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. 12s.

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.

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

and scholarly edition of a work which till now has been beset with hindrances and difficulties, but which Mr. Febb's critical skill and judgment have at length placed within the grasp and comprehension of ordinary readers."

Thring.-Works by the Rev. E. THRING, M.A., Head Master of Uppingham School.

A LATIN GRADUAL. A First Latin Construing Book for Beginners. New Edition, enlarged, with Coloured Sentence Maps. Fcap. 8vo. 2s. 6d.

These

The Head Master of Uppingham has here sought to supply by easy steps a knowledge of grammar, combined with a good Vocabulary. Passages have been selected from the best Latin authors in prose and verse. passages are gradually built up in their grammatical structure, and finally printed in full. A short practical manual of common mood constructions, with their English equivalents, forms a second part. To the New Edition a circle of grammatical Constructions with a Glossary has been added; as also some coloured Sentence Maps, by means of which the different parts of a sentence can easily be distinguished, and the practice of dissecting phrases carried out with the greatest benefit to the student.

A MANUAL OF MOOD CONSTRUCTIONS. Fcap. 8vo. Is. 6d. Treats of the ordinary mood constructions, as found in the Latin, Greek, and English languages. The EDUCATIONAL TIMES thinks it "very well suited to young students."

A CONSTRUING BOOK. Fcap. 8vo.

2s. 6d.

Thucydides.-THE SICILIAN EXPEDITION. Being Books VI. and VII. of Thucydides, with Notes. A New Edition, revised and enlarged, with a Map. By the Rev. PERCIVAL FROST, M.A., late Fellow of St. John's College, Cambridge. Fcap. 8vo. 5s. This edition is mainly a grammatical one. Attention is called to the force of compound verbs, and the exact meaning of the various tenses employed. "The notes are excellent of their kind. Mr. Frost seldom passes over a difficulty, and what he says is always to the point."EDUCATIONAL TIMES.

Virgil.-THE WORKS OF VIRGIL RENDERED INTO ENGLISH PROSE, with Notes, Introductions, Running Analysis, and an Index, by JAMES LONSDALE, M.A. and SAMUEL LEE, M.A.

Second Edition. Globe 8vo. 3s. 6d.; gilt edges, 45. 62.

The original has been faithfully rendered, and paraphrase altogether avoided. At the same time, the translators have endeavoured to adapt the book to the use of the English reader. Some amount of rhythm in the structure of the sentence has been generally maintained; and, when in the Latin the sound of the words is an echo to the sense (as so frequently happens in Virgil), an attempt has been made to produce the same result in English. The general introduction contains whatever is known of the poet's life, an estimate of his genius, an account of the principal editions and translations of his works, and a brief view of the influence he has had on modern poets; special introductory essays are prefixed to the "Eclogues," Georgics," and "Eneid." The text is divided into sections, each of which is headed by a concise analysis of the subject; the Index contains references to all the characters and events of any importance. A more complete edition of Virgil in English it is scarcely possible to conceive than the scholarly work before us.”—GLOBE.

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Wright.-Works by J. WRIGHT, M.A., late Head Master of Sutton Coldfield School.

HELLENICA; OR, A HISTORY OF GREECE IN GREEK, as
related by Diodorus and Thucydides; being a First Greek Reading
Book, with explanatory Notes, Critical and Historical.
Edition, with a Vocabulary. 12mo.

3s. 6d.

Third

In the last twenty chapters of this volume, Thucydides sketches the rise and progress of the Athenian Empire in so clear a style and in such simple language, that the editor has doubts whether any easier or more instructive passages can be selected for the use of the pupil who is commencing Greek. This book includes a chronological table of the events recorded. The GUARDIAN speaks of the work as a good plan well executed."

A HELP TO LATIN GRAMMAR; or, The Form and Use of Words in Latin, with Progressive Exercises. Crown 8vo. 4s. 6d.

This book is not intended as a rival to any of the excellent Grammars now in use; but as a help to enable the beginner to understand them.

THE SEVEN KINGS OF ROME. An Easy Narrative, abridged from the First Book of Livy by the omission of Difficult Passages; being a First Latin Reading Book, with Grammatical Notes. Fifth Edition. Fcap. 8vo. 35. With Vocabulary, 3s. 6d.

Wright-continued.

This work is intended to supply the pupil with an easy construing book, which may at the same time be made the vehicle for instructing him in the rules of grammar and principles of composition. The notes profess to

teach what is commonly taught in grammars. It is conceived that the pupil will learn the rules of construction of the language much more easily from separate examples, which are pointed out to him in the course of his reading, and which he may himself set down in his note-book after some scheme of his own, than from a heap of quotations amassed for him by others." The Notes are abundant, explicit, and full of such grammatical and other information as boys require."-ATHENÆUM. "This is really," the MORNING POST says, "what its title imports, and we believe that its general introduction into Grammar Schools would not only facilitate the progress of the boys beginning to learn Latin, but also relieve the Masters from a very considerable amount of irksome labour a really valuable addition to our school libraries."

....

FIRST LATIN STEPS; OR, AN INTRODUCTION BY A SERIES OF EXAMPLES TO THE STUDY OF THE LATIN LANGUAGE. Crown 8vo. 5s.

-I.

The following points in the plan of the work may be noted :The pupil has to deal with only one construction at a time. 2. This construction is made clear to him by an accumulation of instances. 3. As all the constructions are classified as they occur, the construction in each sentence can be easily referred to its class. 4. As the author thinks the pupil ought to be thoroughly familiarized, by a repetition of instances, with a construction in a foreign language, before he attempts himself to render it in that language, the present volume contains only Latin sentences. 5. The author has added to the Rules on Prosody in the last chapter, a few familiar lines from Ovid's Fasti by way of illustration. In a brief Introduction the author states the rationale of the principal points of Latin Grammar. Copious Notes are appended, to which reference is made in the text. From the clear and rational method adopted in the arrangement of this elementary work, from the simple way in which the various rules are conveyed, and from the abundance of examples given, both teachers and pupils will find it a valuable help to the learning of Latin.