Principia Mathematica (Motte Translation, 1848) — part 3 of 45

the areas to the times of their description, our author inferred that the force which retained the planet in its orbit was always directed to the sun ; and from the second, namely, that every planet moves in an ellipse with the sun in one of its foci, he drew the more general inference that the force by which the planet moves round that focus varies inversely as the square of its dis- tance therefrom : and he demonstrated that a planet acted upon by such a force could not move in any other curve than a conic section ; showing when the moving body would describe a circu- lar, an elliptical, a parabolic, or hyperbolic orbit. He demon- strated, too, that this force, or attracting, gravitating power re- sided in every, the least particle ; but that, in spherical masses, it operated as if confined to. their centres ; so that, one sphere or body will act upon another sphere or body, with a force directly proportional to the quantity of matter, and inversely as the square of the distance between their centres ; and that their velocities of mutual approach will be in the inverse ratio of their quantities o^ matter. Thus he grandly outlined the Universal Law. Verify- ing its truth by the motions of terrestrial bodies, then by those of the moon and other secondary orbs, he finally embraced, in one mighty generalization, the entire Solar System — all the move- ments of all its bodies — planets, satellites and comets — explain- ing and harmonizing the many diverse and theretofore inexplica- ble phenomena.

Guided by the genius of Newton, we see sphere bound to sphere, body to body, particle to particle, atom to mass, the min- utest part to the stupendous whole — each to each, each to all, and all to each— in the mysterious bonds of a ceaseless, recipro- cal influence. An influence whose w^orkings are shown to be alike present in the globular dew-drop, or oblate-spheroidal earth ; in the falling shower, or vast heaving ocean tides ; in the flying thistle-down, or fixed, ponderous rock ; in the swinging pendulum, or time-measuring sun ; in the varying and unequal moon, or earth's slowly retrograding poles ; in the uncertain meteor, or blazing comet wheeling swiftly away on its remote, yet determined round. An influence, in fine, that may link system to system through all the star-glowing firmament ; then firmament to firma-

LIFE OF SIR ISAAC NEWTON. 35

meni ; aye, firmament to firmament, again and again, till, con- verging home, it may be, to some ineffable centre, where more presently dwells He who inhabiteth immensity, and where infini- tudes meet and eternities have their conflux, and where around move, in softest, swiftest measure, all the countless hosts that crowd heaven's fathomless deeps.

And yet Newton, amid the loveliness and magnitude of Om- nipotence, lost not sight of the 'Almighty One. A secondary, however universal, was not taken for the First Cause. An im- pressed force, however diffused and powerful, assumed not the functions of the creating, giving Energy. Material beauties, splendours, and sublimities, however rich in glory, and endless in extent, concealed not the attributes of an intelligent Supreme. From the depths of his own soul, through reason and the Word, he had risen, a priori^ to God : from the heights of Omnipotence, through the design and law of the builded universe, he proved a posteriori, a Deity. " I had," says he, " an eye upon such prin- ciples as might work, with considering men, for the belief of a Deity," in writing the Principia ; at the conclusion whereofj he teaches that — " this most beautiful system of the sun, planets and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. And if the fixed stars are the centres of other like systems, these, being formed by the like wise counsels, must be all subject to the dominion of One ; especially since the light of the fixed stars is of the same nature with the light of the sun, and from every system light passes into all other systems : and lest the systems of the fixed stars should, by their gravity, fall on each other mutually, he hath placed those systems at immense distances one from another.

