praised, it was little read. The style was concise even to obscurity. A requisite and excellent commentary was, however, furnished by Dr. Walmesley in 1753 (Analyse des Mesures, des Rapports, et des Angles). Cotes's ‘theorem of harmonic means,’ discovered by Smith among his papers, and communicated to Maclaurin, was made the basis of the latter's treatise, ‘De linearum geometricarum proprietatibus generalibus’ (London, 1720).
Smith announced his intention of publishing further papers by Cotes on arithmetic, the resolution of equations, dioptrics, and the nature of curves, but it remained unfulfilled. Only in his own work on optics he founded a chapter (ch. v. book ii.) on a ‘noble and beautiful theorem,’ stated to have been the last invention of his lamented relative. He edited, moreover, in 1738, his ‘Hydrostatical and Pneumatical Lectures,’ issued for the third time in 1775, and translated into French by Lemonnier in 1740 under the title ‘Leçons de Physique Expérimentale.’ The course of experiments for which they were composed, begun at Cambridge by Cotes and Whiston conjointly, 5 May 1707, was among the earliest of its kind given in England. Twelve lectures were written by each of the partners, and were repeated by Whiston and Hauksbee in London, and, in part, by Smith at Cambridge. The publication of Cotes's set was finally compelled by the prospect of a surreptitious edition. Whiston considered his own so inferior that he could never prevail upon himself to print them.
A ‘Description of the Great Meteor,’ a brilliant aurora, ‘which was on the 6th of March 1716 sent in a letter from the late Rev. Mr. Roger Cotes to Robert Dannye, D.D., rector of Spofferth in Yorkshire,’ was included in the ‘Philosophical Transactions’ for 1720 (xxxi. 66). Cotes's zeal for practical astronomy only waited opportunity for full development. He remodelled Flamsteed's and Cassini's solar and planetary tables, and had undertaken to construct tables of the moon on Newtonian principles; while his description of a heliostat-telescope furnished with a mirror revolving by clockwork (Corr. of Newton and Cotes, p. 198) showed that he had already in 1708 (independently, it is probable, of Hooke's project of 1674), anticipated the system of equatorial mounting.
[Biog. Brit. (Kippis); Phil. Trans. Abridg. vi. 77 (1809); Gen. Dict. iv. 441 (1736); Nichols's Lit. Anecd. ii. 126; Nichols's Leicestershire, iv. 35, 472; Knight's Life of Colet, p. 429; Monk's Life of Bentley, passim; Whiston's Memoirs, pp. 133–5; Edleston's Correspondence of Newton and Cotes; Rigaud's Correspondence of Scientific Men, i. 257–70; Smith's Pref. to Harmonia Mensurarum; Cole's Athenæ Cantab. Add. MS. 5865, f. 53; Hutton's Mathematical Dict. (1815), Introduction to Math. Tables, p. 112, and Math. Tracts, i. 437; Montucla's Hist. des Mathématiques, iii. 149; Suter's Gesch. der math. Wissenschaften, ii. 133; Nouvelles Annales de Math. ix. 195 (1850); Delambre, Hist. de l'Astronomie au xviiie Siècle, p. 449; Marie's Hist. des Math. vii. 222.]
COTES, SAMUEL (1734–1818), miniature painter, was third son of Robert Cotes, mayor of Galway, who settled in London, adopting the medical profession, and married Elizabeth, daughter of Francis Lynn, chief secretary to the Royal African Company, by whom he was the father of Francis Cotes [q. v.] and Samuel. The latter was brought up by his father to the medical profession, but was encouraged by his brother's great success as a painter to throw over medicine for the fine arts. He received instruction from his brother, who greatly assisted him; and though he never attained the eminence his brother succeeded in doing, he became deservedly and highly esteemed as a portrait painter, and was reckoned the first miniature painter of his time. His crayon portraits were also much admired. He painted in miniature both on enamel and on ivory, and exhibited from 1760 to 1789 at the exhibitions of the Incorporated Society of Artists, of which he was a fellow, and at the Royal Academy. During this time he resided at 25 Percy Street, Rathbone Place. He was devotedly attached to his brother, and after the latter's death he painted a large miniature of him from memory. Cotes retired from active life some years before his death, and then resided in Paradise Row, Chelsea, where he died 7 March 1818 in his eighty-fifth year. He was twice married, first to a Miss Creswick, and secondly to Miss Sarah Shepherd, a lady of great attainments, especially as an artist, who died 27 Sept. 1814, aged 76. A portrait by him of Mrs. Yates, as Electra, was engraved in mezzotint by Philip Dawe, and a portrait of Thomas Pownall, governor of New Jersey, was similarly engraved by Richard Earlom.
[Redgrave's Dict. of English Artists; Gent. Mag. (1814) lxxxiv. 403, (1818) lxxxviii. 276; Edwards's Anecdotes of Painting; Chaloner Smith's Catalogue of British Mezzotinto Portraits; Catalogues of the Royal Academy and the Incorporated Society of Artists.]
COTGRAVE, JOHN (fl. 1655), probably related to Randle Cotgrave [q. v.], and a member of the Cheshire family of Cotgreve,
