2 vols. New York: Longmans, Green & Co. $9 net.
CSP, identification: Haskell, Index to The Nation. See also: Burks, Bibliography,
Fisch and Haskell, Additions to Cohen's Bibliography; MS 1507 (draft).
Josiah Willard Gibbs (1839-1903) was one of the greatest mathematicians of his time.
He was a Yale man throughout, having taken his undergraduate degree there and his Ph.D.
there in 1863. He was elected professor of mathematical physics at Yale in 1871. Gibbs
delivered a series of lectures at Johns Hopkins University during the time Peirce was asso-
ciated with that school. Gibbs is credited with the development of a new system of vector
notation, for which work he was elected to membership in the Royal Society of London in
That Josiah Willard Gibbs advanced science the world over more than it has ever been given to any other American researcher to do, can hardly be questioned. He published but one separate book, his "Elementary Principles in Statistical Mechanics" (Charles Scribner's Sons), which appeared in the Yale Bicentennial Series in 1902, the year before his death. Another volume in the same series, written by his pupil, Edwin B. Wilson, was founded on his lectures. His only other printed remains are the papers now collected, which are few but fundamental. They are substantially limited to three, not counting an unusually small number of preliminary and supplementary outputs.
Of the earliest, relating to diagrams and models representing the effects of temperature and pressure on all sorts of substances, Clerk Maxwell once spoke to the present reviewer in terms of warm laudation, before Gibbs had produced anything else, and when he was all but unknown in this country. His second work, on the equilibrium of heterogeneous substances, taught chemists how to reason about the final results of reactions (without reference to the processes by which they were reached), and it stands to-day the stone at the head of the corner of dynamical chemistry. The memoir itself (in which, by the way, was first given the now celebrated "phase rule") occupies three hundred pages of the first of these two volumes, a good many more pages being substantially parts of the same whole.
The second volume is mainly occupied with Gibbs's peculiar calculus called "vector analysis," which was designed to supersede quaternions and Grassmann's Ausdehnungslehre. It is now taught in sundry European universities; but its vogue was prevented or hindered by a trait of its author's character that struck everybody that ever met him, and that we know not how otherwise to designate than as diffidence. Yet this is not a fit name for it. It certainly was not that diffidence which consists in timidity; nor can we assent to his brilliant scholar Prof. Bumstead's apparent view that he was unconscious of his own superiority, which would come too near to making him a gifted idiot, rooting up his mathematical truffles like a Périgord pig, and as oblivious of being deprived of them. We should rather conceive of it as an exaggerated estimate of the possibility of any opinion of his being erroneous that might concern a difficult question not sus-