tion on its right footing may be discussed within a small compass, and are in fact contained in four letters that passed between Newton and Leibnitz, through the medium of Oldenburg, the Secretary of the Royal Society, and which are published in the Commercium Epistolicum. All the subsequent proceedings that took place from the publication of Newton's Optics in 1704, when the quarrel began, till the death of Leibnitz in 1716, when it terminated, though they throw some light on the literary history of that age, may be flung aside without detriment to the question at issue.

The first is a letter from Newton, addressed to Oldenburg for the purpose of being transmitted to Leibnitz, and is dated June 23, 1676. This contains the binomial theorem, and some results found by Newton relative to series, but gives no hint whatever of any peculiar method by which these results had been obtained. Newton merely states that he was in possession of a method, by the aid of which, when the series were given, he could find the quadratures of the curves whence they were derived, as well as the volumes and centres of gravity of the solids engendered by their revolution. Leibnitz replied to this letter by another, which bears the date of the 27th of the following August; and after remarking that all the objects mentioned in Newton's letter could be effected by a method already published by Mercator, he adds, that he himself, in the investigation of similar problems, employed a different method, which consisted in the decomposition of the given curve into its elements, and in the subsequent transformation of these infinitely small elements into other equivalents. He then gives some examples of the application of his method, and adds, that with regard to those questions, in the solution of which it is necessary to pass from the tangent to the curve, he had already solved many of them by a direct analysis; and instances one, which, though it had appeared of great difficulty to Descartes and Beaune, neither of whom was able to find the solution, yielded to his method on the first attempt.*

A less specific statement than the above might have sufficed to show Newton that Leibnitz already closely touched upon a method equivalent to that of fluxions, if, indeed, he was not actually in possession of it. Accordingly, as if anxious to establish the priority of his claim, he lost no time in addressing a second and very elaborate letter to Oldenburg, dated the 24th of October of the same year (1676), in which, after giving an account of the process by which he had been led to the discovery of the series referred to in his former letter, he states, that he was in possession

Commercium Epistolicum, 2d ed. p. 141.

of two methods applicable to the problems involving the inverse method of tangents. But instead of frankly communicating these methods, he thought fit to conceal them in anagrams, or sentences of transposed characters, in order, doubtless, as Biot remarks, that he might have a proof of the priority of the invention in the hands of Leibnitz himself. It would appear that this letter, from some unexplained cause, did not come into the hands of Leibnitz till a considerable time after it was written, as his reply to it bears the date of the 21st of June in the following year 1677. In this second reply, Leibnitz adopted the precise course which might be expected would be taken by a man perfectly conscious of the independence of his discoveries. Laying aside all mystery and concealment whatever, he gave a frank, full, and explicit exposition of the differential calculus, with its algorithm, its rules, the method of forming differential equations, and the application to examples; employing, moreover, the identical notation which he had made use of in his first letter, or that of the previous year.

The question to be considered is, not whether Newton or Leibnitz was the first inventor,-because it is admitted that Newton was in possession of his method of fluxions so early as the year 1669; but whether Leibnitz borrowed his calculus from Newton. To determine this question, it is obviously most essential to take into consideration the first letter of Leibnitz, that of the 27th of August, 1676, which clearly proves him to have been in possession of his differential calculus before the famous letter of Newton was written, in which the method of fluxions was not indeed communicated (being locked up in anagrams which no one ever pretended were deciphered), but, according to Sir D. Brewster," so fully described, that Leibnitz could scarcely fail to discover that Newton possessed the secret of which geometers had been so long in quest." (p. 197.) Now it is a most extraordinary fact, that this very important letter has not been once mentioned, or its existence so much as alluded to by Sir D. Brewster. "Heaven defend us," exclaims Biot," from supposing there was an intention of infidelity in this omission, but it was inevitably necessary that we should repair it, on account of the importance of the omitted document."-Journal des Savans, Mai, 1832, p. 267.

Even from the brief account which we have been able to give of the early communications between Newton and Leibnitz, it will be readily perceived that their intercourse was at first of the most friendly nature, though marked on Newton's side by some traces of suspicion. Had any dispute arisen at this time about their respective claims to the invention, it would, in all probability, have been settled amicably and satisfactorily. Unfortunately, it

sprung up thirty years later, when the different steps by which the inventors had been led to their discoveries were in a great measure forgotten, and when Newton and Leibnitz themselves could only appeal to the correspondence we have quoted for facts respecting which, at the time of the discovery, there could have been no dispute. Leibnitz, conscious of his own rights, appealed against the attacks that began to be levelled at his good faith to the Royal Society, which was presided over by Newton, and which contained many members who had taken up the matter as a national, or even a personal quarrel. The committee appointed to examine into the circumstances acted, we must admit, with the most scrupulous impartiality, so far as regarded the collection and publication of documentary evidence; but in their report, by insinuating that Leibnitz might have taken advantage of the previous discoveries of Newton, they seemed to leave it doubtful if he had not actually done so. By the decision of posterity, the originality and independence of Leibnitz's discoveries have been fully allowed. The subject might here, then, be allowed to drop, for although the biographer of Newton must needs give an account of those lamentable dissensions, he is not called upon to revive them, or to renew exploded calumnies, which, first uttered in a moment of irritation, were better consigned to oblivion. Sir D. Brewster has not, however, viewed the subject in this light; and in his one-eyed zeal to promote the glory of Newton, or rather to justify Newton's instigators in the controversy, he has not hesitated to cast aspersions on the character of Leibnitz, which his conduct, violent as it sometimes was, certainly did not warrant. The following is his account of the breaking out of the quarrel :

