AN ELEMENTARY TREATISE ON MECHANICS, FOR THE USE OF THE JUNIOR CLASSES AT THE UNIVERSITY WITH A Collection of Examples. BY S. PARKINSON, B.D. FELLOW AND PRÆLECTOR OF ST JOHN'S COLLEGE, CAMBRIDGE. 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, CONTENTS. 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 PAGE 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 |