Chapter XV

<36>

CHAPTER XV.

NICOLAS FACIO DE DUILLIER ATTACKS LEIBNITZ — LEIBNITZ APPEALS TO NEWTON — HE REVIEWS NEWTON'S 'QUADRATURE OF CURVES,' AND ACCUSES HIM OF PLAGIARISM — NEWTON'S OPINION OF THE REVIEW — DR. KEILL DEFENDS NEWTON AS THE TRUE INVENTOR OF FLUXIONS, AND APPARENTLY RETORTS THE CHARGE OF PLAGIARISM ON LEIBNITZ, WHO COMPLAINS TO THE ROYAL SOCIETY — KEILL EXPLAINS HIS DEFENCE — THE ROYAL SOCIETY APPROVES OF HIS EXPLANATION — LEIBNITZ CALLS KEILL AN UPSTART, AND BEGS THE ROYAL SOCIETY TO SILENCE HIM — THE SOCIETY APPOINTS A COMMITTEE TO INQUIRE INTO THE CLAIMS OF LEIBNITZ AND NEWTON — THE COMMITTEE REPORT TO THE SOCIETY, WHO PUBLISH THE RESULT IN THE 'COMMERCIUM EPISTOLICUM' — INSTIGATED BY LEIBNITZ, JOHN BERNOULLI ATTACKS THE REPORT, AND ASSERTS, IN A PRIVATE LETTER TO LEIBNITZ, THAT HE WAS THE FIRST INVENTOR OF THE NEW CALCULUS — LEIBNITZ CIRCULATES THIS LETTER IN A CHARTA VOLANS, AND GIVES UP BERNOULLI AS THE AUTHOR OF IT — KEILL REPLIES TO THIS LETTER, AND ATTACKS BERNOULLI AS ITS AUTHOR, WHO SOLEMNLY DENIES IT TO NEWTON — LEIBNITZ ATTACKS NEWTON IN A LETTER TO THE ABBÉ CONTI — NEWTON REPLIES TO IT — THE CONTROVERSY EXCITES GREAT INTEREST — LEIBNITZ URGES BERNOULLI TO MAKE A PUBLIC DECLARATION IN HIS FAVOUR — BERNOULLI SENDS TO LEIBNITZ THE CELEBRATED LETTER 'PRO EMINENTE MATHFMATICO,' EN CONDITION OF HIS NAME BEING KEPT SECRET — LEIBNITZ AND WOLF ALTER THIS LETTER IMPROPERLY, AND PUBLISH IT IN SUCH A FORM, THAT BERNOULLI IS PROVED TO BE ITS AUTHOR — BERNOULLI IS ANNOYED BY THE DISCOVERY, AND ENDEAVOURS, BY IMPROPER MEANS, TO EVADE THE TRUTH — THE ABBÉ VARIGNON RECONCILES NEWTON AND BERNOULLI — DEATH OF LEIBNITZ — NEWTON WRITES A HISTORY OF THE CALCULUS — GENERAL VIEW OF THE CONTROVERSY, AND OF THE CONDUCT OF THE PARTIES.

NICOLAS FACIO DE DUILLIER, a Genevese by birth, came to England in the spring of 1687, and with the exception of a visit to Switzerland in 1699, 1700, and 1701, re <37> mained there during the rest of his life. He had become acquainted with the celebrated Huygens at the Hague in 1686, and had attained to such a proficiency in mathematics, that he was introduced to Sir Isaac Newton, and visited him at Cambridge in the month of November 1692. Though only in the 28th year of his age, his health was precarious, and he seems to have consulted Newton on the subject of his spiritual as well as of his bodily condition. On his return from Cambridge, he caught a severe cold, which affected his lungs, and gave him great alarm. In communicating to Sir Isaac an account of his symptoms, he says, "I thank God that my soul is extremely quiet, in which you have had the chief hand;" and fearing that his illness would prove fatal, he expresses the "wish that his eldest brother, a man of an extraordinary integrity, shoidd succeed him in his friendship." Sir Isaac answered this letter in course of post, making inquiries about his brother, and telling Facio that he remembered him in his prayers; and Facio in reply gave him his most humble thanks, both for his prayers and his kindness, requested him thus to remember him as long as he lived, and assuring him that he always remembered him in a similar manner.^[1]

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Having been elected a Fellow of the Royal Society in 1687, he took an active part in its proceedings, and communicated papers to its Transactions. In the year 1699 he published a tract entitled a "Geometrical Investigation <39> of the Solid of least Resistance," in which he made the following reference to the history of the new calculus.^[2]

"The celebrated Leibnitz may perhaps inquire how I became acquainted with the calculus which I use. About the month of April, and the following months in the year 1687, and subsequent years, when nobody, as I thought, used such a calculus but myself, I invented its fundamental principles, and several of its rules. Nor would it have been less known to me if Leibnitz had never been born. He may, therefore, boast of other disciples, but certainly not of me. And this would be sufficiently evident if the letters which passed between me and the illustrious Huygens were given to the public.^[3] Compelled by the evidence of facts, I hold Newton to have been the first inventor of the calculus, and the earliest by several years: And whether Leibnitz, its second inventor, has borrowed anything from him, I would prefer to my own judgment that of those who have seen the letters of Newton and copies of his <40> other manuscripts. Nor will the silence of the more modest Newton, or the active exertions of Leibnitz in everywhere ascribing the invention of this calculus to himself, impose upon any person who shall examine these documents as I have done."^[4]

Strong as these expressions are, they cannot be regarded as charging Leibnitz with plagiarism. He is styled the second inventor, the title with which he, on many occasions, expressed himself satisfied, and he is blamed only for everywhere ascribing the invention to himself. In replying to Duillier,^[5],Leibnitz appealed to Newton himself as having stated, in the celebrated scholium, that the new calculus was common to them both, and that neither had received any light from the other;^[6] and, without disputing or acknowledging the priority of Newton's claim, he asserted his own right to the discovery of the differential calculus. Facio sent a reply to the editors of the Acta Eruditorum, but they refused to print it on the ground of their aversion to controversy.^[7] The controversy therefore terminated for the present, and the contending parties laid down their arms, ready to resume them on the slightest provocation.

When Newton published his Treatise on the Quadrature ot Curves, along with his Optics in 1704, he mentioned in his introduction that he had gradually found the method of fluxions in the year 1665 and 1666. A review of this <41> work, by Leibnitz,^[8] but without his name, was published in the Acta Eruditorum for January 1705. After giving an imperfect analysis of its contents, he compared the method of fluxions with the differential calculus, and, in a sentence of some ambiguity, he states that Newton employed fluxions in place of the difterences of Leibnitz, and made use of them in his Principia in the same manner as Honoratus Fabri, in his Synopsis of Geometry, had substituted progressive motion in place of the indivisibles of Cavalieri. As Fabri, therefore, was not the inventor of the method which is here referred to, but borrowed it from Cavalieri, and only changed the mode of its expression, there can be no doubt that the artful insinuation contained in the above passage was intended to convey the impression that Newton had stole his method of fluxions from Leibnitz. That this was the view of it taken by the friends of Newton will presently appear. That it was the view taken by Newton himself we are fortunately able to prove from the following passage in his own handwriting,^[9] which is so important that we copy it without any change.

