144 CARNEGIE INSTITUTION OF WASHINGTON. 



dine from Laacher See, and adularia from St. Gotthard, show the same kind 

 of behavior, though in these the upper hmit of melting (disappearance of 

 leucite) is lowered somewhat through the presence of foreign matter. 



This incongruent melting of orthoclase is of particular importance in 

 petrogenic theoiy, because it shows plainly how by fractional crystallization 

 a homogeneous liquid could form a differentiated mass consisting of orthoclase 

 and leucite in one part and of orthoclase and free silica in another. It shows, 

 too, that leucite can form from a liquid containing an adequate amount of 

 silica to form orthoclase and that a mass may have leucite as early crystals 

 (phenocrysts) together with free silica as late crystals (groundmass) . These 

 considerations explain the occurrence of such a rock as the leucite-granite 

 porphyry of Brazil and such a differentiated mass as the syenite laccolith at 

 Loch Borolan, Scotland. It is to be noted that both these occurrences show 

 pseudo-leucites, formed secondarily after leucite, and consisting, as do the 

 leucites of intrusive rocks in general, of an intergrowth of orthoclase and 

 nephelite (or secondary products after nephelite). This regular behavior of 

 leucite in breaking up into orthoclase and nephelite suggests that the early 

 separation of leucite, with a subsequent change of that nature, may afford a 

 key to the origin of many nephelite rocks as well as leucite rocks. 



(454) Augite and hornblende from Kilimanjaro. Henry S. Washington and H. E. Merwin. 



Am. Mineralogist, 7, 121-125. 1922. 



The chemical and optical characteristics found for the augite from Kili- 

 manjaro are almost identical with those of several augites of high diopside- 

 content from rocks markedly different chemically. Similar comparisons of 

 the hornblende can not be made on account of the lack and questionable 

 character of data. 



(455) The application of thermodynamics to heterogeneous equilibria. George W. Morey. 



J. FrankHn Inst., 194, 425-484. 1922. 



The underlying purpose of the four lectures included in this paper was to 

 present, in as simple a form as possible, the fundamental features of that 

 portion of Gibbs's great paper, "Equilibrium of Heterogeneous Substances," 

 which lead up to and are essential to the development of his equation 97. 

 As is emphasized throughout, this equation is a powerful weapon for attack- 

 ing the problem of equilibria between phases, and affords a more direct 

 and simple, as well as a far more potent, attack than does the usual statement 

 of the phase rule, which is but an incidental qualitative deduction from equa- 

 tion 97. By the detailed application of this equation, problems of hetero- 

 geneous equilibria may be solved completely if the entropy and volume 

 changes are known in their entirety. But more than this, by the applica- 

 tion of this equation, and such a general knowledge of entropy and volume 

 differences as are involved in the knowledge that a vapor phase has a 

 greater entropy and volume than the liquid phase with which it is in equili- 

 brium, or that the high-temperature modification of a phase has a greater 

 entropy than the low-temperature modification, it is possible to predict, 

 with an approach to quantitative accuracy, the behavior of the system when 

 subjected to changes in pressure, temperature, and composition. Further- 

 more, this thermodynamic method is not limited in its application to two or 

 three component systems, but can be extended readily to include any desired 

 number of components. 



A sharp line must be drawn between those relations which are derived 

 from the two laws of thermodynamics without the aid of further assumptions 

 and those whose derivation involves not only the thermodynamic laws proper, 

 but also further assumptions extraneous to thermodynamics. To this latter 



