NEWTON, Sir Isaac (1642-1727), the greatest of natural philosophers, was born on the 25th of December 1642 (o.s.), at Woolsthorpe, a hamlet in the parish of Colsterworth, Lincolnshire, about 6 miles from Grantham. His father (also Isaac Newton) was the farmer of a small freehold property of his own. He died before his son’s birth, a few months after his marriage to Hannah Ayscough, a daughter of James Ayscough of Market-Overton. When Newton was little more than two years old his mother married Mr Barnabas Smith, rector of the neighbouring parish of North Witham. Of this marriage there was issue, Benjamin, Mary, and Hannah Smith, and to their children Sir Isaac Newton subsequently left the greater part of his property. After having acquired the rudiments of education at two small schools in hamlets in close proximity to Woolsthorpe, Newton was sent at the age of twelve to the grammar school of Grantham, the headmaster of which was Mr Stokes. While attending Grantham school Newton lived in the house of Mr Clark, an apothecary of that town. According to his own confession he was far from industrious, and stood very low in his class. An unprovoked attack from the boy next above him led to a fight, in which Newton’s pluck gave him the victory. This success seems to have led him to greater exertions in school, and after some time he rose to be the head boy of the school. He cared but little for the ordinary amusements of his schoolfellows, but he displayed very early a taste and an aptitude for mechanical contrivances. He made windmills, water-clocks, kites, and dials, and he is said to have invented a four-wheeled carriage which was to be moved by the rider. In 1656 Mr Smith died, and Newton’s mother came back with her three children to Woolsthorpe. Newton was then in ...his fifteenth year, and, as his mother in all probability intended him to be a farmer, he was taken away from school. He was frequently sent on market days to Grantham with an old and trusty servant, who made all the purchases, while Newton spent his time among the books in Mr Clark’s house. It soon became apparent to Newton’s relatives that they were making a great mistake in attempting to turn him into a farmer, and he was therefore sent back again to school at Grantham. His mother’s brother, Mr W. Ayscough, the rector of the next parish, was a graduate of Trinity College, Cambridge, and when he found that Newton’s mind was wholly devoted to mechanical and mathematical problems; he· urged upon Mrs Smith the desirability of sending her son to his own college, a proposal to which she was not at all unwilling to give her consent. He was accordingly admitted a member of Trinity College on June 5, 1661, as a subsizar, and was matriculated on July 8. We have scarcely any information as to his attainments when he commenced residence, and very little as to his studies at the university before he took the degree of bachelor of arts. It is known that while still at Woolsthorpe Sanderson’s Logic, a book which his uncle had given him, had been read by him to such purpose that his tutor at Trinity College excused his attendance at a course of lectures on that subject. Newton tells us himself that, when he had purchased a book on astrology at Stourbridge fair, a fair held close to Cambridge, he was unable, on account of his ignorance of trigonometry, to understand a figure of the heavens which was drawn in this book. He therefore bought an English edition of Euclid with an index of propositions at the end of it, and, having turned to two or three which he thought likely to remove his difficulties, he found them so self-evident that he expressed his astonishment that any one should have taken the trouble to offer demonstrations of them. He therefore put aside Euclid “as a trifling book,” and applied himself to the study of Descartes’s Geometry. He had some difficulty in mastering this work, but he succeeded in doing so without any assistance. It is reported that in his examination for a scholarship at Trinity, to which he was elected on April 28, 1664, he was examined in Euclid by Dr Barrow, who formed a poor opinion of his knowledge, and that in consequence Newton was led to read the Elements again with care, and thereby to form a more favourable estimate of Euclid’s merits.
