CONTENT S. PART I. GENERAL INFORMATION ON SUBJECTS OF MATHEMATICS, NATURAL PHILOSOPHY AND HISTORY, CHRONOLOGY, GEOGRAPHY, STATISTICS, &c. I. A short Account of some recent Discoveries in England and II. Great Exhibition of 1851 : Facts and Figures III. Census of Great Britain, 1841 and 1851 IV. The County Courts V. Railways of the United Kingdom VI. The Public Debts and Standing Armies of the European States 104 VII. Fluctuations of the Funds 107 PART II. THE LEGISLATION, STATISTICS, PUBLIC IMPROVEMENTS, AND CHRONICLE of 1850-51. VIII. Abstracts of important Public Acts passed in the Fourth Session of the Fifteenth Parliament of Great Britain and Ireland : 108 Smithfield Market Removal Passengers' Act Amendment.. 108 | Ecclesiastical Titles Assumption 118 .... .... Sale of Arsenic Regulation. ...... Inhabited House Duty... Arrest of Absconding Debtors 120 .. 108 Customs 122 109 Metropolitan Sewers 123 110 New Forest Deer Removal, &c. 123 110 Battersea Park.... 124 IX. Abstracts of Parliamentary Documents, &c. : Page 136 142 143 164 166 168 v. Poor Law....... VI.-Miscellaneous X. Chronicle of the Session of Parliament, 1851 ............ 175 XI. Private Bills of the Session of Parliament, 1851... XII. Public Petitions, 1851 ..... XIII. Public Improvements : 1. Metropolitan Street Architecture 2. Churches and Chapels 3. Buildings connected with Education, Science, &c. XIV. Chronicle of Occurrences XV. Necrological Table of Literary Men, Artists, &c. .... 212 218 ........ 259 FOR 1852. PART I. GENERAL INFORMATION ON SUBJECTS OF MATHEMATICS, NATURAL PHILOSOPHY AND HISTORY, CHRONOLOGY, GEOGRAPHY, STATISTICS, &c. I.-A SHORT ACCOUNT OF SOME RECENT DISCOVERIES IN ENGLAND AND GERMANY RELATIVE TO THE CONTROVERSY ON THE INVENTION OF FLUXIONS. THE celebrated controversy on the invention of fluxions has, any one would suppose, been so fully argued that it would be difficult to make out a reasonable case for introducing the subject again. It is nevertheless true that several disclosures of great importance in the way of evidence have never been made at all until very lately. This controversy resembles one of those well-worn law cases which must be cited and discussed whenever a certain question arises. Every dispute about priority of mathematical invention* revives it. At the same time, the main and turning points of it can be presented without any such amount of mathematical language as would render an article upon the subject unfit for the majority of readers. We therefore propose to present some of these points, with an account of the recently published materials, and of their bearing on the result. When, after some petty and indecisive controversy, Leibnitz appealed (1711) to the Royal Society for protection against imputations of plagiarism which had at last assumed a distinct form, the Society, in 1712, appointed the celebrated partisant committee to maintain the side of Newton. The report of this committee, published with epistolary evidence in 1712, under the name of Commercium Epistolicum, contains the following sentence, which is the whole of that report, so far as it insinuates that Leibnitz did take, or might have taken, his method from that of Newton ;-"And we find *One most fortunate circumstance about it, as a precedent, is that it fixed the meaning of the word publication to the genuine and legal sense. It is the sufficient answer to any one who would restrict this word to its colloquial sense of circulation by means of type. + We have shown the committee to have had this character in Phil. Trans., part ii. for 1846, and in the life of Newton in Knight's British Worthies; and nobody has contested the point. It was, however, universally believed that the intended function of the Committee was judicial, and both Newton and Leibnitz speak of it as if it had been so. But though the Committee itself overstepped its own proper function in the form of its decision, and thereby gave rise to the misconception, we hold the intention of its proposers to have been stated with perfect clearness. We cannot here detail all the circumstances. The reader may consult the articles Commercium Epistolicum and Fluxions in the Penny Cyclopædia, the life of Newton already cited, Brewster's life of Newton, that in the Library of Useful Knowledge, or Weld's history of the Royal Society. B no mention of his (i.e. Leibnitz's) having any other Differential Method than Mouton's before his Letter of 21st of June 1677, which was a Year after a Copy of Mr. Newton's Letter, of 10th of 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 describ'd to any intelligent Person." The committee in their English have "any intelligent person"; in their Latin, subjoined for foreigners, they have "idoneo harum rerum cognitori." Raphson, no stickler for accurate description, as we shall see, could not second this; so he converts the Latin into the original, and gives his own English translation, " to any proper judge of these matters." But even this was too much; so some one else (copied by Hutton in his Dictionary; we do not think Hutton did it himself) has invented a new report, in which we find "a man of his sagacity." How far this celebrated letter deserves the character here given of it, is one question; whether Leibnitz actually received it, is another. Comparatively little notice was taken of either; so that in many subsequent writings it reminds us of the tree which was cut down that the action for trespass might try the ownership of the estate. It gives, nevertheless, the only possibility, such as it is, which the evidence offers of Leibnitz having seen anything to the point from the pen of Newton. In order to prove the passage quoted above, it is stated that there existed, among the papers of Collins in the possession of the Royal Society, in the handwriting of Collins, a parcel (collectio) of papers containing extracts from Gregory's letters, together with the letter of Newton