MATO RE 
THURSDAY, FEBRUARY’ 14, 
1907. 
THE SCIENTIFIC WORK OF WILLARD 
GIBBS. 
The Scientific Papers of J. Willard Gibbs. In two 
volumes. Vol. i., Thermodynamics. Vol. ii., 
Dynamies, Vector Analysis, Light, &c. WACK Sor, 
pp. Xxvilit+ 434, price 24s. net; vol. ii., pp. vili+ 254, 
price 18s. net. (London: Longmans, Green and 
Co., 1906.) 
HESE two handsome volumes are a_ fitting 
memorial to one who carved out for himself 
a very remarkable niche in the temple of scientific 
fame. With the exception of his one published book 
on statistical dynamics, we have in these collected 
papers practically all that Willard Gibbs put into 
form suitable for publication. Compared with the 
literary output of the leaders of science of the passing 
generation, this is a very limited contribution if 
judged only in regard to quantity. But the quality 
and far-reaching importance of Willard Gibbs’s work 
_ place it on an eminence of excellence comparatively 
rarely reached. This remark specially applies to his 
great papers on the equilibrium of heterogencous 
substances, which with his other papers on thermo- 
dynamics constitute the first volume of 434 pages. 
All are agreed as to the supreme importance of the 
thermodynamic memoirs, which give to their author 
a unique place among those who have done most to 
establish and develop the principles of this funda- 
mental part of the doctrine of energy. It is not 
quite the same with the papers which form the second 
volume, of 284 pages, although in these also the 
author’s characteristic qualities of mind show them- 
selves. There is always an originality of view and a 
logical severity of treatment which indicate that the 
author has well digested his material before putting 
it in printed form before the eye of the public. 
Nevertheless, even if we do not consider the contents 
of vol. ii. as attaining the same high average of 
excellence as the contents of vol. i., their comparative 
brevity makes good the claim that in Willard Gibbs 
we had a writer and thinker of very exceptional 
merit. 
Unlike most young scientific men, Willard Gibbs 
was in no hurry to publish, his earliest papers dating 
from 1873, when he was thirty-four years of age. 
The second of these papers, that on thermodynamic 
surfaces, became speedily known to the scientific 
world through the pages of Maxwell’s ‘“‘ Theory 
of Heat ’’; and Maxwell was himself the first to con- 
struct a model of the volume-entropy-energy surface. 
Copies of this model were distributed by Maxwell 
evidently with a certain amount of playful mystery, 
for each recipient thought that he was the happy 
possessor of one of (at most) three. The writer 
kknows of six at least, and possibly there are more. 
We also owe to Maxwell a very clear, brief state- 
ment of the essential feature of the great papers on 
the equilibrium of heterogeneous substances. In spite 
of this, however, the immense value of these memoirs 
NO. 1946, VOL. 75 | 
361 
came to be fully recognised only very gradually, in 
many instances after important had 
obtained independently by later investigators. In 
1892 Ostwald brought out a German translation which 
was reviewed at the time in these columns (vol. 
xlvi., p. 245). A French translation followed in 1899, 
and now at length have these epoch-making 
papers reproduced so as to be accessible to everyone. 
In their new dress they cover about a third more 
pages than in their original form in the Transactions 
of the Connecticut Academy of Arts and Science, and 
the larger type and broader page impart a dignity 
worthy of their high position in the literature of 
thermodynamics. 
The first with some unpublished 
fragments which were intended to form a _ supple- 
ment to the ‘ Equilibrium of Heterogeneous Sub- 
” Only two of a list of nine subjects are 
touched upon, and one cannot but have a feeling of 
deep regret that the distinguished author was unable 
to carry out his project. 
The volume twenty-one distinct 
papers and articles arranged under four headings. 
In a paper on the fundamental formule of 
dynamics, Gibbs suggests using 6x, dy, 42 instead 
of the usual 6x, dy, 6z, and shows that for certain 
problems the modification is of advantage. The 
second paper is a single-page abstract from the Pro- 
ceedings of the American Association for the Advance- 
ment of Science on the fundamental formula of 
statistical mechanics, and is of interest as showing 
the trend of his thinking sixteen years before the 
publication of his great work on the subject. Eight 
papers then follow on vector analysis and multiple 
algebra. The first of these is the reprint of the 
famous ‘‘ not published ’’ pamphlet which was printed 
for private circulation in 1881-4, and it is in reply 
to certain criticisms of this pamphlet that some of 
the succeeding papers were written, chiefly as letters 
to Nature. Willard Gibbs received his first impulse 
towards the study of vector methods from Maxwell, 
who used the quaternion notation in his ‘‘ Electricity 
and Magnetism.’’ Not caring for the quaternion 
approach, for reasons which are explained fully in 
his controversial articles, he elaborated a notation of 
his own for the frequently recurring functions familiar 
to students of Hamilton and Tait. What gives 
Gibbs’s method its character is, however, his 
“dyadic”? notation for the linear vector function. 
Unlike Hamilton’s ¢, which has, so to speak, only 
one hand to grip the operand which follows, Gibbs’s 
dyadic has two hands, with one of which it may grip 
forward and with the other backward, as occasion 
may offer. It cannot, however, grip with both at 
once, so that the double-handedness is only apparent. 
Moreover, it is only in its expanded form that the 
dyadic is able thus to cleelk on to an operand on 
either side. When, as is frequently the case, the 
Hamiltonian function ¢ is used, the method becomes 
identical with that of quaternions. 
A very readable paper is that on multiple algebra, 
which Gibbs originally delivered as his presidential 
address before the mathematical section of the 
R 
results been 
we 
volume closes 
stances. 
second contains 
