British spelling
Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English orthography, the two most notable variations being British and American ...
) or meter (
American spelling
Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English orthography, the two most notable variations being British and American ...
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
noun , "measure"), symbol m, is the primary unit of
length
Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Interna ...
in the
International System of Units
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(SI), though its prefixed forms are also used relatively frequently.
The metre was originally defined in 1793 as one ten-millionth of the distance from the
equator
The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can als ...
to the
North Pole
The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is the point in the Northern Hemisphere where the Earth's axis of rotation meets its surface. It is called the True North Pole to distinguish from the Mag ...
along a
great circle
In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point.
Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geomet ...
, so the
Earth's circumference
Earth's circumference is the distance around Earth. Measured around the Equator, it is . Measured around the poles, the circumference is .
Measurement of Earth's circumference has been important to navigation since ancient times. The first know ...
is approximately km. In 1799, the metre was redefined in terms of a prototype metre bar (the actual bar used was changed in 1889). In 1960, the metre was redefined in terms of a certain number of wavelengths of a certain emission line of
krypton-86
There are 34 known isotopes of krypton (36Kr) with atomic mass numbers from 69 through 102. Naturally occurring krypton is made of five stable isotopes and one () which is slightly radioactive with an extremely long half-life, plus traces of radi ...
. The current definition was adopted in 1983 and modified slightly in 2002 to clarify that the metre is a measure of
proper length
Proper length or rest length is the length of an object in the object's rest frame.
The measurement of lengths is more complicated in the theory of relativity than in classical mechanics. In classical mechanics, lengths are measured based on ...
. From 1983 until 2019, the metre was formally defined as the length of the path travelled by
light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
in a vacuum in of a
second
The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ...
. After the
2019 redefinition of the SI base units
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 144t ...
, this definition was rephrased to include the definition of a second in terms of the caesium frequency .
Spelling
''Metre'' is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States and the Philippines, which use ''meter.'' Other
West Germanic languages
The West Germanic languages constitute the largest of the three branches of the Germanic languages, Germanic family of languages (the others being the North Germanic languages, North Germanic and the extinct East Germanic languages, East Germanic ...
, such as German and Dutch, and
North Germanic languages
The North Germanic languages make up one of the three branches of the Germanic languages—a sub-family of the Indo-European languages—along with the West Germanic languages and the extinct East Germanic languages. The language group is also r ...
, such as Danish, Norwegian, and Swedish, likewise spell the word ''Meter'' or ''meter''.
Measuring devices (such as
ammeter
An ammeter (abbreviation of ''Ampere meter'') is an instrument used to measure the current in a circuit. Electric currents are measured in amperes (A), hence the name. For direct measurement, the ammeter is connected in series with the circuit ...
,
speedometer
A speedometer or speed meter is a gauge that measures and displays the instantaneous speed of a vehicle. Now universally fitted to motor vehicles, they started to be available as options in the early 20th century, and as standard equipment f ...
) are spelled "-meter" in all variants of English. The suffix "-meter" has the same Greek origin as the unit of length.
Etymology
The etymological roots of ''metre'' can be traced to the Greek verb () (to measure, count or compare) and noun () (a measure), which were used for physical measurement, for poetic metre and by extension for moderation or avoiding extremism (as in "be measured in your response"). This range of uses is also found in Latin (), French (), English and other languages. The Greek word is derived from the Proto-Indo-European root '' *meh₁-'' 'to measure'. The motto () in the seal of the
International Bureau of Weights and Measures
The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation, through which its 59 member-states act together on measurement standards in four areas: chemistry, ...
(BIPM), which was a saying of the Greek statesman and philosopher
Pittacus of Mytilene
Pittacus (; grc-gre, Πιττακός; 640 – 568 BC) was an ancient Mytilenean military general and one of the Seven Sages of Greece.
Biography
Pittacus was a native of Mytilene and son of Hyrradius. He became a Mytilenaean general who, with ...
and may be translated as "Use measure!", thus calls for both measurement and moderation. The use of the word ''metre'' (for the French unit ) in English began at least as early as 1797.
Oxford English Dictionary
The ''Oxford English Dictionary'' (''OED'') is the first and foundational historical dictionary of the English language, published by Oxford University Press (OUP). It traces the historical development of the English language, providing a com ...
Jean Picard
Jean Picard (21 July 1620 – 12 July 1682) was a French astronomer and priest born in La Flèche, where he studied at the Jesuit Collège Royal Henry-Le-Grand.
