The Progressive Higher Arithmetic

phy and mechanical execution; the philosophical and scientific arrangement of the subjects; clear and concise definitions; full and rigid analyses; exact and comprehensive rules; brief and accurate methods of operation: the wide range of subjects and the large number and practical character of the examples—in a word, SCIENTIFIC ACCURACY combined with PRACTICAL UTILITY, throughout the entire work.

Much labor and attention have been devoted to obtaining correct and adequate information pertaining to mercantile and commercial transactions, and the Government Standard units of measures, weights, and money. The counting-room, the bank, the insurance and broker's office, the navy and ship-yard, the manufactory, the wharves, the custom-house, and the mint, have all been visited, and the most reliable statistics and the latest statutes have been consulted, for the purpose of securing entire accuracy in those parts of this work which relate to these subjects and departments. As the result of this thorough investigation, many statements found in most other arithmetics of a similar grade will not agree with the facts presented in this work, and simply because the statements in these other books have been copied from older works, while laws and customs have undergone great changes since the older works were written.

New material and new methods will be found in the several subjects throughout the entire work. Considerable prominence has been given to Percentage and its numerous applications, especially to Stocks, Insurance, Interest, Averaging Accounts, Domestic and Foreign Exchange, and several other subjects necessary to qualify students to become good accountants or commercial business men. And while this work may embrace many subjects not necessary to the

course usually prescribed in Mercantile and Commercial Colleges, yet those subjects requisite to make good accountants, and which have been taught orally in that class of institutions from want of a suitable text-book, are fully discussed and practically applied in this work; and it is therefore believed to be better adapted to the wants of Mercantile Colleges than any similar work yet published. And while it is due, it is also proper here to state that J. C. Porter, A. M., an experienced and successful teacher of Mathematics in this State, and formerly professor of Commercial Arithmetic, in Iron City Commercial College, Pittsburgh, Penn., has rendered valuable aid in the preparation of the above-named subjects, and of other portions of the work. He is likewise the author of the Factor Table on pages 72 and 73, and of the new and valuable improvement in the method of Cube Root.

Teachers entertain various views relative to having the answers to problems and examples inserted in a text-book. Some desire the answers placed immediately after the examples; others wish them placed together in the back part of the book; and still others desire them omitted altogether. All these methods have their advantages and their disadvantages.

If all the answers are given, there is danger that the pupil will become careless, and not depend enough upon the accuracy of his own computations. Hence he is liable to neglect the cultivation of those habits of patient investigation and self-reliance which would result from his being obliged to test the truth and accuracy of his own processes by proof,—the only test he will have to depend upon in all the computations in real business transactions in after life. Besides, the work of proving the correctness of a result is often of quite as much value to the pupil as the work of

performing the operation; as the proof may render simple and clear some part or the whole of an operation that was before complicated and obscure.

The improvements in Percentage made necessary by the financial changes of the last few years are especially noticeable. The different kinds of United States' Securities, Bonds, and Treasury Notes are described, and their comparative value in commercial transactions illustrated by practical examples. The difference between Gold and Currency, and the corresponding difference in prices, exhibited in trade, are taught and illustrated, and many other things that every commercial student and business man ought to know and understand.

There has also been added a full and practical presentation of the Metric System of Weights and Measures, containing many new and original improvements in the arrangement, notation, and applications, not before presented to the public, and which greatly simplify and adapt the system to general use.

Many valuable hints and suggestions which have been received from teachers and friends of education, have been incorporated into this work. The author desires to make especial acknowledgment of the valuable services rendered in the preparation of this work by D. W. Fish, A.M., of Rochester, N. Y., a gentleman who has had long and successful experience as a teacher, and an intimate acquaintance with the plans and operations of some of the best schools in the country.

August 1, 1860.