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area of the Hyperbola at Boothby,1 in Lincolnshire, to two and fifty figures by the same method.

- Is. NEWTON."

In consequence of the devotion of his mind to these abstract studies, and his long continued observations upon a comet in 1664, which made him sit up late at night, Sir Isaac's health was impaired to such a degree, as Mr. Conduit informs us, that from this illness " he learnt to go to bed betimes.” In the beginning of the same year, on the 19th February, Sir Isaac's attention was directed to the subject of circles round the moon, by two coronas of three and five-and-a-half degrees each, accompanied by the halo of 22° 35', of which he subsequently gave the theory in his Treatise on Optics. In this year there were forty-four vacancies in the scholarships of Trinity College, and Newton was elected to one of them on the 28th of April. On this occasion he was examined in Euclid by Dr. Barrow, who formed an indifferent opinion of his knowledge, and hence he was led not only to read Euclid with care, but to form a more favourable estimate of the ancient geometer when he came to the interesting propositions on the equality of parallelograms on the same base and between the same parallels. In the month of January 1665, Newton took the degree of Bachelor of Arts, along with twenty-five other members of Trinity College, but we are not able to ascertain the academical rank which he held among the graduates, as the grace for

be given by Newton hiniself in the Phil. Truns., vol. vi. p. 3080. Rigaud's Hist. Essay on the first publication of Sir Isaac Newton's Principia, p. 1, note.

? A village in Lincolnsliire, near Sleaford), where Newton was probably on a visit. 2 This comet passed its perihelion on the 4th December at midnight. 3 Book II., Part IV., Obs. 13.

* Conduit's MSS.

that year does not contain the order of seniority of the Bachelors of Arts. The Proctors at this time were John Slader of Trinity, and Benjamin Pulleyn of Trinity, Newton's tutor, and the persons appointed in conjunction with them to examine the Questionists, were John Eachard of Catherine Hall, the satirical author of the Grounds, &c., of the Contempt of the Clergy, and Thomas Gipps of Trinity.1

In the same year Newton committed to writing his first discovery of Fluxions. This paper, written by his own hand, and dated May 20, 1665, represents in pricked letters the fluxions applied to their fluents, and in another leaf of the same waste book the method of fluxions is described without pricked letters, and bears the date of May 16, 1666. In the same book, with the date of November 13, 1665, there is another paper on Fluxions, with their application to the drawing of tangents, and “ the finding the radius of curvity of any curve.”2 In the month of October 1666, Newton drew up another small tract, in which the method of Fluxions is again put down without pricked letters, and applied to Equations involving facts or surds. 3

It was doubtless in the same remarkable year 1666, or perhaps in the autumn of 1665, that Newton's mind was first directed to the subject of Gravity. He appears to have left Cambridge some time before the 8th of August 1665, when the College was " dismissed” on account of the Plague, and it was therefore in the autumn of that year, and not in that of 1666, that the apple is said to have fallen from the tree at Woolsthorpe, and suggested to Newton the idea of gravity. When sitting alone in the garden, and speculating on the power of gravity, it occurred to him that as the same power by which the apple fell to the ground, was not sensibly diminished at the greatest distance from the centre of the earth to which we can reach, neither at the summits of the loftiest spires, nor on the tops of the highest mountains, it might extend to the moon and retain her in her orbit, in the same manner as it bends into a curve a stone or a cannon ball, when projected in a straight line from the surface of the earth. If the moon was thus kept in her orbit by gravitation to the earth, or, in other words, its attraction, it was equally probable, he thought, that the planets were kept in their orbits by gravitating towards the sun. i Kepler had discovered the great law of the planetary motions, that the squares of their periodic times were as the cubes of their distances from the sun, and hence Wewton drew the important conclusion that the force of gravity or attraction, by which the planets were retained in their orbits, varied as the square of their distances from the sun. Knowing the force of gravity at the earth's surface, he was, therefore, led to compare it with the force exhibited in the actual motion of the moon, in a circular orbit; but having assumed that the distance of the moon from the earth was equal to sixty of the earth's semidiameters, he found that the force by which the moon was drawn from its rectilineal path in a second of time was only 13:9 feet, whereas at the surface of the earth it was 16-1 in a second. This great discrepancy between his theory and what he then considered to be the fact, induced him

| Edleston's Correspondence, &c. &c., App. xxi, xlv.

