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The design of this work is to furnish the schools of the lonited States with a methodical and comprehensive system of Practical Arithmetic, in which I have endeavoured, through the whole, to have the rules as concise and familiar as the nature of the subject will permit. During the long period which I have devoted to the instruction of youth in Arithmetic, I have made use of various systems which have just claims to scientific merit; but the authors appear to have been deficient in an important point—the practical teacher's experience. They have been too spuring of examples, especially in the first rudiments; in consequence of which, the young pupil is hurried through the ground rules too fast for his capacity. This objection I have endeavoured to obviate in the following treatise. In teaching the first rules, I have found it best to entourage the attention of scholars by a variety of easy and familiar questions, which might serve to strengthen their minds as their studies grew more arduous. The rules are arranged in such order as to introduce the most simple and necessary parts, previous to those which are more abstruse and difficult. To enter into a detail of the whole work would be teduous; I shall therefore notice only a few particulars, and refer the reader to the contents. Although the Federal Coin is purely decimal, it is so nearly allied to whole numbers, and so absolutely necessary to be understood by every one, that I have introduced it immediately after addition of whole numbers, and also shown how to find the value of goods therein, immediately after simple multiplication; which may be of great advantage to many, who perhaps will not have an opportunity of learning fractions. In the arrangement of fractions, I have taken or to: new method, the advantages and facility of wor" of **iciently apologize f its not heing w riot a ro a 2

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annition, simple, - - - - - - - - 17 - of Federal Money, - - - - - - -1 - Compound, - - - - - - - 33 Alligation, - - - - - - - - - 177 Annuities or Pensions, at Compound Interest, - - - 19Arithmetical Progression, - - - - - - 182 Barter, - - - - - - - - - - 126 Brokerage, - - - - - - - - 113 Characters. Explanation of - - - - - - 14 Commission, - - - - - - - - 112 Conjoined Proportion. - - - - - - - 137 Coins of the United States, weights of - - - - 220 Division of whole Numbers, - - - - - - o-Contractions in. - - - - - - o Compound, - - - - - - - 53 Discount, - - - - - - - - 123 Duodecimals, - - - - - - - - 216 Ensurance, --- - - - - - - - 114 Equation of Payments, - - - - - - - 125 Evolution or Extraction of Root-, - - - - - 167 Exchange, - - - - - - - - - 139 Federal Money, - --- - - - - - 21 - subtraction of - - - - - 25 Fellowship, - - - - - - - - - 1-2 Compound, - - - - - - - 134 Fractions, Vulgar and Decimal, - - - - -59-143 Interest. Simple, - - - - - - - 104. - by Decimal-, - - - - - - 157 - Compound, - - - - - - - 122 - by Decimals, - - - - - - 155 Inverse Proportion, - - - - - - - 155 involution, - - - - - - - - - 166 Loss and Gain, - - - - - - - - 128 Multiplication, Simple, - - - - * - - -7 - Application and Use of - - . - -0 Supplement to, - - - - - 37 Compound, - - - - - - 48 Numeration, * * - - - - - - - 15 Practice, - . - - - - - - - og Position, - . - - - - - -- o Permutation of Quantities - - - - . 19

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Double, - - - - - -

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