The Open Court Publishing Company (Chicago) publishes _The Lectures on Elementary Mathematics_ (_Leçons élémentaires sur les mathématiques_) of _Joseph Louis Lagrange_, "the greatest of modern analysts," in a translation from the new edition of the author's collected works by Thomas J. McCormack. These lectures, which were delivered in 1765 at the École Normale, have never before been published in separate form, except in the first printing in the Journal of the Polytechnic School and in the German. "The originality, elegance, and symmetrical character of these lectures have been pointed out by De Morgan, and notably by Dühring, who places them in the front rank of elementary expositions as an example of their kind. They possess, we might say, a unique character as a reading book in mathematics, and are interwoven with helpful historical and philosophical remarks." They present with great clearness the subjects of arithmetic and its operations, algebra, equations of the third and fourth degrees, the evolution of numerical equations, and the employment of curves in the solution of problems. The translator has prefixed a short biographical sketch of Lapouge, and an excellent portrait is given. A book of _Observation Blanks for Beginners in Mineralogy_ has been prepared by _Herbert E. Austin_, as an aid to the laboratory course, and is published by D. C. Heath & Co. (Boston, 30 cents). The laboratory course is intended to make the pupil familiar with the characteristics of minerals and the terms used in describing them by directing him to observe typical specimens and describe what he sees, and to develop his faculties of observation, conception, reasoning, judgment, comparison, and memory. A description is given of apparatus that may be home-made. The blanks follow, containing spaces for the insertion of notes under the heads of Experiment, Observation, Statement, and Conclusion.