J. W. Gibbs
(1839–1903)

Advances in the Physical Sciences

JOSHUA WILLARD GIBBS¹)

(On the centenary of his birth)

On February 11, 1839, in New Haven, in the state of Connecticut, Joshua Willard Gibbs was born—the great thermodynamicist and founder of statistical mechanics as a distinct science.

He was the son of a professor of the same university at which he himself later taught and to which he devoted his entire life. Professor Joshua Willard Gibbs the elder was a major authority in the field of comparative philology and instilled in his son a love of the sciences and, in particular, of linguistics. It is known that in the first period of his teaching activity the young Gibbs taught at New Haven College both Latin and physics.

Gibbs’s ancestors moved from England to Boston around 1685. From that time they lived in the province of Massachusetts and then settled permanently in New Haven. For more than six generations in succession, among Gibbs’s ancestors there were professors of New Haven College. The Gibbs family was a family of scholars. Gibbs, an only son, brought up together with his three sisters, was distinguished from early years by extremely poor health.

In 1854 Gibbs entered Yale College, graduated from it in 1858, and for five years continued his studies in New Haven. During his studies at the college he was repeatedly awarded prizes for success in Latin and in mathematics. In 1863 he received the degree of Doctor of Philosophy, remained to teach at the same college, and then in 1866 set out, for further improvement in the sciences, on his only trip to Europe. He was, together with his sisters, in Paris; then he studied in Berlin, under Magnus and other professors of physics and mathematics. Especially noteworthy was his stay in Heidelberg, where he attended the lectures of Kirchhoff and Helmholtz. In 1869 he returned to New Haven, where he then lived without leaving for 34 years, until his death in 1903. Of these years, for 32 years, from 1871, Gibbs held the position of professor of mathematical physics at New Haven University.

Gibbs died in 1903 after a brief illness. Gibbs

¹) Based on a report by P. A. Rebinder, read at the ceremonial meeting of the Zelinskii Institute of Physics and Chemistry of the Academy of Sciences, dedicated to the 100th anniversary of Gibbs’s birth.

was always in poor health, but an extremely regular and healthy way of life enabled him not to interrupt his scientific pursuits. Gibbs was never married. His household was managed by his sisters, with whose families he lived all his life in the house built by his father. This house was located not far from the college, which he attended first as a student and later as a professor.

Gibbs was distinguished by an unusual modesty in the appraisal of his own work. Everyone who knew him spoke of him with deep respect, both as a scholar and as a man exceptionally attentive to those around him. He always responded with great sensitivity to all requests from his colleagues and, without regard for his time, received them both at the university and at home.

Gibbs was characterized by reserve and a certain unsociability. It is known that almost the only speech he made in the University Council during the 32 years of his professorial activity amounted to the following. When a heated dispute arose in the council over which was more important at the first stage of education, the native language or mathematics, Gibbs, on the occasion of this serious question, which was subjected to comprehensive discussion and gave rise to animated disputes between representatives of the humanities and representatives of the natural-mathematical disciplines, rose and said only: “Mathematics is a language.”

Gibbs’s scientific work began in 1873, when in the little-known journal Transaction of the Connecticut Academy he published his first memoir, devoted to graphical methods in thermodynamics. This memoir was followed in the same year, 1873, by a second memoir devoted to thermodynamic surfaces in connection with the general equation of state, and then by a remarkable third memoir, consisting of two parts. Its first part, which forms the foundation of chemical thermodynamics, appeared in 1876, and the second part in 1878. In the second part, the chief attention was devoted to the thermodynamics of surface phenomena, as well as to certain special questions.

These thermodynamic works of Gibbs long remained unknown, and only a few specialists—particular devotees of this field of knowledge—became acquainted with them in the original, especially rarely in Europe, where the journal was little known.

It is very important that these memoirs were issued as two separate monographs in translation into two other European languages—German and French—by two celebrated scientists: Wilhelm Ostwald in 1892 (he translated Gibbs’s second memoir) and Henri Le Chatelier in 1899 (he translated the first part of the second memoir on chemical thermodynamics). Both scholars noted in their prefaces that their translation was prompted by the desire to acquaint researchers with a theoretical apparatus distinguished by extraordinary power and a wide range of applications. These translations played a major role, and from the end of the last century Gibbs’s thermodynamic works began to receive wide application and general recognition among physicists and especially physical chemists.