The study of Descartes’s Geometry seems to have inspired Newton with a love of the subject, and to have introduced him to the higher mathematics. In a small commonplace book, bearing on the seventh page the date of January 1663-4, there are several articles on angular sections, and the squaring of curves and “crooked lines that may be squared,” several calculations about musical notes, geometrical propositions from Francis Vieta and Schooten, annotations out of Wallis’s Arithmetic of Infinites, together with observations on refraction, on the grinding of “spherical optic glasses,” on the errors of lenses and the method of rectifying them, and on the extraction of all kinds of roots, particularly those “in affected powers.” And in this same commonplace book the following entry made by Newton himself, many years afterwards, gives a further account of the nature of his work during the period when he was an undergraduate:—
“July 4, 1699.—By consulting an account of my expenses at Cambridge, in the years 1663 and 1664, I find that in the year 1664, a little before Christmas, I, being then Senior Sophister, bought Schooten’s Miscellanies and Cartes’ Geometry (having read this Geometry and Oughtred’s Clavis clean over half a year before), and borrowed Wallis’s works, and by consequence made these annotations out of Schooten and Wallis, in winter between the years 1664 and 1665. At such time I found the method of Infinite Series; and in summer 1665, being forced from Cambridge by the plague, I computed the area of the Hyperbola at Boothby, in· Lincolnshire, to two and fifty figures by the same method.”
That Newton must have begun early to make careful observations of natural phenomena is sufficiently testified by the following remarks about halos, which appear in his Optics, book ii. part iv. obs. 13:—
“The like Crowns appear sometimes about the moon; for in the beginning of the Year 1664, February 19th, at night, I saw twosuch Crowns about her. The Diameter of the first or innermost was about three Degrees, and that of the second about five Degrees· and an half. Next about the moon was a Circle of white, and next about that the inner Crown, which was of a bluish green within next the white, and of a yellow and red without, and next about these Colours were blue and green on the inside of the Outward Crown, and red on the outside of it. At the same time there appear’d a Halo about 22 Degrees 35' distant from the center of the moon. It was elliptical, and its long Diameter was perpendicular to the Horizon, verging below farthest from the moon.”
In the month of January 1665 Newton took the degree-of bachelor of arts. The persons appointed (in conjunction with the proctors, John Slade of Catharine Hall, and Benjamin Pulleyn of Trinity College, Newton’s tutor) to examine the questionists were John Eachard of Catharine Hall and Thomas Gipps of Trinity College. It is a curious accident that we have no information about the respective merits of the candidates for a degree in this year, as the “ordo senioritatis” of the bachelors of arts for the year is omitted in the “Grace Book.”
It is supposed that it was in 1665 that the method of fluxions first occurred to Newton’s mind. There are several papers still existing in Newton’s handwriting bearing dates 1665 and 1666 in which the method is described, in some of which dotted or dashed letters are used to represent fluxions, and in some of which the method is explained without the use of dotted letters.
Both in 1665 and in 1666 Trinity College was dismissed on account of the plague. On each occasion it was agreed, as appears by entries in the “Conclusion Book” of the college, bearing dates August 7, 1665, and June 22, 1666, and signed by the master of the college, Dr Pearson, that all fellows and scholars who were dismissed on account of the pestilence be allowed one month’s commons. Newton must have left college before August 1665, as his name does not appear in the list of those who received extra commons on that occasion, and he tells us himself in the extract from his commonplace book already quoted that he was “forced from Cambridge by the plague” in the summer of that year.
Newton was elected a fellow of his college on October 1, 1667. There were nine vacancies, one of which was caused by the death of Cowley in the previous summer, and the nine successful candidates were all of the same academical standing. A few weeks after his election to a fellowship Newton went to Lincolnshire, and did not return to Cambridge till the February following. On the 16th of March 1668 he took his degree of Μ. A.
