the examination of a number of commercial products. This section includes descriptions of the new indicators derived from the azo-colors, which have been introduced recently by R. T. Thompson. The third section deals with analysis by oxidation or reduction, and the fourth with analysis by precipitation. The foregoing principles are then applied to the estimation of the important elements and radicals, which are taken up in alphabetical order. A chapter is devoted to the analysis of urine, potable waters, sewage, etc., and another to gas analysis. In the latter field there has been marked improvement in technical processes since the last edition of this work was issued. The book is well supplied with illustrations showing forms of apparatus, and methods of arranging it for special operations.
Mineral Resources of the United States. 1885. By Albert Williams, Jr. Washington: Government Printing-Office. Pp. 576.
The present volume is the third of a series designed to present the principal statistics concerning the mineral productions of the United States, together with such descriptive matter as will throw light upon the condition of the industries which those products materially affect, or will aid in utilizing material which has no value at present. The first volume covered 1882 and the first half of 1883; the second volume continued the record till the end of 1884. These volumes were noticed in the "Monthly" when they appeared. The present volume includes the calendar year 1885. The material for the accounts has been obtained by canvass for precise returns where that was practicable; otherwise, from estimates of authorities as checked by actual returns from all available sources. Much of it appears in the form of special articles by persons who are experts, or have given particular attention to the subject. The principle is observed of not repeating (except in the tables) information given the previous year; hence it happens that, where no change has been made in the conditions, attending any product, that title may temporarily disappear from the record. Prominence is given in the presentation to coal, coke, petroleum, natural gas, and the economical metals under some of which headings several articles of special value appear. Thus, Mr. Joseph D. Weeks treats of the manufacture of coke, of natural gas, manganese, and glass materials; Mr. S. H. Stowell, of petroleum; J. M. Swank, General Manager of the American Iron and Steel Association, gives a review of twenty-one years of progress in manufacture; C. Kirchhoff, Jr., contributes articles on the copper, lead, and zinc industries of the United States; Mr. David T. Day, on chromium, zirconium, phosphatic rock fertilizers, and iodine; Mr. N. S. Sproule, on structural materials; Mr. George F. Kunz, on precious stones; William C. Day, on sulphur and feldspar; Herbert J. Davis, on pyrites; Marcus Benjamin, on mineral paints; G. F. Perrenoud, on talc; and A. C. Peale, on mineral waters.
A Treatise on Algebra. By Professors Oliver, Wait, and Jones, of Cornell University Ithaca, N. Y.: Dudley F. Finch. Pp. 412.
This work is a text-book for college classes, being planned especially for the classes conducted by its authors. It is, therefore, not a book for beginners, but for students who have already studied the elements of algebra and geometry. In writing it the authors have had two rules for their guidance. One was, to assume no previous knowledge of algebra, but, starting from primary definitions and axioms, to develop the elementary principles in logical order; the other was to define clearly every word and symbol used in a technical sense, to state formally every general principle, and, if not an axiom, to prove it rigorously, to state formally every general problem, and to give a rule for its solution with reasons, examples, and checks. The book contains much matter that is not found in the common college algebras—more, in fact, than can be used with ordinary classes—yet its wide range is expected to make it valuable as a reference-book for teachers, and as a guide for students who wish to pursue the study beyond the usual limits. The authors have pursued a course which they believe accords with the tendencies of modern algebraic work, in utilizing graphic representation, the elements of infinitesimal analysis, and the
