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,

the definition, the solution, or the rule, is at once clearly indicated by a difference of type. A running series of articles, with numbered paragraphs, enhances the convenience of the text-book for recitation and for reference.

The analytic solutions and written operations have been carefully separated. All obsolete Tables of Weights and Measures, such as Beer Measure and Cloth Measure, and all obsolete denominations, such as drams, roods, etc., are discarded. The Metric System of Weights and Measures is presented in accordance with its now widely extended usage, and is assigned its proper place immediately after Decimals.

A few subjects, such as Factoring and the principles of Fractions, have been entirely rewritten, and in many instances the definitions and rules have been simplified. The subject of Percentage has been much expanded, and an endeavor has been made to systematize its numerous applications; many novel and interesting features, both of subject-matter and classification, will here be met with for the first time. The subjects of Interest and Discount have received that careful attention which their importance demands. The publishers desire to express their thanks to the many teachers whose suggestions and corrections are embodied in the present edition. Especial mention is due Prof. M. W. Smith and Mr. A. P. Morgan for many valuable features of this revision.

In conclusion, the publishers wish to reiterate that the object throughout has been to combine practical utility with scientific accuracy; to present a work embracing the best methods, with all real improvements. How far this object has been secured is again submitted to those engaged in the laborious and responsible work of education.

CINCINNATI, August, 1877.