Page:Scientific Papers of Josiah Willard Gibbs.djvu/84

48 W. Thomson in his paper "On the equilibrium of a vapor at the curved surface of a liquid" (Proc. Roy. Soc. Edinb., Session 1869-1870, and Phil. Mag., vol. xlii, p. 448), leave no room for doubt. By experiments like that suggested by Professor J. Thomson in his paper already referred to, we may be able to carry vapors father beyond the limit of absolute stability. As the resistance to deformation characteristic of solids evidently tends to prevent a discontinuous change of state from commencing within them, substances can doubtless exist in solid states very far beyond the limit of absolute stability.

The surface of absolute stability, together with the triangle representing a compound of three states, and the three developable surfaces which have been described representing compounds of two states, forms a continuous sheet, which is everywhere concave upward except where it is plane, and has only one value of $$\epsilon$$ for any given values of $$v$$ and $$\eta$$. Hence, as $$t$$ is necessarily positive, it has only one value of $$\eta$$ for any given values of $$v$$ and $$\epsilon$$. If vaporization can take place at every temperature except $$0$$, $$p$$ is everywhere positive, and the surface has only one value of $$v$$ for any given values of $$\eta$$ and $$\epsilon$$. It forms the surface of dissipated energy. If we consider all the points representing the volume, entropy, and energy of the body in every possible state, whether of equilibrium or not, these points will form a solid figure unbounded in some directions, but bounded in others by this surface.