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,

Leicester Square, May 7, 1762.

GEO. LEWIS SCOTT.

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. However, 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 Elémens d'Astronómie, 2 vols. 4to. As to the physical

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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 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 are 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, sur le calcul des projections en général. 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 Mathématiques, 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 or 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.

N° XV.

EDWARD GIBBON, Esquire, to Mrs. GIBBON, Beriton.

DEAR MADAM,

Paris, February the 12th, 1763. You remember our agreement,—short and frequent 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 connections, 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 communica

tion 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 * * * * * *