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. Q=Fz + 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 + Rd a integrable. Call this factor S, and make S d x + SR dad 'T, and make SFd @= log. B. He finds for the values required PBS': T, Q consequently z = Bf: T. 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. IV. '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 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 in the Faubourg St. Martin, at some distance from the Hotel de Ville. The church of St. Jean le Rond, at the gate of which he was exposed, and from which he took his name, was near the church of Notre Dame, to which it belonged; and it has long since been pulled down. 25* "Your very obliging letter was the first messenger that conveyed to me Lord Sandwich's intentions. Promotion, 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, "Dear Sir, "Your most obliged humble servant, "JAMES COOK." "DEAR SIR, CAPT. COOK TO MR. BANKS. Resolution,' Cape of Good Hope, “Some cross circumstances which happened at the latter part of the equipment of the Resolution' created, I have reason to think, a coolness betwixt you and I; but I can by no means think it was sufficient to me to break off all correspondence with a man I am under many obligations to. "I wish I had something interesting to communicate, but our passage here has rather been barren on that head.__We touched at St. Jago, where we remained two days, and Mr. Forster got some things there new in your way. Mr. Brand has got for you a fine collection, as I am told, I depart from hence in a day or two well stored with every necessary thing, but I am told the French from the Mauritius have got the start of me. About eight months ago, two ships from that island discovered land in the latitude of 48 degrees, and about the meridian of the Mauritius, along which they sailed forty miles till they came to a bay, into which they were about to enter, when they were separated and drove off the coast by a gale of wind. The one got to the Mauritius soon after, and the other is since arrived from Batavia with a cargo of arrack, as the report goes here; also, in March last, two frigates from the same island touched here in their way to the South Sea, having on board the man Bougainville brought from Otaheite, and who died before the ships departed hence, a circumstance I am really sorry for. These ships were to touch some where on the coast of America, and afterwards to proceed round Cape Horn. "I am in your debt for the pickled and dried salmon which you left on board, which a little time ago was most excellent; but the eight casks of pickled salted fish I kept for myself proved so bad that even the hogs would not eat it. These hints may be of use to you in providing for your intended expedition, in which I wish you all the success you can wish yourself'; and am, with great esteem and respect, "Dear Sir, "As you was so obliging as to say you would give a description of the New Zealand spruce tree, or any other plant, the drawing of which might accompany my Journal, I desired Mr. Strahan and Mr. Stuart, who have the charge of the publication, to give you extracts out of the manuscript of such descriptions as I had given (if any), for you to correct or describe yourself, as may be most agreeable. I know not what plates Mr. Forster may have got engraved of natural history that will come into my books; nor do I know of any that will be of use to it, but the spruce tree and tea plant and scurvy grass; and I know not if this last is engraved. The flax plant is engraved; but whether the publishing of this in my Journal will be of any use to seamen I shall not determine. In short, whatever plates of this kind falls to my share, I shall hope for your kind assistanae in giving some short account of them. On my arrival here I gave Omai three guineas, which sent him on shore in high spirits; indeed he could hardly be otherwise, for he is very much caressed here by every person of note; and, upon the whole, I think he rejoices at the prospect of going home. "I now only wait for a wind to put to sea; unless Capt. Clarke makes good haste down, he will have to follow me. Sir John Pringle writes me that the Council of the Royal Society have de creed me the Prize Medal of this year. I am obliged to you and my other good friends for this unmerited honour. "Omai joins his best respects to you and Dr. Solander with, "Dear Sir, "Your most obedient and very humble servant, "JAMES COOK." NOTE TO THE LIVES OF CAVENDISH, WATT, AND BLACK. I HAD not read M. Cuvier's "Eloge de M. Cavendish" when the former volume of these Lives was published. That Eloge is contained in the Mémoires of the Institute for 1811.