The
Contents 1 Units and prefixes 1.1 Base units 1.2 Derived units 1.3 Prefixes 1.4 Non-SI units accepted for use with SI 1.5 Common notions of the metric units 2 Lexicographic conventions 2.1 Unit names 2.2 Unit symbols and the values of quantities 2.2.1 General rules 2.2.2 Printing SI symbols 3 International System of Quantities 4 Realisation of units 5 Evolution of the SI 5.1 Changes to the SI 5.2 Proposed redefinitions 6 History 6.1 The improvisation of units
6.2
7 See also 8 Notes 9 References 10 Further reading 11 External links Units and prefixes[edit]
The
Unit name Unit symbol Dimension symbol Quantity name Definition [n 1] metre m L length Prior (1793): 1/7007100000000000000♠10000000 of the meridian through Paris between the North Pole and the Equator.FG Interim (1960): 7006165076373000000♠1650763.73 wavelengths in a vacuum of the radiation corresponding to the transition between the 2p10 and 5d5 quantum levels of the krypton-86 atom. Current (1983): The distance travelled by light in vacuum in 1/7008299792458000000♠299792458 second. kilogram[n 2] kg M mass Prior (1793): The grave was defined as being the mass (then called weight) of one litre of pure water at its freezing point.FG Current (1889): The mass of a small squat cylinder of ~47 cubic centimetres of platinum-iridium alloy kept in a laboratory in France. Also, in practice, any of numerous official replicas of it.[8][9] second s T time Prior: 1/7004864000000000000♠86400 of a day of 24 hours of 60 minutes of 60 seconds Interim (1956): 1/7007315569259747000♠31556925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time. Current (1967): The duration of 7009919263177000000♠9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. ampere A I electric current Prior (1881): A tenth of the electromagnetic CGS unit of current. The [CGS] electromagnetic unit of current is that current, flowing in an arc 1 cm long of a circle 1 cm in radius, that creates a field of one oersted at the centre.[10] IEC Current (1946): The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 6993200000000000000♠2×10−7 newtons per metre of length. kelvin K Θ thermodynamic temperature Prior (1743): The centigrade scale is obtained by assigning 0 °C to the freezing point of water and 100 °C to the boiling point of water. Interim (1954): The triple point of water (0.01 °C) defined to be exactly 273.16 K.[n 3] Current (1967): 1/273.16 of the thermodynamic temperature of the triple point of water mole mol N amount of substance Prior (1900): A stoichiometric quantity which is the equivalent mass
in grams of
candela cd J luminous intensity Prior (1946): The value of the new candle is such that the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per square centimetre. Current (1979): The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 7014540000000000000♠5.4×1014 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. Note: both old and new definitions are approximately the luminous intensity of a whale blubber candle burning modestly bright, in the late 19th century called a "candlepower" or a "candle". Notes ^ Interim definitions are given here only when there has been a significant difference in the definition. ^ Despite the prefix "kilo-", the kilogram is the base unit of mass. The kilogram, not the gram, is used in the definitions of derived units. Nonetheless, units of mass are named as if the gram were the base unit. ^ In 1954 the unit of thermodynamic temperature was known as the "degree Kelvin" (symbol °K; "Kelvin" spelt with an upper-case "K"). It was renamed the "kelvin" (symbol "K"; "kelvin" spelt with a lower case "k") in 1967. ^ When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. The Prior definitions of the various base units in the above table were made by the following authorities: FG = French Government IEC = International Electrotechnical Commission ICAW = International Committee on Atomic Weights All other definitions result from resolutions by either CGPM or the CIPM and are catalogued in the SI Brochure. The early metric systems defined a unit of weight as a base unit,
while the SI defines an analogous unit of mass. In everyday use, these
are mostly interchangeable, but in scientific contexts the difference
matters. Mass, strictly the inertial mass, represents a quantity of
matter. It relates the acceleration of a body to the applied force via
Newton's law, F = m × a: force equals mass times acceleration. In SI
units, if you apply a force of 1 N (newton) to a mass of
1 kg, it will accelerate at 1 m/s2. This is true whether the
object is floating in space or in a gravity field e.g. at the Earth's
surface.