" This Being governs all things, not as the soul of the world, but as Lord over all ; and on account of his dominion he is wont to be called Lord God TravroKQarcjQ or Universal Ruler ; for God is a relative word, and has a respect to servants ; and Deity is the dominion of God, not over his own body, as those imagine who fancy God to be the soul of the world, but over servants. The Supreme God is a Being eternal, infinite, absolutely perfect ; but a being, however perfect, without dominion, cannot be said to

36 LIFE OF SIR ISAAC NEWTON.

be Lord God ; for we say, my God, your God, the God of Israel, the God of Gods, and Lord of Lords ; but we do not say, my E-ternal, your Eternal, the Eternal of Israel, the Eternal of Gods ; we do not say my Infinite, or my Perfect : these are titles w^hich have no respect to servants. The word God usually signifies Lord ; but every Lord is not God. It is the dominion of a spir- itual Being which constitutes a God ; a true, supreme, or imagi- nary dominion makes a true, supreme, or imaginary God. And from his true dominion it follows that the true God is a living, intelligent and powerful Being ; and from his other perfections, that he is supreme or most perfect. He is eternal and in- finite, omnipotent and omniscient ; that is, his duration reaches from eternity to eternity ; his presence from infinity to infinity ; he governs all things and knows all things, that are or can be done. He is not eternity or infinity, but eternal and infinite ; he is not duration and space, but he endures and is present. He endures forever and is everywhere present ; and by existing always and everywhere, he constitutes duration and space. Since every particle of space is ahvays, and every indivisible moment of duration is everywhere, certainly the Maker and Lord of things cannot be never and nowhere. Every soul that has perception is, though in different times and different organs of sense and mo- tion, stiH the same indivisible person. There are given succes- sive parts in duration, co-existent parts in space, but neither the one nor the other in the person of a man, or his thinking principle ; and much less can they be found in the thinking sub- stance of God. Every man, so far as he is a thing that has per- ception, is one and the same man during his w^hole life, in all and eac'i of his organs of sense. God is one and the same God, al- w^ays and everyv^here. He is omnipresent, not virtually only, but also substantially ; for virtue cannot subsist without sub- stance. In him are all things contained and moved ; yet neither affects the other ; God suffers nothing from the motion of bodies ; bodies find no resistance from the omnipresence of God. It is allowed by all that the Supreme God exists necessarily ; and by the same necessity he exists ahvays and evei^y where. Whence also he is all similar, all eye, all ear, all brain, all arm, all power

LIFE OF SIR ISAAC NEWTON. 37

to perceive, to understand, and to act ; but in a manner not at all human, in a manner not at all corporeal, in a manner utterly un- known to us. As a blind man has no idea of colours, so have we no idea of the manner by which the all-wise God perceives and understands all things. He is utterly void of all body, and bodily figure, and can therefore neither be seen, nor heard, nor touched ; nor ought he to be worshipped under the representation of any corporeal thing. We have ideas of his attributes, but what the real substance of anything is we know not. In bodies we see onlv their figures and colours, we hear only the sounds, we touch only their outward surfaces, we smell only the smells, and taste only the savours ; but their inward substances are not to be known, either by our senses, or by any reflex act of our minds : much less, then, have we any idea of the substance of God. We know him only by his most wise and excellent contrivances of things, and final causes ; we admire him for his perfections ; but we rev- erence and adore him on account of his dominion ; for w^e ador^ him as his servants ; and a god without dominion, providence, and final causes, is nothing else but Fate and Nature. BKnd meta- physical necessity, which is certainly the same always and every- where, could produce no variety of things. Ail that diversity of natural things which we find suited to different times and places could arise from nothing but the ideas and will of a Being neces- sarily existing."

Thus, the diligent student of science, the earnest seeker of truth, led, as through the courts of a sacred Temple, wherein, at each step, new wonders meet the eye, till, as a crowning grace, they stand before a Holy of Holies, and learn that all science and all truth are one which hath its beginning and its end in the- knowledge of Him whose glory the heavens declare, and w^hose handiwork the firmament showeth forth.

