MECHANICS. 347 



seated by the two contiguous sides of a parallelogram; having the 

 directions of the forces for those of the sides, and the momentum of 

 the forces proportional to the lengths of the sides ; in which case the 

 diagonal will represent the resultant, both in momentum and direc- 

 tion. The moment, or leverage, of a force, is the product of its mo- 

 mentum by the perpendicular distance from it to a fixed point called 

 the origin of moments: and it measures the tendency of the force to 

 turn the body around the origin, considered as a fixed axis. In any 

 system of forces, the moment of the resultant is equal to the sum of 

 the moments of all the components. This important fact is called 

 the principle of moments. The centre of gravity, of any body, or 

 system, is a point through which will pass the resultant of all the 

 component forces of gravity, acting on the different particles, or parts 

 of the system. It may be found by the principle of moments ; and 

 if this point be supported, the whole body is supported thereby. 



The rope machine, or funicle, consisting of forces acting on three 

 or more cords, or ropes, connected together at one point, is some- 

 times regarded as a mechanical power. There are, however, usually 

 reckoned six mechanical powers, or simple machines for rendering 

 forces more available ; viz. the lever, wheel and axle, pulley, inclined 

 plane, screw, and wedge. The lever, is essentially an inflexible rod 

 or bar, supported by a fulcrum, either a prop or a pivot, and acted 

 upon by two or more forces tending to turn it, or to resist its turning. 

 In the case of the balance, or steelyard, the forces, when in equili- 

 brium, are inversely as their distances from the fulcrum. In the 

 wheel and axle, capstan, or windlass, the forces are inversely as the 

 radii on which they act. In the simple fixed pulley, the power is 

 equal to the resistance, but acts in a different direction ; whereas, in 

 the simple moveable pulley, the weight supported by the pivot, is 

 double the force at either end of the rope. 



In the inclined plane, the force parallel to the slqpe, is to the 

 weight of the body which it sustains, as the height to the slope. In 

 the screw, acted upon by a lever, the power is to the resistance, as 

 the distance between the spiral threads, is to the circumference de- 

 scribed by the power. In the common wedge, the forces are as the 

 length of the sides against which they act. Such are the ratios re- 

 quired to produce equilibrium ; but, having regard to friction, the 

 forces must be considerably augmented when they are designed to 

 produce motion. The principle of virtual velocities, is, that what- 

 ever is gained in the pressure exerted, or mass moved, is compen- 

 sated for by the greater space which the power must move over : so 

 that what is gained in weight is lost in velocity. Friction, always 

 acts as a retarding force, proportional to the pressure which pro- 

 duces it. 



2. Dynamics, treats of variable motion, produced by continuous 

 forces, applied particularly to solid bodies. An impulsive force, is 

 one which acts momentarily ; or is imparted momentarily, from one 

 body to another. The body receiving it, moves consequently in a 

 right line, and with a uniform motion, unless affected by the resistance 

 of the air, or by gravity, or other forces ; and whew it strikes another 



