( 528 ) 



In the problem, for which — = 00 at the plaitpoint, this case is 



dx 



dv 

 the transition for the cases where — is positive or negative. In the 



dx 



dv 

 same way in the problem for which — =0 in the plaitpoint, this 



dx 



dv 

 is a transition case between — positive or negative. So the cases 



mav also exist for which on the side of the small volumes, the 



dv 

 quantity in the plaitpoint may have reversed sign. 

 dx 



f) 3 if' b*tp 



When we examine the shape ol the curves ^r— s~ = and — = 0, 



it appears thai it is required for the realisation of the case, that when 



dh da d*a 



is positive, also — and — are positive, and that the calculated 

 dx dx dx* 



temperature must lie above 71 of the tirst component when we want 



to apply the result to the coexistence of gas and liquid phases. 



At the top we have the limiting case of two coexisting phases. 

 If the tangent is // #-axis, the molecular volume is equal and the 

 density will be proportional to wi, (1 — a?) + m a %. 



Put 



m 1 (l—x)~\-m a x m^l—x'y-^m^x' (w a — m l ){x'— x) 



<t= — — and(/=— — and a — a= . 



v v v 



When (m s — wij and (#'- x) have the same sign, d' — </ is positive.. 

 As ui'-r-x is negative when the first component has the smallest size 

 of molecule, m, — m l must also be negative, which is satisfied for 

 helium and hydrogen. 



We can, in general, represent the limiting density of a substance 



171 



by -, and then the law would hold : When the most volatile substance 

 b 



has the greatest limiting density, the gas phase can be specifically 



heavier than the liquid phase. For Helium the limiting density is 



probably equal to that of the heavy metals. From the supposition 



that it is formed by splitting off from heavy metals this follows 



already with a certain degree of probability. 



l ) On further investigation it has appeared to me that a point that satisfies the 



eauations - = — ^- = 0, and =r-~- — 0, possesses the analytical character of 



4 dx* ' oxov o&' a 



a plaitpoint. but at least in many cases, does not behave practically as such. I 



hope to show this before long. (Added in the English translation). 



