books in arithmetic, will be found to accord with the practice of men of business at the present time; so that the learner, when he goes from the school-room into the world, and from dealing with textbooks comes to deal with men, may not be obliged to unlearn what he has learned at school, before he can put in practice the methods adopted by business men, in solving questions that occur in their intercourse with each other. The different methods of equating accounts current and interest accounts, though discussed in very few arithmetics for common schools, are of so much practical importance to most young men of good education, that the author has introduced them into this work. These topics, when properly presented, are not so difficult to be understood as much of the less practical matter which is found in most text-books in arithmetic. If the exercises on these topics contained in this book are fully mastered, the pupil may anticipate little difficulty in understanding and adjusting such accounts when he shall meet them in actual business. The sections which treat of Mensuration, the Mechanic Powers, and Book-keeping, will be valuable to those who have not time or opportunity to study more extended treatises on these subjects. The numerous articles on Analysis interspersed through the work will, it is believed, be peculiarly acceptable to the teacher. The author would call the attention of teachers and others to Art. 101, 122, 124, 131, 138, 146, and Sections XVIII. and XIX. 3. The authors of most arithmetics seem to have labored to divorce Integral and Fractional Decimals from each other, having almost uniformly presented Decimal Fractions to the pupil as something to be studied, if ever, after all the elementary rules, Compound Numbers, Vulgar Fractions, &c., have been learned; as though their relation to integers was so slight, and the subject so difficult, or so unimportant, that it should be wholly omitted until these other things are learned.* The consequence has been, that a large majority of those who have completed their common school education have either not studied decimals at all, or have done it with the feeling that a knowledge of them was of little practical utility; and, therefore, the knowledge they have acquired of the subject has been altogether vague and indefinite. This ignorance is the more to be lamented in our own country, from the fact that our currency is a decimal currency, and that operations in it can be safely trusted to those only who are familiar with the principles of Decimal Notation, fractional as well as integral. Numerous specific rules, indeed, are given to the learner for performing operations in dollars, cents, and mills; but these rules, being arbitrary, and based upon no general principle already explained and understood, are very uncertain in their application, for the reason, if for no other, that arbitrary rules are easily forgotten. It is presumed that the experience of every reader, whether a teacher or not, will fully attest to the truth of these remarks. *The works on arithmetic by Pliny E. Chase are the only exceptions to this remark that the author has seen. The author of this book has endeavored so to present the whole subject of decimal notation, that the pupil will become as familiar with fractional as with integral decimals, and as little liable to embarrassment or error in one case as in the other; thus rendering the whole class of specific and arbitrary rules, relating to operations in dollars, cents and mills, entirely useless. Whether the effort has been a successful one, remains for those who may use his book to decide. He has no doubt of its practicability, or of its necessity, in order to make the youth of our country expert and correct accountants in our Federal currency. This mode of presenting decimals to the learner may require some more patient labor at first, but this will be amply repaid by his subsequent progress. 4. So far as the author's experience and observation extend, mental exercises in arithmetic are very generally neglected after the pupil has commenced" ciphering" on the slate. This is doubtless owing partly to the fact that very few arithmetics have been prepared in which mental and written exercises are combined to any great extent in the same book. The author has endeavored to supply this want, by introducing a great variety of mental exercises, by which means the pupil is not only allowed to retain his familiarity with what he has learned from Colburn, but is allowed to make still greater proficiency in mental calculations. There are in our common schools different classes of learners, whose wants the author has had in view, in the preparation of this work. The first, and probably the largest of these classes, consists of those who never progress to the more advanced rules, and whose knowledge of arithmetic must be chiefly limited to the elementary rules. In this work, a great variety of practical examples are introduced under these elementary rules, so that it is believed that the scholar who can perform intelligently and with facility the questions on the first 83 pages, can solve correctly ninety-nine in a hundred of the practical questions which occur in common business tran actions. Another class consists of those who are preparing for the counting-room and for commercial business. It is believed that this work contains more that will be practically useful to this class than most other arithmetics that have been published. Others, not expecting to be merchants, are to be farmers, mechanics, &c. To these the sections on Mensuration, the Mechanic Powers, and the elements of Book-keeping by Single Entry, will be particularly useful. It may be remarked, in conclusion, that the introduction of mathematical puzzles has been carefully avoided in this work; and that the gradations from the easier to the more difficult topics are such that the careful pupil will generally be able to pass from one to the other without the assistance of his teacher. The work is submitted to the public with the hope that it may be found adapted to the wants of both teachers and learners; tending to render the duties of the one less arduous, and to make the studies of the other both profitable and pleasant. RUFUS PUTNAM. Salem, May, 1849. -- Numeration Table of Whole Numbers,. 11 Exercises in Reading Whole Numbers,. 11 Exercises in Writing Whole Numbers, . 12 Exercises in Reading Decimals, Exercises in Writing Decimals, Mental Exercise in Reducing Integers to Decimals, and Decimals to Integers, 15 Exercises in Reading and Writing Fed- Questions for Examination in Section I., 16 Exercises for the Slate in Integers and Examples for Practice in Integers, Fed- Mental Exercise in Multiplication, Exercises for the Slate in Multiplying Rule for Multiplication of Decimals, . To Multiply by Composite Numbers, To Multiply by 10, 100, 1000, &c., To Multiply by 80, 700, 3000, &c.,. To Multiply when the Multiplier has Miscellaneous Mental Exercises in Ad- dition, Subtraction, and Multiplica- tion, and Reduction by Multiplication, 32 Miscellaneous Exercises for the Slate in Addition, Subtraction, and Multipli- cation, 39-43 General Rule for Division of Decimals, . 46 To Divide by 10, 100, 1000, &c., . To Divide by 80, 700, 9000, &c.,. Long Division. To Divide Integers when the Divisor has Significant Fig- 47 • To Divide Integers and Decimals, Mental Exercise in Reduction by Divis Practical Exercises for the Slate in Fed- eral Money, and in Reduction by Di- Miscellaneous Examples in Reduction, . 54 Mental Exercise- Review-Miscella- Practical Examples in all the preceding Avoirdupois Weight. Long Measure,. 68 Square Measure. Cubic Measure, Mental Exercises in Multiplying and Exercise for the Slate in Multiplying To Reduce Integers or Fractions to a Numbers Reduced to Fractions and To Reduce the Fraction of one Denom- ination to the Fraction of another De- To Reduce Fractional Compound Num- Division of Fractions. General Rule,. 107 Division by Mixed Numbers. Particu- Miscellaneous Exercises in Fractions, Partial Payments. Common Rule,. . 136 Miscellaneous Examples in Percentage, 158 Accounts Current, and Interest Ac- SECTION XII.-RATIO. PROPORTION. Proportion by Cause and Effect, To find the interest of $1 for any given time, when the rate per annum is 6 To find the interest on any given prin- 130 To compute the interest when the rate Partnership, Miscellaneous Examples in Sect. XII., 185 Geometrical Definitions, . Mensuration of Solids, 210 SECTION XXII. . 210 SECTION XX. -PROBLEMS IN MENSURA- TION. The Pulley, The Inclined Plane, The Wedge. The Screw, SECTION XXI. - THE MECHANIC POWERS. The Wheel and Axle, CISES. Page Mental and Oral, Particular Accounts, |