him in his fourth section, where he treats of the centre of oscillation and percussion; he having made several mistakes there, as M. de Mairan has shown, p. 196, Mém. de l'Acad. Royale des Sciences, edit. Paris, 1735. After Carré, you may read Bougain

ville.

I have recommended French authors to you, because you are a thorough master of that language, and because, by their studying style and clearness of expression, they seem to me best adapted to beginners. Our authors are often profound and acute, but their laconisms, and neglect of expression, often perplex beginners. I except Mr. Maclaurin, who is very clear; but then he has such a vast variety of matter, that a great part of his book is, on that account, too difficult for a beginner. I might recommend other authors to you, as a course of elements; for instance, you might read Mr. Thomas Simpson's Geometry, Algebra, Trigonometry, and Fluxions; all which contain a great variety of good things. In his Geometry he departs from Euclid without a sufficient reason. However, you may read him after Dr. Robert Simson's Euclid, or together with it, and take notice of what is new in Thomas Simpson. His Algebra you may join with Clairaut; and the rather that Clairaut has been sparing of particular problems, and has, besides, omitted several useful applications of algebra. Simpson's Fluxions may go hand in hand with L'Hôpital, Maclaurin, Carré, and Bougainville. If you come to have a competent knowledge of these authors, you will be far advanced, and you may proceed to the works of Newton, Cotes, the Bernoullis, De Moivre, &c., as your inclination and time will permit. Sir Isaac Newton's treatise of the Quadrature of Curves has been well commented by Mr. Stewart, and is of itself a good institution of fluxions. Sir Isaac's Algebra is commented in several places by Clairaut, and in more in Maclaurin's Algebra; and Newton's famous Principia are explained by the Minims Jacquier et Le Seur, Geneva, 4 vols. 4to. Cotes is explained by Don Walmesley, in his Analyse des Mesures, &c. Paris, 4to. You see you may find work enough. But my paper bids me subscribe myself, dear sir, your most obedient servant, GEO. LEWIS SCOTT.

Leicester-square, May 7th, 1762.

P. S.—But I recollect, a little late, that the books I have mentioned, excepting Newton's Principia, and the occasional problems in the rest, treat only of the abstract parts of the mathematics; and you are, no doubt, willing to look into the concrete parts, or what is called mixed mathematics, and the physico-mathematical sciences. Of these the principal are, mechanics, optics, and astronomy. As to the principles of mechanics, M. d'Alembert has recommended M. Trabaud's "Principes du Mouvement et de l'Equilibre," to beginners; and you cannot do better than to study this book. In optics we have Dr. Smith's Complete System, 2 vols. 4to. I wish, though, we had a good institution, short and clear; the Doctor's book entering into too great details for beginners. How

ever, you may consider his first book, or popular treatise, as an institution, and you will from thence acquire a good deal of knowledge. In Astronomy I recommend M. le Monnier's Institutions Astronomiques, in 4to. Paris, 1746. It is a translation from Keil's Astronomical Lectures, but with considerable additions. You should also have Cassini's Elemens d'Astronomie, 2 vols. 4to. As to the physical causes of the celestial motions, after having read Maclaurin's account of Sir Isaac Newton's philosophical discoveries, and Dr. Pemberton's View of Sir Isaac's Philosophy, you may read the great author himself, with the comment. But if But if you read Maclaurin's Fluxions throughout, you will find many points of Sir Isaac's philosophy well explained there. The theory of light and colours should be studied in Sir Isaac himself. In the English edition of his Optics, 8vo. there is a branch of the optical sciences which I have not mentioned, that is, perspective. Dr. Brook Taylor's is the best system, but his style and expression is embarrassed and obscure. L'Abbé de la Caille has also given a good treatise of perspective, at the end of his Optique: these are of use to painters; but the theory of mathematical projection in general is more extensive, and has been well treated of by old writers, Clavius, Aguillonius, Tacquet, and De Chules: and lately M. de la Caille has given a memoir among those of the Acad. Roy. des Sciences of Paris, anno 1741, 66 sur le Calcul des Projections en general." This subject is necessary for the understanding of the theory of maps and planispheres. Mathematicians have also applied their art to the theory of sounds and music. Dr. Smith's Harmonics is the principal book of the kind.

