PRINCIPLES UNDERLYING METAMORPHIC PROCESSES 599 
In concluding this section we wish to state again our precise 
standpoint with reference to the application of the phase rule. 
To say that the phase rule must always hold for metamorphic 
systems is equivalent to the assumption that such systems always 
attained a state of equilibrium; which is certainly not true. Many 
rocks will be found to contain a larger number of minerals than the 
maximum number required by the phase rule. On the other 
hand, the fact that the number of minerals found agrees with this 
maximum is absolutely no criterion of the attainment of a state 
of stable equilibrium within the system; for at equilibrium there 
will in many cases be present fewer phases than this maximum 
number. One may say only that the rocks will show a tendency 
toward equilibrium, that they will tend to attain the state corre- 
sponding to the ideal PT diagram; the ideal types therefore are 
to be considered merely as representative examples which also will 
be of use in classifying actual rocks. 
Consideration of ideal types may also be of great advantage 
in classifying metamorphic rocks; just as in the classification of 
crystals the ideal crystal form is used, although it is seldom that 
two crystals of the same substance separate out in precisely identical 
form. As an instance of its use in this way we may recall the well- 
known work of V. M. Goldschmidt on the contact rocks of the 
Christiania region. 
The foregoing treatment applies only to cases where the meta- 
morphic process has not been accompanied by any change in the 
gross composition of the material; the question of what happens 
in such case is taken up later. Here we will remark only that it is 
by no means necessary that rocks which now show identical chemi- 
cal compositions should be made up of the same mineral constitu- 
ents; for the reason that differences, and comparatively slight 
differences, in the amounts of volatile components (‘‘mineralizers’’) 
originally present might easily alter the character, and order of 
separation, of the minerals formed in the metamorphic process. 
THE GENERAL EFFECTS OF NON-UNIFORM COMPRESSION 
The effects produced by exposure to non-uniform compression 
are in general permanent; that is, the original state of the system 
