Properties of the Feldspars. 133 



An extended discussion of existing data from this stand- 

 point would involve us in unnecessary detail, but there can be 

 no question that Kuster's Rule represents the data which have 

 been gathered upon isomorphous mixtures — at least approxi- 

 mately — while the laws of dilute solutions appear to fail of 

 application there. On the other side, the Rule admits of no 

 independent theoretical derivation. Van't HofP suggests that 

 judgment be suspended pending the accumulation of further 

 data and intimates that the close similarity of chemical com- 

 position and molecular structure in compounds which form 

 isomorphous mixtures, gives them an unusually close inter- 

 relation, and their influence one upon the other may render a 

 simple theoretical treatment very difficult. 



Our case is especially interesting when considered from this 

 standpoint, but it distinctly emphasizes the difficulty rather than 

 helping toward its solution : (1) Although the chemical reac- 

 tions of albite and anorthite are not of such a character as to . 

 prove or disprove a close analogy between them, a comparison of 

 their formulas certainly does not suggest an isomorphous rela- 

 tion. If their formula weights represent true molecules, they 

 possess the same number of atoms to the molecule (NaAlSi 3 8 , 

 CaAl 2 Si 2 8 ) and the group Si 2 8 in common, but the remaining 

 atoms taken separately are not mutually replaceable. (2) The 

 melting points of the components in the feldspar series are very 

 far apart — more than 300° — while Kuster's organic mixtures 

 were all included within a narrow temperature interval (2° to 

 56°). For reasons which will appear presently, both Garellif 

 and Roozeboom have pointed out that the farther apart the 

 melting points of the components, the less probable is the linear 

 relation. (3) The homogeneity of the solid phase is established 

 within 1 per cent by the optical examination of the slides. 

 Moreover separate chemical analyses of the solid and liquid 

 phases of the mixtures Ab.An. in an exceptionally favorable 

 case showed still closer identity of composition. 



It appears altogether improbable that the laws of solutions 

 can apply in the face of so extreme a controverting case. 



If it has proved difficult to bring the isomorphous mixture 

 within the general laws of solutions, a most satisfactory theo- 

 retical derivation of the conditions of equilibrium in such 

 mixtures has been developed by Roozeboom. ISTo other prin- 

 ciple is required than the second law of thermodynamics as 

 applied to solutions by G-ibbs : — A system of substances will be 

 in equilibrium for a particular pressure when the thermo- 

 dynamic potential (f-function) of the system is a minimum. 

 The scheme of representation is the graphical one proposed by 



* Van't Hoff, Vorlesungen ub. Theoret. u. Phys. Chem. (Braunschweig 

 1901.) Part II, p. 64. fF. Garelli, loc. cit. 



