Prof. _Augustus de Morgan's_ book _On the Study and Difficulties of Mathematics_,[65] though originally published more than sixty years ago, is still fresh and suggestive and full of matter valuable alike to students and teachers, and possesses qualities of clearness of reasoning and intelligibility from which many mathematical treatises are unfortunately free. Its purpose is to notice particularly several important points in the principles of algebra and geometry which have not obtained their due importance in elementary works in those sciences. Metaphysical points are avoided, and the method of explaining by reference to some particular problem, with hints as to more general adaptation, is adopted. Among the points taken up and classified are the nature and objects of mathematics, arithmetical and algebraic notation, rules and principles, equations, the negative sign, roots and logarithms, geometrical subjects, and application of algebra to measurements. The editor of the present edition, Mr. Thomas J. McCormack, has corrected the errata of the old edition and incorporated such changes as the progress of time and mathematical literature have made seem proper. An excellent portrait of De Morgan is given. [Footnote 65: On the Study and Difficulties of Mathematics. By Augustus De Morgan. New edition. Chicago: The Open Court Publishing Company. Pp. 288.] The purpose of _Carpenter's Geographical Reader, North America_ (American Book Company), is to give its readers a living knowledge of some of the wonders of the country and continent in which they live. They are taken by the author, Mr. _Frank G. Carpenter_, on a personally conducted tour through the most characteristic parts of the American continent, studying the most interesting features of life and work among the people, learning how they are governed, and how they make their living. Much information is also given concerning the natural resources and the physical features of the countries visited. The _Japan-American Commercial Journal_ is a monthly periodical started with the beginning of the year, with an especial view to the opening of the empire of Japan to unrestricted foreign trade and residence, for the advancement of the reciprocal interests of Japan and the United States. It is printed in English and Japanese, and is published at Tokio by the Japan-American Commercial and Industrial Association, for $2.50 a year.