Measurement

Last updated

Four measuring devices having metric calibrations FourMetricInstruments.JPG
Four measuring devices having metric calibrations

Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. [1] [2] In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind. [3] The scope and application of measurement are dependent on the context and discipline. In natural sciences and engineering, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International vocabulary of metrology published by the International Bureau of Weights and Measures. [2] However, in other fields such as statistics as well as the social and behavioural sciences, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales. [1] [4]

Contents

Measurement is a cornerstone of trade, science, technology and quantitative research in many disciplines. Historically, many measurement systems existed for the varied fields of human existence to facilitate comparisons in these fields. Often these were achieved by local agreements between trading partners or collaborators. Since the 18th century, developments progressed towards unifying, widely accepted standards that resulted in the modern International System of Units (SI). This system reduces all physical measurements to a mathematical combination of seven base units. The science of measurement is pursued in the field of metrology.

Measurement is defined as the process of comparison of an unknown quantity with a known or standard quantity.

History

Detail of a cubit rod in the Museo Egizio of Turin Coudee-turin detail.jpg
Detail of a cubit rod in the Museo Egizio of Turin
The earliest recorded systems of weights and measures originate in the 3rd or 4th millennium BC. Even the very earliest civilizations needed measurement for purposes of agriculture, construction and trade. Early standard units might only have applied to a single community or small region, with every area developing its own standards for lengths, areas, volumes and masses. Often such systems were closely tied to one field of use, so that volume measures used, for example, for dry grains were unrelated to those for liquids, with neither bearing any particular relationship to units of length used for measuring cloth or land. With development of manufacturing technologies, and the growing importance of trade between communities and ultimately across the Earth, standardized weights and measures became critical. Starting in the 18th century, modernized, simplified and uniform systems of weights and measures were developed, with the fundamental units defined by ever more precise methods in the science of metrology. The discovery and application of electricity was one factor motivating the development of standardized internationally applicable units.

Methodology

The measurement of a property may be categorized by the following criteria: type, magnitude, unit, and uncertainty.[ citation needed ] They enable unambiguous comparisons between measurements.

Standardization of measurement units

Measurements most commonly use the International System of Units (SI) as a comparison framework. The system defines seven fundamental units: kilogram, metre, candela, second, ampere, kelvin, and mole. All of these units are defined without reference to a particular physical object which serves as a standard. Artifact-free definitions fix measurements at an exact value related to a physical constant or other invariable phenomena in nature, in contrast to standard artifacts which are subject to deterioration or destruction. Instead, the measurement unit can only ever change through increased accuracy in determining the value of the constant it is tied to.

The seven base units in the SI system. Arrows point from units to those that depend on them. SI base unit.svg
The seven base units in the SI system. Arrows point from units to those that depend on them.

The first proposal to tie an SI base unit to an experimental standard independent of fiat was by Charles Sanders Peirce (1839–1914), [5] who proposed to define the metre in terms of the wavelength of a spectral line. [6] This directly influenced the Michelson–Morley experiment; Michelson and Morley cite Peirce, and improve on his method. [7]

Standards

With the exception of a few fundamental quantum constants, units of measurement are derived from historical agreements. Nothing inherent in nature dictates that an inch has to be a certain length, nor that a mile is a better measure of distance than a kilometre. Over the course of human history, however, first for convenience and then for necessity, standards of measurement evolved so that communities would have certain common benchmarks. Laws regulating measurement were originally developed to prevent fraud in commerce.

Units of measurement are generally defined on a scientific basis, overseen by governmental or independent agencies, and established in international treaties, pre-eminent of which is the General Conference on Weights and Measures (CGPM), established in 1875 by the Metre Convention, overseeing the International System of Units (SI). For example, the metre was redefined in 1983 by the CGPM in terms of the speed of light, the kilogram was redefined in 2019 in terms of the Planck constant and the international yard was defined in 1960 by the governments of the United States, United Kingdom, Australia and South Africa as being exactly 0.9144 metres.

