( ^79 ) 



rest, were ah'eadv known. (The ehiel' [)oiii(s had already lieen 

 previously described by Koktewkc; and van der Waals). 



Li a later paper ') tlie ])lace of' tbe double point, tli? knowledge 

 of which is important, because it imlicates the separation of two 

 very diftereni types, was determined for the perfectly genei-al case 



^'i-^/'j, and (he disenssion of the shape of the plailpoint line was 



extended to the case rr = 1, i. e. to the case which is of frequent 



occurrence, tliat the critical i)ressures of the two components are 



equaL In this latter case it Avas inter alia found, that not before 



ö]>9,9 the case of fig. 'J loc. cit. is found. 



I further deri\'ed from the perfectly general expression : 



RTz=/{v,a:) ; F (v, .i') = 



1 / IT* \ '^\ 

 of the iilaitpoint line also the initial course, viz. — [ — ^i , chietly 



in connection with opinions expressed previously on this point. 



As I remarked before (loc. cit. p. 34), van dek Waals had already 



drawn up the differential equation of the plaitpoint line, and drawn 



a series of general conclusions from it. Also in a few papers of very 



recent date ') he has demonstrated in his own masterly way how 



far we may get with general thennodpiamical considerations and 



general relations, deri\ed from the equation of state. But seeing that 



VAN DER Waals himself in his Ternary Systems IV (These Proc. V, 



p. 1 — 2) with perfect Justice em])hatically points out the absurdity 



of the often prevailing opinion as if an equation of state should not 



be rccjuired for the knowledge of the binary systems, I ha\'e consi- 



derotl it not unprofitable to transform the c////WY'?iY/c?/ equation of the 



Ö/" df fèv\ 

 i»lait|>oiut line, viz. v- "I" <r\ '^ > where / represents the second 



memlter of J\T :=/{v, .v) — the equation of the spiuodal lines — - 

 by means of the equation of state into a finite relation I'\i;iv), which 

 in combination with RT := f {r,.r) expresses the plaitpoint line in the 

 usual data Ï', r, .r. This enabled me to get acquainted with new par- 

 ticulars concerning its course (inter alia its ^splitting up into two 

 separate branches), and to examine this course in its details more closely 



1) Arch. Teyler (2) X, Première parlie, p. 1—26 (1905). 



2) These Proc. VIII, p. 144. 



S) These Proc, VItt, p. 271—298. The first mentioned paper was cited by me 

 (loc, cit. p. 34), so it has by no means "been overlooked", that already ten years 

 ago v.\x DER Waals determined the principal properties of the critical line, (cfr 

 V. D. Waals loc. cit. p. 271). 



