subject which forms the principal part of his posthumous work, entitled Harmonia Mensurarum, edited in 1722 by his cousin, Dr. Robert Smith. In 1716, he communicated to the Society an account of the great fiery meteor seen on the 6th March of that year, but it is obvious from his description of it that it was only an Aurora Borealis. In a few weeks after he wrote this communication to the Society, he was seized with fever, and, after a relapse, accompanied with violent diarrhoea and constant delirium, he died on the 5th June 1716, amid the deep regrets of the University and the scientific world. When Newton received the sad intelligence of the loss of his friend, he made the memorable observation, "If Mr. Cotes had lived we might have known something." A short time before his death, when he was only in his thirtysecond year, he demonstrated the beautiful optical theorem, that "the magnitude of the image of an object seen through any number of lenses is to that of the object itself, as the distance of the image from the eye is to the apparent distance of the object.”1 In 1722, there appeared the Epistola ad Amicum de Cotesii Inventis, addressed to Mr. James Wilson, by Henry Pemberton, and an Appendix, bearing the date of May 1822. Beside some tracts in Latin, which have not been published, he left behind him a course of lectures on Hydrostatics and Pneumatics, which was published by Dr. Smith in 1738. In Mr. Edleston's Correspondence, he has published twenty-four letters from Cotes to his friends, from one of which it appears that he had anticipated S'Gravesende in the invention of the Heliostate.2 Cotes was interred in the chapel of Trinity College, and the following beautiful and much admired inscription on his monument, was written by Dr. Bentley. 1 See Smith's Optics, vol. i. p. 191, cor. 19; and vol ii., Remarks, p. 76. 2 Mr. Edleston refers to the Register of the Royal Society for evidence, that Hooke and Halley had previously invented the Heliostate. The first publication, however, of the invention, is due to the Dutch philosopher.-See S'Gravesende's Physices Elem. Math. vol. ii. p. 715, ? 2660, Tab. 84, 85. Edit. 1742. H. S. E. ROGERUS ROBERTI FILIUS COTES, Hujus Collegii S. Trinitatis Socius, Et Astronomiæ et Experimentalis Philosophiæ Professor Plumianus ; Qui immatura morte præreptus, Pauca quidem ingenii sui Pignora reliquit, Sed egregia, sed admiranda, Cui ad summam doctrinæ laudem Natus Burbagii In agro Leicestriensi Jul. x. MDCLXXXII. No. XI. (Referred to in page 340, as No. XIII.) THE great interest excited by the Principia even among persons who were not qualified by their mathematical knowledge to comprehend it, led some individuals of active and powerful minds to acquire as much geometrical and analytical knowledge as would enable them to understand and appreciate the leading truths which Newton had discovered. Dr. Bentley, as we have already seen, was anxious to expound the discoveries of Newton 1 in a popular form, and to adduce them as proofs of the wisdom and benevolence of the Deity; and having resolved to study the work which contained them, he applied, through his friend, Mr. William Wotton,2 to John Craige, an able Scotch mathema 1 Dr. Monk is of opinion that Bentley had previously attended Newton's lectures. "The true system of the universe," he says, "and the proper methods of philosophical investigation, had not become public by the writings of Newton, but the light of the Newtonian discoveries was partially revealed to Cambridge before the rest of the world by the lectures of the philosopher himself, delivered in the character of the Lucasian Professor. These Bentley had an opportunity of attending; and that he did not neglect it, I am induced to believe, by his selection of the Newtonian discoveries as a prominent subject of his Boyle's Lectures, and his familiarity with the train of reasoning by which they are established.”—Monk's Life of Bentley, pp. 6, 7. 2 William Wotton, the friend of Bentley and of Craige, was a very remarkable person; and Dr. Monk informs us that he was the only one of Bentley's contemporaries with whom he maintained a friendship in after life. "He was," adds Dr. Monk, "the able antagonist of Sir W. Temple on the controversy On Ancient and Modern Learning.' As their combined efforts on that occasion have associated together the names of Wotton and Bentley, it is right to take some notice of the former, who, when he entered the University, was a child, and presents the best authenticated instance of a juvenile prodigy that I have ever found upon record. It is certified by the testimony not of one, but many persons of sense and learning, that