He is principally notable for his accurate measure of the size of the Earth, base ...
measured the length of a "
seconds pendulum
A seconds pendulum is a pendulum whose period is precisely two seconds; one second for a swing in one direction and one second for the return swing, a frequency of 0.5 Hz.
Pendulum
A pendulum is a weight suspended from a pivot so that ...
" and proposed a unit of measurement twice that length to be called the universal toise (French: ''Toise universelle''). In 1675,
Tito Livio Burattini
Tito Livio Burattini ( pl, Tytus Liwiusz Burattini, 8 March 1617 – 17 November 1681) was an inventor, architect, Egyptologist, scientist, instrument-maker, traveller, engineer, and nobleman, who spent his working life in Poland and Lithuania. ...
suggested the term metre for a unit of length based on a
pendulum
A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the ...
length, but then it was discovered that the length of a seconds pendulum varies from place to place.
Since
Eratosthenes
Eratosthenes of Cyrene (; grc-gre, Ἐρατοσθένης ; – ) was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandria ...
, geographers had used
meridian arc
In geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length.
The purpose of measuring meridian arcs is to de ...
s to assess the size of the Earth, which in 1669,
Jean Picard
Jean Picard (21 July 1620 – 12 July 1682) was a French astronomer and priest born in La Flèche, where he studied at the Jesuit Collège Royal Henry-Le-Grand.
He is principally notable for his accurate measure of the size of the Earth, base ...
determined to have a radius of
toise
A toise (; symbol: T) is a unit of measure for length, area and volume originating in pre-revolutionary France. In North America, it was used in colonial French establishments in early New France, French Louisiana (''Louisiane''), Acadia (''Acadi ...
s, treated as a simple sphere. In the 18th century,
geodesy
Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivale ...
grew in importance as a means of empirically demonstrating the
theory of gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...
, which
Émilie du Châtelet
Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet (; 17 December 1706 – 10 September 1749) was a French natural philosopher and mathematician from the early 1730s until her death due to complications during childbirth in 1749. ...
promoted in France in combination with
Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathema ...
mathematical work, and because the
radius of the Earth
Earth radius (denoted as ''R''🜨 or R_E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly (equatorial radius, deno ...
was the unit to which all celestial distances were to be referred.
Meridional definition
As a result of the
Lumières
The Lumières (literally in English: ''The Lights'') was a cultural, philosophical, literary and intellectual movement beginning in the second half of the 17th century, originating in western Europe and spreading throughout the rest of Europe. It ...
and during the
French Revolution
The French Revolution ( ) was a period of radical political and societal change in France that began with the Estates General of 1789 and ended with the formation of the French Consulate in November 1799. Many of its ideas are considere ...
, the
French Academy of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...
charged a commission with determining a single scale for all measures. On 7 October 1790 that commission advised the adoption of a decimal system, and on 19 March 1791 advised the adoption of the term ''mètre'' ("measure"), a basic unit of length, which they defined as equal to one ten-millionth of the
quarter meridian
In geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length.
The purpose of measuring meridian arcs is to d ...
, the distance between the
North Pole
The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is the point in the Northern Hemisphere where the Earth's axis of rotation meets its surface. It is called the True North Pole to distinguish from the Mag ...
and the
Equator
The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can als ...
along the
meridian
Meridian or a meridian line (from Latin ''meridies'' via Old French ''meridiane'', meaning “midday”) may refer to
Science
* Meridian (astronomy), imaginary circle in a plane perpendicular to the planes of the celestial equator and horizon
* ...
French Academy of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...
commissioned an expedition led by
Jean Baptiste Joseph Delambre
Jean Baptiste Joseph, chevalier Delambre (19 September 1749 – 19 August 1822) was a French mathematician, astronomer, historian of astronomy, and geodesist. He was also director of the Paris Observatory, and author of well-known books on t ...
and
Pierre Méchain
Pierre François André Méchain (; 16 August 1744 – 20 September 1804) was a French astronomer and surveyor who, with Charles Messier, was a major contributor to the early study of deep-sky objects and comets.
Life
Pierre Méchain was born i ...
