translated into French by La Chappe and Lalande in 1754 and 1759, and continued in general use for many years. The mass of Halley's observations are preserved in manuscript at the Royal Observatory, in four small quarto volumes; a fifth, not included in the collection, was stated by Maskelyne to have been found at his death. They were copied for the Astronomical Society, at the instance of Baily, in 1832. No advantage adequate to the labour could accrue from their reduction. Halley took no account of fractional parts of seconds of time, and considered 10″ of arc ‘as the utmost attainable limit of accuracy.’ His clocks were besides ill-regulated, and his system of registration unmethodical. He seems, as Professor Grant remarks, ‘to have undervalued those habits of minute attention which are indispensable to the attainment of a high degree of excellence in the practice of astronomical observation.’ His administration of the Royal Observatory was the least successful part of his career. Pursuing one end too exclusively, he virtually failed to reach it. His revival of the ‘saros’ was not for the advantage of science, yet he devoted to the scheme of lunar correction based upon it the most sustained efforts of his life. The dilapidated state of the observatory at his death was the natural consequence of his prolonged infirmity. The screws of the quadrant were broken, its adjustment was widely erroneous; the mark on the park wall for setting the transit instrument was intercepted by the growth of trees (Bradley, Miscellaneous Works, p. 382).
Halley's discovery of the ‘long inequality’ of Jupiter and Saturn was published at the end of his ‘Tables.’ He first attributed their opposite discrepancies from theory to the effects of mutual perturbation, assigning to each planet a secular equation increasing as the square of the time. From a comparison of ancient with modern eclipses he inferred in 1693 a progressive acceleration of the moon's mean motion (Phil. Trans. xvii. 913), explained on gravitational principles by Laplace in 1787. He set forth the conditions of the daylight visibility of Venus in 1716, ‘by some reckoned to be prodigious’ (ib. xxix. 466); collected observations of meteors (ib. p. 159), and deduced a height from the earth's surface of seventy-three miles for that seen in England on 19 March 1719 (ib. xxx. 978), while maintaining the origin of such objects from terrestrial exhalations (ib. p. 989). His most celebrated work, however, was ‘Astronomiæ Cometicæ Synopsis’ (ib. xxiv. 1882), communicated to the Royal Society in 1705, and separately published in English at Oxford the same year. It was reprinted with his ‘Tables’ in 1749, and translated into French by Le Monnier in 1743. Having computed, with ‘immense labour,’ the orbits of twenty-four comets, he found three so nearly alike as to persuade him that the comets of 1531, 1607, and 1682 were apparitions of a single body, to which he assigned a period of about seventy-six years. In predicting its return for 1758, he appealed to ‘candid posterity to acknowledge that this was first discovered by an Englishman.’ The reappearance of ‘Halley's comet’ on Christmas day 1758 verified the forecast, and laid a secure foundation for cometary astronomy. A period of 575 years was erroneously assigned by Halley to the comet of 1680.
The employment of transits of Venus for ascertaining the sun's distance was first recommended by Halley in 1679; again in more detail in 1691 (ib. xvii. 511); finally in 1716, when his ‘method of durations’ was elaborated with special reference to the transit of 1761 (ib. xxix. 454). He believed that the great unit might in this way be measured within 1/500 of its value, and his enthusiasm stimulated the efforts made to turn the opportunity to account. An inquiry into precession led Halley in 1718 to the discovery of stellar proper motions evinced in the changes of latitude, since Ptolemy's epoch, of Sirius, Aldebaran, and Arcturus (ib. xxx. 736). From the instantaneousness of occultations he gathered the spurious nature of star-discs, and estimated the number of stars corresponding to each magnitude on the hypothesis of their uniform distribution through space (ib. xxxi. 1, 24). Nebulæ were regarded by him as composed of a ‘lucid medium shining with its own proper lustre,’ and as occupying ‘spaces immensely great, and perhaps not less than our whole solar system.’ Six such objects were enumerated by him in 1716 (ib. xxix. 390), and he discovered, in 1677 and 1714 respectively, the star clusters in the Centaur and in Hercules.
Halley divined and demonstrated in 1686 the law connecting elevation in the atmosphere with its density, consequently with barometrical readings (ib. xvi. 104); he materially improved diving apparatus, and himself made a descent in a diving-bell (ib. xxix. 492, xxxi. 177); experimented on the dilatation of liquids by heat (ib. xvii. 650); and by his scientific voyages laid the foundation of physical geography. As the compiler of the ‘Breslau Table of Mortality’ he takes rank as the virtual originator of the science of life-statistics. His papers on the subject (ib. pp. 596, 654) were reprinted in the ‘Assurance Magazine’ (vol. xviii.). It has been observed by M. Marie (Hist. des
