2oo THE POPULAR SCIENCE MONTHLY 



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 : 151 

 " Every known physical fact leads to the conclusion that diffusion or 

 a homogeneous distribution of energy is the general aim of all happen- 

 ings. ... 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." 152 Through the labors of Joule and Kel- 

 vin, 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 con- 

 tinually 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 prin- 

 ciple 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 uni- 

 verse, 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 

 te dyadics," a variety of the multiple or matricular algebras which Ben- 

 jamin 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 



151 W. Ostwald, " Individuality and Immortality," Boston, 1906, 42. 



152 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 dissipational 

 potential (emissives Potential) and Pr the negative or coneentrational potential 

 {rezeptives Potential) of any given set of forces, then Pe -\- Pr = or 



f d Pe + i' dPr— 0. This is, however, only another restatement of 

 Newton's Third Law of Motion, that action and reaction are equal and in 

 opposite directions. 



