Editing Josiah Willard Gibbs (section)

=== Career, 1873–1880 ===
[[File:Maxwell's letters plate IV.jpg|thumb|upright|alt=Maxwell's handmade sketch of the thermodynamic surface for water|right|Maxwell's sketch of the lines of constant temperature and pressure, made in preparation for his construction of a solid model based on Gibbs's definition of a thermodynamic surface for water (see [[Maxwell's thermodynamic surface]])]]

Gibbs published his first work in 1873.<ref name="MacTutor" /> His papers on the geometric representation of thermodynamic quantities appeared in the ''Transactions of the Connecticut Academy''. These papers introduced the use of different type phase diagrams, which were his favorite aids to the imagination process when doing research, rather than the mechanical models, such as the ones that [[James Clerk Maxwell|Maxwell]] used in constructing his electromagnetic theory, which might not completely represent their corresponding phenomena.<ref>{{cite web | url =http://www.ub.uni-heidelberg.de/helios/fachinfo/www/math/htmg/gibbs-bumstead.htm | title =Josiah Willard Gibbs [Reprinted with some additions from the American Journal of Science, ser. 4, vol. xvi., September, 1903.] | last =Bumstead | first =Henry A. | publisher =Universitätsbibliothek Heidelberg | access-date =September 30, 2015 | archive-url =https://web.archive.org/web/20140427182622/http://www.ub.uni-heidelberg.de/helios/fachinfo/www/math/htmg/gibbs-bumstead.htm | archive-date =April 27, 2014 | url-status =dead }}</ref> Although the journal had few readers capable of understanding Gibbs's work, he shared reprints with correspondents in Europe and received an enthusiastic response from [[James Clerk Maxwell]] at [[University of Cambridge|Cambridge]]. Maxwell even made, with his own hands, a [[Maxwell's thermodynamic surface|clay model illustrating Gibbs's construct]]. He then produced two plaster casts of his model and mailed one to Gibbs. That cast is on display at the Yale physics department.<ref>{{cite journal |doi=10.1103/physrevseriesi.10.228 |title=Gibbs' Thermodynamical Model |journal=Physical Review |series=Series I |volume=10 |issue=4 |pages=228–233 |year=1900 |last1=Boynton |first1=W. P. |bibcode=1900PhRvI..10..228B |url=https://zenodo.org/record/1996925 }}</ref><ref>{{cite web |url=http://esm.rkriz.net//classes/ESM4714/methods/Gibbs.html |title=Thermodynamic Case Study: Gibbs' Thermodynamic Graphical Method |last = Kriz | first = Ronald D. |year=2007 |publisher=Virginia Tech, Dept. of Engineering Science and Mechanics|archive-url=https://web.archive.org/web/20140201163858/http://www.sv.vt.edu/classes/ESM4714/methods/Gibbs.html|archive-date=February 1, 2014|url-status=live | access-date = September 30, 2015}}</ref>

Maxwell included a 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]]''.<ref>Rukeyser 1988, p. 201.</ref><ref>{{Cite EB1911|wstitle= Diagram |volume= 8 |last= Maxwell |first= James Clerk |author-link= James Clerk Maxwell | pages = 146–149 }}</ref> Prospects of collaboration between him and Gibbs were cut short by Maxwell's early death in 1879, aged 48. 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."<ref>Rukeyser 1988, p. 251.</ref>

Gibbs then extended his thermodynamic analysis to multi-phase chemical systems (i.e., to systems composed of more than one form 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,<ref name="Cropper-monograph">Cropper 2001, p. 109.</ref> 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."<ref>Quoted in Rukeyser 1988, p. 233.</ref>

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.<ref name="Wheeler-thermodynamics">Wheeler 1998, ch. V.</ref> The work has been described as "the ''[[Philosophiæ Naturalis Principia Mathematica|Principia]]'' of thermodynamics" and as a work of "practically unlimited scope".<ref name="Cropper-monograph" /> It solidly laid the foundation for physical Chemistry.<ref name="Jordan1910">{{cite book |author=David Starr Jordan |title=Leading American Men of Science |year=1910 |publisher=H. Holt |url=https://archive.org/details/leadingamerican00jordgoog |pages=[https://archive.org/details/leadingamerican00jordgoog/page/n389 350] |quote=for it laid the foundation of the new science of physical science}}</ref> [[Wilhelm Ostwald]], who translated Gibbs's monograph into German, referred to Gibbs as the "founder of chemical energetics".<ref name="Britannica-1911">{{Cite EB1911|wstitle=Gibbs, Josiah Willard}}</ref> According to modern commentators,
{{blockquote|
It is universally recognised that its publication was an event of the first importance in the history of chemistry&nbsp;... Nevertheless it was a number of years before its value was generally known, this delay was due largely to the fact that its mathematical form and rigorous deductive processes make it difficult reading for anyone, and especially so for students of experimental chemistry whom it most concerns.
|J. J. O'Connor and E. F. Robertson, 1997<ref name="MacTutor" />}}

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.<ref>Wheeler 1998, p. 91.</ref>

In 1879, Gibbs derived the [[Appell's equation of motion|Gibbs–Appell equation of motion]],<ref name="gibbs1879">{{cite journal |last=Gibbs |first=J. W. |year=1879 |title=On the Fundamental Formulae of Dynamics |journal=American Journal of Mathematics |volume=2 |issue=1 |pages=49–64 |doi=10.2307/2369196 |jstor=2369196}}</ref> rediscovered in 1900 by [[Paul Émile Appell]].<ref name="appell_1900a">{{cite journal |last=Appell |first=P |year=1900 |title=Sur une forme générale des équations de la dynamique |lang=fr |journal=Journal für die reine und angewandte Mathematik |volume=121 |pages=310}}</ref>