Sir Isaac Newton

Sir Isaac Newton (1642-1727), English natural philosopher, was born on the 25th of December 1642 (o.s.), at Woolsthorpe, a hamlet in the parish of Colsterworth, Lincolnshire, about 6 m. from Grantham. His father (also Isaac Newton) who farmed a small freehold property of his own, 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 Barnabas Smith, rector 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 close to Woolsthorpe, Newton was sent at the age of twelve to the grammar school of Grantham. 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, and he rose to be the head boy of the school. 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, William Ayscough, the rector of Burton Coggles, 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. He was accordingly admitted a member of Trinity College on the 5th of June 1661, as a subsizar, and was matriculated on the 8th of July. We have scarcely any information as to his attainments when he commenced residence, and very little as to his studies as an undergraduate. It is known that while still at Woolsthorpe Sanderson's Logic 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 selfevident that he put aside Euclid " as a trifling book," and applied himself to the study of Descartes's Geometry. It is reported that in his examination for a scholarship at Trinity, to which he was elected on the 28th of April 1664, he was examined in Euclid by Dr Isaac 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 1663/1664, 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 Frans van Schooten, annotations out of Wallis's Arithmetic of Infinities, 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 two such 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 January 1665 Newton took the degree of B.A. 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 7th, 1665, and June 22nd, 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. He was elected a fellow of his college on the 1st of October 1667. There were nine vacancies, one of which was caused by the death of Abraham 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 M.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 Lucasian professor of mathematics), at the same time giving him permission to communicate the contents to their common friend John Collins (1624-1683), a mathematician of no mean order. 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. In a subsequent letter on the 10th 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 resigned his chair, and was instrumental in securing Newton's election as his successor. Newton was elected Lucasian professor on the 29th 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. The success which attended his researches in optics must have been great, although the results were known only through his own oral lectures, until he presented an account of them to the Royal Society in the spring of 1672. On the 21st of December 1671 he was proposed as a candidate for admission into the Royal Society by Dr Seth Ward, bishop of Salisbury, and on the 11th of January 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 the 18th of January 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 Henry Oldenburg, the secretary of the Royal Society, on the 6th of February 1672, and which was read before the society two days afterwards. The whole is printed in No. 80 of the Philosophical Transactions. 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 itself 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." 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." 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 may be 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 in red, and so Bise appeareth indifferently of any colour with which 'tis illustrated, but yet most luminous in blew. And therefore minium reflecteth Rays of any colour, but most copiously those indued with red; and consequently when illustrated with day-light, that is with all sorts of Rays promiscuously blended, those qualified with red shall abound most in the reflected light, and by their prevalence cause it to appear of that colour. And for the same reason Bise, reflecting blew most copiously, shall appear blew by the excess of those Rays in its reflected light; and the like of other bodies. And that this is the intire and adequate cause of their colours, is manifest, because they have no power to change or alter the colours of any sort of Rays incident apart, but put on all colours indifferently, with which they are inlightened.

" Reviewing what I have written, I see the discourse it self will lead to divers Experiments sufficient for its examination: And therefore I shall not trouble you further, than to describe one of those, which I have already insinuated.

" In a darkened Room make a hole in the shut of a window whose diameter may conveniently be about a third part of an inch, to admit a convenient quantity of the Suns light: And there place a clear and colourless Prisme, to refract the entring light towards the further part of the Room, which, as I said, will thereby be diffused into an oblong coloured Image. Then place a Lens of about three foot radius (suppose a broad Object-glass of a three foot Telescope), at the distance of about four or five foot from thence, through which all those colours may at once be transmitted, and made by its Refraction to convene at a further distance of about ten or twelve feet. If at that distance you intercept this light with a sheet of white paper, you will see the colours converted into whiteness again by being mingled.

" But it is requisite, that the Prisme and Lens be placed steddy, and that the paper, on which the colours are cast be moved to and fro; for, by such motion, you will not only find, at what distance the whiteness is most perfect but also see, how the colours gradually convene, and vanish into whiteness, and afterwards having crossed one another in that place where they compound Whiteness, are again dissipated and severed, and in an inverted order retain the same colours, which they had before they entered the composition. You may also see, that, if any of the Colours at the Lens be intercepted, the Whiteness will be changed into the other colours. And therefore, that the composition of whiteness be perfect, care must be taken, that none of the colours fall besides the Lens." He concludes his communication with the words: " This, I conceive, is enough for an Introduction to Experiments of this kind: which if any of the R. Society shall be so curious as to prosecute, I should be very glad to be informed with what success: That, if any thing seem to be defective, or to thwart this relation, I may have an opportunity of giving further direction about it, or of acknowledging my errors, if I have committed any." The publication of these discoveries led to a series of controversies which lasted for several years, in which Newton had to contend with the eminent English natural philosopher Robert Hooke; Lucas, mathematical professor at Liege; Linus, a physician in Liege, and many others. Some of his opponents denied the truth of his experiments, refusing to believe in the existence of the spectrum. Others criticized the experiments, saying that the length of the spectrum was never more than three and a half times the breadth, whereas Newton found it to be five times the breadth. It appears that Newton made the mistake of supposing that all prisms would give a spectrum of exactly the same length; the objections of his opponents led him to measure carefully the lengths of spectra formed by prisms of different angles and of different refractive indices; and it seems strange that he was not led thereby to the discovery of the different dispersive powers of different refractive substances.

Newton carried on the discussion with the objectors with great courtesy and patience, but the amount of pain which these perpetual discussions gave to his sensitive mind may be estimated from the fact of his writing on the 18th of November 1676 to Oldenburg: " I promised to send you an answer to Mr Lucas this next Tuesday, but I find I shall scarce finish what I have designed, so as to get a copy taken of it by that time, and therefore I beg your patience a. week longer. I see I have made myself a slave to philosophy, but if I get free of Mr Lucas's business, I will resolutely bid adieu to it eternally, excepting what I do for my private satisfaction, or leave to come out after me; for I see a man must either resolve to put out nothing new, or to become a slave to defend it." It was a fortunate circumstance that these disputes did not so thoroughly damp Newton's ardour as he at the time felt they would. He subsequently published many papers in the Philosophical Transactions on various parts of the science of optics, and, although some of his views have been found to be erroneous, and are now almost universally rejected, his investigations led to discoveries which are of permanent value. He succeeded in explaining the colour of thin and of thick plates, and the inflexion of light, and he wrote on double refraction, polarization and binocular vision. He also invented a reflecting sextant for observing the distance between the moon and the fixed stars, - the same in every essential as the instrument which is still in everyday use at sea under the name of Hadley's quadrant. This discovery was communicated by him to Edmund Halley in 17bo, but was not published, or communicated to the Royal Society, till after Newton's death, when a description of it was found among his papers.

