In like manner, all the preceding parts of Dr. R.'s proof may be translated, by any one who is moderately versed in mathematics, into Euler's language; and such a translation (made in the strictest manner) will incontestibly manifest the sameness of the two proofs, the sameness of their principles, rhe same combinations, and nearly in the same order*. If our readers, now, will for a moment refer to our number for February 1807, p. J 64 they will (we conceive) ackno wlcge that we then exerted our powers of censure with remarkable lenity and moderation, and will agree that in an evil hour has the author challenged us to make good the charge of similarity in the two demonstrations.—Professor R. says that we torture his formulae \ and the original purpose of tortuc has been attained: they confess the truth. There are undoubtedly degrees of similarity: bul we believe that it will be difficult to find a similarity nearer to identity, than that which the present instance affords: yet Dr. R., with this similarity pointed out to him, and reference made to the proof, denies the one and prints the other I The resemblance of the demonstrations is so much a matter of fact, and so little dependent on opinion, that we are absolved from the irritation that usually attends questions which are doubtful and debateable : indeed, that Dr. R. should have wasted hit time, his money, and his temper in proving himself wrong, furnishes a fit occasion for pity rather than for anger. If, enlightened by our explanation of Euler's Symbols, he shall at length recognise the sameness of the *t Euler's proof was inserted in the Nov'i Comm. Pttrop. tom. xix: but it hat been given, with acknowlegement, by Lacroix, in his Complement dct tlemtnt d'Algelr:, page J33: which work was published in 1800. , proofs, proofs, he may find some slight excuse for his intemperate -and precipitate reply, by pleading that he did not understand Euler's notation. It is very possible that it did perplex him; but otherwise, how will our preceding statements be answered? By his random volley of scrap quotations? By his little Greek and little Latin? By vague charges of ignorance and malignity? Or by coarse terms that disgrace only the person who uses them? Dr. R. complains that we so deformed and mutilated his proof, that it was only by the occasional mention of his name, that he found it to be his paper that was criticized !—What were the mighty and momentous mutilations which astonished and bewildered a Savilian professor of geometry? Instead of an x we put a v \ instead of n, we put m'; instead of A, B, C, we put A, A,' A"; and since this species of change and of mutilation produced such confusion and perplexity in his mind, we need not wonder that he no longer recognizes Euler's proof when it appears under his own symbols.—Dr. R. endeavours to make us contradict ourselves, because in -our Number for February we disavowed a wish to found a charge of plagiarism, whereas in that for September we do insinuate such a charge. Be it so; during the interval between the writing of the two critiques, our sentiments were changed; and in that interval, had nothing happened to induce a change? Had we not seen the pages of Thomas Simpson transplanted into the volumes of the Transactions ?—and if we did not contest the possibility of one marvellous coincidence, ■were we bound to acquiesce in the possibility of two i Notwithstanding the fulminations of the Professor, we Still venture to think, as we thought in our original criticism, that both Euler's and his own demonstration rest essentially on the principle of the composition of the coefficients of the series which is the product of two series. Euler remarks, " Hoc ratiociniunt non vulgare probe notetttr, quoniam ei tota vis nostra ■demonstrations innititur," but Dr. R. rather boldly than wisely says that every scbotl-boy understands and could point out the principle. For our parts, wc would rather be schooled by Euler than profess with Dr. R.—The two proofs of the binomial, it has been shewn, almost to excess, are the same; if Dr. Robertson, when he devised that which he has suggested, had never seen the substance of that of Euler, the coincidence must be reckoned very marvellous; and it is a little unfortunate for the Doctor's mathematical fame, that he should Jiave been born so many years after Euler :—both hit on a ■curious demonstration, but Euler happened to publish first. Rev. June, 1808. L Here Here then we shall close our second criticism on this subject) which, like the first, Dr. R. may assert to be a bungling and grors misrepresentation from beginning to end: but which may meet with a different judgment from those who can distinguish refutation from plain downright railing We now come to the Precession of tht Equinoxes; on which Dr. Robertson has pronounced a great part of our criticism to be • nonsense', and the remainder * malice'. Concerning this paper, we said that the greatest part of it was taken from Thomas Simpson; and against this remark the Professor contends that lie could have had some of the matter elsewhere. On this point, better than on any other, both the author and the critic agree. According to us, the paper was not original, and according to Dr. R., the substance of it was a kind of common property. It came from Thomas Simpson; or, if not, from Lalande, who had it from Simpson; or one part of it, though contained in Simpson, might have been derived from Newton or Friai. So that, according to our first statement, and to the confession of the author himself, it has no claim to originality, unless such claim be founded on the articles relating to the composition of angular velocities : now the theory of that composition has been known ts mathematicians for years ; and nothing, consequently, is peculiar to Dr. R., besides the very aukward and obscure manner ef Stating it. We pointed out, by particular reference, eleven or twelve articles taken from Thomas Simpson, and among these the nth article: but of the whole of this