EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



123 



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 variation 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 

 0. 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 part of the 

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

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

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



Fig. 2. 



Fig. 3. 



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 surface, 

 portions of the six developable surfaces formed by a double tangent 

 plane rolling 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. 



But when the points of contact with the quadruple tangent plane 

 which represent the four coexistent phases can be joined so as to 



