( 332 ) 



d*y 

 two curves meet again; and al still higher temperature — lies 



dx 



d*Hb 

 again entirely within = 0. Then three-phase-pressure is to be 



dv* 



expected between two temperatures, whose values though nol coin- 

 ciding with 7', and 7',. are yet in close connection with these values. 

 Bui for this I refer to previous papers. 



The two values of x, between which the locus of the points of 



d*\p '/-'if* 



intersection - = 0and = O is contained, lie in general not 

 dx* dv* 



symmetrically with respect to x = and x = l. Lei these values 



be denoted by ,i\ and ./',. then : 



p, — n*s. 



1 ^ s ^ {n-iy 



or if the value of x, which lies halfway between them is eal le< I ./•„,: 



2.,,,, = 1 4 ' ' - "''' • 

 T (n-1)' 



So if f x y> n*s„ then x m ^> h and vice versa. This remark may 



contribute to the solution of the question whether for mixtures for 



which three-phase-pressure exists between two temperatures 7', and 



7 T 2 , the quantity A' > 1 or <J. If /' J <l, and if, therefore, the 



points for which >-, and r-, are the coordinates, can but lie on an 



ellipse which can only enter the space between the t- l and s, axis 



and the tirst parabola in a point s, ^> and e s =0, then x m ^> \ 



may be expected. On the other hand if l*^>\, and the considered 



points lie on a hyperbola, p., ^> and e, << n*s 3 is to be expected. 



Then the discussed locus lies on the side of the component of the 



smallest size of the molecules which occurs for mixtures of 



ethane and alcohols. For the case e 1 =0 and ra s e s ]>0, as l = and 



x. = 1 — — . l>nt x, = for v — 1 = 0, from which follows 



(n-iy 



at the same time T x = , so there is in this case three-phase-pressure 



al all temperatures below 7',. In the same way the value of 7', 



would be equal to zero for e„ <-» and ?- 1 ^> ,) . 



In all this it mnsl not be overlooked thai though the presence or 



absence of three-phase-pressure is, indeed, closely connected with 



the presence or absence of the locus of the points of intersection of 



d*\p '/-if' 



- = and =0, there 1 are differences to be expected in the 



dx* do* l 



particulars. Thus the temperatures for the limits between which three- 

 phase-pressure can be observed, arc not the same as we have denoted 