In the United States, the National Institute of Standards and Technology (NIST), a division of the United States Department of Commerce, regulates commercial measurements. In the United Kingdom, the role is performed by the National Physical Laboratory (NPL), in Australia by the National Measurement Institute, [8] in South Africa by the Council for Scientific and Industrial Research and in India the National Physical Laboratory of India.

Units and systems

unit is known or standard quantity in terms of which other physical quantities are measured.

A baby bottle that measures in three measurement systems--metric, imperial (UK), and US customary. MetricImperialUSCustomaryUnits.jpg
A baby bottle that measures in three measurement systemsmetric, imperial (UK), and US customary.

Imperial and US customary systems

Before SI units were widely adopted around the world, the British systems of English units and later imperial units were used in Britain, the Commonwealth and the United States. The system came to be known as U.S. customary units in the United States and is still in use there and in a few Caribbean countries. These various systems of measurement have at times been called foot-pound-second systems after the Imperial units for length, weight and time even though the tons, hundredweights, gallons, and nautical miles, for example, are different for the U.S. units. Many Imperial units remain in use in Britain, which has officially switched to the SI system—with a few exceptions such as road signs, which are still in miles. Draught beer and cider must be sold by the imperial pint, and milk in returnable bottles can be sold by the imperial pint. Many people measure their height in feet and inches and their weight in stone and pounds, to give just a few examples. Imperial units are used in many other places, for example, in many Commonwealth countries that are considered metricated, land area is measured in acres and floor space in square feet, particularly for commercial transactions (rather than government statistics). Similarly, gasoline is sold by the gallon in many countries that are considered metricated.

Metric system

The metric system is a decimal system of measurement based on its units for length, the metre and for mass, the kilogram. It exists in several variations, with different choices of base units, though these do not affect its day-to-day use. Since the 1960s, the International System of Units (SI) is the internationally recognised metric system. Metric units of mass, length, and electricity are widely used around the world for both everyday and scientific purposes.

International System of Units

The International System of Units (abbreviated as SI from the French language name Système International d'Unités) is the modern revision of the metric system. It is the world's most widely used system of units, both in everyday commerce and in science. The SI was developed in 1960 from the metre–kilogram–second (MKS) system, rather than the centimetre–gram–second (CGS) system, which, in turn, had many variants. The SI units for the seven base physical quantities are: [9]

Base quantityBase unitSymbolDefining constant
time second shyperfine splitting in caesium-133
length metrem speed of light, c
mass kilogram kg Planck constant, h
electric current ampere A elementary charge, e
temperature kelvin K Boltzmann constant, k
amount of substance mol mol Avogadro constant, NA
luminous intensity candela cd luminous efficacy of a 540 THz source, Kcd

In the SI, base units are the simple measurements for time, length, mass, temperature, amount of substance, electric current and light intensity. Derived units are constructed from the base units, for example, the watt, i.e. the unit for power, is defined from the base units as m2·kg·s−3. Other physical properties may be measured in compound units, such as material density, measured in kg/m3.

Converting prefixes

The SI allows easy multiplication when switching among units having the same base but different prefixes. To convert from metres to centimetres it is only necessary to multiply the number of metres by 100, since there are 100 centimetres in a metre. Inversely, to switch from centimetres to metres one multiplies the number of centimetres by 0.01 or divides the number of centimetres by 100.

Length

A 2-metre carpenter's ruler CarpentersRule.png
A 2-metre carpenter's ruler

A ruler or rule is a tool used in, for example, geometry, technical drawing, engineering, and carpentry, to measure lengths or distances or to draw straight lines. Strictly speaking, the ruler is the instrument used to rule straight lines and the calibrated instrument used for determining length is called a measure, however common usage calls both instruments rulers and the special name straightedge is used for an unmarked rule. The use of the word measure, in the sense of a measuring instrument, only survives in the phrase tape measure, an instrument that can be used to measure but cannot be used to draw straight lines. As can be seen in the photographs on this page, a two-metre carpenter's rule can be folded down to a length of only 20 centimetres, to easily fit in a pocket, and a five-metre-long tape measure easily retracts to fit within a small housing.

