( m ) 



hAOh' con-esponds to Koutkwkg's first boniidary '). Oiilsidc tl»c parabola 

 T,,i>T,, inside 'J\;>i<T,. 



The plaitpointpre.^Kïin'. Fi-om form. ((JO) wc derive Ihat i>.q,i^ or 

 <Ci)k as Poi (^ — Poi «)" > or <^ C^ Pil i^- Tlie equation of the boundary 



is that of a [)ai'abohi represented in the ligure by cOBc' . Outside 

 tlie i)arabola [tjpi^ pk-, inside <^7>A;. 



IVte ijlaltpoititüohime. The manner in wliich h\fji d('[)ends on u and {i 

 may be derived from form. (61) ; it is expressed by Keesom's formula 

 (2c'), which I borrow from him in my notalions: 



^ 4V21V80 

 Hence the boundary is here : 



This is a curve of the third degree, like KoRTEWECi's third boundary, 

 with whicli it corresponds in this diagram. 



In order to investigate this curve I introduce, tollowing the example 

 of KoRTEWEG, a parameter z, by putting 



and I iind that « and /?, by means of that paramelcr are expressed thus: 



iV 



where 



iV=:C%P„P3„(p„, -i)-3r,p%.^-. 



As a and ^ are single valued functions of z, all lines which are 

 parallel to the straight line /?=v\i« (Oa of the figure) intersect 

 the curve at one single point at a finite distance. 



If we put : 



_ C>,o(Po - 1) ') 



the straight line /? = v\i « + "u being a dotted line in the figure (CD), 



1) To avoid mistakes I n.se here the word boundary, instead of the expression 

 border curve used by Kortewkg ; for in our demonstrations the word border curve 

 has a very special meaning, viz. that of a boundary between sta])le and unstable states. 



2) As p 1 is also equal to the direction-cosine I — I of the tangent to the re- 

 duced vapour tension curve at the critical point, and as it follows from the form 

 of that hue thai > 1, c^ must necessarily be posiUve. 