Named SI derived units[5]:3 Namenote 1 Symbol Quantity In other SI units In SI base units radiannote 2 rad angle (m⋅m−1) steradiannote 2 sr solid angle (m2⋅m−2) hertz Hz frequency s−1 newton N force, weight kg⋅m⋅s−2 pascal Pa pressure, stress N/m2 kg⋅m−1⋅s−2 joule J energy, work, heat N⋅m kg⋅m2⋅s−2 watt W power, radiant flux J/s kg⋅m2⋅s−3 coulomb C electric charge or quantity of electricity s⋅A volt V voltage (electrical potential), emf W/A kg⋅m2⋅s−3⋅A−1 farad F capacitance C/V kg−1⋅m−2⋅s4⋅A2 ohm Ω resistance, impedance, reactance V/A kg⋅m2⋅s−3⋅A−2 siemens S electrical conductance Ω−1 kg−1⋅m−2⋅s3⋅A2 weber Wb magnetic flux V⋅s kg⋅m2⋅s−2⋅A−1 tesla T magnetic flux density Wb/m2 kg⋅s−2⋅A−1 henry H inductance Wb/A kg⋅m2⋅s−2⋅A−2 degree Celsius °C temperature relative to 273.15 K K lumen lm luminous flux cd⋅sr cd lux lx illuminance lm/m2 m−2⋅cd becquerel Bq radioactivity (decays per unit time) s−1 gray Gy absorbed dose (of ionizing radiation) J/kg m2⋅s−2 sievert Sv equivalent dose (of ionizing radiation) J/kg m2⋅s−2 katal kat catalytic activity mol⋅s−1 Notes 1. The table is ordered so that derived units are listed after the units that define them. 2. The radian and steradian are defined as dimensionless derived units. Prefixes[edit] Main article: Metric prefix Prefixes are added to unit names to produce multiples and sub-multiples of the original unit. All of these are integer powers of ten, and above a hundred or below a hundredth all are integer powers of a thousand. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth, so there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined, so for example a millionth of a metre is a micrometre, not a millimillimetre. Multiples of the kilogram are named as if the gram were the base unit, so a millionth of a kilogram is a milligram, not a microkilogram.[3]:122[12]:14 When prefixes are used with SI units, the resulting units are no longer coherent.[3]:106 v t e Standard prefixes for the SI units of measure Multiples Prefix name deca hecto kilo mega giga tera peta exa zetta yotta Prefix symbol da h k M G T P E Z Y Factor 100 101 102 103 106 109 1012 1015 1018 1021 1024
Submultiples Prefix name deci centi milli micro nano pico femto atto zepto yocto Prefix symbol d c m μ n p f a z y Factor 100 10−1 10−2 10−3 10−6 10−9 10−12 10−15 10−18 10−21 10−24 Non-SI units accepted for use with SI[edit] Main article: non-SI units accepted for use with SI Many non-SI units continue to be used in the scientific, technical, and commercial literature. Some units are deeply embedded in history and culture, and their use has not been entirely replaced by their SI alternatives. The CIPM recognised and acknowledged such traditions by compiling a list of non-SI units accepted for use with SI, which are grouped as follows:[3]:123–129[12]:7–11[Note 1] The litre is classed as a non-SI unit accepted for use with the SI. Being one thousandth of a cubic metre, the litre is not a coherent unit of measure with respect to SI. Non-SI units accepted for use with the SI: Certain units of time, angle, and legacy non-SI metric units have a long history of consistent use. Most societies have used the solar day and its non-decimal subdivisions as a basis of time and, unlike the foot or the pound, these were the same regardless of where they were being measured. The radian, being 1/2π of a revolution, has mathematical advantages but it is cumbersome for navigation, and, as with time, the units used in navigation have a large degree of consistency around the world. The tonne, litre, and hectare