2 cents cheaper than the compeditor, and two book store qualities better. A very durable and easy to read textbook. IN republishing this short treatise in book form the author solicits criticism but offers no apology. The type of the book he has sought to imitate is that shown in the " mathematical tracts " of the late Sir George B. Airy. The brevity and the concrete illustrations of these " tracts " have served very effectively in introducing students to a number of the more difficult fields of applied mathematics; and it is hoped that this treatise will serve a similar end. The theory of probability and the theory of errors now con- stitute a formidable body of knowledge of great mathematical interest and of great practical importance. Though developed largely through applications to the more precise sciences of astronomy, geodesy, and physics, their range of applicability extends to all of the sciences; and they are plainly destined to play an increasingly important r6le in the development and in the applications of the sciences of the future. Hence their study is not only a commendable element in a liberal education, but some knowledge of them is essential to a correct understanding of daily events. No special novelty of presentation is claimed for this work; but the reader may find it advantageous to know that a definite plan has been followed. This plan consists in presenting each principle, first, by means of a simple, concrete example; passing, secondly, to a general statement by means of a formula; and, thirdly, illustrating applications of the formula by concrete examples. Great pains have been taken also to secure clear and correct statements of fundamental, facts. If these latter are duly understood, the student needs little additional aid; if they are not duly understood, no amount of aid will forward him.