"In the Acta Eruditorum for 1705,^[10] an account of the Introduction to the Book of Quadratures was published in these words: — 'Quæ [Isagogen or Preface] ut MELIUS intelligatur sciendum est cum magnitudo aliqua continue crescit veluti linea, exempli gratia crescit fluxu puncti, quod eam describit, incrementa illa momentanea est producta appellavi DIFFERENTIAS, nempe inter magnitudinem quæ antea erat et quæ per mutationem momentaneam est producta; atque hinc natum esse calculum <42> Differentialem, eique reciprocum summatorium,^[11] cujus elementa ab INVENTORE D. Godofredo Guillielmo Leibnitio in his actis sunt tradita, variisque usus tum ab ipso, tum a DD. Fratribus Bernoulliis, tum a D. Marchione Hospitalio sunt ostensi. Pro Differentiis IGITUR Leibnitianis D. Newtonus adhibet, semperque [pro iisdem] adhibuit fluxiones, iisque tum in suis Principiis Naturæ Mathematicis, tum in aliis postera editis [pro Differentiis Leibnitianis] eleganter est usus, QUEMADMODUM ut Honoratus Fabrius in sua synopsi Geometrica motuus progressus Cavallerianæ methodo SUBSTITUIT.' And all this is as much as to say that I did not invent the method of fluxions in the years 1665 and 1666, as I affirmed in this Introduction, but that after Mr. Leibnitz, in his letter of 21st June 1677, had sent me his differential method, instead of that method, I began to use, and have ever since used, the method of fluxions."^[12]

That Newton was virtually accused of plagiarism by the reviewer, cannot, we think, admit of a doubt. The indirect and ambiguous manner in which the charge is couched, and the artful reference to the case of Fabri and Cavalieri, make it doubly reprehensible; and we are persuaded that no candid reader can peruse the passage without a strong conviction that it justifies, in the fullest manner, the indignant feelings which it excited among the English philosophers. If Leibnitz, in place of being the author of the review, had been merely a party to it, <43> he merited the full measure of rebuke which was dealt out to him by the friends of Newton, and deserved those severe reprisals which doubtless embittered the rest of his days. He who dares to accuse a man like Newton, or indeed any man holding a fair character in society, of the odious crime of plagiarism, places himself without the pale of the ordinary courtesies of life, and deserves to have the same charge thrown back upon himself. The man who conceives his fellow to be capable of such intellectual felony, avows the possibility of himself committing it, and almost substantiates the weakest evidence of the worst accusers.

Dr. Keill, as the representative of Newton's friends, could not brook this concealed attack upon his countryman. In a letter on the Laws of Centripetal Forces, addressed to Halley, and printed in the Philosophical Transactions for 1708,^[13] he stated that Newton was "beyond all doubt" the first inventor of fluxions; and he asserted "that the same calculus was afterwards published by Leibnitz, the name and the mode of notation being changed." If the reader is disposed to consider this passage as retorting the charge of plagiarism upon Leibnitz, he will readily admit that the mode of its expression is neither so coarse nor so insidious as that which is used by the writer in the Acta Eruditorum. In a letter to Hans Sloane, dated 4th March 1711, Leibnitz complained to the Royal Society of the treatment he had received. "Nobody", says he, "knew better than Newton that this charge is false, for certainly I never heard of the name of the Calculus of Fluxions, nor saw with these eyes the characters which Newton used." He expressed his conviction that Keill had erred <44> more from rashness of judgment than from any improper motive. He did not regard the accusation as a calumny; and he requested that the Society would desire Mr. Keill to disown publicly the injurious sense which his words might bear. When this letter was read to the Society, Keill justified himself to Sir Isaac Newton and the other members, by showing them the obnoxious article on the Quadrature of Curves in the Acta Eruditorum, and they all agreed in attaching the same injurious meaning to the passage in the review. The discussion excited so much interest, that, on the 5th April 1711, Newton gave, from the chair of the Society, "a short account of his invention, with the particular time of his first mentioning or discovering it ;^[14] upon which Mr. Keill was desired to draw up an account of the matter in dispute, and set it in a just light."^[15] This account, contained in a letter to Sir Hans Sloane, was read at the Society on the 24th May 1711, and a copy of it was ordered to be sent to Leibnitz. In this letter, which is one of considerable length, Dr. Keill declares that he never meant to state that Leibnitz knew either the name of Newton's method or the form of notation, and that the real meaning of the <45> passage was, "that Newton was the first inventor of fluxions, or of the differential calculus, and that he had given, in two letters to Oldenburg, and transmitted to Leibnitz, indications of it sufliciently intelligible to an acute mind,^[16] from which Leibnitz derived, or was able to derive, the principles of his calculus."

The charge of plagiarism which Leibnitz thought was implied in the former letter of his antagonist, is here greatly modified, if not altogether denied. Keill expresses only an opinion that the letters seen by Leibnitz contained intelligible indications of the fluxionary calculus, from which he either derived, or might derive, the principles of his calculus. Even if this opinion were correct, it is no proof that Leibnitz either saw these indications or availed himself of them; or if he did perceive them, it might have been in consequence of his having previously been in possession of the differential calculus, or having enjoyed some distant view of it. Leibnitz should, therefore, have allowed the dispute to terminate here; for no ingenuity on his part, and no additional facts, could affect an opinion which any other person as well as Keill was entitled to maintain.^[17]

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Leibnitz, however, took a different view of the subject, and wrote a letter to Sir Hans Sloane, dated December 29, 1711, which excited new feelings, and involved him in new embarrassments. Insensible to the mitigation which had been kindly impressed upon the supposed charge against his honour, he alleges that Keill had attacked his candour and sincerity more openly than before; — that he acted without any authority from Sir Isaac Newton, who was the party interested; — and that it was in vain to justify his proceedings by referring to the provocation in the Acta Eruditorum, because, in that journal, no injustice had been done to any party, but every one had received what was his due. He asserts, that he discovered the calculus some years before he published it, that is in 1675, or earlier. He brands Keill with the odious appellation of an upstart, and one little acquainted with the circumstances of the case;^[18] and he calls upon the Society to silence his vain and unjust clamours,^[19] which, he believed, were disapproved by Newton himself, <47> who was well acquainted with the facts, and who, he was persuaded, would willingly give his opinion on the matter.

This unfortunate letter was doubtless the cause of all the rancour and controversy which so speedily followed, and it placed his antagonist in a new and a more favourable position. It may be correct, though few will admit it, that Keill's second letter was more injurious than the first; but it was not true that Keill acted without the authority of Newton, because Keill's letter was approved of, and transmitted, by the Royal Society, of which Newton was the president, and therefore became the act of that body. The obnoxious part, however, of Leibnitz's letter, consisted in his appropriating to himself the opinions of the reviewer in the Leipsic Acts, by declaring that, in a review which charged Newton with plagiarism, every person had got what was their due. The whole character of the controversy was now changed: Leibnitz places himself in the position of the party who had first disturbed the tranquillity of science by maligning its most distinguished ornament; and the Royal Society was imperiously called upon to throw all the light they could upon a transaction which had exposed their venerable president to so false a charge. The Society, too, had become a party to the question, by their approbation and transmission of Keill's second letter, and were on that account alone bound to vindicate the step which they had taken.