were adopted by the CGPM in 1879 and have been retained as units that may be used alongside SI units, having been given unique symbols. The catalogued units are minute, hour, day, degree of arc, minute of arc, second of arc, hectare, litre, tonne, astronomical unit and [deci]bel Non-SI units whose values in SI units must be obtained experimentally (Table 7). Physicists often use units of measure that are based on natural phenomena, particularly when the quantities associated with these phenomena are many orders of magnitude greater than or less than the equivalent SI unit. The most common ones have been catalogued in the SI Brochure together with consistent symbols and accepted values, but with the caveat that their values in SI units need to be measured. electronvolt (symbol eV), and dalton/unified atomic mass unit (Da or u)
Other non-SI units (Table 8): A number of non-SI units that had never been formally sanctioned by the CGPM have continued to be used across the globe in many spheres including health care and navigation. As with the units of measure in Tables 6 and 7, these have been catalogued by the CIPM in the SI Brochure to ensure consistent usage, but with the recommendation that authors who use them should define them wherever they are used. bar, millimetre of mercury, ångström, nautical mile, barn, knot and neper In the interests of standardising health-related units of measure used in the nuclear industry, the 12th CGPM (1964) accepted the continued use of the curie (symbol Ci) as a non-SI unit of activity for radionuclides;[3]:152 the SI derived units becquerel, sievert and gray were adopted in later years. Similarly, the millimetre of mercury (symbol mmHg) was retained for measuring blood pressure.[3]:127 Non-SI units associated with the CGS and the CGS-Gaussian system of units (Table 9) The SI manual also catalogues a number of legacy units of measure that are used in specific fields such as geodesy and geophysics or are found in the literature, particularly in classical and relativistic electrodynamics where they have certain advantages: The units that are catalogued are: erg, dyne, poise, stokes, stilb, phot, gal, maxwell, gauss, and oersted. Common notions of the metric units[edit] The basic units of the metric system, as originally defined, represented common quantities or relationships in nature. They still do – the modern precisely defined quantities are refinements of definition and methodology, but still with the same magnitudes. In cases where laboratory precision may not be required or available, or where approximations are good enough, the original definitions may suffice.[13] A second is 1/60 of a minute, which is 1/60 of an hour, which is 1/24
of a day, so a second is 1/86400 of a day; a second is the time it
takes a dense object to freely fall 4.9 metres from rest.
The metre is close to the length of a pendulum that has a period of 2
seconds; most dining tabletops are about 0.75 metre high; a very tall
human (basketball forward) is about 2 metres tall.
The kilogram is the mass of a litre of cold water; a cubic centimetre
or millilitre of water has a mass of one gram; a 1-euro coin,
7.5 g; a Sacagawea US 1-dollar coin, 8.1 g; a UK 50-pence
coin, 8.0 g.
A candela is about the luminous intensity of a moderately bright
candle, or 1 candle power; a 60 W tungsten-filament incandescent
light bulb has a luminous intensity of about 64 candela.
A mole of a substance has a mass that is its molecular mass expressed
in units of grams; the mass of a mole of table salt is 58.4 g.
