436 K T. Allen, F. K Wright and J. K. Clement— 



gators that, experimentally, amphiboles may be readily changed 

 into pyroxenes but not pyroxenes into amphiboles. 



False Equilibria in Nature. — Since these studies have 

 shown the instability of enstatite and the amphiboles of the com- 

 position MgSi0 3 , it may be at once inferred that not all natural 

 minerals are stable. The occurrence of the unstable forms 

 alone constitutes what is commonly called a metastable condi- 

 tion (apparent false equilibrium of JDuhem), in which it is gener- 

 ally assumed that equilibrium may be brought about by contact 

 w T ith the stable phase. In another part of this paper it has 

 been demonstrated that such a contact is inadequate, in the 

 case of the magnesium silicates, to determine equilibrium dur- 

 ing periods of time which are within the limits of laboratory 

 observation. 



Duhem, in his Thermodynamique et Chimie (p. 436), draws 

 a very apt comparison between chemical and mechanical sys- 

 tems. The statics of both are commonly treated as if the sys- 

 tems were frictionless, whereas in both we have to deal with a 

 resistance which in the former is ordinary friction, in the latter 

 an internal friction between the molecules. Chemical systems, 

 in the majority of cases so far studied, seem capable of reach- 

 ing a true equilibrium, or at least a state which approaches 

 it within measurable limits, but where the systems are com- 

 posed of viscous liquids or more especially of solids at low 

 temperatures, true equilibrium may not be reached even after 

 an indefinite time, the condition finally attained being not 

 alone the result of molecular forces as conditioned by temper- 

 ature and pressure, but of these retarding forces which offer 

 an internal resistance of by no means negligible magnitude. 

 (Duhem's genuine false equilibria.) "We find in nature false 

 equilibria of this kind, e. g., intergrowths of pyrite and mar- 

 casite* among the sulphides, and among the silicates inter- 

 growths of sillimanite and andalusite, and enstatite with 

 monoclinic pyroxene. f It has been generally supposed that 

 the monoclinic pyroxene in the last-named case was a diopside, 

 but our experiments show that similar aggregates form in arti- 

 ficial systems which contain no calcium and that they exist in 

 the Bishopville meteorite. In some cases it is not at all impos- 

 sible that these systems are in process of very slow change, but 

 there is no optical evidence that this is true of the above-men- 

 tioned silicates; in other cases it may be that the two forms 

 were deposited at different times, though in some it would 

 appear that they were actually crystallized together; the 

 important fact to note in them all is that they are systems 

 which are not in equilibrium. Because a rock or mineral aggre- 



* Stokes, H. N., U. S. Geol. Survey, Bull. 186. 



f We have also obtained intergrowths of the two magnesian amphiboles. 

 Therefore the aggregates of monoclinic and orthorhombic amphiboles in. 

 nature probably form another example of this principle. 



