A judicious combination of both methods is doubtless the best; and it is hoped that this result may be arrived at in some degree by the use of this book, which is simply a collection of examples, with helps for solution, arranged in progressive sections. The new edition has been enlarged by the addition of chapters on the straight line and plane, with explanatory diagrams and exercises on tangent planes, and on the cases of the spherical triangle. Ferrers.-AN ELEMENTARY TREATISE ON TRILINEAR CO-ORDINATES, the Method of Reciprocal Polars, and Theory of Projectors. By the Rev. N. M. FERRERS, M.A., Fellow and Tutor of Gonville and Caius College, Cambridge. Second Edition. Crown 8vo. 6s. 6d. The object of the author in writing on this subject has mainly been to place it on a basis altogether independent of the ordinary Cartesian system, instead of regarding it as only a special form of Abridged Notation. A short chapter on Determinants has been introduced. Frost. Works by PERCIVAL FROST, M.A., formerly Fellow of St. John's College, Cambridge; Mathematical Lecturer o King's College. AN ELEMENTARY TREATISE ON CURVE TRACING. The author has written this book under the conviction that the skill and power of the young mathematical student, in order to be thoroughly available afterwards, ought to be developed in all possible directions. The subject which he has chosen presents so many faces, that it would be difficult to find another which, with a very limited extent of reading, combines, to the same extent, so many valuable hints of methods of caiculations to be employed hereafter, with so much pleasure in its present In order to understand the work it is not necessary to have much knowledge of what is called Higher Algebra, nor of Algebraical Geometry of a higher kind than that which simply relates to the Conic Sections. From the study of a work like this, it is believed that the student wi derive many advantages. Especially he will become skilled in making correct approximations to the values of quantities, which cannot be found exactly, to any degree of accuracy which may be required. use. Frost-continued. THE FIRST THREE SECTIONS OF NEWTON'S PRINCIPIA. With Notes and Illustrations. Also a collection of Problems, principally intended as Examples of Newton's Methods. By PERCIVAL FROST, M.A. Second Edition. 8vo. cloth. IOS. 6d. The author's principal intention is to explain difficulties which may be encountered by the student on first reading the Principia, and to illustrate the advantages of a careful study of the methods employed by Newton, by showing the extent to which they may be applied in the solution of problems; he has also endeavoured to give assistance to the student who is engaged in the study of the higher branches of mathematics, by representing in a geometrical form several of the processes employed in the Differential and Integral Calculus, and in the analytical investigations of Dynamics. Frost and Wolstenholme.-A TREATISE ON SOLID GEOMETRY. By PERCIVAL FROST, M.A., and the Rev. J. WOLSTENHOLME, M. A., Fellow and Assistant Tutor of Christ's College. 8vo. cloth. 185. The authors have endeavoured to present before students as comprehensive a view of the subject as possible. Intending to make the subject accessible, at least in the earlier portion, to all classes of students, they have endeavoured to explain completely all the processes which are most useful in dealing with ordinary theorems and problems, thus directing the student to the selection of methods which are best adapted to the exigencies of each problem. In the more difficult portions of the subject, they have considered themselves to be addressing a higher class of students; and they have there tried to lay a good foundation on which to build, if any reader should wish to pursue the science beyond the limits to which the work extends. Godfray.—Works by HUGH GODFRAY, M.A., Mathematical Lecturer at Pembroke College, Cambridge. A TREATISE ON ASTRONOMY, for the Use of Colleges and Schools. 8vo. cloth. 12s. 6d. This book embraces all those branches of Astronomy which have, from time to time, been recommended by the Cambridge Board of Mathematical Studies: but by far the larger and easier portion, adapted to the first three days of the Examination for Honours, may be read by the more Cambridge Senate-House Problems and Riders, WITH SOLUTIONS : 1848-1851.-PROBLEMS. By FERRERS and JACKSON. 8vo. 1848-1851.-RIDERS. BY JAMESON. 8vo. cloth. 7s. 6d. 1854. - PROBLEMS AND RIDERS. By WALTON and MACKENZIE. 8vo. cloth. IOS. 6d. 1857.- PROBLEMS AND RIDERS. WALTON. 8vo. cloth. 8s. 6d. By CAMPION and 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, Jellett, and other distinguished mathematicians. Candler.-HELP TO ARITHMETIC. Designed for the use of Schools. By H. CANDLER, M.A., Mathematical Master of This work is intended as a companion to any text-book that may be "The main difficulties which boys experience in the different in use. 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 Crown 8vo. cloth. 8s. 6d. Royal Military Academy, Woolwich. This series of Mathematical Exercises is collected from those which the author has, from time to time, proposed for solution by his pupils during a long career at the Royal Military Academy. A student who finds that he is able to solve the larger portion of these Exercises, may consider that he is thoroughly well grounded in the elementary principles of pure and mixed Mathematics. Dalton.-ARITHMETICAL EXAMPLES. Progressively arranged, with Exercises and Examination Papers. By the Rev. T. DALTON, M.A., Assistant Master of Eton College. New Edition. 18mo. cloth. 2s. 6d. Answers to the Examples are appended. Day.-PROPERTIES OF CONIC SECTIONS PROVED GEOMETRICALLY. PART I., THE ELLIPSE, with Problems. By the Rev. H. G. DAY, M.A., Head Master of Sedburgh Grammar School. Crown 8vo. 3s. 6d. The object of this book is the introduction of a treatment of Conic Sections which should be simple and natural, and lead by an easy transition to the analytical methods, without departing from the strict geometry of Euclid. Dodgson.-AN ELEMENTARY TREATISE ON DETER MINANTS, with their Application to Simultaneous Linear IOS. 6d. The object of the author is to present the subject as a continuous chain of argument, separated from all accessories of explanation or illustration. All such explanation and illustration as seemed necessary for a beginner are introduced, either in the form of foot-notes, or, where that would have occupied too much room, of Appendices. "The work," says the EDUCATIONAL TIMES, "forms a valuable addition to the treatises we possess on Modern Algebra." Drew.-GEOMETRICAL TREATISE ON CONIC SECTIONS. By W. H. DREW, M. A., St. John's College, Cambridge. Fourth Edition. Crown 8vo. cloth. 4s. 6d. In this work the subject of Conic Sections has been placed before the student in such a form that, it is hoped, after mastering the elements of Euclid, he |