J. W. Gihbs — Equilibrium of Heterogeneous Substances. 181 



Such a mass, if exposed to constant temperature and pressure, would 

 be in neutral equilibrium. A point in the developable surfaces repre- 

 sents a mass of which the matter is divided between two coexisting 

 phases, which are represented by the extremities of the line iu the 

 figure passing through that point. A point in the primitive surface 

 rejjresents of course a homogeneous mass. 



To determine the eftect of a change of temperature without change 

 of pressure upon the general features of the surface of dissipated 

 energy, we must know whether heat is absorbed or yielded by a 

 mass in passing from the phase represented by the point D in the 

 primitive surface to the composite state consisting of the phases A, 



B, and C which is represented by the same point. If the first is the 

 case, an increase of temperature will cause the sheet (D) (i. e., the 

 sheet of the primitive surface to which the point D belongs) to sep- 

 ai-ate from the plane tangent to the three other sheets, so as to be 

 situated entirely above it, and a decrease of temperature, will cause 

 a part of the sheet (D) to protrude through the plane tangent to 

 the other sheets. These effects will be produced by the opposite 

 changes of temperature, when heat is yielded by a mass passing 

 from the homogeneous to the composite state above mentioned. 



In like manner, to determine the effect of a vai-iation of pressure 

 without change of temperature, we must know whether the volume 

 for the homogeneous phase represented by D is greater or less than 

 the volume of the same matter divided between the phases A, B, and 



C. If the homogeneous phase has the greater volume, an increase of 

 pressure will cause the sheet (D) to separate from the plane tangent to 

 the other sheets, and a diminution of pressure will cause a pai't of the 

 sheet (D) to protrude below that tangent plane. And these effects 

 will be produced by the opposite changes of pressure, if the homoge- 

 neous phase has the less volume. All this appears from precisely the 

 same considerations which were used in the analogous case for two 

 component substances. 



Now when the sheet (D) rises above the plane tangent to the other 

 sheets, the general features of the surface of dissipated energy are 

 not altered, except by the disappearance of the point D. But when 

 the sheet (D) protrudes below the plane tangent to the other sheets, 

 the surface of dissipated energy will take the form indicated in figure 3. 

 It will include portions of the four sheets of the primitive sui-face, 

 portions of the six developable surfaces formed by a double tangent 

 plane rollino- upon these sheets taken two by two, and portions of 

 three triple tangent planes for these sheets taken by threes, the sheet 

 (D) being always one of the three. 



