Josiah IFillard Gibbs. 293 



but lictle distinctively electrical that is left except the frame; there 

 remains a very general scheme of formal analytical relations, not unlike 

 Hertz's later manner of conceiving the Maxwellian electrical equations, 

 which has to become more restricted and particularised for practical 

 use. In a subsequent paper he contrasted Lord Kelvin's remarkable 

 labile mechanical aether, then recently announced, with electric theory 

 in the same general manner, again laying stress on the formal optical 

 fitness of the system of equations which are the expression of the latter. 

 In all this work we recognise the same penetration and skill, in the 

 formulation and expression of the utmost generality of outlook, which 

 he showed in pure mathematics by his partiality for the study of 

 generalized algebras and vectorial analysis, and which in thermo- 

 dynamics has largely constituted the strength of his work, though at 

 the same time it has retarded its absorption into the general body of 

 scientific doctrine. 



After a period in which Prof. Gibbs' work was much interrupted by 

 ill health, he again appeared before the scientific world early in 1902 

 as the author of a notable treatise of 207 pages octavo, entitled 

 ''Elementary Principles in Statistical Mechanics, developed with 

 especial reference to the Rational Foundation of Thermodynamics," 

 which was published in connexion with the Bi-centenary of the Univer- 

 sity of Yale. Having had a principal share in evolving the ultimate 

 form of the principles that govern physical and chemical equilibrium, 

 when matter in bulk is considered in terms of its observable properties 

 alone, and having taken care to state them free of all vestige 

 of molecular theory, it was natural that his thoughts should 

 have turned to the less definite problems opened out by the 

 molecular hypothesis of the constitution of matter, which provides a 

 rational base for the axioms on which Carnot, Clausius, and Thomson 

 originally built. While, however, Maxwell and Boltzmann, the creators 

 of the subject here called statistical dynamics, had treated of 

 molecules of matter directly, it is characteristic of Prof. Gibbs that his 

 exposition relates primarily to the statistics of a definite vast aggrega- 

 tion of ideal similar mechanical systems of types completely defined 

 beforehand, and then compares the precise results reached in this ideal 

 discussion with the principles of thermodynamics, already ascertained in 

 the semi-empirical manner. This reversal of order can only profitably 

 be made, as he remarks, after the pioneers of statistical molecular 

 theory have cleared the ground and defined the scope of the relations 

 that are to be explored ; but, nevertheless, he holds that the interests 

 of precision invite such a paraphrase of their results. " Moreover, we 

 avoid the gravest difficulties when, giving up the attempt to frame 



