50". The true explanation in a 'nodding' movement of the axis, due to the moon's unequal action upon the equatorial parts of the earth, was more than suspected early in 1732 ; but Bradley did not consider the proof complete until he had tracked each star through an entire revolution of the moon's nodes (18.6 years) back to its mean place (allowance being made for annual precession). In September 1747 he was at length fully satisfied of the correspondence of his hypothesis with facts ; and 14 Feb. 1748 a letter to the Earl of Macclesfield, in which he set forth the upshot of his twenty years' watching and waiting, was read before the Royal Society (Phil. Trans. xlv. 1). The idea of a possible nutation of the earth's axis was not unfamiliar to astronomers ; and Newton had predicted the occurrence of a semi-annual, but scarcely sensible, effect of the kind. A phenomenon such as Bradley detected, however, depending on the position of the lunar orbit, was unthought of until its necessity became evident with the fact of its existence. The complete development of its theory went beyond his mathematical powers, and he invited assistance, promptly rendered by D'Alembert in 1749. Bradley's coefficient of nutation (9") has proved nearly a quarter of a second too small. He might probably have gone even nearer to the truth had he trusted more implicitly to his own observations. His confidence was, however, embarrassed by the proper motions of the stars, the ascertainment of which he, with his usual clear insight into the conditions of exact astronomy, urged upon well-provided observers ; while his sagacious hint that they might be mere optical effects of a real translation of the solar system (Phil. Trans. xlv. 40) gave the first opening for a scientific treatment of that remarkable subject.
As regards nutation, the novelty of his announcement had been somewhat taken off by previous disclosures. On his return from Lapland, Maupertuis consulted him as to the reduction of his observations, when Bradley imparted to him, 27 Oct. 1737, his incipient discovery. Maupertuis was not bound to secrecy, nor did he observe it. He transmitted the information to the Paris Academy (Mem. de l'Ac. 1737, p. 411), while Lalande published in 1745 (ib. 1745, p. 512) the confirmatory results of observations undertaken at Bradley's suggestion.
The discovery of aberration earned for its author, 14 Dec. 1730, exemption on the part of the Royal Society from all future payments ; that of nutation was honoured in 1748 with the Copley medal. His heightened reputation further enabled him to ask and obtain a new instrumental outfit for the Royal Observatory. He took advantage of the annual visitation by members of the Royal Society to represent its absolute necessity ; and a petition drawn up by him and signed by the president and members of council in August 1748 produced an order for 1,000l. under the sign-manual, paid, as a note in Bradley's handwriting informs us, by the treasurer of the navy out of the proceeds of the sale of old stores. The wise expenditure of this paltry sum laid the firm foundation of modern practical astronomy. Bradley was fortunate in the co-operation of John Bird. The eight-foot mural quadrant, for which he paid him 300l., was an instrument not unworthy the eye and hand that were to use it. He had also from him a movable quadrant forty inches in radius, and a transit-instrument of eight-feet focal length. From Short a six-foot reflector was ordered, but not delivered until much later ; and 20l. was paid for a magnetic apparatus, changes in dip and variation having been objects of attention to Bradley as early as 1729. For the Wanstead sector, removed to Greenwich in July 1749, 45l. was allowed to him.
The first employment of Bird's quadrant was in a series of observations, 10 Aug. 1750 to 31 July 1753, for the purpose of determining the latitude of the observatory and the laws of refraction. Simultaneously with Lacaille and Mayer, Bradley introduced the improvement of correcting these for barometrical and thermometrical fluctuations. His formula for computing mean refraction at any altitude closely represented the actual amounts down to within 10 of the horizon (Grant, Hist. Phys. Astr. pp. 329-30). After its publication by Maskelyne in 1763, it was generally adopted in England, and was in use at Greenwich down to 1833.
In 1751 Bradley made observations for determining the distances of the sun and moon in concert with those of Lacaille at the Cape of Good Hope (Mém. de l'Ac. 1752, p. 424). From the combined results for Mars, Delisle deduced a solar parallax of 10.3" (Bradley, Misc. Works, p. 481). A series of 230 comparisons with the heavens of Tobias Mayer's 'Lunar Tables,' between December 1755 and February 1756, enabled Bradley to report them to the admiralty as accurate generally within 1'. His hopes of bringing the lunar method of longitudes into actual use were thus revived ; and he undertook, aided by Mason, a laborious correction of the remaining errors founded on 1,220 observations. The particulars of these were inserted in the 'Nautical Almanac' for 1774 but the amended tables, completed from
