temperature, or in Lord Kelvin's phrase, a general dissipation of energy in all irreversible phenomena. For each potential, with appropriate choice of coordinates, a solid model or relief map can be constructed, upon which the different minima of the potentials appear as depressions in the landscape. When the lowest depression or minimum has been reached, complete and permanent equilibrium is attained, and we have what Gibbs calls a "phase of dissipated energy," at which, as in a bar of metal or a block of granite, no further spontaneous changes of physical state are possible so long as the system remains isolated from external forces. In connection with his discussion of equilibrium we may note Gibbs's forethought in extending his equations to n dimensions, since for more than three components a three-dimensional model no longer suffices; his early introduction of the time element into the discussion of chemical reactions and his pages on "passive resistance to change," which should be read by every chemist, since they are of the essence of his subject, especially in regard to carbon compounds or colloidal substances. In applying dynamic principles to chemical phenomena Gibbs, and after him Helmholtz, thought decrease of free energy at uniform temperature to be the most important condition for equilibrium, since it measures the actual work done and is thus the "force function" of mechanics with reversed sign. The electromotive force of a reversible galvanic cell turns out to be identical with the free energy of chemical decomposition in the cell, and in the field of biology free energy is of equal importance, for relative uniformity of temperature is as common in living processes as in the laboratory. Well did Boltzmann say that "the struggle for existence of living matter is a war for free energy," for when the free energy of a living body becomes a minimum its death is at hand.
The Phase Rule.—Any aspect of a chemical substance which is homogeneous in regard to physical state and percentage composition has been called by Gibbs a phase of the substance, the components of a phase being its constituents of independently variable concentration. The phase rule asserts that a homogeneous substance having n components is capable of only n + 1 independent phases, while a heterogeneous system of r coexistent phases, each of which has n independ-
- Gibbs, loc. cit., 113.
- Ibid., 111-3.
- See Gibbs, Am. J. Sc, 1878, 3. s., XVI., 442. "The transition from the systems considered in ordinary mechanics to thermodynamic systems is most naturally made by this formula. . . the mechanical properties of a thermodynamic system maintained at constant temperature being such as might be imagined to belong to a purely mechanical system, and admitting of representation by a force function."
- Gibbs, Tr. Connect. Acad., III., 520.
- Ibid., 152-6.