The introduction of the pure and lofty doctrines of the Prin- ciPiA was perseveringly resisted. Descartes, with his system of vortices, had sown plausibly to the imagination, and error had struck down deeply, and shot up luxuriantly, not only in the- popular, but in the scientific mind. Besides the idea — in itself so simple and so grand — that the great masses of the planets were

38 LIFE OF SIR ISAAC NEWTON.

suspended in empty space, and retained in tlieir orbits bj an in- visible influence residing in the sun- — was to the ignorant a thing inconceivable, and to the learned a revival of the occult qualities of the ancient physics. This remark applies particularly to the continent. Leibnitz misapprehended ; Huygens in part rejected ; John Bernouilli opposed ; and Fontenelle never received the doc- trines of the Principia. So that, the saying of Voltaire is prob- ably true, that though Newton survived the publication of his great work more than forty years, yet, at the time of his death, he had not above twenty followers out of England.

But in England, the reception of our author's philosophy was rapid and triumphant. His own labours, while Lucasian Pro- fessor; those of his successors in that Chair — Whiston and Saunderson ; those of Dr. Samuel Clarke, Dr. Laughton, Roger Cotes, and Dr. Bentley ; the experimental lectures of Dr. Keill and Desaguliers ; the early and powerful exertions of David Gregory at Edinburgh, and of his brother James Gregory at St. Andrew's, tended to diffuse widely in England and Scotland a knowledge of, and taste for the truths of the Principia. Indeed, its mathematical doctrines constituted, from the first, a regular part of academical instruction ; while its physical truths, given to the public in popular lectures, illustrated by experiments, had, before the lapse of twenty years, become familiar to, and adopted by the general mind. Pemberton's popular " View of Sir Isaac Newton's Philosophy" was published, in 1728 ; and the year after- ward, an English translation of the Principia, and System of the World, by Andrew Mptte. And since that period, the labours of Le Seur and Jacquier, of Thorpe, of Jebb, of Wright and others have greatly contributed to display the most hidden treasures of the Principia.

About the time of the publication of the Principia, James IL, bent on re-establishing the Romish Faith, had, among other ille- gal acts, ordered by mandamus, the University of Cambridge to confer the degree of Master of Arts upon an ignorant monk. Obedience to this mandate was resolutely refused. Newton was one of the nine delegates chosen to defend the independence of the University. They appeared before the High Court ; — and

LIFE OP SIR ISAAC NEWTON. 39

successfully: the king abandoned his design. The prominent part which our author took in these proceedings, and his eminence in the scientific world, induced his proposal as. one of the parlia- mentary representatives of the University. He was elected, in 1688, and sat in the Convention Parliament till its dissolution. After the first year, however, he seems to have given little or no attention to his parliamentary duties, being seldom absent from the University till his appointment in the Mint, in 1695.

Newton began his theological researches sometime previous to 1691 ; in the prime of his years, and in the matured vigour of his intellectual powers. From his youth, as we have seen, he had devoted himself with an activity the most unceasing, and an energy almost superhuman to the discovery of physical truth ; — giving to Philosophy a new foundation, and to Science a new temple. To pass on, then, from the consideration of the material, more directly to that of the spiritual, was a natural, nay, with so large and devout a soul, a necessary advance. The Bible was to him of inestimable worth. In the elastic freedom, which a pure and unswerving faith in Him of Nazareth gives, his mighty facul- ties enjoyed the only completest scope for development. His original endowment, however great, combined with a studious application, however profound, would never, without this libera- tion from the dominion of passion and sense, have enabled him to attain to that wondrous concentration and grasp of intellect, for which Fame has as yet assigned him no equal. Gratefully he owned, therefore, the same Author in the Book of Nature and the Book of Revelation. These were to him as drops of the same unfathomable ocean ; — as outrayings of the same inner splendour ; — as tones of the same ineffable voice ; — as segments of the same infinite curve. With great joy he had found himself enabled to proclaim, as an interpreter, from the hieroglyphs of Creation, the existence of a God : and now, w^ith greater joy, and in the fulness of his knowledge, and in the fulness of his strength, he laboured to make clear, from the utterances of the inspired Word, the far mightier confirmations of a Supreme Good, in all its glorious amplitude of Being and of Attribute ; and to bring the infallible workings thereof plainly home to the understandings and the

40 LIFE OF SIR ISAAC NEWTON.

affections of his fellow-men ; and finally to add the weight of his own testimony in favour of that Religion, whose truth is now, in- deed, " girded with the iron and the rock of a ponderous and co- lossal demonstration."

