GEOPHYSICAL LABORATORY. 129 



The above theorem relates only to the slope of the P-T curves which pass 

 through the invariant point. Of necessity, the portion of the P-T curve lying 

 on one side of the invariant point represents stable conditions, the portion on 

 the other side metastable conditions. The above theorem does not tell us 

 on which side of the invariant point the equilibrium we are considering is 

 stable. To answer this question absolutely requires a knowledge of the vol- 

 ume and entropy changes which take place when the reaction proceeds, but 

 without such knowledge the following generalizations may be made. The 

 P-T curves of condensed systems, i. e., systems containing only solid and 

 liquid phases, are almost vertical, and go from the invariant point to regions of 

 higher pressure and (usually) higher temperature. The P-T curves of systems 

 composed solely of solid and vapor phases, e. g., dissociation pressure curves, 

 go from the invariant point to regions of lower temperature and pressure. 

 Also, from the fundamental conditions of stability laid down by Gibbs, the fol- 

 lowing theorem can be proved : 



When two adjoining P-T curves coincide, due to a linear relation being possible 

 between the compositions of the n phases common to both the monovariant equili- 

 bria, i. e., to these n phases lying on the one-fold (n), whose position is deter- 

 mined by the above linear relation, these equilibria are stable in the same direc- 

 tion from the invariant point, i. e., their stable portions coincide, when the other 

 two phases lie on opposite sides of the one-fold (n), and vice versa. 



By "the other two phases" is meant the phases, one in each of the mono- 

 variant equilibria, which do not lie on the one-fold (n) . 



The above considerations make possible (with no other knowledge than the 

 composition of the phases at an invariant point) the fixing of the order of suc- 

 cession of the (n-\-2) P-T curves which proceed from an invariant point in a sys- 

 tem of n components and (when the state of aggregation of the phases is known 

 in addition) the fixing of their actual position within fairly narrow limits. 

 This is illustrated by considering the P-T curves which proceed from the five 

 quintuple points in the ternary system H20-K2Si03-Si02. 



The general relation given above between the variations in pressure and 

 temperature (equation 129 of Gibbs) is not in a form which is convenient to 

 apply. A general method is given for casting it into a convenient form for 

 practical use and a concrete interpretation of the coefficients involved is given. 

 In a system of three components, the equation becomes: 



jD (vi—n*)-\ — z—(vi-vi) — ^— ('72-'?3) 



dP AU3 AU3 



dT Am, ^ Avu 



{V3 — Vi) -\-—. {Vl—Vz) — — {V2 — Vi) 



A 123 A\t3 



In this the subscripts 1, 2, 3, 4 refer to the different coexisting phases; the 

 coefficients A123, A134, A234 refer to the areas of the triangles formed by con- 

 necting up the points in the composition diagram representing the composition 

 of phases 1, 2, and 3; 1, 3, and 4; and 2, 3, and 4, respectively, the areas being 

 circumscribed in the directions given. The application of this equation to 

 the actual slope of the P-T curves, and especially to the change in slope with 

 change in composition of phases of variable composition, is discussed in detail, 

 taking as examples typical P-T curves from the ternary system H20-K2Si03- 

 SiOa. 



(5) The necessary physical assumptions underlying a proof of the Planck radiation law. 

 F. Russell V. Bichowsky. Phys. Rev., 11, 58-65 (1918). 

 In order to prove Planck's radiation law by means of the quantum theory 

 only two physical assumptions need be made : first, that energy is absorbed or 



