Rankin and Wright — Ternary System CaO-Al 2 0-Si0 2 . 13 



figures are easy to obtain even on grains measuring only -01 mm 

 in diameter. The grains often contain fine threadlike inclu- 

 sions of a higher refracting, weakly birefracting isotropic sub- 

 stance which are too fine for satisfactory determination. Their 

 total amount is very slight. 



(II) The unstable form crystallizes occasionally from the 

 rapidly cooled liquid. It occurs rarely in the ternary mixtures ; 

 has no definite melting point and apparently no definite region 

 of real stability ; it inverts so rapidly at high temperatures to 

 the stable form that perfectly homogeneous preparations could 

 not be obtained. Crystal habit, prismatic to fibrous with fair 

 prismatic cleavage. Luster, vitreous. Hardness 5*5 to 6. 

 Crystal system orthorhombic, or monoclinic, probably ortho- 

 rhombic, though in one preparation twinning phenomena were 

 observed which might indicate monoclinic symmetry. Re- 

 fractive indices: y Na = 1-674 db 0-002, Na = 1-671 =b 0-002, 

 a Na = 1-662 d± 0-003 ; birefringence medium, y-a approxi- 

 mately 0-013. Optic axial angle 2V Na = 35° db 5°. Optical 

 character negative. Axial dispersion strong, 2Y r > 2V V . 

 Plane of optic axes and extinction parallel to the prismatic, 

 positive elongation. 



THE PHASE RULE AND ITS APPLICATION TO TERNARY SYSTEMS. 



It may be well to review briefly the general principles upon 

 which is based the experimental investigation of a ternary 

 system, before- the actual methods of experiment and the 

 results obtained are given. The main and essential guiding 

 principle is the phase rule, which is, of course, just as applicable 

 to mixtures of mineral oxides which are liquid only at high 

 temperatures as it is to ordinary solutions. In either case it is 

 necessary that the phase rule be applied properly ; indeed this 

 constitutes the only method of attack in problems so com- 

 plicated as the investigation of the system CaO-Al 2 3 -Si0 2 : 

 for in this system we have found no fewer than 14 distinct 

 compounds, each with a stable region of existence correlated 

 with a definite range of conditions. 



THE PHASE RULE. 



" Gibbs showed how in a perfectly general manner, free 

 from all hypothetical assumptions as to the molecular condition 

 of the participating substances, all cases of equilibrium could 

 be surveyed and grouped into classes and how similarities in 

 the behavior of apparently different kinds of systems and dif- 

 ferences in apparently similar systems could be explained." 



"In deducing the law of equilibrium, Gibbs regarded a 

 system as possessing only three independently variable factors — 



