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THE

MATHEMATICAL PRINCIPLES

OF

MECHANICAL PHILOSOPHY,

AND THEIR APPLICATION TO

THE THEORY

OF

UNIVERSAL GRAVITATION.

BY

JOHN HENRY PRATT, M.A. 1809-1871

FELLOW OF GONVILLE AND CAIUS COLLEGE, AND OF
THE CAMBRIDGE PHILOSOPHICAL SOCIETY.

CAMBRIDGE;

PRINTED BY JOHN W. PARKER, UNIVERSITY PRINTER.

PUBLISHED BY J. & J. J. DEIGHTON, CAMBRIDGE;
J. H. PARKER, OXFORD; MILLIKEN AND Co., DUBLIN;
MACLACHLAN & STEWART, EDINBURGH;

AND

JOHN W. PARKER, WEST STRAŃD, LONDON.

M.DCCC.XXXVI.

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10-1-26.FW?

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

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PREFACE.

Mr Airy's Mathematical Tracts. But notwithstanding the great and happy changes thus brought about we still cling to the old methods, not as a whole, but just so far as to derange our system and give to it the ambiguous character of being neither strictly geometrical, nor strictly analytical. But I wish not to be misunderstood; I mean not to imply that geometry should be discarded and banished from our academical course of study; far from it; for the analyst will find his analysis of little benefit if he have not the power of gathering from his formulæ geometrical conceptions. Neither would I have it for a moment conceived, that I would in the least degree repudiate the profound veneration, which is so justly due even to the letter of of the Principia: my own admiration of the clearness and conciseness of its demonstrations rather induces me to invite others to participate of the pleasures they may enjoy from its attentive and diligent study. But this I desire, that we should pay more regard to system than we hitherto have done; if our course is to be geometrical let us adhere to geometry, if analytical to analysis; if we are to admit both (the preferable course) let us keep our systems well apart, and not have our course of reading confused, here analysis and there geometry.

My own experience has impressed me also with the conviction, that many of our candidates for University honours are debarred the high enjoyment of penetrating into the sublimer investigations of Physical Astronomy from the want of some treatise that would lead them by

a clear and distinct path, and with an undivided attention, through the train of reasoning which leads from elementary mechanical principles to the demonstration of celestial phenomena. Some, it is true, of our first rate students do attain this eminence; but might not this few be considerably augmented, if their path were well pointed out and disencumbered of many of the obstacles which lie in their way and impede their course?

Let it not be imagined, however, that I send forth the present volume with the presumptuous confidence, that the want of a complete analytical system of mechanics is supplied by its appearance; though I will so far commit myself as to confess, that to supply this want has been my earnest desire;—no, I would rather use the experience of a distinguished Author, whose name I have already used, who is a far better judge, in such a case, than myself, and say in his words, "a few years experience has a great tendency to diminish the confidence of producing what shall satisfy himself and others, with which a young author sets out and he learns that the vivid impression of fancied deficiencies and imperfections of preceding works which at first induced him to write, is a very insufficient warrant of his own skill and judgment." But yet my object has been unique; and it has not been till after much time and thought spent upon the subject, that I have ventured to lay my work before the public: how I have satisfied my own desire I leave to the candour of my readers to determine.

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