( 280 ) 
character of the equilibria between liquid and vapour in binary sys- 
tems had become fully understood, that efforts could be made to con- 
struct a complete graphical representation of the conditions of equili- 
brium in which solid phases occur. 
The simplest possible case is found when only the two components 
of the binary system occur as solid phases. For such a case, I have 
since 1896 arrived at the representation in space of which photographs 
are given in the accompanying figures. For the case that chemical 
compounds or mixed crystals occur as solid phases other figures have 
been constructed which, however, may be deduced in a simple manner 
from the present ones. 
In this figure the length represents the temperature, the breadth 
the concentrations « of the mixtures which can exist as vapour 
or liquid, the component A being placed at the left and the 
component B at the right. The height represents the pressure. The 
figure does not represent any particular case, but is so constructed 
that the different details come out plainly and the dimensions are not 
too great. 
We start from the equilibria between liquid and vapour, which 
researches on the critical constants of mixtures have proved to be 
capable of representation by a surface of two sheets, the upper part of 
which represents the liquids and the lower part the vapours. The 
coexisting conditions of these two must have equal values of p and ¢ 
and are therefore, situated on a horizontal line which is parallel to 
the r-axis. The said surfaces meet at the left side in the vapour- 
pressure line O4 C of the liquid A, at the right side in the vapour- 
pressure line Op D of the liquid B and in front in the critical curve CD. 
The points in the space between the two surfaces indicate complexes 
of liquid and vapour. In the representation, this space is massive, 
like all other spaces which represent complexes of two phases. 
The surface of two sheets for liquid + vapour is so constructed that 
A is the substance with the greatest vapour pressure. It has further 
been assumed that the liquids are miscible in all proportions and that 
no maxima or minima occur in the equilibrium pressure. 
Descending continuously, the surface would reach the absolute zero 
if A or B or both did not solidify first. 
The pure liquids A and B solidify in O4 and Og; from there the 
vapour-pressure lines O47 and OgK of the solid substances run in 
the left and right vertical side-plane. 
Considering now the liquid-mixtures with an increasing amount of 
B, solid A can only be deposited at temperatures lower than O4. 
At each temperature there is a definite liquid and a definite vapour 
