# measurement

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## 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**weights and measures,**

units and standards for expressing the amount of some quantity, such as length, capacity, or weight; the science of measurement standards and methods is known as metrology.

Crude systems of weights and measures probably date from prehistoric times.

**.....**Click the link for more information. ), the most important and widely used are the metric system

**metric system,**

system of weights and measures planned in France and adopted there in 1799; it has since been adopted by most of the technologically developed countries of the world.

**.....**Click the link for more information. and the English units of measurement

**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.

**.....**Click the link for more information. . Certain units have been defined for special applications, e.g., the light-year

**light-year,**

in astronomy, unit of length equal to the distance light travels in one sidereal year. It is 9.461 × 10

^{12}km (about 6 million million mi). Alpha Centauri and Proxima Centauri, the stars nearest our solar system, are about 4.3 light-years distant.

**.....**Click the link for more information. and parsec

**parsec**

[

*par*allax +

*sec*ond], in astronomy, basic unit of length for measuring interstellar and intergalactic distances, equal to 206,265 times the distance from the earth to the sun, 3.26 light-years, or 3.08 × 10

^{13}km (about 19 million million mi).

**.....**Click the link for more information. in astronomy and the angstrom

**angstrom**

, abbr. Å, unit of length equal to 10

^{−10}meter (0.0000000001 meter); it is used to measure the wavelengths of visible light and of other forms of electromagnetic radiation, such as ultraviolet radiation and X rays.

**.....**Click the link for more information. in physics. Measurement is one of the fundamental processes of science

**science**

[Lat.

*scientia*=knowledge]. For many the term

*science*refers to the organized body of knowledge concerning the physical world, both animate and inanimate, but a proper definition would also have to include the attitudes and methods through which this body of

**.....**Click the link for more information. . 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

**interference,**

in physics, the effect produced by the combination or superposition of two systems of waves, in which these waves reinforce, neutralize, or in other ways interfere with each other.

**.....**Click the link for more information. ) 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

**quantum theory,**

modern physical theory concerned with the emission and absorption of energy by matter and with the motion of material particles; the quantum theory and the theory of relativity together form the theoretical basis of modern physics.

**.....**Click the link for more information. 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

**uncertainty principle,**

physical principle, enunciated by Werner Heisenberg in 1927, that places an absolute, theoretical limit on the combined accuracy of certain pairs of simultaneous, related measurements.

**.....**Click the link for more information. as an absolute limitation on certain pairs of related measurements.

## measurement

see CRITERIA AND LEVELS OF MEASUREMENT.## Measurement

an operation by means of which the ratio of one quantity (the quantity being measured) to another quantity of the same kind (taken as a unit) is determined; the number that expresses this ratio is called the numerical value of the quantity being measured.

Measurement is one of the oldest operations; it was used by man in practical activities (for distributing plots of land, in construction, and in irrigation work). Modern economic and social activities would be inconceivable without measurement.

An organic relation between observation and experiment, including the determination of the numerical values of the characteristics of objects and processes under study, is characteristic of the exact sciences. D.I. Mendeleev repeatedly emphasized that science begins with measurement.

A completed measurement includes the following elements: the object of measurement, a property or state of which is characterized by the measured quantity; a unit of measurement; technical measurement devices, graduated in the selected units; a method of measurement; an observer or recording device to register the result of the measurement; and the final result of the measurement.

Direct measurement, in which the result is obtained directly from measurement of the quantity itself (for example, measurement of the length of a graduated ruler or of the mass of a body by means of weights), is the simplest and historically the first known type of measurement. However, direct measurements are not always possible. In such cases, indirect measurements based on a known relation between the unknown quantity and the quantities being measured directly are used.

The causes and quantitative relationships that have been established by science between physical phenomena that differ in nature made it possible to devise a self-consistent system of units (the International System of Units) that is used in all fields of measurement.

Measurement should be distinguished from other means of quantitative characterization of quantities that are used when there is no unambiguous correspondence between a quantity and its quantitative expression in specified units. Thus, the visual determination of wind speed according to the Beaufort scale or of the hardness of minerals according to Mohs’ scale should be regarded as estimation rather than measurement.

