Airy (Osmund). — A TREATISE ON GEOMETRICAL OPTICS. Adapted for the use of the Higher Classes in Schools. By OSMUND AIRY, B.A., one of the Mathematical Masters in Wellington College. Extra fcap. 8vo. 3s. 6d. This is, I imagine, the first time that any attempt has been made to adapt the subject of Geometrical Optics to the reading of the higher classes in our good schools. That this should be so is the more a matter for remark, since the subject would appear to be peculiarly fitted for such an adaptation. I have endeavoured, as much as possible, to avoid the example of those popular lecturers who explain difficulties by ignoring them. But as the nature of my design necessitated brevity, I have omitted entirely one or two portions of the subject which I considered unnecessary to a clear understanding of the rest, and which appear to me better learnt at a more advanced stage."—AUTHOR'S PREface. "This book," the ATHENÆUM says, "is carefully and lucidly written, and rendered as simple as possible by the use in all cases of the most elementary form of investigation." Bayma.-THE ELEMENTS OF MOLECULAR MECHA- Of the Twelve Books into which the present treatise is divided, the first and second give the demonstration of the principles which bear directly on the constitution and the properties of matter. The next three books contain a series of theorems and of problems on the laws of motion of elementary substances. In the sixth and seventh, the mechanical constitution of molecules is investigated and determined: and by it the general properties of bodies are explained. The eighth book treats of luminiferous æther. The ninth explains some special properties of bodies. The tenth and eleventh contain a radical and lengthy investigation of chemical principles and relations, which may lead to practical results of high importance. twelfth and last book treats of molecular masses, distances, and powers. The Beasley.-AN ELEMENTARY TREATISE ON PLANE 3s. 6d. Fourth This treatise is specially intended for use in schools. The choice of matter has been chiefly guided by the requirements of the three days' examination B at Cambridge. About four hundred examples were added to the second edition, mainly collected from the Examination Papers of the last ten years. In this edition several new articles have been added, the examples have been largely increased, and a series of Examination Papers appended. Blackburn ELEMENTS OF (Hugh). PLANE TRIGONOMETRY, for the use of the Junior Class of Mathematics in the University of Glasgow. By HUGH BLACKBURN, M. A., Professor of Mathematics in the University of Glasgow. Globe 8vo. Is. 6d. The author having felt the want of a short treatise to be used as a Text-Book after the Sixth Book of Euclid had been learned and some knowledge of Algebra acquired, which should contain satisfactory demonstrations of the propositions to be used in teaching Junior Students the solution of Triangles, and should at the same time lay a solid foundation for the study of Analytical Trigonometry, thinking that others may have felt the same want, has attempted to supply it by the publication of this little work. Boole.-Works by G. BOOLE, D.C.L., F.R.S., Professor of Mathematics in the Queen's University, Ireland. New and Crown 8vo. cloth. A TREATISE ON DIFFERENTIAL EQUATIONS. 145. Professor Boole has endeavoured in this treatise to convey as complete an account of the present state of knowledge on the subject of Differential Equations as was consistent with the idea of a work intended, primarily, for elementary instruction. The earlier sections of each chapter contain that kind of matter which has usually been thought suitable for the beginner, while the latter ones are devoted either to an account of recent discovery, or the discussion of such deeper questions of principle as are likely to present themselves to the reflective student in connection with the methods and processes of his previous course. "A treatise incomparably superior to any other elementary book on the same subject with which we are acquainted."-PHILOSOPHICAL MAGAZINE. A TREATISE ON DIFFERENTIAL EQUATIONS. Supplementary Volume. Edited by I. TODHUNTER. Crown 8vo. cloth. Boole-continued. This volume contains all that Professor Boole wrote for the purpose of enlarging his treatise on Differential Equations. THE CALCULUS OF FINITE DIFFERENCES. Crown 8vo. cloth. 10s. 6d. New Edition, revised by J. F. Moulton. In this exposition of the Calculus of Finite Differences, particular attention has been paid to the connection of its methods with those of the Differential Calculus-a connection which in some instances involves far more than a merely formal analogy. The work is in some measure designed as a sequel to Professor Boole's Treatise on Differential Equations. "As an original book by one of the first mathematicians of the age, it is out of all comparison with the mere second-hand compilations which have hitherto been alone accessible to the student."-PHILOSOPHICAL MAGAZINE. Brook - Smith (J.)