, lasting from 1792 to 1799, which attempted to accurately measure the distance between a belfry in
Dunkerque
Dunkirk (french: Dunkerque ; vls, label=French Flemish, Duunkerke; nl, Duinkerke(n) ; , ;) is a commune in the department of Nord in northern France.Montjuïc castle
Montjuïc Castle ( ca, Castell de Montjuïc, es, Castillo de Montjuich) is an old military fortress, with roots dating back from 1640, built on top of Montjuïc hill in Barcelona, Catalonia, Spain. It currently serves as a Barcelona municipal faci ...
in
Barcelona
Barcelona ( , , ) is a city on the coast of northeastern Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second most populous municipality of Spain. With a population of 1.6 million within ci ...
at the
longitude
Longitude (, ) is a geographic coordinate that specifies the east–west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter l ...
of the Paris Panthéon (see meridian arc of Delambre and Méchain). The expedition was fictionalised in Denis Guedj, ''Le Mètre du Monde''. Ken Alder wrote factually about the expedition in ''The Measure of All Things: the seven year odyssey and hidden error that transformed the world''. This portion of the
Paris meridian
The Paris meridian is a meridian line running through the Paris Observatory in Paris, France – now longitude 2°20′14.02500″ East. It was a long-standing rival to the Greenwich meridian as the prime meridian of the world. The "Paris merid ...
was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator. From 1801 to 1812 France adopted this definition of the metre as its official unit of length based on results from this expedition combined with those of the Geodesic Mission to Peru. The latter was related by Larrie D. Ferreiro in ''Measure of the Earth: The Enlightenment Expedition that Reshaped Our World''.
In the 19th century, geodesy underwent a revolution through advances in mathematics as well as improvements in the instruments and methods of observation, for instance accounting for individual bias in terms of the
personal equation The term personal equation, in 19th- and early 20th-century science, referred to the idea that every individual observer had an inherent bias when it came to measurements and observations.
Astronomy
The term originated in astronomy, when it was ...
. The application of the
least squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...
method to
meridian arc
In geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length.
The purpose of measuring meridian arcs is to de ...
measurements demonstrated the importance of the
scientific method
The scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century (with notable practitioners in previous centuries; see the article history of scientific m ...
in geodesy. On the other hand, the invention of the
telegraph
Telegraphy is the long-distance transmission of messages where the sender uses symbolic codes, known to the recipient, rather than a physical exchange of an object bearing the message. Thus flag semaphore is a method of telegraphy, whereas p ...
made it possible to measure
parallel
Parallel is a geometric term of location which may refer to:
Computing
* Parallel algorithm
* Parallel computing
* Parallel metaheuristic
* Parallel (software), a UNIX utility for running programs in parallel
* Parallel Sysplex, a cluster of IBM ...
arcs, and the improvement of the reversible pendulum gave rise to the study of the Earth's
gravitational field
In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenome ...
. A more accurate determination of the
Figure of the Earth
Figure of the Earth is a Jargon, term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. A Spherical Earth, sphere is a well-k ...
would soon result from the measurement of the
Struve Geodetic Arc
The Struve Geodetic Arc is a chain of survey triangulations stretching from Hammerfest in Norway to the Black Sea, through ten countries and over , which yielded the first accurate measurement of a meridian arc.
The chain was established ...
(1816–1855) and would have given another value for the definition of this standard of length. This did not invalidate the metre but highlighted that progress in science would allow better measurement of Earth's size and shape.
In 1832,
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
studied the
Earth's magnetic field
Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic f ...
and proposed adding the
second
The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ...
to the basic units of the metre and the
kilogram
The kilogram (also kilogramme) is the 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 ...
centimetre
330px, Different lengths as in respect to the Electromagnetic spectrum, measured by the Metre and its deriveds scales. The Microwave are in-between 1 meter to 1 millimeter.
A centimetre (international spelling) or centimeter (American spellin ...
,
gram
The gram (originally gramme; SI unit symbol g) is a Physical unit, unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram.
Originally defined as of 1795 as "the absolute weight of a volume of pure wate ...
