COTES, ROGER (1682–1716), mathematician, was the second son of the Rev. Robert Cotes, rector of Burbage in Leicestershire, where he was born 10 July 1682. His mother, Grace, daughter of Major Farmer of Barwell in the same county, was connected with the noble family of the De Greys. Before the age of twelve he discovered, while at Leicester school, so marked an aptitude for mathematics, that his uncle, the Rev. John Smith, took him to his house in Lincolnshire, that he might personally forward his studies. Removed to St. Paul's School, London, he made rapid progress in classics under Dr. Gale, then head-master, while keeping up a scientific correspondence with his uncle, portions of which have been preserved and published (Correspondence of Newton and Cotes, p. 190 et seq.) He was admitted a pensioner of Trinity College, Cambridge, 6 April 1699, was chosen fellow at Michaelmas 1705, and acted as tutor to his relatives, the sons of the Marquis, afterwards Duke, of Kent. In the following year he proceeded M.A., having taken a degree of B.A. in 1702. While still an undergraduate, his extraordinary proficiency in science had attracted the notice of Dr. Bentley, the master of his college. Bentley introduced him to Newton and Whiston, whose testimonials in his favour, combined with Bentley's influence, procured his election, in January 1706, to the new professorship of astronomy and natural philosophy founded by Dr. Plume, archdeacon of Rochester, then recently dead. Whiston, who, as occupant of the Lucasian chair, was one of the electors, thus describes his share in the transaction: ‘I said that I pretended myself to be not much inferior in mathematics to the other candidate's master, Dr. Harris, but confessed that I was a child to Mr. Cotes; so the votes were unanimous for him’ (Whiston, Memoirs, p. 133).
The project of founding, with his co-operation, a first-class astronomical observatory in Trinity College was now eagerly embraced by Bentley. He raised a subscription for its erection over the King's Gate, and obtained a college order, assigning the chambers there in perpetuity to the Plumian professor. Here, accordingly, during the remaining decade of his life, Cotes dwelt with his cousin, Robert Smith, whom he chose as his assistant; and here his lectures were delivered. He did not live to see the observatory finished, and it was demolished in 1797. A brass sextant of five feet radius, constructed by Rowley at a cost of 150l., was part of its equipment; Newton contributed a fine pendulum clock; and a transit instrument was in hand early in 1708 (Corr. of Newton and Cotes, p. 198). The total solar eclipse of 22 April (O.S.) 1715 furnished Cotes with the opportunity of making his only recorded astronomical observation, relative to which Halley communicated the following particulars to the Royal Society:—
‘The Rev. Mr. Roger Cotes at Cambridge had the misfortune to be opprest by too much company, so that, though the heavens were very favourable, yet he missed both the time of the beginning of the eclipse and that of total darkness. But he observed the occultations of the three spots … also the end of total darkness, and the exact end of the eclipse’ (Phil. Trans. xxix. 253).
His description and drawing, however, of the sun's corona, transmitted 12 May to Newton, amply compensate some technical shortcomings. A brilliant ring, about one-sixth the moon's diameter, was perceived by him superposed upon a luminous cross, the longer and brighter branches of which lay very nearly in the plane of the ecliptic. The light of the shorter (polar) arms was so faint as not to be constantly visible (Corr. of Newton and Cotes, pp. 181–4). This is precisely the type of corona seen in 1867 and 1878, and associated therefore with epochs of sunspot minimum. But spots were numerous in 1715, so that Cotes's observation goes far to disprove the supposed connection.
In the beginning of 1709 Bentley at length persuaded Newton, by the offer of assistance from Cotes, to consent to a reissue of the ‘Principia.’ It was not, however, until September that a corrected copy of the work was placed in the hands of the new editor, when the remarkable correspondence between him and Newton ensued, preserved in the original in the library of Trinity College, and published by Mr. Edleston in 1850. It must be admitted that the younger man's patience was often severely tried by Newton's long cogitations over the various points submitted to him; but it proved imperturbable. ‘I am very desirous,’ he wrote to Sir William Jones, 30 Sept. 1711, ‘to have the edition of Sir Isaac Newton's “Principia” finished, but I never think the time lost when we stay for his further corrections and improvements’ (Corr. of Newton and Cotes, p. 209). Of all his contemporaries, Cotes possessed the strongest and clearest grasp of the momentous principles enunciated by his author. He suggested many rectifications and improvements, for the most part adopted by Newton. The frequently interrupted process of printing occupied some three and a half years. Cotes's preface, an able defence of the Newtonian
