( 152 ) 



The following considerations are an abbreviated sur\ ey of a more 

 elaborate paper \\lii('ii will be i)iibli8hc(l elsewhere ^). 



II. I have shown in a previous communication^), that we may 

 express the niolcculnr thei-niodynamic ])Otentials of the (wo compo- 

 nents of a liquid mixture — if we assume the etpiation of state of 

 VAN DEH Waals — as folIoAvs: 



ft, = (\ - <\ T - {k, + AO 2' %/ T + ''f + RTlori (1 - .v)^ 



f,, =:= e, - c, T - {k^ -f R) T lor, T + ^^ + RTlog x 



Tiie different quantities occurring in these equations have the well 

 known signification, indicated in the paper quoted above. 



In order to simplify the calculation we shall always assume in 



the following, that r ( := =1 = 0, and therefore that the equa- 



A A 



tions «1 = — and a.^ = 7— . — are identically satisfied, A representing 



'h ^^-2^ — 2 r/j2 f>i l>.2 + ''2 ^>C'- This assumption comes to the same as 

 the supposition that the molecular volumes of the two conq)onents 

 differ only slightly, which supposition may be considered to be 



«i-r^ «2(1 — ,/;)"^ 



iustified, as the (ei-ms and represent the mutual 



(1+n.r (l + '-.'O^ 



influence of the two components in the mixture only (ipijroxiinntehj. 



In the second place I shall assume that the above expressions also 

 apply to the solid state, an assumption which we may expect to be 

 satisfied in first approximation, as the case \ve are dealing with, 

 namely that of mixed crystals or solid solutions '), shows in many 

 respects the greatest analogy with liquid solutions. 



If we also suppose r in the solid phase to differ little from zero, and if 

 we indicate all quantities in that phase with accents, then we may write: 



For the liquid phase: 

 ft, —e^—e^T — {k^ 4- i?) Tlof/ T + a x- -^ RT loo (l — x) 



ft, = e, — c,T— {k, + R) Tlog T -\- u {l-xf + RT log x 

 For the solid phase : J . . (1) 



ft\ ^ e\ - c\ T - {k, + R) Tlog T^ a' x" + RTlog{l-x') 



fi', = e', -c\T- {k, + R) T log T+ a' (1 - x'f -f RTlog x' 



1) In the Archives Teyler. 



2) These proceedings April 24, 1903. 



3) Mixed crystal will always be treated here as solid solutions, though in these 

 latter years difficulties have sometimes arisen against this view. See i.a. Stoute.n- 



BEKEK, I.e., p. 633. 