"When Newton's Optics appeared, in 1704, accompanied by his Treatise on the Quadrature of Curves, and his Enumeration of Lines of the Third Order, the Editor of the Leipzig Acts (whom Newton supposed to be Leibnitz himself) took occasion to review the first of these tracts. 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 differences 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 Cavaleri. As Fabri, therefore, was not the inventor of the method which is here referred to, but borrowed it from Cavaleri, and ouly 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

* Pro differentiis igitur Leibnitianis D. Newtonus adhibet, semperque adhibuit, fluxiones; ... iisque tam in suis Principiis Naturæ Mathematicis, tum in aliis postea editis, eleganter est usus; quemadmodum et Honoratus Fabrius in sua Synopsi Geometrica motuum que progressus Cavallerianæ methodo substituit.

Newton bad stole his method of fluxions from Leibnitz. The indirect character of this attack, in place of mitigating its severity, renders it doubly odious; and we are persuaded that no candid reader can peruse the passage without a strong conviction that it justifies, to the fullest extent, the indignant feelings which it excited among the English philosophers."-pp. 202, 203.

So far from participating in this conviction, we feel persuaded, on the contrary, that no reader but one blinded by party prejudice, would ever have dreamed of giving the words of the reviewer any such interpretation. We cannot, however, accuse Sir D. Brewster of being the discoverer of the " artful insinuation" contained in the comparison above quoted; he has only repeated the interpretation put on the passage in the Observations on the Commercium Epistolicum. But, unfortunately, he does not seem to think it necessary to listen to two sides of an argument, for he could not but know, though he has carefully kept it out of view, that Leibnitz, in a letter to the Abbé Conti, pointedly declares the interpretation given by the friends of Newton to be the malignant interpretation of one who sought occasion to make mischief, —an interpretation which the author of the review seemed particularly to have guarded against by the words " adhibet, semperque adhibuit;" and triumphantly appeals to the plain sense of the passage, to which no other meaning can justly be given than that Newton had employed fluxions, not only after having seen the differences of Leibnitz, but even before. Newton, indeed, did not acquiesce in this explanation, and made some remarks on the original passage tending to justify the interpretation of his friends. Sir D. Brewster follows the same line of argument, and it is amusing to see how confidently he assumes as incontestable facts that the review was written by Leibnitz, and that the interpretation which he has adopted is the correct one. "If it would have been criminal to charge Leibnitz with plagiarism, what must we think of those who dared to charge Newton with borrowing his fluxions from Leibnitz? This odious accusation was made by Leibnitz himself, and by Bernoulli, and we have seen that the former repeated it again and again, as if his own good name rested on the destruction of that of his rival."-p. 217.

The revival of charges originally brought forward in the heat of controversy, and supported by such feeble evidence, is in exceedingly bad taste. Transcendent as was the genius of Newton, and justly as England glories in him as the first of her sons, Leibnitz was in every respect a rival worthy of him. Few men have ranged over a more extensive domain. His vast genius, seconded by a-memory of extraordinary tenacity, had rendered itself master of almost every department of human knowledge, In general lite

rature, history, poetry, jurisprudence, physics, metaphysics, theology, he was one of the most illustrious writers of his age; and with regard to the particular province in which the controversy we have been considering arose, he was at least the undisputed inventor of the algorithm and notation which have been universally adopted, and to which the infinitesimal analysis is principally indebted for its progress. Genius and talents, we admit, are no excuse for injustice, but after all, to what do the charges brought against him amount? There are two only which have assumed a tangible shape. One is, that "he was the first who dared to breathe the charge of plagiarism against Newton." This, we have seen, rests at best on a strained interpretation of a passage which it is not certain that Leibnitz ever wrote. The other is, that he "calumniated that great man (Newton) in his correspondence with the Princess of Wales, by whom he was respected and beloved." The calumny, it seems, consisted in his representing the philosophy of Newton as tending to materialism, and therefore dangerous to religion. In all accusations of this sort it is the motive that inflicts the sting; and it is not affirmed that Leibnitz's representations did not proceed from his serious conviction. Others, at that time, took the same view of Newton's argument; and theological tolerance was not one of the virtues of the age. But if such failings, deplorable we admit, must necessarily be dragged to light, at all events the balance ought to be held evenly between the two parties. Newton's own conduct in the affair does not appear to advantage. "He went so far," says Biot," as to affirm that Leibnitz had deprived him of the differential calculus, and then, that this calculus was identical with Barrow's method of tangents." In the first and second editions of the Principia, he had inserted a Scholium, in which he generously but justly acknowledges the independent rights of Leibnitz to the differential calculus. Afterwards, irritated perhaps by the violence of Leibnitz and Bernoulli, he gave out that the paragraph was solely intended to assert his claim to priority; and in the third edition he had the weakness to suppress it altogether. Nay, more after the death of his rival, when all feelings of animosity might be supposed to have ceased, he published two new letters of Leibnitz, accompanied with a bitter refutation, which he had indeed written before that event, but shown only to his friends. These proceedings, surely, do not form part of the conduct which Sir D. Brewster describes as having been " at all times dignified and just." Unfortunately, the world does not now require to be told that the possession of the greatest genius and the loftiest intellect does not necessarily imply the absence of those petty passions which agitate and prey on the weakest minds.