A COLLECTION OF PROBLEMS IN ILLUSTRATION OF THE PRINCIPLES OF THEORETICAL MECHANICS BY WILLIAM WALTON, M.A. FELLOW AND ASSISTANT TUTOR OF TRINITY HALL, "Examples give a quicker impression than arguments."-BACON. THIRD EDITION. CAMBRIDGE: DEIGHTON, BELL AND CO. LONDON: G. BELL AND SONS. 1876. PREFACE TO THE FIRST EDITION. THE design of this Work is to facilitate the study of Theoretical Mechanics, by presenting to the student a systematic collection of problems in illustration of the more important principles of the science. The want of any such treatise, it is believed, has been felt by many as a serious impediment to the acquisition of adequate ideas in this branch of mathematical philosophy. Much importance, it may be observed, was attached by the great discoverers of the mechanical theories to the full discussion of numerous problems, as will be evident from a reference to the works of the three Bernoullis, of Leibnitz, and of D'Alembert, and to the beautiful investigations scattered throughout so long a series of volumes of the St. Petersburgh Transactions by the liberal hand of Euler. The author of this volume has endeavoured, as much as possible, to direct the attention of the student to the original memoirs of which he has so largely availed himself. This he has done, partly, to enable the beginner to obtain more detailed information than is compatible with the nature of this work, on particular questions which may excite an interest in his mind: his chief object, however, has been, to offer every facility to those, who have already overcome at least the elementary difficulties of the subject, for acquiring a practical familiarity with the historical development of the science. Although it be admitted that useful and exact knowledge may be obtained from even an exclusive perusal of the concise and methodical treatises which are generally adopted for the purpose of academic instruction; yet it may be asserted with confidence, that an excessive adherence to such a system b W. S. 44381 of study, must deprive the student of much delightful and most valuable information. In regard to the mode in which the author of this treatise has completed the task which he has proposed to himself, he feels every degree of diffidence, and would willingly that it had been undertaken by an abler hand. In apology for the imperfections, of which either he is himself aware or which may have eluded his observation, he can plead only the fact of engrossing occupations, or of perhaps insufficient preparation for a work requiring greater research than was originally contemplated. Many of the problems in this volume have been extracted, with appropriate modifications, from the Ancient Transactions of the various Academies and learned Societies of Europe; many have been selected from the Cambridge Senate-House Papers; and for not a few the author is under obligation to the contributions of his friends. In arriving at original sources of information, it is scarcely necessary to state that great assistance has been obtained from the historical matter of Lagrange's Mécanique Analytique, and from Montucla's Histoire des Mathématiques. CAMBRIDGE, October, 1842. PREFACE TO THE SECOND EDITION. IN preparing for the press a Second Edition of this Treatise, the author has adhered to the general design of the First Edition; he has, however, effected numerous alterations and corrections, many of which are due to the kind suggestions of readers of the work; he has also considerably augmented the matter of those chapters which in the former edition appeared to be inadequately supplied with problems. Certain entirely new chapters have also been written; one on the Attractions of Solid Bodies, two on Miscellaneous Problems, and one on Live Things. CAMBRIDGE, September 8, 1855, PREFACE TO THE THIRD EDITION. IN the Third Edition of the Mechanical Problems the whole Work has been carefully revised, and all errors, which have been pointed out to the author or detected by himself, have been corrected. Some of the matter of the last edition has been cancelled, and the Treatise has been enriched by the addition of a considerable number of new problems, taken principally, when not assigned to their authors, from the examination papers proposed in the various Colleges of the University of Cambridge, in the Senate-House for the Mathematical Tripos, and to the candidates for the Smith's Prizes. Several additional classes of Problems, in illustration of various Theorems, might have been introduced into the Work with advantage: the bulk of the Book would however have been thereby increased beyond the limits within which it would seem expedient to confine it. TRINITY HALL, CAMBRIDGE, January 15, 1876. |