自然哲学的数学原理-5

this difficult and most salutary reform. In 1699, he was promoted to the Mastership of the Mint an office worth twelve orfifteen hundred pounds per annum, and which he held during theremainder of his life. He wrote, in this capacity, an official Report on the Coinage, which has been published ; he also prepareda Table of Assays of Foreign Coins, which was printed at theend of Dr. Arbuthnot s Tables of Ancient Coins, Weights, andMeasures, 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 emolumentsof the office ; and, on finally resigning, procured his nomination tothe vacant Chair.In January 1697, John Bernouilli proposed to the most distinguished mathematicians of Europe two problems for solution.Leibnitz, admiring the beauty of one of them, requested the timefor solving it to be extended to twelve months twice the periodoriginally named. The delay was readily granted. Newton, however, sent in, the day after he received the problems, a solution ofthem to the President of the Royal Society. Bernouilli obtainedsolutions from Newton, Leibinitz and the Marquis De L Hopital ;but Newton s though anonymous, he immediately recognised" tanquam ungue leonem" as the lion is known by his claw.We may mention here the famous problem of the trajectoriesproposed by Leibnitz, in 1716, for the purpose of "feeling thepulse of the English Analysts." Newton received the problemabout five o clock in the afternoon, as he was returning from theLIFE OF SIR ISAAC NEWTON. 45Mint ; and though it was extremely difficult and he himself muchfatigued, yet he completed its solution, the same evening beforehe went to bed.The history of these problems affords, by direct comparison, astriking illustration of Newton s vast superiority of mind. Thatamazing concentration and grasp of intellect, of which we havespoken, enabled him to master speedily, and, as it were, by asingle effort, those things, for the achievement of which, the manywould essay utterly in vain, and the very, very few attain onlyafter long and renewed striving. And yet, with a modesty asunparalleled as his power, he attributed his successes, not to anyextraordinary sagacity, but solely to industry and patient thought.Mr- kept the subject of consideration constantly before him, andwaited till the first dawning opened gradually into a full andclear light ; never quitting, if possible, the mental process till theobject of it were wholly gained. He never allowed this habit ofmeditation to appear in his intercourse with society ; but in theprivacy of his own chamber, or in the midst of his own family, hegave himself up to the deepest abstraction. Occupied with someinteresting 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 requisite quantity of nourishment. But notwithstanding his anxiety to be left undisturbed, he would, when occasion required,turn aside his thoughts, though bent upon the most intricate research, and then, when leisure served, again direct them to thevery point where they ceased to act : and this he seemed to accomplish not so much by the force of his memory, as by the forceof his inventive faculty, before the vigorous intensity of which, nosubject, however abstruse, remained long unexplored.Me was elected a member of the Royal Academy of Sciencesat 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 reflecting instrument for observing the moon s distance from thefixed stars. This description was published in the Philosophical46 LIFE OF SIR ISAAC NEWTON,Transactions, in 1742. The instrument was the same as thatproduced by Mr. Hadley, in 1731, and which, under the name ofHadley s Quadrant, has been of so great use in navigation. Onthe assembling of the new Parliament, in 1701, Newton was reelectedone of the members for the University of Cambridge. In1703, he was chosen President of the Royal Society of London,to which office he was annually re-elected till the period of hisdecease about twenty-five years afterward.Our author unquestionably devoted more labour to, and, inmany respects, took a greater pride in his Optical, than his otherdiscoveries. This science he had placed on a new and indestructible basis ; and he wished not only to build, but to perfect thecostly and glowing structure. He had communicated, before thepublication of the PRINCIPIA, his most important researches onlight to the Royal Society, in detached papers which were insertedin successive numbers of the Transactions ; but he did not publish a connected view of these labours till 1704, when they appearedunder 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 Treatises, entitled, TRACTATUS DUO DE SPECIEBUS ET MAGNITUDINEFIGURARUM cuRViLiNEARUM ; the one bearing the title TRACTATUSDE QUADRATURA CuRVARUM ; and the other, that of ENUMERATIOLINEARUM TERTII ORDiNis. The publication of these Mathematical Treatises was made necessary in consequence of plagiarismsfrom the manuscripts of them loaned by the author to his friends.Dr. Samuel Clarke published a Latin translation of the Optics, inin 1706 ; whereupon he was presented by Newton, as a mark ofhis grateful approbation, with five hundred pounds, or one hundred pounds for each of his children. The work was afterwardtranslated into French. It had a remarkably wide circulation,and appeared, in several successive editions, both in England andon the Continent. There is displayed, particularly on this Optical Treatise, the author s talent for simplifying and communicating the profoundest speculations. It is a faculty rarely united tothat of the highest invention. Newton possessed both ; and thusthat mental perfectness which enabled him to create, to combine,LIFE OF SIR ISAAC NEWTON. 