AN ELEMENTARY TREATISE ON MECHANICS, FOR THE USE OF THE JUNIOR CLASSES AT THE UNIVERSITY AND THE HIGHER CLASSES IN SCHOOLS, WITH I Collection of Examples. BY S. PARKINSON, B.D. FELLOW AND PRÆLECTOR OF ST JOHN'S COLLEGE, CAMBRIDGE. THIRD EDITION REVISED. MACMILLAN AND CO. Cambridge and London. 1863. 180 b. 125 b. PREFACE TO THE THIRD EDITION. In preparing a third edition of this work I have kept the same object in view as I had in the former editions,—namely, to include in it such portions of Theoretical Mechanics as can be conveniently investigated without the use of the Differential Calculus, and so render it suitable as a manual for the Junior Classes in the University and the Higher Classes in Schools. With one or two short exceptions, the Student is not presumed to require a knowledge of any branches of Mathematics beyond the elements of Algebra, Geometry and Trigonometry. Motion on a Curve, which is treated of in the last Chapter of the Dynamics, does not seem to admit of any complete discussion without the aid of the Differential Calculus; but in consequence of the present requirements of the Senate-House Examinations, I have put together those theorems respecting cycloidal oscillations and curvilinear motion which admit of a tolerably simple Geometrical exposition. Several additional propositions have been incorporated in the work for the purpose of rendering it more complete :and the collection of Examples and Problems has been largely increased :—to most of them I have annexed results, which I hope will render the collection more useful both to tutor and pupil. St John's COLLEGE, Nov. 1863. Def. of the terms particle, rigid, Art. 1; motion, absolute and relative, 2 ; def. of force, line of action, equilibrium, 3; pressure, tension, 4; mass, 7; mode of comparing forces, standard of weight, 8—11; principle of Of forces acting in one plane. Def. of component, resultant, 15; parallelogram of forces, 18—21; triangle of forces, 22; Lami's theorem, 23; polygon of forces, 25; Leibnitz's theorem, 26; converse of parallelogram of forces, 27; resultant of any system of forces in one plane, 28; of two parallel forces, 29, 30; moment of a force, 31; moment of two or more forces equal to that of their resultant, 32—34; def. of a fulcrum, a lever, 35; principle of the lever, 36; condition of equilibrium of a system of forces in one plane, 38—40; remarks on the mutual action of smooth and rough surfaces, 41, 42; tension of strings, 43; conditions of equilibrium of Explanation of the action of friction, 52, 53; laws of friction, 54; rolling friction, &c. 55; practical method of finding the coefficient of fric- tion, 57. |