charge Dr. R. endeavours to get rid, by arguing that the 1 nh article, which is in Simpson, might have been obtained from Frisi, Silvabelle, &c.; whence he contends that we were wrong in saying that he borrowed from Simpson, and that we are malicious and every thing that is bad. The best comment on this matter is a plain statement; twelve articles are the same in Simpson and in Dr. R.'s paper, but one of the 12 might have been taken from other stores than those of Simpson: now whence was it most probable that this contested article came? and if it did not come from Simpson, did the remainder also cease to be his property? Professor R. enumerates the authors from whom he could have procured this nth article. Why did he not proceed to specify those from whom the other articles might have been obtained? Could no room be found among his thronged sentences of recrimination, for a short reference to the page of the authors in which, for instance, articles 13, 14, 15, 16, . &c. could be found? Instead of a reference, he gives in the next paragraph an assertion, which, from any one but an author who could print his own and Euler's proof of the binomial and then deny their similarity, would indeed have surprised us. « No one of them,' says Dr. R. 'was borrowed from Simpson!' Really the Professor's perceptions arc so Vitiated by the malady of controversy and anger, that we advise him, before he iodites his second reply, to go through a regular course of common Algebra. • No one of them was borrowed from Simpson !' neither Art. 13, 14, 15, &c: could these be borrowed from Silvabelle, or Emerson, or Walmesley, or Frisi, or Mr. Vince? We ask with considerable hesitation, because, since Dr. R. denies a similarity between his and Euler's proofs of the binomial, so here he may possibly discover a similarity that escapes vulgar notice.—One page has been employed in an attempt to shew that the nth article might have been taken from other authors than Simpson, but one line will suffice for reference to the authors whence the other articles were derived. We are anxious that authors should have their property restored, but Simpson, we perceive, will never recover his; or perhaps the Professor will contend, with a sprightly verbal finesse, that there could have been no borrowing where there was no intention of restoring. In this case, the Doctor must admit of a more decisive term. If we were not to notice Lalande's Astronomy, Dr. R. might apparently triumph through two or three pages, in shewing that the articles, which we have said to be taken from Simpson, might have been obtained from that treatise: we will endeavour to prevent this waste of labour. Lalande borrows from Simpson, and acknowleges the loan: so that, if we take in thi3 part from Lalande, we in fact take from Simpson: but, if Lalande borrows, why should not Dr. R., since the acknowlegement of the debt is a trilling circumstance? Lalande, in composing a regular scientific work, properly, and as is usual, extracted and collected from various sources: but we never heard that the volumes of the Royal Society Transactions were destined to receive large extracts from Simpson and Euler*. The Professor remarks, however, that he did make an acknowlegement. Now at the end of the general description of the nature of his paper, he says, * the quantity of the precession * The advertisement to each volume of the Transactions states that the grounds of the choice of papers are, < the importance and singularity of the subjects, or the advantageous manner of treating them,' i s calculated the usual way*; and an ordinary readrr would say that this acknowlegement applied merely to the latter articles, beginning at the 22d, and could not 'refer to the preceding articles: yet this feeble attempt to convert a particular acknowlegement into a general one, together with the preceding instance, and his exultation over an oversight in which the number 50* was suffered to stand for 30, will evince the extreme shifts to which the author was reduced in findingmatter for his reply. We shall give another instance. In page 7, Review for September 1807, we said that, 'in Simpson's solution, D'Alembert pointed out errors which had never been amended.' Now does not this passage relate solely to the errors pointed out by D'Alembert; and can it possibly be made to refer to errors stated by other authors? Yet Dr. R. makes it apply to eirors detected by Lander) and Dr. Young, and this he does purposely that he may introduce the Rev. Matthew Young, D.D. S.F.T.C.D. and M.R.I.A, and four pages of words, because, we suppose, he expects that with the multitude four more pages will look like four more pages of refutation. * If (he adds) by the last remark the reviewer means to say'— we beg leave to say and to think for ourselves; and above all, we are desirous that Dr. R. should neither say nor think for us. In another passage, the author slightly compliments himself for having neatly put together his materials, and says that we ought to have remarked that his paper bore 'no marks of borrowing, sameness, or servile imitation.' Alterations, then, as important as the putting v instead of y, or an a for a b, are to exonerate an author from the charge of sameness and servile imitation! ,' If the Professor, then, be unable to m^ke out any claims to originality, in what does the merit of his paper consist? Is the nature of its value like that of the famous Corinthian metal? and docs the author expect distinction for having cast together the gold of Newton, the silver of Simpson, and his own lead? If we had not before us Dr. R.'s direct assertion that he perused our strictures with perfect composure, we should have suspected, from his language and unguarded assertions, that his serenity had been in some slight degree disturbed; and that he was conscious that, in our remarks, some unlucky truths and provoking detections had occurred. The syrnp • That this was a mere oversight, Dr. R. had before him evidence amounting to absolute proof. tomsf |