The difficulties among physicists and chemists in mastering Gibbs’s works became proverbial; they were also the reason for the limited dissemination of Gibbs’s works (together with the fact that these works were published in a journal that was hard to obtain).

Many, however, mistakenly suppose that Gibbs’s works are entirely abstract and detached. Their abstractness is purely external. Internally these works are extremely closely connected with living science, and one may say with confidence that the abstract form of Gibbs’s writings stands in a certain, perhaps even complete, separation from the topicality of their content.

Gibbs’s works were printed at long intervals, but these were not interruptions in his scientific work. He worked continuously and very much, and the intervals in publication are explained only by the fact that all his works were allowed to mature, were carefully polished, and only when brought to perfect form were they published. Gibbs did not recognize any preliminary communications for the purpose of securing priority.

Owing to the fact that Gibbs’s works were at first little known, very many of his fundamental propositions were discovered a second time by other investigators. Gibbs’s priority in all these cases, however, proved absolutely indisputable. Among those who rediscovered propositions stated by Gibbs, we may point, for example, to such a great scholar as Helmholtz.

It should be noted that Gibbs’s first memoir, the simplest in exposition, at the same time received the fastest and broadest application among heat engineers and rendered great service to the theory of steam engines. In this first memoir the entropy diagram, well known to all, was presented in detail. This diagram later became the basis of modern scientific heat engineering.

Engaged in critical studies in the field of vector algebra and analysis, Gibbs, not long before his death, in 1901, published a separate course of vector analysis.

At the end of his life Gibbs returned to his initial works. Without using molecular models, he gave formal thermodynamics a rigorous molecular statistical foundation. He created statistical mechanics as a science, the foundations of which had been laid in the kinetic theory of gases in the works of Gibbs’s predecessors in this field—Maxwell and Boltzmann (this work of his is set forth in the book Elementary Principles in Statistical Mechanics, published in 1903). In this connection it should be noted that the first scientist who particularly emphasized the significance of Gibbs’s work was Maxwell. Not long before his death he sent Gibbs a model of the thermodynamic surface of water, made by him with his own hands according to Gibbs’s theoretical instructions.

Gibbs published only 28 scientific works in all. Among these works, in addition to those mentioned, there are also works on theoretical optics and on astronomy. The latter consist in the application of vector analysis to astronomical calculations. Gibbs also has works in

in the field of concrete applications of thermodynamics to chemistry, on the theory of the dissociation of gases. Here Gibbs shows himself to be a scholar with an excellent command of all the chemical literature of his day. And in this he also stands out among the mathematicians and physicists of his time, who, as is known, often treated experimental chemistry with neglect.

In 1881 the American Academy of Sciences awarded Gibbs the Rumford Medal, and in 1900 the Royal Society of London awarded him the Copley Medal. Gibbs was a corresponding member of 16 academies of sciences and scientific societies: the American academies, the Royal Society in London, and the academies in Amsterdam, Berlin, Munich, and Paris.

Among us in the Soviet Union, the development of science since the October Revolution clearly shows that we must make every possible use of the legacy of the great Gibbs, as the scientists of the Soviet Union are successfully doing.

It is necessary to use Gibbs’s works for the fullest development of Soviet science in close connection with life and in accordance with Comrade Stalin’s great slogan, with his simple and remarkable words that we need a science that serves the people.

We are convinced that Gibbs’s great theoretical works also provide the foundations for the development of such a science.

BIBLIOGRAPHY OF GIBBS’S WORKS

1. Graphical methods in the thermodynamics of fluids, Trans. Conn. Acad., vol. ii, pp. 309—342.

A method of geometrical representation of the thermodynamic properties of substances by means of surfaces, Ibid., pp. 382—404.

1875—1878. On the equilibrium of heterogeneous substances, Ibid., vol. iii, pp. 108—248; pp. 343—524. Extracts Amer. Jour. Sci. (3), vol. xvi, pp. 441—458.

B. Ostwald translated the three preceding works into German under the title “Thermodynamische Studien,” Leipzig, 1892; the first two works were translated into French by Roy under the title “Diagrammes et surfaces thermodynamiques,” Paris, 1903, and the first part of “Equilibrium of Heterogeneous Substances” by Le Chatelier under the title “Equilibre des Systèmes Chimiques,” Paris, 1899).

