Hill, George William

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Hill, George William

(b. New York, N.Y., 3 March 1838; d. West Nyack, New York, 16 April 1914)

mathematical astronomy.

In the opinion of Simon Newcomb, Hill was destined to rank “as the greatest master of mathematical astronomy during the last quarter of the nineteenth century.” In 1903 Hill was ranked second after E. H. Moore by the leading mathematicians in the United States and first, tied with Newcomb, by the leading astronomers. He was honored in his lifetime by the bestowal of advanced degrees and medals and by honorary memberships in the most prestigious professional scientific societies and institutions throughout the world. Yet throughout all of this recognition he remained a simple man of the country.

Hill’s father, John William Hill, was born in England while his mother, Catherine Smith, was descended from an old Huguenot family. His grandfather had been a successful engraver in London before emigrating to Philadelphia in 1816. Both Hill’s father and younger brother were painters, and in 1846 his father retired to a farm in Nyack Turnpike (now West Nyack), New York. Country residence during Hill’s youth was likely to carry with it grave drawbacks in the education of the young; teaching was frequently restricted to a few subjects on an elementary level. Hill was extremely fortunate, while at Rutgers College, to come under the influence of Theodore Strong, a friend of Nathaniel Bowditch, who had translated Laplace’s Mécanique céleste into English. Strong’s deep respect for tradition was reflected in the contents of his library. Hill relates that under Strong he read Sylvestre Lacroix’s Traité du calcul différential et intégral, Poission’s Traité de mécanique, Philippe de Pontécoulant’s Théorie analytique du systéme du monde, Laplace’s Mécanique céleste, Lagrange’s Mécanique analytique, and Legendre’s Fonctions elliptiques. Hill quoted Strong as saying that “Euler is our great Master” and noted that Strong “scarcely had a book in his library published later than 1840.” Poincaré said that to Strong Euler was “the god of mathematics” whose death marked the beginning of the decline of mathematics.

Hill’s knowledge of the techniques of the old masters strengthened his ingenuity in the creation of new methodology. The extent of the Eulerian method in its use of moving rectangular axes and the same first approximation. This device led to Hill’s variational curve, the reference orbit in describing lunar motion. E. W. Brown developed the work still further for the preparation of lunar ephemerides.

After receiving the B.A. from Rutgers in 1859, Hill went to Cambridge, Massachusetts, to further his mathematical knowledge. In 1861 he joined the staff of scientists working in Cambridge on the American Ephemeris and Nautical Almanac. He had already begun to publish in 1859, while still at college, and his third paper, “On the Conformation of the Earth,” in J. D. Runkle’s Mathematical Monthly (1861) brought him a prize and the attention of Runkle as well, R. S. Woodward, president of the Royal Society at the time he wrote Hill’s obituary notice, counted the paper as still worthy of reading and considered Hill as having become the leading contributor to the advances in dynamic astronomy during the half-century after its publication. At the Almanac office Hill was assigned the task of calculating the American ephemeris, work he was later authorized to continue at his home in West Nyack.

When Simon Newcomb became director of the American Ephemeris in 1877, he undertook the reconstruction of the theories and tables of lunar and planetary motion. Hill was induced to work on the theories of Jupiter and Saturn, known to be exceptionally difficult in the determination of their mutual perturbations. Because the Nautical Almanac office had meanwhile been transferred to Washington to be under the more immediate jurisdiction of the Navy Department, Hill resided there for a ten-year period beginning in 1882. His success with the Newcomb assignment represented one of the most important contributions to nineteenth-century mathematical astronomy. The calculation of the effects of the planets on the moon’s motion was a particular case of the famous three-body problem, which dates back to Newton (1686).

Hill’s “Researches in the Lunar Theory,” published in the first issue of American Journal of Mathematics (1878), had, through its introduction of the periodic orbit, initiated a new approach to the study of three mutually attracting bodies. F. R. Moulton wrote in 1914 that no earlier work had approached it in practical application and no subsequent work had then surpassed it. The article became fundamental in the development of celestial mechanics.

The memoir of 1877 entitled On the Part of the Motion of the Lunar Perigee Which Is a Function of the Mean Motions of the Sun and Moon contains the incontrovertible evidence of Hill’s mathematical genius. He was led to a differential equation, now called Hill’s equation, that is equivalent to an infinite number of algebraic linear equations. Hill showed how to develop the infianite determinant corresponding to these equations.

Hill’s procedures reflect his preference for the methodology of Charles Delaunay, as developed in the two-volume Théorie du mouvement de la lune (1860–1867), and he is said to have perfected it. Yet the methods adopted in the Nautical Almanac work were essentially those of P. A. Hansen, the other lunar theorist of eminence at that time.

