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correspondence of Newton and Cotes, with what is called a synoptical view of Newton's life. This is far below sufficient description; for the synopsis is followed by a body of notes of such research and digestion as make it difficult to give adequate praise to the whole without appearance of exaggeration. We differ much from the editor as to many matters of opinion and statements the character of which is determined by opinion; and we take particular exception to the following account (p. xlvii) of the point before us:

"Doubts have been expressed whether these papers" (Comm. Epist., p. 47, or 128, 2nd ed.)" were actually sent to Leibniz. We have, however, Collins's own testimony that they were sent as had been desired (Comm. Epist., p. 48, or 129, 2nd ed.), besides Leibniz's and Tschirnhaus's acknowledgments of the receipt of them (Ib. pp. 58, 66, or 129, 142). It may also be observed that the papers actually sent (in a letter dated July 26, 1676) to Leibniz by Oldenburg have been recently printed from the originals in the Royal Library at Hanover (Leibn. Math. Schrift., Berlin, 1849), and that in them, as in Collins's draught, which is preserved at the Royal Society (To Leibnitz, the 14th of June, 1676 About Mr. Gregories remains,' MSS. lxxxi.), we find the contents of Newton's letter of Dec. 10, 1672, except that instead of the example of drawing a tangent to a curve, there is merely allusion made to the method. Collins's larger paper (called "Collectio" and "Historiola" in the Commercium Epistolicum), of which the paper just quoted " About Mr. Gregories remains" is an abridgment, and which contains Newton s letter of Dec. 10 without curtailment, is stated in the second edition of the Commercium to have been sent to Leibniz, but whether that was the case may be fairly questioned."

There are two things in which we have never failed. We have never examined a point of mathematical history without finding either error or difficulty arising from bad bibliography: and we have never come fresh to this controversy of Newton and Leibnitz, without finding new evidence of the atrocious unfairness of the contemporary partisans of Newton. Nor had we a perception, until we wrote out the preceding paragraph, of the full extent of what it proves. It proves that at the time when the Committee of the Royal Society mentioned the "collectio" which contained Newton's letter uncurtailed of any part relating to fluxions, and asserted in their final report (without venturing to mention it in its place) that this letter had been forwarded to Leibnitz-they had, and must have seen, among the papers they were appointed* to examine, Collins's own abridgment of this collectio, headed "To Leibnitz," and containing Newton's letter curtailed of the very part of which they asserted that it described the method of fluxions sufficiently for any intelligent person. Of this abridgment they make no mention. We now see why the statement that the collectio was sent to Leibnitz was not allowed to appear in its place; that is, when the collectio was mentioned in the body of the work. Had the blot been hit, they would have pleaded some mistake or forgetfulness, would have produced "There is not the least reason to suppose that any papers of Collins's ever came into the possession of the Royal Society after the Comm. Epist. was published,

the abridgment, and would have taken their stand on the fragment of the letter descriptive of results. We neither believe, nor would have others believe, that in the proceeding just described we are necessarily to impute guilty unfairness to the Committee of 1712, or to some of them: though all the circumstances make it impossible to avoid including this hypothesis among the probable ones. Independently of our knowledge of what hero-worship can lead to, even in our own day, we are bound to remember that all the notions as to what is fair and what is unfair in controversy, have undergone much change since the commencement of the last century. And above all, the idea that a party in literary controversy resembles one in a court of law, who may, with certainty of allowance, choose his own evidence, suppress what does not suit, and mystify what does, is now much less in force. In the particular case before us, perhaps something is to be allowed for hurry. The Committee was appointed in parcels on March 6, 20, 27, and April 17; and their report was read on April 24. But the hurry, if any, was their own fault. This striking fact, that the very papers which were examined in 1712 prove that the celebrated letter was not* sent to Leibnitz, but only a description (amounting to extract) of a part of it, and that part not the one which most appears to sustain the report of the Committee, throws into the background the remarks which we intended to make on part of the paragraph above extracted from the synoptical life of Newton. These must now be mixed up with remarks on the whole.

The editor begins by stating that doubts have been thrown on the question whether "these papers were actually sent to Leibnitz." By these papers the reference tells us we are to understand the collectio which has been spoken of. To remove the doubts and prove that "these papers" were actually sent, we are first referred to Collins's own testimony. The reference given would exclude Newton's letter, since nothing is there mentioned as sent to Paris except either Gregory's writings, or what had been done on the method of series: the drawing of tangents to curves was a perfectly distinct thing in the language of the day. But this reference leads us to a proof (though one is not needed) that the Committee actually saw the abridgment which was sent, and contrived to introduce reference to it in an unintelligible way: so that no one who was ignorant of the existence of the abridgment could infer that anything was sent except the complete collectio. The reference is to Comm. Epist. (pp. 47, 48, 2nd ed. 129), where we find a letter from Collins to David Gregory (the brother of James, whose papers were in question) of August 11, 1676, in which Collins says that he had put together an historiola

