later reviews are placed in the Appendix, while subjects of no practical value in a modern arithmetic are omitted. 8. Chapter on the Equation. The importance of introducing this simple and easy chapter cannot well be overestimated. Arithmetical methods are adhered to, and by simple inductive exercises and comparative solutions the conceptions of the use of letters as the general representatives of positive numbers, and of the equation to express their relations, are developed as far as the purpose of the chapter demands. By the aid of this simple chapter, equations which have a meaning to the pupil can be substituted for the dead formulas sometimes used in percentage problems and interest problems, and a much clearer understanding can be had of such subjects as the greatest common divisor, the square and cube roots, etc. The subject is further developed in the brief but attractive chapter on "Introduction to Algebra" given in the Appendix. 9. Division of Problems. Experience has shown that the same problems should not be solved by the same class from term to term. It is wiser to add fresh fuel than to be constantly stirring the old coals. The pupil's interest must be kept alive. With this in view, we have divided the problems into two parts; the first to be used when the class first goes over a subject, the second when it reviews that subject. For a similar reason the reviews have also been so divided. 10. Character of Problems. In the preparation of problems the actual business practice of to-day has been kept in mind. In addition to their practical and mathematical value, many of the problems furnish much useful and scientific information that is reliable and strictly up-to-date. The aim has been to make them as practical and useful as possible. 11. Scope of the Work. The series meets the needs not only of the primary and the grammar school, but also of the high school. For the latter there is sufficient theory, and an abundance of practice work, owing to the "Supplementary Exercises" for advanced classes, and matter included in the Appendix. 12. Bank Practice of to-day is given in a concise and accurate chapter. The information has been furnished by officials of prominent banks in the States mentioned in the exercises. 13. The unique treatment of various processes will appeal to the intelligent and progressive teacher. The merits of these processes can be determined only by careful examination of the text itself. 14. The matter and method of the Primary book are designed to serve as an introduction to and foundation for the more formal and rigorous treatment presented in these pages. The authors desire to express their thanks for valuable criticisms and suggestions from many educators during the preparation of this series. They especially acknowledge their indebtedness to Prof. Frank W. Duke, of Hollins Institute, Hollins, Va., for help of this kind. July 2, 1900. J. M. COLAW, J. K. ELLWOOD. |