In March 1673 Newton took a prominent part in a dispute in the university. The public oratorship fell vacant, and a contest arose between the heads of the colleges and the members of the senate as to the mode of electing to the office. The heads claimed the right of nominating two persons, one of whom was to be elected by the senate. The senate insisted that the proper mode was by an open election. The duke of Buckingham, who was the chancellor of the university, endeavoured to effect a compromise which, he says, " I hope may for the present satisfy both sides. I propose that the heads may for this time nominate and the body comply, yet interposing (if they think fit) a protestation concerning their plea that this election may not hereafter pass for a decisive precedent in prejudice of their claim," and, " whereas I understand that the whole university has chiefly consideration for Dr Henry Paman of St John's and Mr Craven of Trinity College, I do recommend them both to be nominated." The heads, however, nominated Dr Paman and Ralph Sanderson of St John's, and the next day one hundred and twenty-one members of the senate recorded their votes for Craven and ninety-eight for Paman. On the morning of the election a protest in which Newton's name appeared was read, and entered in the Regent House. But the vice-chancellor admitted Paman the same morning, and so ended the first contest of a non-scientific character in which Newton took part.

On the 8th of March 1673 Newton wrote to Oldenburg, the secretary of the Royal Society: " Sir, I desire that you will procure that I may be put out from being any longer Fellow of the Royal Society: for though I honour that body, yet since I see I shall neither profit them, nor (by reason of this distance) can partake of the advantage of their assemblies, I desire to withdraw." Oldenburg must have replied to this by an offer to apply to the Society to excuse Newton the weekly payments, as in a letter of Newton's to Oldenburg, dated the 23rd of June 1673, he says, " For your proffer about my quarterly payments, I thank you, but I would not have you trouble yourself to get them excused, if you have not done it already." Nothing further seems to have been done in the matter until the 28th of January 1675, when Oldenburg informed " the Society that Mr Newton is now in such circumstances that he desires to be excused from the weekly payments." Upon this " it was agreed to by the council that he be dispensed with, as several others are." On the 18th of February 1675 Newton was formally admitted into the Society. The most probable explanation of the cause why Newton wished to be excused from these payments is to be found in the fact that, as he was not in holy orders, his fellowship at Trinity College would lapse in the autumn of 1675. It is true that the loss to his income which this would have caused was obviated by a patent from the crown in April 1675, allowing him as Lucasian professor to retain his fellowship without the obligation of taking holy orders. This must have relieved Newton's mind from a great deal of anxiety about pecuniary matters, as we find him in November 1676 subscribing £40 towards the building of the new library of Trinity College.

It is supposed that it was at Woolsthorpe in the summer of 1666 that Newton's thoughts were directed to the subject of gravity. Voltaire is the authority for the well-known anecdote about the apple. He had his information from Newton's favourite niece Catharine Barton, who married Conduitt, a fellow of the Royal Society, and one of Newton's intimate friends. How much truth there is in what is a plausible and a favourite story can never be known, but it is certain that tradition marked a tree as that from which the apple fell, till 1820, when, owing to decay, the tree was cut down and its wood carefully preserved.

Johann Kepler had proved by an elaborate series of measurements that each planet revolves in an elliptical orbit round the sun, whose centre occupies one of the foci of the orbit, that the radius vector of each planet drawn from the sun describes equal areas in equal times, and that the squares of the periodic times of the planets are in the same proportion as the cubes of their mean distances from the sun. The fact that heavy bodies have always a tendency to fall to the earth, no matter at what height they are placed above the earth's surface, seems to have led Newton to conjecture that it was possible that the same tendency to fall to the earth was the cause by which the moon was retained in its orbit round the earth. Newton, by calculating from Kepler's laws, and supposing the orbits of the planets to be circles round the sun in the centre, had already proved that the force of the sun acting upon the different planets must vary as the inverse square of the distances of the planets from the sun. He therefore was led to inquire whether, if the earth's attraction extended to the moon, the force at that distance would be of the exact magnitude necessary to retain the moon in its orbit. He found that the moon by her motion in her orbit was deflected from the tangent in every minute of time through a space of thirteen feet. But by observing the distance through which a body would fall in one second of time at the earth's surface, and by calculating from that on the supposition of the force diminishing in the ratio of the inverse square of the distance, he found that the earth's attraction at the distance of the moon would draw a body through 15 ft. in r min. Newton regarded the discrepancy between the results as a proof of the inaccuracy of his conjecture, and " laid aside at that time any further thoughts of this matter." But in 1679 a controversy between Hooke and Newton, about the form of the path of a body falling from a height, taking the motion of the earth round its axis into consideration, led Newton again to revery() his former conjectures on the moon. The measure of the earth, which had hitherto been accepted by geographers and navigators, was based on the very rough estimate that the length of a degree of latitude of the earth's surface measured along a meridian was .60 m. More accurate estimates had been made by R. Norwood and W. Snell, and more recently by P. Picard. At a meeting of the Royal Society on the 11th of January 1672, Oldenburg the secretary read a letter from Paris describing the method followed by Picard in measuring a degree, and specifically stating the precise length that he calculated it to be. It is probable that Newton had become acquainted with this measurement of Picard's, and that he was therefore led to make use of it when his thoughts were redirected to the subject. This estimate of the earth's magnitude, giving 69.1 m. to 1°, made the two results, the discrepancy between which Newton had regarded as a disproof of his conjecture, to agree so exactly that he now regarded his conjecture as fully established.

In January 1684 Sir Christopher Wren, Halley and Hooke were led to discuss the law of gravity, and, although probably they all agreed in the truth of the law of the inverse square, yet this truth was not looked upon as established. It appears that Hooke professed to have a solution of the problem of the path of .a body moving round a centre of force attracting as the inverse square of the distance; but Halley, finding, after a delay of some months, that Hooke " had not been so good as his word " in showing his solution to Wren, started in the month of August 1684 for Cambridge to consult Newton on the subject. Without mentioning the speculations which had been made, he asked Newton what would be the curve described by a planet round the sun on the assumption that the sun's force diminished as the square of the distance. Newton replied promptly, "an ellipse," and on being questioned by Halley as to the reason for his answer he replied, " Why, I have calculated it." He could not, however, put his hand upon his calculation, but he promised to send it to Halley. After the latter had left Cambridge, Newton set to work to reproduce the calculation. After making a mistake and producing a different result he corrected his work and obtained his former result.

In the following November Newton redeemed his promise to Halley by sending him, by the hand of Mr Paget, one of the fellows of his own college, and at that time mathematical master of Christ's Hospital, a copy of his demonstration; and very soon afterwards Halley paid another visit to Cambridge to confer with Newton about the problem; and on his return to London on the 10th of December 1684, he informed the Royal Society " that he had lately seen Mr Newton at Cambridge, who had showed him a curious treatise De Motu," which at Halley's desire he promised to send to the Society to be entered upon their register. " Mr Halley was desired to put Mr Newton in mind of his promise for the securing this invention to himself, till such time as he could be at leisure to publish it," and Paget was desired to join with Halley in urging Newton to do so. By the middle of February Newton had sent his paper to Aston, one of the secretaries of the Society, and in a letter to Aston dated the 23rd of February 1685, we find Newton thanking him for " having entered on the register his notions about motion." This treatise De Motu was the germ of the Principia, and was obviously meant to be a short account of what that work was intended to embrace. It occupies twenty-four octavo pages, and consists of four theorems and seven problems, some of which are identical with some of the most important propositions of the second and third sections of the first book of the Principia.

