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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.

AN ELEMENTARY TREATISE ON CURVE TRACING. B

PERCIVAL FROST, M.A. 8vo. 125.

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.

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. Tos, 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. Svo. 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 endea. voured 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 Godfraycontinued. 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. 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 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 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. 45. 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 :-1. 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 Problems, 1. 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. 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. 25. 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 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. The book being intended chiefly for Schools and Junior Students, the higher parts of Algebra have not been included.

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. New Edition. 4to. 25.

It is the object of this book to make some way in 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.

Newton's PRINCIPIA. Edited by Professor Sir W. THOMSON

and Professor BLACKBURN. 4to. cloth. 315. 6d.

It is a sufficient guarantee of the excellence of this complete edition of Newton's Principia that it has been printed for and under the care of Professor Sir William Thomson and Professor Blackburn, of Glasgow University. The following notice is prefixed :-“ Finding that all the editions of the Principia are now out of print, we have been induced to reprint Newton's last edition [of 1726] without note or comment, only introducing the Corrigenda' of the old copy and correcting typographical errors.The book is of a handsome size, with large type, fine thick paper, and cleanly cut figures, and is the only modern edition containing the whole of Newton's great work. Undoubtedly the finest edition of the text of the 'Principia' which has hitherto appeared.”—EDUCATIONAL TIMES.

Parkinson.-Works by S. PARKINSON, D.D., F.R.S., Fellow and

Tutor of St. John's College, Cambridge.

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