Hill’s many honors included membership in the National Academy of Sciences (1874), presidency of the American Mathematical Society (1894–1896), and the gold medal of the Royal Astronomical Society for his researches on lunar theory (1887). He was a foreign member of the Royal Society, the Paris Academy, and the Belgian Academy.

In 1898 J. K. Rees, who held the Rutherfurd chair of astronomy at Columbia University, persuaded Hill to accept the newly created lectureship in celestial mechanics. Since few students were qualified to comprehend work on that level, Hill objected to receiving pay and finally resigned in 1901. He was urged to write out his lectures, which he did very painstakingly; he gave them to Columbia but insisted on returning the money that had been paid to him.

Hill remained a recluse in West Nyack, devoted to his researches and to his large scientific library, which he bequeathed to Columbia University. Illness during the last years reduced his physical activity and a failing heart brought his career to a close.


The Collected Mathematical Works of George William Hill, 4 vols. (Washington, D. C., 1905–1907), includes eightythree papers and has a biographical intro. by H. Poincaré, pp. vii-xviii. A complete bibliography of Hill’s papers is in Ernest W. Brown, “Biographical Memoir of George William Hill, 1838–1914,” in Biographical Memoirs. National Academy of Sciencess, 8 (1916), 275–309; and “History of the N. Y. Mathematical Society,” in American Mathematical Society Semicentennial Publications, I (New York, 1938), 117–124, with 101 items and a complete list of his honors (p. 118).

A condensed version of Brown’s memoir (see above), entitled “G. W. Hill, 1838–1914,” is in Obituary Notices of Fellows of the Royal Society, 91A (1915), xlii-li, repr. in Bulletin of the American Mathematical Society, 21 (1915), 499–511. See also E. W. Brown, “George William Hill, Mathematical and Astronomer,” in Nation, 98 , no. 2549 (7 may 1914), 540–541; J. W. L. Glaiser, “Address Delivered by the President... on Presenting the Gold Medal of the Society to Mr. G. W. Hill,” in Monthly Notices of the Royal Astronomical Society, 47 (Feb. 1887), 203–220; Harold Jacoby, “George William Hil,” in Columbia University Quarterly, 16 (Sept. 1914), 439–442; F. R. Moulton, “George William Hill,” in Popular Astronomy, 22 , no. 7 (Aug-Sept. 1914), 391–400; Simon Newcomb, “The Work of George W. Hill,” in Nation, 85 , no. 2209 (1907), 396, a letter to the editor; and R. S. Woodward, “George William Hill,” in Astronomical Journal, 28 , no. 20 (5 June 1914), 161–162.

Columbia University Bulletin, no. 8 (July 1894), 24–25, contains a list of the materials in the course of thirty lectures on celestial mechanics given by Hill; on p. 63 of the same issue is the citation accompanying his honorary degree.

The following contain references important to Hill’s work: G. D. Birkhoff, “Fifty Years of American Mathematics,” in American Mathematical Society Semicentennial Publications, II (New York, 1938), 270–315; F. R. Moulton, Differential Equations (New York, 1930), pp. 224, 318, 353–354; Felix Klein, inaugural address at the general session of the Congress of Mathematics and Astronomy, Chicago, in Bulletin of the New York Mathematical Society, 3 (Oct. 1893), 1–3, also in Monist, 4 (Oct, 1893), 1–4; C. S. Peirce, “Note on Mr. G. W. Hill’s Moon Theory,” in Nation, 81 (19 Oct. 1905), 321; and review of Hill’s Collected Works, ibid., 85 (17 Oct. 1907), 355; E. H. Roberts, “Note on Infinite Determinants,” in Annals of Mathematics, 10 (1896), 35–50; and D. E. Smith and J. Ginsburg, History of Mathematics in America Before 1900 (Chicago, 1934), passim.

Further references are in Dictionary of American Biography, IX (New York, 1932), 32–33; National Cyclopedia of American Biography (New York, 1918), p. 388; Poggendorff, III, 631–632; IV, 639; V, 538; and American Men of Science, I (1906), 146.

Additional citations are found in Encyklöpedie der mathematischen Wissenschaften VI (Leipzig, 1912–1926); J. J. [erwood], in Monthly Notices of the Royal Astronomical Society, 75 (1915); S. Newcomb, Reminiscences of an Astronomer (London, 1903); T. Muir, Theory of Determinants in the Historical Order of Development, III (London, 1920); and F. Schlesinger, “Recollections of George William Hill,” in Publications of the Astronomical Society of the Pacific, 49 (1937).

Carolyn Eisele

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