# Scientific Papers of Josiah Willard Gibbs, Volume 1

THE
SCIENTIFIC PAPERS
OF
J. WILLARD GIBBS, Ph.D., LL.D.
FORMERLY PROFESSOR OF MATHEMATICAL PHYSICS IN YALE UNIVERSITY
IN TWO VOLUMES
VOL. I
THERMODYNAMICS
WITH PORTRAIT
LONGMANS, GREEN, AND CO.
39 PATERNOSTER ROW, LONDON
NEW YORK AND BOMBAY
1906
All rights reserved
Permission for the present reprint of the different
papers contained in these volumes has in every case
been obtained from the proper authorities.
PREFACE.
With the exception of Professor J. Willard Gibbs's last work, Elementary Principles in Statistical Mechanics, and of his lectures upon Vector Analysis, adapted for use as a text-book by his pupil Dr. E. B. Wilson, and printed like the former as a volume of the Yale Bicentennial Series, none of his contributions to mathematical and physical science were published in separate form, but appeared in the transactions of learned societies and in various scientific journals.
These scattered papers, which constitute the larger and perhaps the more important part of his published work, are here presented in a collected edition, from which, so far as known to the editors, no printed paper has been omitted. A small amount of hitherto unpublished matter has also been included. Permission for the present reprint of the different papers contained in these volumes has in every case been granted by the authorities in charge of the publications in which they originally appeared, a courtesy for which the editors desire here to make due acknowledgment.
In the arrangement of the papers a grouping by subject has been adopted in preference to a strict chronological order. Within the separate groups, however, the chronological order has in general been preserved.
​Shortly before the author's death he had yielded to numerous requests for a republication of his thermodynamic papers, and had arranged for a volume which was to contain the Equilibrium of Heterogeneous Substances and the two earlier papers, Graphical Methods in the Thermodynamics of Fluids, and A Method of Geometrical Representation of the Thermodynamic Properties of Substances by means of Surfaces. To these he proposed to add some supplementary chapters, the preparation of which he had hardly more than commenced when he was overtaken by his last illness. The manuscript of a portion of this additional material (evidently a first draft) was found among the author's papers and has been printed at the end of this first volume. It is believed that it will be of interest and value in spite of its unfinished and somewhat fragmentary condition.
The remaining papers, which compose the second volume, are divided between mathematical and physical science. Most of them naturally fall under one of the following heads: Dynamics, Vector Analysis and Multiple Algebra, the Electromagnetic Theory of Light, and are so grouped in the volume in the order named. A fourth section is made up of the unclassified papers.
In the first section the short abstract of a paper read before the American Association for the advancement of Science is worthy of notice as showing that the fundamental ideas and methods of the treatise on Statistical Mechanics were well developed in the author's mind at least seventeen years before the publication of that work.
The second edition includes the Elements of Vector Analysis, privately printed in 1881–1844 for the use of the author's classes, but never published. It contains in a very condensed form all the essential features of Professor Gibbs's system of Vector Analysis, but without the illustrations on this subject. Copies of this pamphlet have been for many years past practically unobtainable. Here is also placed a hitherto unpublished letter to the editor of Klinkerfues' Theoretische Astronomie, on the use of the author's vector method for the determination of orbits.
Five papers on the Electromagnetic Theory of Light constitute the third section. The fourth and last is composed of miscellaneous papers, including biographical sketches of Clausius and of the author's colleague Hubert A. Newton.
The editors have spared no pains to make the reprint typographically accurate. In a few cases slight corrections had been made by Professor Gibbs in his own copies of the papers. These changes, together with the correction of obvious misprints in the originals, have been incorporated in the present edition without comment. ​Where for the sake of clearness it has seemed desirable to the editors to insert a word or two in a footnote or in the text itself, the addition has been indicated by enclosing it within square brackets, a sign which is otherwise used only in the formulæ.
A sketch of the life and estimate of the work of Professor Gibbs, by one of the editors, is placed at the beginning of the first volume. It is taken, with some additions, from the American Journal of Science, September 1903.
HENRY ANDREWS BUMSTEAD. RALPH GIBBS VAN NAME.
    Yale University,
       New Haven,
          October 1906.
* ↑ "Elementary Principles in Statistical Mechanics developed with especial reference to the Rational Foundation of Thermodynamics." By J. Willard Gibbs. Charles Scribner's Sons, New York. Edwin Arnold, London. 1902.
* ↑ "Vector Analysis, a text-book for the use of the students of Mathematics and Physics, founded upon the Lectures of J. Willard Gibbs." By E. B. Wilson. Charles Scribner's Sons, New York. Edwin Arnold, London. 1901.