The years 1685 and 1686 will ever be memorable in the history of science. It was in them that Newton composed almost the whole of his great work. During this period Newton had a very extensive correspondence with John Flamsteed, who was then the astronomer-royal. Many of the letters are lost, but it is clear from one of Newton's, dated the 19th of September 1685, that he had received many useful communications from Flamsteed, and especially regarding Saturn, " whose orbit, as defined by Kepler," Newton " found too little for the sesquialterate proportions." In the other letters written in 1685 and 1686 he applies to Flamsteed for information respecting the orbits of the satellites of Jupiter and Saturn, respecting the rise and fall of the spring and neap tides at the solstices and the equinoxes, respecting the flattening of Jupiter at the poles (which, if certain, he says, would conduce much to the stating the reasons of the precession of the equinoxes), and respecting the difference between the observed places of Saturn and those computed from Kepler's tables about the time of his conjunction with Jupiter. On this last point the information supplied by Flamsteed was peculiarly gratifying to Newton; and it is obvious from the language of this part of his letter that he had still doubts of the universal application of the sesquialteral proportion. " Your information," he says, " about the errors of Kepler's tables for Jupiter and Saturn has eased me of several scruples. I was apt to suspect there might be some cause or other unknown to me which might disturb the sesquialteral proportions, for the influences of the planets one upon another seemed not great enough, though I imagined Jupiter's influence greater than your numbers determine it. It would add to my satisfaction if you would be pleased to let me know the long diameters of the orbits of Jupiter and Saturn, assigned by yourself and Mr Halley in your new tables, that I may see how the sesquialteral proportion fills the heavens, together with another small proportion which must be allowed for." Upon Newton's return from Lincolnshire in the beginning of April 1685, he seems to have devoted himself to the preparation of his work. In the spring he had determined the attractions of masses, and thus completed the law of universal gravitation. In the summer he had finished the second book of the Principia, the first book being the treatise De Motu, which he had enlarged and completed. Excepting in the correspondence with Flamsteed we hear nothing more of the preparation of the Principia until the 21st of April 1686, when Halley read to the Royal Society his Discourse concerning Gravity and its Properties, in which he states " that his worthy countryman Mr Isaac Newton has an incomparable treatise of motion almost ready for the press," and that the law of the inverse square " is the principle on which Mr Newton has made out all the phenomena of the celestial motions so easily and naturally, that its truth is past dispute." At the next meeting of the Society, on the 28th of April, " Dr Vincent presented to the Society a manuscript treatise entitled Philosophiae Naturalis Principia Mathematica, and dedicated to the Society by Mr Isaac Newton." Although this manuscript contained only the first book, yet such was the confidence the Society placed in the author that an order was given " that a letter of thanks be written to Mr Newton; and that the printing of his book be referred to the consideration of the council; and that in the meantime the book be put into the hands of Mr Halley, to make a report thereof to the council." Although there could be no doubt as to the intention of this report, yet no step was taken towards the publication of the work. At the next meeting of the Society, on the igth of May, some dissatisfaction seems to have been expressed at the delay, as it was ordered " that Mr Newton's work should be printed forthwith in quarto, and that a letter should be written to him to signify the Society's resolutions, and to desire his opinion as to the print, volume, cuts and so forth." Three days afterwards Halley communicated the resolution to Newton, and stated to him that the printing was to be at the charge of the Society. At the next meeting of the council, on the 2nd of June, it was again ordered " that Mr Newton's book be printed," but, instead of sanctioning the resolution of the general meeting to print it at their charge, they added " that Mr Halley undertake the business of looking after it, and printing it at his own charge, which he engaged to do." In order to explain to Newton the cause of the delay, Halley in his letter of the 22nd of May alleges that it arose from " the president's attendance on the king, and the absence of the vicepresidents, whom the good weather had drawn out of town"; but there is reason to believe that this was not the true cause, and that the unwillingness of the council to undertake the publication arose from the state of the finances of the Society. Halley certainly deserves the gratitude of posterity for undertaking the publication of the work at a very considerable pecuniary risk to himself. In the same letter Halley found it necessary to inform Newton of Hooke's conduct when the manuscript of the Principia was presented to the Society. Sir John Hoskyns was in the chair when Dr Vincent presented the manuscript, and passed a high encomium on the novelty and dignity of the subject. Hooke was offended because Sir John did not mention what he had told him of his own discovery. Halley only communicated to Newton the fact " that Hooke had some pretensions to the invention of the rule for the decrease of gravity being reciprocally as the squares of the distances from the centre," acknowledging at the same time that, though Newton had the notion from him, " yet the demonstration of the curves generated thereby belonged wholly to Newton." " How much of this," Halley adds, " is so, you know best, so likewise what you have to do in this matter; only Mr Hooke seems to expect you should make some mention of him in the preface, which 'tis possible you may see reason to prefix. I must beg your pardon that 'tis I that send you this ungrateful account; but I thought it my duty to let you know it, so that you might act accordingly, being in myself fully satisfied that nothing but the greatest candour imaginable is to be expected from a person who has of all men the least need to borrow reputation." In thus appealing to Newton's candour, Halley obviously wished that some acknowledgment of Hooke should be made. He knew indeed that before Newton had announced the inverse law Hooke and Wren and himself had spoken of it and discussed it, and therefore justice demanded that, though none of them had given a demonstration of the law, Hooke especially should receive credit for having maintained it as a truth of which he was seeking the demonstration. On the loth, of June 1686 Newton wrote to Halley the following letter: " Sir, - In order to let you know the case between Mr Hooke and me, I give you an account of what passed between us in our letters, so far as I could remember; for 'tis long since they were writ, and I do not know that I have seen them since. I am almost confident by circumstances, that Sir Chr. Wren knew the duplicate proportion when I gave him a visit; and then Mr Hooke (by his book Cometa written afterwards) will prove the last of us three that knew it. I intended in this letter to let you understand the case fully; but it being a frivolous business, I shall content myself to give you the heads of it in short, viz. that I never extended the duplicate proportion lower than to the superficies of the earth, and before a certain demonstration I found the last year, have suspected it did not reach accurately enough down so low; and therefore in the doctrine of projectiles never used it nor considered the motions of the heavens; and consequently Mr Hooke could not from my letters, which were about projectiles and the regions descending hence to the centre, conclude me ignorant of the theory of the heavens. That what he told me of the duplicate proportion was erroneous, namely, that it reached down from hence to the centre of the earth.

