FA111577.770 HARVAND COLLEGE LIBRARI GIFT OF GEORGE ARTHUR PLIMPTON RAY'S MATHEMATICAL SERIES. REGULAR SERIES. Ray's New Primary Arithmetic. Ray's Surveying and Navigation. Ray's Differential and Integral Calculus. TWO-BOOK SERIES IN ARITHMETIC. Ray's New Elementary Arithmetic. COPYRIGHT, BY VAN ANTWERP, BRAGG & Co. Eclectic Press: VAN ANTWERP, BRAGG & CO., CINCINNATI. PREFACE. CHANGES in the methods of instruction in our schools and in the modes of transacting business have made it necessary to revise Ray's Practical Arithmetic. No other work on Arithmetic ever had so extensive use or widespread popularity. Teachers every-where, throughout the length and breadth of the land, are familiar with its pages, and millions of pupils have gained their arithmetical knowledge from the study of its principles. More than ten thousand editions of it have gone forth from the press. In view of these facts, it has been the constant aim in making this revision to preserve carefully those distinctive features of the former editions, which constituted the peculiar philosophical method of its learned author, viz.: 1st. Every principle is clearly explained by an analysis or solution of simple examples, from which a Rule is derived. This is followed by graduated exercises designed to render the pupil familiar with its application. 2d. The arrangement is strictly philosophical; no principle is anticipated; the pupil is never required to perform any operation until the principle on which it is founded has first been explained. The changes made fall naturally under two heads: (1) those which adapt the book better to the advanced methods of instruction; (2) those which exhibit present methods of computation in business. In the first place, special attention is invited to the beauty and elegance of the typography. The different matter of the volume, |