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THACKER, SPINK AND CO.
BOMBAY THACKER, VINING & Co. MADRAS: HIGGINBOTHAM & Co.
LONDON: W. THACKER AND CO.

1874.

[All rights reserved.]

CALCUTTA :

PRINTED BY THACKER, SPINK AND CO.

Melus is 10-25-37

PREFACE.

THE following elementary treatise on Dynamics (commonly called Mechanics) will be found to differ in some important respects from the text-books in common use. Some of these differences will be here noticed. The term Dynamics is used in its true logical sense as the science which treats of the action of force on matter whether it maintains relative rest or produces acceleration of relative motion, and Dynamics is thus sub-divided into Statics and Kinetics. In both of these branches the unit of force adopted is the Kinetic unit, derived from the unit of mass which is taken to be the pound avoirdupois. As a secondary unit of force, convenient in certain cases and sufficiently accurate for most practical purposes, although varying in value at different places, the common Gravitation unit, the weight of the unit of mass (that is, the weight of one pound), has been adopted.

It is presumed that, at the present day, there can be no question as to the great advantages, both as regards simplicity and clearness for beginners, and also as regards scientific accuracy, of Gauss's method over the methods which have been in common use, in which the so-called Statical unit of force is a variable quantity, and in which it is necessary in the Kinetic branch to employ a different unit of force, the so-called Dynamical unit, from which a variable and very inconvenient unit of mass is derived, altogether different from the fixed standards of mass (commonly, but incorrectly, called standards of weight) used in

commerce.

Care has been taken throughout the book, both in the text and in the examples, to avoid the use of the term weight, except in its true sense as the apparent force of gravity on a body.

The chapters on Kinematics, which are, of course, independent of the rest of the book, are placed in the order

in which the subjects are now usually read. Kinematics, however, involving only the ideas of space and time, is a much less complex subject than Dynamics, which introduces the further ideas of force and mass, and might with advantage be studied by beginners before even commencing the Static branch. The chapter on Dynamical Laws and part of the chapter on the Force of Gravity might also be read as an introduction to the whole subject.

The importance, however, particularly for beginners, of clearly separating results and formulas derived from conventions, with regard to methods of estimating velocity and acceleration of velocity, from conclusions depending on the laws which are observed to regulate the action of force on matter, cannot, it is thought, be too strongly insisted upon. Nothing, perhaps, in Dynamics has given rise to more confusion of ideas with beginners than the use of the expression "accelerating force" for acceleration of velocity, and the arbitrary distinction drawn between "accelerating" and "moving" forces.

Any treatise on Dynamics, in the present state of science, would be incomplete without some reference to the Principle of Conservation of Energy. It has been attempted in chapter VIII of the Statics to explain the scientific sense in which the terms work and energy are now used, and to illustrate the Law of Energy, and some consequences from it, in connection with the Simple Machines. Further explanations and illustrations are given in the chapter on Energy in Kinetics, and it is hoped that these chapters combined may form a sufficient introduction to the subject for those readers who are commencing the study of Physical Science.

This little treatise was originally designed to supply a text-book on Dynamics, in conformity with late methods and improvements, for the pass students of the Calcutta University, and the greater portion of it has been compiled from notes, taken from various sources, which the author has used for some years with his classes. The book, however, as it now stands, contains most of the propositions which can be advantageously investigated by the aid of Elementary Algebra, Geometry and Trigonometry, such

as are usually found in elementary treatises, together with some additions. Of the examples, very few are original; some have been taken from University Examination papers, and others, which have been considered as more or less common property, have been taken from various sources, including some of the text-books in common use. In many of these examples the wording and notation have been altered and a few have been altogether re-cast.

It seems scarcely necessary in a text-book, which, from its very nature and the purpose for which it is intended, must be, more or less, a compilation of well known methods and propositions, to specify, in detail, sources from which information has been obtained. It should, however, be stated that, as regards arrangement, method and demonstrations, much has been derived from Sir W. Thomson and Professor Tait's Treatise on Natural Philosophy. The thanks of the author are due to Mr. M. H. L. Beebee for many valuable suggestions in the chapters on Kinematics and Kinetics.

It is felt that some apology may be due for imperfections in type and diagrams, which will be noticed throughout the book. Any one who has had the misfortune to be obliged to get Mathematical printing done, and diagrams engraved, in this country, will fully appreciate the difficulties. which had to be encountered in attempting to secure even tolerable accuracy and neatness of arrangement. The scarcity of mathematical type rendered it necessary that each form should be passed and printed off before the next was commenced, and thus mistakes and inaccuracies which might have been corrected, had a general revision been. possible, may have escaped notice. It is hoped, however, that no errors of a serious nature have been overlooked. The publishers, with the limited means at their disposal, have done all that it was possible for them to do.

CALCUTTA:

January, 1874. J

W. G. WILLSON.

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