47and to teach, and so render himself, not the "ornament" cnly;but inconceivably more, the pre-eminent benefactor of his species.The honour of knighthood v/as conferred on our author in1705. Soon afterward, he was a candidate again for the Representation of the University, but was defeated by a large majority.It is thought that a more pliant man was preferred by both ministers and electors. Newton was always remarkable for simplicityof dress, and his only known departure from it was on this occasion, when he is said to have appeared in a suit of lacedclothes.The Algebraical Lectures which he had, Juring nine years,delivered at Cambridge, were published by Whiston, in 1707,under the title of ARITHMETICS UNIVERSALIS, SINE DE COMPOSITIONS ET RESOLUTIONS ARITHMETICA LIBER. This publicationis 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, wasissued 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 asecond edition of the PRINCIPIA to Roger Cotes, Plumian Professor of Astronomy at Cambridge. The first edition had beensold off for some time. Copies of the work had become veryrare, and could only be obtained at several times their originalcost. A great number of letters passed oetween the author andMr. Cotes during the preparation of the edition, which finallyappeared in May, 1713. It had many alterations and improvements, and was accompanied by an admirable Preface from thepen of Cotes.Our author s early Treatise, entitled, ANALYSIS PER EQUATIONESNUMERO TERMINORUM INFINITAS, as well as a small Tract, Gearingthe title of METHODUS DIFFERENTIALS, was published, witn nisconsent, in 1711. The former of these, and the Treatise DeQuadratura Curvarum, translated into Englisn, witn a .arge commentary, appeared in 1745. His work, entitled. ARTIS ANALYTICS SPECIMINA, VEL GEOMETRIA ANALYTICA, was iirs; givento the world in the edition of Dr. Horsley, 1779.48 LIFE OF SIR ISAAC NEWTON.It is a notable fact, in Newton s history, that he never volun*tarily published any one of his purely mathematical writingsThe cause of this unwillingness in some, and, in other instances,of his indifference, or, at least, want of solicitude to put forth hisworks may be confidently sought for in his repugnance to everything like contest or dispute. But, going deeper than this aversion, we find, underlying his whole character and running parallelwith all his discoveries, that extraordinary humility which alwayspreserved him in a position so relatively just to the behests oftime and eternity, that the infinite value of truth, and the utterworthlessness of fame, were alike constantly present to him.Judging of his course, however, in its more temporary aspect, asbearing upon his immediate quiet, it seemed the most unfortunate.For an early publication, especially in the case of his Method ofFluxions, would have anticipated all rivalry, and secured himfrom the contentious claims of Leibnitz. Still each one will solvethe problem of his existence in his own way, and, with a manlikeNewton, his own, as we conceive, could be no other than the bestway. The conduct of Leibnitz in this affair is quite irreconcilablewith the stature and strength of the man ; giant-like, and doingnobly, in many ways, a giant s work, yet cringing himself into thedimensions and performances of a common calumniator. Openingin 1699, the discussion in question continued till the close ofLeibnitz s life, in 1716. We give the summary of the case ascontained in the Report of the Committee of the Royal Society,the deliberately weighed opinion of which has been adopted as anauthoritative decision in all countries." We have consulted the letters and letter books in the custodyof the Royal Society, and those found among the papers of Mr.John Collins, dated between the years 1669 and 1677, inclusive ;and showed them to such as knew and avouched the hands of Mr.Barrow, Mr. Collins, Mr. Oldenburg, and Mr. Leibnitz ; andcompared those of Mr. Gregory with one another, and with copiesof some of them taken in the hand of Mr. Collins ; and haveextracted from them what relates to the matter referred to us :all which extracts, herewith delivered to you, we believe to begenuine and authentic. And by these letters and papers wffind:LIFE OF SIR ISAAC NEWTON. 49"I. Mr. Leibnitz was in London in the beginning of the year1673 ; and went thence in or about March, to Paris, where hekept a correspondence with Mr. Collins, by means of Mr. Oldenburg, till about September, 1676, and then returned, by Londonand Amsterdam, to Hanover: and that Mr. Collins was very freein communicating to able mathematicians what he had receivedfrom Mr, Newton and Mr. Gregory." II. That when Mr. Leibnitz was the first time in London,he contended for the invention of another differential method,properly so called ; and, notwithstanding he was shown by Dr.Pell that it was Newton?s method, persisted in maintaining it tobe his own invention, by reason that he had found it by himselfwithout knowing what Newton had done before, and had muchimproved it. And we find no mention of his having any otherdifferential method than Newton s before his letter of the 21st ofJune, 1677, which was a year after a copy of Mr. Newton s letterof the 10th of December, 1672, had been sent to Paris to becommunicated