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KEILL, JOHN (1671–1721), mathematician and astronomer, was born at Edinburgh on 1 Dec. 1671. James Keill [q. v.] was his brother, and Dr. John Cockburn [q. v.] was his uncle (cf. Hearne, Coll., Oxf. Hist. Soc., ii. 202). After attending school at Edinburgh he joined the university, attained distinction in mathematics and natural philosophy under Dr. David Gregory, and graduated M.A. When Gregory in 1691 became Savilian professor of astronomy at Oxford, Keill accompanied him, and being admitted at Balliol College on a Scotch exhibition, was ‘incorporated M.A.’ on 2 Feb. 1694, although, according to Hearne, it was customary to incorporate Scottish masters of arts as bachelors only. Like Gregory, Keill was an enthusiastic student of Newton's ‘Principia,’ and began expounding the Newtonian principles ‘by proper experiments in his private chamber at the college.’ He was appointed lecturer in experimental philosophy at Hart Hall, and, as soon as suitable apparatus could be contrived, he opened the first course of lectures on the new philosophy which had been delivered in Oxford. Desaguliers, who in 1710 succeeded him at Hart Hall, calls him the ‘first who taught natural philosophy by experiments in a mathematical manner … instructing his auditors in the laws of motion, the principles of hydrostatics and optics, and some of the chief propositions of Sir Isaac Newton concerning light and colours.’

Keill's ‘Examination of Dr. Burnet's Theory of the Earth’ (Oxford, 1698) increased his reputation. He disproved Burnet's deductions and the similar hypothesis which Whiston had propounded earlier, while at the same time he refuted the notion of ‘vortices’ on which Descartes and others had based their systems. Incidentally he attacked Spinosa, Hobbes, and Malebranche, and vindicated the literal interpretation of the Mosaic account of the creation; he also applied Huyghens's theorems of centrifugal force to explain the figure of the earth. To a new edition, issued in 1724 in London, he appended a dissertation on the celestial bodies by Maupertuis (who was then in England).

After printing in 1699 a somewhat severe rejoinder to the replies of Burnet and Whiston, Keill was chosen deputy to Dr. Millington, Sedleian professor at Oxford, and seems to have joined Christ Church (ib. ii. 26). His lectures were from the first highly successful. They were printed in 1701 under the title ‘Introductio ad Veram Physicam,’ and became well known on the continent. Halley is said to have pointed out in a friendly way numerous errors in the first edition (ib. i. 90). Two additional lectures and many corrections were introduced into the second edition, published at Oxford in 1705. Other editions appeared in London in 1715, and at Cambridge in 1741. To a translation into English, published in 1736, Maupertuis, who suggested the venture, appended his theory of the ring of the planet Saturn. The ‘Introductio’ was considered Keill's ‘best performance,’ and was generally welcomed as an excellent introduction to the ‘Principia’ of Newton.

Disappointed of obtaining Gregory's chair at Oxford on his death in 1708, Keill apparently sought some post under government, and in 1709 he was appointed ‘treasurer of the Palatines,’ i.e. of the fund subscribed for refugees from the Palatinate. In this capacity he conducted the exiles to New England, and on his return in 1711 received vague promises of other preferment from Harley, the lord treasurer. After subsisting for nine months on Harley's bounty, he was offered in September the post of mathematician to the Venetian republic, and having informed his patron of the offer, was finally induced to decline it on being nominated ‘decypherer’ to Queen Anne, apparently after the death of William Blencowe in August 1712 (Letters of Eminent Lit. Men, Camden Soc., p. 349). His skill in deciphering manuscripts was accounted remarkable, but he only received 100l. a year, half his predecessor's income (cf. Cal. Treasury Papers, 1714–19, p. 180), and on 14 May 1716 he was superseded by Edward Willes (ib. p. 206). Meanwhile, in May 1712, Keill was unanimously elected to the coveted chair of astronomy, vacated by the death of Dr. John Caswell or Carswell, Gregory's successor, and on 9 July 1713 the degree of D.M. was conferred on Keill by the university.