Thus have I given you some account of the principal elementary authors in the different branches of mathematical knowledge, and it were much to be wished that we had a complete institution, or course, of all these things of a moderate size, which might serve as an introduction to all the good original authors. Wolfius attempted this; his intention was laudable, but his book is so full of errors of the press, besides some of his own, that I cannot recommend him to a beginner. He might be used occasionally for the signification of terms, and for many historical facts relating to mathematics; and, besides, may be considered as a collector of problems, which is useful.

Besides the books I have mentioned, it might be of use to you to have M. Montucla's Histoire des Mathematiques, in 4to. 2 vols. You will there find a history of the progress of the mathematical sciences, and some account of the principal authors relating to this subject.

I mentioned to you in conversation, the superior elegance of the ancient method of demonstration. If you incline to examine this point, after being well versed in Euclid, you may proceed to Dr. Simson's Conic Sections; and to form an idea of the ancient analysis of method of investigating the solution of geometrical problems, read Euclid's Data, which Dr. Simson will publish, together with his new edition of Euclid; and then read his Loci Plani, in 4to. The elegance of the method of the ancients is confessed; but it

seems to require the remembrance of a great multitude of propositions, and in complicated problems it does not seem probable that it can be extended so far as the algebraic method.

XV. EDWARD GIBBON, ESQ. TO MRS. GIBBON, BERITON.

Paris, February 12th, 1763. Dear Madam,-You remember our agreement,-short and fre quent letters. The first part of the treaty you have no doubt of my observing. I think I ought not to leave you any of the second. A propos of treaty: our definitive one was signed here yesterday, and this morning the Duke of Bridgewater and Mr. Neville went for London with the news of it. The plenipotentiaries sat up till ten o'clock in the morning at the ambassador of Spain's ball, and then went to sign this treaty, which regulates the fate of Europe.

Paris, in most respects, has fully answered my expectations. I have a number of very good acquaintance, which increase every day; for nothing is so easy as the making them here. Instead of complaining of the want of them, I begin already to think of making a choice. Next Sunday, for instance, I have only three invitations to dinner. Either in the houses you are already acquainted, you meet with people who ask you to come and see them, or some of your friends offer themselves to introduce you. When I speak of these connexions, I mean chiefly for dinner and the evening. Suppers, as yet, I am pretty much a stranger to, and I fancy shall continue so; for Paris is divided into two species, who have but little communication with each other. The one, who is chiefly connected with the men of letters, dine very much at home, are glad to see their friends, and pass the evenings till about nine, in agreeable and rational conversation. The others are the most fashionable, sup in numerous parties, and always play, or rather game, both before and after supper. You may easily guess which sort suits me best. Indeed, madam, we may say what we please of the frivolity of the French, but I do assure you, that in a fortnight passed at Paris, I have heard more conversation worth remembering, and seen more men of letters among the people of fashion, than I had done in two or three winters in London.

Amongst my acquaintance I cannot help mentioning M. Helvetius, the author of the famous book De l'Esprit. I met him at dinner at Madame Geoffrin's, where he took great notice of me, made me a visit next day, has ever since treated me, not in a polite but a friendly manner. Besides being a sensible man, an agreeable companion, and the worthiest creature in the world, he has a very pretty wife, an hundred thousand livres a year, and one of the best tables in Paris. The only thing I dislike in him is his great attachment to, and admiration for, ****, whose character is indeed at Paris beyond any thing you can conceive. To the great civility of this foreigner, who was not obliged to take the least notice of me, I must just contrast the behaviour of ******.

XVI. MR. GIBBON TO HIS FATHER.

Paris, February 24th, 1763.

Dear Sir, I received your letter about twelve days after its date, owing, as I apprehend, to Mr. Foley's negligence. My direction is A Monsieur Monsieur Gibbon, Gentilhomme Anglais, à l'Hôtel de Londres, rue de Columbier, Fauxbourg St. Germains, à Paris. You see I am still in that part of the town; and indeed, from all the intelligence I could collect, I saw no reason to change, either on account of cheapness or pleasantness, Madame Bontems, Mrs. Mallet's friend, and a Marquis de Mirabeau, (I got acquainted with at her house,) have acted a very friendly part; though all their endeavours have only served to convince me that Paris is unavoidably a very dear place. I am sorry to find my English clothes look very foreign. The French are now excessively long-waisted. At present we are in mourning for the Bishop of Liege, the king's uncle; and expect soon another of a singular nature, for the old Pretender, who is very ill. They mourn for him, not as a crowned head, but as a relation of the king's. I am doubtful how the English here will behave; indeed we can have no difficulties, since we need only follow the example of the Duke of Bedford.

