small Pamphlet in support of his opinions and assertions, under the title of Lettre au Rédacteur du Monthly Review, which we examined in our 32d vol. p. 495. Difference of opinion, however, has created no animosity; and we are happy to be brought together again, and not on the terms of decided contention. Of the present volume, the contents are six Eulogies; a discourse delivered in the name of the Royal Society, and addressed to the president; a Memoir on the originality of the maritime discoveries of the Portuguese in the 15th century; and a mathematical letter to M. Felkel. Among the Eulogies, the most important for its subject, but on account of the notoriety of that subject the least requisite, is that on M D'Alembert. The life of this great mathematician is sketched only with conciseness: but, in the narration of the transactions of his younger days, our attention is for a moment arrested by the observation that D'Alembert began his career as Newton ended, with a religious tract, a Commentary on St. Paul's Epistles. The account of D'Alembert's mathematical progress, and of the several works successively published by him, is judiciously and ably given. We wish, however, that the writer had more particularly insisted on one of the first of this philosopher's productions, his Dynamics: the merit of that performance being very high. Authors speak of it with sufficient elevation of praise: but they do not, with proper precision and fullness, state its peculiar excellence;^ nor explain to the satisfaction of students their frequent assertion, that Alembert in that work reduced all problems in Dynamics to a dependance on the equations of equilibrium. The principle of this reduction is not, however, entirely due to D'Alembert. As M. La Grange observes in his Mecanique Analytique, and as M. STOCKLER remarks in the paper before us, the principle is really laid down and used by James Bernoulli, in his problem of the centre of oscillation: Acta Erud. Lips. 1691. Guiding his narration by the historical arrangement of D'Alembert's writings, the author passes on to notice, first, his treatise on the equilibrium and motion of fluids; in which the principle, that was the foundation of his solutions in Dynamics, was again employed, and by means of which he ob tained fluxional equations. Next occurs his treatise on the general cause of the winds, in which were sown the first germs of the theory of partial differences. This narration of M. STOCKLER is interspersed and enlivened by many just and pertinent observations. The The application of his methods and of his analysis to phy sical astronomy, and to the theory of the moon,-the remarkable and unexpected result obtained at the same time by D'Alembert, Euler, and Clairaut, relative to the motion of the lunar apogee,-what astronomer is ignorant of these circumstances? yet the continuity of historical narration requires the notice of them, and the present eulogist has inserted them; at the same time properly commending the superior prudence and caution of D'Alembert, who, unlike Clairaut, was unwilling to give up the received law of gravitation, and rather distrusted the exactness of his own computations. Of the mathematician's labours in the Encyclopedie, M. STOCKLER speaks in favorable terms, and especially of his celebrated preface. It is mentioned that the project of the Encyclopedie did not originate with Diderot, as it is generally believed, but with M. Gua. The problem of vibrating chords, first solved by Taylor, caused a long controversy between D'Alembert and Euler: the latter of whom asserted that the arbitrary functions, contained in the integral of the differential equation which expressed the conditions of the problem, might be discontinued. The several arguments employed by these philosophers, in support of their respective opinions, are exposed and criticised by M. STOCKLER. The integral is expressed by means of symbols f, F, &c. which denote functions of variable quantities; and the fluxionary equation is this: and s=--==a2 = • * = a P hence pPx+Q• and hence ap+T = (aP+Q) (x*+at•) ap-q = (aP—Q) (x'—at·) From these fluxionary equations, we easily deduce ap q = F(x-at) and then, adding and subtracting, and substituting for p and q their values, viz. which is the complete integral, and involves two arbitrary func tions. From this equation, applied to the vibrating string, it may be shewn that the functions f and F are the same; and thence y={(f(x+at) + f (x—at) Most mathematicians have coincided with Euler; among whom is Arbogast, who has resumed the question in the Petersburgh Acts for 1790. He transforms the equation, oa which the question depends, into ལ་ On this method and determination, M. STOCKLER makes some remarks. He does not entirely agree with Arbogast, but acknowleges that he is acquainted with the memoir of that mathematician only through the medium of La Croix's Integral Calculus. The next essay in this volume is an Eulogy on Barros, a considerable mathematician and astronomer of Portugal: yet we must confess that, previously to the perusal of M. STOCKLER'S discourse, we were ignorant of his labours and his merits. M. Barros has left a number of manuscripts, and his printed works are also many. He published new equations for the perfection of the theory of Jupiter's satellites; explained the remarkable phænomenon in the passage of Mercury over the Sun's disk, &c. and wrote on the difference of the population of Portugal in antient and modern times, &c. We now arrive at an Eulogy on Robert Nunes da Costa, who early in life was placed in a professor's chair; and who, according to the present writer, possessed considerable knowlege in language and metaphysics, enlightened by a large portion of philosophic spirit. In the latter part of his life, which was shortened. by too great fatigue in the discharge of his duties, he was employed in the formation of a dictionary. The The three next Eulogies are those of M. Mello de Castro, M. Sanches d'Orto, and M. de Valleré: the first a statesman, the second an astronomer, and the third a General.