Professor Peck's book belongs to neither of the two classes of text-books indicated, but to a class intermediate between the two. It is at once too good, too difficult a book for general, popular use, and too incomplete for the purposes of the professional student. As it assumes that the student is already acquainted with the elements of Algebra, Trigonometry, Analytic Geometry, and the Calculus, the successful use of this text-book in the general classes of any academy or college will be good evidence that the Mathematics are there taught more thoroughly than is usual in this country. In few American colleges is the study of the Calculus required of all students. In preparing a scientific text-book of this sort, originality is neither aimed at nor required. A judicious selection of materials, correct translation from the excellent French and German hand-books, with such changes in the notation as will better adapt it for American use, and a clear, logical arrangement are the chief merits of such a treatise; and these are merits which seldom gain much praise, though their absence would expose the author to censure. The definitions of Professor Peck's book are exact and concise, every proposition is rigidly demonstrated, and the illustrations and descriptions are brief, pointed, and intelligible. Professor Peck says in the Preface, that the book was prepared "to supply a want felt by the author when engaged in teaching Natural Philosophy to college classes"; but surely a teacher who prepares a text-book for his own classes must need a double share of patience and zeal. Every error which the book contains will be exposed, and the author will have ample opportunity to repent of all the inaccuracies which may have crept into his work. Again, the instructor who uses his own text-book encounters, besides the inevitable monotony of teaching the same subject year after year, the additional weariness of finding in the pages of his text-book no mind but his own, which he has read so often and with so little satisfaction. Even in teaching Mechanics, there is no exception to the general rule, that two heads are better than one. * * * * * _Stories from Famous Ballads_. For Children. By GRACE GREENWOOD, Author of "History of my Pets," "Merrie England," etc., etc. With Illustrations by BILLINGS. Boston: Ticknor & Fields.