Chapter II

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CHAPTER II.

NEWTON ENTERS TRINITY COLLEGE, CAMBRIDGE — ORIGIN OF HIS LOVE OF MATHEMATICS — STUDIES DESCARTES' GEOMETRY, AND THE WRITINGS OF SCHOOTEN AND WALLIS — IS DRIVEN FROM CAMBRIDGE BY THE PLAGUE — OBSERVES LUNAR HALOS IN 1664 — TAKES HIS DEGREE OF B.A. IN 1665 — DISCOVERS FLUXIONS IN THE SAME YEAR — HIS FIRST SPECULATIONS ON GRAVITY — PURCHASES A PRISM TO STUDY COLOURS — REVISES BARROW'S OPTICAL LECTURES — BUT DOES NOT CORRECT HIS ERRONEOUS OPINIONS ABOUT COLOURS — IS ELECTED A MINOR FELLOW OF TRINITY IN 1667 — AND A MAJOR FELLOW IN 1668 — TAKES HIS DEGREE OF M.A. — HIS NOTE-BOOK, WITH HIS EXPENSES FROM 1666 TO 1669 — MAKES A SMALL REFLECTING TELESCOPE — HIS LETTER OF ADVICE TO FRANCIS ASTON, WHEN GOING UPON HIS TRAVELS — HIS CHEMICAL STUDIES — HIS TASTE FOR ALCHEMY — HIS PAPER ON FLUXIONS SENT TO BARROW AND COLLINS IN 1669.

To a young mind thirsting for knowledge, and ambitious of the distinction which it brings, the transition from a provincial school to a university like that of Cambridge, — from intellectual solitude to the society of men imbued with all the literature and science of the age, must be an event of the deepest interest. To Newton it was a source of peculiar excitement. The history of science affords many examples where the young aspirant had been early initiated into her mysteries, and had even exercised his powers of invention and discovery before he was admitted within the walls of a college; but he who was to give Philosophy her laws, did not exhibit such early talent. No friendly counsel regulated his youthful studies, and no work of a scientific character guided him in <20> his course. In yielding to the impulse of his mechanical genius, his mind obeyed the laws of its own natural expansion, and following in the line of least resistance, it was thus drawn aside from the precipitous path which it was fitted to climb, and the unbarred strongholds which it was destined to explore.

When Newton, therefore, entered Trinity College, he brought with him a more slender portion of science than at his age falls to the lot of ordinary scholars; but this state of his acquirements was perhaps not unfavourable to the development of his powers. Unexhausted by premature growth, and invigorated by healthful repose, his mind was the better fitted to make those vigorous and rapid shoots which soon covered with foliage and with fruit the genial soil to which it had been transferred. Cambridge was consequently the real birth-place of Newton's genius. Her teachers fostered his earliest studies, — her institutions sustained his mightiest efforts, — and within her precincts were all his discoveries made and perfected. When he was called to higher official functions, his disciples kept up the pre-eminence of their master's philosophy, and their successors have maintained this seat of learning in the fulness of its glory, and rendered it the most distinguished among the universities of Europe.

With letters of introduction from his uncle, the Rev. James Ayscough, to his friends in Cambridge, Sir Isaac left Woolsthorpe in June 1661, and was admitted Subsizar at Trinity College on the 5th of that month, and matriculated Sizar^[1] on the 8th of July. Neither history <21> nor tradition has handed down to us any distinct account of the studies which Newton pursued at Cambridge during the first three or four years of his residence in that University. In Conduit's Memoirs of Newton, transmitted to Fontenelle,^[2] we find very little information on this point, and even that little is by no means correct. Before Newton left Woolsthorpe, his uncle had given him a copy of Sanderson's Logic, which he seems to have studied so thoroughly, that when he afterwards attended the lectures on that work, he found that he knew more of it than his tutor. Finding him so far advanced, his tutor intimated to him that he was about to read Kepler's Optics to some Gentlemen Commoners, and that he might attend the Readings if he pleased. Newton immediately studied the book at home, and when his tutor gave him notice that his Lectures upon it were to commence, he was surprised to learn that it had been already mastered by his pupil.

