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COMMERCIUM EPISTOLICUM. 



COMMINATION, THE OFFICE OF. 



COMME'RCIUM EPISTO'LICUM (commerce of letters), a name 

 which was at one time frequently given to published collections of letters, 

 such as were common about the end of the 17th century and the be- 

 ginning of the 18th. Thus we have the ' Commercium Epistolieuni ' 

 of Wallis in the second and third volumes of his works (1693and 1699); 

 that of Kepler (though his name does not appear in the title-page), 

 published in 1718 ; and that of John Bernoulli and Leibnitz, published 

 in 1745. 



But the name by itself is generally understood to apply to the cele- 

 brated collection published by the Royal Society in 1712, in vindication 

 of their decision upon the dispute between Keill and Leibnitz as to 

 the right to the invention of the Differential Calculus, or Method of 

 Fluxions. We have not space here to enter upon the subject-matter 

 of the quarrel itself, but only to give some account of the ' Commer- 

 cium Epistolicum ' [referring for the rest to FLUXIONS, METHOD OF]. 



In the year 1708, Newton and Leibnitz being then both alive, Keill, 

 an astronomer, now better known by his concern in this matter than 

 by his writings or discoveries, inserted in the 'Philosophical Trans- 

 actions' (No. 317) an article in which he defended Newton against the 

 editors of the Leipsic Acts, who had spoken of Newton's ' Quadratura 

 Curvarum ' as a secondary work in comparison of the previous writings 

 of Leibnitz. He asserted that the method of fluxions was first invented 

 by Newton, and that Leibnitz, changing the name and notation, had 

 inserted' it in the Leipsic Acts : his words will bear the construction 

 that he conceived Leibnitz to be a plagiarist, but not that of his being 

 an independent inventor. Leibnitz, on the receipt of this volume 

 (March, 1711), complained of the accusation in a letter to Dr. Sloane 

 (then secretary of the Koyal Society) ; reminded him that on a similar 

 accusation having been made a few years before by M. Fatio de Duillier, 

 the Society and Newton himself had disapproved of it ; pointed out 

 the dishonourable stigma implied by Keill (whom he presumed to be 

 innocent of all bad intention), and requested the interference of the 

 Royal Society to induce him to disavow the intention of imputing 

 fraud. Keill (in a letter to Dr. Sloane, May, 1711,) denied that he 

 meant to charge Leibnitz with having known the science of Newton by 

 name and notation ; but asserted that Newton had explained his 

 Fluxions in two letters to Oldenburg (then secretary of the Royal 

 Society), which were transmitted to Leibnitz; and that the latter 

 either did draw, or at least could have drawn, the principles of Differ- 

 entials from thence. On this subject he wrote a long detail of what 

 he considered to be the proof of his assertion. Leibnitz, in another 

 letter (December, 1711), complains that the charge was now more open 

 than before ; that he and his friends had never contested the inde- 

 pendent invention of Newton ; and that he appealed to the Royal 

 Society and to Newton himself. The Royal Society accordingly ap- 

 pointed a committee, which collected and reported upon a large mags 

 of documents, consisting mostly of letters from and to Newton, Leib- 

 nitz, Oldenburg, Walks, Collins, Ac., Ac. Their report was to the 

 effect that Leibnitz was in London at the beginning of the year 1673, 

 from which time to September, 1676 (when he visited London before 

 returning to Hanover), he was in correspondence with Collins and 

 Oldenburg; that when first in London, he was in possession of a 

 differential method, which was no other than that of Moutou ; and 

 that he never mentioned any other till he wrote a letter of June, 1677, 

 being a year after a copy of Newton's letter to Oldenburg, of December 

 10, 1672, had been sent to Paris to be communicated to him, and four 

 yean after Collins began to communicate the contents of that letter. 

 Also that by a former letter of Newton, of June, 1676, it appeared that 

 he had been in possession of his Fluxions five years before : that Leib- 

 nitz's method is hi fact the same as that of Newton, with a difference 

 of name and notation ; finally, that Newton being the first inventor, 

 Koill, in asserting the same, had been no ways injurious to Leibnitz. 

 This report, preceded by a large mass of letters or extracts, apptnred 

 in the year 1712 ; and again with a ' Hecensio,' Ac., prefixed, and some 

 other additions in 1722; this reprint was also issued with another title- 

 page in 1725. It was translated into French, and was also published in 

 a journal at the Hague. Leibnitz only protested in private letters 

 against the injustice of the proceeding : he declared that he would not 

 answer a reasoning so weak ; and it appears moreover that he had on 

 his mind an impression that the acrimony excited against him in Eng- 

 land was political. Ho was in the service of the Elector of Hanover, 

 the health of the queen was declining, and many of the men of science 

 were Jacobites. 



With regard to the 'Commercium Epistolicum,' and the Report 



attached, it is obvious that the final conclusion was not to the point. 



Mieition was not whether Newton was the first inventor, but 



ii(;r Leibnitz had stolen the method. The committee did not 



attempt to prove that Leibnitz had received the letter which was sent 



to Paris to be sent to Hanover : nor do they formally venture to assert 



tln-ir belief that Leibnitz was a plagiarist ; but, with a subterfuge 



wholly unworthy of them, they conclude that because Leibnitz might 



have seen Newton's letter, Ac., which they could not prove, Keill did 



him no injustice in asserting the priority of Newton's invention 



which was not the matter of complaint. Moreover, they published 



much of their evidence in the form of extract, and their omissions are 



'ways justifiable. It does not appear on the face of the report 



itself that Leibnitz knew of the appointment of the committee, or had 



any opportunity of stating any objections he might entertain to its 



members, or of furnishing any documents relating to the question 

 under consideration. There runs throughout the extracts a desire of 

 proving Leibnitz guilty of more than they meant positively to affirm. 