A temperature difference of one kelvin is the same as one degree
Celsius: 1/100 of the temperature differential between the freezing
and boiling points of water at sea level; the absolute temperature in
kelvins is the temperature in degrees
Lexicographic conventions[edit]
Unit names[edit]
Names of units follow the grammatical rules associated with common
nouns: in English and in French they start with a lowercase letter
(e.g., newton, hertz, pascal), even when the symbol for the unit
begins with a capital letter. This also applies to "degrees Celsius",
since "degree" is the unit.[14][15] The official British and American
spellings for certain SI units differ – British English, as well as
Australian, Canadian and New Zealand English, uses the spelling deca-,
metre, and litre whereas
The value of a quantity is written as a number followed by a space (representing a multiplication sign) and a unit symbol; e.g., 2.21 kg, 7002730000000000000♠7.3×102 m2, 22 K. This rule explicitly includes the percent sign (%)[3]:134 and the symbol for degrees of temperature (°C).[3]: 133 Exceptions are the symbols for plane angular degrees, minutes, and seconds (°, ′, and ″), which are placed immediately after the number with no intervening space. Symbols are mathematical entities, not abbreviations, and as such do not have an appended period/full stop (.), unless the rules of grammar demand one for another reason, such as denoting the end of a sentence. A prefix is part of the unit, and its symbol is prepended to the unit symbol without a separator (e.g., k in km, M in MPa, G in GHz). Compound prefixes are not allowed. Symbols for derived units formed by multiplication are joined with a centre dot (⋅) or a non-breaking space; e.g., N⋅m or N m. Symbols for derived units formed by division are joined with a solidus (/), or given as a negative exponent. E.g., the "metre per second" can be written m/s, m s−1, m⋅s−1, or m/s. A solidus must not be used more than once in a given expression without parentheses to remove ambiguities; e.g., kg/(m⋅s2) and kg⋅m−1⋅s−2 are acceptable, but kg/m/s2 is ambiguous and unacceptable.
The first letter of symbols for units derived from the name of a
person is written in upper case; otherwise, they are written in lower
case. E.g., the unit of pressure is named after Blaise Pascal, so its
symbol is written "Pa", but the symbol for mole is written "mol".
Thus, "T" is the symbol for tesla, a measure of magnetic field
strength, and "t" the symbol for tonne, a measure of mass. Since 1979,
the litre may exceptionally be written using either an uppercase "L"
or a lowercase "l", a decision prompted by the similarity of the
lowercase letter "l" to the numeral "1", especially with certain
typefaces or English-style handwriting. The American NIST recommends
that within the
Printing SI symbols[edit] The rules covering printing of quantities and units are part of ISO 80000-1:2009.[19] Further rules[Note 2] are specified in respect of production of text using printing presses, word processors, typewriters and the like. International System of Quantities[edit] SI Brochure Cover of brochure The International System of Units The CGPM publishes a brochure which defines and presents the SI.[3] Its official version is in French, in line with the Metre Convention.[3]:102 It leaves some scope for local interpretation, particularly regarding names and terms in different languages.[20][5] The writing and maintenance of the CGPM brochure is carried out by one of the committees of the International Committee for Weights and Measures (CIPM). The definitions of the terms "quantity", "unit", "dimension" etc. that are used in the SI Brochure are those given in the International vocabulary of metrology.[21] Main article: International System of Quantities
The quantities and equations that define the SI units are now referred
to as the
Realisation of units[edit] Main article: Realization (metrology) Silicon sphere for the
Metrologists carefully distinguish between the definition of a unit and its realisation. The definition of each base unit of the SI is drawn up so that it is unique and provides a sound theoretical basis on which the most accurate and reproducible measurements can be made. The realisation of the definition of a unit is the procedure by which the definition may be used to establish the value and associated uncertainty of a quantity of the same kind as the unit. A description of the mise en pratique[Note 3] of the base units is given in an electronic appendix to the SI Brochure.[25][3]:168–169 The published mise en pratique is not the only way in which a base unit can be determined: the SI Brochure states that "any method consistent with the laws of physics could be used to realise any SI unit."[3]:111 In the current (2016) exercise to overhaul the definitions of the base units, various consultative committees of the CIPM have required that more than one mise en pratique shall be developed for determining the value of each unit.[citation needed] In particular: At least three separate experiments be carried out yielding values
having a relative standard uncertainty in the determination of the
kilogram of no more than 6992500000000000000♠5×10−8 and at least
one of these values should be better than
6992200000000000000♠2×10−8. Both the
Evolution of the SI[edit]
Changes to the SI[edit]
The
Dependencies of proposed SI unit definitions (in colour) and seven physical constants (in grey) with fixed numerical values. Unlike the current (2014) definition, the base units are derived from one or more constants of nature. Main article: Proposed redefinition of SI base units
After the metre was redefined in 1960, the kilogram remained the only
In addition to the speed of light, four constants of nature – the
Planck constant, an elementary charge, the
The redefinitions are expected to be adopted at the 26th CGPM in November 2018.[31] The CODATA task group on fundamental constants has announced special submission deadlines for data to compute the values that will be announced at this event.[32] History[edit] Stone marking the Austro-Hungarian/Italian border at Pontebba
displaying myriametres, a unit of 10 km used in
Main article: History of the metric system
The improvisation of units[edit]
The units and unit magnitudes of the metric system which became the SI
were improvised piecemeal from everyday physical quantities starting
in the mid-18th century. Only later were they moulded into an
orthogonal coherent decimal system of measurement.
