302 HAROLD L ALLING 



rule states that one of the phases must of necessity be destroyed^ 

 which, according to the diagram, is impossible. This absurdity 

 can be appreciated by an illustration. Consider the solid substances 

 H and / as already mentioned, composed of three phases, soda ortho- 

 clase, soda microcline, and potash albite. Let the temperature be 

 lowered 5 degrees and the composition be enriched by i per cent of 

 KAlSijOs, shifting the point to a position within the triangle FGH. 

 Within this area orthoclase and microcline are in equilibrium. Now 

 one of the phases must disappear, according to the rule. Potash 

 albite should then vanish. But how? Apparently the diagram 

 is in error. Perhaps the error is not really in the diagram after all, 

 but rather in our insistence that all three phases are in equilibrium 

 with each other. The diagram would be correct if it was stated to 

 be an "unstable equilibrium" diagram. A thoroughly satisfactory 

 diagram showing the dimorphism of the potash component would 

 have the inversion boundary indicated by a line, and not by an area. 



The real point is that we should not fit the feldspars to the dia- 

 gram, but rather the diagram to the feldspars. Thus if Makinen's 

 diagram is for plutonic feldspars, indicating cooling slowly under 

 quiet conditions, we can expect that orthoclase can form and remain 

 unchanged during the cooling of the rock, until jarred or subjected 

 to variable pressure. Then it would pass from the potential micro- 

 cline form into the stable modification microcline, not all at once 

 probably, but by slow degrees, and hence orthoclase and microcline 

 would exist side by side during the time interval of change. A dia- 

 gram to express this would obviously be an unstable equilibrium 

 diagram. Makinen's diagram is incorrect^if perfect equilibrium is 

 insisted upon, but it is very likely relatively correct if unstable con- 

 ditions are to be represented graphically. 



The writer through thermal treatment^ has been led to suspect 

 that the transition range, in which both orthoclasic and microclinic 

 feldspars exist, is to be represented by a transition line with the 



' The mathematical expression of the phase rule is C—P-\-2 = F, where C=nimiber 

 of components, P the number of phases and F number of degrees of freedom. C= 2. 

 (KAlSijOg and NaAlSijOg.) -P = 3 (as said above). Hence 2—3+2 = 1. But we 

 said that H is invariant which should give us a zero for an answer. (All this provided 

 equilibrium prevailed.) We can conclude therefore that the diagram is in error. 



^ Experiments were conducted in the laboratories of the department of physics 

 of the University of Rochester in platinum furnaces. Temperature was measured 

 by platinum-iridium pyrometers of high quality. 



