tionably fix and intensify impressions. They furnish the natural way of learning of infants and of the unschooled.

But the schooled adult soon acquires from his experiences that great economizer, the generalization, which he thereafter uses constantly; hence the limitations of the spiral plan in an arithmetic. It should be used long enough to establish generalizations. When this has been done for any subject, it should be dropped. The period for induction has passed. Thereafter topics should be treated topically, except as frequent reviews are used to freshen and deepen impressions.

The problems are drawn, in so far as possible, from fields of activity within the experience or ready comprehension of children, and likely to appeal to their interest. But when, to illustrate a principle, there is need of problems that are not derived naturally from the common experiences of children, the authors have deemed it better to supply good problems that meet the mathematical need than to introduce inferior illustrations that stimulate interest. Vital problems are important, but the mathematical principle is the thing, after all.

This book is intended for the fifth and sixth years of the average graded school. The normal age of the pupils will range from ten to twelve years.

This is the psychological age for drill, when memory is at its best and reason is just beginning to show strength. Consequently, memory should be utilized and reason developed.

The arrangement of this book is increasingly topical, only a few of the more difficult subjects, as percentage, being treated recurrently, in preparation for their final discussion in Book Three.

As many pupils leave school after completing the sixth year, a few important business applications are given, such as interest and the simplest facts of banking.