belief, a literary or humane analogy, a leaning in the direction of the "fair humanities of old religion," but not a scientific fact. To fix our ideas for the material world we may accept the expanded statement of the second law which Ostwald gave in his Ingersoll lecture in 1906: i(Every known physical fact leads to the conclusion that diffusion or a homogeneous distribution of energy is the general aim of all happenings. . . . A partial concentration may be brought in a system, but only at the expense of greater dissipation, and the sum total is always an increase in dissipation." Through the labors of Joule and Kelvin, Maxwell and Boltzmann, Gibbs and Helmholtz, Carnot's simple generalization about heat engines has been elevated to the dignity of an irrevocable law of nature, a principle of scientific determinism, giving one of the most complete and satisfactory answers that man can furnish to the great question: How does any event in the material universe come to pass? In Darwin's picture of nature the quiet woods and waters, so calm and peaceful on the surface, are in reality centers of "strange and cruel life," the struggle and turmoil of creatures continually preying upon each other, even trees and plants and the tiniest particles of animate bodies taking part in a definite, never-ending war for existence. But the stern law of life, whereby the strong war down the weak, loses all moral, or human significance when seen as due, in the last analysis, to an inevitable tendency to dissipation of energy or as the resultant of a play of complex forces, which, through some principle of "least action," must inexorably flow from higher to lower potentials. As Spinoza pointed out long ago, Nature could 'not change these laws which flow from its very being, without ceasing to be itself, and the conclusion of physics and biology that Nature is never on the side of the weak becomes, as far as man is related to the material universe, identical with Spinoza's denial of final causes.
Apart from his work in mathematical physics, Gibbs made several important contributions to pure mathematics, notably in his theory of "dyadics," a variety of the multiple or matricular algebras which Benjamin Peirce classified as "linear associative." The tendency of his mind was always toward broad, general views and the simplifications that go with such an outlook, and here mention should be made of his charming address on multiple algebra and his innovation of vector analysis, a calculus designed to give the student of physics a clearer
- W. Ostwald, "Individuality and Immortality," Boston, 1906, 42.
- As a fundamental formula for all material happenings, analogous to the "world-formula" of Laplace, J G. Vogt proposes the following (Polit. Anthrop. Rev., Leipzig, 1907-8, VI., 573): If Pe represent the positive or dissipation potential (emissives Potential) and Pr the negative or concentrational potential (rezeptives Potential) of any given set of forces, then or . This is, however, only another restatement of Newton's Third Law of Motion, that action and reaction are equal and in opposite directions.