, second). In 1836, he founded the ''Magnetischer Verein'', the first international scientific association, in collaboration with
Alexander von Humboldt
Friedrich Wilhelm Heinrich Alexander von Humboldt (14 September 17696 May 1859) was a German polymath, geographer, naturalist, explorer, and proponent of Romantic philosophy and science. He was the younger brother of the Prussian minister, p ...
and Wilhelm Edouard Weber. The coordination of the observation of geophysical phenomena such as the Earth's magnetic field,
lightning
Lightning is a naturally occurring electrostatic discharge during which two electric charge, electrically charged regions, both in the atmosphere or with one on the land, ground, temporarily neutralize themselves, causing the instantaneous ...
and
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
in different points of the globe stimulated the creation of the first international scientific associations. The foundation of the ''Magnetischer Verein'' would be followed by that of the Central European Arc Measurement (German: ''Mitteleuropaïsche Gradmessung'') on the initiative of
Johann Jacob Baeyer
Johann Jacob Baeyer (born 5 November 1794 in Berlin, died 10 September 1885 in Berlin) was a German geodesist and a lieutenant-general in the Royal Prussian Army. He was the first director of the Royal Prussian Geodetic Institute and is regarded ...
Heinrich von Wild
Heinrich von Wild or Heinrich Wild I (1833–1902) was a Swiss meteorologist and physicist who established a modern meteorological system throughout the Russian empire and developed meteorological instruments.
Biography
He was born on 17 Decembe ...
would represent
Russia
Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...
at the
International Committee for Weights and Measures
The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established i ...
(CIPM).
International prototype metre bar
In 1816,
Ferdinand Rudolph Hassler
Ferdinand Rudolph Hassler (October 6, 1770 – November 20, 1843) was a Swiss-American surveyor who is considered the forefather of both the National Oceanic and Atmospheric Administration (NOAA) and the National Institute of Standards and Techno ...
was appointed first Superintendent of the Survey of the Coast. Trained in geodesy in Switzerland, France and Germany, Hassler had brought a standard metre made in Paris to the United States in 1805. He designed a baseline apparatus which instead of bringing different bars in actual contact during measurements, used only one bar calibrated on the metre and optical contact. Thus the metre became the unit of length for
geodesy
Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivale ...
in the United States.
Since 1830, Hassler was also head of the Bureau of Weights and Measures which became a part of the Coast Survey. He compared various units of length used in the United States at that time and measured coefficients of expansion to assess temperature effects on the measurements.
In 1841,
Friedrich Wilhelm Bessel
Friedrich Wilhelm Bessel (; 22 July 1784 – 17 March 1846) was a German astronomer, mathematician, physicist, and geodesist. He was the first astronomer who determined reliable values for the distance from the sun to another star by the method ...
, taking into account errors which had been recognized by
Louis Puissant
Louis Puissant (22 September 1769, in Le Châtelet-en-Brie – 10 January 1843, in Paris) was a French topographical engineer, geodesist, and mathematician.
He was appointed an officer in the corps of topographical engineers (''ingénieurs géo ...
in the French meridian arc comprising the
arc measurement of Delambre and Méchain
The arc measurement of Delambre and Méchain was a geodetic survey carried out by Jean-Baptiste Delambre and Pierre Méchain in 1792–1798 to measure an arc section of the Paris meridian between Dunkirk and Barcelona. This arc measurement ...
which had been extended southward by
François Arago
Dominique François Jean Arago ( ca, Domènec Francesc Joan Aragó), known simply as François Arago (; Catalan: ''Francesc Aragó'', ; 26 February 17862 October 1853), was a French mathematician, physicist, astronomer, freemason, supporter of t ...
and
Jean-Baptiste Biot
Jean-Baptiste Biot (; ; 21 April 1774 – 3 February 1862) was a French physicist, astronomer, and mathematician who co-discovered the Biot–Savart law of magnetostatics with Félix Savart, established the reality of meteorites, made an early ba ...
, recalculated the
flattening
Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening is ...
of the
Earth ellipsoid
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations ...
making use of nine more arc measurements, namely Peruan, Prussian, first East-Indian, second East-Indian, English, Hannover, Danish, Russian and Swedish covering almost 50 degrees of
latitude
In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...
, and stated that the
Earth quadrant
In geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length.
The purpose of measuring meridian arcs is to ...
used for determining the length of the metre was nothing more than a rather imprecise conversion factor between the
toise
A toise (; symbol: T) is a unit of measure for length, area and volume originating in pre-revolutionary France. In North America, it was used in colonial French establishments in early New France, French Louisiana (''Louisiane''), Acadia (''Acadi ...
and the metre.