Any measurement inevitably entails errors. Measurement errors caused by imperfection of the measuring method, by inaccurate gradation, and by incorrect installation of measuring equipment are called systematic errors. Systematic errors are eliminated by introducing experimentally determined corrections. Errors of another type—random errors—are due to the influence of uncontrollable factors, such as vibrations or random fluctuations of temperature, on the result of the measurement. Random errors are estimated by methods of mathematical statistics on the basis of data from repeated measurements.

In some cases—which are encountered particularly frequently in atomic and nuclear physics—the variability of the results of measurement is associated not only with equipment errors but also with the nature of the very phenomena being studied. For example, if a bundle of identically accelerated electrons is passed through the slit of a diffraction grating, electrons will strike various points of a screen mounted beyond the grating with a certain probability. This example shows that the extension of measurement to new fields of physics requires review and revision of the concepts used in measurements in other fields. Another important problem, the automation of measurement, arose with the development of science and technology. It is connected, on the one hand, with the conditions under which modern measurements are made (such as nuclear reactors and outer space) and, on the other, with the imperfection of the human sense organs. In modern industry, particularly at high speeds, pressures, and temperatures, the direct coupling of measuring devices to controls, bypassing humans, makes possible conversion to the most advanced form of production—automated production.

In metrology, aggregate and joint measurements are considered in addition to direct and indirect measurements. Measurements of several similar quantities whose values are found by solving a system of equations obtained as a result of direct measurements of various combinations of these quantities (such as the calibration of a set of weights when the values of the mass of the weights are found on the basis of direct measurement of the mass of one and comparison of the masses of various combinations of the weights) are called aggregate measurements. Joint measurements are simultaneous measurements of two or more various quantities for the purpose of finding a relation between or among them (for example, finding the dependence of the elongation of a body on temperature).

A distinction is also made between absolute and relative measurements. Absolute measurements include indirect measurements, which are based on the measurement of one or more basic quantities (such as length, mass, or time) and on the use of the values of fundamental physical constants in terms of which the physical quantity being measured can be expressed. Relative measurements are understood to be measurements either of the ratio of a quantity to a like quantity that plays the role of an arbitrary unit or of a change in a quantity with respect to another quantity that is used as a base.

The value of a quantity that is found as a result of measurement is the product of an abstract number (the numerical value) and a unit of the given quantity.

Because of errors, the results of a measurement always differ somewhat from the true value of the quantity being measured; therefore, the results of measurement are usually accompanied by an indication of the estimated error.

The uniformity of measurements in a country is provided by the metrological service, which keeps standard units and checks the measuring devices used. The classification of measurements according to the objects being measured has come into wide use. According to this classification, distinction is made among linear measurements (measurements of length, area, and volume), mechanical measurements (measurements of force, pressure, and other quantities), and electrical measurements. In general this classification corresponds to the main branches of the discipline of physics.

### REFERENCES

Malikov, S. F., and N.I. Tiurin.*Vvedenie v metrologiiu*, 2nd ed. Moscow, 1966.

Malikov, S.F.

*Vvedenie v tekhniku izmerenii*, 2nd ed. Moscow, 1952.

Jánossy, L.

*Teoriia i praktika obrabotki rezul’tatov izmerenii*, 2nd ed. Moscow, 1968. (Translated from English.)

*Izmeritel’naia tekhnika*, 1961, no. 12; 1962, nos. 4, 6, 8, 9, and 10. [section updated]

In mathematical theory, measurement moves away from the limited accuracy of physical measurements. The problem of measuring a quantity

*Q*by means of a unit of measurement

*U*consists in finding the numerical factor

*q*in the equation

*Q*=

*qU*

In this case

*Q*and

*U*are considered to be positive scalar quantities of the same kind, and the factor

*q*is a positive real number that may be either rational or irrational. For a rational number

*q*=

*m/n*(

*m*and

*n*are natural numbers), equation (

**1**) has an extremely simple meaning: it indicates that there exists a quantity

*V*(an

*n*th of

*U*) which, when taken as a term

*n*times, gives

*U*or, when taken as a term

*m*times, gives

*Q*:

*U*=

*nV Q*=

*mV*

In this case the quantities

*Q*and

*U*are said to be commensurable. For incommensurable

*U*and

*Q*the factor

*q*is irrational (for example, it may be equal to π if

*Q*is the circumference and

*U*the diameter of a circle). In this case the determination of the meaning of equation (1) is somewhat more complex. It may be determined in the following manner: equation (1) means that for any rational number