When the letter of Leibnitz, therefore, was read, Keill appealed to the registers of the Society for the proofs of what he had advanced. Sir Isaac also expressed his displeasure at the obnoxious passage in the Acta Eruditorum, and at the defence of it by Leibnitz, and he left it to the Society to act as they thought proper.

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In this emergency, a committee of the Royal Society was appointed on the 6th March 1712, "to inspect the letters and papers relating to the dispute, consisting of Dr. Arbuthnot, Mr. Hill, Dr. Halley, Mr. Jones, Mr. Machin, and Mr. Burnet." Mr. Robarts, a contributor to the Transactions, was added to the committee on the 20th of March, M. Bonet, the Prussian Minister, on the 27th, and Mr. De Moivre, Mr. Aston, and Dr. Brook Taylor, on the 17th of April.^[20] The committee, thus constituted, was instructed to examine the registers of the Society, and to lay before it such documents as they might discover, with their own opinions on the subject. This committee, probably from being called consessus arbitrorum, has been supposed to have been a judicial committee; but, as Professor De Morgan has shewn, and as Newton himself has asserted, it had no such character, since none of Leibnitz's friends were placed upon it, and no invitation given him to produce documents in his defence. The committee consisted entirely of Newton's friends; and several of them, though qualified to attest the genuineness of the documents in the report, were not fitted, by their mathematical acquirements, to give an opinion on the subject.^[21]

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On the 24th of April the committee gave in the following report, which was in the handwriting of Halley: —

"We have consulted the letters and letter-books in the custody of 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; and compared those of Mr. Gregory with one another, and with copies of some of them taken in the hand of Mr. Collins; and have extracted from them what relates to the matter referred to us; all which extracts herewith delivered to you, we believe to be genuine and authentic; and by these letters and papers we find, —

"I. That Mr. Leibnitz was in London in the beginning of the year 1673; and went thence, in or about March, to Paris; where he kept a correspondence with Mr. Collins, by means of Mr. Oldenburg, till about September 1676, and then returned by London and Amsterdam to Hanover: and that Mr. Collins was very free in communicating to able mathematicians, what he had received from 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 that he was shown by Dr. Pell, that it was Mouton's method, he persisted in maintaining it to be his own invention, by reason that he had found it by himself, without <50> knowing what Mouton had done before, and had much improved it. And we find no mention of his having any other differential method than Mouton's, before his letter of 21st June 1677, which was a year after a copy of Mr. Newton's letter, of the 10th December 1672, had been sent to Paris to be communicated to him; and above four years after, Mr. Collins began to communicate that letter to his correspondents; in which letter the method of fluxions was sufficiently described to any intelligent person.

"III. That by Mr. Newton's letter of the 13th June 1676, it appears that he had the method of Fluxions above five years before the writing of that letter, and by his Analysis, per Æquationes numero Terminorum Infinitas, communicated by Dr. Barrow to Mr. Collins in July 1669, we find that he had invented the method before that time.

"IV. That the differential method is one and the same with the method of fluxions, excepting the name and the mode of notation; Mr. Leibnitz calling those quantities differences, which Mr. Newton calls moments or fluxions; and marking them with the letter d, a mark not used by Mr. Newton. And therefore we take the proper question to be, not who invented this or that method, but who was the first inventor of the 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. Newton's having that method above fifteen years before Mr. Leibnitz began to publish it in the Acta Eruditorum of Leipsic.

"For which reasons we reckon Mr. Newton the first inventor; and are of opinion that Mr. Keill, in asserting <51> the same, has been noways injurious to Mr. Leibnitz. And we submit to the judgment of the Society, whether the extracts, and letters, and papers, now presented, together with what is extant to the same purpose, in Dr. Wallis's third volume, may not deserve to be made public."

This report being read and agreed to, the Society unanimously adopted it, ordered the collection of letters and manuscripts to be printed, and appointed Dr. Halley, Mr. Jones, and Mr. Machin, to superintend the press. Complete copies of it, under the title of Commercium Epistolicum D. Johannis Collins et aliorum de analysi promota, were laid before the Society on the 8th January 1713; and Sir Isaac Newton, as president, ordered a copy to be delivered to each person of the Committee appointed for that purpose, to examine it before its publication.^[22]

According to Leibnitz, he received information of the appearance of the Commercium Epistolicum when he was at Vienna, and "being satisfied, as he expresses it, that it must contain malicious falsehoods, I did not think proper to send for it by post, but wrote to M. Bernoulli to give me his sentiments.^[23] M. Bernoulli wrote me a letter, dated at Basle, June 7, 1713, in which he said, that it appeared prohable that Sir Isaac Newton had formed his calculus after having seen mine."^[24] This letter was published in Latin, by Leibnitz, with reflections, in a loose sheet, entitled Charta Volans, dated July 29, 1713, and <52> was widely circulated, without either the name of the author, printer, or place of publication, and giving the names of N——n and L——z, with their initial and final letters.

The origin of this letter is curious and instructive. In writing to Leibnitz on the 28th February, 1713, Bernoulli says, that he has informed Newton of some of his mistakes,^[25] but in a very gentle manner, that he might not give offence to one who had been very kind to him in getting him elected a Fellow of the Royal Society, and as showing much attention to his son when in London. In Leibnitz's reply of the 16th March, he remarks that Newton wishes to ingratiate himself with him, and he adds, we shall see what can be elicited from the correspondence with Collins, which, owing to his absence from home, he may not see so early as he will. Bernoulli had now received from Paris a copy of the Commercium Epistolicum, and in replying to Leibnitz on the 7th of June he gives him a general account of the Report of the Committee, and adds in a couple of pages his own opinion of it, which constitutes the celebrated letter of the 7th June 1713, inserted by Leibnitz in the Charta Volans. He concludes the letter by imploring Leibnitz "to make a right use of what he has written, and not compromise him with Newton and his countrymen, as he was unwilling to be mixed up with these controversies."^[26] In spite of this request, Leibnitz not only gave up Bernoulli as the author of the letter, but had insidiously inserted in a parenthesis, and in the same type, as if it had been written by the author, the words, as was long ago remarked by a certain eminent mathematician, which placed Bernoulli in the ridiculous position of praising himself.

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Previous to the publication of the Charta Volans, Dr. Keill sent to the Journal Littéraire for 1713,^[27] some remarks on the controversy, with the Report of the Committee, and Newton's important letter to Collins, dated 10th December, 1672. An anonymous answer,^[28] but certainly written by Leibnitz, appeared in the same work for November and December 1713. It contained a French translation of the Charta Volans, and of the letter of a very eminent mathematician, dated 7th June 1713, on the subject of the controversy, the same letter which Leibnitz mentions to Count Bothmar, as the production of Bernoulli.^[29] In this letter Bernoulli asserts that Newton in his researches confesses that he never even thought of Fluxions, and had not invented them before the differential calculus. He maintains that he was ignorant, when he wrote the Principia, of the true way of taking the fluxions of fluxions, and he accused him of having deprived Hook and Flamsteed of their just honours, the one for his hypothesis of the planets, and the other for the use of his observations.