* Its composition certainly justifies the title of Eloge; for it is a very indiscriminate, and not very accurate panegyric of an illustrious man whose memory was best preserved and honoured by a correct statement of the facts. M. Cuvier makes no mention whatever of Watt in connexion with the discovery of the composition of water. But he is not much more just to Black himself on that of fixed air; or, as he calls him, Blake, clearly showing that he had never taken the trouble even to look at any work of that great man. As to Mr. Cavendish, he gave it for part of his Eulogy that he explained his doctrines" dans une manière plus etonnante encore que leur decouverte même," (p. cxxvi.) Now if M. Cuvier had read the paper upon the combustion of inflammable air, he certainly would have found that this remark in no respect whatever applies to it, for the composition of water is but darkly shadowed out in that celebrated Memoir. He proceeds to say, that in 1766 Mr. Cavendish undertook, in his paper read before the Royal Society, to establish propositions, "presqu'inouies jusque la; l'eau n'est pas un element; il existe plusieurs sortes d'airs, essentiellement differentes." He then mentions Von Helmont inaccurately, as having ascertained that there were "permanently elastic vapours other than atmospheric air;" and Hales still more inaccurately as having measured these permanently elastic fluids, whereas Hales considered them all as common air, combined with impure exhalations, an opinion which prevailed a century and half after Von Helmont, and was adopted by D'Alembert in his article "Air" in the Encyclopædia, 1751. Black's discovery of fixed air, he confines solely to its explaining the causticity of the alkalies and earths. No one, he says, before Cavendish had distinguished it as a separate aeriform substance; *Nothing can be more confused, more inconsistent, than the manner of publishing the volumes of this great work. It is generally a year or two, and even three or four, after the real date of the papers; thus this twelfth volume of the new series is called "Mem. année 1811," yet it contains only two papers of 1810-11; all the rest were received in 1812-13. I have remarked this more fully in the Lives of Lavoisier and D'Alembert. and though emanations vere qui a ceed fun des te a knew m what her consistet. Cavendish, he says in 17760 irst settled all these questions, and showed that tus ar wieder a chalk or fermentacion, or mines was one and the sune fini "auquel on a demus reserve le nom d'ar ise. Finally he das covered that it was de ar evoited from burning cina vval (2 cxxx) He can describes the application of infammaze ar de raising baloons in the air to M. Charies's application of Mr. Cavendish's experiments on the sectic gravity of that gis This is really somewhat astounding. That a person of Mr. Cuvier's eminent attainments, filling the high office of Secretaire Perpetual, and charged with the delicate and important duty of recording the history of science yearly, should not have deemed it worth his while to read either the celebrated experiments on Magnesia Alba and Quicklime published in 1755, or the Lectures published in 1963. before assuming to write the history of chemical discovery, is wholly beyond beliet Had he read the former work he would have found that Dr. Black gave to the air which he had discovered the name of fixed air, and that he did so, not because it was the same with, or any modification of, atmospheric air, but simply because air was a known term in common use to represent a permanently elastic fluid, and because this kind of air was found fixed in combination with bodies. Had he looked at the Lectures, he would have found that two years after the publication of his capital discovery, viz., in 1757, and one year before Mr. Cavendish's paper was received, Dr. Black discovered that fixed air is the gas evolved in fermentation, and that he found it to be so by the very experiment now in use to show it, namely, emptying half of a phial filled with lime water in the air of a brewer's vat, when the remaining lime water becomes turbid, the carbonate of lime being formed and precipitated; that he discovered on the same day the identity of fixed air with that evolved from burning charcoal; and finally, that he also ascertained the air evolved from the lungs in respiration to be fixed air, by breathing through a syphon half filled with lime water. All this, which M. Cuvier ascribes to Mr. Cavendish's discoveries, in 1766, had been published by Dr. Black in 1755, and explained by the experiments themselves being performed by his own hands, in his public lectures, every year before nearly three hundred persons, from the year 1757 to the time of Mr. Cavendish's supposed discovery in 1766. Of these Lectures numberless copies were taken, were in general circulation, and were sold to the students attending the classes of the College in Edinburgh. It is, however, very possible that Mr. Cavendish was not apprized of Dr. Black's experiment made before 1752 and published in 1755. But it is quite certain that he never arrogated to himself the discovery of fixed air being a peculiar body different from common air, for he expressly says, "By fixed air I mean that peculiar species of factitious air which is separated from alcaline substances by solution in acids, or by calcination, and to which Dr. Black has given that name in his Treatise on Quicklime." ("Phil. Trans." lvi. p. 140.) Now this |