-The English reader is not particularly interested in their con tents. The letter to M. Felkel is written in French, and is purposed to be explanatory of his method of finding the factors of numbers not divisible by 2, 3, 5; and to give the base of his method by the simple principles of arithmetic. The work or memoir of M. Felkel we have not seen, and therefore the comment is not, in all places, very intelligible to us. that M. STOCKLER had indulged in greater fullness of explaWe wish nation. This letter forms the conclusion of the present volume, and the second has not yet reached us. ART. VIII. Histoire Particuliere des Evénemens, &c. i. e. A Particular History of the Events in France during the Months of June, July, August, and September 1792, and which occasioned the Fall of the Throne; in which will be found new Details, supported by Proofs, respecting these deplorable Epochs; two Secret and unpublished Letters of Louis XVI; the Orders and Ordinances of the public Authorities, and of the Sections with regard to the Murders of September; the Sums paid to the vile Instruments of these bloody Executions; an Alphabetical List of all the Victims massacred at Paris, Lyons, Orleans, Versailles, and Meaux; Sketches and Particulars of the Lives, Works, and, last Moments of the Principal also of the guilty Perpetrators, who have been convicted and executed or banished, and of other Persons Antient and Modern, famous and celebrated, &c. &c. By M. MATON-DE-LA-VARENNE, Advocate, Member of many Academies and learned Societies, and one of the Proscribed who escaped the St. Bartholomew of 1792. Imported by De Boffe. Price 8s. 8vo. Paris. 18c6, AFTER having copied the wordy title page of this volume, we need not particularize its contents. the merit of stating facts which had not been previously publishIt unquestionably has ed: but whether the relations are authentic, or not, is a question which we own we have no means of deciding. only say that the writer, when furnishing details which We can had been before supplied by others, seems not always worthy of dependance; and that he incurs the charge which we have already had occasion more than once to prefer, however extraordinary it may seem, that of imputing crimes to the monsters of the sanguinary æra of the French Revolution, of which they were not guilty. We have heard it observed in the way of of pleasantry, that some minds have an innate love of lying; and nothing can more strongly corroborate this opinion, than the circumstance of falsehoods having been circulated with regard to Robespierre and his colleagues. It is most evident that it was the intention of these false accusers, to render hideous and detestable the wretches whose conduct they undertook to describe; and it is not less clear that nothing could so effectually have led to that end, as a true and exact statement, of the particulars of their conduct. How are we then to account for this preference given to falsehoods when truth would have better answered the object designed? How are we to account for the glaring falsehoods of the Revolutionary Plutarchs, the Histories of Jacobinism, Conspiracies, and that class of writings which served to shew the credulity and ignorance of so many of our worthy countrymen? We would not be understood as ranking the present writer with those to whom we have been alluding; since it is our own opinion that, in the new relations for which we are beholden to him, he mixes some false with much of true statement, as we perceive he has done in those parts of his detail which admit of a comparison with the testimonies of a host of other writers. The novel part of the volume is so atrocious, that we do not think that any selections from it would gratify our readers. Those who would learn to what excesses a multitude which has broken loose from the ties of civil authority, religion, and law, may be carried, will find what they seek in the present work; which, though it be disgusting, is not uninstructive.. ART. IX. Saggio Idrografico del Piemonte, i. e. An Essay on the Hydrography of Piedmont, by G. T. MICHELOTTI, late Mathematical Professor in the University of Turin, dedicated to his Royal Highness the Prince of Brazil, Regent of Portugal, &c. 4to. pp. 126. Rome, 10}. Ensayo Hydrographico, &c. The same work translated into Portuguese, by Father Francesco Furtado de Mendonça. 4to. Rome. T 'HE vast chains of mountains which extend themselves over the greater part of the late principality of Piedmont, and the neighbouring districts of Dauphiné, Savoy, Le Valais, and Swisserland, give rise to numerous rivers and torrents, which, in their course to the Po, exhibit almost every variety of character that can interest the hydraulic engineer. The fall and consequent rapidity of these streams are in general very considerable, and offer to agriculture and manufactures the most important advantages, at little trouble or expence. On the other hand, the tremendous floods, to which they are all more |