The degree centigrade as a unit of temperature resulted from the scale
devised by Swedish astronomer
Carl Friedrich Gauss In March 1791, the Assembly adopted the committee's proposed principles for the new decimal system of measure including the metre defined to be 1/10,000,000th of the length of the quadrant of earth's meridian passing through Paris, and authorised a survey to precisely establish the length of the meridian. In July 1792, the committee proposed the names metre, are, litre and grave for the units of length, area, capacity, and mass, respectively. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as centi for a hundredth and kilo for a thousand.[40]:82 Thomson Maxwell William Thomson (Lord Kelvin) and
Later, during the process of adoption of the metric system, the Latin
gramme and kilogramme, replaced the former provincial terms gravet
(1/1000 grave) and grave. In June 1799, based on the results of the
meridian survey, the standard mètre des Archives and kilogramme des
Archives were deposited in the French National Archives. Subsequently,
that year, the metric system was adopted by law in France.[46] [47]
The French system was short-lived due to its unpopularity. Napoleon
ridiculed it, and in 1812, introduced a replacement system, the
mesures usuelles or "customary measures" which restored many of the
old units, but redefined in terms of the metric system.
During the first half of the 19th century there was little consistency
in the choice of preferred multiples of the base units: typically the
myriametre (7004100000000000000♠10000 metres) was in widespread
use in both France and parts of Germany, while the kilogram
(7003100000000000000♠1000 grams) rather than the myriagram was used
for mass.[33]
In 1832, the German mathematician Carl Friedrich Gauss, assisted by
Wilhelm Weber, implicitly defined the second as a base unit when he
quoted the Earth's magnetic field in terms of millimetres, grams, and
seconds.[41] Prior to this, the strength of the Earth's magnetic field
had only been described in relative terms. The technique used by Gauss
was to equate the torque induced on a suspended magnet of known mass
by the Earth's magnetic field with the torque induced on an equivalent
system under gravity. The resultant calculations enabled him to assign
dimensions based on mass, length and time to the magnetic
field.[48][49]
A candlepower as a unit of illuminance was originally defined by an
1860 English law as the light produced by a pure spermaceti candle
weighing 1⁄6 pound (76 grams) and burning at a specified rate.
Spermaceti, a waxy substance found in the heads of sperm whales, was
once used to make high-quality candles. At this time the French
standard of light was based upon the illumination from a Carcel oil
lamp. The unit was defined as that illumination emanating from a lamp
burning pure rapeseed oil at a defined rate. It was accepted that ten
standard candles were about equal to one Carcel lamp.
