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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 Cam

bridge 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 refined department of analysis.

35. 6d.

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

Parallels, Triangles, Equivalent Figures, the Circle, and Proportion. By J. M. Wilson, M.A., late Fellow of St. John's College, Cambridge, and Mathematical Master of Rugby School. Second

Edition. Extra fcap. Svo. 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.
reference to axioms; and the treatment of parallels.

" The methods enz. 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. Svo.

9s. 6d.

SOLID GEOMETRY AND CONIC SECTIONS. With Appen

dices on Transversals and Harmonic Division. For the use of

Schools. By J. M. Wilson, M.A. Extra fcap. 8vo. 35. 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 varieds 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 Mathe

matics at Christ's College. Crown 8vo. cloth. 8s. 6d. CONTENTS:— Geometry (Euclid) --AlgebraPlane TrigonometryGeometrical Conic SectionsAnalytical Conic Sections— Theory of Equa. tionsDifferential CalculusIntegral Calculus-Solid Geometry-Statics

- Elementary Dynamics— Newton-Dynamics of a Point-Dynamics of a Rigid Body-HydrostaticsGeometrical OpticsSpherical Trigonometry and Plane Astronomy. Judicious, symmetrical, and weli arranged."GUARDIAN.

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. 45. 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 minutice 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 viescription 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. 55. 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 Nebulie; 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.

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QUESTIONS ON LOCKYER'S ELEMENTARY LESSONS

IN ASTRONOMY. For the use of Schools. By JOHN FORBES.
ROBERTSON. 18mo. cloth limp. Is. 6d.

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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. 45. 6d.

Elementary Class-Books-continued.

This book describes and explains, in a series of graduated lessons, the principles of Human Physiology ; or the Structure and Functions of the Human Body. The first lesson supplies a general view of the subject. This is followed by sections on the Vascular or Venous System, and the Circulation ; the Blood and the Lymph; Respiration ; Sources of Loss and of Gain to the Blood; the Function of Alimentation ; Motion and Locomotion ; Sensations and Sensory Organs; the Organ of Sight ; the Coalescence of Sensations with one another and with other States of Con. sciousness; the Nervous System and Innervation ; Histology, or the Alinute Structure of the Tissues. A Table of Anatomical and Physiological Constants is appended. The lessons are fully illustrated by numerous engravings. Pure gold throughout.GUARDIAN. questionably the clearest and most complete elementary treatise on this subject that we possess in any language.”-WESTMINSTER REVIEW.

66 Un

QUESTIONS ON HUXLEY'S PHYSIOLOGY FOR SCHOOLS. By T. ALCOCK, M.D. 18mo.

IS, 6d. These Questions were drawn up as aids to the instruction of a class of young people in Physiology.

BOTANY.

PROFESSOR OLIVER'S LESSONS IN ELEMENTARY
BOTANY. With nearly Two Hundred Illustrations. 'Twelfth

Thousand. 18mo. cloth. 45. 6d. This book is designed to teach the Elements of Botany on Professor Henslow's plan of selected Types and by the use of Schedules. The earlier chapters, embracing the elements of Structural and Physiological Botany, introduce us to the methodical study of the Ordinal Types. The concluding chapters are entitled, How to dry Plantsand How to describe Plants.A valuable Glossary is appended to the volume. In the preparation of this work free use has been made of the manuscript materials of the late Professor Henslow.

D

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