Time

Time is an abstract measurement of elemental changes over a non-spatial continuum. It is denoted by numbers and/or named periods such as hours, days, weeks, months and years. It is an apparently irreversible series of occurrences within this non spatial continuum. It is also used to denote an interval between two relative points on this continuum.

Mass

Mass refers to the intrinsic property of all material objects to resist changes in their momentum. Weight, on the other hand, refers to the downward force produced when a mass is in a gravitational field. In free fall, (no net gravitational forces) objects lack weight but retain their mass. The Imperial units of mass include the ounce, pound, and ton. The metric units gram and kilogram are units of mass.

One device for measuring weight or mass is called a weighing scale or, often, simply a scale. A spring scale measures force but not mass, a balance compares weight, both require a gravitational field to operate. Some of the most accurate instruments for measuring weight or mass are based on load cells with a digital read-out, but require a gravitational field to function and would not work in free fall.

Economics

The measures used in economics are physical measures, nominal price value measures and real price measures. These measures differ from one another by the variables they measure and by the variables excluded from measurements.

Survey research

Measurement station C of EMMA experiment situated at the depth of 75 meters in the Pyhasalmi Mine. EMMA experiment.jpg
Measurement station C of EMMA experiment situated at the depth of 75 meters in the Pyhäsalmi Mine.

In the field of survey research, measures are taken from individual attitudes, values, and behavior using questionnaires as a measurement instrument. As all other measurements, measurement in survey research is also vulnerable to measurement error, i.e. the departure from the true value of the measurement and the value provided using the measurement instrument. [10] In substantive survey research, measurement error can lead to biased conclusions and wrongly estimated effects. In order to get accurate results, when measurement errors appear, the results need to be corrected for measurement errors.

Exactness designation

The following rules generally apply for displaying the exactness of measurements: [11]

Difficulties

Since accurate measurement is essential in many fields, and since all measurements are necessarily approximations, a great deal of effort must be taken to make measurements as accurate as possible. For example, consider the problem of measuring the time it takes an object to fall a distance of one metre (about 39  in). Using physics, it can be shown that, in the gravitational field of the Earth, it should take any object about 0.45 second to fall one metre. However, the following are just some of the sources of error that arise:

Additionally, other sources of experimental error include:

Scientific experiments must be carried out with great care to eliminate as much error as possible, and to keep error estimates realistic.

Definitions and theories

Classical definition

In the classical definition, which is standard throughout the physical sciences, measurement is the determination or estimation of ratios of quantities. [13] Quantity and measurement are mutually defined: quantitative attributes are those possible to measure, at least in principle. The classical concept of quantity can be traced back to John Wallis and Isaac Newton, and was foreshadowed in Euclid's Elements. [13]

Representational theory

In the representational theory, measurement is defined as "the correlation of numbers with entities that are not numbers". [14] The most technically elaborated form of representational theory is also known as additive conjoint measurement. In this form of representational theory, numbers are assigned based on correspondences or similarities between the structure of number systems and the structure of qualitative systems. A property is quantitative if such structural similarities can be established. In weaker forms of representational theory, such as that implicit within the work of Stanley Smith Stevens, [15] numbers need only be assigned according to a rule.

The concept of measurement is often misunderstood as merely the assignment of a value, but it is possible to assign a value in a way that is not a measurement in terms of the requirements of additive conjoint measurement. One may assign a value to a person's height, but unless it can be established that there is a correlation between measurements of height and empirical relations, it is not a measurement according to additive conjoint measurement theory. Likewise, computing and assigning arbitrary values, like the "book value" of an asset in accounting, is not a measurement because it does not satisfy the necessary criteria.

