Halley, Edmund (DNB00)
HALLEY, EDMUND (1656–1742), astronomer, was born at Haggerston, in St. Leonard's parish, Shoreditch, London, on 8 Nov. 1656. His father, Edmund Halley, a member of a good Derbyshire family, had a soap-boiling establishment in Winchester Street in the city of London. He was rich, and sent his only son to St. Paul's School, under the care of Dr. Thomas Gale [q. v.] Here he was equally distinguished in classics and mathematics, rose to be captain of the school at fifteen, constructed dials, observed the change in the variation of the compass, and studied the heavens so closely that it was remarked by Moxon the globe maker ‘that if a star were displaced in the globe he would presently find it out.’ He entered Queen's College, Oxford, as a commoner at midsummer term 1673, carrying with him, besides a competent knowledge of Greek, Latin, and Hebrew, a ‘curious apparatus’ of instruments. With a telescope of 24 feet he observed a lunar eclipse on 27 June 1675 in Winchester Street, and at Oxford a remarkable sunspot in July and August 1676 (Phil. Trans. xl. 687), and the occultation of Mars by the moon on 21 Aug. 1676 (ib. p. 683). Before he was twenty he communicated to the Royal Society a ‘Direct and Geometrical Method of finding the Aphelia and Eccentricity of the Planets’ (ib. p. 683), finally abolishing the notion of a ‘centre of uniform motion;’ invented shortly afterwards an improved construction for solar eclipses, and noted defects in the theories of Jupiter and Saturn. For the correction of these he perceived that a revision of the places of the fixed stars was indispensable, and with the design of supplementing in the southern hemisphere the labours of Flamsteed and Hevelius in the northern, he left the university without a degree, and embarked for St. Helena in November 1676. His father allowed him 300l. a year; a recommendation from Charles II to the East India Company procured him facilities of transport; but the climate proved unfavourable, and by assiduous observations during eighteen months with a 5½-foot sextant he succeeded in determining only 341 stars. His enterprise, however, laid the foundation of austral stellar astronomy, and earned for him from Flamsteed the title of the ‘Southern Tycho.’ In the course of the voyage he improved the sextant, collected a number of valuable facts relative to the ocean and atmosphere, noted the equatorial retardation of the pendulum, and made at St. Helena, on 7 Nov. 1677, the first complete observation of a transit of Mercury.
On his return to England in October 1678 Halley presented to the king a planisphere of the southern constellations, including that of ‘Robur Carolinum,’ newly added by himself, and was rewarded with a mandamus to the university of Oxford for a degree of M.A., conferred on 3 Dec. 1678. His ‘Catalogus Stellarum Australium’ was laid before the Royal Society on 7 Nov. 1678, and immediately translated into French; but owing to his dependence upon Tycho's fundamental points it was of little practical value until Sharp reduced and included in the third volume of Flamsteed's ‘Historia Cœlestis’ (p. 77) 265 of the stars it contained. Halley appended to his ‘Catalogue’ a proposal for amending lunar theory by the introduction of an annual equation, and an account of the transit of Mercury, from which he deduced a solar parallax of 45″. He was elected a fellow of the Royal Society on 30 Nov. 1678 at the age of 22, and was, six months later, sent by that body to Danzig as arbiter of a dispute between Hooke and Hevelius on the respective advantages of telescopic and plain sights. He shared the observations of Hevelius from 26 May to 18 July 1679, and testified to their accuracy in a letter printed by Hevelius in his ‘Annus Climactericus’ (1685, p. 101).
Towards the close of 1680 he started on a continental tour with his school-friend, Robert Nelson, and caught sight near Calais of the great comet of that year, upon which he made, with Cassini, at Paris, observations of great service to Newton in fixing its orbit. He spent most of 1681 in Italy, and married in England in 1682 Mary, daughter of Mr. Tooke, auditor of the exchequer, an amiable and attractive woman. His first house was at Islington, where his instruments excited much curiosity; but he removed later to Golden Lion Court, Aldersgate Street. He lost no time in entering upon his favourite project of perfecting the lunar theory by means of observations continued through a ‘sarotic’ period of 223 lunations, or a little more than eighteen years, and secured at Islington in 1683–4 nearly two hundred observations, by which his expectation of the regular recurrence of errors was confirmed. These results were published by him in 1710 as an appendix to the second edition of Street's ‘Caroline Tables.’ He was, however, interrupted by the death of his father in 1684 in unexpectedly bad circumstances, and was obliged to postpone everything to the defence of the little that was left of his patrimony.