1. On the fundamental formulae of dynamics, Amer. Jour. Math., vol. ii pp. 49—64.

On the vapor-densities of peroxide of nitrogen, formic acid, acetic acid, and perchloride of phosphorus, Amer. Jour. Sci. (3) vol. xviii, pp. 277—293; pp. 371—387.

1881 and 1884. Elements of vector analysis arranged for the use of students in physics, New Haven, 8°, pp. 1—36 in 1881 and pp. 37—83 in 1884 (not published).

1882—1883. Notes on the electromagnetic theory of light. I. On double refraction and the dispersion of colors in perfectly transparent media. Amer. Jour. Sci. (3), vol. xxiii, pp. 262—275. II. On double refraction in perfectly transparent media which exhibit the phenomena of circular polarization, Ibid., pp. 460—476. III. On the general equations of monochromatic light in media of every degree of transparency. Ibid.; vol. xxv, pp. 107—118.

1. On an alleged exception to the second law of thermodynamics, Science, vol. I, p. 160.

2. On the fundamental formula of statistical mechanics, with applications to astronomy and thermodynamics (extracts), Proc. Amer. Assoc. Adv. Sci., vol. XXXIII, pp. 57, 58.

3. Notices of Newcomb and Michelson’s “Velocity of light in air and refracting media” and of Ketteler’s “Theoretische Optik,” Amer. Jour. Sci. (3), vol. XXXI, pp. 62–67.

On the velocity of light as determined by Foucault’s revolving mirror, Nature, vol. XXXIII, p. 582.

On multiple algebra (Vice-president’s address before the section of mathematics and astronomy of the American Association for the Advancement of Science), Proc. Amer. Assoc. Adv. Sci., vol. XXXV, pp. 37–66.

1887 and 1889. Electro-chemical thermodynamics (Two letters to the secretary of the electrolysis committee of the British Association), Rep. Brit. Assoc. Adv. Sci. 1886, pp. 388–389; 1888, pp. 343–346.

1. A comparison of the elastic and electrical theories of light, with respect to the law of double refraction and the dispersion of colors, Amer. Jour. Sci. (3), vol. XXV, pp. 467–475.

2. A comparison of the electric theory of light and Sir William Thomson’s theory of a quasi-labile ether, Amer. Jour. Sci., vol. XXXVII, pp. 129–144.

Reprint. Phil. Mag. (5), vol. XXVII, pp. 238–253.

On the determination of elliptic orbits from three complete observations, Mem. Nat. Acad. Sci., vol. IV, pt. 2, pp. 79–104.

Rudolf Julius Emanuel Clausius, Proc. Amer. Acad., new series, vol. XVI, pp. 458–465.

1. On the rôle of quaternions in the algebra of vectors, Nature, vol. XLIII, pp. 511–513.

Quaternions and the Ausdehnungslehre, Nature, vol. XLIV, pp. 79–82.

1. Quaternions and the algebra of vectors, Nature, vol. XLVII, pp. 463, 464.

2. Quaternions and vector analysis, Nature, vol. XLVII, pp. 364–367.

3. Velocity of propagation of electrostatic force, Nature, vol. LIII, p. 509.

4. Semi-permeable films and osmotic pressure, Nature, vol. LV, pp. 461, 462.

Hubert Anson Newton, Amer. Jour. Sci. (4), vol. III, pp. 359–376.

1898–1899. Fourier’s series, Nature, vol. LIX, pp. 200, 606.

1. Vector analysis, a text book for the use of students of mathematics and physics, founded upon the lecture of J. Willard Gibbs, by E. B. Wilson. Pp. XVII 436. Yale Bicentennial Publications. C. Scribner’s Sons.

2. Elementary principles in statistical mechanics developed with especial reference to the rational foundation of thermodynamics. Pp. XVIII 207. Yale Bicentennial Publications. C. Scribner’s Sons.

3. Unpublished excerpts from the additions to “Equilibrium of Heterogeneous Substances,” Scientific Papers, vol. I, pp. 418–434.

On the use of the vector method in the determination of orbits.

Letter to Dr. Hugo Buchholz, editor of Klinkerfues’ Theoretische Astronomie, Scientific Papers, vol. II, pp. 149–154.