" That it is not candid to require me now to confess myself, in print, then ignorant of the duplicate proportion in the heavens; for no other reason, but because he had told it me in the case of projectiles, and so upon mistaken grounds accused me of that ignorance. That in my answer to his first letter I refused his correspondence, told him I had laid philosophy aside, sent him only the experiment of projectiles (rather shortly hinted than carefully described), in compliment to sweeten my answer, expected to hear no further from him; could scarce persuade myself to answer his second letter; did not answer his third, was upon other things; thought no further of philosophical matters than his letters put me upon it, and therefore may be allowed not to have had my thoughts of that kind about me so well at that time. That by the same reason he concludes me then ignorant of the rest of the duplicate proportion, he may as well conclude me ignorant of the rest of that theory I had read before in his books. That in one of my papers writ (I cannot say in what year, but I am sure some time before I had any correspondence with Mr Oldenburg, and that's above fifteen years ago), the proportion of the forces of the planets from the sun, reciprocally duplicate of their distances from him, is expressed, and the proportion of our gravity to the moon's conatus recedendi a centro terrae is calculated, though not accurately enough. That when Hugenius put out his Horol. Oscil., a copy being presented to me, in my letter of thanks to him I gave those rules in the end thereof a particular commendation for their usefulness in Philosophy, and added out of my aforesaid paper an instance of their usefulness, in comparing the forces of the moon from the earth, and earth from the sun; in determining a problem about the moon's phase, and putting a limit to the sun's parallax, which shews that I had then my eye upon comparing the forces of the planets arising from their circular motion, and understood it; so that a while after, when Mr Hooke propounded the problem solemnly, in the end of his attempt to prove the motion of the earth, if I had not known the duplicate proportion before, I could not but have found it now. Between ten and eleven years ago there was an hypothesis of mine registered in your books, wherein I hinted a cause of gravity towards the earth, sun and planets, with the dependence of the celestial motions thereon; in which the proportion of the decrease of gravity from the superficies of the planet (though for brevity's sake not there expressed) can be no other than reciprocally duplicate of the distance from the centre. And I hope I shall not be urged to declare, in print, that I understood not the obvious mathematical condition of my own hypothesis. But, grant I received it afterwards from Mr Hooke, yet have I as great a right to it as to the ellipsis. For as Kepler knew the orb to be not circular but oval, and guessed it to be elliptical, so Mr Hooke, without knowing what I have found out since his letters to me, can know no more, but that the proportion was duplicate quam proxime at great distances from the centre, and only guessed it to be so accurately, and guessed amiss in extending that proportion down to the very centre, whereas Kepler guessed right at the ellipsis. And so Mr Hooke found less of the proportion than Kepler of the ellipsis.

" There is so strong an objection against the accurateness of this proportion, that without my demonstrations, to which Mr Hooke is yet a stranger, it cannot be believed by a judicious philosopher to be any where accurate. And so, in stating this business, I do pretend to have done as much for the proportion as for the ellipsis, and to have as much right to the one from Mr Hooke and all men, as to the other from Kepler; and therefore on this account also he must at least moderate his pretences.

" The proof you sent me I like very well. I designed the whole to consist of three books; the second was finished last summer being short, and only wants transcribing, and drawing the cuts fairly. Some new propositions I have since thought on, which I can as well let alone. The third wants the theory of comets. In autumn last I spent two months in calculations to no purpose for want of a good method, which made me afterwards return to the first book, and enlarge it with divers propositions, some relating to comets, others to other things, found out last winter. The third I now design to suppress. Philosophy is such an impertinently litigious lady, that a man has as good be engaged in lawsuits, as have to do with her. I found it so formerly, and now I am no sooner come near her again, but she gives me warning. The two first books, without the third, will not so well bear the title of Philosophiae Naturalis Principia Mathematica; and therefore I had altered it to this, De Motu Corporum libri duo. But, upon second thoughts, I retain the former title. 'Twill help the sale of the book, which I ought not to diminish now 'tis yours. The articles are, with the largest, to be called by that name; if you please you may change the word to sections, though it be not material. In the first page, I have struck out the words ` uti posthac docebitur,' as referring to the third book; which is all at present, from your affectionate friend, and humble servant, " Is. Newton." On the 29th of June 1686 Halley wrote to Newton: - " I am heartily sorry that in this matter, wherein all mankind ought to acknowledge their obligations to you, you should meet with anything that should give you unquiet "; and then, after an account of Hooke's claim to the discovery as made at a meeting of the Royal Society, he concludes: " But I found that they were all of opinion that nothing thereof appearing in print, nor on the books of the Society, you ought to be considered as the inventor. And if in truth he knew it before you, he ought not to blame any but himself for having taken no more care to secure a discovery, which he puts so much value on. What application he has made in private, I know not; but I am sure that the Society have a very great satisfaction, in the honour you do them, by the dedication of so worthy a treatise. Sir, I must now again beg you, not to let your resentments run so high, as to deprive us of your third book, wherein the application of your mathematical doctrine to the theory of comets and several curious experiments, which, as I guess by what you write, ought to compose it, will undoubtedly render it acceptable to those, who will call themselves Philosophers without Mathematics, which are much the greater number. Now you approve of the character and paper, I will push on the edition vigorously. I have sometimes had thoughts of having the cuts neatly done in wood, so as to stand in the page with the demonstrations. It will be more convenient, and not much more charge. If it please you to have it so, I will try how well it can be done; otherwise I will have them in somewhat a larger size than those you have sent up. - I am, Sir, your most affectionate humble servant, E. Halley." On the 30th of June 1686 the president was desired by the council to license Newton's book, entitled Philosophiae Naturalis Principia Mathematica. On the 14th of July 1686 Newton wrote to Halley approving of his proposal to introduce woodcuts among the letterpress, stating clearly the different things which he had from Hooke, and adding, " And now having sincerely told you the case between Mr Hooke and me, I hope I shall be free for the future from the prejudice of his letters. I have considered how best to compose the present dispute, and I think it may be done by the inclosed scholium to the fourth proposition." This scholium was- " The inverse law of gravity holds in all the celestial motions, as was discovered also independently by my countrymen Wren, Hooke and Halley." After this letter of Newton's the printing of the Principia was begun. The second book, though ready for the press in the autumn of 1686, was not sent to the printers until March 1687. The third book was presented to the Society on the 6th of April 1687, and the whole work published about midsummer in that year. It was dedicated to the Royal Society, and to it was prefixed a set of Latin hexameters addressed by Halley to the author. The work, as might have been expected, caused a great deal of excitement throughout Europe, and the whole of the impression was very soon sold. In 1691 a copy of the Principia was hardly to be procured.

