THE MINERALOGRAPHY OF THE FELDSPARS 195 
The components here considered are the K-, Na-, Ca-, and 
Ba-feldspars, which are assumed to be stable under the conditions 
of the present investigation. There is no difficulty in under- 
standing the term “‘component’’ employed here as an example of 
the nomenclature of the phase rule. It is well for the purpose of 
this discussion that we understand the term “phase.” ‘‘ Phases 
are the homogeneous states, whether of freedom, solution, or 
combination, and whether solid, liquid, or gaseous, into which the 
components present pass or group themselves .... the phases 
are the transitory stages, states, or conditions, physical cr chemical, 
through which the components pass as they are heated up and 
cooled down, or as their pressure rises and falls.’”! 
The mathematics of the phase rule applies to systems which 
are in a state of perfect equilibrium. It cannot be disputed that 
many metallic alloys and silicate complexes (silicate alloys) are in 
a state of imperfect or false equilibrium. So frequently does this 
condition occur that the phase-rule method of considering such 
systems has been the object of considerable criticism. These 
critics are entirely justified so far as the strict application of the 
rule is concerned, but apparently overlook the value of thermo- 
equilibrium diagrams. ‘The use of the diagrams and the application 
of the phase rule are distinct. Such diagrams help to explain the 
phenomena of crystallization and microscopic textures of silicate 
and metallic alloys. Howe’? points out that hardened steel is a 
metastable system, that is, it is not in equilibrium, and yet that 
fact does not depreciate the value of the iron-carbon diagram to 
the steel manufacturer. A condition of imperfect equilibrium can 
be, definitely indicated upon the diagram. Ostwald’ says: ‘‘In 
spite of my great admiration for the progress that has been made in 
metallography through the introduction into this field of the con- 
cepts of chemical equilibrium, the phase rule and van’t Hoff’s 
-concept of solid solution, I cannot help emphasizing the need of 
caution in all this, for those concepts are all based upon the truth 
1H. M. Howe, The Metallography of Steel and Cast Iron, 1916, p. 240. 
2 I(iilon (De Beit 
3 Wolfgang Oswald, Theoretical and Applied Colloid Chemistry, translated by 
Martin H. Fischer (1917), p. 108. 