-ARITHMETIC IN THEORY AND PRACTICE. By J. BROOK-SMITH, M.A., LL.B., St. John's College, Cambridge; Barrister-at-Law; one of the Masters of Cheltenham College. Complete, Crown 8vo. 4s. 6d. Part I. 3s. 6d. Writers on Arithmetic at the present day feel the necessity of explaining the principles on which the rules of the subject are based, but few as yet feel the necessity of making these explanations strict and complete. If the science of Arithmetic is to be made an effective instrument in developing and strengthening the mental powers, it ought to be worked out rationally and conclusively; and in this work the author has endeavoured to reason out in a clear and accurate manner the leading propositions of the science, and to illustrate and apply those propositions in practice. In the practical part of the subject he has advanced somewhat beyond the majority of preceding writers; particularly in Division, in Greatest Common Measure, in Cube Root, in the Chapters on Decimal Money and the Metric System, and more especially in the application of Decimals to Percentages and cognate subjects. Copious examples, original and selected', are given. "This strikes us as a valuable Manual of Arithmetic of the Scientific kind. Indeed, this really appears to us the best we have seen. -LITERARY CHURCHMAN. "This is an essentially practical book, providing very definite help to candidates for almost every kind of competitive examination."--BRITISH QUARTERLY. Cambridge Senate-House Problems and Riders, WITH SOLUTIONS: 1848-1851.-PROBLEMS. By FERRERS and JACKSON. 1848-1851.-RIDERS. BY JAMESON. 8vo. cloth. 7s. 6d. 8vo. By WALTON and 1857.- PROBLEMS AND RIDERS. By CAMPION and WALTON. 8vo. cloth. 8s. 6d. 1860.-PROBLEMS AND RIDERS. By WATSON and ROUTH. Crown 8vo. cloth, 7s. 6d. 1864.-PROBLEMS AND RIDERS. By WALTON and WILKINSON. 8vo. cloth. IOS. 6d. These volumes will be found of great value to Teachers and Students, as indicating the style and range of mathematical study in the University of Cambridge. CAMBRIDGE COURSE OF ELEMENTARY NATURAL PHILOSOPHY, for the Degree of B.A. Originally compiled by J. C. SNOWBALL, M.A., late Fellow of St. John's College. Fifth Edition, revised and enlarged, and adapted for the MiddleClass Examinations by THOMAS LUND, B.D., Late Fellow and Lecturer of St. John's College, Editor of Wood's Algebra, &c. Crown 8vo. cloth. 5s. This work will be found adapted to the wants, not only of University Students, but also of many others who require a short course of Mechanics and Hydrostatics, and especially of the candidates at our Middle Class Examinations. At the end of each chapter a series of easy questions is added for the exercise of the student. CAMBRIDGE AND DUBLIN MATHEMATICAL JOURNAL. The Complete Work, in Nine Vols. 8vo. cloth. 77. 45. Only a few copies remain on hand. Among Contributors to this work will be found Sir W. Thomson, Stokes, Adams, Boole, Sir W. R. Hamilton, De Morgan, Cayley, Sylvester, Fellett, and other distinguished mathematicians. Candler.-HELP TO ARITHMETIC. Designed for the use of Schools. By H. CANDLER, M.A., Mathematical Master of in use. This work is intended as a companion to any text-book that may be "The main difficulties which boys experience in the different rules are skilfully dealt with and removed."-MUSEUM. Cheyne.-Works by C. H. H. CHEYNE, M.A., F. R.A.S. AN ELEMENTARY TREATISE ON THE PLANETARY THEORY. With a Collection of Problems. Second Edition. Crown 8vo. cloth. 6s. 6d. In this volume an attempt has been made to produce a treatise on the Planetary theory, which, being elementary in character, should be so far complete as to contain all that is usually required by students in the University of Cambridge. In the New Edition the work has been carefully revised. The stability of the Planetary System has been more fully treated, and an elegant geometrical explanation of the formula for the secular variation of the node and inclination has been introduced. THE EARTH'S 3s. 6d. MOTION OF ROTATION. Crown 8vo. The first part of this work consists of an application of the method of the variation of elements to the general problem of rotation. In the second part the general rotation formula are applied to the particular case of the earth. Childe.-THE SINGULAR PROPERTIES OF THE ELLIPSOID AND ASSOCIATED SURFACES OF THE NTH DEGREE. By the Rev. G. F. CHILDE, M.A., Author of "Ray Surfaces," ""Related Caustics," &c. 8vo. IOS. 6d. The object of this volume is to develop peculiarities in the Ellipsoid; and, further, to establish analogous properties in the unlimited congeneric series of which this remarkable surface is a constituent. Christie.-A COLLECTION OF ELEMENTARY TESTQUESTIONS IN PURE AND MIXED MATHEMATICS; with Answers and Appendices on Synthetic Division, and on the Solution of Numerical Equations by Horner's Method. By JAMES R. CHRISTIE, F. R.S., late First Mathematical Maste. at the Royal Military Academy, Woolwich. Crown 8vo. cloth. 8s. 6d. This series of Mathematical Exercises is collected from those which the author has, from time to time, proposed for solution by his pupils during |