PRINCIPLES UNDERLYING METAMORPHIC PROCESSES 589 
any moment definitely fixed. Thus a system with two degrees of 
freedom can in general exist throughout a range of temperatures 
and pressures; if the system actually had only one degree of 
freedom, it could only be accidental if the corresponding values 
were chosen. Therefore the number of possible phases coexisting 
in equilibrium during metamorphic processes will in general not be 
greater than the number of components. The essentials of the 
phase rule and their application to simple systems are so readily 
understood that there is always a temptation to neglect their 
specific limitations; limitations which are especially prominent 
when, as in the case of metamorphic processes, we endeavor to 
reason backward from the end-result of the process. 
Limitations to the applicability of the phase rule to metamor phic 
systems.—Application of the phase rule presupposes that the 
pressure (and temperature) is uniform throughout the system’. 
Now it is clear that absolutely uniform pressure (or temperature) 
can never occur during rock metamorphism; we may have any- 
thing from great inequality in the stresses in the three principal 
directions to a nearly equal distribution of the three stresses. On 
the relative and absolute magnitude of the variation of the resultant 
stress from point to point depends its influence on the result. If 
the particular paragenetic transformation can still go on in spite 
of considerable variations of either temperature or pressure from 
the mean values which actually obtain, it will not be much affected 
by the local stress variation; if otherwise, great local variation of 
results may be expected. Moreover, similarly variable results will 
be produced by the changes of temperature and pressure which 
accompany the process of metamorphism. 
Reference to the discussion of phases and components given 
in the textbooks renders it evident that great caution must be 
exercised in guessing (inferring) the actual components from an 
examination of the more or less ultimate state of any given rock. It 
is an essential property of a component that it is always in reaction 
with the other members of the system throughout the establishment 
of equilibrium. But the fact that under laboratory conditions 
«Further, that there are (cuter alia) no surface effects; this condition might be 
unfulfilled in certain cases, e.g., with very porous rock-masses. 