Regarding the precision of the conversion from the
toise
A toise (; symbol: T) is a unit of measure for length, area and volume originating in pre-revolutionary France. In North America, it was used in colonial French establishments in early New France, French Louisiana (''Louisiane''), Acadia (''Acadi ...
to the metre, both
units of measurement
A unit of measurement is a definite magnitude (mathematics), 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 ...
were then defined by primary
standard Standard may refer to:
Symbols
* Colours, standards and guidons, kinds of military signs
* Standard (emblem), a type of a large symbol or emblem used for identification
Norms, conventions or requirements
* Standard (metrology), an object th ...
s, and unique artifacts made of different
alloy
An alloy is a mixture of chemical elements of which at least one is a metal. Unlike chemical compounds with metallic bases, an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductility, ...
s with distinct coefficients of
expansion
Expansion may refer to:
Arts, entertainment and media
* ''L'Expansion'', a French monthly business magazine
* ''Expansion'' (album), by American jazz pianist Dave Burrell, released in 2004
* ''Expansions'' (McCoy Tyner album), 1970
* ''Expansio ...
were the legal basis of units of length. A wrought iron ruler, the Toise of Peru, also called ''Toise de l'Académie'', was the French primary standard of the toise, and the metre was officially defined by the ''Mètre des Archives'' made of platinum. Besides the latter, another platinum and twelve iron standards of the metre were made in 1799. One of them became known as the ''Committee Meter'' in the United States and served as standard of length in the Coast Survey until 1890. According to geodesists, these standards were secondary standards deduced from the Toise of Peru. In Europe, surveyors continued to use measuring instruments calibrated on the Toise of Peru. Among these, the toise of Bessel and the apparatus of Borda were respectively the main references for geodesy in
Prussia
Prussia, , Old Prussian: ''Prūsa'' or ''Prūsija'' was a German state on the southeast coast of the Baltic Sea. It formed the German Empire under Prussian rule when it united the German states in 1871. It was ''de facto'' dissolved by an em ...
and in
France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...
. A French scientific instrument maker,
Jean Nicolas Fortin Jean Nicolas Fortin (1750–1831) was a French maker of scientific instruments, born on 9 August 1750 in Mouchy-la-Ville in Picardy. Among his customers were such noted scientists as Lavoisier, for whom he made a precision balance, Gay-Lussac, Fr ...
, had made two direct copies of the Toise of Peru, the first for
Friedrich Georg Wilhelm von Struve
Friedrich Georg Wilhelm von Struve (russian: link=no, Василий Яковлевич Струве, trans. ''Vasily Yakovlevich Struve''; 15 April 1793 – ) was a Baltic German astronomer and geodesist from the famous Struve family. He is bes ...
in 1821 and a second for
Friedrich Bessel
Friedrich Wilhelm Bessel (; 22 July 1784 – 17 March 1846) was a German astronomer, mathematician, physicist, and geodesist. He was the first astronomer who determined reliable values for the distance from the sun to another star by the method ...
in 1823.
On the subject of the theoretical definition of the metre, it had been inaccessible and misleading at the time of Delambre and Mechain arc measurement, as the
geoid
The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended ...
is a ball, which on the whole can be assimilated to an oblate
spheroid
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has cir ...
, but which in detail differs from it so as to prohibit any generalization and any extrapolation. As early as 1861, after
Friedrich von Schubert
Theodor Friedrich von Schubert (1789–1865) was a Russian general and scientist of Baltic German descent. Born in Saint Petersburg as the son of astronomer Theodor von Schubert. When he was sixteen years old, he accompanied his father on the ...
showed that the different meridians were not of equal length, Elie Ritter, a mathematician from
Geneva
Geneva ( ; french: Genève ) frp, Genèva ; german: link=no, Genf ; it, Ginevra ; rm, Genevra is the List of cities in Switzerland, second-most populous city in Switzerland (after Zürich) and the most populous city of Romandy, the French-speaki ...
, deduced from a computation based on eleven meridian arcs covering 86 degrees that the meridian equation differed from that of the ellipse: the meridian was swelled about the 45th degree of latitude by a layer whose thickness was difficult to estimate because of the uncertainty of the latitude of some stations, in particular that of
Montjuïc
Montjuïc () is a hill in Barcelona, Catalonia, Spain.
Etymology
Montjuïc translates to "Jewish Mountain" from medieval Latin and Catalan, and remains of a medieval Jewish cemetery have been found there. Some sources suggest that Montjuïc ...
in the French meridian arc. By measuring the latitude of two stations in
Barcelona
Barcelona ( , , ) is a city on the coast of northeastern Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second most populous municipality of Spain. With a population of 1.6 million within ci ...
