FOR SCHOOLS AND COLLEGES. WORKS by ISAAC TODHUNTER, M.A., F.R.S.-continued. 5. 8. The The Integral Calculus Differential Calculus. And its Applications. With numerous Examples. Second Edition. 342 pp. (1862). Crown 8vo. cloth. 10s. 6d. In writing the present Treatise on the Integral Calculus, the object has been to produce a work at once elementary and complete-adapted for the use of beginners, and sufficient for the wants of advanced students. In the selection of the propositions, and in the mode of establishing them, the author has endeavoured to exhibit fully and clearly the principles of the subject, and to illustrate all their most important results. In order that the student may find in the volume all that he requires, a large collection of Examples for exercise has been appended to the different chapters. With numerous Examples. Third Edition, 398 pp. (1860). Crown 8vo. cloth, 10s. 6d. 5 This work is intended to exhibit a comprehensive view of the Differential Calculus on the method of Limits. In the more elementary portions, explanations have been given in considerable detail, with the hope that a reader who is without the assistance of a tutor may be enabled to acquire a competent acquaintance with the subject. More than one investigation of a theorem has been frequently given, because it is believed that the student derives advantage from viewing the same proposition under different aspects, and that in order to succeed in the examinations which he may have to undergo, he should be prepared for a considerable variety in the order of arranging the several branches of the subject, and for a corresponding variety in the mode of demonstra 6. Analytical Statics. tion. With numerous Examples. Second Edition. 330 pp. (1858). Crown 8vo. cloth. 10s. 6d. 9. Plane Co-Ordinate Geometry In this work will be found all the pro- AS APPLIED TO THE STRAIGHT LINE positions which usually appear in treatises on Theoretical Statics. To the different chapters Examples are appended, which have been selected principally from the University and College Examination Papers; these will furnish ample exercise in the application of the principles of the subject. 7. EXAMPLES OF AND THE CONIC SECTIONS. Crn. 8vo. cl. 326 pp. (1862). 78. 6d. This Treatise exhibits the subject in a simple manner for the benefit of beginners, and at the same time includes in one volume all that students usually require. Analytical Geometry The Examples at the end of each chapter of Three Dimensions. 76 pp. (1858). Crn. 8vo. cloth. 48. A collection of examples in illustration of Analytical Geometry of Three Dimensions has long been required both by students and teachers, and the present work is published with the view of sup will, it is hoped, furnish sufficient exercise, as they have been carefully selected with the view of illustrating the most important points, and have been tested by repeated experience with pupils. In consequence of the demand for the work proving much greater than had been originally anticipated, a large number of copies of the Third Edition has been printed, and a considerable reduction 6 CAMBRIDGE CLASS BOOKS 11. History of the Progress of the Calculus of Variations During the Nineteenth Century. 8vo. cloth. 532 pp. (1861). 12s. It is of importance that those who wish to cultivate any subject may be able to ascertain what results have already been obtained, and thus reserve their strength for difficulties which have not yet been conquered. The Author has endeavoured in this work to ascertain distinctly what has been effected in the Progress of the Calculus, and to form some estimate of the manner in which it has been effected. 12. Algebra for Beginners. 18mo. cloth, 264 pp. (1863). 2s. 6d. Great pains have been taken to render this work intelligible to young students by the use of simple language and by copious explanations. In accordance with the recommendation of teachers, the ples for exercise are very numerous By J. H. PRATT, M.A. Archdeacon of Calcutta, late Fellow of Gonville and Caius College, Cambridge. A Treatise on La Place's Functions, and the Figure of the Earth. Second Edition. Crown 8vo. 126 pp. (1861). Cloth. 68. 6d. In the present Treatise the author has endeavoured to supply the want of a work on a subject of great importance and high interest-La Place's Coefficients and Functions and the calculation of the Figure of the Earth by means of his remarkable analysis. No student of the higher branches of Physical Astronomy should be ignorant of La Place's analysis and its result-“a calculus," says Airy, "the most singular in its nature and the most powerful in its application that has ever appeared." Theory of Errors of And the Combination of Observations. Astronomer Royal. 