( -442 ) 



drty 

 value of i) found in the point in which = has the smallest 



• I /■* 



volume. Ami if we now consider t he case that the whole closed 

 curve discussed above, has contracted to a single point, and the 



intersection of the two curves = and has disappeared, and 



ax dx 



the 0-line runs parallel to the ./-axis in that single point ami possesses 



there a point of inflection, the realizable plaitpoinl still exists, and 



so also the other, the hidden one. A fortiori this is the case when 



the closed curve still exists, and the intersection of the two curves, 



//'-'if' '/ -i ifc 



— and = has onlv disappeared because thev touch. 

 ax 'I' 



Ynv then the online, which passes through the point id* contact, will 



still possess the points with maximum and minimum volume, and 



it will lie below the ydine where thev have coincided. 



So we are justified in the following graphical representation. Lei 



us take an ./-axis and a p-axis. Let us construct a figure indicating 



,/> 

 lirst the pressure along the liquid branch of the line , 0, and 



secondly the pressure along the liquid branch of the spinodal line. 



Nol to interrupt our train of reasoning too much, we shall pass 

 o\er the other branches in silence, and moreover confine ourselves 

 to the case in which '//,,> 7/,, . Then the first-mentioned line is a 

 continually descending one. If the temperatures are low — according 

 to the approximate equation of state below ■• „ 1\ - all the points 

 of this line lie below the .r-axis. But as we onlv wish to consider 

 the relative position of the two curves which are to be represented 

 we disregard the absolute height at which we think them drawn. 

 The second line begins and terminate- as hi.uh as the first, and 

 always remains above it. So in the main it is also a fast descend- 

 ing line. Now if there are on the lirst line two points, indicating 



dp 'J-ty 



the points of intersection of the line with - - =0, the second 



1 dv ''■'■' 



line will not continually descend, but possess a minimum and a 



maximum value for />. The minimum value at a value of ./■ which 



is smaller than the value of x of the first point of intersection, and 



the maximum value at a value of x, which is greater than that of 



the second point of intersection. This minimum and this maximum 



value are those of the pair of heterogeneous plaitpoints. If the two 



points of intersection have coincided on the first-mentioned line, 



minimum and maximum pressure Mill occurs on the second. And 



