II. DERIVED MECHANICAL UNITS.-
Area.-The unit of area is the square centimetre.
Volume.—The unit of volume is the CUBIC CENTIMETRE.
VELOCITY is rate of change of position. It involves the idea of direction as well as that of magnitude. VELOCITY is UNIFORM when equal spaces are traversed in equal intervals of time The unit of velocity is the velocity of a body which moves through unit distance in unit time, or the VELOCITY OF ONE CENTIMETRE PER SECOND.
MOMENTUM is the quantity of motion in a body, and is measured by mass x velocity.
ACCELERATION is the rate of change of velocity, whether that change take place in the direction of motion or not. The unit of acceleration is the acceleration of a body which undergoes unit change of velocity in unit time, or an acceleration of one centimetre-per-second per second The acceleration due to gravity is considerably greater than this, for the velocity imparted by gravity to falling bodies in one second is about 981 centimetres per second (or about 32.2 feet per second). The value differs slightly in different latitudes. At Greenwich the value of the acceleration due to gravity is g=981.17; at the Equator g=978.1; at the North Pole g=983.1.
FORCE is that which tends to alter a body's natural state of rest or of uniform motion in a straight line.
FORCE is measured by the acceleration which it imparts to mass—i. e., mass x acceleration.
THE UNIT OF FORCE, or DYNE, is that force which, acting for one second on a mass of one gramme, gives to it a velocity of one centimetre per second. The force with which the earth attracts any mass is usually called the "weight" of that mass, and its value obviously differs at different points of the earth's surface The force with which a body gravitates—i e, its weight (in dynes), is found by multiplying its mass (in grammes) by the value of g at the particular place where the force is exerted.
Work is the product of a force and a distance through which it acts. The unit of work is the work done in overcoming unit force through unit distance—i e, in pushing a body through a distance of one centimetre against a forch of one dyne. It is called the Erg. Since the "weight" of one gramme is 1 X 981 or 981 dynes, the work of raising one gramme through the height of one centimetre against the force of gravity is 981 ergs or g ergs. One kilogramme-metre = 100,000 (g) ergs = 9 8 1 X 10^7 ergs. One foot- pound = 13,825 (g) ergs, = 1 356 X 10^7 ergs.
Energy is that property which, possessed by a body, gives it the capability of doing work. Kinetic energy is the work a body can do in virtue of its motion. Potential energy is the work a body can do in virtue of its position. The unit of energy is the Erg.
Power or Activity is the rate of work; the practical unit is called the Watt—10^7 ergs per second.
A Horse-power = 33,000 ft—Ibs per minute = 550 ft—Ibs per second, but as seen above under Work, 1 ft—Ib = 1 356 X 10^7 ergs, and under Power, 1 Watt = 10^7 ergs per sec a Horsepower = 550 X 1 356 X 10^7 ergs = 746 Watts; or, =EC/746=C^2R/746=E^2/(746 R) =HP where E = volts, C = amperes, and R = ohms.
The French "force de cheval" = 75 kilogramme metres per sec = 736 Watts = 542 48 ft—lbs. per sec. = .9863 H.P.; or one H.P. = 1.01385 "force de cheval."
DERIVED ELECTRICAL UNITS.—There are two systems of electrical units derived from the fundamental "C.G.S." units, one set being based upon the force exerted between two quantities of electricity, and the other upon the force exerted between two magnetic poles. The former set are termed electro-static units, the latter electro-magnetic units.