About the same time probably he bought a book on Judicial Astrology at Stourbridge fair,^[3] and in the course of perusing it he came to a figure of the Heavens, which he could not understand without a previous knowledge of trigonometry. He therefore purchased an English Euclid, <22> with an index of all the problems at the end of it, and having turned to two or three which he thought likely to remove his difficulties, he found the truths which they enunciated so self-evident, that he expressed his astonishment that any person should have taken the trouble of writing a demonstration of them. He therefore threw aside Euclid "as a trifling book," and set himself to the study of Descartes' Geometry,^[4] where problems not so simple seem to have baffled his ingenuity. Even after reading a few pages, he got beyond his depth, and laid aside the work; and he is said to have resumed it again and again, alternately retreating and advancing till he was master of the whole, without having received any assistance.^[5] The neglect which he had shown of the elementary truths of geometry he afterwards regarded as a mistake in his mathematical studies; and on a future occasion he expressed to Dr. Pemberton his regret that "he had applied himself to the works of Descartes, and other algebraic writers, before he had considered the Elements of Euclid with that attention which so excellent a writer deserved."^[6]

The study of Descartes' 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 7th page the date of Jan. 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 Schoo <23> ten; — 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." ^[7]

This commonplace book is particularly interesting from its containing the following important entry by Newton himself, after the lapse of thirty-five years, and when he had completed all his discoveries.

"July 4, 1699. — By consulting an account of my expenses at Cambridge,^[8] 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^[9] 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,^[10] I computed the <24> area of the Hyperbola at Boothby,^[11] in Lincolnshire, to two and fifty figures by the same method.

"Is. Newton."

In consequence of the devotion of his mind to these abstract studies, and his long continued observations upon a comet in 1664,^[12] which made him sit up late at night, Sir Isaac's health was impaired to such a degree, as Mr. Conduit informs us, that from this illness "he learnt to go to bed betimes." In the beginning of the same year, on the 19th February, Sir Isaac's attention was directed to the subject of circles round the moon, by two coronas of three and five-and-a-half degrees each, accompanied by the halo of 22° 35′, of which he subsequently gave the theory in his Treatise on Optics.^[13] In this year there were forty-four vacancies in the scholarships of Trinity College, and Newton was elected to one of them on the 28th of April. On this occasion he was examined in Euclid by Dr. Barrow, who formed an indifferent opinion of his knowledge, and hence he was led not only to read Euclid with care, but to form a more favourable estimate of the ancient geometer when he came to the interesting propositions on the equality of parallelograms on the same base and between the same parallels.^[14] In the month of January 1665, Newton took the degree of Bachelor of Arts, along with twenty-five other members of Trinity College, but we are not able to ascertain the academical rank which he held among the graduates, as the grace for <25> that year does not contain the order of seniority of the Bachelors of Arts. The Proctors at this time were John Slader of Trinity, and Benjamin Pulleyn of Trinity, Newton's tutor, and the persons appointed in conjunction with them to examine the Questionists, were John Eachard of Catherine Hall, the satirical author of the Grounds, &c., of the Contempt of the Clergy, and Thomas Gipps of Trinity.^[15]

In the same year Newton committed to writing his first discovery of Fluxions. This paper, written by his own hand, and dated May 20, 1665, represents in pricked letters the fluxions applied to their fluents, and in another leaf of the same waste book the method of fluxions is described without pricked letters, and bears the date of May 16, 1666. In the same book, with the date of November 13, 1665, there is another paper on Fluxions, with their application to the drawing of tangents, and "the finding the radius of curvity of any curve." ^[16] In the month of October 1666, Newton drew up another small tract, in which the method of Fluxions is again put down without pricked letters, and applied to Equations involving facts or surds.^[17]

