Theory of measurement.

Metrology

the science of measurement. From three fundamental quantities, length, mass, and time, all other mechanical quantities—e.g., area, volume, acceleration, and power—can be derived. A comprehensive system of practical measurement should include at least three other bases, taking in the measurement of electromagnetic quantities, of temperature, and of intensity of radiation—e.g., light.

Accordingly, the 11th General Conference of Weights and Measures in 1960 adopted six quantities and units as the bases on which was established the International System of Units (q.v.). Since 1887 many national standards laboratories have been founded to set up and maintain standards of measurement, both for the six basic quantities and for their systematic derivatives. They also do attendant test and verification work for science and industry. Examples are the National Bureau of Standards (NBS) in the United States, the National Physical Laboratory (NPL) in the United Kingdom, and similar bodies in many other countries. The international metric organization created by the Metric Convention of 1875 (amended in 1921) also has a central laboratory, the International Bureau of Weights and Measures, at Sèvres (near Paris). It has duties analogous to those of the national laboratories but is concerned especially with the international coordination of all scientific work relating to the maintenance and improvement of the metric system of units and standards. This organization acts under the authority of the General Conference of Weights and Measures with the aid of an elected executive body, the International Committee of Weights and Measures, which meets every year.

Measuring a quantity means ascertaining its ratio to some other fixed quantity of the same kind, known as the unit of that kind of quantity. A unit is an abstract conception, defined either by reference to some arbitrary material standard or to natural phenomena. For example, the standard of length in the metric system was defined (1889–1960) by the separation of two lines on a particular metal bar, but it is now defined as equal to a certain number of wavelengths of light produced by a particular kind of atom under given conditions.

Theory of measurement.

Measurement theory is the study of how numbers are assigned to objects and phenomena, and its concerns include the kinds of things that can be measured, how different measures relate to each other, and the problem of error in the measurement process. Any general theory of measurement must come to grips with three basic problems: error; representation, which is the justification of number assignment; and uniqueness, which is the degree to which the kind of representation chosen approaches being the only one possible for the object or phenomenon in question.

Various systems of axioms, or basic rules and assumptions, have been formulated asa basis for measurement theory. Some of the most important types of axioms include axioms of order, axioms of extension, axioms of difference, axioms of conjointness, and axioms of geometry. Axioms of order ensure that the order imposed on objects by the assignment of numbers is the same order attained in actual observation or measurement. Axioms of extension deal with the representation of such attributes as time duration, length, and mass, which can be combined, or concatenated, for multiple objects exhibiting the attribute in question. Axioms of difference govern the measuring of intervals. Axioms of conjointness postulate that attributes that cannot be measured empirically (for example, loudness, or intelligence, or hunger) can be measured by observing the way their component dimensions change in relation to each other. Axioms of geometry govern the representation of dimensionally complex attributes by pairs of numbers, triples of numbers, or even n-tuples of numbers.

The problem of error is one of the central concerns of measurement theory. At one time it was believed that errors of measurement could eventually be eliminated throughthe refinement of scientific principles and equipment. This belief is no longer held by most scientists, and almost all physical measurements reported today are accompanied by some indication of the limitation of accuracy or the probable degree of error. Among the various types of error that must be taken into account are errors of observation (which include instrumental errors, personal errors, systematic errors, andrandom errors), errors of sampling, and direct and indirect errors (in which one erroneous measurement is used in computing other measurements).

Measurement theory dates back to the 4th century BC, when a theory of magnitudes developed by the Greek mathematicians Eudoxus of Cnidus and Thaeatetus was included in Euclid's Elements. The first systematic work on observational error was produced by the English mathematician Thomas Simpson in 1757, but the fundamental work on error theory was done by two 18th-century French astronomers, Joseph-Louis, Count de Lagrange, and Pierre-Simon, Marquess de Laplace. The first attempt to incorporate measurement theory into the social sciences also occurred in the 18th century, when Jeremy Bentham, a British utilitarian moralist, attempted to create a theory for the measurement of value. Modern axiomatic theories of measurement derive from the work of two German scientists, H.L.F. von Helmholtz and L.O. Hölder, and contemporary work on the application of measurement theory to psychology and economics derives in large part from the work of Oskar Morgenstern and John von Neumann.

Since most social theories are speculative in nature, attempts to establish standard measuring sequences or techniques for them have met with limited success. Some of the problems involved in social measurement include the lack of universally accepted theoretical frameworks and thus of quantifiable measurands, sampling errors, problems associated with the intrusion of the measurer on the object being measured,and the subjective nature of the information received from human subjects. Economics is probably the social science that has had the most success in adopting measurement theories, primarily because many economic variables (like price and quantity) can be measured easily and objectively. Demography has successfully employed measurement techniques as well, particularly in the area of mortality tables.

Weights and measures. Measurement is accomplished through the comparison of a measurand with some known quantity of the same kind. The term weights and measures signifies those standard quantities by which such comparisons are achieved. Standard quantities may be established arbitrarily or by reference to some universal constant. Standards for different kinds of quantities may develop separately or may be integrated into logical systems of units. Originally standard measures were four in number: those for mass (weight), volume (liquid or dry measure), length, and area. To these have been added standard measurements of temperature, luminosity, pressure, electric current, and others.

