236 



MOREY 



ART. G 



improbable that there are four coexistent phases of any simple 

 substance.* An example of n = 2 and r = 4 is seen in a solution 

 of a salt in water in contact with vapor of water and two differ- 

 ent kinds of crystals of the salt." Coexistence of r = w + 2 

 phases gives rise to an invariant equilibrium, and such a co- 

 existence is frequently called an invariant point. Invariant 

 points are also referred to by the number of phases present ; for 

 example, a triple point in a one-component system, quadruple 

 point in a two-component system, etc. 



When r = 7i -\- 1, there are n -{- 1 equations of the form of 

 (1) [97], one for each of the coexisting phases, and the system 

 has one degree of freedom. We may eliminate n of the n -\- 2 

 independent variables, giving an equation between the two 

 remaining. If the quantities dm, dti2, ■ ■ ■ djin are eliminated by 

 the usual method of cross multiplication, we obtain a linear 

 equation between the changes in pressure and temperature, 

 which for the general case takes the form 



7j' m/ rrii . . . rrin 

 t\" mx" rri'i' . . . rrin" 



dp _ T?" mi" Tn?" . . . m 

 dt 



v' m\' rrh' 

 v" wi" m^" 



m„ 

 m. 



yn ^n ^^n _ _ _ ^^n 



(6) [129] 



We shall develop in detail the application of this equation to 

 several types of systems. 



III. Application of Equation [97] to Systems of One Component 



3. The Pressure-Temperature Curve of Water. A simple case 

 of heterogeneous equilibrium is that of a one-component 



* For an extended discussion of the possibility of the coexistence of 

 more than n + 2 phases, see R. Wegscheider, Z. physik. Chem., 43, 93 

 (1903) et seq.; A. Byk, ibid., 45, 465 (1903) et seq. 



