being functions of the temperature and the chemical potentials. The only stable substance which can be formed between two other phases will be the one having the least surface tension. The chemical equilibrium of solids in contact with liquids, including the delicate mathematical conditions for the formation of crystals in mother liquor, is treated dynamically as a matter of stresses and strains, and this together with the theory of interfacial formations and liquid films will embrace the possible physics of colloid substances. Gibbs gives for the first time a mathematical discussion of the mode of formation of liquid films and the conditions for their stability and his dynamic explanation of the black spots on soap films was proved quantitatively in 1887 by Reinold and Rücker's micrometric data of the relations between the thickness and surface tension of these films. The importance of liquid films in biology is obvious, and this phase of Gibbs's theory, which is capable of the widest development, has as yet received the slightest attention.
Electrochemical Thermodynamics.—One of the most important features of energetics is Gibbs's theory of the galvanic cell which shows the close interrelation existing between chemical, thermal and electric energy. The earliest pioneer in this field was Lord Kelvin, and, prior to 1878, physicists had accepted the Joule-Kelvin theory that the electromotive force of a galvanic apparatus is the mechanical equivalent of the total chemical energy liberated per unit strength in unit time. But this view, which implies that all the electric energy of a chemical cell is available, did not agree entirely with the experimental data of Boscha, Raoult and others. It was corrected and modified by Gibbs, who showed that the electromotive force of the cell is in reality its free energy per electrochemical equivalent of decomposition, from which it follows that neither solidification nor fusion of the metals at the temperature of liquefaction should cause any abrupt alteration of the electromotive force. In 1882, six years later, this important theorem was rediscovered from a different view-point by Helmholtz and brilliantly developed as to experimental confirmation. The Gibbs Helmholtz doctrine enables the physicist to trace out the variations in electromotive force due to chemical differences in different cells. In a letter to Professor Bancroft, now printed in the memorial edition, Gibbs connects the mathematical part of his theory of the electric cell with the fundamental principles of physical chemistry, the theories of van't Hoff and Arrhenius, Nernst's osmotic theory of the Voltaic cell
- Ibid., 403.
- Ibid., 479-81.
- Phil Tr., 1887, CLXXVII., 627, 684.
- "The quantities of the different substances combined in connection with the passage of a unit electricity are called the electrochemical equivalents of these substances." Bryan, "Thermodynamics," 164.
- Helmholtz, Sitzungsb. d. Berl Akad., 1882, 22 et seq.