( 835 ) 

 For values of x g differing little from \ we find approximately: 



1 v - l f A Y 



2 9 128 VI + i Ay 



If for A we take the value 4, which must be considered large for 



1 1 



molecules of about the same size, then as„ would be = — . The 



2 54 



conclusion which we draw from all this as to the situation of the 



point in which = disappears, with respect to the curve 



tPxb 



= 0, is the following. In most cases this point disappears within 



d.vdv 



fdv\ ( r dp\ 



the curve — =0, and so in the region where [ — is negative, 

 \dxjv \dxj v 



'dp\ 



dx) v 



fdp\ 

 but this can also take place on the other side of I — = 0, so at 



a volume which is smaller than that of this curve. 



That at positive value of A, so at positive value of 



A ii (1 — 2asfl» 



= 4 — — has always a root, appears immediately when 



1+*A x-k{\—xfU 



we represent the two members of this equation graphically. The 



lirst member, namely, represents then a branch of a hyperbola which 



at x = has a height above the axis of x equal to that of A, and 



A 

 at x = 1 a height equal to - — — , and which, therefore, proceeds 



continuously at a certain positive though decreasing height above the 



t oaxis. The second member represents a line which for x = has 



a point infinitely far above, and for x = 1 a point infinitely far 



1 

 below r the .i'-axis. This line passes through the point x = - , and on 



the left and the right of this point the ordinates are equal, but with 



reversed sign. So intersection will certainly take place, and for 



1 d> 



positive A at a value of #<[— . For the case that ■— =0 disappears 



dp 

 at smaller volume than that of the curve — = 0, the first member 



dm 



must be larger than the second. As A is larger, the point of inter- 

 section will be further removed from x = — , and so the series of the 

 values of x for which the condition is that the first member be larger 



