Of forces, the directions of which meet in a point;-tension of strings on smooth and rough surfaces Parallelopiped of forces, 60; resultant of any system of forces acting at a point, 62; conditions of equilibrium, 63; tension of a string passing over a smooth surface, 65; . . . over a rough surface, 66; the funi- Def. of vertical, horizontal, centre of gravity, 69; there is one and only one centre of gravity for any system, 70; centre of parallel forces, 70, Cor. 3; centre of gravity of a right line, a parallelogram, a triangle, perimeter of a triangle, 72, 73; centre of gravity of a system of particles in a line, in a plane, arranged in any manner, 74; def. of moment of a force with respect to a plane, centre of mean position, centre of figure, 75; general remarks, 77, 78; centre of gravity of a pyramid, 79; stable and unstable equilibrium, 80-84; centre of gravity of a circular arc, sector and segment, 85, 86; Leibnitz's The lever discussed, 88-93; the common steelyard, 94; Danish steelyard, 95; common balance, 96-98; Balance of Quintenz, 99; wheel and axle, 100, 101; single pully, 102, 103; systems of pullies, 104—106; Spanish Barton, 107; inclined plane, smooth and rough, 108-110; screw, 111—114; wedge, 115; explanation of the principle of virtual velocities, 116–118; the principle applied to the several mechanical powers, 119-128; mechanical advantage and efficiency, 129; labour- ing force, what is gained in power is lost in velocity, horse-power, Def. and measure of velocity, Art. 2; formula for uniform motion, 4; measure of acceleration, 5, 6; mass, 8—11; momentum, 12; mov- ing force, 15; impulsive force, 17, 18; geometrical resolution and composition of velocities, and accelerations, 19, 20; parallelogram of velocities and accelerations, 21-25; first law of motion, 27, 28; second law of motion, 29—33; dynamical parallelogram of velocities, 35; relative motion, 40; third law of motion, 42-45; action and Of uniform motion and collision Relative motion of two points or balls, 50, 51; def. of elasticity, force of Path of a projectile, 85; range, time of flight, elevation, 85, 86; on an Velocity acquired down a curve, 96, 97; on a circle, 97; properties of the cycloid, 99-101; time of falling down an arc of a cycloid, 102; oscillation in a cycloid, 102, Cor.; length of seconds pendulum, 103; problem, 104; normal acceleration of a particle moving in a curve, 105; centrifugal force, 106; pressure on a curve, 107; pro- blems, 108, 109; Newton's method of determining the elasticity of STATIC S. 1. CHAPTER I. INTRODUCTION. MECHANICS is the science which treats of the laws of rest and motion of matter. A general notion of the meaning of the term matter is acquired in the daily experience of life, since matter in various forms and under various circumstances is perpetually affecting our senses: we shall therefore assume that the notion of it is familiar to the student. A particle or material point is a portion of matter indefinitely small in all its dimensions; so that its length, breadth, and thickness are less than any assignable linear magnitude. A body of finite size may be regarded as an aggregation of an indefinitely great number of particles; and the dimensions of any given body being limited in every direction, it will consequently have a determinate form and volume. A body or system of bodies all the points of which are held together in an invariable position with respect to one another, is said to be rigid. 2. When a body or particle constantly occupies the same position in space, it is said to be at rest; and when its position. in space changes continuously in any manner whatever, it is said to be in motion. All matter is capable of motion, but we can only judge of the state of rest or motion of a particle P. M. 1 by comparing it with other particles; for this reason all the motions which we can observe are necessarily relative motions. When a great number of objects maintain the same relative position, our first impression is to consider them as at rest; and if one of them changes its position relatively to the others, it is to it that we ascribe the motion. Thus for instance, the earth was for a long time considered to be fixed in space, notwithstanding the motions of the sun, moon and stars relatively to objects on the earth's surface with which the observer compared them. The motion was ascribed to them whilst the earth was assumed to be fixed. A careful study of natural phenomena may modify this first impression, but we can never arrive at absolute certainty in this respect; and the conclusions respecting absolute motions, to which we are led by the observation of relative motions, can only be regarded as inductions which may have indeed a high degree of probability, but which have always need of being verified by the accordance between the logical consequences to which they lead, and the phenomena directly observed. 3. The following principle we assume as being in accordance with experiment and observation, viz. a particle which is absolutely at rest will continue so, until some cause, extraneous to itself, begins to operate so as to put it in motion. This principle asserts that matter at rest has no tendency to put itself in motion, and that any motion or tendency to motion which it may possess, must arise entirely from some external cause. To such causes we give the name of forces, and we give the following definition : Any cause which excites motion in a particle, or which only tends to excite it when its effect is prevented or modified |