His work, entitled, Observations upon the Prophecies op Holy Writ, particularly the Prophecies of Daniel and the Apocalypse of St. John, first published in London, in 1733 4to. consists of two parts : the one devoted to the Prophecies of Daniel, and the other to the Apocalypse of St. John. In the first part, he treats concerning the compilers of the books of the Old Testament ; — of the prophetic language ; — of the vision of the four beasts ; — of the kingdoms represented by the feet of the image composed of iron and clay ; — of the ten kingdoms repre- sented by the ten horns of the beast ; — of the eleventh horn of Daniel's fourth beast ; of the power which should change times and laws ; — of the kingdoms represented in Daniel by the ram and he-goat ; — of the prophecy of the seventy weeks ; — of the times of the birth and passion of Christ ; — of the prophecy of the Scripture of Truth ; — of the king who doeth according to his will, and magnified himself above every god, and honoured Mahuzzims, and regarded not the desire of women ; — of the Mahuzzim, hon- oured by the king who doeth according to his will. In the sec- ond part, he treats of the time when the Apocalypse was written ; of the scene of the vision, and the relation which the Apocalypse has to the book of the law of Moses, and to the worship of God in the temple ; — of the relation w^hich the Apocalypse has to the prophecies of Daniel, and of the subject of the prophecy itself Newton regards the prophecies as given, not for the gratification of man's curiosity, by enabling him to foreknow ; but for his con- viction that the world is governed by Providence, by witnessing their fulfilment. Enough of prophecy, he thinks, has already been fulfilled to afford the diligent seeker abundant evidence of God's providence. The whole work is marked by profound 'erudition, sagacity and argument.

And not less learning, penetration and masterly reasoning are conspicuous in his Historical Account of Two Notable Corruptions of Scriptures in a Letter to a Friend. This

LIFE OF SIR ISAAC NEWTON. 41

Treatise, first accurately published in Dr. Horsley's edition of his works, relates to two texts : the one, 1 Epistle of St. John v. 7 ; the other, 1 Epistle of St. Paul to Timothy iii. 16. As this work had the effect to deprive the advocates of the doctrine of the Trinity of two leading texts, Newton has been looked upon as an Arian ; but there is absolutely nothing in his writings to warrant such a conclusion.

His remaining theological works consist of the Lexicon Pro- PHETicuM, which was left incomplete ; a Latin Dissertation on the sacred cubit of the Jews, which was translated into English, and published, in 1737, among the Miscellaneous Works of John Greaves ; and Four Letters addressed to Dr. Bentley, contain- ing some arguments in proof of a Deity. These Letters were dated respectively : 10th December, 1692 ; 17th January, 1693 ; 25th February, 1693; and 11th February, 1693— the fourth bearing an earlier date than the third. The best faculties and the profoundest acquirements of our author are convincingly manifest in these lucid and powerful compositions. They were published in 1756, and reviewed by Dr. Samuel Johnson.

Newton's religious writings are distinguished by their absolute freedom from prejudice. Everywhere, throughout them, there glows the genuine nobleness of soul. To his whole life, indeed, we may here fitly extend the same observation. He was most richly imbued with the very spirit of the Scriptures which he so delighted to study and to meditate upon. His was a piety, so fervent, so sincere and practical, that it rose up like a holy incense from every thought and act. His a benevolence that not only willed, but endeavoured the best for all. His a philanthropy that held in the embracings of its love every brother-man. His a toleration of the largest and the truest ; condemning per- secution in every, even its mildest form ; and kindly encouraging each striving after excellence : — a toleration that came not of indifference — for the immoral and the impious met with their quick rebuke — but a toleration that came of the wise humbleness and the Christian charity, which see, in the nothingness of self and the almightiness of Truth, no praise for the ablest, and no blame for the feeblest in their strugglings upward to light and life.

