1269 
We may ‘also imagine the case that the sublimationeurve of 
rth’ +r’ goes casually through the point /. We see easily 
that then in the P?, 7-diagram the sublimationeurves of FHH’ //, 
F+ ik’, F+  F" and F touch one another. 
_ The sublimationeurve of /’-+ /” + F'' ends when a new phase 
X occurs; Y can be « solid substance or a liquid. This equilibrium 
IH IH FH X-+G is invariant; it exists, therefore, only at 
a definite Z’ and under a definite P. In the P, 7-diagram it is con- 
sequently represented by a point, the quintuple point. Five quadruple- 
curves proceed from this quintuplepoint, the position of these curves 
and of the threephase regions with respect to one another is fixed 
by definite rules and is dependent on the position of the five phases 
in the concentration-diagram. *) 
2. I, F’ and F" are situated in a straight line. 
We distinguish, with respect to the position of this line /’/’ /" 
two cases. 
_ A. The substances together contain the three components, the line 
FIFE" is, therefore, situated within the components-triangle. In order 
to find the vapour, which is in equilibrium with “+ 4” + F", we 
may act in the following way. We represent the &s of the solid 
snlistances. Jy 4E and, 2 by aly, Fi and 2) As 20k and £" 
are situated on a straight line, /,, #,' and /’," are situated in a 
vertical plane, but generally not on a straight line. Consequently 
the equilibrium /’+ /” + F" cannot occur and of the equilibria 
EKA FF’, F+ F" and #” + F" two (one) are stable and, therefore, 
one (two) are metastable. Now we take a definite P and 7’; we 
keep the temperature constant and we change the pressure; under 
a definite pressure the points /’,, #' and #,” fall then ina straight 
line, so that the equilibrium / + #” + F" occurs. 
When this line is situated below the vapourleaf of the ¢-surface, 
then the equilibrium /’+ /” + F" is stable; we can construct then 
through this line two tangentialplanes to the vapourleaf; we call 
w and v the projections of the two points of contact. These points 
u and v are situated on either side of the line “’/” /'". At the assumed 
temperature consequently a pressure P. = P, exists, under which 
occur the equilibria: A+ HP, FHH! HG, and 
RAR +R" + G,. 
Generally the vapoursaturationcurves of /’, /” and /'" intersect 
one another in six points; it is apparent from the previous that 
IF. A. H. Scureinemakers, Die heterogenen Gleichgewichte von Baxuuis Roo- 
ZEBOOM, III!, 218—248, 
84° 