While Newton was writing the second and third books of the Principia, a very important event occurred at Cambridge which had the effect of bringing him before the public in a new light. James II. had already, in 1686, in open violation of the law, conferred the deanery of Christ Church at Oxford on John Massey, a person whose sole qualification was that he was a member of the Church of Rome; and the king had boasted to the pope's legate that " what he had done at Oxford would very soon be done at Cambridge." In accordance with this boast, in February 1687 he issued a mandate directing that Father Alban Francis, a Benedictine monk, should be admitted a master of arts of the university of Cambridge, without taking the oaths of allegiance and supremacy. Upon receiving the mandamus Dr Pechell, the master of Magdalene College, who was vicechancellor, sent a messenger to the duke of Albemarle, the chancellor, to request him to get the mandamus recalled; and the registrary and the bedells waited upon Francis to offer him instant admission to the degree if only he would take the necessary oaths. Both the king and the monk were inexorable. The court and the university were thus placed in open collision. A menacing letter was despatched by Sunderland to shake the firmness of the university; but, though humble and respectful explanations were returned, the university showed no sign of compliance, nor even of a desire to suggest a compromise. In consequence the vice-chancellor and deputies from the senate were summoned to appear before the High Commission Court at Westminster. Newton was one of the eight deputies appointed by the senate for this purpose. The deputies, before starting for London, held a meeting to prepare their case for the court. A compromise which was put forward by one of them was stoutly and successfully resisted by Newton, and on the 21st of April the deputation, with their case carefully prepared, appeared before the court. Lord Jeffreys presided at the board. The deputation appeared as a matter of course before the commissioners, and were dismissed. On the 27th of April they gave in their plea. On the 7th of May it was discussed, and feebly defended by the vicechancellor. The deputies maintained that in the late reign several royal mandates had been withdrawn, and that no degree had ever been conferred without the oaths having been previously taken. Jeffreys spoke with his accustomed insolence to the vicechancellor, silenced the other deputies when they offered to speak, and ordered them out of court. When recalled the deputies were reprimanded, and Pechell was deprived of his office as vice-chancellor, and of his emoluments as master of Magdalene. Newton returned to Trinity College to complete the Principia. While thus occupied he had an extensive correspondence with Halley, a very great part of which is extant. The following letter from Halley, dated London, July 5th, 1687, announcing the completion of the Principia, is of peculiar interest: " I have at length brought your book to an end, and hope it will please you. The last errata came just in time to be inserted. I will present from you the book you desire to the Royal Society, Mr Boyle, Mr Paget, Mr Flamsteed, and if there be any else in town that you design to gratify that way; and I have sent you to bestow on your friends in the University 20 copies, which I entreat you to accept. In the same parcel you will receive 40 more, which having no acquaintance in Cambridge, I must entreat you to put into the hands of one or more of your ablest booksellers to dispose of them. I intend the price of them, bound in calves' leather, and lettered, to be 9 shillings here. Those I send you I value in quires at 6 shillings, to take my money as they are sold, or at 5sh' for ready, or else at some short time; for I am satisfied there is no dealing in books without interesting the booksellers; and I am contented to let them go halves with me, rather than have your excellent work smothered by their combinations. I hope you will not repent you of the pains you have taken in so laudable a piece, so much to your own and the nation's credit, but rather, after you shall have a little diverted yourself with other studies, that you will resume those contemplations wherein you had so great success, and attempt the perfection of the lunar theory, which will be of prodigious use in navigation, as well as of profound and public speculation.. .. You will receive a box from me on Thursday next by the waggon, that starts from town to-morrow." In 1692 and 1693 Newton seems to have had a serious illness, the nature of which has given rise to very considerable dispute. In a letter dated the 13th of September 1693, addressed to Samuel Pepys, he writes: " Some time after Mr Millington had delivered your message, he pressed me to see you the next time I went to London. I was averse, but upon his pressing consented, before I considered what I did, for I am extremely troubled at the embroilment I am in, and have neither ate nor slept well this twelvemonth, nor have my former consistency of mind. I never designed to get any thing by your interest, nor by King James's favour, but am now sensible that I must withdraw from your acquaintance, and see neither you nor the rest of my friends any more, if I may but have them quietly. I beg your pardon for saying I would see you again, and rest your most humble and obedient servant." And in a letter written to John Locke in reply to one of his about the second edition of his book, and dated the 15th of October 1693, Newton wrote: " The last winter, by sleeping too often by my fire, I got an ill habit of sleeping; and a distemper, which this summer has been epidemical, put me farther out of order, so that when I wrote to you, I had not slept an hour a night for a fortnight together, and for five days together not a wink. I remember I wrote to you, but what I said of your book I remember not. If you please to send me a transcript of that passage, I will give you an account of it if I can." The loss of sleep to a person of Newton's temperament, whose mind was never fiat rest, and at times so wholly engrossed in his scientific pursuits that he even neglected to take food, must necessarily have led to a very great deal of nervous excitability. It is not astonishing that rumours got abroad that there was a danger of his mind giving way, or, according to a report which was believed at the time, that it had actually done so. Pepys must have heard such rumours, as in a letter to his friend Millington, the tutor of Magdalene College at Cambridge, dated the 26th of September 1693, he wrote: " I must acknowledge myself not at the ease I would be glad to be at in reference to excellent Mr Newton; concerning whom (methinks) your answer labours under the same kind of restraint which (to tell you the truth) my asking did. For I was 10th at first dash to tell you that I had lately received a letter from him so surprising to me for the inconsistency of every part of it, as to be put into great disorder by it, from the concernment I have for him, lest it should arise from that which of all mankind I should least dread from him and most lament for - I mean a discomposure in head, or mind, or both. Let me, therefore, beg you, Sir, having now told you the true ground of the trouble I lately gave you, to let me know the very truth of the matter, as far at least as comes within your knowledge." On the 30th of September 1693 Millington wrote to Pepys that he had been to look for Newton some time before, but that " he was out of town, and since," he says, " I have not seen him, till upon the 28th I met him at Huntingdon, where, upon his own accord, and before I had time to ask him any question, he told me that he had writt to you a very odd letter, at which he was much concerned; added, that it was in a distemper that much seized his head, and that kept him awake for above five nights together, which upon occasion he desired I would represent to you, and beg your pardon, he being very much ashamed he should be so rude to a person for whom he hath so great an honour. He is now very well, and though I fear he is under some small degree of melancholy, yet I think there is no reason to suspect it bath at all touched his understanding, and I hope never will; and so I am sure all ought to wish, that love learning or the honour of our nation, which it is a sign how much it is looked after, when such a person as Mr Newton lyes so neglected by those in power." The illness of Newton was very much exaggerated by foreign contemporary writers. In a manuscript journal of Huygens is to be found an entry: " 29 Maj. 1694. - Narravit mihi D. Colm Scotus virum celeberrimum ac summum geometram Is. Neutonum in phrenesin incidisse abhinc anno et sex mensibus. An ex nimia studii assiduitate, an dolore infortunii, quod incendio laboratorium chymicum et scripta quaedam amiserat ? Cum ad Archiepiscopum Cantabrigiensem venisset, ea locutum, quae alienationem mentis indicarent. Deinde ab amicis curam ejus susceptam, domoque clauso remedia volenti nolenti adhibita, quibus jam sanitatem recuperavit ut jam rursus librum suum Principiorum Philosophiae Mathematicorum intelligere incipiat." Huygens, in a letter dated the 8th of June 1694, wrote to Leibnitz, " I do not know if you are acquainted with the accident which has happened to the good Mr Newton, namely, that he has had an attack of phrenitis, which lasted eighteen months, and of which they say his friends have cured him by means of remedies, and keeping him shut up." To which Leibnitz, in a letter dated the 22nd of June, replied, " I am very glad that I received information of the cure of Mr Newton at the same time that I first heard of his illness, which doubtless must have been very alarming." The active part which Newton had taken in defending the legal privileges of the university against the encroachments of the crown had probably at least equal weight with his scientific reputation when his friends chose him as a candidate for a seat in parliament as one of the representatives of the university. The other candidates were Sir Robert Sawyer and Mr Finch. Sir Robert stood at the head of the poll with 125 votes, Newton next with 122 and Mr Finch was last with 117 votes. Newton retained his seat only about a year, from January 1689 till the dissolution of the Convention Parliament in February 1690. During this time Newton does not appear to have taken part in any of the debates in the House; but he was not neglectful of his duties as a member. On the 30th of April 1689 he moved for leave to bring in a bill to settle the charters and privileges of the university of Cambridge, just as Sir Thomas Clarges did for Oxford at the same time, and he wrote a series of letters to Dr Lovel, the vice-chancellor of the university, on points which affected the interests of the university and its members.

