( 728 ) 

 «-axis in such a poinl of intersection. So a '/-line meeting — = 0, 



il.r" 



will l»c twice directed parallel to the «-axis, and have a shape as 



'/> fdp\ 

 represented in fig. 3 — at least as long as the curve — — = — =0 



dasdv \dxj v 



does not occur. Such a shape may. therefore, be found for the g-lines, 



in the case that the second component has a higher value of b, and 



lower value of Tk — > and such a shape will certainly present itself 



in the case mentioned when the temperature is low enough. 



Then there is a group of '/-lines, for which maximum volume, 



and minimum volume is found. The outmost line on one side of 



this group of '/-linos, viz. that for which q possesses the highest 



value, is that for which maximum and minimum volume have coincided, 



d'xp 



and which touches the curve = in the point, in which this curve 



dx 1 



itself has the smallest volume. The other outmost line of this group 



of 7-lines, viz. that for which q possesses the smallest value, is thai 



for which again maximum and minimum volume have coincided, and 



which also touches the curve - = 0, but in that point in which 



this curve itself has its largest volume. So for these two points of 



d*q> 

 contact the equation — = holds. These two points of contact are, 



dx* 



dhV '/'if' 



therefore, found by examining where the curves - = 0and — =0 



dx 1 dx z 



intersect. This last locus appears to be independent of the temperature, 



d'a 



as we may put — equal to 0. We find from the equation on p. 638 

 dx l 



fdb\ l d*b 



d'tif I 1—2* Vdx) dx 1 ) 



— = MRT h 2 r—£- A = 0. 



dx 3 f .r s (l — x) 1 (v—b) l '(v-0y\ 



d' l b d z y 



If we neglect — , we find from — — = 

 b dx 1 dx % 



db 



1—2* 



dx - 3 / 1 



V—b~~ V ¥x' 



(1-xf 



d*ib 



The locus = occurs, therefore, only in the left side of the 



dx 3 



figure or for values of x below \. The line x = V, is an asymptote 



for this curve, and only at infinite volume this value of «is reached. 



