juft notions concerning the inferior orders of fociety. And I am the more emboldened to expect the public approbation on this occafion, from the confideration, that in my endeavours to promote those prime views, no new burthen has been impofed, or any very confiderable encroachment made on the time of the pupil, the information in queftion being incorporated with a branch of education in which ALL must be converfant. The title announces this small treatise to be defigned for the ufe of YOUNG LADIES, because the author's department of teaching is folely confined to them. Perhaps, however, it may be thought equally adapted to the other fex, when it is confidered that a youth, capable of working through the whole book, and of delivering a fatisfactory account of each operation, would be qualified for almoft any of the common concerns of business. Vulgar and decimal fractions, and the extraction of roots are of little utility, except in a few particular employments; and as to intereft, profit and lofs, barter, fellowship, exchange, and fome other rules which have diftinct heads in the ordinary treatises of arithmetic, they all belong to the rule of three, and the questions in each may be worked with the greateft facility, by any one well verfed in that and practice. The generality of the questions being too long for the learner's tranfcription, they have all been numbered. Accordingly, the number, with a word or two of the fum (for inftance, No. 1, Chronology, No. 2, Solar Syftem) will be a fufficient reference to the operation at large, at any future period. The pupil, however, if fufficiently qualified in writing, fhould by no means omit copying the whole process of each fum in a common fumbook. To prevent the poffibility of plagiarism, and to perfect the students completely in this important branch of education, they should, on presenting a fum, be conftantly made to affign a reafon for every part of the operation, and, moreover, occafionally be exercised with a variety of manufcript fums in each rule. Oxford-Court, Cannon-Street, WILLIAM BUTLER. ADVER ADVERTISEMENT. Published by the fame Author, for the Use of YOUNG LADIES. A N engraved INTRODUCTION to ARITHMETIC, confifting of examples in the four principal rules, and a collection of tables: defigned to facilitate the progrefs of young beginners, and to diminish the labour of the tutor. Ready for the Prefs, and speedily to be Published. An Eafy INTRODUCTION to the USE of the GLOBES, in which will be incorporated fome Miscellaneous Matter which the Author has found to be entertaining and ufeful to his own pupils. The above little manual will be immediately fucceeded by a fmall tract of Scripture Geography, with maps: to which will be annexed, a brief sketch of the different principles maintained by the chief Chriftian fects, and other introductory information. On the completion of this laft-mentioned work, which is already nearly prepared for the prefs, the Author means to resume the printing of his larger geographical and biographical performance (advertised in his Introduction to Arithmetic) which will be accompanied with a general ATLAS. ADDRESS TO THE PUBLIC. R. BUTLER, Teacher of WRITING, ACCOUNTS, and GEOGRAPHY, refpectfully informs his friends and the public, that, having frequently found himself prevented, by prior engagements, from attending LADIES SCHOOLS and PRIVATE FAMILIES, which had honoured him with applications for that purpose, he has engaged as partner, Mr. THOMAS BOURN, Jun. of Mare-Street, HACKNEY. This connection will not only better enable Mr. B. to avail himself of the kind partiality of his friends, but, by introducing to their acquaintance, will recommend to their protection, a much-esteemed pupil of exemplary moral conduct, and great profeffional ability, with the happy talent of communicating inftruction, united to indefatigable affiduity and zeal in the difcharge of his engage ments. ARITHMETICAL QUESTIONS. Is ARITHMETIC 'S a fcience, which explains the properties of numbers, and shows the method or art of computing by them. It has five principal rules, namely, NUMERATION, ADDITION, SUBTRACTION, MULTIPLICATION, and DIVISION; and these are the foundation of all arithmetical operations. We have very little information respecting the origin and invention of arithmetic; history neither fixes the author of it, nor the time of its difcovery. Some imagine, that it must have taken its rise from the introduction of commerce, and ascribe its invention to the Tyrians. That, however, it had a much earlier introduction into the world, even before the deluge, we may gather from the following expreffion in the prophecy of Enoch, as mentioned by Jude: "Behold the Lord cometh with ten thousand of his faints." This fhows that, even at that time, men had ideas of very high numbers, and computed them alfo in the fame manner that we do, namely, by tens. The directions alfo given to Noah, concerning the dimenfions of the ark, leave us no room to doubt that he had a knowledge of numbers, and likewife of measures. When Rebecca was fent away to Ifaac, Abraham's fon, her relations wifhed that the might be the mother of thoufands of millions; and if they had been totally unacquainted with the rule of multiplication, it is impoffible to conceive that they could have formed fuch a wifh. It appears, therefore, certain, that the four fundamental rules of arithmetic were known, in some nations, in very early ages of the world; though at what time they were difcovered or invented cannot now be exactly ascertained. The Greeks were the first European nation among whom arithmetic arrived at any great degree of perfection, and they made ufe of the letters of the alphabet to reprefent their numbers. The Romans followed a like method, and, befides characters for each rank of claffes, they introduced others for five, fifty, and five hundred. Their method is ftill used for diftinguishing the chapters