Some of the members of the university who had lately sworn allegiance to James had some difficulty in swearing allegiance to his successor. On the 12th of February 1689, the day of the coronation of William and Mary, Newton intimated to the vicechancellor that he would soon receive an order to proclaim them at Cambridge. He enclosed a form of the proclamation, and expressed a hearty " wish that the university would so compose themselves as to perform the solemnity with a reasonable decorum." During his residence in London Newton had made the acquaintance of John Locke. Locke had taken a very great interest in the new theories of the Principia. He was one of a number of Newton's friends who began to be uneasy and dissatisfied at seeing the most eminent scientific man of his age left to depend upon the meagre emoluments of a college fellowship and a professorship.

At one time Newton's friends had nearly succeeded in getting him appointed provost of King's College, Cambridge, but the college offered a successful resistance on the ground that the appointment would be illegal, as the statutes required that the provost should be in priest's orders. Charles Montague, who was afterwards earl of Halifax, was a fellow of Trinity College, and was a very intimate friend of Newton; and it was on his influence that Newton relied in the main for promotion to some post of honour and emolument. His hopes, however, were blighted by long delay. In one of his letters to Locke at the beginning of 1692, when Montague, Lord Monmouth and Locke were exerting themselves to obtain some appointment for him, Newton wrote that he was " fully convinced that Mr Montague, upon an old grudge which he thought had been worn out, was false to him." Newton was now in his fifty-fifth year, and whilst those of his own standing at the university had been appointed to high posts in church or state, he still remained without any mark of national gratitude. But this blot upon the English name was at last removed by Montague in 1694, when he was appointed chancellor of the exchequer. He had previously consulted Newton upon the subject of the recoinage, and on the opportunity occurring he appointed Newton to the post of warden of the mint. In a letter to Newton announcing the news, Montague writes: " I am very glad that at last I can give you a good proof of my friendship, and the esteem the king has of your merits. Mr Overton, the warden of the mint, is made one of the Commissioners of Customs, and the king has promised me to make Mr Newton warden of the mint. The office is the most proper for you. 'Tis the chief office in the mint: 'tis worth five or six hundred pounds per annum, and has not too much business to require more attendance than you can spare." This letter must have convinced Newton of the sincerity of Montague's good intentions towards him; we find them living as friends on the most intimate terms until Halifax's death in 1715.

Newton's chemical and mathematical knowledge proved of great use in carrying out the recoinage. This was completed in about two years. In 1697 Newton was appointed to the mastership of the mint, a post worth between £1200 and £150o per annum. While he held this office, Newton drew up a very extensive table of assays of foreign coins, and composed an official report on the coinage.

Up to the time of the publication of the Principia in 1687 the method of fluxions which had been invented by Newton, and had been of great assistance to him in his mathematical investigations, was still, except to Newton and his friends, a secret. One of the most important rules of the method forms the second lemma of the second book of the Principia. Though this new and powerful method was of great help to Newton in his work, he did not exhibit it in the results. He was aware that the wellknown geometrical methods of the ancients would clothe his new creations in a garb which would appear less strange and uncouth to those not familiar with the new method. The Principia gives no information on the subject of the notation adopted in the new calculus, and it was not until 1693 that it was com municated to the scientific world in the second volume of Dr Wallis's works.

Newton's admirers in Holland had informed Dr Wallis that Newton's method of fluxions passed there under the name of Leibnitz's Calculus Di fferentialis. It was therefore thought necessary that an early opportunity should be taken of asserting Newton's claim to be the inventor of the method of fluxions, and this was the reason for this method first appearing in Wallis's works. A further account of the method was given in the first edition of Newton's Optics, which appeared in 1704. To this work were added two treatises, entitled Tractatus duo de speciebus et magnitudine figurarum curvilinearum, the one bearing the title Tractatus de Quadratura Curvarum, and the other Enumeratio linearum tertii ordinis. The first contains an explanation of the doctrine of fluxions, and of its application to the quadrature of curves; the second, a classification of seventy-two curves of the third order, with an account of their properties. The reason for publishing these two tracts in his Optics, from the subsequent editions of which they were omitted, is thus stated in the advertisement: " In a letter written to M Leibnitz in the year 1679, and published by Dr Wallis, I mentioned a method by which I had found some general theorems about squaring curvilinear figures on comparing them with the conic sections, or other the simplest figures with which they might be compared. And some years ago I lent out a manuscript containing such theorems; and having since met with some things copied out of it, I have on this occasion made it public, prefixing to it an introduction, and joining a Scholium concerning that method. And I have joined with it another small tract concerning the curvilineal figures of the second kind, which was also written many years ago, and made known to some friends, who have solicited the making it public." In 1707 William Whiston published the algebraical lectures which Newton had delivered at Cambridge, under the title of Arithmetica Universalis, sive de Compositione et Resolutione Arithmetica Liber. We are not accurately informed how Whiston obtained possession of this work; but it is stated by one of the editors of the English edition " that Mr Whiston, thinking it a pity that so noble and useful a work should be doomed to a college confinement, obtained leave to make it public." It was soon afterwards translated into English by Raphson; and a second edition of it, with improvements by the author, was published at London in 1712, by Dr Machin, secretary to the Royal Society. With the view of stimulating mathematicians to write annotations on this admirable work, the celebrated 's Gravesande published a tract, entitled Specimen Commentarii in Arithmeticam Universalem; and Maclaurin's Algebra seems to have been drawn up in consequence of this appeal.

Newton's solution of the celebrated problems proposed by John Bernoulli and Leibnitz deserves mention among his mathematical works. In June 1696 Bernoulli addressed a letter to the mathematicians of Europe challenging them to solve two problems - (1) to determine the brachistochrone between two given points not in the same vertical line, (2) to determine a curve such that, if a straight line drawn through a fixed point A meet it in two points P 1, P 2, then AP 1 m +AP 2 m will be constant. This challenge was first made in the Ada Lipsiensia for June 1696. Six months were allowed by Bernoulli for the solution of the problem, and in the event of none being sent to him he promised to publish his own. The six months elapsed without any solution being produced; but he received a letter from Leibnitz, stating that he had "cut the knot of the most beautiful of these problems," and requesting that the period for their solution should be extended to Christmas next, that the French and Italian mathematicians might have no reason to complain of the shortness of the period. Bernoulli adopted the suggestion, and publicly announced the prorogation for the information of those who might not see the Acta Lipsiensia. On the 29th of January 1696/7 Newton received from France two copies of the printed paper containing the problems, and on the following day he transmitted a solution of them to Montague, then president of the Royal Society. He announced that the curve required in the first problem must be a cycloid, and he gave a method of determining it. He solved also the: second problem, and he showed that by the same method other curves might be found which shall cut off three or more segments having the like properties. Solutions were also obtained from Leibnitz and the Marquis de L'Hopital; and, although that of Newton was anonymous, yet Bernoulli recognized the author in his disguise; " tanquam," says he, " ex ungue leonem." In 1699 Newton's position as a mathematician and natural philosopher was recognized by the French Academy of Sciences.. In that year the Academy was remodelled, and eight foreign associates were created. Leibnitz, Domenico Guglielmini (1655-1710), Hartsoeker, and E. W. Tschirnhausen were appointed on the 4th of February, James Bernoulli and John Bernoulli on the 14th of February, and Newton and Olaus Roemer on the 21st of February.