It was doubtless in the same remarkable year 1666, or perhaps in the autumn of 1665, that Newton's mind was first directed to the subject of Gravity. He appears to have left Cambridge some time before the 8th of August 1665, when the College was "dismissed" on account of <26> the Plague, and it was therefore in the autumn of that year, and not in that of 1666, that the apple is said to have fallen from the tree at Woolsthorpe, and suggested to Newton the idea of gravity. When sitting alone in the garden, and speculating on the power of gravity, it occurred to him that as the same power by which the apple fell to the ground, was not sensibly diminished at the greatest distance from the centre of the earth to which we can reach, neither at the summits of the loftiest spires, nor on the tops of the highest mountains, it might extend to the moon and retain her in her orbit, in the same manner, as it bends into a curve a stone or a cannon ball, when projected in a straight line from the surface of the earth. If the moon was thus kept in her orbit by gravitation to the earth, or, in other words, its attraction, it was equally probable, he thought, that the planets were kept in their orbits by gravitating towards the sun. Kepler had discovered the great law of the planetary motions, that the squares of their periodic times were as the cubes of their distances from the sun, and hence Newton drew the important conclusion that the force of gravity or attraction, by which the planets were retained in their orbits, varied as the square of their distances from the sun. Knowing the force of gravity at the earth's surface, he was, therefore, led to compare it with the force exhibited in the actual motion of the moon, in a circular orbit; but having assumed that the distance of the moon from the earth was equal to sixty of the earth's semidiameters, he found that the force by which the moon was drawn from its rectilineal path in a second of time was only 13.9 feet, whereas at the surface of the earth it was 16.1 in a second. This great discrepancy between his theory and what he then considered to be the fact, induced him <27> to abandon the subject, and pursue other studies with which he had been previously occupied.^[18]

It does not appear from any of the documents which I have seen, at what time Newton made his first optical discoveries. On the authority of one of his memorandum books, containing an account of his expenses, it is stated by Conduit that he purchased a prism, in order to make some experiments on Descartes' Theory of Colours, and that he not only detected the errors of the French philosopher, but established his own views of the subject; but this is contradicted by Newton himself, who distinctly informs us that it was in the beginning of the year 1666, that he procured a glass prism "to try therewith the phenomena of colours."^[19] There is no evidence, however, that he used it for this purpose, and there is every reason to believe that he was not acquainted with the true composition of light when Dr. Barrow completed his Optical Lectures, published in 1669.^[20] In the preface of this work, Dr. Barrow acknowledges his obligation to his colleague Mr. Isaac Newton, as a man of a fine disposition <28> and great genius, for having revised the MSS., and corrected several oversights, and made some additions of his own.^[21] Now, in the twelfth Lecture there are some observations on the nature and origin of colours, which are so erroneous and unphilosophical, that Newton could not have permitted his friend to publish them had he been then in the possession of their true theory. According to Barrow, who introduces the subject of colours as an unusual digression, White is that which discharges a copious light, scattered, equally in every direction. Black is that which emits light not at all, or very sparingly. Red is that which emits light more condensed than usual, but interrupted by shady interstices. Blue is that which discharges a rarefied light, or one excited by a weaker force, as in bodies which consist of white and black particles arranged alternately, such, for example, as the clear ether in which there float fewer particles that reflect light, while the rest take away light, the sea in which the white salt is mixed with the black water, and the blue shadows seen at the same time by candle and day light, which are produced by the whiteness of the paper mixed with the faint light or blackness of the twilight. Yellow consists of much white and a little red interspersed, and Purple of much blue and some red. Green seems to have puzzled Dr. Barrow. He says that it is somehow allied to Blue; but he adds, let wiser men find out the difference, I dare not conjecture. These opinions are so unsound, that they could not fail to have attracted the attention of Newton, who had certainly begun to study the subject of colours; and if he had discovered at this time that white was a <29> mixture of all the colours, and black a privation of them all, he could not have permitted the absurd speculations of his friend and master to pass uncorrected.^[22]

