Oli-22-21 Jan PREFACE. | THE present work is constructed on the same plan as the author's Algebra for Beginners and Trigonometry for Beginners; and is intended as a companion to them. It is divided into short Chapters, and a collection of Examples follows each Chapter. Some of these examples are original, and others have been selected from College and University Examination papers. The work forms an elementary treatise on demonstrative mechanics. It may be true that this part of mixed mathematics has been sometimes made too abstract and speculative; but it can hardly be doubted that a nowledge of the elements at least of the theory of the subject is extremely valuable even for those who are 1. mainly concerned with practical results. The author has accordingly endeavoured to provide a suitable introduction to the study of applied as well as of theoretical Mechanics. The demonstrations will, it is hoped, be found simple and convincing. Great care has been taken to arrange them so as to assume the smallest possible knowledge of pure mathematics, and to furnish the clearest illusNtration of mechanical principles. At the same time there has been no sacrifice of exactness; so that the beginner may here obtain a solid foundation for his future studies : afterwards he will only have to increase his knowledge without rejecting what he originally acquired. The ex perience of teachers shews that it is especially necessary to guard against the introduction of erroneous notions at the commencement of the study of Mechanics. The work consists of two parts, namely, Statics and Dynamics. It will be found to contain all that is usually comprised in elementary treatises on Mechanics, together with some additions. Thus, for example, an investigation has been given of the time of oscillation of a simple pendulum. The more important cases of central forces are also discussed ; partly because they are explicitly required in some examinations, and partly because by the mode of discussion which is adopted they supply valuable exemplifications of fundamental mechanical theorems. It would be easy to give in the same manner the other cases of central forces which are contained in the first three sections of Newton's Principia. As the Chapters of the work are to a great extent independent of each other, it will be possible to vary the order of study at the discretion of the teacher. The Dynamics may with advantage be commenced before the whole of the Statics has been mastered. Any remarks on the work, and especially the indication of difficulties or omissions, will be most thankfully received. I. TODHUNTER. CAMBRIDGE, July 1867. CORRECTIONS. Page 29, Example 11. For throughout the points read through the point. CONTENTS. PAGS I. Introduction ............... 111. Forces in one plane acting on a particle ......... IV. Resultant of two Parallel Forces ... VI. Forces in one Plane ................ VII. Constrained Body .................. VIII. Centre of Parallel Forces............ IX. Centre of Gravity ............. X. Properties of the Centre of Gravity .......... XIII. The Wheel and Axle. The Toothed Wheel .... XIV. The Pully ................ XV. The Inclined Plane ............... .............. XVI. The Wedge. The Screw .......... .............. XVII. Compound Machines.......... II. The First and Second Laws of Motion ............ 210 III. Motion in a straight line under the influence of a uniform force.................. ............ IV. Motion in a straight line under the influence of a ' uniform force, with given initial velocity.....228 V. Second Law of Motion. Motion, under the in. fluence of a uniform force in a fixed direc- tion, but not in a straight line. Projectiles .. 235 VI. Projectiles continued ............ ............. 248 VII. Mags ....................................... VIII. Third Law of Motion ......... IX. The Direct Collision of Bodies ........................ X. The Oblique Collision of Bodies .. XI. Motion of the Centre of Gravity of two or more XII. Laws of Motion. General Remarks ............... XIII. Motion down a Smooth Curve ................. 304 XIV. Uniform motion in a Circle............. |