the civil war; after it General Sherman gave the scheme a great impulse, and the Union Pacific Railroad was built--when and how are graphically and dramatically told in Mr. Warman's book. Next came the Atchison, Topeka, and Santa Fé, and other transcontinental lines, the histories of all of which are related in similar style, with stories of adventures, perils encountered, and lively incidents, including the war between two of the lines for the possession of the Arkansas Cañon; financial mishaps, and political scandal. Then came the settlement of the plains, road-making in Mexico, and the opening of Oklahoma, all of which were made possible by the railroads, and have in turn contributed to support them. The beginnings and growth of the express business are described, and the later lines that have penetrated the plains are mentioned. Prof. _William Benjamin Smith's_ treatise on the _Infinitesimal Analysis_[18] has been written, the author says, on what appeared, in the light of ten years' experience in teaching the calculus, to be lines of least resistance. The aim has been, within a prescribed expense of time and energy, to penetrate as far as possible into the subject, and in as many directions, so that the student shall attain as wide knowledge of the matter, as full comprehension of the methods, and as clear consciousness of the spirit and power of this analysis as the nature of the case would admit. The author has accordingly often followed what seemed to be natural suggestions and impulses toward near-lying extensions or generalizations, and has even allowed them to direct the course of the discussion. In accordance with the plan and purpose of the book as given, "Weierstressian rigor" has been excluded from many investigations, and the postponement has been compelled of some important discussions, which were considered too subtle for an early age of study. Real difficulties, however, have not been knowingly disguised, and pains have been taken on occasion to warn the reader that the treatment given is only provisional, and must await further precision or delimitation. Where the subject has been found too large for the compass of the intended work, or too abstruse or difficult for the contemplated students, the treatment has been compressed or curtailed. The book is, in fact, written for such as feel a genuine interest in the subject; and the illustrations and exercises have been chosen with frequent reference to practical or theoretic importance or to historic interest.