CGPM vocabulary French English Pages[3] étalons [Technical] standard 5, 95 prototype prototype [kilogram/metre] 5,95 noms spéciaux [Some derived units have] special names 16,106 mise en pratique mise en pratique [Practical realisation][Note 4] 82, 171 Main article:
Closeup of the National Prototype Metre, serial number 27, allocated to the United States This section is missing information about all 22 named derived units of SI. Please expand the section to include this information. Further details may exist on the talk page. (December 2017) This section is missing information about a period of ~35-40 years between early 20th century and end of WW2 covering most of the industrial revolution. Please expand the section to include this information. Further details may exist on the talk page. (December 2017) In the 1860s, James Clerk Maxwell, William Thomson (later Lord Kelvin)
and others working under the auspices of the British Association for
the Advancement of Science, built on Gauss' work and formalised the
concept of a coherent system of units with base units and derived
units christened the centimetre–gram–second system of units in
1874. The principle of coherence was successfully used to define a
number of units of measure based on the CGS, including the erg for
energy, the dyne for force, the barye for pressure, the poise for
dynamic viscosity and the stokes for kinematic viscosity.[44]
In 1879, the CIPM published recommendations for writing the symbols
for length, area, volume and mass, but it was outside its domain to
publish recommendations for other quantities. Beginning in about 1900,
physicists who had been using the symbol "μ"(mu) for "micrometre" or
"micron", "λ"(lambda) for "microlitre", and "γ"(gamma) for
"microgram" started to use the symbols "μm", "μL" and "μg".[54]
At the close of the 19th century three different systems of units of
measure existed for electrical measurements: a CGS-based system for
electrostatic units, also known as the Gaussian or ESU system, a
This section is missing information about changeover
centigrade->
In 1948, the 9th CGPM commissioned a study to assess the measurement
needs of the scientific, technical, and educational communities and
"to make recommendations for a single practical system of units of
measurement, suitable for adoption by all countries adhering to the
This section needs expansion. You can help by adding to it. (December 2017)
In 1960, the 11th CGPM synthesized the results of the 12-year study into a set of 16 resolutions. The system was named the International System of Units, abbreviated SI from the French name, Le Système International d'Unités.[3]:110[61] See also[edit] Introduction to the metric system Outline of the metric system List of international common standards Metre–tonne–second system of units Organisations Institute for Reference Materials and Measurements Standards and conventions Conventional electrical unit
Coordinated Universal
Notes[edit] ^ This grouping reflects the 2014 revision of the 8th Edition of the
SI Brochure (2006).
^ a b Except where specifically noted, these rules are common to both
the SI Brochure and the NIST brochure.
^ This term is a translation of the official [French] text of the SI
Brochure.
^ The 8th edition of the SI Brochure (2008) notes that [at that time
of publication] the term "mise en pratique" had not been fully
defined.
^ The text "Des comparaisons périodiques des étalons nationaux avec
les prototypes internationaux" (English: the periodic comparisons of
national standards with the international prototypes) in article 6.3
of the
References[edit] ^ "Convocation of the
^ McGreevy, Thomas (1997). Cunningham, Peter, ed. The Basis of
Measurement: Volume 2 –
Further reading[edit]
External links[edit] Wikimedia Commons has media related to International System of Units. Official
ISO 80000-1:2009 Quantities and units – Part 1: General NIST On-line official publications on the SI NIST
Rules for SAE Use of SI (Metric) Units
History LaTeX SIunits package manual gives a historical background to the SI system. Research The metrological triangle Recommendation of ICWM 1 (CI-2005) v t e SI units Authority:
Base units ampere candela kelvin kilogram metre mole second Derived units with special names becquerel coulomb degree Celsius farad gray henry hertz joule katal lumen lux newton ohm pascal radian siemens sievert steradian tesla volt watt weber Other accepted units astronomical unit bar dalton day decibel degree of arc electronvolt hectare hour litre minute minute of arc neper second of arc tonne atomic units natural units See also Conversion of units Metric prefixes Proposed redefinitions Systems of measurement Book Category v t e Systems of measurement Current General
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