During the years 1666 to 1669 Newton’s studies were of a very varied kind. It is known that he purchased prisms and lenses on two or three several occasions, and also chemicals and a furnace, apparently for chemical experiments; but he also employed part of his time on the theory of fluxions and other branches of pure mathematics. He wrote a paper Analysis per Equationes Numero Terminorum Infinitas, which he put, probably in June 1669, into the hands of Isaac Barrow (then a fellow of Trinity College, and the first occupant of the Lucasian chair of mathematics), at the same time giving him permission to communicate the contents to their common friend Mr John Collins, a mathematician of no mean order, and a correspondent of many of the eminent men of his time. Barrow did this on the 31st of July 1669, but kept the name of the author a secret, and merely told Collins that he was a friend staying at Cambridge, who had a powerful genius for such matters, and expressed a hope that the paper would not a little delight him. In a subsequent letter on the 20th of August, Barrow expressed his pleasure at hearing the favourable opinion which Collins had formed of the paper, and added, “the name of the author is Newton, a fellow of our college, and a young man, who is only in his second year since he took the degree of master of arts, and who, with an unparalleled genius (eximio quo est acumine), has made very great progress in this branch of mathematics.” Shortly afterwards Barrow, who had resolved to devote his attention to theological in preference to mathematical studies, resigned the Lucasian chair, and was instrumental in securing Newton’s election as his successor. Newton was elected Lucasian professor on the 29 th of October 1669. It was his duty as professor to lecture at least once a week in term time on some portion of geometry, arithmetic, astronomy, geography, optics, statics, or some other mathematical subject, and also for two hours in the week to allow an audience to any student who might come to consult with the professor on any difficulties he had met with. The subject which Newton chose for his lectures was optics. He gave courses of lectures on this subject, and the success which attended his researches in optics must have been great. The results of his investigations, however, were known only through his own oral lectures, and were not published until he presented an account of them to the Royal Society in the spring of 1672. On December 21, 1671, he was proposed as a candidate for admission into the Royal Society by Dr Seth Ward, bishop of Salisbury, and on January 11, 1672, he was elected a fellow of the Society. At the meeting at which Newton was elected a description of a reflecting telescope which he had invented was read, and “it was ordered that a letter should be written by the secretary to Mr Newton to acquaint him of his election into the Society, and to thank him for the communication of his telescope, and to assure him that the Society would take care that all right should be done him with respect to this invention.”
In his reply to the secretary on January 18, 1672, Newton writes :—
“I desire that in your next letter you would inform me for what time the society continue their weekly meetings; because, if they continue them for any time, I am purposing them to be considered of and examined an account of a philosophical discovery, which induced me to the making of the said telescope, and which I doubt not but will prove much more grateful than the communication of that instrument, being in my judgment the oddest if not the most considerable detection which hath hitherto been made into the operations of nature.”
The promise here made was fulfilled in a communication which Newton addressed to Oldenburg, the secretary of the Royal Society, on February 6, 1672, and which was read before the Society two days afterwards. The whole is printed in No. 80 of the Philosophical Transactions, and the first part of it has been already printed in the article Light, voL xiv. p. 590. After explaining his discovery of the composition of white light, he proceeds:—
“When I understood this, I left off my aforesaid Glass works; for I saw, that the perfection of Telescopes was hitherto limited, not so much for want of glasses truly figured according to the prescriptions of Optick Authors (which all men have hitherto imagined), as because that Light it self is a Heterogeneous mixture of differently refrangible Rays. So that, were a glass so exactly figured as to collect any one sort of rays into one point, it could not collect those also into the same point, which having the same Incidence upon the same Medium are apt to suffer a different refraction. Nay, I wondered, that seeing the difference of refrangibility was so great, as I found it, Telescopes should arrive to that perfection they are now at.”
He then points out why
‘ ‘ The object-glass of any Telescope cannot collect all the rays which come from one point of an object, so as to make them convene at its focus in less room than in a circular space, whose diameter is the 50th part of the Diameter of its Aperture: which is an irregularity some hundreds of times greater, than a circularly figured Lens, of so small a section as the Object-glasses of long Telescopes are, would cause by the unfitness of its figure, were Light uniform"·, and he adds—
“This made me take reflections into consideration, and finding them regular, so that the Angle of Reflection of all sorts of Rays was equal to their Angle of Incidence; I understood, that by their mediation Optick instruments might be brought to any degree of perfection imaginable, provided a Reflecting substance could be found, which would polish as finely as Glass, and reflect as much light, as glass transmits, and the art of communicating to it a Parabolick figure be also attained. But these seemed very great difficulties, and I have almost thought them insuperable, when I further considered, that every irregularity in a reflecting superficies makes the rays stray 5 or 6 times more out of their due course, than the like irregularities in a refracting one; so that a much greater curiosity would be here requisite, than in figuring glasses for Refraction.
