Josiah Willard Gibbs (1839-1903) was an American mathematical physicist whose pioneer work in statistical mechanics laid the basis for the development of physical chemistry as a science.

# Josiah Willard Gibbs

When Josiah Willard Gibbs began his work, thermodynamics had become a true science, firmly based on recently formulated laws of the conservation of energy. These included the law that equated heat and energy and the law of the dissipation or degradation of energy (first and second laws of thermodynamics), which had been worked out mathematically.

Gibbs began with the known thermodynamic theory of homogeneous substances and worked out the theory of the thermodynamic properties of heterogeneous substances. It was this work which, some years later, provided the basic theory for the new branch of science known as physical chemistry. Gibbs's great contribution, "On the Equilibrium of Heterogeneous Substances," was published in the *Transactions of the Connecticut Academy of Arts and Sciences* in 1876 and 1878. Before the end of the 19th century it had been translated into French and German, and Gibbs was widely recognized as one of the greatest mathematical physicists since Isaac Newton. He was one of the few American physicists of that century to achieve an international reputation and the only one to make a theoretical contribution of fundamental importance.

## Early Life and Education

Josiah Willard Gibbs was born Feb. 11, 1839, in New Haven, Conn., of a distinguished and learned family. His father was professor of sacred literature in the Yale Divinity School for many years and a well-known linguist. Gibbs graduated from Yale College in 1858 with prizes in mathematics and Latin. He continued his studies at Yale, earning his doctorate of philosophy in 1863. Afterward he was appointed tutor in the college, where he taught Latin for 2 years and natural philosophy for a third year. From 1866 to 1869 he studied in Paris, Berlin, and Heidelberg, where his teachers were some of the world's most distinguished mathematicians and physicists. This period in Europe constituted his only residence outside of New Haven, for in 1871 he was appointed professor of mathematical physics in Yale College—the first such chair in an American college—and he served in that capacity for the rest of his life.

## Work in Thermodynamics

From the beginning of his professorship, Gibbs devoted himself to the development and presentation of his theory of thermodynamics. His first two scientific papers made an exhaustive study of geometrical methods of representing by diagram the thermodynamic properties of homogeneous substances. These early papers brought Gibbs to the attention of England's leading physicist, James Clerk Maxwell. Maxwell constructed a model illustrating a portion of the work and sent a plaster cast to Gibbs. After investigating homogeneous substances, Gibbs went on to his great work, "On the Equilibrium of Heterogeneous Substances." It was this thesis that contained the "phase rule," which has been of such great practical value in industrial chemistry.

## Later Work

Gibbs's subsequent work in thermodynamics was valuable but not on the same order as the earlier papers. During the 1880s his interests began to turn in other directions. He modified his earlier work on quaternions and geometric algebra into a system of vector analysis especially suited to the needs of mathematical physicists, and he developed his own theory of optics based on electricity rather than electromagnetism. His theory was built chiefly upon the hypothesis that light is a periodic disturbance propagated through media whose structures are more fine-grained than the wavelength of light. The theory was published in the *American Journal of Science between 1883 and 1889.* As in his paper on thermodynamics, Gibbs relied to an unusual degree upon mathematical logic and avoided all special hypotheses concerning the constitution of matter.

During the 1890s Gibbs published nothing at all. His last and perhaps his greatest contribution, *The Elementary Principles of Statistical Mechanics,* was published in 1902. The book, termed by one authority "a monument in the history of physics which marks the separation between the nineteenth and twentieth centuries," laid the foundation for a new branch of theoretical physics that ultimately developed into quantum mechanics.

Although Gibbs received many honors during his lifetime, including the Royal Society's Copley Medal and the Rumford Medal of the American Academy of Arts and Sciences, his immediate influence was limited to a small circle of advanced physicists. The esoteric nature of his work made him practically unintelligible to students. Shy and retiring by nature, he made no effort to attract followers or to communicate to a wider audience. The first impact of his work, both theoretical and applied, was in Europe, for America had neither physicists nor a chemical industry capable of taking advantage of the many insights his work provided.

Gibbs never married. He died on April 28, 1903, in New Haven.

## Further Reading on Josiah Willard Gibbs

There are two book-length biographies of Gibbs: Muriel Rukeyser, *Willard Gibbs* (1942), studies Gibbs as a creative thinker from a poet's point of view, and Lynde P. Wheeler, *Josiah Willard Gibbs: The History of a Great Mind* (1951), deals best with the technical side of Gibbs's work. Solid studies of Gibbs are in James Gerald Crowther, *Famous American Men of Science* (1937); Bernard Jaffe, *Men of Science in America* (1954; rev. ed. 1958); and Mitchell Wilson, *American Science and Invention* (1954).