Definition-properties of the center of gravity, 37; stable, unstable, and neutral equilibrium, 38; nature of the equi- librium when one body rests on another, 39; conditions that a body may stand or fall, 40; the center of gravity of any number of particles, 41; of a straight line-of a triangle, 43; of a parallelogram, 44; of a polygon- of a triangular pyramid, 45; of any pyramid and cone, 47; of a frustum of a pyramid, 48; of the perimeter of a triangle, ON THE EQUILIBRIUM OF A SYSTEM OF WEIGHTS SUSTAINED BY Tensions in two cords which sustain a weight, 104; the funicular polygon, 105; reactions in beams sustaining a Measure of force of friction, 110; coefficient of friction, 111 inclined plane with friction, 111; screw with friction, 112; Definitions, 115; laws of motion, 118; parallelogram of ve- locities, 120; composition and resolution of velocities, 121 Measure of elasticity, 123; table of moduli of elasticity, 125; impact of non-elastic bodies, 126; impact of imperfectly elastic bodies, 127; motion of the center of gravity before ON UNIFORM ACCELERATING FORCES AND GRAVITY The relations of time, space, and force, 134; measure of gravity, 136; bodies projected in the direction of the force, Form of the path of a projectile, 143; equation of path, 144; time of flight-range, 145; greatest height, 146; velocity is what would be acquired in falling from the directrix, Motion on an inclined plane, 150; motion down the chords of a circle, 151; motion of two bodies hanging from the ends of a cord over a pulley, 152; body falling down a curve, 153; velocity down a circular arc, 154; time of fall- ing down an arc of a cycloid, 154; centripetal force equals the centrifugal in a circle, 157; conical pendulum, 159; ELEMENTARY MECHANICS. INTRODUCTION. MECHANICAL Science is that in which the laws of forces, and the effects they produce on bodies, are investigated. It is subdivided into four Sciences-Statics, Dynamics, Hydrostatics, and Hydrodynamics. In Statics the effects of forces on solid bodies at rest are examined. In Dynamics the effects when motion is produced. In Hydrostatics the effects of forces on fluid bodies at rest are considered. In Hydrodynamics the effects on fluid bodies when motion ensues. In the present treatise, Elementary Statics and Dynamics only, are treated of. The mass of a body is the quantity of matter which it contains; and matter is defined to be, whatever possesses bulk and affords resistance to the occupation of the same portion of space by other matter. We are ignorant of the ultimate nature of matter, but we know that dense matter consists of atoms,* which have each their * See Dr. Daubeny on the Atomic Theory. B peculiar masses constant and unchangeable by any mechanical or chemical means within our reach. The term subtile matter has been applied to the agents which cause the phenomena of electricity, heat, &c. Though evidently closely connected with the development of forces, we as yet only know some of the properties and laws of the effects of these agents upon dense matter. Whenever the term matter is used in Mechanics, it is understood to mean what is called above dense matter. The quantity of matter in a body is measured by its inaptitude to receive motion (inertia) when acted on by a given force; and is proportional to the weight at the same place on the Earth's surface. So that a body of two, three, &c. pounds weight contains twice, thrice, &c. respectively the matter that a body of one pound does. We define force to be, whatever causes or tends to cause motion, or change of motion in bodies. We see force acting continually around us, and developed by various means, though we cannot trace it to its ultimate origin. We measure forces by their effects, and in Statics they are often called pressures; being compared with the pressures produced by known weights, they can thus be expressed numerically. We speak, for instance, of a pressure of twelve ounces, of thirty pounds, of two tons, &c. &c. when the unit of measure is an ounce, a pound, or a ton respectively. In Dynamics, forces are measured in two different manners, according to the nature of the problem,—namely, in some cases by the velocity generated in a unit of time; and in other cases by the momentum (or velocity multiplied into the mass of the body moved) generated in a unit of time. In Statics, we continually represent forces by lines of definite lengths. A unit of length being taken to represent the unit |