( 647 ) 



as. 



(nv — vs) (ni — n*) 



mi 



may become negative. Now it is true that we cannot properly say 

 that ij B — rig is a heat of sublimation and r t i — ij« a latent heat of 

 melting, because the rfs do not refer to the same concentration, but 

 we may say that r\ — i\ s is of the order of magnitude of a heat of 

 sublimation, m — i^ of the order of a latent heat of melting. Or in 

 other words ij — i] s will be about 7 or 8 times tji — ?; s . So in all 



cases where f - - ) <* 7 the pressure maximum in the three phase 



line will also fail. Here too the necessary data are wanting to 



X 



ascertain whether there are many systems for which the - at the 



triple point will descend to this amount. For, determinations of vapour 

 tension or direct determinations of the required ratio have been 

 nearly always carried out at considerably higher temperature l ), and 

 for the calculation by the aid of the just used formula the necessary 

 data fail here too; besides, it would be doubtful whether the 

 formula would be accurate enough, now that we have to deal with 

 such small amounts. But — quite apart from the existence of mix- 

 tures with minimum vapour pressure — the existence of a system 

 like ether-chloroform 2 ) where on the chloroform side x becomes 

 almost equal to a?/, already proves, that such systems exist. 



In any case to the scheme for the possible course of the two three 

 phase lines in a binary system plotted by Bakhuis Roozeboom in 

 Fig. 108 of Vol. II of his "Heterogene Gleichgewichte", must be 

 added types VII and VIII, characterized by a succession of sections, 



*) Particularly when we notice that the ratio of x v and xi would have to be 

 calculated from the formula : 



1 dp x„ — x[ 1 dp x v — xi 



or — 



p dx x^l — Xu) pdxi xi(l—xi) 



and the value obtained will, therefore, strongly vary in consequence of a change 

 of temperature of some ten degrees, which have generally an enormous influence 

 per cent on the pressure in the neighbourhood of the triple point. 



2 ) Kohnstamm and van-Dalfsen, These Proc. IV, p. 159. Bakhuis Roozeboom 

 (I.e. I p. 41) deems it probable that also systems of gases with water and of 

 water with many salts will show a similar shape. However, for such systems 

 whose three phase line for the least volatile substance shows a pressure maximum, 

 at least at temperatures that do not lie too far from the triple point, the shape 

 of the p , a'-line will have to deviate considerably from the line drawn there in 

 Figs. 15 and 19, because from that shape would follow x.- = xi. 



44 



Proceedings Royal Acad. Amsterdam. Vol. IX. 



