ELEMENTS OF NATURAL PHILOSOPHY SIR WILLIAM THOMSON, LL. D., D. C. L., F. R. S., PROFESSOR OF NATURAL PHILOSOPHY IN THE UNIVERSITY OF GLASGOW, PETER GUTHRIE TAIT, M. A., PROFESSOR OF NATURAL PHILOSOPHY IN THE UNIVERSITY OF EDINBURGH. PART I. NEW EDITION. AT THE UNIVERSITY PRESS. 1882 All Rights reserved PEINTBB BY 0. J. CLA. T SON, AT THE ONIVEKSITT PRESS. PREFACE. To the first Edition of this work, published in 1872, the following statement was prefixed The work consists, in great part, of the large-type, or non-mathematical, portion of our Treatise on Natural Philosophy. As it is designed more especially for use in Schools and in the junior classes in Universities, the mathematical methods employed are, almost without exception, limited to those of the most elementary geometry, algebra, and trigonometry. Where higher methods are required for an investigation, the reader is, in general, simply referred to our larger work. It is particularly interesting to note how many theorems, even among those not ordinarily, attacked without the help of the Differential Calculus, have here been found to yield easily to geometrical methods of the most elementary cha racter. Simplification of modes of proof is not merely an indi cation of advance in our knowledge of a subject, but is also the surest guarantee of readiness for farther progress. A large part of Chapter VII is reprinted from a series Vl PREFACE. of notes of a part of the Glasgow course, drawn up for Sir W. Thomson by John Ferguson, Esq., and printed for the use of his students. We have had considerable difficulty in compiling this treatise from the larger work arising from the necessity for condensation to a degree almost incompatible with the design to omit nothing of importance and we feel that it would have given us much less trouble and anxiety, and would probably have ensured a better result, had we written the volume anew without keeping the larger book constantly before us. The sole justification of the course we have pur sued is that wherever, in the present volume, the student may feel further information to be desirable, he will have no difficulty in finding it in the corresponding pages of the larger work. A great portion of the present volume has been in type since the autumn of 1863, and has been printed for the use of our classes each autumn since that date. To this we would now only add that the whole has been revised, and that we have endeavoured to simplify those portions which we have found by experience to present difficulties to our students. The present edition has been carefully revised by Mr W. BURNSIDE, of Pembroke College and an Index of which we have recognized the necessity, has been drawn up for us by Mr SCOTT LANG. W. THOMSON. P. G. TAIT. fan-nary, 1879. CONTENTS. DIVISION I. PRELIMINARY. PAGE CHAP. I. KINEMATICS i, II. DYNAMICAL LAWS AND PRINCIPLES . . 56 III. EXPERIENCE in IV. MEASURES AND INSTRUMENTS . . . 122 DIVISION II. ABSTRACT DYNAMICS. V. INTRODUCTORY 136 VI. STATICS OF A PARTICLE. ATTRACTION . . 140 VII. STATICS OF SOLIDS AND FLUIDS . . .199 APPENDIX 282 DIVISION I. PRELIMINARY. CHAPTER I KINEMATICS. 1. THE science which investigates the action of Force is called, by the most logical writers, DYNAMICS. It is commonly, but erroneously, called MECHANICS a term employed by Newton in its true sense, the Science of Machines, and the art of making them. 2. Force is recognized as acting in two ways i so as to compel rest or to prevent change of motion, and 2 so as to produce or to change motion. Dynamics, therefore, is divided into two parts, which are conveniently called STATICS and KINETICS. 3. In Statics the action of force in maintaining rest, or preventing change of motion, the balancing of forces, or Equilibrium, is investigated in Kinetics, the action of force in producing or in changing motion. 4. In Kinetics it is not mere motion which is investigated, but the relation of forces to motion...