It is now clear that the Royal Society owes the world more publication from its archives than has yet taken place: unfortunately, it is not yet alive to the feeling that such disclosures as those of the surreptitious additions to the reprint of the Comm. Epist., and of the suppression now noted, would come most gracefully from itself. It is on record, that in 1716, the Abbé Conti, a friend of both parties, spent some hours in looking over the letter books of the Royal Society, to see if he could find anything omitted in the Comm. Epist. which made either for Leibnitz, or against Newton; and that he found nothing. But it now appears either that he did not know what to look for, or that there were papers which did not come in his way. Be it one or the other, the credit of his search is now upset; and Mr. Edleston's discovery proves that another is wanted.

of the writings of his brother and others, in about twelve sheets, for preservation in the archives of the Society; and that he would find from what followed the letter (ex sequentibus comperies) that care had been taken to satisfy the wishes of the French mathematicians. Annexed to the letter is a memorandum to the effect that the sequentia had been sent both to the members of the French Academy, and to David Gregory. Here then are two things; the historiola mentioned in the letter, and the sequentia of the letter: the latter was sent to Paris, and therefore by the sequentia we are to understand Collins's abridgment. That is to say, the Committee, which extracted as much from Collins as would prove that something was sent, did not give a word to explain what was sent: and inserted in their report a deliberate statement that the whole of what they chose to call the fluxional part of Newton's letter had been sent.

We are next told that Leibnitz‡ acknowledged the receipt of "these papers:" we look at the reference indicated, and we find that Leibnitz does (August 27, 1676) acknowledge letters of July 26, which the editor himself immediately proceeds to inform us, both from the Hanoverian publication and from Collins's draught, did not contain "these papers," but only an abridgment. Finally, the editor concludes that it may be "fairly questioned" whether the transmission ever took place. How can this be? the doubts as to the transmission he has just told us are removed by the testimony of Collins the transmitter, and Leibnitz the receiver. The answer is, that the editor himself immediately proceeds to prove, both from the transmitter and the receiver, that what was transmitted was not the collectio of the Comm. Epist., but an abridgment. We cannot but suppose that the editor imagined the existence of the abridgment to be known, and having no idea that he himself was the first to draw it from its retirement, considered the collectio and its abridgment as convertible documents, and the information they conveyed as substantially the same. We, however, had never found a trace, in any writing upon the subject, of any mention of the smaller document; and it is clear that the omission of the example of Newton's

*It is now, Mr. Edleston informs us, extant in thirteen sheets: from which it is clear that this historiola, as Collins calls it, is what the Committee called the collectio; as the editor notes.

+ Among these was Leibnitz, who, as we learn from the letter of Collins to Oldenburg, attached to the collectio, was one of the French Academy who had desired to have an account of Gregory's writings. In fact, Leibnitz was at Paris when he received Oldenburg's account of Collins's abridgment. The Committee who say that Newton's letter was sent to Paris to be communicated to him, may seem by this phrase to have supposed him to have been at Hanover.

Our extract says, Leibnitz and Tschirnhaus. Now though the latter did write from Paris, in September, acknowledging something, yet he does not sufficiently say what, and even the Committee have put a note to his letter, doubting, from its internal evidence, whether he could have seen those extracts from Gregory which were sent to Leibnitz. So that the Committee knew nothing positive as to what was transmitted to Tschirnhaus. Moreover, Tschirnhaus was not Leibnitz. The whole of the passage on which this note is written struck us as so singular, so contrary, in the antagonism of its two portions, to the usual clearness of the whole of which it forms a part, that we could not help suspecting that the editor had been misled by some predecessor. And at last we found out by whom. Keill, in the account of the Comm. Epist., published in English in the Phil. Trans. for 1715, and in Latin as a preface to the reprint, has the whole argument, with the affirmation of Collins and the replies of Leibnitz and Tschirnhaus, Keill was more noted, while alive, for getting his friends into embarrassments, than for his discoveries: will he never leave off his old tricks?

method, poor as the pretext against Leibnitz would have been even if it had been there, destroys the pretext* altogether.

We shall join the complete elucidation of the last assertion with the establishment of another statement of Leibnitz, namely, that the Committee of the Royal Society had been guilty of gross suppression of facts unfavourable to themselves, and within their own knowledge. We, who have not right of access to the archives of the Society, can of course only further show this (beyond what is shown by the suppression of the abridgment) by proving suppression of documents which had been already printed; that is, by showing that the Committee either entirely suppressed what they ought to have brought forward, or contented themselves with reference where they ought to have produced extracts. We shall confine ourselves to what is immediately connected with the unlucky fragment of Newton's letter, which was never sent.