Newton was indignant at this new attack upon his character, which was sent to him in the autumn of 1713, by Mr. Chamberlayne, who then kept a correspondence with Leibnitz, and he immediately drew up a sharp <54> reply,^[30] which was probably sent to Keill, as the groundwork of his long and elaborate answer, which appeared in the Journal Littéraire for July and August 1714.^[31] Bernoulli was supposed by both to be the very eminent mathematician^[32] who wrote the letter of the 7th June 1713, and but for Leibnitz's indiscretion, his name would never have been known. Never doubting that Bernoulli was the author, Keill endeavoured to prove it, and exposed with great severity the incorrectness and injustice of his charges against Newton. Notwithstanding the repeated declarations of Leibnitz, that Bernoulli was the author of this letter, Bernoulli himself disavowed it to M. Des Maizeaux, to M. Montmort, and to the Abbé Varignon; and in a letter to Newton, dated 3d November 1719, he declared that he was not the author of it, and that too with such solemnity that Newton believed him, and would not <55> listen to Keill and his other friends when they expressed an opposite opinion. "I beseech you," says he,^[33] "and I adjure you, by all that is sacred, that you will firmly believe that anything published without a name, in which a sufficiently honourable mention of you has not been made, has been falsely imputed to me. . . . Far be it from me to believe that Leibnitz, that truly excellent man, wished to deceive you by mentioning me. It is more credible that he was deceived either by his own conjecture or that of others, and yet he was not altogether blameless, in so far as he rashly and imprudently committed to writing anything of which he had no knowledge." The dishonesty of Bernoulli, thus placed beyond a doubt, is equalled only by the dishonourable conduct of Leibnitz in betraying his friend.^[34] Anxious to obtain the opinion of a great mathematician in favour of his own claims, and against those of Newton, he asked Bernoulli, as we have seen, to do him this favour. This request of his patron and friend was readily granted, but under the obligation that his name should be concealed. Leibnitz, however, was not satisfied with this anonymous tribute to his genius, and did not scruple to obtain for it all its value by violating his word, and exposing his friend to the enmity of Newton, and the keen shafts of Keill, of <56> which we shall presently see he stood in great alarm. During the interval between the date of Bernoulli's letter, namely, the 7th June, and that of the Charta Volans, in which Leibnitz published it, namely, the 29th July 1713, he seems to have felt how little was the value of the anonymous testimony which he had received; he therefore writes to Bernoulli on the 28th June, "that he expects from his justice and candour that he will, as soon as possible, declare publicly among his friends, when the opportunity occurs, that the Calculus of Newton was posterior to his."^[35] In replying to this letter Bernoulli assures him, that he will conceal nothing either among his friends or publicly, when the occasion demands it, and he comforts Leibnitz by saying that his fate was like that of his prince, the Elector of Hanover, whom the villanous English wished to deprive of the succession to the kingdom, in the same manner as they wished to deprive him of the possession of his calculus. Leibnitz, however, was very uneasy on the subject. He was anxious to know what the Parisians thought, for though he had no doubt that Varignon would be his friend, he feared that others would take the opportunity of attacking him.^[36] He expresses the hope, however,^[37] in a letter containing some severe strictures on Newton, that Varignon would take care, Bernoulli prompting him, that nothing was done in France of which he might complain.

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This extreme sensitiveness, on the part of Leibnitz, we can readily excuse, but we can find no apology for his conduct in betraying so ardent a friend as Bernoulli. On a future occasion we shall find him prompting the German mathematician to another act of hostility against Newton and Keill, and a second time divulging the secret under which the favour was granted. And at the very close of his career, when his great powers had been appreciated by the world, and an immortality of reputation was dazzling his failing sight, he did not scruple to conspire with Wolf, another German mathematician of feeble morality, to vitiate a letter of Bernoulli, and leave a shadow upon his name which the lustre of his genius will never be able to efface.

Amid the feelings excited by the letter of the eminent mathematician, Mr. Chamberlayne, whom we have already mentioned as the correspondent of Leibnitz, conceived the design of reconciling the two distinguished philosophers; and, in a letter, dated April 28th, 1714,^[38] he addressed himself to Leibnitz, who was still at Vienna. In replying to this letter, Leibnitz declared that he had given no occasion for the dispute; "that Newton procured a book to be published, which was written purposely to discredit him, and sent it to Germany, France, and Italy, as in the name of the Society;" and he stated "that there was great room to doubt whether Newton knew his invention before he had it from him." Mr. Chamberlayne communicated this letter to Sir Isaac Newton, who replied, that Leibnitz had attacked his reputation in 1705, by intimating that he had borrowed from him the method of fluxions; that if Mr. C. could point out to him anything in which he had injured Mr. Leibnitz, he would endeavour <58> to give him satisfaction; that he would not retract things which he knew to be true; and that he believed that the committee of the Royal Society had done no injustice by the publication of the Commercium Epistolicum. In another letter, Leibnitz expressed his entire disapprobation of the Report of the Committee, and of the Commercium, declaring, at the same time, more than a year and a half after two copies had been sent to him, that he had not yet seen the book published against him, and requesting Mr. Chamberlayne to submit his letter to the Society.

When the letter was laid before a meeting of the Society on the 20th of May, 1714, they came to the following resolution: —

" It was not judged proper (since this letter was not directed to them) for the Society to concern themselves therewith, nor were they desired so to do. But if any person had any material objection against the Commercium, or the Report of the Committee, it might be reconsidered at any time."

This resolution was sent to Leibnitz, who, in a letter to Chamberlayne, dated 25th August 1714, justly observes that the Society "did not pretend that the Report of the Committee should pass for a decision of the Society."^[39] <59> Along with the resolution, Mr. Chamberlayne sent to Leibnitz, Sir Isaac's letter and Dr. Keill's answer to the papers inserted in the Journal Littéraire, and after perusing them, he replied, "that Sir Isaac's letter was written with very little civility, that he considered it non scripta, as well as the piece printed in French (by Dr. Keill); that he was not in a humour to put himself in a passion against such people; that there were other letters among those of Oldenburg and Collins which should have been published; and that on his return to Hanover he would be able to publish a Commercium Epistolicum, which would be of service to the history of learning." When this letter was read to the Royal Society, Sir Isaac remarked, that the last part of it injuriously accused the Society of having made a partial selection of papers for the Commercium Epistolicum; that he did not interfere in any way in the publication of that work, and had even withheld from the committee two letters, one from Leibnitz in 1693, and another from Wallis in 1695, which were highly favourable to his cause.^[40] He stated that he did not think it right for Mr. Leibnitz himself to publish a Commercium Epistolicum, but if he had letters to produce in his favour, that they might be published in the Philosophical Tratisactions, or in Germany.

