14 Rankin and Wright — Ternary System CaO-Al^O^-SiO^. 



temperature, pressure, and the concentration of the components 

 of the system — and enunciated the general theorem now usually 

 known as the Phase Rule, by which he defined the conditions 

 of equilibrium as a relationship between the number of what 

 are called the phases and the components of the system." * 



jPhases.-f — " A heterogeneous system is made up of different 

 portions, each in itself homogeneous, but marked off in space 

 and separated from the other portions by bounding surfaces. 

 These homogeneous, physically distinct and mechanically 

 separable portions are called phases." 



Components. X — " As the components of a system there are to 

 be chosen the smallest number of independently variable con- 

 stituents by means of which the composition of each phase 

 participating in the state of equilibrium can be expressed in 

 the form of a chemical equation." 



" Variable factors or degrees of freedom, ."§ — "The number 

 of degrees of freedom of a system is the number of the variable 

 factors, temperature, pressure and concentration of the com- 

 ponents, which must be arbitrarily fixed in order that the con- 

 dition of the system may be perfectly defined." 



" The Phase Pule of Gibbs, now, which defines the condition 

 of equilibrium by relation between the number of coexisting 

 phases and the components, may be conveniently summarized 

 in the form of an equation as follows : 



P + F= C + 2 ov F = C + 2 - P 

 where P denotes the number of phases, F the degrees of 

 freedom and C the number of components. From the second 

 form of the equation it can be readily seen that the greater the 

 nnmber of phases the fewer are the degrees of freedom. 

 With increase in the number of phases, therefore, the condi- 

 tion of the system becomes more and more defined, or less and 

 less variable." J 



" In accordance with the phase rule, therefore, we may clas- 

 sify the different systems which may be found into invariant, 

 univariant, bivariant, multivariant, according to the relation 

 which obtains between the number of components and the 

 number of coexisting phases ; and we shall expect that in each 

 case the members of any particular group will exhibit a uni- 

 form behavior. By this means we are enabled to obtain an 

 insight into the general behavior of any system, so soon as we 

 have determined the number of the components and the num- 

 ber of coexisting phases. 



*Findlay, " Phase Rule," p. 8. 

 \ Findlav, ibid., p. 9. 

 JFindlay, ibid., p. 12. 

 gFindlay, ibid. 

 ||Findlay, ibid., p. 16. 