103 pp. (1861). Crown 8vo. 68. 6d. In order to spare astronomers and observers in natural philosophy the confusion and loss of time which are produced by referring to the ordinary treatises embracing both branches of Probabilities, the author has thought it desirable to draw up this work, relating only to Errors of Observation, and to the rules derivable from the consideration of these Errors, for the Combination of the Results of Observations. The Author has thus also the advantage of entering somewhat more fully into several points of interest to the observer, than can possibly be done in a General Theory of Probabilities. AN ELEMENTARY TREATISE ON The Planetary Theory. WITH A COLLECTION OF PROBLEMS. By C. H. H. CHEYNE, B.A. Scholar of St. John's College, Cambridge. 148 pp. 1862. Crn. 8vo. cloth. bs bd Differential Equations 468 pp. (1859). Crn. 8vo. cloth. 148. The Author has endeavoured in this treatise to convey as complete an account of the present state of knowledge on the subject of Differential Equations as was consistent with the idea of a work intended, primarily, for elementary instruction. The object has been first of all to meet the wants of those who had no previous acquaintance with the subject, and also not quite to disappoint others who might seek for more advanced information. The earlier sections of each chapter contain that kind of matter which has usually been thought suitable for the beginner, while the latter ones are devoted either to an account of recent discovery, or to the discussion of such deeper questions of principle as are likely to present themselves to the reflective student in con By P. G. TAIT, M.A., and W. J. STEELE, B.A. Late Fellows of St. Peter's Coll. Camb. Dynamics of a Particle. With numerous Examples. 304 pp. (1856). Cr. 8vo. cl. 10s. 6d. In this Treatise will be found all the ordinary propositions connected with the Dynamics of Particles which can be conveniently deduced without the use of D'Alembert's Principles. Throughout the book will be found a number of illustrative Examples introduced in the text, and for the most part completely worked out; others, with occasional solutions or hints to assist the student are appended to each Chapter. By the Rev. G. F. CHILDE, M.A. Mathematical Professor in the South African College. nection with the methods and processes Singular Properties of of his previous course. 2. The Calculus of Finite Differences. 248 pp. (1860). Crown 8vo. cloth. 10s. 6d. In this work particular attention has been paid to the connexion of the methods with those of the Differential Calculus-a connexion which in some instances involves far more than a merely formal analogy. The work is in some measure designed as a sequel to the Author's Treatise on Differential Equations, and it has been composed on the same plan. Elementary Statics. By the Rev. GEORGE RAWLINSON, Professor of Applied Sciences, Elphinstone Coll., Bombay. Edited by the Rev. E. STURGES. M.A. Rector of Kencott, Oxfordshire. (150 pp.) 1860. Crn. 8vo. cl. 48. 6d. This work is published under the authority of H. M. Secretary of State for the Ellipsoid And Associated Surfaces of the Nth Degree. 152 pp. (1861). 8vo. boards. 10s. 6d. As the title of this volume indicates, its object is to develope peculiarities in the Ellipsoid; and further, to establish analogous properties in unlimited congeneric series of which this remarkable surface is a constituent. By Rev. S. PARKINSON, B.D. Fellow and Prælector of St. John's Coll. Cambridge. 1. Elementary Treatise on Mechanics. With a Collection of Examples. By R. D. BEASLEY, M.A. Head Master of Grantham School. AN ELEMENTARY TREATISE ON Plane Trigonometry. Second Edition. 345 pp. (1861). 106 pp. (1858), strongly bound in Crown 8vo. cloth. 9s. 6d. The Author has endeavoured to render the present volume suitable as a Manual for the junior classes in Universities and the higher classes in Schools. With this object there have been included in it those portions of theoretical Mechanics which can be conveniently investigated without the Differential Calculus, and with one or two short exceptions the student is not presumed to require a knowledge of any branches of Mathematics beyond the elements of Algebra, Geometry, and Trigonometry. A collection of Problems and Examples has been added, chiefly taken from the Senate-House and College Examination Papers-which will be found useful as an exercise for the student. In the Second Edition several additional propositions have been incorporated in the work for the purpose of rendering it more complete, and the Collection of Examples and Problems has been largely increased. 