ELEMENTARY INTRODUCTION ΤΟ PRACTICAL MECHANICS. ILLUSTRATED BY NUMEROUS EXAMPLES. BEING THE SECOND EDITION OF ELEMENTARY EXAMPLES IN PRACTICAL MECHANICS.' BY THE REV. JOHN F. TWISDEN, M.A. PROFESSOR OF MATHEMATICS IN THE STAFF COLLEGE. LONDON: LONGMAN, GREEN, LONGMAN, ROBERTS, & GREEN. PREFACE. THE following Treatise is designed to be an Introduction to the science of Applied Mechanics: in this it differs from all the elementary works commonly in use, which are introductory to Rational Mechanics. How great a difference is caused by this circumstance will appear from an inspection of the Contents; it may, however, be mentioned that, at the least, one half of the present work has no counterpart in any Elementary Treatise that has fallen under the author's notice: that so great a divergence from the usual type should be possible seems sufficient reason for believing that something is wanting in the ordinary works, but how far the present will supply that want is, of course, another question. It was originally intended to be a book of examples, and a supplement to others already in existence; it was, however, soon found that by a few additions it could be made independent, and it was thought that what was gained in point of convenience by completeness, would more than compensate a small increase of size and cost. The work is intended to comprise two courses; the first is contained in Chapter I., the first section of Chapter II. and Chapter III. of Part I. and in Chapter I. of Part II.; the second forms the remainder of the book. The first course may be read by any one who understands arithmetic, a little algebra, practical geometry, and the rules of mensuration; in many of the examples it is intended that a geometrical construction should take the place of calculation: instances of the use of construction are given in Examples 177, 209, &c. In this course the principles of the science are merely stated, their formal demonstration being reserved to the second course; in other words, the order most convenient for teaching and learning has been followed at some sacrifice of the systematic development of the subject. The second course presupposes that the reader is acquainted with Euclid, algebra, and trigonometry, as commonly taught in schools; a very few examples are inserted which require some acquaintance with co-ordinate geometry and the differential calculus ;* the reason for their insertion will generally be obvious from the context in which they occur. Frequent use has been made of simple geometrical limits; they will probably present but little difficulty to the reader; some remarks on the subject of limits will be found in the Appendix. Very many examples require numerical answers; it is hoped that but few of the arithmetical operations will prove laborious to any one who possesses a proper facility in manipulating numbers, and it must be remembered that few things are more important to a learner in the earlier stages of his progress than that he should be continually referred to the numerical results that follow from the formulæ he investigates. Hints and explanations have been freely given in connection with the more difficult * Most of these examples are contained in Chap. IX. Part I.; the others are distinguished by an asterisk. |