In an address delivered at Cambridge on 19 April 1888 Dr. Glaisher expressed the conviction that ‘but for Halley the “Principia” would not have existed.’ His suggestions originated it; he averted the threatened suppression of the third book. ‘He paid all the expenses, he corrected the proofs, he laid aside all his own work in order to press forward to the utmost the printing. All his letters show the most intense devotion to the work.’ Keenly alive to the importance of the problem of gravity, Halley obtained from Kepler's third law in January 1684 the law of inverse squares, but failed to deduce from it the planetary motions. Having fruitlessly applied to Wren and Hooke, he in August 1684 paid a visit to Newton at Cambridge, and ‘learned from him the good news that he had brought this demonstration to perfection.’ The first eleven propositions of the ‘Principia’ were communicated three months later to Halley, who again repaired to Cambridge to confer with their author, and on 10 Dec. gave an account of them to the Royal Society. Although now a poor man, he undertook on 2 June 1686 to print Newton's work at his own charge, and in a letter to him of 5 July 1687 was able to announce its completion. His outlay was eventually reimbursed by the sale of copies. A ‘Discourse concerning Gravity’ was read by Halley before the Royal Society on 21 April 1686, by way of preparation for the ‘incomparable treatise of motion almost ready for the press’ (Phil. Trans. xvi. 3). He prefixed to the first edition a set of Latin verses ending with the line
Nec fas est propius mortali attingere Divos,
and presented to James II a copy of the ‘Principia’ with a discourse ‘On the true Theory of the Tides’ (ib. xix. 445).
Halley was refused the Savilian professorship of astronomy at Oxford in 1691, owing to a suspicion, which he vainly tried to combat, of his holding materialistic views. Flamsteed, lately become his enemy, did his utmost to hinder his election. Halley acted as assistant secretary to the Royal Society and editor of the ‘Philosophical Transactions’ from 1685 to 1 Jan. 1693. Among his numerous contributions to them about this time were an ‘Historical Account of the Trade Winds and Monsoons’ (ib. xvi. 153), giving the first detailed description and a sketch of a circulatory theory of these winds; ‘An Account of the Circulation of the Watery Vapours of the Sea, and of the Cause of Springs’ (ib. xvii. 468), establishing an equilibrium between expenditure by evaporation and supply by condensation in the waters of the globe; a ‘Discourse tending to prove at what Time and Place Julius Cæsar made his first Descent upon Britain’ (ib. p. 495); and a ‘New and General Method of finding the Roots of Equations’ (ib. xviii. 136). Appointed by Newton's influence deputy-controller of the mint at Chester in 1696, he held the post, in spite of ‘intolerable’ annoyances from his fellow-officials, until its abolition two years later. He corresponded meantime actively with the Royal Society through Sir Hans Sloane, observed at Chester the partial lunar eclipse of 19 Oct. 1697 (ib. xix. 784), and ascended Snowdon for the purpose of testing his method of determining heights by the barometer. His theory of the variation of the compass was proposed in 1683, and further developed in 1692 (ib. xiii. 208, xvii. 563). It assumed the direction of the needle to be governed by the influence of four magnetic poles, two fixed in the outer shell of the earth, two revolving with an inner nucleus in a period roughly estimated at seven hundred years. This hypothesis explained with surprising success the ‘abstruse mystery’ of secular magnetic changes. It was revived by Hansteen in 1819. Desirous of investigating thoroughly phenomena which he hoped might prove regular enough to serve for the determination of longitudes, Halley obtained from William III in 1698 the command of a war-sloop, the Paramour Pink, with orders to study the variation of the compass, and ‘attempt the discovery of what land lies to the south of the western ocean.’ He sailed from Portsmouth at the end of November 1698, but was compelled by the refractory conduct of his crew to return from Barbadoes in the following June. Having got his lieutenant cashiered, he started again in September, and penetrated to 52° south latitude, where he ‘fell in with great islands of ice, of so incredible a height and magnitude that I scarce dare write my thoughts of it.’ After a narrow escape from destruction he steered north, explored the Atlantic from shore to shore, and cast anchor in the Thames on 7 Sept. 1700, his ship's company diminished only by the loss of one boy swept overboard. Of this incident he could never afterwards speak without tears. His ‘General Chart’ of the variation of the compass appeared in 1701. It set the example of a method, since extensively employed, of representing to the eye a mass of complex facts, and gave the first general view of the distribution of terrestrial magnetism by means of lines of equal declination, long called ‘Halleyan lines.’