42 ■ LIFE OF SIR ISAAC NEWTON.

Tn the winter of 1691-2, on returning from chapel, one morn- ing, Newton found that a favourite little dog, called Diamond, had overturned a lighted taper on his desk, and that several pa- pers containing the results of certain optical experiments, were nearly consumed. His only exclamation, on perceiving his loss, was, " Oh Diamond, Diamond, little knowest thou the mischiet thou hast done." Dr. Brewster, in his life of our author, gives the following extract from the manuscript Diary of Mr. Abraham De La Pry me, a student in the University at the time of this oc- currence.

" 1692. February, 3. — What I heard to-day I must relate. There is one Mr. Newton (whom I have very oft seen). Fellow of Trinity College, that is mighty famous for his learning, being a most excellent mathematician, philosopher, divine, &c. He has been Fellow of the Eoyal Society these many years ; and among other very learned books and tracts, he's written one upon the mathe- matical principles of philosophy, which has given him a mighty name, he having received, especially from Scotland, abundance of congratulatory letters for the same ; but of all the books he ever wrote, there was one of colours and light, established upon thou- sands of experiments which he had been twenty years of making, and w^hich had cost him many hundreds of pounds. This book which he valued so much, and which was so much talked of, had the ill luck to perish, and be utterly lost just when the learned author was almost at putting a conclusion at the same, after this manner: In a w^inter's morning, leaving it among his other papers on his study table while he went to chapel, the candle, which he had unfortunately left burning there, too, catched hold by some means of other papers, and they fired the aforesaid book, and ut- terly consumed it and several other valuable writings ; and which is most wonderful did no further mischief But when Mr. New- ton came, from chapel, and had seen what was done, every one thought he would have run mad, he was so troubled thereat that he was not himself for a month after. A long account of this his system of colours you may find in the Transactions of the Royal Society, which he had sent up to them long before this sad mis- chance happened unto him."

LIFE OP SIR ISAAC NEWTON. 43

It will be borne in mind that all of Newton's theological v.Ti- tings, with the exception of the Letters to Dr. Bentley, were composed before this event which, we must conclude, from Pryme's w^ords, produced a serious impression upon our author for about a month. But M. Biot, in his Life of Newton, relying on a memorandum contained in a small manuscript Journal of Huygens, xieclares this occurrence to have caused a derangement of New- ton's intellect. M. Biot's opinions and deductions, however, as well as those of La Place, upon this subject, w^ere based upon erroneous data, and have been overthrown by the clearest proof There is not, in fact, the least evidence that Newton's reason was, for a single moment, dethroned ; on the contrary, the testimony is conclusive that he was, at all times, perfectly capable of carry- ing on his mathematical, metaphysical and astronomical inquiries. Loss of sleep, loss of appetite, and irritated nerves v/ill disturb somewhat the equanimity of the most serene ; and an act done, or language employed, under such temporary discomposure, is not a just criterion of the general tone and strength of a man's mind. As to the accident itself, we may suppose, whatever might have been its precise nature, that it greatly distressed him, and, still further, that its shock may have originated the train of nervous derangements, which afEicted him, more or less, for two years afterward. Yet, during this very period of ill health, we find him putting forth his highest powers. In 1692, he prepared for, and transmitted to Dr. Wallis the first proposition of the Treatise on Quadratures, with examples of it in first, second and third flux- ions. He investigated, in the same year, the subject of haloes ; making and recording numerous and important observations rela- tive thereto. Those profound and beautiful Letters to Dr. Bentley were written at the close of fliis and the beginning of the next year. In October, 1693, Locke, who w^as then about publishing a second edition of his work on the Human Understanding, request- ed Newton to reconsider his opinions on innate ideas. And in 1694, he was zealously occupied in perfecting his lunar theory ; visiting Flamstead, at the Royal Observatory of Greenwich, in September, and obtaining a series of lunar observations : and

44 LIFE OF SIR ISAAC NEWTOX.

commencing, in October, a correspondence with that distinguished practical Astronomer, which continued till 1698.

