This textbook is a seventh-grade course in arithmetic. The plan pursued in this series of arithmetics is that of giving constant practice in those principles already acquired at the same time that new topics are presented. Accordingly, many review examples in percentage are given as the subject is more fully developed. The form lessons, which have been an important part of the previous books, are here continued, and their scope broadened to include the simple principles of concrete geometry, the mastery of which renders the transition to theoretical geometry devoid of the usual difficulties. The first principles of Algebra are also introduced. There are, throughout the arithmetical portion of the book, many examples that should be solved by letting x stand for the unknown term. Wherever this method of solution is the simpler, teachers should encourage children to make use of it. Putting into algebraic language the conditions of an arithmetical problem forms an easy transition from the concrete language of arithmetic to the abstract and general language of algebra.