I have now passed nearly a month in this place, and I can say with truth, that it has answered my most sanguine expectations. The buildings of every kind, the libraries, the public diversions, take up a great part of my time; and I have already found several houses, where it is both very easy and very agreeable to be acquainted. Lady Hervey's recommendation to Madame Geoffrin was a most excellent one. Her house is a very good one; regular dinners there every Wednesday, and the best company of Paris, in men of letters and people of fashion. It was at her house I connected myself with M. Helvetius, who, from his heart, his head, and his fortune, is a most valuable man. ·

At his house I was introduced to the Baron d'Olbach, who is a man of parts and fortune, and has two dinners every week. The other houses I am known in, are the Duchess d'Aiguillon's, Madame la Comtesse de Froulay's, Madame du Bocage, Madame Boyer, M. le Marquis de Mirabeau, and M. de Foncemagne. All these people have their different merit; in some I meet with good dinners; in others, societies for the evening; and in all good sense, entertainment, and civility; which, as I have no favours to ask, or business to transact with them, is sufficient for me. Their men of letters are as affable and communicative as I expected. My letters to them did me no harm, but were very little necessary. My book had been of great service to me, and the compliments I have received upon it would make me insufferably vain, if I laid any stress on them. When I take notice of the civilities I have received, I must take notice too of what I have seen of a contrary behaviour. You know how much I always built upon the Count de Caylus: he has not been of the least use to me. With great difficulty I have seen him, and that is

all. I do not, however, attribute his behaviour to pride, or dislike to me, but solely to the man's general character, which seems to be a very odd one. De la Motte, Mrs. Mallet's friend, has behaved very drily to me, though I have dined with him twice. But I can forgive him a great deal, in consideration of his having introduced me to M. d'Augny (Mrs. Mallet's son.) Her men are generally angels or devils; but here I really think, without being very prone to admiration, that she has said very little too much of him. As far as I can judge, he has certainly an uncommon degree of understanding and knowledge, and, I believe, a great fund of honour and probity. We are very much together, and I think our intimacy seems to be growing into a friendship. Next Sunday we go to Versailles; the king's guard is done by a detachment from Paris, which is relieved every four days; and as he goes upon this command, it is a very good occasion for me to see the palace. I shall not neglect, at the same time, the opportunity of informing myself of the French discipline.

The great news at present is the arrival of a very extraordinary person from the Isle of France in the East Indies. An obscure Frenchman, who was lately come into the island, being very ill, and given over, said, that before he died he must discharge his conscience of a great burden he had upon it, and declared to several people, he was the accomplice of Damien, and the very person who held the horses. Unluckily for him, the man recovered after this declaration, was immediately sent prisoner to Paris, and is just landed at Port L'Orient, from whence he is daily expected here, to unravel the whole mystery of that dark affair. This story (which at first was laughed at) has now gained entire credit, and I apprehend must be founded on real fact.

A lady of Miss Caryll's acquaintance has desired me to convey the enclosed letter to her. You will be so good as to send it over to Lady Holt. I hope I need say nothing of my sentiments towards our friends at Beriton, nor of my readiness to execute any of their commands here. I am, dear sir, most affectionately yours,

E. GIBBON.

XVII. MR. GIBBON. TO MR. HOLROYD AT LAUSANNE.

Borromean Islands, May 16th, 1764.

Dear Holroyd,-Hurry of running about, time taken up with seeing places, &c., are excellent excuses; but I fancy you will guess that my laziness and aversion to writing to my best friend are the real motives, and I am afraid you will have guessed right.

We are at this minute in a most magnificent palace, in the middle of a vast lake; ranging about suites of rooms without a soul to interrupt us, and secluded from the rest of the universe. We shall sit down in a moment to supper attended by all the Count's household. This is the fine side of the medal: turn to the reverse. We are got here wet to the skin; we have crawled about fine gardens