We now arrive at the period when Newton permanently with- drew from the seclusion of a collegiate, and entered upon a more active and public life. He was appointed Warden of the Mint, in 1695, through the influence of Charles Montague, Chancellor of the Exchequer, and afterward Earl of Halifax. The current coin of the nation had been adulterated and debased, and Mon- tague undertook a re-coinage. Our author's mathematical and chemical knowledge proved eminently useful in accomplishing this difficult and most salutary reform. In 1699, he was pro- moted to the Mastership of the Mint — an office worth twelve or fifteen hundred pounds per annum, and which he held during the remainder of his life. He wrote, in this capacity, an official Re- port on the Coinage, which has been published ; he also prepared a Table of Assays of Foreign Coins, which was printed at the end of Dr. Arbuthnot's Tables of Ancient Coins, Weights, and Measures, in 1727.

Newton retained his Professorship at Cambridge till 1703, But he had, on receiving the appointment of Master of the Mint, in 1699, made Mr. Whiston his deputy, with all the emoluments of the office ; and, on finally resigning, procured his nomination to the vacant Chair.

In January 1697, John Bernouilli proposed to the most distin- guished mathematicians of Europe two problems for solution. Leibnitz, admiring the beauty of one of them, requested the time for solving it to be extended to twelve months — twice the period originally named. The delay was readily granted. Newton, how- ever, sent in, the day after he received the problems, a solution of them to the President of the Eoyal Society. Bernouilli obtained solutions from Newton, Leibinitz and the Marquis De L'Hopital ; but Newton's though anonymous, he immediately recognised " tanquain iingue leonem^^^ as the lion is known by his claw. We may mention here the famous problem of the trajectories proposed by Leibnitz, in 1716, for the purpose of "' feeling the pulse of the English Analysts." Newton received the problem about ^YQ o'clock in the afternoon, as he was returning from the

LIFE OF SIR ISAAC NEWTON. 45

Mint ; and though it was extremely difficult and he himself much fatigued, yet he completed its solution, the same evening before he went to bed.

The history of these problems affords, by direct comparison, a striking illustration of Newton's vast superiority of mind. That amazing concentration and grasp of intellect, of which we have spoken, enabled him to master speedily, and, as it were, by a single effort, those things, for the achievement of which, the many would essay utterly in vain, and the very, very few attain only after long and renewed striving. And yet, with a modesty as unparalleled as his power, he attributed his successes, not to any extraordinary sagacity, but solely to industry and patient thought. He kept the subject of consideration constantly before him, and waited till the first dawning opened gradually into a full and clear light ; never quitting, if possible, the mental process till the object of it were wholly gained. He never allowed this habit of meditation to appear in his intercourse with society ; but in the privacy of his own chamber, or in the midst of his own family, he gave himself up to the deepest abstraction. Occupied with some interesting investigation, he would often sit down on his bedside, after he rose, and remain there, for hours, partially dressed. Meal-time would frequently come and pass unheeded ; so that, unless urgently reminded, he would neglect to take the re- quisite quantity of nourishment. But notwithstanding his anx- iety to be left undisturbed, he w^ould, when occasion required, turn aside his thoughts, though bent upon the most intricate re- search, and then, when leisure served, again direct them to the very point where they ceased to act : and this he seemed to ac- complish not so much by the force of his memory, as by the force of his inventive faculty, before the vigorous intensity of which, no subject, however abstruse, remained long unexplored.