When

First, the Committee refer to the method which Sluse had given for drawing tangents (p. 106, we quote the second edition as more accessible than the first), and which was printed in the Phil. Trans. as early as 1673. They give Oldenburg's communication to Sluse of Newton's letter, in which Sluse learns that what he had communicated was already known to Newton (p. 106). They also give Newton's admission (p. 107) that Sluse not only had probably an actual priority of discovery, but that, whether or no, he was the first promulgator. All this, so far as it goes, is fair, though it militates strongly against the conclusion of their report with respect to Leibnitz. But it was not fair to suppress all account of the manner in which this celebrated letter of Newton was drawn out. they state that Collins had been for four years circulating the letter in which the method of fluxions was sufficiently described to any intelligent person, they suppress two facts: first, that the letter itself was in consequence of Newton's learning that Sluse had a method of tangents; secondly, that it revealed no more than Sluse had done. In the third volume (1699) of Wallis's works (in Latin P. 617, in English p. 636) is a fragment of a letter from Collins to Newton, of June 18, 1673, in which he reminds Newton, for what purpose does not appear, of his having communicated the fact of Sluse's discovery, and having received an answer (which was no doubt the letter) for the purpose of transmission to Sluse. Again, this method of Sluse is never allowed to appear: reference is made to the Phil. Trans., though many things which had been printed before appear in the Comm. Epist. when they serve the right purpose.

To show what we assert we shall compare the two methods. The paragraph of Newton's letter, from the original in the Macclesfield collection, is as follows (December 10, 1672) :—

* If the editor meant that Newton's letter is substantially the same as to the real information it could give, whether with or without the example of the method of tangents, we not only agree with him as to the fact, but should have agreed, if he had asserted that a sheet of blank paper (after what Sluse had already published) would have done just as well. But our reader must remember that it is not the rational interpretation of the letter which is the matter in discussion, but the interpretation of the Royal Society's Committee.

"I am heartily glad at the acceptance, which our rev. friend Dr. Barrow's Lectures find with foreign mathematicians, and it pleased me not a little to understand that they* are fallen into the same method of drawing tangents with me [eandem. ... ducendi tangentes methodum]. What I guess their method to be you will apprehend by this example. Suppose C B, applied to A B in any given angle, be terminated at any curve line AC, and calling AB r and BC y, let the relation between x and y be expressed by any equation, as x3-2xxy+ bxx―bbx+byy-y=0, whereby this curve is determined. To draw the tangent CD, the rule is this. Multiply the terms of the equation by any arithmetical progression according to the dimensions of y, suppose thus ̧x3 —2xxy + bxx―bbx+byy—y3 0 1

0 0 2 3 x3 −2xxy+bxx

also according to the dimensions of x, suppose thus 3

[blocks in formation]

-bbx+byy-y3. The first product shall be the numerator, and the

1

0 0

last divided by the denominator of a fraction, which expresseth the length of B D, to whose end D the tangent C D must be drawn. The length of BD therefore is—2xxy+2byy — 3y3 divided by 3xx-4xy+2bx-bb."

Not many days afterwards (January 17, 1673) Sluse wrote an account of the method which he had previously signified to Collins, for the Royal Society, by whom it was printed (Phil. Trans. No. 90; also Lowthorp, vol. i. pp. 18-20). The rule is precisely that of Newton, the exponents are multipliers, without any subsequent reduction of the exponents (which prevents both explanationst from describing the method of fluxions to any intelligent person), and instead of dividing by x, Sluse changes one a into BD, and then equates the two results. To have given this would have shown the world that the grand communication which was asserted to have been sent to Leibnitz in June, 1676, might have been seen in print, and learned from Sluse, at any time in several previous years: accordingly, it was buried under a reference. But, worse than this, the Committee had evidence before them that it had been so seen by Leibnitz, and this evidence they deliberately mutilated.

March 5, 1677, Collins wrote to Newton, giving him certain extracts from a letter of Leibnitz, dated November 18, 1676. This was printed (1699) in the third volume of Wallis. Leibnitz had seen Hudde at Ainsterdam, and had found that Hudde was in possession of even more than Sluse; and this he states, referring to the published method of Sluse, as known to himself. He gives also an example, or rather its result, not as showing the method, which was known, but in order further to show how to eliminate one of the

* There is no end of the curiosities of this Committee. After their Latin for the word they, they inserted in brackets [Sluse and Gregory], the latter not being a foreigner. If they had given the letter of Collins, just referred to, of June 18, 1673, the reader would have known that Sluse and Ricci are the parties understood.

+ If Newton's example had been sent to Leibnitz, and the latter had not known the method already from Sluse, the direction to multiply by the terms of any arithmetical progression (a mere slip of the pen on Newton's part, properly preserved by the Latin translator) might have puzzled any idoneus harum rerum cognitor.

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