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Todhunter (I.)-continued.

itself, as well as of its most valuable applications. Every attempt has been made to explain those difficulties which usually perplex beginners, especially with reference to the limits of integrations. A new method has been adopted in regard to the transformation of multiple integrals. The last chapter deals with the Calculus of Variations. A large collection of exercises, selected from College Examination Papers, has been appended to the several chapters.

EXAMPLES OF ANALYTICAL GEOMETRY OF THREE DIMENSIONS. Second Edition, revised. Crown 8vo. cloth 4s. A TREATISE ON ANALYTICAL STATICS. With numerous Examples. Third Edition, revised and enlarged. Crown 8vo. cloth. IOS. 6d.

In this work on statics (treating of the laws of the equilibrium of bodies) will be found all the propositions which usually appear in treatises on Theoretical Statics. To the different chapters examples are appended, which have been principally selected from University Examination Papers. In the Third Edition many additions have been made, in order to illus trate the application of the principles of the subject to the solution of problems.

A HISTORY OF THE MATHEMATICAL THEORY OF PROBABILITY, from the time of Pascal to that of Laplace. 18s.

8vo.

The subject of this volume has high claims to consideration on account of the subtle problems which it involves, the valuable contributions to analysis which it has produced, its important practical applications, and the eminence of those who have cultivated it. The subject claims all the interest which illustrious names can confer: nearly every great mathematician within the range of a century and a half comes up in the course of the history. The present work, though principally a history, may claim the title of a comprehensive treatise on the Theory of Probability, for it assumes in the reader only so much knowledge as can be gained from an elementary book on Algebra, and introduces him to almost every process and every species of problem which the literature of the subject can furnish. The author has been careful to reproduce the essential elements of the original

Todhunter (I.)—continued.

works which he has analysed, and to corroborate his statements by exact quotations from the originals, in the languages in which they were published.

RESEARCHES IN THE

CALCULUS OF VARIATIONS, principally on the Theory of Discontinuous Solutions: an Essay to which the Adams Prize was awarded in the University of Cambridge in 1871. 8vo. 6s.

The subject of this Essay was prescribed in the following terms by the Examiners:-"A determination of the circumstances under which discontinuity of any kind presents itself in the solution of a problem of maximum or minimum in the Calculus of Variations, and applications to particular instances. It is expected that the discussion of the instances should be exemplified as far as possible geometrically, and that attention be especially directed to cases of real or supposed failure of the Calculus." The Essay, then, is mainly devoted to the consideration of discontinuous solutions; but incidentally various other questions in the Calculus of Variations are examined and elucidated. The author hopes that he has definitely contributed to the extension and improvement of our knowledge of this ref.ned department of analysis.

Wilson (J. M.)-ELEMENTARY GEOMETRY. Angles,

Parallels, Triangles, Equivalent Figures, the Circle, and Propor-
tion. By J. M. WILSON, M.A., late Fellow of St. John's College,
Cambridge, and Mathematical Master of Rugby School. Second
Edition. Extra fcap. 8vo. 35. 6d.

The distinctive features of this work are intended to be the following. The classification of Theorems according to their subjects; the separation of Theorems and Problems; the use of hypothetical constructions; the adoption of independent proofs where they are possible and simple; the introduction of the terms locus, projection, &c.; the importance given to the notion of direction as the property of a straight line; the intermixing of exercises, classified according to the methods adopted for their solution; the diminution of the number of Theorems; the compression of proofs, especially in the later parts of the book; the tacit, instead of the explicit,

Wilson (J. M.)-continued.

"The methods em

reference to axioms; and the treatment of parallels. ployed have the great merit of suggesting a ready application to the solution of fresh problems."—GUARDIAN.

ELEMENTARY GEOMETRY. PART II. (separately). The Circle and Proportion. By J. M. WILSON, M.A. Extra fcap. 8vo. 2s. 6d. Wilson (W. P.) — A TREATISE ON DYNAMICS.

By

W. P. WILSON, M.A., Fellow of St. John's College, Cambridge, and Professor of Mathematics in Queen's College, Belfast. 8vo. 9s. 6d.

SOLID GEOMETRY AND CONIC SECTIONS.