While Newton held the office of warden of the mint, he retained his chair of mathematics at Cambridge, and discharged the duties. of the post, but shortly after he was promoted to be master of the mint he appointed Whiston his deputy with " the full profits of the place." Whiston began his astronomical lectures as Newton's deputy in January 1701. On the 10th of December 1701 Newton resigned his professorship, thereby at the same time resigning his fellowship at Trinity, which he had held with the Lucasian professorship since 1675 by virtue of the royal mandate. Whiston's claims to succeed Newton in the Lucasian chair were successfully supported by Newton himself.

On the 26th of November 1701 Newton was again elected one of the representatives of the university in parliament, but he retained his seat only until the dissolution in the following July.. Newton does not seem to have been a candidate at this election,. but at the next dissolution in 1705 he was again a candidate for the representation of the university. He was warmly supported by the residents, but being a Whig in politics he was opposed by the non-residents, and beaten by a large majority.

In the autumn of 1703 Lord Somers retired from the presidency of the Royal Society, and Newton on the 30th of November 1703 was elected to succeed him. Newton was annually reelected to this honourable post during the remainder of his life. He held the office in all twenty-five years, a period in which he has been exceeded by but one other president of the Royal Society, Sir Joseph Banks. As president Newton was brought into close connexion with Prince George of Denmark, the queen's husband, who had been elected a fellow of the Royal Society. The prince had offered, on Newton's recommendation, to be at the expense of printing Flamsteed's observations, and especially his catalogue of the stars. It was natural that the queen should form a high opinion of one whose merits had made such a deep impression on her husband. In April 1705, when the queen,. the prince and the court were staying at the royal residence at Newmarket, they paid a visit to Cambridge, where they were the guests of Dr Bentley, the master of Trinity. Her Majesty went in state to the Regent House, where a congregation of the senate was held, and a number of honorary degrees conferred. Afterwards the queen held a court at Trinity Lodge, where (16th of April 1705) she conferred the order of knighthood upon Sir Isaac Newton.

As soon as the first edition of the Principia was published Newton began to prepare for a second edition. He was anxious to improve the work by additions to the theory of the motion of the moon and the planets. Dr Edleston, in his preface to Newton's correspondence with Cotes, justly remarks: " If Flamsteed the Astronomer-Royal had cordially co-operated with him in the humble capacity of an observer in the way that Newton pointed out and requested of him. .. the lunar theory would, if its creator did not overrate his own powers, have been completely investigated, so far as he could do it, in the first few months of 1695, and a second edition of the Principia would probably have followed the execution of the task at no long interval." Newton, however, could not get the information he wanted from Flamsteed, and after the spring of 1696 his time was much occupied by his duties at the mint. Rumours, however, of his work, and of a new edition, were heard from time to time. In February 1700 Leibnitz writes of Newton, " J'ai appris aussi (je ne sgai on) qu'il donnera encore quelque chose sur le mouvement de la lune: et on m'a dit aussi qu'il y aura une nouvelle edition de ses principes de la nature." Dr Bentley, the master of Trinity College, had for a long time urged Newton to give his consent to the republication of the Principia. In the middle of 1708 Newton's consent was obtained, but it was not till the spring of 1709 that he was prevailed upon to entrust the superintendence of it to a young mathematician of great promise, Roger Cotes, fellow of Trinity College, who had been recently appointed the first Plumian professor of astronomy and experimental philosophy. On the 21st of May 1709, after having been that day with Newton, Bentley announced this arrangement to Cotes: - " Sir Isaac Newton," he said, " will be glad to see you in June, and then put into your hands one part of his book corrected for the press." About the middle of July Cotes went to London, in the expectation doubtless to bring down with him to Cambridge the corrected portion of the Principia. Although Cotes was impatient to begin his work, it was nearly the end of September before the corrected copy was put into his hands.

During the printing of this edition a correspondence went on continuously between Newton and Cotes. On the 31st of March 1713, when the edition was nearly ready for publication, Newton wrote to Cotes: " I heare that Mr Bernoulli has sent a Paper of 40 pages to be published in the Acta Leipsica relating to what I have written upon the curve Lines described by Projectiles in resisting Mediums. And therein he partly makes Observations upon what I have written & partly improves it. To prevent being blamed by him or others for any disingenuity in not acknowledging my oversights or slips in the first edition, I believe it will not be amiss to print next after the old Praefatio ad Lectorem, the following account of this new Edition.

" ` In hac secunda Principiorum Editione, multa sparsim emendantur & nonnulla adjiciuntur. In Libri primi Sect. ii. Inventio virium quibus corpora in Orbibus datis revolvi possint, facilior redditur et amplior. In Libri secundi Sect. vii. Theoria resistentiae fluidorum accuratius investigatur & novis experimentis confirmatur. In Libro tertio Theoria Lunae & Praecessio Aequinoctiorum ex Principiis suis plenius deducuntur, et Theoria Cometarum pluribus et accuratius computatis Orbium exemplis confirmatur.

" ` 28 Mar. 1713. I. N.' " If you write any further Preface, I must not see it, for I find that I shall be examined about it. The cuts for y e Comet of 1680 & 1681 are printed off and will be sent to Dr Bently this week by the Carrier." Newton's desire to have no hand in writing the preface seems. to have proceeded from a knowledge that Cotes was proposing to allude to the dispute about the invention of fluxions. At last, about midsummer 1713, was published the long and impatiently expected second edition of the Principia, and, on the 27th of July, Newton waited on the queen to present her with a copy of the new edition.

