COMMERCIAL ARITHMETIC, FOR THE USE OF THE GRAND RAPIDS BUSINESS COLLEGE, GRAND RAPIDS, MICHIGAN, AND ALSO FOR THE USE OF Universities, Private Students, Schools and Counting-Houses, EMBRACING AN EXTENSIVE COURSE BOTH IN THEORY AND PRACTICE. TOGETHER WITH THE LAWS OF THE UNITED STATES RELATING TO INTEREST, DAMAGES ON BY T. A. BRYCE, M.A., LL.D., AUTHOR OF TREATISES ON ALGEBRA AND GEOMETRY, PUBLISHED BY C. G. SWENSBERG, PROPRIETOR GRAND RAPIDS BUSINESS COLLEGE AND TELEGRAPHIC INSTITUTE. 1873. Entered according to Act of Congress, in the year 1866, by GILBERT Y. BURNS, in the Clerk's Office of the District Court of the Northern District of New York. PREFACE THOUGH elementary works on Arithmetic are in abundance, yet it seems desirable that there should be added to this an extensive treatise on the commercial rules, and commercial laws and usages. It is not enough that the school-boy should be provided with s course suited to his age. There must be supplied to him something higher as he advances in age and progress, and nears the period when he is to enter on real business life. The Author's aim has, therefore, been to combine these two objects, and to produce a work adequate to carry the learner from the very elements up to the highest rules required by those preparing for business. As the work proceeded, it was found necessary to extend the original programme considerably, and, therefore, also the limits of the book, so as to make it useful to all classes in the community. In carrying out this plan, much care has been taken to unfold the theory of Arithmetic as a SCIENCE in as concise a manner as scemed consistent with clearness, and at the same time to show its applications as an ART. Every effort has been made to render the business part so copious and practical as to afford the young student ample information and discipline in all the principles and usages of commercial intercourse. For the same reason some articles on Commercial Law have been introduced, as it was a prominent part of the Author's aim to produce a work which should be found useful, not only in the class-room, and the learner's study, but also on the merchant's table, and the accountant's desk. The Author begs to tender his best thanks to J. Smith Homans, Esq., New York City, Editor and Proprietor of the "Banker's Magazine and Statistical Register," for the able manner in which he supplied this part of the work. Throughout the work particular care has been taken not to enunciate any rule without explaining the reason of the operation, for, without a knowledge of the principle, the operator is a merc calculating machine that can work but a certain round, and is almost sure to be at fault when any novel case arises. The explanations are, of course, more or less the result of reading, but, nevertheless, they are mainly derived from personal study and experience in teaching. The great mass of the exercises are likewise entirely new, though the Author has not scrupled to make selections from some of the most approved works on the subject; but in doing so, he has confined himself almost entirely to such questions as are to be found in nearly all popular books, and which, therefore, are to be looked upon as the common property of science. Algebraic forms have been avoided as much as possible, as being unsuited to a large proportion of those for whom the book is intended, and to many altogether unintelligible, and besides, those who understand Algebraic modes will have all the less difficulty in understanding the Arithmetical ones. Even in the more purely mathematical parts the subject has been popularized as much as possible. In arranging the subjects it was necessary to follow a certain logical order, but the intelligent teacher and learner will often find it necessary to depart from that order. (See suggestions to teachers.) Every one will admit that rules and definitions should be expressed in the smallest possible number of words, consistent with perspicuity and accuracy. Great pains have been taken to carry out this principle in every case. Indeed, it might be desirable, if practicable, not to enunciate any rules, but simply to illustrate each case by a few examples, and leave the learner to take the principle into his mind, as his rule, without the encumbrance of words. Copious exercises are appended to each rule, and especially to the most important, such as Fractions, Analysis, Percentage, with its applications, &c. Besides these, there have been introduced extensive collections of mixed exercises throughout the body of the work, besides a large number at the end. The utility of such miscellaneous questions will be readily admitted by all, but the reason why they are of so much importance seems strangely overlooked or misunderstood even by writers on the subject. They are spoken of as review exercises, but their great value depends on something still more important. An illustration will best serve here. A class is working questions on a certain rule, and each member of the class has just heard the rule enunciated and explained, and therefore readily applies it. So far one important object is attained, viz., freedom of operation. But something more is necessary. The learner must be taught to discern what rule is to be applied for the solution of each question proposed. The pupil, under careful teach ing, may be able to understand fully every rule, and never con found any one with any other, and yet be doubtful what rule is to be applied to an individual case. The miscellaneous problems, therefore, are intended not so much as exercises on the operations of the different rules as on the mode of applying those rules; or, in other words, to practice the pupil in perceiving of what rule any proposed question is a particular case. Great importance should be attached to this by the practical educator, not only as regards readi ness in real business, but also as a mental exercise to the young. student. The Author is far from supposing, much less asserting, that the work is complete, especially as the whole has been prepared in less than the short space of six months. It is presented, however, to the public in the confident expectation that it will meet, in a great degree at least, the necessities of the times. With this view, there are given extensive collections of examples and exercises, involving money in dollars and cents, with, however, a number in pounds, shillings and pence, sufficient for the purpose of illustration. This seems necessary, as many must have mercantile transactions with Britain and British America. The Rule for finding the Greatest Common Measure, though not new, is given in a new, and it is hoped, a concise and convenient form of operation, The Rule for finding the Cabe Root is a modification of that given by Dr. Hinds, and will be found ready and short. In treating of Common Fractions, Multiplication and Division have been placed before Addition and Subtraction, for two reasons. FIRST,-In Common Fractions, Multiplication and Division present much less difficulty than Addition and Subtraction; and, SECONDLY, as in Whole Numbers Addition is the Rule that regulates all others; 50 in Fractions, which originate from Division, we see, in like manner, that all other operations result from Division, and, in connection with it, Multiplication. Several subjects, commonly treated of in works on Arithmetic, have been omitted in order to leave space for more important matter bearing on commercial subjects. Duodecimals, for example, have been omitted, as that mode of calculation is now virtually superseded |