Resuming the command of the Paramour Pink, Halley made in 1701, by the king's orders, a thorough survey of the tides and coasts of the British Channel, of which he published a map in 1702. He was next sent by Queen Anne, at the Emperor Leopold's request, to inspect the harbours of the Adriatic, and, on a second journey thither, aided the imperial engineers to fortify Trieste. In passing through Hanover he supped with the elector (afterwards George I) and his sister, the queen of Prussia, and at Vienna was presented by the emperor with a diamond ring from his own finger. Dr. Wallis [q. v.] having died just before his arrival in England, in November 1703, he was appointed in his room Savilian professor of geometry at Oxford, where he was created D.C.L. on 16 Oct. 1710. He was no sooner installed in the Savilian chair than Dr. Aldrich engaged him to complete a translation from Arabic into Latin, begun by Dr. Bernard, of Apollonius's ‘De Sectione Rationis,’ till then unknown to European scholars. His success, and the useful emendations of the original manuscript which, notwithstanding his previous ignorance of Arabic, he suggested, were extremely surprising to Dr. Sike, the greatest orientalist of his time. He added a restoration, from the description of Pappus, of ‘De Sectione Spatii,’ by the same author, and the whole was published from the university press in 1706. The first complete edition of the ‘Conics’ of Apollonius, including a masterly restoration of the lost eighth book, was issued by him, with Serenus's ‘De Sectione Cylindri et Coni,’ in 1710. His edition of Ptolemy's ‘Catalogue’ formed part of the third volume of Hudson's ‘Geographiæ Veteris Scriptores Græci’ (Oxford, 1712), and his edition of the ‘Spherics’ of Menelaus was published by his friend Dr. Costard in 1758.
Halley was a leading member of the committee entrusted by Prince George of Denmark with preparing Flamsteed's observations for the press, and edited the first or ‘spurious’ version of the ‘Historia Cœlestis’ in 1712. His accurate prediction of the circumstances of the total solar eclipse of 2 May 1715 added greatly to his reputation. He observed the event, in company with the Earl of Abingdon and Chief-justice Parker (afterwards Earl of Macclesfield), from the roof of the Royal Society's house in Crane Court; and minutely described the corona, without venturing to decide whether it belonged to the sun or to the moon (Phil. Trans. xxix. 245). The great aurora of 16 March 1715, the first he had seen, was observed by him at London. He explained the auroral crown as an optical effect due to the ‘concourse’ of many streamers, and suggested a mode of determining the height of such phenomena (ib. p. 407). The hypothesis of their magnetic origin was a development of his views on terrestrial magnetism. He supposed auroræ to be occasioned by the escape of a ‘luminous medium,’ by which a subterranean globe was rendered habitable.
Halley became secretary to the Royal Society on Sir Hans Sloane's resignation, 13 Nov. 1713, and on 9 Feb. 1721 was appointed, through Lord-chancellor Parker's interest, astronomer-royal in succession to Flamsteed. He took possession of the house on 7 March, but on 6 May had not ‘yet got into the observatory,’ which he found ‘wholly unprovided with instruments, and, indeed, of everything else that was moveable.’ Five hundred pounds were allotted by the board of ordnance for supplying the needful apparatus, and in 1721 the first transit-instrument erected at Greenwich—one 5½ feet in length, constructed twenty years earlier by Hooke—was in its place. Halley's observations with it, however, begun on 1 Oct. 1721, were rendered useless by the absence of any means of taking zenith distances. After October 1725 his main depen- dence was on a new iron quadrant, by Graham, of 8-feet radius. His leading object was to bring the lunar tables to the perfection required for gaining the prize offered for the solution of the problem of longitudes, and although in his sixty-fourth year at the time of his appointment, he resumed and carried out the design conceived forty years previously of observing the moon through a complete period of eighteen years. He immediately began to draw up lists of lunar errors, but published nothing; and at a meeting of the Royal Society on 2 March 1727 Newton remarked upon the neglect of the late queen's precept regarding the communication of results, whereupon Halley acquainted the council that he had numerous observations of the moon, but ‘had hitherto kept them in his own custody, that he might have time to finish the theory he designed to build upon them, before others might take the advantage of reaping the benefit of his labours’ (Baily, Memoirs Royal Astron. Society, viii. 188). It is said by Hearne that a quarrel ensued which shortened Newton's life. Four years later Halley announced to the Royal Society that he had made nearly fifteen hundred lunar observations, and was able to predict the place of the ‘sidus contumax’ (as he called it) within two minutes of arc. He added a narrative of his efforts towards the improvement of its theory (Phil. Trans. xxxvii. 185). He published, however, only his observations of a partial solar eclipse on 27 Nov. 1722 (ib. xxxii. 197), of the transit of Mercury on 29 Oct. 1723 (ib. xxxiii. 228), and of an eclipse of the moon on 15 March 1736 (ib. xl. 14).