In 1714 the question of finding the longitude at sea, which had been looked upon as an important one for several years, was brought into prominence by a petition presented to the House of Commons by a number of captains of Her Majesty's ships and merchant ships and of London merchants. The petition was referred to a committee of the House, who called witnesses. Newton appeared before them and gave evidence. He stated that for determining the longitude at sea there had been several projects, true in theory but difficult to execute. He mentioned four: (1) by a watch to keep time exactly, (2) by the eclipses of Jupiter's satellites, (3) by the place of the moon, (4) by a new method proposed by Mr Ditton. Newton criticized all the methods, pointing out their weak points, and it is due mainly to his evidence that the committee brought in the report which was accepted by the House, and shortly afterwards was converted into a Bill, passed both Houses, and received the royal assent. The report ran " that it is the opinion of this committee that a reward be settled by parliament upon such person or persons as shall discover a more certain and practicable method of ascertaining the longitude than any yet in practice; and the said reward be proportioned to the degree Hof exactness to which the said method shall reach." Sir Isaac Newton was a very popular visitor at the court of George I. The princess of Wales, afterwards Queen Caroline, wife of George II., took every opportunity of conversing with him. Having one day been told by Sir Isaac that he had composed a new system of chronology while he was still resident at Cambridge, she requested him to give her a copy. He accordingly drew up an abstract of the system from his papers, and sent it to the princess for her own private use; but he afterwards allowed a copy to be made for the Abbe Conti on the express understanding that it should not be communicated to any other person. The abbe, however, lent his copy to M Freret, an antiquary at Paris, who translated it, and endeavoured to refute it. The translation was printed under the title Abrege de chronologie de M le Chevallier Newton, fait par lui-meme et traduit sur le manuscrit anglais. Upon receiving a copy of this work, Sir Isaac Newton printed, in the Philosophical Transactions for 1725, a paper entitled " Remarks on the observations made on a Chronological Index of Sir Isaac Newton, translated into French by the observator, and published at Paris." In these remarks Sir Isaac charged the abbe with a breach of promise, and gave a triumphant answer to the objections which Freret had urged against his system. Father Souciet entered the field in defence of Freret; and in consequence of this controversy Sir Isaac was induced to prepare his larger work, which was published in 1728, after his death, and entitled The Chronology of Ancient Kingdoms amended, to which is prefixed a short Chronicle from the First Memory of Kings in Europe to the Conquest of Persia by Alexander the Great. From an early period of his life Newton had paid great attention to theological studies, and it is well known that he had begun to study the subject of the prophecies before the year 1690. M Blot, with a view of showing that his theological writings were the productions of his dotage, has fixed their date between 1712 and 1719. That Newton's mind was even then quite clear and powerful is sufficiently proved by his ability to attack the most difficult mathematical problems with success. For it was in 1716 that Leibnitz, in a letter to the Abbe Conti, proposed a problem for solution " for the purpose of feeling the pulse of the English analysts." The problem was to find the orthogonal trajectories of a series of curves represented by a single equation. Newton received this problem about 5 o'clock in the afternoon as he was returning from the mint, but, though he was fatigued with business, he solved the problem the same evening.

One of the most remarkable of Sir Isaac's theological productions is his Historical Account of Two Notable Corruptions of the Scripture, in a letter to a friend. This friend was Locke, who received the letter in November 1690. Sir Isaac seems to have been then anxious for its publication; but, as the effect of his argument was to deprive the Trinitarians of two passages in favour of the Trinity, he became alarmed at the probable consequences of such a step. He therefore requested Locke, who was then going to Holland, to get it translated into French, and published on the continent. Being prevented from going to Holland, Locke copied the manuscript, and sent it, without Newton's name, to Le Clerc, who received it before the 11th of April 1691. On the 20th of January 1692 Le Clerc announced to Locke his intention to publish the pamphlet in Latin; and, upon the intimation of this to Sir Isaac, he entreated him " to stop the translation and impression as soon as he could, for he designed to suppress them." This was accordingly done; but Le Clerc sent the manuscript to the library of the Remonstrants, and it was afterwards published at London in 1754, under the title of Two Letters from Sir Isaac Newton to M le Clerc. This edition is imperfect, and in many places erroneous. Dr Horsley therefore published a genuine one, which is in the form of a single letter to a friend, and was taken from a manuscript in Sir Isaac's own hand.

Sir Isaac Newton left behind him in manuscript a work entitled Observations on the Prophecies of Daniel and the Apocalypse of St John, which was published in London in 1733, in one volume 4to; another work, entitled Lexicon Propheticum, with a dissertation on the sacred cubit of the Jews, which was printed in 1737; and four letters addressed to Bentley, containing some arguments in proof of a Deity, which were published by Cumberland, a nephew of Bentley, in 1756. Sir Isaac also left a Church History complete, a History of the Creation, Paradoxical Questions regarding Athanasius, and many divinity tracts.

Newton devoted much of his time to the study of chemistry; but the greater number of his experiments still remain in manuscript. His Tabula Quantitatum et Graduum Caloris contains a comparative scale of temperature from that of melting ice to that of a small kitchen fire. He wrote also another chemical paper De Natura Acidorum, which has been published by Dr Horsley. Sir Isaac spent much time in the study of the works of the alchemists. He had diligently studied the works of Jacob Boehme, and there were found amongst his manuscripts copious abstracts from them in his own handwriting. In the earlier part of his life he and his relation Dr Newton of Grantham had put up furnaces, and had wrought for several months in quest of the philosopher's tincture. Among the manuscripts in the possession of the earl of Portsmouth there are many sheets in Sir Isaac's hand of Flamsteed's Explication of Hieroglyphic Figures, and in another hand many sheets of William Yworth's Processus Mysterii Magni Philosophicus. In the last few years of his life Newton was troubled with incontinence of urine, which was supposed to be due to stone; but with care he kept the disease under control. In January 1725 he was seized with a violent cough and inflammation of the lungs, which induced him to reside at Kensington; and in the following month he had a severe attack of gout, which produced a decided improvement in his general health. His duties at the mint were discharged by John Conduitt, and he therefore seldom went from home. On the 28th of February 1727, feeling well, he went to London to preside at a meeting of the Royal Society; but the fatigue which attended this duty brought on a violent return of his former complaint, and he returned to Kensington on the 4th of March, when Dr Mead and Dr Chesselden pronounced his disease to be stone. He endured the sufferings of this complaint with wonderful patience. He seemed a little better on the 15th of March, and on the 18th he read the newspapers and conversed with Dr Mead; but at 6 o'clock in the evening he became insensible, and continued in that state till Monday the 20th of March 1727, when he expired without pain between one and two o'clock in the morning. His body was removed to London, and on Tuesday the 28th of March it lay in state in the Jerusalem Chamber, and was thence conveyed to Westminster Abbey, where it was buried.

AuTxoRITIEs

Commercium Epistolicum D. Johannis Collins et aliorum de analysi promotes: jussu Societatis Regiae in lucem editum, &c. (1712; 2nd ed., 1722); H. Pemberton, A View of Sir Isaac Newton's Philosophy (1728); Colin Maclaurin, Sir Isaac Newton's Philosophical Discoveries (1775); F. Baily, An Account of the Rev. John Flamsteed, the First Astronomer-Royal, &c. (1835); W. Whewell's History of the Inductive Sciences (1837); S. P. Rigaud, Historical Essay on the First Publication of Sir Isaac Newton's Principia (1838); Edleston, Correspondence of Sir Isaac Newton and Professor Cotes, &c. (1850); Sir D. Brewster, Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton (1855; new ed. 1893); Lord Brougham and Routh's Analytical View of Sir Isaac Newton's Principia (1855); S. P. Rigaud, Correspondence of Scientific of the 17th Century, &c., from the Originals in the Collection of the Earl of Macclesfield (1841); J. Raphson, History of Fluxions, showing in a compendious manner the First Rise of and Various Improvements made in that Incomparable Method (1715); W. W. R. Ball, Essay on Newton's Principia (1893). A complete bibliography of Newton's writings has been given by G. J. Gray (Cambridge, 1880). The collected works of Newton were published in1779-1785by Dr Samuel Horsley, F.R.S., under the title Isaaci Newtoni Opera quae exstant Omnia. (H. M. T.)