A TREATISE ON OF THE SITY OF MICH DYNAMICS OF A PARTICLE, WITH NUMEROUS EXAMPLES. BY PETER GUTHRIE TAIT, M.A., LATE FELLOW OF ST PETER'S COLLEGE, CAMBRIDGE, PROFESSOR OF NATURAL PHILOSOPHY IN THE UNIVERSITY OF EDINBURGH, AND THE LATE WILLIAM JOHN STEELE, B. A., FELLOW OF ST PETER'S COLLEGE, CAMBRIDGE. THIRD EDITION. London: MACMILLAN AND CO. 1871. [All Rights reserved.] PREFACE. To the first edition of this work, published in 1856, the following was prefixed : "In the present Treatise will be found all the ordinary propositions, connected with the Dynamics of particles, which can be conveniently deduced without the use of D'Alembert's Principle. "Its publication has been delayed by many unforeseen occurrences; more especially by the early and lamented death of Mr STEELE, whose portion of the work was left uncompleted, and whose assistance in its final arrangement and revision would have been invaluable. The principal portions due to him are the greater part of Chapters III., V. and VIII. together with a few pages of Chapter I. "Considerable use has been made of Pratt's Mechanical Philosophy: indeed a large portion of Chapter XI. is reprinted verbatim from that work. 66 Throughout the book will be found a number of illustrative examples introduced in the text, and for the most part completely worked out; others with occasional solutions or hints to assist the student are appended to each Chapter. For by far the greater portion of these the Cambridge SenateHouse and College Examination Papers have been applied To this was added, in the second edition, published in 1865: "I am glad of the opportunity, presented by the call for a second edition, to make reparation for many of the faults of the first. Numerous trivial errors, and a few of a more serious character, have now been corrected; many sections and several new examples have been added; and the whole of the second Chapter has been rewritten, upon the basis of the corresponding portion of Thomson and Tait's Natural Philosophy which, though as yet unpublished, was printed off nearly two years ago. "When I wrote that Chapter, in 1855, I had not read Newton's admirable introduction to the Principia; and I endeavoured to make the best of the information I had then acquired from English and French treatises on Mechanics. These five pages, faulty and even erroneous as I have since seen them to be, cost me almost as much labour and thought as the utterly disproportionate remainder of my contributions to the volume. And I cannot but ascribe this result, in part at least, to the vicious system of the present day, which ignores Newton's Third Law of Motion, though constantly assuming it (tacitly) as an axiom; and erects Statics upon a separate basis from Kinetics, thereby necessitating several additional Physical Axioms, the splitting of Newton's Second Law into two, and the introduction of a so-called Statical measure of Force. "To be enabled to preserve the title of the work, I have added (apropos of the Second Law of Motion) a few hints about Statics of a particle. "The examples are, for the most part, reprinted verbatim from the papers in which they were set; in a few the language has been altered, or the theorem involved has been generalized; several, however, have defied all attempts at |