2 Rigaud's Hist. Essay, &c., App. No. II. p. 20. From the Macclesfield MSS. Raphson Historia Fluxionum, Cap. I. p. 1, Cap. xiii. p. 92, and English Edition,

pp. 115, 116.

* These papers in the Macclesfield Collection are quoted by Newton himself in his Observations on Leibnitz's celebrated Letter to the Abbé Conti, dated 9th April 1716. See Raphson's Hist. of Fluxions, pp. 103 and 116.

to abandon the subject, and pursue other studies with which he had been previously occupied. 1

It does not appear from any of the documents which I have seen, at what time Newton made his first optical discoveries. On the authority of one of his memorandum books, containing an account of his expenses, it is stated by Conduit that he purchased a prism, in order to make some experiments on Descartes' Theory of Colours, and that he not only detected the errors of the French philosopher, but established his own views of the subject; but this is contradicted by Newton himself, who distinctly informs us that it was in the beginning of the year 1666, that he procured a glass prism“ to try therewith the phenomena of colours." 2

There is no evidence, however, that he used it for this purpose, and there is every reason to believe that he was not acquainted with the true composition of light when Dr. Barrow completed his Optical Lectures, published in 1669.3 In the preface of this work, Dr. Barrow acknowledges his obligation to his colleague Mr. Isaac Newton, as a man of a fine disposition and great genius, for having revised the MSS., and corrected several oversights, and made some additions of his own. Now, in the twelfth Lecture there are some observations on the nature and origin of colours, which are so erroneous and unphilosophical, that Newton could not have permitted his friend to publish them had he been then in the possession of their true theory. According to Barrow, who introduces the subject of colours as an unusual digression, White is that which discharges a copious light, scattered equally in every direction. Black is that which emits light not at all, or very sparingly. Red is that which emits light more condensed than usual, but interrupted by shady interstices. Blue is that which discharges a rarefied light, or one excited by a weaker force, as in bodies which consist of white and black particles arranged alternately, such, for example, as the clear ether in which there float fewer particles that reflect light, while the rest take away light, the sea in which the white salt is mixed with the black water, and the blue shadows seen at the same time by candle and day light, which are produced by the whiteness of the paper mixed with the faint light or blackness of the twilight. Yellow consists of much white and a little red interspersed, and Purple of much blue and some red. Green seems to have puzzled Dr. Barrow. He says that it is somehow allied to Blue; but he adds, let wiser men find out the difference, I dare not conjecture. These opinions are so unsound, that they could not fail to have attracted the attention of Newton, who had certainly begun to study the subject of colours ; and if he had discovered at this time that white was a

1 Neither Pemberton nor Whiston, who received from Newton himself the History of his first Ideas of Gravity, records the story of the falling apple. It was mentioned, however, to Voltaire by Catherine Barton, Newton's niece, and to Mr. Green by Martin Folkes, the President of the Royal Society. We saw the apple tree in 1814, and brought away a portion of one of its roots. The tree was so much decayed that it was taken down in 1820, and the wood of it carefully preserved by Mr. Turnor of Stoke Rocheford. See Voltaire's Philosophie de Newton, 3me part. Chap. III. Green's Philosophy of Expansive and Contractive Forces, p. 972, and Rigaud's Hist. Essay, p. 2.

2 Phil. Trans. vol. vi. p. 3075.

3 “Verum quod tenellæ matres factitant, a me depulsum partum amicorum haud recusantium nutriciæ curæ commisi, prout ipsis visum esset, educandum aut exponendum, quorum unus (ipsos enim honestum duco nominatim agnoscere) D. Isaacus Newtonus, collega noster (peregregiæ vir indolis ac insignis peritiæ) exemplar revisit, aliqua corrigenda monens, sed et de suo nonulla penu suggerens quæ nostris alicubi cum laude innexa cernes. The other friend was John Collins, whom he calls the Mersennus of our nation. Epist, al Lectorem. The imprimatur of this volume is dated March 1668-9.

| The addition by Newton is a singularly elegant and expeditious method at the end of Lect. xiv., of determining geometrically in every case, the image former by lenses, and describing the lens which projects the image on a given point.

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