above-mentioned (but which was not alluded to in the title or docket which Collins placed on the parcel), and that the parcel was marked as to be communicated to Leibnitz, and was accompanied by a copy of a letter to Oldenburg, the party who was to make the communication. Not a word is said on the date at which the parcel was transmitted: so that the committee, in their report, actually added a statement for which there was no pretext of evidence, namely, that Newton's letter was transmitted about a year before June 21, 1677. Further, the evidence does not mention the date at which Collins died (1682), nor how his papers came into the possession of the Society, nor whether there was any guarantee that papers found tied together in 1712 had been so tied up by Collins before 1682, nor whether there was any evidence that Collins had fulfilled his intention of sending the parcel on to Oldenburg, &c. When Leibnitz, who did not remember receiving any such letter, declared that he did not think it necessary to answer anything so weak, his contempt for this unattested statement was of course construed by the other side as being of that kind whieh parties who cannot answer find it convenient to assume. The editors, whoever they were, of the reprint of the Commercium Epistolicum, made under the sanction of the Royal Society in * We say reprint, and not second edition, because even the old title-page and the old date (1712) were reprinted. Everything was done which could lead the reader to suppose that he had in every respect a repetition of the original work, preceded by a preface of the new editors. 1722, took the liberty of secretly making a few additions* and alterations. Among these, they add the date at which Collins died, and the date of transmission of the parcel: they say it was sent June 26, 1676. How they got this date is not said; but as the next parcel sent by Oldenburg to Leibnitz was stated to have been sent on June 26, it may have happened that the revisors of the second edition borrowed this date for their purpose. So the matter rested until recently, when the publication of a portion of Leibnitz's papers took place. And it now appears that if the manuscripts which Leibnitz left behind him, and which found their way into the royal library at Hanover, had been examined, it could have been ascertained what Leibnitz really did receive from Oldenburg. It appears that the latter wrote to the former from London, with the date of July 26, 1676, not forwarding Collins's parcel, but describing its contents himself. He gives various matters connected with Gregory's researches, and then proceeds to allude to a method in a letter from Newton of December 10, 1672. But though he gives, almost verbatim, what we may call the descriptive paragraphs of this letter, he does not even allude to the example of the method, in which, according to the report of the committee, the method of fluxions is sufficiently described to any intelligent person. So that, with reference to this asserted description of the method of fluxions, there is now clear and positive evidence that Leibnitz did not receive it as stated, but received only an account of the rest of the letter, which describes the sort of results attainable. Towards the end of 1850 the Master and Fellows of Trinity College, Cambridge, published (from among their manuscripts) the This fact was discovered by us in 1848; and the additions are exposed in the Philosophical Magazine for June 1848. The first edition is now scarce. 8vo. Leibnizens mathematische Schriften, herausgegeben von C. J. Gerhardt. Berlin, Erste Abtheilung, Band i., 1849, Band fi., 1850. We have not seen any more, if indeed any more has yet appeared. + Collins had desired, in the title of the parcel, that the contents, after being read by Leibnitz, should be returned to himself. Oldenburg appears to have thought it more prudent to write his own account than to trust the papers to accident by land and sea. (At least, this was our impression before we came to the discovery presently mentioned.) 'Defuncto Gregorio," says Oldenburg, "congessit Collinius amplum illud commercium litterarium, quod ipsi inter se coluerant, in quo habetur argumenti hujus de seriebus historia: cui Dn. Newtonus pollicitus est se adjecturum suam methodum inventionis illius, prima quaque occasione commoda edendam; de qua interea temporis hoc scire præter rem non fuerit, quod scilicet Dn. Newtonus cum in literis suis Dcbr. 10. 1672 communicaret nobis methodum ducendi tangentes ad curvas geometricas ex æquatione exprimente relationem ordinatarum ad Basin, subjicit hoc esse unum parti. culare, vel corollarium potius, methodi generalis, quæ extendit se absque molesto calculo, non modo ad ducendas tangentes accomodatas omnibus curvis, sive Geometricas sive Mechanicas, vel quomodocunque spectantes lineas rectas, aliisve lineis curvis; sic etiam ad resolvenda alia abstrusiora problematum genera de curvarum flexu, areis, longitudinibus, centris gravitatis etc. Neque (sic pergit) ut Huddenii methodus de maximis et minimis, proinde que Slusii nova methodus de tangentibus (ut arbitror) restricta est ad æquationes, Surdarum quantitatum immunes. Hanc methodum se intertextuisse, ait Nowtonus [sic], alteri illi, quæ æquationes expedit reducendo eas ad infinitas series; adjicit que, se recordari, aliquando data occasione, se significasse Doctori Barrovio lectiones suas jam jam edituro, instructum se esse tali methodo ducendi tangentes, sed avocamentis quibusdam se præpeditum, quominus eam ipsi describeret." The word nobis, put by us in Italics, should be ei; Oldenburg forgot that he was de scribing, not copying, the account Collins had given him. Correspondence of Sir Isaac Newton and Professor Cotes....now first published from the originals in the Library of Trinity College, Cambridge, together with an appendix....by J. Edleston, M. A. Fellow of Trinity College, Cambridge. London, 1850, 8vo. |