JO SI AH WILLABD GIBBS 191 



JOSIAH WILLARD GIBBS AND HIS RELATION TO 

 MODERN SCIENCE. IV 



By FIELDING H. GAKRISON, M.D. 



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. 127 " We have reason to believe of the second law," says Max- 

 well, " 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 cer- 

 tainty." 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 prob- 

 ability 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 intro- 

 duction of new dynamic factors, as seasonal change, epidemics, vaccina- 

 tion, 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 cal- 

 culations, will, if enclosed and left to themselves, gradually tend to an 

 ultimate steady condition of perfectly equalized and permanently dis- 

 tributed velocities (i. e., uniform temperature or thermal equilibrium) 

 called " Maxwell's state." " This possible form of the final partition of 

 127 Mature, 1877-8, XVII., 280. 



