( 237 ) 



we follow the border-ourve from T^ Ti dowu to very low tompe- 

 ratures, at which the vapour volumes are very large, a lar^-o pro- 

 portion may be found in the beginnino-, but very soon that proportion 

 must become nearly equal to unity. 



By means of the knowledge of v' — v^ we may conclude to the 

 course of A,,, the increase of volume when two substances mix under 

 constant pressure. If we call the molecular volume of the first 

 component under a given pressure vj, of the second component t>2 



and of the mixture », then r'l and )•'., and v' are equal to ■ 



P 

 and so equal to each other. 



For Ai- = r — (1 — -r) vi — x v„ we may therefore write 



A,.- = (1 — -r) (i''i — fi) + r (w'o — ro) - (y' — v) , 



and so we find A,- from the values of r' — v for each of the sub- 

 stances. 



For t'l = I'jj = r zir 00 wo find 



A. = (1 - X) {a\ - h{) + X (a'o - h) - {a!^ - 6,) . 



If we put (1 + a,) (1 — h,), (1 + «,) (1 -ij) en (1 +«,) (!-/<,) 

 equal to 1, we obtain equation (4) of my former communication 

 (Proceedings Xov. 1S9S, p. 181). There also the same approximation 

 is applied in equating pv\, pvn and pv. But from the result now 

 obtained, it appears clearly that 



(a, 4- a.i — 2 a-in i 



f 1 + «' ) 



is only the limiting value of Ay for infinite rarefaction and we are 

 led to the question, whether something further may be deduced with 

 regard to the course of Ad under increasing pressure, and whether 

 it may be possible to account for the fact that the values for A« 

 which may be deduced by means of Kuenen's observations, do not 

 show that symmetry which follows from the factoT x {I — x) and 

 which appears so clearly from this observations of A^,. 



If we substitute the values found for v\ — vi, «'g — r^ and v' — v 

 we find 



