( 152 ) 



certain limits not only three phase equilibrium but even four phase 

 equilibrium would be possible, then of course always at a single 

 value of T. So the supposition a Xi * = a x a 7 is not one without far- 

 reaching consequences. Yet we see repeatedly that this supposition 

 is made. And I have undertaken this investigation to show 

 that such a supposition would also render the existence of minimum 

 plaitpoint temperature impossible. At the same time I wanted to 

 point out how the course of the isobars which I have given in 

 fig. 1 of these contributions would be entirely modified on other 

 suppositions about a lt than those I have started from. If we put 

 in equation: 



d*a /"day 



/da\ d'a 



for — 1 the value ma — in which, if there is minimum plaitpoint 

 \dxj dx* 



temperature the value of m lies between and 1 for the point of 



fdp\ fdp\ 



contact of — =0 and I — =0, we find : 

 \dxj v \dvj x 



d*a 



(2 — m) a — - - = 4 (a : a t — a,/) 

 dx 



d*a 

 Now — = 2 (a l -f- a, — 2a 19 ). As at the same time we cannot 

 dx- 



have a 1 a t = a li * and a x -f- a, = 2a M , unless in the case a x = a 2 , 



this equation cannot be fulfilled but by putting a x a,^>a l ^. 



The supposition a x a^ =z a x J gives for m the value 2, but then 



also for - in the point of contact of ( — ) = and ( — J = 0, the 

 b \dxj \dvjx 



value 1 (see fig. 32). — Only when we put a x a^<^a li ' does in 



become ]> 2, and do we find for the point of contact of the curve 



mentioned, values of- which are larger than J , and which can there- 

 b 



fore exist, but then this value can rise to 2 at the utmost. In such 

 cases there is contact of ( — )= with the liquid branch of ( — 1= 0. 

 And this means for fig. 1 of these contributions that then again the 

 liquid branch of [ — J = may approach to f — J = on the right 

 side, but then to that part of this curve that lies beyond the minimum 