*r*,

*Q*>

*rU*follows from

*q*>

*r*

and

*Q*<

*rU*follows from

*q*<

*r*

It is sufficient to require that condition (2) be satisfied for all decimal approximations of

*q*that are less than or greater than

*q*. It should be noted that historically the very concept of irrational number arose from the problem of measurement, so that the original problem in the case of incommensurate quantities consisted not in determining the meaning of equation (1) on the basis of the ready theory of real numbers but in determining the meaning of the symbol

*q*, which reflects the result of a comparison of quantity

*Q*and the unit of measurement

*U*. For example, according to the definition of the German mathematician R. Dedekind, an irrational number is a “cross section” in the system of rational numbers. Such a cross section appears naturally when the two incommensurate quantities

*Q*and

*U*are compared. With respect to these quantities, all rational numbers are divided into two classes: the class

*R*

_{1}of the rational numbers

*r*, for which

*Q*>

*rU*, and the class

*R*

_{2}of the rational numbers

*r*, for which

*Q*<

*rU*.

The approximate measurement of quantities by means of rational numbers is of great importance. The error of an approximate equation

*Q*≃

*rU*is equal to Δ = (

*r*–

*q*)

*U*. It is natural to seek

*r*=

*m/n*for which the error is less than for any number

*r′ = m′/n′*with the denominator

*n′ ≤ n*. Approximations of this type are supplied by the suitable fractions r

_{1}, r

_{2}, r

_{3}, … of the number

*q*, which are found by using the theory of continued fractions. For example, for a circumference

*S*measured in the diameter

*U*, the approximations are

and so on; for the length of the year *Q* measured in days *U*, the approximations are

A. N. KOLMOGOROV

Measurement in social research (such as statistics, sociology, psychology, economics, and ethnology) is a method of ordering social data in which the systems of numbers and relationships among them are placed in correspondence with a number of social factors being measured. The different measures of the recurrence and reproducibility of social facts are the social measurements, or scales. Simple scales—such as monetary evaluation of labor, skill ratings, and the assessment of success in schooling (the grading system) and sports—come into use with the development of society. Measurement in the social sciences differs from such “natural” scales in the precise determination of measured attributes and rules for constructing the scale.

Measurements first came into use in social studies in the 1920’s and 1930’s, when investigators encountered the problem of reliability in the study of social consciousness, sociopsychological aims (relations), social and occupational status, public opinion, and qualitative characterization of working and everyday conditions. These measurements are an example of standardized group assessment, in which the “intensity” of public opinion is measured by sampling statistics.

Measurements are divided into three types: (1) nominal measurements, which are numbers assigned to objects on a nominal scale that merely state the difference or identity of the objects (that is, a nominal scale is essentially a grouping or classification); (2) ordinal measurements, in which the numbers assigned to objects on the scale order them according to the measured attribute but indicate only the procedure of placing the objects on the scale and not the distance between objects, much less the coordinates; (3) interval measurements, in which the numbers assigned to objects on the scale indicate not only the order of the objects but also the distance between them. For example, the scale of attractiveness of vocations is an interval measurement. Such a scale, by assigning a standard rating to each vocation, makes it possible to compare vocations in terms of popularity, that is, to assert that, for example, the job of driver is *M* points more popular than that of mechanic and *K* points less popular than that of pilot. However, it does not make possible the assertion that the interest in the jobs of driver and mechanic exceeds the interest in the job of pilot if the sum of corresponding points exceeds the rating of the vocation of pilot. The determination of a quantitative measure of social phenomena and processes is limited to these three types of measurement. Attempts are being made to create a fourth type of measurement—quantitative measurement—by introducing a unit of measurement.

### REFERENCES

Iadov, V.A.*Metodologiia i protsedury sotsiologicheskikh issledovanii*. Tartu, 1968.

Zdravomyslov, A.G.

*Metodologiia i protsedura sotsiologicheskikh is sledovanii*. Moscow, 1969.

IU. B. SAMSONOV

## What does it mean when you dream about measurement?

If we dream about something being measured out, it may represent a feeling of waiting, of “How long will this last?” It could also allude to the fact that we are making comparisons in our waking life.