# Josiah Willard Gibbs : biography

Gibbs returned to Yale in June 1869 and briefly taught French to engineering students. It was probably also around this time that he worked on a new design for a steam-engine governor, his last significant investigation in mechanical engineering.Wheeler 1998, pp. 54–55 In 1871 he was appointed Professor of Mathematical Physics at Yale, the first such professorship in the United States. Gibbs, who had independent means and had yet to publish anything, was assigned to teach graduate students exclusively and was hired without salary.Rukeyser 1988, pp. 181–182 Unsalaried teaching positions were common in German universities, on which the system of graduate scientific instruction at Yale was then being modeled.Wheeler 1998, pp. 57–59

### Middle years

Gibbs published his first work in 1873, at the unusually advanced age of 34. His papers on the geometric representation of thermodynamic quantities appeared in the *Transactions of the Connecticut Academy*. This journal had few readers capable of understanding Gibbs’s work, but he shared reprints with his correspondents in Europe and received an enthusiastic response from James Clerk Maxwell, at the University of Cambridge. Maxwell even made, with his own hands, a clay model illustrating Gibbs’s construct. He then produced three plaster casts of his model and mailed one to Gibbs. That cast is on display at the Yale physics department.

Maxwell included a new chapter on Gibbs’s work in the next edition of his *Theory of Heat*, published in 1875. He explained the usefulness of Gibbs’s graphical methods in a lecture to the Chemical Society of London and even referred to it in the article on "Diagrams" that he wrote for the *Encyclopædia Britannica*.Rukeyser 1988, p. 201 Maxwell’s early death in 1879, at the age of 48, precluded further collaboration between him and Gibbs. The joke later circulated in New Haven that "only one man lived who could understand Gibbs’s papers. That was Maxwell, and now he is dead."Rukeyser 1988, p. 251

Gibbs then extended his thermodynamic analysis to multi-phase chemical systems (i.e., to systems composed of more than one kind of matter) and considered a variety of concrete applications. He described that research in a monograph titled "On the Equilibrium of Heterogeneous Substances", published by the Connecticut Academy in two parts that appeared respectively in 1875 and 1878. That work, which covers about three hundred pages and contains exactly seven hundred numbered mathematical equations,Cropper 2001, p. 109 begins with a quotation from Rudolf Clausius that expresses what would later be called the first and second laws of thermodynamics: "The energy of the world is constant. The entropy of the world tends towards a maximum."Quoted in Rukeyser 1988, p. 233

Gibbs’s monograph rigorously and ingeniously applied his thermodynamic techniques to the interpretation of physico-chemical phenomena, explaining and relating what had previously been a mass of isolated facts and observations.Wheeler 1998, ch. V The work has been described as "the *Principia* of thermodynamics" and as a work of "practically unlimited scope". Wilhelm Ostwald, who translated Gibbs’s monograph into German, referred to Gibbs as the "founder of chemical energetics". According to modern commentators,

Gibbs continued to work without pay until 1880, when the new Johns Hopkins University in Baltimore, Maryland offered him a position paying $3,000 per year. In response, Yale offered him an annual salary of $2,000, which he was content to accept.Wheeler 1998, p. 91

### Later years

From 1880 to 1884, Gibbs worked on developing the exterior algebra of Hermann Grassmann into a vector calculus well-suited to the needs of physicists. With this object in mind, Gibbs distinguished between the dot and cross products of two vectors and introduced the concept of dyadics. Similar work was carried out independently, and at around the same time, by the British mathematical physicist and engineer Oliver Heaviside. Gibbs sought to convince other physicists of the convenience of the vectorial approach over the quaternionic calculus of William Rowan Hamilton, which was then widely used by British scientists. This led him, in the early 1890s, to a controversy with Peter Guthrie Tait and others in the pages of *Nature*.