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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



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TIONS. An Essay towards an entirely New Method of Inte-
grating 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

Containing Problems with help for Solutions. By J. H. EDGAR,
M.A., Lecturer on Mechanical Drawing at the Royal School of
Mines, and G. S. PRITCHARD, late Master for Descriptive
Geometry, Royal Military Academy, Woolwich. Second Edition,
revised and enlarged. Globe 8vo. 3s.

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 th 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.


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 use. 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.


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. 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


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. 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.


tary Treatise in which the Conic Sections are defined as the Plane
Sections of a Cone, and treated by the Method of Projection.
By J. STUART JACKSON, M. A., late Fellow of Gonville and Caius
College, Cambridge. 4s. 6d.

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

they have their name as plane sections of a cone. This method is calculated to produce a material simplification in these curves, and to make the proof of their properties more easily understood and remembered. It is also a powerful instrument in the solution of a large class of problems relating to these curves.

Jellet (John H.)—A TREATISE ON THE THEORY OF FRICTION. By JOHN H. JELLET, B.D., Senior Fellow of Trinity College, Dublin; President of the Royal Irish Academy. 8vo. 8s. 6d.

The theory of friction is as truly a part of Rational Mechanics as the theory of gravitation. This book is taken up with a special investigation of the laws of friction; and some of the principles contained in it are believed to be here enunciated for the first time. The work consists of eight Chapters as follows:—I. Definitions and Principles. II. Equilibrium with Friction. III. Extreme Positions of Equilibrium. IV. Movement of a Particle or System of Particles. V. Motion of a Solid Body. VI. Necessary and Possible Equilibrium. VII. Determination of the Actual Value of the Acting Force of Friction. VIII. Miscellaneous Problems1. Problem of the Top. 2. Friction Wheels and Locomotives. 3. Questions for Exercise. "The work is one of great research, and will add much to the already great reputation of its author.”—SCOTSMAN.

Jones and Cheyne.-ALGEBRAICAL EXERCISES. Progressively arranged. By the Rev. C. A. JONES, M.A., and C. H. CHEYNE, M.A., F.R. A.S., Mathematical Masters of Westminster School. New Edition. 18mo. cloth. 2s. 6d.

This little book is intended to meet a difficulty which is probably felt more or less by all engaged in teaching Algebra to beginners. It is, that while new ideas are being acquired, old ones are forgotten. In the belief that constant practice is the only remedy for this, the present series of miscel laneous exercises has been prepared. Their peculiarity consists in this, that though miscellaneous they are yet progressive, and may be used by the pupil almost from the commencement of his studies. The book being intended chiefly for Schools and Junior Students, the higher parts of Algebra have not been included.

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