About September 1729 Queen Caroline visited the Royal Observatory, and finding that Halley had held the commission, she procured for him the pay of a post-captain. His salary as astronomer-royal was 100l. a year, with no allowance for an assistant. Owing to the pressure of official duties he resigned in 1721 the secretaryship to the Royal Society, and declined some years later the post of mathematical preceptor to the Duke of Cumberland. He was elected in 1729 a foreign member of the Paris Academy of Sciences. Until 1737, when his right hand became affected with paralysis, he had never experienced a constitutional ailment, and was accustomed to relieve slight fever on catching cold with doses of quinine in water-gruel, which he called his ‘chocolate.’ Every Thursday regularly he went to London to dine with his friends and attend the meetings of the Royal Society; and he ‘stuck close to his telescope,’ aided only by his friend Gale Morris, F.R.S., as amanuensis, until 31 Dec. 1739. His bodily powers now failed rapidly, although his memory and cheerfulness remained unimpaired. At last, tired of the doctors' cordials, he asked for a glass of wine, drank it, and expired, on 14 Jan. 1741–2, in the eighty-sixth year of his age. He was buried in the churchyard of Lee, near Greenwich, with his wife, who died in 1737. The inscription marking the tomb was placed there in 1742 by the two daughters who survived him. Of these, the elder, Margaret, died unmarried on 13 Oct. 1743; the second, Mrs. Price, lived until 1765. His son, Edmund Halley, a surgeon in the royal navy, died before him, and he lost several children in infancy. His will was proved on 9 Feb. 1741–2, one of the witnesses to it being James Bradley [q. v.]
In person Halley was ‘of a middle stature, inclining to tallness, of a thin habit of body, and a fair complexion,’ and it is added that ‘he always spoke as well as acted with an uncommon degree of sprightliness and vivacity.’ His disposition was ardent, generous, and candid; he was disinterested and upright, genial to his friends, an affectionate husband and father, and was wholly free from rancour or jealousy. He passed a life of almost unprecedented literary and scientific activity without becoming involved in a single controversy, and was rendered socially attractive by the unfailing gaiety which embellished the more recondite qualities of a mind of extraordinary penetration, compass, and power. One of his admirers was Peter the Great, who in 1697 not only consulted him as to his shipbuilding and other projects, but admitted him familiarly to his table. Portraits of Halley were painted by Murray, Phillips, and Kneller, and engravings from each were published. There is no trace in his writings of the sceptical views attributed to him by Whiston (Memoirs, i. 123). S. J. Rigaud, bishop of Antigua, endeavoured (in his ‘Defence of Halley,’ 1844) to exonerate him wholly from a charge perpetuated by the dedication to him, in the character of an ‘infidel mathematician,’ of Bishop Berkeley's ‘Analyst,’ but he doubtless habitually expressed free opinions. His moral character has been impeached, perhaps on insufficient grounds.