About this time the Abbé Conti, a noble Venetian, came to England. He was a correspondent of Leibnitz, <60> and in the postscript of a letter which he had received from him soon after his arrival,^[41] and written in November or December 1715, he enters upon his dispute with Newton. He charges the English with "wishing to pass for almost the only inventors." He declares "that Bernoulli has judged rightly in saying, that Newton did not possess before him the infinitesimal characteristic and algorithm." He remarks that Newton preceded him only in series; and he confesses that during his second visit to England, "Collins showed him part of his correspondence," or, as he afterwards expresses it, he saw "some of the letters of Newton at Mr. Collins's." He represents the metaphysics of the English as narrow, (borée,) and their mathematics as common or superficial. He then attacks Sir Isaac's philosophy, particularly his opinions about gravity and a vacuum, the intervention of God for the preservation of his creatures; and he accuses him of reviving the occult qualities of the schools. But the most remarkable passage in the letter is the following: "I am a great friend of experimental philosophy, but Newton deviates much from it when he pretends that all matter is heavy, or that each particle of matter attracts every other particle." The letter concludes with a problem, which he requests Conti to propose, "in order to feel the pulse of the English analysts."

Under these cirumstances, and influenced by the advice of Keill, which we have already mentioned, Sir Isaac became anxious that foreigners of distinction should see the original papers which had been preserved in the archives of the Society, and compare them with the other letters of Leibnitz. He therefore requested the Abbé Conti to assemble the ambassadors and other foreign <61> ministers for this purpose, and when they had met in the apartment of the Society and collated the papers, the Baron de Kilmansegg, the Hanoverian minister, remarked that this measure was not a sufficient one, and that the right way of terminating the dispute was that Newton himself should write a letter to Leibnitz, stating to him "his reasons," and demanding a direct answer to them. All the ministers who were present approved of this suggestion, and the king, to whom it was mentioned in the evening, gave it his hearty approbation.

Conti reported these proceedings to Sir Isaac, and in five or six days he received a letter from him, dated February 26, 1715-16, to be sent to Leibnitz, who was then in Hanover. As this letter was addressed to Conti, he enclosed it in one of his own, dated — March 1716, which he had previously read to Newton. Mr. Demoivre had corrected it, and added the part which related to the equivocal manner in which Leibnitz had proposed the problem for the English analysts. The letter of Conti, with Newton's enclosed, which was to be taken to Hanover by the Baron de Discau, remained more than a month in London. Madame de Kilmansegg had it translated into French. The king read it, and approved of it so highly as to say, that the reasons were very simple and clear, and that it would be difficult to reply to the facts.^[42]

This letter of Newton's was the first occasion on which he appeared in the controversy in his own person. Reluctantly driven into the field, he did not hesitate to give utterance to the opinions which had been maintained by Keill. In a tone of dignified severity he gave a brief <62> notice of the controversy, and triumphantly refuted the allegations of his adversary. "Finding it impossible," he says, "to reply to matter of fact, Leibnitz invoked the opinion of a mathematician or pretended mathematicians, dated 7th June 1713, and inserted it in an anonymous defamatory letter of the 29th July, which he circulated in Germany," — a letter which had been answered by Keill, and to which no reply had been returned. He charges Leibnitz with trying to engage him in philosophical disputes, and challenging him to the solution of problems which have no relation whatever to the question in dispute; and he makes some severe observations on Leibnitz's doctrine of the Preestablished Harmony, which he pronounces a true miracle, and contrary to all experience. He cites a passage from Leibnitz's letter to himself, dated March 7, 1693, in which he acknowledges the value of Newton's discoveries; and he makes the following observations on that branch of the dispute which relates to Leibnitz's having seen part of Newton's letters to Mr. Collins. "He (Leibnitz) complains of the committee of the Royal Society, as if they had acted partially in omitting what made against me; but he fails in proving the accusation. He quotes a passage concerning my ignorance, pretending that it was omitted in the Commercium Epistolicum, and yet you will find it there in p. 74, lines 10, 11, and I am not ashamed of avowing it. He says that he saw this paragraph in the hands of Mr. Collins when he was in London the second time, that is in October 1676; and as this is in my letter of the 24th of October 1676, he therefore then saw that letter. And in that and some other letters writ before that time, I described my method of fluxions; and in the same letter I described also two general methods of series, one of which is now claimed <63> from me by Mr. Leibnitz." The letter concludes with the following paragraph: "But as he has lately attacked me with an accusation which amounts to plagiary; if he goes on to accuse me, it lies upon him by the laws of all nations to prove his accusations, on pain of being accounted guilty of calumny. He hath hitherto written letters to his correspondents full of affirmations, complaints, and reflections, without proving anything. But he is the aggressor, and it lies upon him to prove the charge."

In transmitting this letter to Leibnitz, the Abbé Conti informed him that he himself had read with great attention, and without the least prejudice, the Commercium Epistolicum, and the little piece^[43] that contains the extract; that he had also seen at the Royal Society the original papers of the Commercium Epistolicum, and some other original pieces relating to it. "From all this," says he, "I infer, that, if all the digressions are cut off, the only point is, whether Sir Isaac Newton had the method of fluxions or infinitesimals before you, or whether you had it before him. You published it first, it is true, but you have owned also that Sir Isaac Newton had given many hints of it in his letters to Mr. Oldenburg and others. This is proved very largely in the Commercium, and in the extract of it. What answer do you give? This is still wanting to the public, in order to form an exact judgment of the affair." The Abbé adds, that Mr. Leibnitz's own friends waited for his answer with great impatience, and that they thought he could not dispense with <64> answering, if not Dr. Keill, at least Sir Isaac Newton himself, who had given him a defiance in express terms. In the close of his letter he informs Leibnitz that several geometers in London and Oxford have solved his problem, and he tells him that he will take some other opportunity of speaking to him of Newton's philosophy, which has been greatly misapprehended.

Leibnitz was not long in replying to the request of the Abbé Conti, and the defiance of Newton. He addressed a letter to the former on the 9th of April 1716, but he sent it through M. Remond de Montmort, to be communicated to the mathematicians^[44] in Paris, as neutral and intelligent witnesses, and then transmitted to Conti. In the letter to the Abbé, which was dated 14th April, he tells him that he may judge from all this, if "the wicked chicanery of his new friends has greatly embarrassed him," and he closes his letter with a reference to the pro <65> blem, "for feeling the pulse of the English analysts," which he tells him was proposed by Bernoulli.^[45]

The letter of Leibnitz of the 9th April is bold and ingenious. He defends the statements in the anonymous attacks upon Newton as if they were his own. He gives an account of his two visits to London, and mentions what he there saw and learned. He charges Newton with retracting his admission in the scholium, and thus considers himself entitled to retract his admission in favour of Newton. He introduces again his metaphysical opinions as having been misrepresented by Newton, and he concludes by denying that he was the aggressor, and had accused Newton of plagiarism.