While Newton was thus occupied with the subjects of Fluxions and Gravity, he "applied himself also to the grinding of optic glasses of other figures than spherical." Descartes, in his Dioptrics, published in 1629, and more recently James Gregory, in his Optica Promota, published in 1663, had shewn that parallel and diverging rays could only be reflected or refracted to a point or focus by mirrors or lenses, whose surfaces were paraboloidal, ellipsoidal, or hyperboloidal, or of some other form not spherical. Descartes had even invented and described machines by which lenses of these shapes could be ground and polished, and it was the universal opinion that the perfection of refracting telescopes and microscopes depended on the degree of accuracy with which lenses of these forms could be executed.

While engaged in this work Newton made his first experiments with the prism, and he was soon induced to abandon what he calls his "glass-works," in consequence of having found "that the perfection of telescopes was 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 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." <31> He was therefore led to "take reflections into consideration," but in consequence of the interruption produced by the Plague, "it was more than two years before he proceeded."

After his return to Cambridge,^[23] on the disappearance of the Plague, he was, on the 1st of October 1667, elected Minor Fellow, and an apartment called "The Spiritual Chamber," assigned to him by the Master, — a locality which Mr. Edleston conjectures to be the ground room next the chapel in the north-cast corner of the great court. A few weeks after this he went to Lincolnshire, and returned on the 12th February 1667-8. On the 16th March 1668, he took his degree of M.A., and was the twenty-third on the list of 148 signed by the Senior Proctor.^[24]

About this time, and during the period extending from 1666 to 1669, when he succeeded to the Lucasian chair, his studies were of a very miscellaneous kind, and were doubtless interrupted not only by the appearance and reap <31> pearance of the plague, but by the preparations necessary for taking his degree. In his common note-book,^[25] which I found among the family papers, and which, along with a number of problems in geometry and the Conic Sections, contains an account of his expenses from 1665 to 1669, there are many entries which throw some light upon his social character as well as upon his studies. During his absence from College in 1665 and 1666, we find him purchasing Philosophical Intelligences, the History of the Royal Society, Gunter's Book and Sector from Dr. Fox, together with magnets, compasses, glass-bubbles, drills, mandrels, gravers, hones, and hammers. In 1667, he purchases Bacon's Miscellany, three prisms, and four ounces of putty.^[26]

He records his jovial expenses, not only on the occasion of his taking his two degrees, but "at the tavern several other times." He acknowledges his having "lost at cards twice;" but this is compensated by his liberality to his "cousin Ayscough," on whom, and "on other acquaintance," he "spends" considerable sums, — by his generosity to his sister, for whom he buys oranges, — and his kindness to Dr. Wickins, to whom he lends considerable sums of money. It appears, too, from this notebook, that Newton went to London on Wednesday the 5th August 1668, and returned to Cambridge on Monday the 28th September, after an absence of nearly two months; but the object of his journey is nowhere mentioned. It is not improbable that he went there to purchase lenses, and apparatus and materials for chemical experiments, — <32> a new branch of science which seems at this time to have occupied his attention, and which he continued to prosecute with much zeal during the most active period of his life. In April 1669, he records the purchase of lenses in London, and there follows a long list of chemical substances, headed by mercury, together with a furnace, and an air-furnace.^[27]

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Towards the end of 1668, Newton carried into effect, on a small scale, his resolution to "take reflections into consideration." Thinking "it best to proceed by degrees," he first "made a small perspective to try whether his conjecture would hold good or not."^[28]