Three type of representational theory

  1. Empirical relation
    In science, an empirical relationship is a relationship or correlation based solely on observation rather than theory. An empirical relationship requires only confirmatory data irrespective of theoretical basis.
  2. The rule of mapping
    The real world is the Domain of mapping, and the mathematical world is the range. when we map the attribute to mathematical system, we have many choice for mapping and the range.
  3. The representation condition of measurement

Theory

All data are inexact and statistical in nature. Thus the definition of measurement is: "A set of observations that reduce uncertainty where the result is expressed as a quantity." [16] This definition is implied in what scientists actually do when they measure something and report both the mean and statistics of the measurements. In practical terms, one begins with an initial guess as to the expected value of a quantity, and then, using various methods and instruments, reduces the uncertainty in the value. In this view, unlike the positivist representational theory, all measurements are uncertain, so instead of assigning one value, a range of values is assigned to a measurement. This also implies that there is not a clear or neat distinction between estimation and measurement.

Quantum mechanics

In quantum mechanics, a measurement is an action that determines a particular property (position, momentum, energy, etc.) of a quantum system. Quantum measurements are always statistical samples from a probability distribution; the distribution for many quantum phenomena is discrete. [17] :197 Quantum measurements alter quantum states and yet repeated measurements on a quantum state are reproducible. The measurement appears to act as a filter, changing the quantum state into one with the single measured quantum value. [17] The unambiguous meaning of the quantum measurement is an unresolved fundamental problem in quantum mechanics; the most common interpretation is that when a measurement is performed, the wavefunction of the quantum system "collapses" to a single, definite value. [18]

Biology

In biology, there is generally no well established theory of measurement. However, the importance of the theoretical context is emphasized. [19] Moreover, the theoretical context stemming from the theory of evolution leads to articulate the theory of measurement and historicity as a fundamental notion. [20] Among the most developed fields of measurement in biology are the measurement of genetic diversity and species diversity. [21]

See also

Related Research Articles

The centimetre–gram–second system of units is a variant of the metric system based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanical units are unambiguously derived from these three base units, but there are several different ways in which the CGS system was extended to cover electromagnetism.

<span class="mw-page-title-main">Kilogram</span> Metric unit of mass

The kilogram is the base unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. It means 'one thousand grams'.

<span class="mw-page-title-main">Mass</span> Amount of matter present in an object

Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple definitions which are conceptually distinct, but physically equivalent. Mass can be experimentally defined as a measure of the body's inertia, meaning the resistance to acceleration when a net force is applied. The object's mass also determines the strength of its gravitational attraction to other bodies.

A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that cannot be explained by a theory and therefore must be measured experimentally. It is distinct from a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement.

<span class="mw-page-title-main">International System of Units</span> Modern form of the metric system

The International System of Units, internationally known by the abbreviation SI, is the modern form of the metric system and the world's most widely used system of measurement. Coordinated by the International Bureau of Weights and Measures it is the only system of measurement with official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce.

<span class="mw-page-title-main">SI base unit</span> One of the seven units of measurement that define the metric system

The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all other SI units can be derived. The units and their physical quantities are the second for time, the metre for length or distance, the kilogram for mass, the ampere for electric current, the kelvin for thermodynamic temperature, the mole for amount of substance, and the candela for luminous intensity. The SI base units are a fundamental part of modern metrology, and thus part of the foundation of modern science and technology.

<span class="mw-page-title-main">Weight</span> Force on a mass due to gravity

In science and engineering, the weight of an object, is the force acting on the object due to acceleration of gravity.

<span class="mw-page-title-main">Metric system</span> Metre-based systems of measurement

The metric system is a decimal-based system of measurement. The current international standard for the metric system is the International System of Units, in which all units can be expressed in terms of seven base units: the metre, kilogram, second, ampere, kelvin, mole, and candela.

