and there is no reason whatever why (2) and (1) should be equal. 
Looking back it is now easy to understand how the opposed view 
could assert itself. After having derived equation (1), vAN DER WAALS 
; dp 
observes loc. cit. that this value is equal to (Fi) > Le, the rise of 
the pressure when we make a section through the saturation plane 
a—w,. And then he goes on a few lines further: “And the p,7- 
projection of the plaitpoint line being the envelope of the p, T-projection 
of the sections of the surface of saturation for constant values of z, 
the plaitpoint line and the p,7-projection of the sections touch and 
so also the final point of the p,7-projection of the three-phase 
pressure, as in that final point the last element of this pressure 
coincides with the section mentioned” '). From two correct premises 
an ineorreet conclusion is drawn here. Equation (1) proves indeed 
that the three-phase pressure must touch the p,7-projection for «, 
constant, or in other words that the increase in pressure along the 
three-phase line at the limit (critical end-point) is equal to the increase 
in pressure of the two-phase equilibrium vapour-liquid, and this 
result is in perfect harmony with the data of tables I, II, and II. 
dp 
dT” 
when we pass the temperature of the critical end-point. It is also 
correct that every plaitpoint line in each of its points must touch 
a section for x constant through the surface of saturation (surface of 
two-phase equilibria), and this thesis is corroborated by equation (2). 
But it has been overlooked in the conclusion from these two theses 
that in the considered case the surface of saturation (surface of two- 
phase equilibria) is not a two-sheet surface, as usual, but a four- 
sheet one. Two of these sheets pass through the critical end-point ; 
so instead of a mutual contact of three lines, as VAN DER WAALS 
assumed, we get a contact of four lines in pairs; the three-phase 
line touches the liquid sheet of the coexistence liquid-vapour, and the 
plaitpoint line touches one of the liquid sheets of the coexistence liquid 
liquid. The experimental corroboration of this last thesis is already 
included in the observations communicated previously by one of us’). 
For it appears convincingly from them, what moveover is a priori 
to be expected, that the concentration of the plaitpoint changes only 
exceedingly little with the temperature, and that certainly in the 
beginning the increase of pressure required to keep a mixture of 
There is no discontinuity whatever to be seen in the value of 
1) Loc. cit. p. 192, 
2) These Proc. XIII p. 507. 
ox 
“I 
Proceedings Royal Acad. Amsterdam. Vol, XIII. 