With Appendices on Transversals and Harmonic Division. For the use of Schools. By J. M. WILSON, M.A. Extra fcap. 8vo. 3s. 6d. This work is an endeavour to introduce into schools some portions of Solid Geometry which are now very little read in England. The first twenty-one Propositions of Euclid's Eleventh Book are usually all the Solid Geometry that a boy reads till he meets with the subject again in the course of his analytical studies. And this is a matter of regret, because this part of Geometry is specially valuable and attractive. In it the attention of the student is strongly called to the subject matter of the reasoning; the geometrical imagination is exercised; the methods employed in it are more ingenious than those in Plane Geometry, and have greater difficulties to meet; and the applications of it in practice are more varied Wolstenholme.-A BOOK OF MATHEMATICAL

PROBLEMS, on Subjects included in the Cambridge Course. By JOSEPH WOLSTENHOLME, Fellow of Christ's College, sometime Fellow of St. John's College, and lately Lecturer in Mathematics at Christ's College. Crown 8vo. cloth. 8s. 6d. CONTENTS:-Geometry (Euclid)—Algebra-Plane TrigonometryGeometrical Conic Sections-Analytical Conic Sections-Theory of Equations-Differential Calculus-Integral Calculus-Solid Geometry-Statics -Elementary Dynamics—Newton—Dynamics of a Point-Dynamics of a Rigid Body-Hydrostatics-Geometrical Optics-Spherical Trigonometry and Plane Astronomy. Judicious, symmetrical, and weli arranged.”— GUARDIAN.

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SCIENCE.

ELEMENTARY CLASS-BOOKS.

THE importance of Science as an element of sound education is now generally acknowledged; and accordingly it is obtaining a prominent place in the ordinary course of school instruction. It is the intention of the Publishers to produce a complete series of Scientific Manuals, affording full and accurate elementary information, conveyed in clear and lucid English. The authors are well known as among the foremost men of their several departments; and their names form a ready guarantee for the high character of the books. Subjoined is a list of those Manuals that have already appeared, with a short account of each. Others are in active preparation; and the whole will constitute a standard series specially adapted to the requirements of beginners, whether for private study or for school instruction.

ASTRONOMY, by the Astronomer Royal.

POPULAR ASTRONOMY. With Illustrations. By G. B. AIRY, Astronomer Royal. Sixth and cheaper Edition. 18mo. cloth. 4s. 6d.

This work consists of six lectures, which are intended “to explain to intelligent persons the principles on which the instruments of an Observatory are constructed (omitting all details, so far as they are merely sub

Elementary Class-Books-continued.

sidiary), and the principles on which the observations made with these instruments are treated for deduction of the distances and weights of the bodies of the Solar System, and of a few stars, omitting all minutiæ of formula, and all troublesome details of calculation." The speciality of this volume is the direct reference of every step to the Observatory, and the full description of the methods and instruments of observation.

ASTRONOMY.

MR. LOCKYER'S ELEMENTARY LESSONS IN ASTRO. NOMY. With Coloured Diagram of the Spectra of the Sun, Stars, and Nebulæ, and numerous Illustrations. By J. NORMAN LOCKYER, F.R.S. Eighth Thousand. 18mo. 5s. 6d. The author has here aimed to give a connected view of the whole subject, and to supply facts, and ideas founded on the facts, to serve as a basis for subsequent study and discussion. The chapters treat of the Stars and Nebule; the Sun; the Solar System; Apparent Movements of the Heavenly Bodies; the Measurement of Time; Light; the Telescope and Spectroscope; Apparent Places of the Heavenly Bodies; the Real Distances and Dimensions; Universal Gravitation. The most recent astronomical discoveries are incorporated. Mr. Lockyer's work supplements that of the Astronomer Royal mentioned in the previous article. "The book is full, clear, sound, and worthy of attention, not only as a popular exposition, but as a scientific 'Index."--ATHENÆUM. "The most fascinating of elementary books

on the Sciences."-NONCONFORMIST.

QUESTIONS ON LOCKYER'S ELEMENTARY LESSONS IN ASTRONOMY. For the use of Schools. By JOHN FORBES. ROBERTSON. 18mo. cloth limp. Is. 6d.

PHYSIOLOGY.

PROFESSOR HUXLEY'S LESSONS IN ELEMENTARY

PHYSIOLOGY. With numerous Illustrations. By T. H. HUXLEY, F.R.S., Professor of Natural History in the Royal School of Mines. Twentieth Thousand. 18mo. cloth. 4s. 6d.

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