J. W. Gibhs — .Equilihriiim of Heterogeneous Sithstances. 179 



are seen in the figure, and will be denoted by the symbols (A), (B), 

 (C). We may, for convenience, speak of these as separate curves, 

 without implying anything in regard to their possible continuity in 

 parts of the diagram remote from their common tangent AC. The 

 line of dissipated energy includes the straight line AC and portions 

 of the primitive curves (A) and (C). Let us first consider how the 



diagram will be altered, if the temper- 

 ature is varied while the pressure re- 

 mains constant. If the temperature 

 receives the increment dt, an ordinate 

 of which the position is fixed will 

 'd'Q^ 



Q. 



b 

 Fig. 1. 



P. 



receive the increment ( -^ 1 dt, or 



\dt I p^ m 



— // dt. (The reader will easily con- 

 vince himself that this is true of the 

 ordinates. for the secondary line AC, as well as of the ordinates for 

 the primitive curves.) Now if we denote by ;/' the entropy of the 

 phase represented by the point B considered as belonging to the 

 curve (B), and by rf the entropy of the composite state of the same 

 matter represented by the point B considered as belonging to the 

 tangent to the curves (A) and (C), t (?/' — //') will denote the heat 

 yielded by a unit of matter in passing from the first to the second 

 of these states. If this quantity is positive, an elevation of temper- 

 ature will evidently cause a part of the curve (B) to protrude below 

 the tangent to (A) and (C), which will no longer form a part of the 

 line of dissipated energy. This line will then include portions of the 

 three curves (A), (B), and (C), and of the tangents to (A) and (B) 

 and to (B) and (C). On the other hand, a lowering of the tempera- 

 ture will cause the curve (B) to lie entirely above the tangent to (A) 

 and (C), so that all the phases of the sort represented by (B) will be 

 unstable. If t {i/ — ;/") is negative, these efl:ects will be produced by 

 the opposite changes of temperature. 



The effect of a change of pressure while the temperature remains 

 constant may be found in a manner entirely analogous. The varia- 



dp or V dp. Therefore, if the 



tion of any ordinate will be ( ^ 



^ \dplt,;,i 



volume of the homogeneous phase represented by the point B is 

 a greater than the volume of the same matter divided betAveen the 

 the phases represented by A and C, an increase of pressure will give 

 diagi'am indicating that all phases of the sort represented by curve 

 (B) are unstable, and a decrease of pressure will give a diagram indi- 