<span class="mw-page-title-main">Metrology</span> Science of measurement and its application

Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in France when a length standard taken from a natural source was proposed. This led to the creation of the decimal-based metric system in 1795, establishing a set of standards for other types of measurements. Several other countries adopted the metric system between 1795 and 1875; to ensure conformity between the countries, the Bureau International des Poids et Mesures (BIPM) was established by the Metre Convention. This has evolved into the International System of Units (SI) as a result of a resolution at the 11th General Conference on Weights and Measures (CGPM) in 1960.

<span class="mw-page-title-main">Kibble balance</span> Electromechanical weight measuring instrument

A Kibble balance is an electromechanical measuring instrument that measures the weight of a test object very precisely by the electric current and voltage needed to produce a compensating force. It is a metrological instrument that can realize the definition of the kilogram unit of mass based on fundamental constants.

A system of units of measurement, also known as a system of units or system of measurement, is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Instances in use include the International System of Units or SI, the British imperial system, and the United States customary system.

<span class="mw-page-title-main">Mass versus weight</span> Distinction between mass and weight

In common usage, the mass of an object is often referred to as its weight, though these are in fact different concepts and quantities. Nevertheless, one object will always weigh more than another with less mass if both are subject to the same gravity.

<span class="mw-page-title-main">Unit of measurement</span> Quantity standard

A unit of measurement, or unit of measure, is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multiple of the unit of measurement.

<span class="mw-page-title-main">Standard (metrology)</span> Object, system, or experiment which relates to a unit of measurement of a physical quantity

In metrology, a standard is an object, system, or experiment that bears a defined relationship to a unit of measurement of a physical quantity. Standards are the fundamental reference for a system of weights and measures, against which all other measuring devices are compared. Historical standards for length, volume, and mass were defined by many different authorities, which resulted in confusion and inaccuracy of measurements. Modern measurements are defined in relationship to internationally standardized reference objects, which are used under carefully controlled laboratory conditions to define the units of length, mass, electrical potential, and other physical quantities.

<span class="mw-page-title-main">2019 redefinition of the SI base units</span> Definition of the units kg, A, K and mol

In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144th anniversary of the Metre Convention, the kilogram, ampere, kelvin, and mole are now defined by setting exact numerical values, when expressed in SI units, for the Planck constant, the elementary electric charge, the Boltzmann constant, and the Avogadro constant, respectively. The second, metre, and candela had previously been redefined using physical constants. The four new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research.

<span class="mw-page-title-main">History of the metric system</span> History of the metric system measurement standards

The history of the metric system began during the Age of Enlightenment with measures of length and weight derived from nature, along with their decimal multiples and fractions. The system became the standard of France and Europe within half a century. Other measures with unity ratios were added, and the system went on to be adopted across the world.

In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants: c, G, ħ, and kB. Expressing one of these physical constants in terms of Planck units yields a numerical value of 1. They are a system of natural units, defined using fundamental properties of nature rather than properties of a chosen prototype object. Originally proposed in 1899 by German physicist Max Planck, they are relevant in research on unified theories such as quantum gravity.

In physics, natural unit systems are measurement systems for which certain physical constants have been set to 1 through nondimensionalization of physical units. For example, the speed of light c may be set to 1, and it may then be omitted, equating mass and energy directly E=m rather than using c as a conversion factor in the typical mass–energy equivalence equation E=mc2. A purely natural system of units has all of its dimensions collapsed, such that the physical constants completely define the system of units and the relevant physical laws contain no conversion constants.

<span class="mw-page-title-main">Outline of the metric system</span> Overview of and topical guide to the metric system

The following outline is provided as an overview of and topical guide to the metric system:

The following is a topical outline of the English language Wikipedia articles on the topic of metrology and measurement. Metrology is the science of measurement and its application.

