day after the sentence, for having offered a bookseller a book which he knew nothing of and had received in payment of a debt:-these were the scenes that passed before the eyes of D'Alembert and Voltaire; nor let us, who have no such excuse for hating the establishment, visit too severely the sentiments which scenes like these not unnaturally raised in generous minds, how much soever we may be disposed to admit that they carried their indignation beyond just bounds when they confounded the use with the abuse, and made religion answerable for the faults of its professors.* The character given of D'Alembert by Grimm, is certainly more remarkable for its epigrammatic composition than its truth; though it may contain an approximation to some features. "Les personnes qui ont vécu le plus avec D'Alembert le trouvaient bon sans bonté, sensible sans sensibilité, vain sans orgueil, chagrin sans tristesse;" all this he explains by ascribing to him a combination of "roideur, faiblesse, et activité." He allows his conversation to have been admirable, that he could lend attraction to the most dry and forbidding subjects, and gave his sallies with a grace and a readiness not easily surpassed. APPENDIX. I. NOTE ON D'ALEMBERT'S PRINCIPLE. Professor Playfair ('Ed. Rev.' xi., 253) has by no means been happy in his enunciation of the Principle. "If the motions which the particles of a moving or a system of moving bodies have at any instant be resolved into each two, one of which is the motion which the particle had in the preceding instant, then the sum of all these third motions must be such that they are in equilibrium with one another." The following are the observations referred to in p. 396, note. The great utility of this principle proceeds from the universality of its operation, and from its supplying the place of the detached artifices and ingenious assumptions by which dynamical problems had hitherto been treated, by a rule directly applicable to the circumstances of the motion of one or more bodies whose motions were any other than those immediately proceeding from the direct and unfettered action of the motive force. The principle applies equally to the most elementary and the most difficult problems-to the motion of a body down an inclined plane-the vibrations of a simple pendulum-or to the theory of the radiation of heat-the vibrations of a chord: two subjects previously of insuperable difficulty, to which the illustrious author applied his new method, and which became remarkable in his hands, not only for the solutions which he obtained, but also for the manner of them for it was his singular good fortune, by a further invention, to overcome the analytical difficulties into which the fecundity of his dynamical principle had led him. The great utility of this principle will not appear from the comparison of the solutions of any one problem obtained by its means, with the detached artifices previously employed; these were all private paths to one solution, whilst that is a high road to all. The solution of every problem is obtained from an equation involving some principle to which the motions of the system are subject-the advantage of D'Alembert's step lay in this, that it was the same principle which he applied to each particular case. Note to p. 396, line 19, by the author mentioned p. 396, note. Since these last forces mutually destroy each other, and that the forces actually impressed were compounded of them and of those (usually called effective) which act in the direction the bodies really move in, so that the force originally applied (usually called the impressed force) is the result of these two forces, it follows that the effective forces would, if they acted in the contrary direction, exactly balance the impressed forces. Problems of dynamics are thus reduced to a general equation of equilibrium and become statical. II. That Euler, in the Memoir published in 1734, solved an equation of Partial Differences is quite incontestable, though he laid down no general method; which, indeed, D'Alembert himself never did, nor any geometrician before the publication of Euler's third vol. of the 'Institutions of the Integral and Differential Calculus.' The problem, as given in the 'Mem. Acad. Petersb.' vol. vii., was this; We have the equation d z = Pdx+Q da, z being a function of x and a; and the problem is to find the most general value of P and Q, which will satisfy the equation. QF + P R, F being a function of a, and R a function of a and x, Euler seeks for the factor which will make d x+R da integrable. Call this factor S, and make Sdx+SR da = d T, and make/F da = log. B. He finds for the values required 2 d B PBSƒ': T, Q= +BRSƒ: T Bda and from thence he deduces dz BS (dx + R da) f': T+≈ = d B =Bdf: T+zand consequently z = Bƒ: T. d B B It is thus clear, that Euler had, in or before 1734, integrated an equation of Partial Differences; and it must further be remarked, that D'Alembert, in his paper on the Winds, the first application of the calculus, quotes Euler's paper of 1734. D'Alembert always differed with Euler respecting the extent to which this calculus can be applied, holding, contrary to Euler's opinion, that it does not include irregular and discontinuous arbitrary functions.* III. The Vitrière's house, in which D'Alembert was brought up and lived afterwards for so many years, can no longer be ascertained. I have examined this matter with some care in the street in which it stood, Rue Michel-le-Comte. That street is very narrow, in no place above eighteen or nineteen feet wide, and the houses on both sides are lofty. D'Alembert, therefore, did not exaggerate when, in his letter to Voltaire, he said he could only see a yard or two of the sky from his room. The street is near the Rue St. Martin, at some distance north of the Hôtel-de-Ville. The church of St. Jean-le-Rond, at the gate of which he was exposed, and from which he took his name, stood near the cathedral of Notre Dame, and was pulled down in 1748. It was a baptistery of Notre Dame, near the Foundling Hospital, and touched the Cathedral Church. Of the Vitrière's house I have inquired everywhere, not only in the Rue Michel-leComte, but at the Prefecture (Hôtel-de-Ville), and among my brethren of the Institute; I can discover no traces of it. D'Alembert's Address given on his admission to the Academy in 1741, only mentions the street without giving any number. * Cousin has mentioned the anticipation of Euler. Astronomie, Disc. Prélim.' ADDITIONAL APPENDIX TO THE LIVES OF SIR JOSEPH BANKS AND ADAM SMITH. "DEAR SIR, CAPT. COOK TO MR. BANKS. "WILLS'S COFFEE-HOUSE, CHARING CROSS, "Sunday Morning, [1768.] Promo "Your very obliging letter was the first messenger that conveyed to me Lord Sandwich's intentions. tion, unsolicited, to a man in my situation in life, must convey a satisfaction to the mind that is better conceived than described. I had this morning the honour to wait upon his Lordship, who renewed his promises to me, and in so obliging and polite a manner as convinced me he approved of the voyage. The reputation I may have acquired on this account, by which I shall receive promotion, calls to my mind the very great assistance I received therein from you, which will ever be remembered with most grateful acknowledgments by, SIR, "Dear Sir, "Your most obliged humble servant, "JAMES COOK." CAPT. COOK TO MR. BANKS. "SHEERNESS, 2nd June, 1772. "I received your letter by one of your people, acquainting me me that you had ordered everything belonging to you to be removed out of the ship, and desiring my assistance therein. "I hope, Sir, you will find this done to your satisfaction, and with that care the present hurry and confused state of the ship required. Some few articles which were for the. |