594 JOHN JOHNSTON AND PAUL NIGGLI 
moves along the boundary curve R-17 until the invariant point 17 
is reached, when the whole solidifies to the three phases (CaO), 
(3CaO-Al,O,;), and (3CaO-SiO,). In this case only part of the free 
CaO is resorbed; but if the original composition had been repre- 
sented by a point on the line QR (i.e., outside the triangle NOP) 
the CaO would be completely resorbed, the final crystallization 
occurring at invariant point 15, at which the phases (3CaO-AL0O,), 
(5CaO-3AL0,), and (2CaO-SiO,) are in equilibrium. All of these 
phenomena occur, be it noted, without interruption of the normal 
cooling or the intervention of any external disturbing factor. 
As regards the second point, consider compositions along the 
line STU, the total length of which corresponds to a change of only 
3 per cent in the amount of CaO present. Compositions on the 
line ST solidify at invariant point 16, 15, or 14, according to the 
original position on the line; the ternary grouping formed is either 
(3CaO-SiO,), (2CaO-SiO.), (3CaO-ALO,), or (5CaO-3AL0;), 
(3CaO-AlO,), (2CaO-SiO,), or (5CaO-3AL0,), (2CaO-SiO,), 
(CaO-AlLO,). Compositions on the line TU solidify at point 6, 
forming the grouping (2CaO-SiO,), (CaO-SiO,), (2CaO-ALO,- 
SiO.); while the compositions corresponding to T (or any point 
on the line joining the compositions 2CaO-SiO,, 2CaO-Al.O,-SiO,) 
behave as binary systems, solidifying to the two phases (2CaO- 
SiO.), (2CaO- ALO, - SiO). | 
These facts—and indeed the general appearance of the diagram 
—illustrate the complications likely to be encountered in relatively 
simple systems, and show that for systems of from four to eight 
or more components appearances afford a plain warning against 
hasty generalization, even if initial homogeneity of material and 
the continuous attainment of equilibrium could be assumed. 
The ternary system CaCl,-MgCl.-H,0.—This system, which 
was very carefully investigated by Van’t Hoff, Kendrick, and Daw- 
son,’ is an example of a system with a variable phase (solution). 
The determination of the quintuple point of such a system will 
always be a matter of great difficulty, since in this case pressure, 
temperature and concentration (composition of the variable phase) 
are all fixed. 
™Z. physik. Chem., XXXIX (1902), 27. 