On his appointment as astronomer-royal, Halley withheld, in the hope of improving, the lunar and planetary tables he had printed in 1719 (Phil. Trans. xxxvii. 193); yet they appeared posthumously in 1749, without further alteration than the addition of the places and errors of the moon deduced from observations at Greenwich, 1722–39. An English edition was issued in 1752; they were 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 Sciences, vii. 125) that ‘his results in pure geometry, though the fruits only of leisure moments, would alone suffice to secure him a distinguished place in scientific history.’ Besides his important restorations of ancient authors, he investigated the properties of the loxodromic curve, and first solved the problem to describe a conic section of which the focus and three points are given. He furnished an improved construction for equations of the third and fourth degrees (Phil. Trans. xvi. 335); his universal theorem for finding the foci of object-glasses (ib. xvii. 960) appeared originally as an appendix to Molyneux's ‘Dioptricks’ (1692); and his account of the relations of weather to barometrical fluctuations was included by Cotes in his ‘Hydrostatical Lectures’ (2nd ed. 1747, p. 246). His papers on the ‘Analogy of the Logarithmic Tangents to the Meridian Line’ and on ‘A compendious Method of Constructing Logarithms’ were reprinted in Baron Maseres's ‘Scriptores Logarithmici’ (vol. ii. 1791). The ‘Miscellanea Curiosa,’ edited by Halley in 1708 (in 3 vols.), was largely composed of his contributions to the ‘Philosophical Trans.’ His ‘Journal’ during his two voyages, 1698–1700, was published in 1775 by Dalrymple in his ‘Collection of Voyages in the South Atlantic’; and a number of interesting letters addressed by him to Josiah Burchett, secretary to the admiralty, are preserved at the Record Office (under the heading ‘Captains' Letters, 1698–1700’). His ‘Southern Catalogue’ was reprinted, with notes and a preface by Baily, in the thirteenth volume of the Royal Astronomical Society's ‘Memoirs’. Dr. Gill recognised in 1877 the foundations of his observatory at St. Helena (see Mrs. Gill, Six Months in Ascension, p. 33).
Lalande styled Halley ‘the greatest of English astronomers,’ and he ranked next to Newton among the scientific Englishmen of his time. Of eighty-four papers inserted by him in the ‘Philosophical Transactions’ a large proportion expounded in a brilliant and attractive style theories or inventions opening up novel lines of inquiry and showing a genius no less fertile than comprehensive. ‘While we thought,’ wrote M. Marian, ‘that the eulogium of an astronomer, a physicist, a scholar, and a philosopher comprehended our whole subject, we have been insensibly surprised into the history of an excellent mariner, an illustrious traveller, an able engineer, and almost a statesman.’[Several abortive attempts have been made to write a complete biography of Halley. Mr. Israel Lyons of Cambridge was, in 1775, interrupted in the task by death in 1775. Professor Rigaud of Oxford had much more extensive collections (deposited after his death in 1839 in the Bodleian Library), which still await an editor. The chief sources of information at present are: Biog. Brit. vol. iv. (1757), where the substance of manuscript memoirs imparted by Halley's son-in-law, Mr. Henry Price, is communicated; Mairan's ‘Éloge,’ in Mémoires de l'Acad. des Sciences, Paris, 1742 (Histoire, p. 182), translated in Gent. Mag. xvii. 455, 503; Wood's Athenæ Oxon. (Bliss), iv. 536; Wood's Fasti Oxon. ii. 368; Aubrey's Lives of Eminent Men, ii. 365; Thomson's Hist. R. Society, pp. 207, 335; Rigaud, in Bradley's Miscellaneous Works (see Index); Memoirs R. Astr. Society, ix. 205; Monthly Notices, iii. 5, vi. 204; Philosophical Mag. viii. 219, 224 (1836); Baily's Account of Flamsteed, pp. xxxi, 193, 213, 747; Hutton's Mathematical Dict. 1815; Brewster's Life of Newton; Grant's Hist. of Phys. Astronomy, p. 477 and passim; Whewell's Hist. of the Inductive Sciences; Phil. Trans. Abridg. (Hutton), ii, 326 (1809); H. Bromley's Cat. of Engraved Portraits, p. 291; Lysons's Environs, iv. 504, 509; Nature, xxi. 303 (Halley's Mount); Walford's Insurance Cyclopædia, v. 616; Graetzer's E. Halley und Caspar Neumann (Breslau, 1883); Poggendorff's Hist. de la Physique (1883), p. 436 and passim; Montucla's Hist. des Mathématiques, iv. 50, 308; Bailly's Hist. de l'Astr. Moderne, ii. 432; Delambre's Hist. de l'Astr. au XVIIIe Siècle, p. 116; Lalande's Préface Historique aux Tables de Halley (1759); Delisle's Lettres sur les Tables de Halley (1749); Wolf's Geschichte der Astronomie; Mädler's Gesch. der Himmelskunde; Cunningham's Lives of Eminent Englishmen, iv. 453; Nichols's Illustr. of Lit. iv. 22, 33; The Observatory, iii. 348 (Oliver), viii. 429 (Lynn); Mailly's Annuaire de l'Observatoire de Bruxelles, 1864, p. 305; Addit. MS. 4222, f. 177; Egerton MSS. 2231, f. 186, 2334 C. 2. Many unpublished letters from Halley to Sir Hans Sloane and others are preserved in the Guard Book and Letter Books of the Royal Society.]