THE GENERAL PRINCIPLES UNDERLYING 
METAMORPHIC PROCESSES 
JOHN JOHNSTON AND PAUL NIGGLI 
Geophysical Laboratory, Carnegie Institution of Washington 
PART II 
THE PHASE RULE 
The phase rule, which recently has been applied to metamorphic 
rocks," orients us as to the number of phases which, for a given 
number of components and for given external conditions, can be in 
equilibrium with one another. According to the phase rule f=c— 
n+2, where f, c, and m are the number of degrees of freedom, of 
components, and of phases, respectively. If fis zero, the system is 
stable only when temperature, pressure, and concentration (com- 
position) of each phase have definite and singular values. If f 
is 1, a change of one of the above three parameters induces definite 
and definitely related alterations of the other two, if the number and 
nature of the phases is to remain unaltered. Iffis 2, any two of the 
above parameters may be changed; such a system can exist at 
any pressure or temperature within certain limits, although under 
such circumstances the composition of all the phases present is at 
tV. M. Goldschmidt, Kontakimetamor phose im Kristiania-Gebiet, Kristiania, 1911, 
and in other papers; P. Niggli, “‘Chloritoidschiefer des nordéstlichen Gotthardmas- 
sives,’’ Beztrdge geol. Karte Schweiz, N. F., XXXVI (1912). 
2“ A heterogeneous system is made up of different portions, each in itself homo- 
geneous, 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” (Findlay, Phase Rule, p. 9). 
“As the components of a system there are to be chosen the smallest number of inde- 
pendently variable constituents 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”? (zb7d., p. 12). 
“The number of degrees of freedom of a system is the number of the variable 
factors, temperature, pressure, and concentration of the components, which must be 
arbitrarily fixed in order that the condition of the system may be perfectly defined”’ 
(cbid., p. 15). 
For a full discussion of these matters the reader is referred to Findlay’s book. 
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