He was elected a member of the Royal Academy of Sciences at Paris, in 1699, when that distinguished Body were empowered, by a new charter, to admit a small number of foreign associates. In 1700, he communicated to Dr. Halley a description of his re- flecting instrument for observing the moon's distance from the fixed stars. This description was published in the Philosophical

46 LIFE OF SIR ISAAC NEWTON.

Transactions, in 1742. The instrument was the same as that produced by Mr. Hadley, in 1731, and which, under the name of Hadley's Quadrant, has been of so great use in navigation. On the assembling of the new Parliament, in 1701, Newton was re- elected one of the members for the University of Cambridge. In 1703, he was chosen President of the Royal Society of London, to which office he was annually re-elected till the period of his decease — about twenty-five years afterward.

Our author unquestionably devoted more labour to, and, in many respects, took a greater pride in his Optical, than his other discoveries. This science he had placed on a new and indestruc- tible basis ; and he wished not only to build, but to perfect the costly and glowing structure. He had communicated, before the publication of the Principia, his most important researches on light to the Royal Society, in detached papers which were inserted in successive numbers of the Transactions ; but he did not pub- lish a connected view of these labours till 1704, when they appeared under the title of Optics : or, a Treatise on the Reflexions, Refractions, Inflexions and Colours of Light. To this, but to no subsequent edition, were added two Mathematical Trea- tises, entitled, Tractatus duo de speciebus et magnitudine FiGURARUM cuRViLiNEARUM ; the ouc bearing the title Tractatus de Quadratura Curvarum ; and the other, that of Enumeratio linearum tertii ordinis. The publication of these Mathemati- cal Treatises was made necessary in consequence of plagiarisms from the manuscripts of them loaned by the author to his friends. Dr. Samuel Clarke published a Latin translation of the Optics, in in 1706 ; whereupon he was presented by Newton, as a mark of his grateful approbation, with five hundred pounds, or one hun- dred pounds for each of his children. The work was afterward translated into French. It had a remarkably wide circulation, and appeared, in several successive editions, both in England and on the Continent. There is displayed, particularly on this Opti- cal Treatise, the author's talent for simplifying and communica- ting the profoundest speculations. It is a faculty rarely united to that of the highest invention. Newton possessed both ; and thus that mental perfectness which enabled him to create, to combine,

LIFE OF SIR ISAAC NEWTON. 47

and to teach, and so render himself, not the " ornament" only, but inconceivably more, the pre-eminent benefactor of his specie^.

The honour of knighthood was conferred on our author in 1705. Soon afterward, he was a candidate again for the Repre- sentation of the University, but was defeated by a large majority. It is thought that a more pliant man was preferred by both min- isters and electors. Newton was always remarkable for simplicity of dress, and his only known departure from it was on this oc- casion, when he is said to have appeared in a suit of laced clothes.

The Algebraical Lectures which he had, during nine years, delivered at Cambridge, were published' by Whiston, in 1707, under the title of Arithmetica Universalis, sine de Composi- TiONE ET Resolutione Arithmetica LiBER. This publication is said to have been a breach of confidence on Whiston's part. Mr. Ralphson, not long afterward, translated the work into English • and a second edition of it, with improvements by the author, was issued at London, 1712, by Dr. Machin. Subsequent editions, both in English and Latin, with commentaries, have been published.

In June, 1709, Newton intrusted the superintendence of a second edition of the Principia to Roger Cotes, Plumian Pro- fessor of Astronomy at Cambridge. The first edition had been sold off for some time. Copies of the work had become very rare, and could only be obtained at several times their original cost. A great number of letters passed between the author and Mr. Cotes during the preparation of the edition, which finally appeared in May, 1713. It had many alterations and improve- ments, and was accompanied by an admirable Preface from the pen of Cotes.

Our author's early Treatise, entitled. Analysis per Equationes NuMERO Terminorum Infinitas, as well as a small Tract, bearing the title of Methodus Differentialis, was published, with his consent, in 1711. The former of these, and the Treatise De Quadratura Curvarum, translated into English, with a large com- mentary, appeared in 1745. His work, entitled, Artis Ana- lytics Specimina, vel Geometria Analytica, was first given to the world in the edition of Dr. Horsley, 1779.

48 LIFE OF SIR ISAAC NEWTON.