On the very day when Leibnitz was writing this letter, Bernoulli was engaged in composing his famous Epistola pro Eminente Mathematico, which has formed so curious <66> and instructive an episode in the fluxionary controversy. He had been stung by the poignancy of Keill's reply to the Charta Volans, and the severity of its animadversions on the letter of his own which it contained; and, as will be seen from his own acknowledgment, he was afraid to encounter without a mask so bold and uncompromising an antagonist. He therefore resolved to attack Keill in an anonymous letter, addressed to Christian Wolf, one of the editors of the Acta Eruditorum. This letter, dated April 8, 1716,^[46] which Bernoulli, the grandson, admits was particularly directed against Newton, was sent to Wolf on condition of the most inviolable secrecy. It was to be first communicated to Leibnitz with power to change or omit what was necessary, and to print it as a letter from an anonymous person, or as if it were written by some other person with a real or a feigned name; but in whatever way this was done, Wolf was directed to manage the whole matter with his usual skill, lest Keill should suspect Bernoulli to be the author; "for," he adds. "it would be very disagreeable to me to be irritated and contumeliously treated by his bile, as his antagonists usually are, after he has hitherto treated me with sufficient politeness." Wolf expressed his great satisfaction with the attack upon "that trifler Keill," and promised to communicate it to Leibnitz, and decide according to his opinion on the form and manner in which it was to be published. The two critics, Wolf and Leibnitz, made such changes in the epistle as were agreeable to the latter, and every means were taken to keep the secret. Herman suspected that Bernoulli was the author of it, and, when he mentioned his suspi <67> cion, Wolf denied it, as he declares he always did; but though every precaution was taken to keep the secret, it was discovered by means of the phrase meam formulam, which had been either heedlessly overlooked, or, as we believe, willingly left, in order to fix it upon Bernoulli, whose public declaration against Newton, and in favour of himself, Leibnitz had expressed his anxiety to obtain. The changes made on the letter were very considerable. M. Bernoulli, the grandson, who had a copy of the original, has published the two in opposite columns,^[47] and, after a careful comparison of them, he observes, "that not a single disobliging expression against Newton and Keill had been omitted or softened. It is true," he continues, "with respect to Keill, who was the more ill-treated, that his name was everywhere suppressed; and when Wolf (and Leibnitz too) calls him an audacious antagonist in one place, where the letter only called him Keill, he did worse than mention him by his name." Without noticing the fulsome praise of Leibnitz and Bernoulli, inserted in the letter, Bernoulli, the grandson, calls our attention to another point, — "to a species of fraud which Leibnitz and Wolf committed against their friend by interpolations, which they ought not to have made without his consent, seeing that they were to his disadvantage, and had principally for their object to claim for Leibnitz discoveries which Bernoulli attributed to himself. There can be no doubt that these interpolations were made by Leibnitz alone, for Wolf would not of his own accord have permitted them; but he was too much devoted to Leibnitz not to adopt what was done by his great patron."^[48]

<68>

Although this letter was published in July 1716, yet Bernoulli was not aware, even in the month of March 1717, of the trick that had been played him, or of the injurious interpolations which had been made in it, or, of the worst fact of all, that the words meam formulam proved him to be the author. It was not till he heard of Herman's conjecture that he was the author, that he was induced to read the letter, and discover these unfortunate words. He immediately saw the use which would be made of them. His friends had already been laughing at the mistake, and his enemies accusing him of being the author of the letter; and he expressed his dread that Keill would seize every opportunity of cutting him up, and employing the matter against him for his own purposes. He, therefore, implored Wolf to think of some method of correcting the blunder in the errata, and he suggested that meam should read eam; but seeing that this would not answer the purpose, he begged Wolf to think of some better method, by which the mistake should be laid upon the printer. Wolf did not obey the mandate of his friend, and, on the advice of Montmort, Bernoulli was induced to avow the letter through his son Nicolas, and to make the best apology he could by throwing much of the blame upon the friends who had deceived him. The avowal, which forms the appendix to a mathematical paper, is written in a good spirit, and concludes by expressing the ardent wish of his father, that the disputants would become good friends, and unite their powers, as citizens of the republic of mathematics, in labouring to extend its <69> domains.^[49] In concluding this strange history, in which Leibnitz performs the least creditable part, we are scarcely surprised at the fact stated by Bernoulli's grandson, that Wolf had the effrontery, in a histoiy of his life and writings, to claim for himself the authorship of the letter Pro Eminente Mathematico!^[50]

This celebrated letter, as might have been expected, excited the indignation of Newton and his friends. They had no difficulty in discovering its author;^[51] and a long and elaborate reply to it, in the form of a letter to Bernoulli, was immediately prepared by Dr. Keill, and submitted to Newton, who proposed numerous alterations, and made many important additions to it. It is written with Keill's usual boldness, and ends with the following observation: — "If any person shall think that you have been treated too severely, I request them to take the trouble of reading your letter, a worthy effort of your genius, and then let them consider if you have not well deserved it.

"Si pergis dicere quæ vis, audies quæ non vis."^[52]

After the death of Leibnitz, which took place on the 14th November 1716, the controversy to a considerable <70> extent ceased.^[53] His champion Bernoulli withdrew from the field, when no longer influenced by his patron and friend; and though Newton has been charged with having made an improper attack upon Leibnitz after his death, he did nothing more than publish an answer, which had been previously in circulation among his friends, in the form of Remarks on the letter of Leibnitz to the Abbé Conti.^[54] This paper, which is erroneously characterized by Biot as a bitter refutation, is, on the contrary, an argumentative defence of his claims, — an interesting notice of his own mathematical discoveries, — a defence of the Royal Society and of Dr. Keill, — and a frank expression of his feelings in reference to the conduct both of Leibnitz and Bernoulli.

Although Bernoulli felt the severity of Newton's censure, he was now more anxious to explain his own conduct than to retaliate upon his adversaries, and a few months had scarcely elapsed after the death of Leibnitz, before he sent messages of kindness to Newton. We have already seen that in April 1717, he not only threw the blame of the pulse-feeling problems upon Leibnitz, <71> but blamed him highly for betraying the secret under which they were sent to him. In a subsequent letter from Montmort to Newton, dated 7th March 1718, he conveys similar messages from Bernoulli and his son Nicolas, expressing their fears that their disputes with Keill had deprived them of his friendship. In replying to Bernoulli, Montmort pointed out to him the inconsistency of these expressions with the Epistola pro Eminente Mathematico, and seems to have suggested to him the propriety of disowning it. Bernoulli, however, took a middle course. He acknowledges that he had, at Leibnitz's request, sent him the facts necessary to defend himself against Keill, and was not answerable either for the praise given to himself, or the harsh language applied to his antagonists.

When Sir Isaac received Montmort's letter, he enclosed it to Keill,^[55] requesting "his sense upon this matter." In his reply,^[56] Keill observes that Bernoulli "is sensible that he had burnt his fingers; that he should beg Newton's pardon for saying that he did not understand second differences, — that no notice should be taken of these letters," and that "it lay on Bernoulli to clear himself, and produce the author of the scurrilous paper.