The earliest standard measurements appeared in the ancient Mediterranean cultures and were based on parts of the body, or on calculations of what man or beast could haul, or on the volume of containers or the area of fields in common use. The Egyptian cubit is generally recognized to have been the most widespread unit of linear measurement in the ancient world. It came into use around 3000 BC and was based onthe length of the arm from the elbow to the extended finger tips. It was standardized by a royal master cubit of black granite, against which all cubit sticks in Egypt were regularly checked. One of the earliest known weight measures was the Babylonian mina. Two surviving examples vary widely—one weighs 640 g (about 1.4 pounds), the other 978 g (about 2.15 pounds).

The terms ounce, inch, pound, and mile come from the Roman adoption of earlier Greek measuring units. The Roman system of measurement persisted into the Middle Ages in Europe, but there was great diversity of standards. Thereafter various national governments made efforts to standardize their systems, producing a welter of often confusing units and standards. The British Imperial and U.S. Customary are two of the most elaborate such systems.

The first proposal for what would later become the metric system was made by a French clergyman, Gabriel Mouton, around 1670. He suggested a standard linear measurement based on the length of the arc of one minute of longitude on the Earth's surface and divided decimally. Mouton's proposal was much discussed and refined, but it was not until 1795 that France officially adopted the metric system. Its spread throughout the rest of Europe was accelerated by the military successes of the French Revolution and Napoleon, but in many places it took a long time to overcome the nonrational customary systems of weights and measures that had been used for centuries.

Now the standard system in most nations, the metric system has been modernized to take into account 20th-century technological advances. In Paris in 1960 an internationalconvention agreed on a new metric-based system of units. This was the Système Internationale (SI). Six base units were adopted: the metre (length), the kilogram (mass), the second (time), the ampere (electric current), the degree Kelvin (temperature), and the candela (luminosity). Each was keyed to a standard value. The kilogram was represented by a cylinder of platinum-iridium alloy kept at the International Bureau of Weights and Measures in Sèvres, France, with a duplicate at the U.S. National Bureau of Standards. The kilogram is the only one of the six units represented by a physical object as a standard. In contrast, the metre was set to be 1,650,763.73 wavelengths in vacuum of the orange-red line of the spectrum of krypton-86, and the other units were related to similarly derived natural standards.

Other units derived from basic SI units include the coulomb (charge), joule (energy), newton (force), hertz (frequency), watt (power), ohm (resistance), and cubic metre (volume).

Metric system

international decimal system of weights and measures, based on the metre for length and the kilogram for mass, that was adopted in France in 1795 and, by the late 20th century, was used officially in almost all nations.

The French Revolution of 1789 provided the opportunity to pursue the frequently discussed idea of replacing the confusing welter of traditional but illogical units of measure with a rational system based on multiples of 10. In 1791 the French National Assembly directed the French Academy of Sciences to address the chaotic state of French weights and measures. It was decided that the new system would be based ona natural physical unit to ensure immutability. The academy settled on the length of 1/10,000,000 of a quadrant of a great circle of the Earth, measured around the poles of the meridian passing through Paris. An arduous six-year survey to determine the arc of the meridian from Barcelona, Spain, to Dunkirk, Fr., eventually yielded a value of 39.37008 inches for the new unit to be called the metre, from Greek metron, meaning “measure.”

All other metric units were derived from the metre, including the gram for weight (one cubic centimetre of water at its maximum density) and the litre for capacity (one-thousandth of a cubic metre). Greek prefixes were established for multiples of 10, ranging from pico- (one-trillionth) to tera- (one trillion) and including the more familiar micro- (one-millionth), milli- (one-thousandth), centi- (one-hundredth), and kilo- (one thousand). Thus, a kilogram equals 1,000 grams, a millimetre 1/1,000 of a metre. In 1799 the Metre and Kilogram of the Archives, platinum embodiments of the new units, were declared the legal standards for all measurements in France, but the motto of the metric system expressed the hope that the new units would be “for all people, for all time.”

Not until 1875 did an international conference meet in Paris to establish an International Bureau of Weights and Measures. The Treaty of the Metre signed there provided for a permanent laboratory in Sèvres, near Paris, where international standards are kept, national standard copies inspected, and metrological research conducted. The General Conference of Weights and Measures, with diplomatic representatives of some 40 countries, meets every six years to consider reform. The conference selects 18 scientists who form the International Committee of Weights and Measures that governs the Bureau.

For a time, the international prototype metre and kilogram were based, for convenience,upon the archive standards rather than directly upon actual measurement of the Earth. Definition by natural constants was readopted in 1960, when the metre was redefined as 1,650,763.73 wavelengths of the orange-red line in the krypton-86 spectrum, and again in 1983, when it was redefined as the distance traveled by light in a vacuum in 1/299,792,458 second. The kilogram is still defined as the mass of the international prototype at Sèvres.

In the 20th century the metric system generated derived systems needed in science and technology to express physical properties more complicated than simple length, weight, and volume. The centimetre-gram-second (CGS) and the metre-kilogram-second (MKS) systems were the chief systems so used until the establishment of the International System of Units (q.v.).

Date: 2016-04-22; view: 1371