science cannot be filled up with a sufficient portion of illustration and remark, without danger of forming a work too bulky and too difficult of reference for the time-pressed Senate-House student, could not the two parts be with advantage separated? the first might then appear under the rigid form of a Syllabus, and the second could be sought in books, whose style should, more nearly than it does at present, approach that in which our continental neighbours are accustomed to write upon Physics. It is often urged that it is better to leave each student to construct his own syllabus than to present him with a printed abstract, the very conciseness of which must be repulsive to him: such may be the theory, but if so, it would seem not to work well in practice; for with rare exceptions the syllabus which an Undergraduate uses, is the production of either his public or his private Tutor. But it is rather with the view of improving the style of our mathematical writing than on account of the specific utility of a published syllabus, that I conceive the system advocated should be more widely extended than it hitherto has been. So strongly did these opinions influence me, that in the early part of this year I offered a Syllabus of Statics for publication. My aim was to present a complete scheme of the subject to the student, wherein the most important propositions, and those which have met with some little neglect at the hands of our University writers, should be illustrated both verbally and graphically; in some instances the definitions would have been given in a new form of words, and the sequence of propositions slightly altered. But it was intended that the marked characteristic of the work should be the copiousness of examples, solved for the most part geometrically, and accompanied by explanations of the circumstances of each case and of the principles involved in it. A few words may here be allowed me in justice to myself to explain why, with my views remaining unchanged, I ultimately gave my work a character so inconsistent with them. Upon submitting the MS. to the consideration of some friends, who were obliging enough to undertake its revisal, and certainly qualified in no ordinary degree for the task, they were pleased to express approbation of its arrangement, but urged me to change in some measure its design; they wished me to turn it into a complete treatise upon Elementary Statics and Dynamics, considering that its simple geometrical character rendered it peculiarly adapted to the wants of Schools and the junior students of the University. I was perhaps too ready to adopt their suggestions, without measuring sufficiently my own power to carry them into effect: at any rate the patchwork that was necessary in order to complete the work of transformation is the cause of, and at the same time affords the only excuse I can offer for, the unevenness of construction which obtains throughout the book. I am well aware of how greatly I stand in need of forbearance at the hands of those who may think it worth their while to pass judgment upon the following treatise; but while I trust that the preceding explanation is sufficient to remove all misconstruction regarding the nature of its pretensions, I hope that its many deficiencies will not render it altogether inefficient and devoid of utility. Clare Hall, Nov. 1850. J. B. P. Explanation of the terms particle and density, 1; rigid and elastic bodies, 2; bodies in motion-at rest, 3; definition of Force, 4; explanation of the term equilibrium, 5; distinctive marks of a FORCES ACTING AT THE SAME POINT IN ONE PLANE Explanation of the terms resultant and resolved parts, 12; resultant of two forces which act in same straight line, 13; resultant of two forces which act at a point, but not in the same straight line: parallelogram of forces, 14; assumptions made in proving the parallelogram of forces, 15; proof of the parallelogram of forces, 16; the triangle of forces, 18; three forces in equilibrium are proportional to the sines of the angles opposite to them, 19; polygon of forces, 20; resolution of forces, 21; Equations of Equi- FORCES ACTING AT DIFFERENT POINTS RIGIDLY CONNECTED TOGETHER Proposition giving the resultant of two parallel forces, 23; relation between the moments of two parallel forces and that of their resultant about any point, 24; of any number of parallel forces and that of their resultant about any point, 25; of any pair of forces not parallel and that of their resultant about any point, 26; of any system of forces whatever in one plane and that of their resultant about any point, 27; of any system of forces about a point in the direction of their resultant, 28; of such a system of forces when it is in equilibrium, 29; conditions of equilibrium of a body which has one point fixed, 30; of a body which has two points fixed, 31; of a body which has one or more points in Definition of the term Centre of Gravity, 33; one such point only exists, 34; centre of gravity of a body may be found when the centres of gravity of two parts into which it is divided are known, 35; similarly when the body is divided into any number of parts, 36; conditions of equilibrium of a heavy body which is acted upon by resistances of smooth surfaces only, 37; defi- nition of the terms stable, unstable, and neutral equilibrium, 38. Definition of the term Friction, 39; nature of the reactions of rough surfaces, 40; a farther explanation of friction, 41; definitions of perfect smoothness and perfect roughness, 42; conditions of equi- librium of a body which is in contact with a rough plane, 43; also when it is in contact with a perfectly rough plane, 44. The object of Machines, 45; enumeration of the simple mechanical powers, 46; definition of the term Lever, 47; the arms of a lever defined, 48; relation between the power and the weight upon a lever which is in equilibrium, 49; the Wheel and Axle, 50; Toothed Wheels, 51; the Pulley, 52; relation between the power and weight upon the simple pulley with strings parallel, 53; upon the simple pulley with strings not parallel, 54; in the first system of pulleys, 55; in the second system of pulleys, 56; in the third system of pulleys, 57; the Inclined Plane, 58; the Wedge, 59; the Screw, 60; of Balances, 61; Common Balance, 62; ON COUPLES AND SOME PROPOSITIONS RELATING TO FORCES NOT IN Couples, 65, 66; equal of Couples, 67; resultant of any number of 115 |