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. appended. Answers to the Examples are Day.- PROPERTIES OF CONIC GEOMETRICALLY. SECTIONS PROVED PART I., THE ELLIPSE, with Problems. By the Rev. H. G. DAY, M.A., Head Master of 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 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 Drew-continued. may find it an easy and interesting continuation of his geometrical studies. With a view, also, of rendering the work a complete manual of what is required at the Universities, there have either been embodied into the text or inserted among the examples, every book-work question, problem, and rider, which has been proposed in the Cambridge examinations up to the present time. SOLUTIONS TO THE PROBLEMS IN DREW'S CONIC SECTIONS. Crown 8vo. cloth. 4s. 6d. Earnshaw (S.) PARTIAL DIFFERENTIAL EQUATIONS. An Essay towards an entirely New Method of Integrating them. By S. EARNSHAW, M.A., St. John's College, Cambridge. Crown 8vo. 5s. The peculiarity of the system expounded in this work is, that in every equation, whatever be the number of original independent variables, the work of integration is at once reduced to the use of one independent variable only. The author's object is merely to render his method thoroughly intelligible. The various steps of the investigation are all obedient to one general principle, and though in some degree novel, are not really difficult, but on the contrary easy when the eye has become accustomed to the novelties of the notation. Many of the results of the integrations are far more general than they were in the shape in which they have appeared in former treatises, and many Equations will be found in this Essay integrated with ease in finite terms which were never so integrated before. Edgar (J. H.) and Pritchard (G. S.)-NOTE-BOOK ON PRACTICAL SOLID OR DESCRIPTIVE GEOMETRY. In teaching a large class, if the method of lecturing and demonstrating from the black board only is pursued, the more intelligent students have generally to be kept back, from the necessity of frequent repetition, for the sake of the less promising; if the plan of setting problems to each pupil is adopted, the teacher finds a difficulty in giving to each sufficient attention. 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 calculations 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. PERCIVAL FROST, M.A. Second Edition. 8vo. cloth. By 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. 18s. 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 Godfray-continued. advanced pupils in many of our schools. The author's aim has been to convey clear and distinct ideas of the celestial phenomena. "It is a working book," says the GUARDIAN, “taking Astronomy in its proper place in mathematical sciences. It is a book which is not likely to be got up unintelligently." ... AN ELEMENTARY TREATISE ON THE LUNAR THEORY, with a Brief Sketch of the Problem up to the time of Newton. Second Edition, revised. Crown 8vo. cloth. 5s. 6d. These pages will, it is hoped, form an introduction to more recondite works. Difficulties have been discussed at considerable length. The selection of the method followed with regard to analytical solutions, which is the same as that of Airy, Herschel, &c. was made on account of its simplicity; it is, moreover, the method which has obtained in the University of Cambridge. "As an elementary treatise and introduction to the subject, we think it may justly claim to supersede all former ones. LONDON, EDIN. AND DUBLIN PHIL. MAGAZINE. Hemming.-AN ELEMENTARY TREATISE ON THE DIFFERENTIAL AND INTEGRAL CALCULUS, for the Use of Colleges and Schools. By G. W. HEMMING, M.A., Fellow of St. John's College, Cambridge. Second Edition, with Corrections and Additions. 8vo. cloth. 25. "There is no book in common use from which so clear and exact a knowledge of the principles of the Calculus can be so readily obtained."LITERARY GAZETTE. Jackson.-GEOMETRICAL CONIC SECTIONS. An Elemen tary Treatise in which the Conic Sections are defined as the Plane This work has been written with a view to give the student the benefit of the Method of Projections as applied to the Ellipse and Hyperbola. When this Method is admitted into the treatment of the Conic Sections, there are many reasons why they should be defined, not with reference to the focus and direction, but according to the original definition from which |