measurement, determination of the magnitude of a quantity by comparison with a standard for that quantity. Quantities frequently measured include time, length, area, volume, pressure, mass, force, and energy. To express a measurement, there must be a basic unit of the quantity involved, e.g., the inch or second, and a standard of measurement (instrument) calibrated in such units, e.g., a ruler or clock. For convenience, such a standard is usually marked off both in multiples and in fractions of the basic unit. Although various systems of units exist for measuring different quantities (see weights and measures), the most important and widely used are the metric system and the English units of measurement. Certain units have been defined for special applications, e.g., the light-year and parsec in astronomy and the angstrom in physics. Measurement is one of the fundamental processes of science. It provides the data on which new theories are based and by which older theories are tested and retested. A good measurement should be both accurate and precise. Accuracy is determined by the care taken by the person making the measurement and the condition of the instrument; a worn or broken instrument or one carelessly used may give an inaccurate result. Precision, on the other hand, is determined by the design of the instrument; the finer the graduations on the instrument's scale and the greater the ease with which they can be read, the more precise the measurement. The choice of the instrument used should be appropriate to the desired precision of the results. The human foot may be a suitable instrument for pacing off short distances if precision is not important; at the other extreme, the interferometer (see interference) is used for extremely precise measurements of distance in science. There is a basic distinction between measurement and counting. The result of counting is exact because it involves discrete entities that are not subdivided into fractions. Measurement, on the other hand, involves entities that may be subdivided into smaller and smaller fractions and is thus always an estimate. This distinction between measurement and counting seems, on the surface, to break down at the atomic level, where the quantum theory reveals that not only mass (in the form of elementary particles and atoms) but also many other quantities occur only in discrete units, or quanta. It would seem, therefore, that one could, in theory, reduce measurement to counting at this level. However, the quantum theory also places limitations on the possibility of counting, stressing such concepts as the wavelike nature and indistinguishability of particles and proposing the uncertainty principle as an absolute limitation on certain pairs of related measurements.

English units of measurement, principal system of weights and measures used in a few nations, the only major industrial one being the United States. It actually consists of two related systems—the U.S. Customary System of units, used in the United States and dependencies, and the British Imperial System. The names of the units and the relationships between them are generally the same in both systems, but the sizes of the units differ, sometimes considerably.

Customary Units of Weights and Measures

Units of Weight

The pound (lb) is the basic unit of weight (which is proportional to mass). Within the English units of measurement there are three different systems of weights. In the avoirdupois system, the most widely used of the three, the pound is divided into 16 ounces (oz) and the ounce into 16 drams. The ton, used to measure large masses, is equal to 2,000 lb (short ton) or 2,240 lb (long ton). In Great Britain the stone, equal to 14 lb, is also used. The troy system (named for Troyes, France, where it is said to have originated) is used only for precious metals. The troy pound is divided into 12 ounces and the troy ounce into 20 pennyweights or 480 grains; the troy pound is thus 5,760 grains. The grain is also a unit in the avoirdupois system, 1 avoirdupois pound being 7,000 grains, so that the troy pound is 5,760/7,000 of an avoirdupois pound. Apothecaries' weights are based on troy weights; in addition to the pound, ounce, and grain, which are equal to the troy units of the same name, other units are the dram (1/8 oz) and the scruple (1/24 oz or 1/3 dram).

Units of Length and Area

The basic unit of length is the yard (yd); fractions of the yard are the inch (1/36 yd) and the foot (1/3 yd), and commonly used multiples are the rod (51/2 yd), the furlong (220 yd), and the mile (1,760 yd). The acre, equal to 4,840 square yards or 160 square rods, is used for measuring land area.

Units of Liquid Measure

For liquid measure, or liquid capacity, the basic unit is the gallon, which is divided into 4 quarts, 8 pints, or 32 gills. The U.S. gallon, or wine gallon, is 231 cubic inches (cu in.); the British imperial gallon is the volume of 10 lb of pure water at 62°F; and is equal to 277.42 cu in. The British units of liquid capacity are thus about 20% larger than the corresponding American units. The U.S. fluid ounce is 1/16 of a U.S. pint; the British unit of the same name is 1/20 of an imperial pint and is thus slightly smaller than the U.S. fluid ounce.

Units of Dry Measure

For dry measure, or dry capacity, the basic unit is the bushel, which is divided into 4 pecks, 32 dry quarts, or 64 dry pints. The U.S. bushel, or Winchester bushel, is 2,150.42 cu in. and is about 3% smaller than the British imperial bushel of 2,219.36 cu in., with a similar difference existing between U.S. and British subdivisions. The barrel is a unit for measuring the capacity of larger quantities and has various legal definitions depending on the quantity being measured, the most common value being 105 dry quarts.

Differences between American and British Systems

Many American units of weights and measures are based on units in use in Great Britain before 1824, when the British Imperial System was established. Since the Mendenhall Order of 1893, the U.S. yard and pound and all other units derived from them have been defined in terms of the metric units of length and mass, the meter and the kilogram; thus, there is no longer any direct relationship between American units and British units of the same name. In 1959 an international agreement was reached among English-speaking nations to use the same metric equivalents for the yard and pound for purposes of science and technology; these values are 1 yd=0.9144 meter (m) and 1 lb=0.45359237 kilogram (kg). In the United States, the older definition of the yard as 3,600/3,937 m is still used for surveying, the corresponding foot (1,200/3,937 m) being known as the survey foot.

The English units of measurement have many drawbacks: the complexity of converting from one unit to another, the differences between American and British units, the use of the same name for different units (e.g., ounce for both weight and liquid capacity, quart and pint for both liquid and dry capacity), and the existence of three different systems of weights (avoirdupois, troy, and apothecaries'). Because of these disadvantages and because of the wide use of the much simpler metric system in most other parts of the world, there have been proposals to do away with the U.S. Customary System and replace it with the metric system.

Association of numbers with physical quantities and natural phenomena by comparing an unknown quantity with a known quantity of the same kind. Weights and measures are standard quantities with which such comparisons are made. The earliest ones measured mass (weight), volume (liquid or dry measure), length, and area using units mostly based on dimensions of the human body. The cubit, representing the distance from elbow to fingertips, was the most widespread unit of measure in the ancient world. As such units were standardized, more were added, including units of temperature, luminosity, pressure, and electric current. Measurements made by the senses instead of by measurement devices are called estimates (see estimation).

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