Excerpt from The Dynamics of Particles and of Rigid, Elastic, and Fluid Bodies: Being Lectures on Mathematical Physics The work divides itself naturally into three parts, the first of which considers the Laws of Motion in general and those methods which are applicable to systems of all sorts. Although not addressed to students who are beginning Mechanics, it seemed necessary to begin at the beginning, and to explain the exhibition of Newton's Laws of Motion in mathematical form. For this purpose the Principle of Hamilton is of so universal application that it has been introduced near the beginning, and considerable attention devoted to it. I consider this principle, together with the equations of Lagrange, a very practical subject, of the highest importance for the physical student. The same may be said of the subject of Energy, upon which it has even been attempted to found the laws of Physics. Although such attempts seem doomed to fail, for the reason that the principle of Energy, though affording an integral, is insufficient to deduce the differential equations, the notion of Energy must remain one of the most important in Dynamics, and is therefore considered in every problem. The subject of Oscillations, of very great physical interest, with its accompanying phenomena of Resonance, is next taken up. After this follows a treatment of the so-called Cyclic Systems, from which, since the labors of Helmholtz and Hertz, it seems that Physics has so much to expect. In fact the first steps have been taken to explain the nature of Potential Energy by means of Motion, perhaps the chief desideratum of Physics. In this connection we way again point to the epochmaking work of Lord Kelvin, both in Mechanics and in the Theory of Light. The second part is devoted to the Motion of Rigid Bodies, particularly to their rotation, a matter of the greatest importance practically, especially to the engineer, but one which is often avoided by the physical student. To this subject Maxwell again called the attention of physicists, and created a charming instrumental demonstration in his celebrated Dynamical Top. To this the writer has ventured to add a small detail, which permits of a number of interesting additional verifications. A number of practical illustrations, of interest to the physicist and engineer, are also included. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.