at six years of age he was able to read and translate Latin, Greek, and Hebrew; to which at seven he added some knowledge of the Arabic and Syriac. On his admission at Catherine Hall, in his tenth year, the Master, Dr. Eachard, the antagonist of Hobbes, recorded Gulielmus Wotton, infra decem annos, nec Hammondo nec Grotio secundus.' This surprising proficiency during his academical career is testified by some of the best scholars of that day. When he proceeded Bachelor of Arts, he was acquainted with twelve languages, and, as tician, for a list of works which should be read in order to understand the Principia. Alarmed with the long list of authors sent him by Craige on the 24th June 1691, Bentley seems to have applied to Newton himself, from whom he received the following directions. Mr. Edleston thinks that the date of it is probably about July 1691: Directions given by Newton to Bentley respecting the books necessary to be read before studying the Principia.1 "Next after Euclid's Elements the Elements of ye Conic sections are to be understood. And for this end you may read either the first part of ye Elementa Curvarum of John De Witt, or De la Hire's late treatise of ye conick sections, or Dr Barrow's Epitome of Apollonius. "For Algebra read first Barth{olin's introduction, & then peruse such Problems as you will find scattered up & down in ye Commentaries on Cartes's Geometry & other Algebraical {sic} writings of Francis Schooten. I do not mean yt you should read over all those Commentaries, but only ye solutions of such Problems as you will here & there meet with. You may meet with De Witt's Elementa Curvarum & Bartholin's Introduction bound up together wth Carte's Geometry & Schooten's Commentaries. "For Astronomy read first ye short account of ye Copernican System in the end of Gassendus's Astronomy & then so much of Mercator's Astronomy as concerns ye same system & the new discoveries made in the heavens by Telescopes in the Appendix. “These are sufficient for understanding my book: but if you can procure Hugenius's Horologium Oscillatorium, the perusal of that will make you much more ready. there was no precedent of granting that degree to a boy of thirteen, Dr. H. Gower, one of the Caput, thought fit to put upon record a notice of his proficiency in every species of literature, as a justification of the University.”—Monk's Life of Bentley, pp. 7, 8; see also Nichol's Literary Anecdotes, vol. iv. pp. 253-259. 1 We have given this paper exactly as it is printed in Mr. Edleston's Correspondence, &c., pp. 273, 274. It is copied from the original, presented, along with the original MSS. of Newton's four celebrated letters to Bentley, by his grandson, Richard Cumberland, to Trinity College.-Cumberland's Memoirs, vol. i. p. 94. “At yo first perusal of my Book it's enough if you understand ye Propositions wth some of ye Demonstrations wch are easier then the rest. For when you understand ye easier they will afterwards give you light into ye harder. When you have read ye first 60 pages, pass on to ye 3d Book & when you see the design of that you may turn back to such Propositions as you shall have a desire to know, or peruse the whole in order if you think fit." The following memorandum is written upon the MS. by Bentley : "Directions from Mr Newton by his own Hand." Directions given by John Craige for understanding the Principia The course of reading proposed by John Craige for understanding the Principia, is much more extensive than that of Newton. It is published in Bentley's Correspondence,1 in a very interesting letter addressed to William Wotton, which, we have no doubt, will be gratifying to some of our readers :— “SIR, WINDSOR, 24 June, 1691. "I would have sent you this line before this, if I had thought you had returned from Cambridge. You may tell your Friend that nothing less than a thorough knowledge of all that is yet known in the most curious parts of Mathematicks can make him capable to read Mr. Newton's book with that advantage which I believe he proposes to himself. Upon this account, then, it may justly seem a very undecent piece of vanity to undertake to give a method for reading a book that involves so much in it, and so far above my strength; however, in compliance with your desire, I shall give you that which appears to me to be the shortest and most proper method for such an end. "Next to Euclid's Elements, let him apply himself to the Conick Sections, for which he need only read De Witt's First Book De Elementis Linearum Curvarum; but let him not meddle with the Second, which treats of the Loca Geometrica. See vol. ii. pp. 736-740; and vol. i. p. xxxii. 1 VOL. I. 2 G |