the processes of the schools: he has preceded them with exercises which lead the student directly and easily to a clear apprehension of the steps in the solution and the necessity for them; and he has accompanied the solutions with explanations which enable the pupil to comprehend all that he needs to know about the operations. By these means the student is led to employ business methods of solution because they are generally natural methods, and to understand and explain every step in the process. A student who has been trained in this manner will never forget a process or a rule, because he can devise the process and frame the rule at will.

The work is of sufficiently comprehensive scope to meet the demands of even the most advanced schools. The unusually practical character of the problems will be discerned by a very cursory examination; oral and written exercises are given in connection with each subject, and frequent and thorough reviews serve to test the pupil's proficiency, to fix the principles of the science in his mind, and to train and develop his power of reasoning.

The method exemplified in presenting the various subjects is in accord with what is deemed best in modern methods of teaching; the order and arrangement of the subjects, though they are in some respects a departure from that usually given, will hasten the pupil's progress by removing to the latter part of the book subjects too difficult for the average pupil when he reaches them, and of little practical value to any student; the explanations are thought to be conspicuously lucid, the steps logical, the definitions, principles, and rules brief and accurate.

The author desires to express his indebtedness to many educators of prominence for valuable suggestions regarding the scope of the work and its educational character. The cordiality with which his former works have been received gives him the hope that this book also may meet with general favor.

WILLIAM J. MILNE.