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 Treasury Papers, 1714–19, p. 180), and on 14 May 1716 he was superseded by Edward Willes (ib.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.]
KEILWAY, KELLWAY, or KAYLWAY, ROBERT (1497–1581), legal reporter, was in 1543 the recipient of a grant of the wardship and marriage of Eliz. and Anne Whittocksmede (Pat. Roll, 35 Henry VIII, p. 2), and subsequently of many other minors, a privilege from which he no doubt reaped considerable profit. In 1547 he was autumn