The celebrated Abbé Varignon had been long desirous of reconciling Newton and Bernoulli, and at last succeeded in the attempt. Sir Isaac had in 1718 sent Varignon three copies of the English edition of his Optics, and in 1719, as many of the Latin edition, to be presented to his friends. Varignon sent a copy of each to Bernoulli in the name of Newton,^[57] and it was in Ber <72> noulli's reply, dated 10th July 1719, thanking him for these presents, that he gave the solemn denial which we have already quoted, that he was not the author of the celebrated letter to Leibnitz of 7th June 1713. In answering this letter,^[58] Newton thus expressed himself, "When I first received your letters, through the mediation of the Abbé Varignon, and understood from them that you were not the author of a certain letter to Mr. Leibnitz, dated 7th June 1713, I at once resolved not only to forget the mathematical disputes which had lately taken place, but to cultivate your friendship, and to estimate highly your great mathematical merits. I have never grasped at fame among foreign nations, but I am very desirous to preserve my character for honesty, which the author of that epistle, as if by the authority of a certain great judge, had endeavoured to wrest from me. Now that I am old, I have little pleasure in mathematical studies, and I have never tried to propagate my opinions over the world, but have rather taken care not to involve myself in disputes on account of them."

The dignified tone of this letter could not fail to disturb the tranquillity of Bernoulli. Conscious of having written the letter which Newton condemns as an attack upon his honesty, he could hardly avoid referring to it in his reply, and we cannot but regret that the terms in which he again denies it are essentially different from those which he had used only a month before.^[59] "I am not aware," says he, "of the nature of the letter to Leibnitz, dated 7 th June 1713, of which you speak. I do not remember that I wrote to him on that day, nor do I altogether deny it, as I do not keep copies of my letters. But if, perhaps, <73> among the innumerable letters which I have written to him, one should be found to which the said day and year is prefixed, I dare solemnly assure you, that nothing is contained in it which in any way could injure your character, and that I never gave him leave to publish any of my letters, and especially one which would not be agreeable to you. I implore you, therefore, to be persuaded, that I never intended to speak of you otherwise than as a great man, and never to attack your character and probity."

The letter of Newton, to which this was the reply, was enclosed in one to Varignon,^[60] in which he thanks him for having reconciled him to Bernoulli, and mentions as the ground of his embracing him as a friend, his denial of having written the obnoxious letter to Leibnitz. Varignon was much gratified at having brought about this reconciliation, but it was a reconciliation merely nominal, and led only to a few interchanges of civility. — Bernoulli sought an explanation through Varignon, of the charge of knight errantry which Newton had made against Leibnitz and his "army of disciples," for challenging the English to the solution of mathematical problems. Newton explained that the phrase was used in a jocular sense, and applied to Leibnitz ;^[61] and we believe that no farther communication took place between them till 1723, when Newton sent Bernoulli a copy of the French edition of his Optics.^[62] In returning thanks for this present, Ber <74> noulli takes occasion to introduce for the third time the subject of the celebrated letter of the 7th June 1713. Hartsoecker, a Dutch philosopher, had attacked Newton's Theory of Colours, and had referred to him as his authority for charging Bernoulli with having called himself "an excellent mathematician" in the Charta Volans. After directing the attention of Newton to the attack upon his Theory of Colours, Bernoulli denies the truth of the charge against himself without distinctly denying, as he formerly did, the authorship of the letter, and seems to expect that Newton should take some step in the matter. "Although the fellow," says he, "is unworthy of any answer from me, yet one thing irritates me greatly, namely, that he exposes me to the laughter of every person, and impudently maintains that I took to myself the title of an excellent mathematician; and in order that the crime of calumny should not attach to himself, he makes you the author of it by citing the passage in which you speak of that letter of 7th June 1713, which Leibnitz maintained was written by me, and in which that eulogium, within parentheses, was ascribed to me. Hence the calumniator maliciously concludes that you wished to insinuate that I had been so arrogant as to assume this title to myself. . . . . In the meantime, whatever be the calumny of Hartsoecker, it applies more to you than to me, for he malignantly endeavours to draw it from your express words. What you think should be done therefore, that my innocence may be protected among those who do not see the Collection of Des Maizeaux,^[63] I would willingly learn from yourself, if you are disposed to honour me with an answer."^[64] It does not <75> appear that Newton answered this letter, or that any further correspondence took place between him and Bernoulli.

In the year 1725, a new edition of the Commercium Epistolicum was published, with notes, a general review of it,^[65] and a preface of some length. A question has arisen respecting the authorship of the review and the preface, some ascribing them to Keill, and others to Newton. From similarity of style, but chiefly on the authority of Dr. James Wilson, the friend of Pemberton, Professor De Morgan had made it highly probable that both the review and the preface were written by Newton.^[66] Of the correctness of this opinion I have found ample evidence in the manuscripts at Hurtsbourne Park;^[67] and it is due to historical truth to state, that Newton supplied all the materials for the Commercium Epistolicum, and that, though Keill was its editor, and the committee of the Royal Society the authors of the Report, Newton was virtually responsible for its contents.

The share which Newton took in the fluxionary controversy either directly or through Dr. Keill, who did nothing without his approbation, and the mass of papers which he has left behind him on the subject, shew the great anxiety which he felt not only to be considered the first inventor of the calculus, but the only inventor who had a right to the reputation which it gave. He firmly believed, not only that Leibnitz might have derived the differential calculus from the papers actually communicated to him, but that he did derive it from that source, or from his ideas either oral or written, which were in circulation at the time of his visit to London.^[68] That these <76> were the views of Newton, and, we may add, of all his friends in England, is evident from the new form given to the celebrated scholium in the third edition of the Principia, which appeared in 1725, under the editorship of Pemberton. The reference to Leibnitz and his method was wholly omitted, and replaced by a quotation from a letter to Collins in December 1672, containing, or supposed to contain, the Germ of Fluxions. This step was perhaps unwise. The statement in the two first editions granted nothing to Leibnitz, and even if it had, the truth which it embodied was not cancelled by its omission from the third; but viewing the matter as Newton did, we think he was justified in omitting the scholium. He had stated it, as he himself has said, as a mere historical fact, that Leibnitz had sent him a method which was similar to his own; and when he found that the German mathematician had regarded this simple statement as a recognition of his independent discovery of the calculus, he was not only entitled but constrained to cancel a passage which had been so erroneously interpreted, and so improperly used.

Some time after the death of Leibnitz, Newton drew up a History of the Method of Fluxions, the Preface to which has been found among his papers. I am disposed to think that this Preface was intended as an Introduction to the new edition of the Commercium Epistolicum and Recensio, which was published in 1725, and that it had not been thought advisable to enter into any fresh discussions on the subject. In the first paragraph of the Preface, Sir Isaac remarks, that as only a few copies of the Commer <77> cium had been published and sent to those only who could judge in such matters, that work and the Recensio should be again printed, in order that a true history of the calculus, drawn from ancient documents, might descend to posterity without any disputes, and "put an end to a controversy which was no longer necessary after the charge of plagiarism had been repelled." He then proceeds to enumerate by their dates seventeen letters from Leibnitz to Oldenburg, written between the 3d February 1673 and the 12th July 1677; and, after establishing his claim to the invention of the new calculus, he concludes with these words: "These things being premised, the Recensio of the Commercium Epistolicum should be read, and the Commercium itself consulted, if any doubt be entertained respecting the facts."