 The latter acted wisely in appealing to posterity ; for though party 

 feeling long adopted the conclusions of the Report in England, it in 

 now nearly, if not quite, the opinion of those who study the matter, 

 that Leibnitz really was an independent inventor. The contemporary 

 supporters of Newton, and their followers down to the present day, 

 have chosen to regard the committee as a judicial body, and then- 

 report as a decision. But this was not the case. The committee was 

 avowedly counsel for Newton, though the form of their report gave 

 countenance to the mistake just mentioned. Faulty as they were ill 

 more points than one, their unfairness was that of advocates, not of 

 judges. 



The part which Newton himself took in the matter at the time was 

 not very well known till lately. In the first edition of the ' Principia ' 

 (1687), he stated (book ii. Scholium to Lemma 11) that ten years 

 before (the Scholium must probably have been written in 1686 at the 

 very latest) he had communicated in cipher a single sentence to Leib- 

 nitz as a key to what he informed him was a method of drawing 

 tangents, &c., and that Leibnitz not only wrote in reply, that he had 

 fallen upon a similar method, but actually communicated it, and that 

 he (Newton) found it to be the same as his own, except iu notation 

 and symbols. No doubt it was upon the strength of this scholium that 

 Leibnitz confidently appealed to Newton himself : and we might have 

 imagined that the question of the date of this letter would have formed 

 a part of the inquiry. But we cannot find it alluded to : the publica- 

 tion of the ' Principia ' is mentioned in its proper place, without a 

 word as to this scholium ; nor can we find any allusion to it. We wish 

 we could end here : but we are compelled to add, that this scholium 

 was omitted by Newton in the third edition of the ' Principia ' (1725), 

 and its place supplied by another, iu which the name of Leibnitz is 

 not mentioned, but an account of what Newton had written to Collins 

 in 1672 begins and ends in nearly the same words. But it must be 

 remembered that between 1687 and 1725, Newton had suffered that 

 illness which perhaps impaired the powers of his mind, and certainly 

 altered his disposition, perhaps even his memory ; for iu a letter pre- 

 served by Raphson, February 26, 1715-16, he gives an account of the 

 letter of Leibnitz differing in several particulars from the printed 

 scholium. 



The ' Commercium Epistolicum ' will be found complete in Horsley's 

 edition of Newton, accompanied by additional letters extracted from 

 Raphson's ' History of Fluxions,' London, 1715. The appendix con- 

 tains the additional letters. 



An edition of the ' Commercium Epistolicum,' with valuable notes, 

 and the most recent information, has been published by MM. Biot and 

 Lefort, Paris, 1856, 4to. To what precedes we may add the following 

 facts, recently established. 



1. The reprint of 1722 contains some small additions and omissions, 

 though it professes to be nothing but a reprint. Some of these altera- 

 tions are important, and of a highly unfair character. (' Phil. Mag." 

 June, 1848.) 



2. The letter actually sent to Leibnitz has been found among his 

 papers at Hanover, and a draft of it in the archives of the Royal Society. 

 It does not contain the mathematical part of Collins'* letter of 

 December, 1672, but only the description given by Newton of the 

 character of his results. This makes little difference ; 'because the 

 mathematical part of Newton's letter contained nothing sufficient, and 

 nothing but the like of what had been printed before ; but the dis- 

 covery convicts the committee of extreme carelessness on the most 

 iin|Tt.int point. (' Comp. Aim.' 1852.) 



'A. Sir D. Brewster, by his recent examination of Newton's | 

 has found that Newton himself is fully responsible for the contents, 

 both of the ' Commercium Epistolicum,' and the reprint. This has 

 very often been denied. 



4. It has recently been proved, both by internal evidence and by 

 the Newton papers, that Newton himself, a foot always strongly denied 

 by his supporters of this century, wrote the account of the ' Com- 

 mercium Epistolicuni,' which appears in the ' Phil. Trans.' No. 342 

 (1714-1*.) 



COMMINATION, THE OFFICE OF, a service in the Liturgy of 

 the Church of England. It is called " A Commutation or denunciation 

 of (i. l's anger and judgments against sinners," from the Latin word 

 ittio, a threatening or cursing. The Protestants at the Refor- 

 mation introduced the reading of this comminatory service as a sub- 

 stitute for the ancient and still continued Catholic ceremony of 

 sprinkling the head, and making the sign of the cross on the forehead 

 with ashes, on the first day of Lent, hence denominated Ash Wednes- 

 day ; but though it is ordered especially to be read on this day, the 

 rubric adds, " and at all other times as the ordinary shall appoint." 

 From Archbishop Grindall's Visitation Articles, published in 1576, it 

 appears at that time to have been used on four days in the year, 

 namely, on Ash Wednesday and on the third Sunday before Easter, 

 Whitsuntide, and Christmas. The origin and object of the service 

 will be best explained by the following extract from its commence- 

 ment. " In the primitive church there was a godly discipline that at 

 the beginning of Lent such persons as stood convicted of notorious sin 

 were but to open penance and punishment in this world, that their 