“Amidst these thoughts I was forced from Cambridge by the Intervening Plague, and it was more than two years before I proceeded further. But then having thought on a tender way of polishing, proper for metall, whereby, as I imagined, the figure also, would be corrected to the last; I began to try, what might be effected in this kind, and by degrees so far perfected an Instrument (in the essential parts of it like that I sent to London), by which I could discern Jupiters 4 Concomitants, and shewed them divers times to two others of my acquaintance. I could also discern the Moon-like phase of Venus, but not very distinctly, nor without some niceness in disposing the Instrument.
“From that time I was interrupted till this last Autumn, when I made the other. And as that was sensibly better than the first (especially for Day-Objects), so I doubt not, but they will be still brought to a much greater perfection by their endeavours, who, as you inform me, are taking care about it at London.”
Then, after a remark that microscopes seem as capable of improvement as telescopes, he adds—
‘ ‘ I shall now proceed to acquaint you with another more notable difformity in its Rays, wherein the Origin of Colour is unfolded: Concerning which I shall lay down the Doctrine first, and then, for its examination, give you an instance or two of the Experiments, as a specimen of the rest.
‘ ‘ The Doctrine you will find comprehended and illustrated in the following propositions :—
“1. As the Rays of light differ in degrees of Refrangibility, so they also differ in their disposition to exhibit this or that particular colour. Colours are not Qualifications of Light, derived from Refractions, or Reflections of natural Bodies (as ’ tis generally believed), but original and connate properties, which in divers Rays are divers. Some Rays are disposed to exhibit a red colour and no other; some a yellow and no other, some a green and no other, and so of the rest. Nor are there only Rays proper and particular to the more eminent colours, but even to all their intermediate gradations.
“2. To the same degree of Refrangibility ever belongs the same colour, and to the same colour ever belongs the same degree of Refrangibility. The least Refrangible Rays are all disposed to exhibit a Red colour, and contrarily those Rays, which are disposed to exhibit a Red colour, are all the least Refrangible: So the most refrangible Rays are all disposed to exhibit a deep Violet Colour, and contrarily those which are apt to exhibit such a violet colour are all the most Refrangible.
“And so to all the intermediate colours in a continued series belong intermediate degrees of refrangibility. And this Analogy ’ twixt colours, and refrangibility is very precise and strict; the Rays always either exactly agreeing in both, or proportionally disagreeing in both.
“3. The species of colour, and degree of Refrangibility proper to any particular sort of Rays, is not mutable by Refraction, nor by Reflection from natural bodies, nor by any other cause, that I could yet observe. When any one sort of Rays hath been well parted from those of other kinds, it hath afterwards obstinately retained its colour, notwithstanding my utmost endeavours to change it. I have refracted it with Prismes, and reflected it with Bodies, which in Day-light were of other colours; I have intercepted it with the coloured film of Air interceding two compressed plates of glass, transmitted it through coloured Mediums, and through Mediums irradiated with other sorts of Rays, and diversly terminated it; and yet could never produce any new colour out of it. It would by contracting or dilating become more brisk, or faint, and by the loss of many Rays, in some cases very obscure and dark; but I could never see it changed in specie.
“Yet seeming transmutations of Colours maybe made, where there is any mixture of divers sorts of Rays. For in such mixtures, the component colours appear not, but, by their mutual allaying each other constitute a midling colour.”
Further on, after some remarks on the subject of compound colours, he says—
“I might add more instances of this nature, but I shall conclude with this general one, that the Colours of all natural Bodies have no other origin than this, that they are variously qualified to reflect one sort of light in greater plenty then another. And this I have experimented in a dark Room by illuminating those bodies with uncompounded light of divers colours. For by that means any body may be made to appear of any colour. They have there no appropriate colour, but ever appear of the colour of the light cast upon them, but yet with this difference, that they are most brisk and vivid in the light of their own day-light colour. Minium appeareth there of any colour indifferently, with which ’ tis illustrated, but yet most luminous iu red, and so Bise appeareth indifferently of any colour with which ’ tis illustrated, but yet most luminous in blew....
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