to him ; and above four years after Mr. Collinsbegan to communicate that letter to his correspondents ;in whichletter the method of fluxions was sufficiently described to anyintelligent person."III. That by Mr. Newton s letter, of the 13th of June, 1676it appears that he had the method of fluxions above five yearsbefore the writing of that letter. And by his Analysis per ^Equationesnumero Terminorum Infmitas, communicated by Dr. Barrowto Mr. Collins, in July, 1669, we find that he had invented themethod before that time."IV. That the differential method is one and the same withthe method of fluxions, excepting the name and mode of notation ;Mr. Leibnitz calling those quantities differences which Mr. Newtoncalls moments, or fluxions ; and marking them with a letter d amark not used by Mr. Newton." And, therefore, we take the proper question to be, not whoinvented this or that method, but, who was the first inventor ofthe method ? And we believe that those who have reputed Mr.Leibnitz the first inventor knew little or nothing of his correspondence with Mr. Collins and Mr. Oldenburg long before, nor of Mr.50 LIFE OP SIR ISAAC NEWTON.Newton s hiving that method above fifteen years before MrLeibnitz began to publish it in the Acta Eruditorum of Leipsic." For which reason we reckon Mr. Newton the first inventor ;and are of opinion that Mr. Keill, in asserting the same, has beenno ways injurious to Mr. Leibnitz. And we submit to the judgment of the Society, whether the extract and papers, now presented to you, together with what is extant, to the same purpose, in Dr. Wallis s third volume, may not deserve to be madepublic."This Report, with the collection of letters and manuscripts,under the title of COMMERCIUM EPISTOLICUM D. JOHANNIS COLLINSET ALIORUM DE ANALYSI PROMOTA JuSSU SoCIETATIS REGIESEDITUM, appeared accordingly in the early part of 1713. Itspublication seemed to infuse additional bitterness into the feelingsof Leibnitz, who descended to unfounded charges and emptythreats. He had been privy counsellor to the Elector of Hanover, before that prince was elevated to the British throne ; andin his correspondence, in 1715 and 1716, with the Abbe Conti,then at the court of George L, and with Caroline, Princess ofWales, he attacked the doctrines of the PRINCIPIA, and indirectlyits author, in a manner very discreditable to himself, both as alearned and as an honourable man. His assaults, however, weretriumphantly met; and, to the complete overthrow of his rivalpretensions, Newton was induced to give the finishing blow. Theverdict is universal and irreversible that the English precededthe German philosopher, by at least ten years, in the inventionof fluxions. Newton could not have borrowed from Leibnitz ;but Leibnitz might have borrowed from Newton. A new editionof the Commercium Epistolicum was published in 1722-5 (?) ; butneither in this, nor in the former edition, did our author take anypart. The disciples, enthusiastic, capable and ready, effectuallyshielded, with the buckler of Truth, the character of the Master,whose own conduct throughout was replete with delicacy, dignityand justice. He kept aloof from the controversy in which Dr.Keill stood forth as the chief representative of the Newtonianside till the very last, when, for the satisfaction of the King,George L. rather than for his own, he consented to put forth hisLIFE OF SI| L^.-vJ NEWTON. 5ihand and firmly secure his rights upon a certain and impregnable,basis.A petition to have inventions for promoting the discovery of thelongitude at sea, suitably rewarded, was presented to the Houseof Commons, in 1714. A committee, having been appointed toinvestigate the subject, called upon Newton and others for theiropinions. That of our author was given in writing, A report,favourable to the desired measure, was then taken up, and a billfor its adoption subsequently passed.On the ascension of George I., in 1714, Newton became anobject of profound interest at court. His position under government, his surpassing fame, his spotless character, and. above all,his deep and consistent piety, attracted the reverent regard of thePrincess of Wales, afterward queen -consort to George II. Shewas a woman of a highly cultivated mind, and derived the greatestpleasure from conversing with Newton and corresponding withLeibnitz. One day, in conversation with her, our author mentioned and explained a new system of chronology, which he hadcomposed at Cambridge, where he had been in the habit " ofrefreshing himself with history and chronology, when he wacweary with other studies." Subsequently, in the year 1718, sherequested a copy of this interesting and ingenious work Newton,accordingly, drew up an abstract of the system from the separatepapers in which it existed, and gave it to her on condition that itshould riot be communicated to any other person. Sometimeafterward she requested that the Abbe Conti might be allowedto have a copy of it The author consented: and the abbereceived a copy of the manuscript, under the like injunction andpromise of secrecy. This manuscript bore the title of " A shortChronicle, from the First Memory of Tilings in Europe, to theConquest of Persia, by Alexander the Great."After Newton took up his residence in London, he lived in astyle suited to his elevated position and rank. He kept his carriage, with an establishment of three male and three female servants. But to everything like vain show and luxury he