403 
certain values of the concentration it is easy to distinguish, what 
quadruple points can occur and what cannot. And in the second 
place it furnishes a simple means to read directly the consecutive 
order of the concentrations from the observations of the three-phase 
lines. 
The former kind of applications is of course far more numerous 
than the second. There are, namely, only few cases as yet, in which 
the situations of all four three-phase lines at the quadruple point are 
determined. 
To elucidate the former kind of applications, I will briefly examine 
what the rule requires for some known quadruple points. The qua- 
druple point of the ordinary spacial figure, in which the succession 
of the phases is 5,GI.8,, has to fulfil the demand that the region 
between S, +G-+1L and G+hL-+58, does not contain metastable 
prolongations. 
If we consider the quadruple point of two salt-hydrates by the 
side of liquid and vapour, in which the order of the concentrations 
is GLH, H,, the rule in question demands that no metastable pro- 
longations occur between the three-phase lines G + L + H, and 
L-+H,+H,. This rule both holds for the ordinary case that the 
hydrate H, rich in water is transformed into that which is poor in 
water on rise of temperature and for the “inverse melting-points’’, 
where the reverse takes place. For the former case the rule requires 
among others that the prolongation of H, LG lies at lower pressure 
than the stable part of H, LG, and reversely, which must really be 
the case, as is known. 
What type of quadruple points must be expected in the case of 
an “inverse melting-point’, will be discussed a little more fully here. 
If we think the transformation of the two salt-hydrates to take 
place in such a way that the one rich in water exists at higher 
temperature than that poor in water, then the quadruple point will 
have to satisfy besides the above-mentioned demand, also the con- 
dition, that at temperatures below the quadruple point the three- 
phase line G+ L + H,, above it the line G+ L+H, is stable. If 
we further consider that on the three-phase line L + H, + H, the 
transformation H,-+ LH, occurs on isobaric supply of heat, and 
this will probably be accompanied with volume-contraction; that on 
the three-phase line G + H, + H, the transformation H, + G— H, 
occurs on supply of heat, and that this is certainly accompanied 
with volume-contraction, then we know that probably both, but 
certainly the line GH H, + H, possesses a negative value for ae 
. 
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