is decisive. Moreover I leave undecided for the present 



dx 



whether also on other suppositions than <^ x <^ 1 there can be 



question of minimum plaitpoint temperature, which is to be distin- 



a x 

 guished from minimum value of — . 



b x 