was utterlyaverse. His household affairs, for the last twenty years of hislife, were under the charge of his niece, Mrs. Catherine Barton,52 LIFE OF SIR ISAAC NEWTON.wife and widow of Colonel Barton a woman of great beauty andaccomplishment and subsequently married to John Conduit, Esq.At home Newton was distinguished by that dignified and gentlehospitality which springs alone from true nobleness. On all proper occasions, he gave splendid entertainments, though withoutostentation. In society, whether of the palace or the cottage,his manner was self-possessed and urbane ;his look benign andaffable ;his speech candid and modest ;his whole air undisturbedly serene. He had none of what are usually called the singularities of genius ; suiting himself easily to every companyexcept that of the vicious and wicked ; and speaking of himselfand others, naturally, so as never even to be suspected of vanity.There was in him, if we may be allowed the expression, a WHOLENESS of nature, which did not admit of such imperfections andweakness the circle was too perfect, the law too constant, andthe disturbing forces too slight to suffer scarcely any of thoseeccentricities which so interrupt and mar the movements of manybright spirits, rendering their course through the world more likethat of the blazing meteor than that of the light and life-imparting sun. In brief, the words GREATNESS and GOODNESS couldnot, humanly speaking, be more fitly employed than when appliedas the pre-eminent characteristics of this pure, meek and venerable sage.In the eightieth year of his age, Newton was seized withsymptoms of stone in the bladder. His disease was pronouncedincurable. He succeeded, however, by means of a strict regimen,and other precautions, in alleviating his complaint, and procuringlong intervals of ease. His diet, always frugai, was now extremelytemperate, consisting chiefly of broth, vegetables, and fruit, with,now and then, a little butcher meat. He gave up the use of hiscarriage, and employed, in its stead, when he went out, a chair.All invitations to dinner were declined ; and only small partieswere received, occasionally, at his own house.In 1724 he wrote to the Lord Provost of Edinburgh, offeringto contribute twenty pounds yearly toward the salary of Mr.Maclaurin, provided he accepted the assistant Professorship ofMathematics in the University of that place. Not only in theLIFE OP SIR ISAAC NEWTON. 53cause of ingenuity and learning, but in that of religion in relievingthe poor and .assisting his relations, Newton annually expendedlarge sums. He was generous and charitable almost to a fault.Those, he would often remark, who gave away nothing till theydied, never gave at all. His wealth had become considerable bya prudent economy ; but he regarded money in no other lightthan as one of the means wherewith he had been intrusted to dogood, and he faithfully employed it accordingly.He experienced, in spite of all his precautionary measures, areturn of his complaint in the month of August, of the same year,1 724, when he passed a stone the size of pea ;it came from himin two pieces, the one at the distance of two day.s from the other.Tolerable good health then followed for some months. In January, 1725, however, he was taken with a violent cough and inflammation of the lungs. In consequence of this attack, he was prevailed upon to remove to Kensington, where his health greatlyimproved. In February following, he was attacked in both feetwith the gout, of the approach of which he had received, a fewyears before, a slight warning, and the presence of which nowproduced a very beneficial change in his general health. Mr.Conduit, his nephew, has recorded a curious conversation whichtook place, at or near this time, between himself and Sir Isaac."I was, on Sunday night, the 7th March, 1724-5, at Kensington, with Sir Isaac Newton, in his lodgings, just after he was outof a fit of the gout, which he had had in both of his feet, for thefirst time, in the eighty-third year of his age. He was better afterit, and his head clearer and memory stronger than I had knownthem for some time. He then repeated to me, by way of discourse, very distinctly, though rather in answer to my queries,than in one continued narration, what he had often hinted to mebefore, viz. : that it was his conjecture (he would affirm nothing)that there was a sort of revolution in the heavenly bodies ; thatthe vapours and light, emitted by the sun, which had their sediment, as water and other matter, had gathered themselves, bydegrees, into a body, and attracted more matter from the planets,and at last made a secondary planet (viz. : one of those that goround another planet), and then, by gathering to them, and54 LIFE OF SIR ISAAC NEWTON.attracting more matter, became a primary planet ; and then, bfincreasing still, became a comet, which, after certain revolutions,by coming nearer and nearer to the sun, had all its volatile partscondensed, and became a matter tit to recruit and replenish thesun (which must waste by the constant heat and light it emitted),as a faggot would this fire if put into it (we were sitting by awood fire), and that that would probably be the effect of thecomet of 1680, sooner or later; for, by the observations madeupon it, it appeared, before it came near the sun, with a tail onlytwo or three degrees long ; but, by the heat it contracted, in goingso near the sun, it seemed to have a tail of thirty or forty degrees