*JOSIAH WILLARD GIBBS*

JOSIAH WILLARD GIBBS AND HIS RELATION TO MODERN SCIENCE. IV |

ASSISTANT LIBRARIAN, ARMY MEDICAL LIBRARY, WASHINGTON, D. C.

The third stage of thermodynamics has for its point of departure Maxwell's observation that the second law is not a mathematical but an empirical or statistical truth, and his prediction that any attempt to deduce it from dynamic principles, such as Hamilton's principle, without introducing some element of probability, is foredoomed to failure.^{[1]} "We have reason to believe of the second law," says Maxwell, "that though true, its truth is not of the same order as that of the first law," being an empirical generalization from the facts of nature in the first instance, while the molecular theory shows it to be "of the nature of a strong probability which, though it falls short of certainty by less than any assignable quantity, is not an absolute certainty." This statement of Maxwell's not only resumes the knowledge of his time, but has not been improved upon by later investigators, whose work shows that the truth of the second law is. certain to the limit of human probability only. The theory of probabilities itself is exact as far as human observation goes. In 6,000 throws of dice, a particular facet will not necessarily turn up 1,000 times, but the probability of its doing so will be more nearly one sixth, the greater the number of throws. In the vital statistics of a great city the data of births, deaths, illegitimacy, etc., will be more nearly the same from week to week, the greater the population of the city; even the introduction of new dynamic factors, as seasonal change, epidemics, vaccination, antitoxin, etc., may alter particular effects but will not change the general tendency towards uniformity. Maxwell has observed that everything irregular, even the motion of a bit of paper falling to the ground, tends, in the long run, to become regular, and this is the rationale of testing the second law with respect to gases. In the kinetic theory of gases, the first scientific statement of which is due to Clausius, we assume a gas to be an assemblage of elastic spheres or molecules, flying in straight lines in all directions, with swift haphazard collisions and repulsions, like so many billiard balls. These, by Maxwell's calculations, will, if enclosed and left to themselves, gradually tend to an ultimate steady condition of perfectly equalized and permanently distributed velocities (*i. e.*, uniform temperature or thermal equilibrium) called "Maxwell's state." "This possible form of the final partition of

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*Nature,*1877–8, XVII., 280.