The following is an exact copy of the title-page of the manuscript :^[69] —

<78>

In studying this controversy, after the lapse of nearly a century and a half, when personal feelings have been extinguished, and national jealousies allayed, it is not difficult, we think, to form a correct estimate of the claims of the two rival analysts, and of the spirit and temper with which they were maintained. The following are the results at which we have arrived: —

1. That Newton was the first inventor of the Method of Fluxions; that the method was incomplete in its notation; and that the fundamental principle of it was not published to the world till 1687, twenty years after he had invented it.

2. That Leibnitz communicated to Newton, in 1677, his Differential Calculus, with a complete system of notation, and that he published it in 1684, three years before the publication of Newton's Method.

The admission of these two facts ought to satisfy the most ardent friends of the rival inventors; but in apportioning to each the laurels which they merit, new considerations have been introduced into the controversy. Conscious of his priority, Newton persisted in maintaining that the only question was, who was the first inventor, and that "second inventors have little or no honour, and no rights."^[70] Upon this principle, which we cannot admit, <79> the whole merit of the new calculus must be given to Newton, and he undoubtedly claimed it. But at variance with this, there is another principle maintained in modern times, and by distinguished men, which transfers all the merit of an invention or discovery to the person who first gives it to the world. Upon this principle the merit of the new calculus must be adjudged to Leibnitz. These two extreme principles have not in the present case been adopted by the mathematical world. No writer has urged the second against the claims of Newton, or the first against those of Leibnitz. Priority of invention may be established otherwise than by publication; and the merit of a second inventor, when really such, is intellectually as great as the first. ^[71] There is a merit, however, of a peculiar kind which must ever attach to the first inventor who freely gives his invention to the public. While society concedes to him a high niche in the temple of fame, it cherishes also a feeling of gratitude for the gift it has received. To a second inventor society owes no obligation.

Hitherto we have taken it for granted that Newton and Leibnitz had borrowed nothing from each other; and, in stating the result of our inquiry, we have supposed this to be true. A very different opinion, however, has been maintained during the controversy. The unquestioned priority of Newton's discoveries has preserved him from the charge of having borrowed any thing from Leibnitz, excepting his ideas of notation; but a variety of circumstances, which it is necessary to mention, have given a certain degree of plausibility to the opinion that Leibnitz may have derived assistance, even of the highest <80> kind, from the previous labours of his rival. At an early period Newton had communicated to his friends, orally and in writing, the elements, or the germ of his method of fluxions, but certainly his discoveries in series. His manuscripts were copied, and, to a considerable extent, circulated in England. The letters and extracts, actually communicated to Leibnitz, may, or may not, have contained the information which Newton and his friends considered as sufficient to convey to him a knowledge of the method of fluxions; but the fact that he was twice in England in 1673 and 1676, and was in communication with the mathematicians who then adorned the metropolis of England, justified the idea that either orally, or from the circulated manuscripts^[72] of Newton casually seen, or actually communicated to him, he might have derived that information.^[73]

Had Leibnitz been an ordinary man, these views might have had much weight; but his powerful intellect, his knowledge of the subject, and the great improvements which he made in the new calculus, place it beyond a doubt that he was capable of inventing the differential method without any extraneous aid. His Theoria Motus Abstracti, dedicated to the Academy of Sciences in Paris in 1671, before he visited England, contains, according to Dr. William Hales,^[74] "no obscure seeds of his diff'erential method;" and shows, in the opinion of Professor De Morgan, "that in 1671 it was working in Leibnitz's mind, that in the doctrine of infinitely small quantities lay the <81> true foundation of that approach to the differential calculus which Cavalieri presented."^[75] Another argument in favour of Leibnitz is deduced by Professor De Morgan from seven MSS. of his, bearing the dates of November 11, 21, 22, 1675; and June 26, July, and November 1676, one bearing no date, and recently published by M. Gerhardt from the originals in the Royal Library at Hanover.^[76] These MSS., of which Professor De Morgan has given a specimen, are, as he says, "study exercises in the use of both the differential and integral calculus,"^[77] and, if genuine, and correct in their dates, possess a historical interest.

In adjudicating on a great question like the present, surrounded as it has been with national sympathies, we are compelled to look into the character of the parties at our bar. We cannot commend the conduct of Newton in concealing from Leibnitz, in transposed letters, the discoveries which he had made, nor can we justify his personal retreat from the battle-field, and his return under the vizor of an accomplished champion.^[78] His representatives, however, were men of station and character, who gave their names, and staked their reputation in the contest; while Leibnitz and his disciples wielded the anonymous shafts of the slanderer, denied what they had written, and were publicly exposed through the very rents which they had left in their masks.

Instead of striving to prove that he was the inventor <82> of the new calculus, Leibnitz evaded the discussion by attacking the philosophy of Newton, which he did not understand, and challenging the English to the solution of mathematical problems. Nor were these problems his own. He obtained them, as we have seen, under the pledge of secrecy, from a friend whose name he did not scruple to betray; and, when the controversy was at its crisis, he tried to substitute authority for argument, by imploring the most distinguished mathematician on the Continent to declare that he was the first and the sole inventor of the new calculus. Bernoulli rashly yielded to the urgency of his patron, but, in the anonymous testimonial which he gave, Leibnitz inserted a parenthetic eulogy on the writer, which had the effect of removing his mask, and exposing him to the ridicule and laughter of the scientific world. Nor is it difficult to discover, or uncharitable to expose, the motive for the interpolation. It was intended to prove that the "eminent mathematician" was John Bernoulli, and, lest the proof should not be thought sufficient, Leibnitz publicly declared, while Bernoulli as publicly denied, that he was the author. Thus, to a certain extent, baffled in his schemes, Leibnitz, as we formerly stated, implored Bernoulli, when an opportunity should present itself, to make an early and public declaration that the method of fluxions was posterior to his calculus — that is, that Newton was a plagiarist. An opportunity soon occurred for the perpetration of this fresh act of injustice. Bernoulli unscrupulously prepared the document,^[79] and, when it came into the hands of Leibnitz, <83> he imparted to it new elements of bitterness, — interpolating passages in praise of himself and Bernoulli, — altering other passages, so as to give to himself a discovery which belonged to his friend, — and, finally, leaving the words meam formulam to prove, as it did prove, to the world, that the testimony in the letter was the testimony of John Bernoulli. We have found nothing in the records of science so dishonest as this. As a portion of scientific history, closely connected with the fluxionary controversy, we have submitted it to the reader; but we have not allowed it to influence the decision which we have ventured to pronounce.

In charging Newton with plagiarism, and in persuading others to repeat and enforce the charge, we may find some apology in the excited feelings of Leibnitz, and in the insinuations which were occasionally thrown out against the originality of his discovery; but for other parts of his conduct, we seek in vain for an excuse. When he assailed the philosophy of Newton in his letters to the Abbé Conti, he exhibited only the petty feelings of a rival; but when he dared to calumniate that great and good man in his correspondence with the Princess of Wales, by whom Newton was respected and loved, — when he ventured to denounce his philosophy as physically false and dangerous to religion, — and when he founded these accusations on passages in the Principia and Optics, glowing with all the fervour of genuine piety, he cast a blot upon his name which all his talents as a philosopher will never be able to efface.^[80]