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Brown, Ernest William

Brown, Ernest William

(b. Hull, England, 29 November 1866; d. New Haven, Connecticut, 22 July 1938)

celestial mechanics.

Brown, who early excelled in mathematics, won a scholarship to Christ’s College, Cambridge, in 1884, and maintained close ties with that school throughout his life: he received a B.A. as sixth wrangler (1887), M.A. (1891), and D.Sc. (1897); and was a fellow (1889–1895) and honorary fellow (1911–1938). In 1891 he moved to the United States to become instructor in, and later (1893) professor of, mathematics at Haverford College. Brown went to Yale University in 1907—largely because Yale agreed to support the computing and publishing of his lunar tables—and he remained there as professor, Sterling professor of mathematics (1921–1931), the first Josiah Willard Gibbs professor of mathematics (1931–1932), and professor emeritus. Among his many honors were those from the Royal Society of London (fellowship, 1897; Royal Medal, 1914) and from the National Academy of Sciences (membership, 1923; Watson Medal, 1937).

While still a student, Brown was encouraged by his professor, George Howard Darwin, to study George Hill’s papers on lunar theory, and from that time on, he devoted himself to reconciling lunar theory and observations by finding “in the most accurate way and by the shortest path the complete effect of the law of gravitation applied to the moon” (“Cosmical Physics,” p. 185). By 1908 Brown had worked out, and published in five papers, his theory of the motion of the moon. Following Hill’s example, he attacked the moon’s motion as an idealized problem of three bodies, assuming the sun, earth, and moon to be spherical and the center of the earth-moon system to move in an elliptical orbit about the sun; he then considered inequalities resulting from the actual figures of the earth and moon, and the direct and indirect gravitational attractions of the other planets.

Brown’s main objective was a new, accurate calculation of each coefficient in longitude, latitude, and parallax as great as one-hundredth of a second of arc, and the result was not to be in error by more than that amount; in fact, he included many terms with coefficients one order of magnitude smaller. Among the few lunar motions he could not account for by gravitation was the relatively large fluctuation in mean longitude; after rejecting numerous other possibilities, he explained this apparent deviation by irregular variations in the earth’s rate of rotation.

After developing his lunar theory Brown proceeded, with the assistance of Henry B. Hedrick, to use it to construct new tables of the moon’s motion. The numerical values of the constants were obtained by comparing the theory with 150 years of Greenwich observations, as analyzed by Philip H. Cowell. The tables were designed for actual computation of the moon’s position, and in 1923 they were adopted by most national ephemerides. Although Brown included nearly 1,500 terms—nearly five times as many as had Peter Andreas Hansen, the author of the previously used table—the format of his tables made them as convenient to use as were Hansen’s. The remainder of his work concerned the interaction of other members of the solar system, such as the Trojan group of asteroids, and the negligible gravitational attraction of Pluto for Uranus and Neptune.


A bibliography of Brown’s writings is in Schlesinger and Brouwer (see below). Among his works are “Theory of the Motion of the Moon,” in Memoirs of the Royal Astronomical Society, 53 (1896–1899), 39–116, 163–202; 54 (1899–1901), 1–63; 57 (1908), 51–145; and 59 (1910), 1–103; Tables of the Motion of the Moon, 3 vols. (New Haven, 1919); and “Cosmical Physics,” in Nature, 94 (1914), 184–190.

A biographical source is Frank Schlesinger and Dirk Brouwer, “Biographical Memoir of Ernest William Brown,” in Biographical Memoirs of the National Academy of Sciences, XXI (Washington, D.C., 1939), 243–273.

Deborah Jean Warner

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