2. A Treatise on Optics 304 pp. (1859). Crown 8vo. 10s. 6d. A collection of Examples and Problems has been appended to this work which are sufficiently numerous and varied in character to afford useful exercise for the student: for the greater part of them recourse has been had to the Examination Papers set in the University and the several Colleges during the last twenty years. Subjoined to the copious Table of Contents the author has ventured to indicate elementary course of reading not unable for the requirements of the First Days in the Cambridge Senate → Examinations. cloth. 3s. 6d. This Treatise is specially intended for use in Schools. The choice of matter has been chiefly guided by the requirements of the three days' Examination at Cambridge, with the exception of proportional parts in logarithms, which have been omitted. About Four hundred Examples have been added, mainly collected from the Examination Papers of the last ten years, and great pains have been taken to exclude from the body of the work any which might dishearten a beginner by their difficulty. By J. BROOK SMITH, M.A. St. John's College, Cambridge. Arithmetic in Theory and Practice. For Advanced Pupils. PART I. Crown 8vo. cloth. 38. 6d. This work forms the first part of a Treatise on Arithmetic, in which the Author has endeavoured, from very simple principles, to explain in a full and satisfactory manner all the important processes in that subject. The proofs have in all cases been given in a form entirely arithmetical: for the author does not think that recourse ought to be had to Algebra until the arithmetical proof has become hopelessly long and perplexing. At the end of every chapter several examples have been worked out at length, in which the best practical methods of operation have been carefully pointed ont FOR SCHOOLS AND COLLEGES. By G. H. PUCKLE, M.A. Conic Sections and Algebraic Geometry. With numerous Easy Examples Progressively arranged. Second Edition. 264 pp. (1856). Crown 8vo. 78. 6d. This book has been written with special reference to those difficulties and misapprehensions which commonly beset the student when he commences. With this object in view, the earlier part of the subject has been dwelt on at length, and geometrical and numerical illustrations of the analysis have been introduced. The Examples appended to each section are mostly of an elementary description. The work will, it is hoped, be found to contain all that is required by the upper classes of schools and by the generality of students at the Universities. CONTENTS: Chap. I. Of Moments of Inertia.—II. D'Alembert's Principle. III. Motion about a Fixed Axis.-IV. Motion in Two Dimensions.-V. Motion of a Rigid Body in Three Dimensions.VI. Motion of a Flexible String.-VII. Motion of a System of Rigid Bodies.VIII. Of Impulsive Forces.-IX. Miscellaneous Examples. The numerous Examples which will be found at the end of each chapter have been chiefly selected from the Examination Papers set in the University and Colleges of Cambridge during the last few The Cambridge Year Book AND UNIVERSITY ALMANACK Crown 8vo. 228 pp. price 2s. 6d. The specific features of this annual publication will be obvious at a glance, and its value to teachers engaged in preparing students for, and to parents who are sending their sons to, the University, and to the public generally, will be clear. 1. The whole mode of proceeding in entering a student at the University and at any particular College is stated. 2. The course of the studies as regulated by the University examinations, the manner of these examinations, and the specific subjects and times for the year 1863, are given. 3. A complete account of all Scholarships and Exhibitions at the several Colleges, their value, and the means by which they are gained. 4. A brief summary of all Graces of the Senate, Degrees conferred during the year 1861, and University news generally are given. 5. The Regulations for the LOCAL EXAMINATION of those who are not members of the University, to be held this year, with the names of the books on which the Examination will be based, and the date on which the Examination will be held. By N. M. FERRERS, M.A. Fellow and Mathematical Lecturer of Gonville and Caius College, Cambridge. AN ELEMENTARY TREATISE ON Trilinear Co-Ordinates The Method of Reciprocal Polars, and the Theory of Projections. 154 pp. (1861). Cr. 8vo. cl. 6s. 6d. The object of the Author in writing on this subject has mainly been to place it on a basis altogether independent of ordinary Cartesian System, instead of garding it as only a special form of e Notation. A short chapter on 1 |