THE MATHEMATICAL PRINCIPLES OF MECHANICAL PHILOSOPHY, AND THEIR APPLICATION TO THE THEORY OF UNIVERSAL GRAVITATION. BY JOHN HENRY PRATT, M.A. FELLOW OF GONVILLE AND CAIUS COLLEGE, AND OF CAMBRIDGE; PRINTED BY JOHN W. PARKER, UNIVERSITY PRINTER. AND JOHN W. PARKER, WEST STRAND, LONDON. M.DCCC.XXXVI. PREFACE. A LEADING object that I have had in view in preparing the present Treatise has been to gather into one uniform system the principles of mechanical science, beginning with the most elementary and ascending to the most general. In attempting to accomplish this I have collected the fundamental principles into separate Chapters, and placed after them Chapters of application of these principles to the demonstration of others of a second class, and have then added collections of problems and, in some instances, hints to guide to their solution. An attachment, and that in most respects a laudable attachment, to the geometry of the Principia had, till of late years, led to the practice of retaining in our course of University reading some parts of that immortal work, rather for the beauty and elegance of its demonstrations, than for the importance of the 'theorems demonstrated. But this practice has been gradually sinking into disuse, a result which we owe to Professor Woodhouse's Physical Astronomy, to M. Poisson's Traité de Mécanique, which has been extensively used amongst us, and very largely to Mr Whewell's Treatises on Statics and Dynamics and a |