of books and fome other purposes. From the Romans arithmetic came to us; but the B common common arithmetic among us, which makes ufe of the ten Arabic figures 1, 2, 3, 4, 5, 6, 7, 8, 9, o, was utterly unknown to the Greeks and Romans, and came into Europe from the Arabians by way of Spain. The Arabians are faid to have received them from the Indians. This moft perfect method of fupputation is fuppofed to have taken its origin from the ten fingers of the hand, which were made ufe of in computations before arithmetic was brought into an art. The Eastern miffionaries affure us, that to this day the Indians are very expert at computing on their fingers without any use of pen or ink. And the natives of Peru in South America, who do all by the different arrangement of grains of maife, are faid to excel any European both for certainty and dispatch with all his rules. NUMERATION EACHES to read or write any propofed fum, and to find the different value of any given number of figures. No. 1. CHRONOLOGY. Chronology is the art of measuring and diftinguishing time paft, and referring each event to the proper year. Its ufe is very great, being called one of the eyes of hiftory. Epocha, in chronology, is a term or fixed point of time, whence fucceeding years are numbered or computed. That principally regarded among Chriftians is the epocha of the nativity of our Saviour; that of the Mahometans the hegira; that of the Jews the creation of the world; that of the ancient Greeks the Olympiads; that of the Romans the building of their city, and that of the ancient Perfians and Affyrians, the epocha of Nabonaffar king of Babylon, its inftitutor, 746 years B. C. The building of Rome took place 753 years B. C. The Olympics or Olympic games, fo famous among the Greeks, were inftituted in honour of Jupiter. They were holden at the beginning of every fifth year, on the banks of the Alpheus, near Olympia, to exercife their youth in five kinds of combats. Those who were conquerors in thefe games were highly honoured by their countrymen. The prize contended for was a crown made of a peculiar kind of wild olive, appropriated to this ufe. The Olympiads ended with the year of Chrift 440, making in all 364. The hegira, or flight of the impoftor Mahomet, the founder of the Mahometan religion, from Mecca to Medina, happened A. D. 622. The computation of years from the birth of Chrift did not begin to be used in hiftory till the year 748. The current year of the Chriftian æra is 1795. N.B. A. M. denote Anno Mundi, the year of the world; U. C. Urbe conditâ (ab, from, being understood) the building of the city, i. e. of Rome; B. C. Before Chrift; A. C. Ante Chriftum, before Chrift; A. D. Anno Domini, in the year of our Lord. No. 2. SOLAR SYSTEM. By the folar fyftem is meant the order and difpofition of the feveral heavenly bodies, which revolve round the SUN, as the centre of their motion, and receive from it their light and heat. These celeftial spheres confist of planets and comets. Under the denomination of planets are comprifed Mercury, Venus, the Earth, Mars, Jupiter, Saturn, and the Georgium Sidus. Mercury is faid to be about 37,000,000 of miles from the fun; Venus 68,000,000; the Earth 95,000,000; Mars 145,000,000; Jupiter 495,000,000; Saturn 908,000,000; and the Georgium Sidus about 1,800,000,000 of miles diftant from the fun. The hourly motion of Mercury in its orbit is about 109,000 miles; Venus 80,000; the Earth 68,000; Mars 55,000; Jupiter 29,000; Saturn 22,000. Saturn is fupposed to be more than 90 times as big as the globe which we inhabit. According to the fame calculation, Jupiter is above 200 times larger than the earth. It has been remarked, that the planets, and all the innumerable host of heavenly bodies, perform their courfes and revolutions with so much certainty and exactness, as never once to fail; but, for almost 6000 years, come conftantly about to the fame period, without the difference of the hundredth part of a minute. It is also observed by Mr. Hervey, that" it may feem unaccountable, to an unlearned reader, that aftronomers fhould fpeak fuch amazing things, and speak them with fuch an air of affurance, concerning the diftances and magnitudes, the motions and relations of the heavenly bodies. I would defire, continues the fame ingenious writer, fuch a perfon to confider the cafe of ECLIPSES, and with what exactnefs they are calculated. They are not only foretold, but the very inftant of their beginning is determined. The precife time of their continuance is affigned; affigned almoft to the nicety of a moment, and what is ftill more furprifing, for the space of hundreds or thousands of years to come. As this is a matter of fact abfolutely indifputable, it is alfo a very obvious yet folid demonftration, that the principles of fcience, on which thofe calculations proceed, are not merely conjecture, or precarious fuppofition, but have a real, a certain foundation in the nature and constitution of things." us. No. 3. COMETS. Comets are defined to be folid compact bodies, like other planets, and regulated by the fame laws of gravity. They move about the fun in very eccentric orbits, and are of a much greater denfity than our earth; for fome of them are heated, in every period, to fuch a degree as would vitrify or diffipate any fubftance known to Comets are always attended with long transparent trains, or tails, iffuing from that fide of them which is turned away from the fun : that which appeared in 1680 drew after it a tail of fire that was computed to be 80,000,000 of miles in length. There are fuppofed to be 450 comets belonging to the folar fyftem; but the periods of three of them only are known with any certainty. Thefe return at intervals of 75, 129, and 575 years. Dr. Halley, at firft, fuppofed the comets of 1532 and 1661, to be one and the fame; and though he afterwards feemed to retract this opinion, it has been generally adopted by |