menter. Hence it is not surprising to find that his next research work was the determination of the constants in Gauss' theory of terrestrial magnetism—a subject to which he devoted much time in his later years, and which he left unfinished. In 1851 Adams was elected president of the Royal Astronomical Society. In 1852 his fellowship at St. John's College expired, because he had not taken clerical orders; he was however elected to a fellowship at Pembroke College, which he retained till his death. In 1853 Adams communicated to the Royal Society his celebrated memoir on the secular acceleration of the Moon's mean motion. Halley was the first to detect this acceleration by comparing the Babylonian observations of eclipses with those of Albatagnius and of modern times, and Newton referred to his discovery in the second edition of the Principia. The first numerical determination of the value of the acceleration is due to Dunthorne, who found it to be about 10″ in a century. Laplace was the first to deduce the acceleration theoretically from Newtonian principles; the result is given by an infinite series of which he calculates only the first term. Plana, an Italian mathematician, found the next term to be ; Adams by his investigation found it to be , which reduced the value of the first term from 10″ to 6″. This paper gave rise to a violent controversy; those opposed holding that the result was contradictory to observation. But Adams was safe; his result depended entirely on algebraical considerations—on the solution of a differential equation, not on observation; consequently his result finally prevailed.
In 1858 Adams' life at Cambridge was interrupted; he was appointed professor of mathematics in the University of St. Andrews, Scotland. At the end of a year he returned to Cambridge as Lowndean professor of astronomy and geometry. As Lowndean professor he lectured during one term in each year, generally on the lunar theory, but sometimes on the theory of Jupiter's satellites, or the figure of the Earth. Two
