( 154 ) 



dp\ fdp\ 



— = O and [ — = O, we obtain a relation between x and T. In 



dxj v \dvj x 



general we find two values of x for the same value of T. The 



value of T, at which these values of x coincide, or in other words, 



the maximum value of T, then gives us the value of x for the 



point of contact of the two curves. 



From 



MRT _2a 



and 



MRT db 1 dv 



(v — by dx v* dx 



db da 

 2— — 

 dx dx 

 we tmd = — for a point of intersection. . (6) 



v a 



As for values of v which will be realisable, v ^> b and v must 

 be positive, a point of intersection of the two curves can only occur if 



da db 



— 2 — 

 da . . . dx dx 



— is positive, and it — <r— — . This latter condition may be written 

 dx a b J 



a 

 d — 



b- 

 — — <[ 0. So the two curves can never intersect in a region of in- 



cLv 



creasing critical pressure. Let us therefore confine ourselves to decreasing 

 critical pressure. The locus (6) has as differential equation : 



n db d-a /day 



2— a — 



dx dv dx* V dx J 

 = ^— L- (7) 



v* dx a 3 V ' 



'day 



^dxj dv 



bo when in = — -—— <r 1, — - is negative. Onlv in a region where 



d~a dx 

 a — 

 dx* 



dv 

 m has become = 1, — will be positive. And if we should assume 

 dx 



a x a 2 = a 13 2 , so if we put m = 2, the locus of the points of inter- 

 section of the two curves would move to greater volume with 

 increasing x; so perfectly diiferent from what happens for mixtures 

 with minimum plaitpoint temperature. If we substitute the value of 

 v which follows from (6), in : 



