Page:Scientific Papers of Josiah Willard Gibbs.djvu/159

Rh 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 $$C.$$. 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 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 homogeneous 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 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