References

  1. 1 2 Pedhazur, Elazar J.; Schmelkin, Leora and Albert (1991). Measurement, Design, and Analysis: An Integrated Approach (1st ed.). Hillsdale, NJ: Lawrence Erlbaum Associates. pp.  15–29. ISBN   978-0-8058-1063-9.
  2. 1 2 International Vocabulary of Metrology – Basic and General Concepts and Associated Terms (VIM) (PDF) (3rd ed.). International Bureau of Weights and Measures. 2008. p. 16.
  3. Young, Hugh D; Freedman, Roger A. (2012). University Physics (13 ed.). Pearson Education Inc. ISBN   978-0-321-69686-1.
  4. Kirch, Wilhelm, ed. (2008). "Level of measurement". Encyclopedia of Public Health. Vol. 2. Springer. p. 81. ISBN   978-0-321-02106-9.
  5. Crease 2011 , pp. 182–4
  6. C.S. Peirce (July 1879) "Note on the Progress of Experiments for Comparing a Wave-length with a Metre" American Journal of Science, as referenced by Crease 2011 , p. 203
  7. Crease, Robert P. (2011). World in the Balance: The Historical Quest for an Absolute System of Measurement. New York & London: W. W. Norton. p. 203. ISBN   978-0-393-34354-0.
  8. "About Us". National Measurement Institute of Australia. 3 December 2020.
  9. Le Système international d’unités [The International System of Units](PDF) (in French and English) (9th ed.), International Bureau of Weights and Measures, 2019, ISBN   978-92-822-2272-0
  10. Groves, Robert (2004). Survey Methodology . New Jersey: Wiley. ISBN   9780471483489. "By measurement error we mean a departure from the value of the measurement as applied to a sample unit and the value provided. " pp. 51–52 .
  11. Page 41 in: VanPool, Todd (2011). Quantitative analysis in archaeology. Chichester Malden: Wiley-Blackwell. ISBN   978-1-4443-9017-9. OCLC   811317577.
  12. Gill, Simeon; Parker, Christopher J. (2017). "Scan posture definition and hip girth measurement: the impact on clothing design and body scanning". Ergonomics. 60 (8): 1123–1136. doi:10.1080/00140139.2016.1251621. PMID   27764997. S2CID   23758581.
  13. 1 2 Michell, J. (1999). Measurement in psychology: a critical history of a methodological concept. New York: Cambridge University Press.
  14. Ernest Nagel: "Measurement", Erkenntnis, Volume 2, Number 1 / December 1931, pp. 313–335, published by Springer, the Netherlands
  15. Stevens, S.S. On the theory of scales and measurement 1946. Science. 103, 677–80.
  16. Douglas Hubbard: "How to Measure Anything", Wiley (2007), p. 21
  17. 1 2 Messiah, Albert (1966). Quantum Mechanics. North Holland, John Wiley & Sons. ISBN   0486409244.
  18. Penrose, Roger (2007). The road to reality : a complete guide to the laws of the universe. New York: Vintage Books. ISBN   978-0-679-77631-4. "The jumping of the quantum state to one of the eigenstates of Q is the process referred to as state-vector reduction or collapse of the wavefunction. It is one of quantum theory's most puzzling features ..." "[T]he way in which quantum mechanics is used in practice is to take the state indeed to jump in this curious way whenever a measurement is deemed to take place." p 528 Later Chapter 29 is entitled the Measurement paradox.
  19. Houle, David; Pélabon, Christophe; Wagner, Günter P.; Hansen, Thomas F. (2011). "Measurement and Meaning in Biology" (PDF). The Quarterly Review of Biology. 86 (1): 3–34. doi:10.1086/658408. ISSN   0033-5770. PMID   21495498. S2CID   570080. Archived from the original (PDF) on 2019-05-29.
  20. Montévil, Maël (2019). "Measurement in biology is methodized by theory". Biology & Philosophy. 34 (3). doi:10.1007/s10539-019-9687-x. ISSN   0169-3867. S2CID   96447209.
  21. Magurran, A.E. & McGill, B.J. (Hg.) 2011: Biological Diversity: Frontiers in Measurement and Assessment Oxford University Press.