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Drew-continued. in such a form that, it is hoped, after mastering the elements of Euclid, he 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 Svo, cloth. 45. Od.

Earnshaw (S.) — PARTIAL DIFFERENTIAL EQUA

TIONS. 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 orily. The author's object is merely to render his method thoroughly intclligible. The various steps of the investigation are all obedient to on? 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 whieh 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.
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. 35.

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 cach sufficient attention. i 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 01, arranged in progressive sections. The new edition has been enlarged by the adilition 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 the 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.--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., late Fellow of St. John's College,
Mathematical Lecturer of King's College, Cambridge. Second

Edition. 8vo. cloth. 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.

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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.

125. 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. 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.'

" It is a

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. 55. 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 accour:t 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. gs. 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 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. 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. This method is calculated to produce a material simplification in the treatment of those curves, and to make the proof of their properties more easily understood in the first instance, and certainly more easily remembered. It is also a powerful instrument in the solution of a large class of problems relating to these curves. When the Method of Projections is adinitted into the treatment of the Conic Sections, there are many reasons why they should be des fined, not as has been the case of late years 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. Among other considerations, it is of some importance that we can see at once from the form of the cone the general form of the curves that may be cut from it by a plane in different positions ; and by turning the plane about a certain line, we see how the curves pass from one into another.

25. 6d.

Jones and Cheyne.-ALGEBRAICAL EXERCISES. Pro

gressively 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. 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 miscellaneous 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. They are not intended to supersede the systematically arranged examples to be found in ordinary treatises on Algebra, but rather to supplement them. The book being intended chiefly for Schools and Junior Students, the higher parts of Algebra have not been included.

2s.

Kitchener.-A GEOMETRICAL NOTE-BOOK, containing

Easy Problems in Geometrical Drawing preparatory to the Study of Geometry. For the Use of Schools. By F. E. KITCHENER,

M.A., Mathematical Master at Rugby. 4to. It is the object of this book to make some way:il overcoming the difficulties of Geometrical conception, before the mind is called to the attack of Geometrical theorems. A few simple methods of construction are given ; and space is left on each page, in order that the learner may draw in the figures.

Morgan.-A COLLECTION OF PROBLEMS AND EXAM.

PLES IN MATHEMATICS. With Answers. By H. A.
MORGAN, M.A., Sadlerian and Mathematical Lecturer of Jesus

College, Cambridge. Crown 8vo. cloth. 6s. 6d. This book contains a number of problems, chiefly elementary, in the Mathematical subjects usually read at Cambridge. They have been selected from the papers set during late years at Jesus College. Very few of them are to be met with in other collections, and by far the larger number are due to some of the most distinguished Mathematicians in the University.

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