The telescope was six inches long. The aperture of the large speculum was something more than an inch, and, as the eye-glass was a plano-convex lens, with a focal length of one-sixth or one- seventh of an inch, "it magnified about forty times in diameter," which he believed was more than any six feet refracting telescope could do with distinctness. Owing to the badness of the materials which he used, and the want of a good polish, it did not represent objects so distinctly as a six-feet refractor, yet Sir Isaac was of opinion that it would discover as much as any three or four feet refractor, especially if the objects are luminous. He saw with it Jupiter distinctly round, with his four satellites, and also the horns or "moonlike phase of Venus," though this last phenomenon required a nice adjustment <34> of the instrument. He therefore considered this small telescope as "an epitome" of what may be done by reflections; and he did not doubt that, in time, a six feet reflector might be made which would perform as much as any sixty or hundred feet refractor. In consequence of interruptions, Sir Isaac did not proceed any farther in the construction of reflectors till the autumn of 1671.

It was during this period of his history, on the 18th of May 1669, that Sir Isaac wrote the celebrated letter of advice to his young friend, Mr. Aston, who, at the age of twenty-seven, was about to make a tour on the Continent. This "letter" is a very interesting production. ^[29] It does not evince much acquaintance with the ways of the world, but it shows some knowledge of the human heart, and throws a strong light on the character and opinions of its author. In his chemical studies, which, as we have just seen, he had recently commenced, his mind was impressed with some belief in the doctrines of alchemy, and he certainly pursued his experiments to a late period of his life, with the hope of effecting some valuable transmutations. Among the subjects, therefore, to which he requests Mr. Aston to pay attention, there are several which indicate this tendency of his mind. He desires him to observe the products of nature, especially in mines, with the circumstances of mining, and of extracting metals or minerals out of their ores, and refining them; and, what he considered as far more important than this, he wishes him to observe if there were any transmutations out of one species into another, as, for example, out of iron into copper, out of one salt into another, or into an insipid body, &c. Such transmutations, he adds, are above all others worth his noting, being the most luciferous, and many times lucri <35> ferous experiments too, in philosophy ! Among the particular observations to which he calls the attention of his friend, is that of a certain vitriol, which changes iron into copper, and which is said to be kept a secret for the lucrative purpose of effecting that transmutation. He is to inquire also whether in Hungary, or in the mountains of Bohemia, there are rivers whose waters are impregnated with gold, dissolved by some corrosive fluids like aqua regis; and whether the practice of laying mercury in the rivers till it be tinged with gold, and then separating the gold by straining the mercury through leather, be still a secret or openly practised. There was at this time in Holland a notorious alchemist of the name of Bory, who, as Sir Isaac says, was some years since imprisoned by the Pope, in order to extort from him secrets of great worth, both "as to medicine and profit," and who made his escape into Holland, where they granted him a guard. "I think," adds Sir Isaac, "he usually goes clothed in green: Pray, inquire what you can of him, and whether his ingenuity be any profit to the Dutch!" We have not been able to discover the results of Mr. Aston's inquiries, but whatever they were they did not damp the ardour of Newton in his chemical researches, nor extinguish the hope which he seems to have cherished, of making "philosophy lucriferous," by transmuting the baser metals into gold.

But however fascinating these studies were to our young philosopher, he did not permit them to interfere with his nobler pursuits. At the very time when writing to Mr. Aston, we find him occupied with his fluxionary calculus, and transmitting to Dr. Barrow his celebrated paper On Analysis by Equations with an infinite number of terms, with permission to communicate it to their <36> mutual friend, Mr. Collins. In announcing this communication on the 20th June 1669, and promising to send it by the next opportunity, Dr. Barrow keeps the name of its author a secret, and merely tells Mr. Collins that he is a friend staying at Cambridge, who has a powerful genius for such matters. In his next letter of the 31st July, accompanying the paper, he expresses the hope that it will not a little delight him; and, in a third letter to Collins of the 20th August, he mentions how much he is pleased with the favourable opinion which his correspondent has of it, and adds, that "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, has made very great progress in this branch of mathematics."