Both as lecturer and writer Keill did much for the study of geometry. In 1715 he published ‘Euclidis Elementorum libri priores sex item undecimus & duodecimus’—urging, in the preface, the revival of the study of Euclid at Oxford and Cambridge. The book included an account of trigonometry and a good chapter on logarithms. In the same year appeared his ‘Trigonometriæ Elementa,’ and in 1718 his ‘Introductio ad Veram Astronomiam.’ The latter, consisting of his Savilian lectures, gives a sketch of the history of astronomy, and he reprinted it in English with many emendations, at the request of the Duchess of Chandos, in 1721.

Meanwhile Keill had become an active member of the Royal Society. Appointed clerk on 30 Nov. 1700, he was admitted a fellow on 25 April 1701, and became thenceforth a constant contributor to the ‘Philosophical Transactions,’ chiefly in support of Newton. In 1708 he wrote ‘On the Laws of Attraction,’ and papers followed ‘On the Laws of Centripetal Force’ (‘Phil. Trans. Abs.’ v. 417, 435), and ‘On the Newtonian Solution of Kepler's Problem’ (ib. vi. 1). Leibnitz had in 1705 accused Newton of plagiary in claiming to be the inventor of the fluxional calculus, and in 1708 Keill prepared a refutation of the charge. Until his death he was largely occupied in maintaining Newton's priority, and in seeking to show that Leibnitz had derived the fundamental ideas of his own differential calculus from papers by Newton, which had been communicated to him many years before by Collins and Oldenburg. Leibnitz, according to Keill, had merely changed the name and the notation (cf. Phil. Trans. 1708, p. 185).

Newton thoroughly believed in the truth of Keill's charges against Leibnitz, and on 5 April 1711, after Newton had given a short account of his invention, Keill was asked by the Royal Society ‘to draw up an account of the matter in dispute,’ and afterwards to send it to Leibnitz. Leibnitz replied contemptuously, and appealed to the registers of the society for evidence of the facts of the case. A committee of eleven persons was therefore appointed on 6 March 1712, and on 24 April gave in a report, which is known as the ‘Commercium Epistolicum,’ and was edited by Keill. Its conclusion ran: ‘We reckon Mr. Newton the first inventor, and are of opinion that Mr. Keill, in asserting the same, has been noways injurious to Mr. Leibnitz.’ In 1713 Keill published a reply in French to a defence of Leibnitz, which had appeared in the ‘Journal Littéraire de la Haye,’ and after the death of Leibnitz, 14 Nov. 1716, he repeatedly wrote in the same sense against Bernouilli and other champions of Leibnitz. In pursuing the controversy with Bernouilli, Keill sought to prove Bernouilli's plagiarism in a solution of the inverse problem of centripetal forces.

Keill died of a ‘violent fever’ at Oxford on Thursday, 31 Aug. 1721, a few days after entertaining ‘the vice-chancellor and other academic dignitaries at his house in Holywell Street with wine and punch,’ and was buried in St. Mary's Church on 2 Sept. at nine o'clock at night. Sir David Brewster, with Keill's private letters to Newton before him, ‘formed a high opinion both of his talents and character,’ and concluded that ‘everything he did was open and manly.’ He was personally popular in the university, and Hearne—no lenient critic—‘always found him to be a man of honesty’ and ingenuity (Macray, Annals of Bodleian Library, p. 188; Reliq. Hearn. ii. 136). He married Mary or Moll, daughter of James Clements, an Oxford bookbinder, a lady twenty-five years his junior, and held to be of very inferior rank. By her he left a son, who is said to have become a linendraper in London. But Keill possessed at his death a large fortune, chiefly inherited from his brother James. He made no will.

In 1742 an edition of Keill's Latin works was printed at Milan.

[Biog. Brit.; Reliquiæ Hearnianæ, ii. 135–6; Martin's Biog. Philos. p. 457; Brewster's Life of Newton, i. 341, ii. 81, &c.; Phil. Trans. ut supra; Rouse Ball's Hist. of Mathematics, pp. 329–30; Rigaud's Correspondence of Scientific Men, ii. 421–2.]

R. E. A.