, Méchain had found that the difference between these latitudes was greater than predicted by direct measurement of distance by triangulation. We know now that, in addition to other errors in the survey of Delambre and Méchain, an unfavourable
vertical deflection
The vertical deflection (VD) or deflection of the vertical (DoV), also known as deflection of the plumb line and astro-geodetic deflection, is a measure of how far the gravity direction at a given point of interest is rotated by local mass anoma ...
gave an inaccurate determination of Barcelona's
latitude
In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...
, a metre "too short" compared to a more general definition taken from the average of a large number of arcs.
Nevertheless
Ferdinand Rudolph Hassler
Ferdinand Rudolph Hassler (October 6, 1770 – November 20, 1843) was a Swiss-American surveyor who is considered the forefather of both the National Oceanic and Atmospheric Administration (NOAA) and the National Institute of Standards and Techno ...
's use of the metre in coastal survey contributed to the introduction of the
Metric Act of 1866
The Metric Act of 1866, also known as the Kasson Act, is a piece of United States legislation that legally protected use of the metric system in commerce from lawsuit, and provided an official conversion table from U.S. customary units.
History ...
allowing the use of the metre in the United States, and also played an important role in the choice of the metre as international scientific unit of length and the proposal by the European Arc Measurement (German: ''Europäische Gradmessung'') to “establish a European international bureau for weights and measures”. However, in 1866, the most important concern was that the Toise of Peru, the standard of the toise constructed in 1735 for the
French Geodesic Mission to the Equator
The French Geodesic Mission to the Equator (french: Expédition géodésique française en Équateur, also called the French Geodesic Mission to Peru and the Spanish-French Geodesic Mission) was an 18th-century expedition to what is now Ecuador c ...
, might be so much damaged that comparison with it would be worthless, while Bessel had questioned the accuracy of copies of this standard belonging to Altona and Koenigsberg Observatories, which he had compared to each other about 1840. Indeed when the primary Imperial
yard
The yard (symbol: yd) is an English unit of length in both the British imperial and US customary systems of measurement equalling 3 feet or 36 inches. Since 1959 it has been by international agreement standardized as exactly 0.914 ...
standard was partially destroyed in 1834, a new standard of reference had been constructed using copies of the "Standard Yard, 1760" instead of the pendulum's length as provided for in the Weights and Measures Act of 1824.
In 1864,
Urbain Le Verrier
Urbain Jean Joseph Le Verrier FRS (FOR) HFRSE (; 11 March 1811 – 23 September 1877) was a French astronomer and mathematician who specialized in celestial mechanics and is best known for predicting the existence and position of Neptune using ...
refused to join the first general conference of the Central European Arc Measurement because the French geodetic works had to be verified.
In 1866, at the meeting of the Permanent Commission of the association in
, Antoine Yvon Villarceau announced that he had checked eight points of the French arc. He confirmed that the metre was too short. It then became urgent to undertake a complete revision of the meridian arc. Moreover, while the extension of the French meridian arc to the
Balearic Islands
The Balearic Islands ( es, Islas Baleares ; or ca, Illes Balears ) are an archipelago in the Balearic Sea, near the eastern coast of the Iberian Peninsula. The archipelago is an autonomous community and a province of Spain; its capital is ...
(1803–1807) had seemed to confirm the length of the metre, this survey had not been secured by any baseline in Spain. For that reason, Carlos Ibáñez e Ibáñez de Ibero's announcement, at this conference, of his 1858 measurement of a baseline in Madridejos was of particular importance. Indeed surveyors determined the size of
triangulation
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points.
Applications
In surveying
Specifically in surveying, triangulation involves only angle me ...
networks by measuring baselines which concordance granted the accuracy of the whole
survey
Survey may refer to:
Statistics and human research
* Statistical survey, a method for collecting quantitative information about items in a population
* Survey (human research), including opinion polls
Spatial measurement
* Surveying, the techniq ...
.
In 1867 at the second general conference of the
International Association of Geodesy )
, merged =
, successor =
, formation =
, founder =
, founding_location =
, extinction =
, merger =
, type = scholarly society
, tax_id ...
held in Berlin, the question of an international standard unit of length was discussed in order to combine the measurements made in different countries to determine the size and shape of the Earth. The conference recommended the adoption of the metre in replacement of the toise and the creation of an international metre commission, according to the proposal of
Johann Jacob Baeyer
Johann Jacob Baeyer (born 5 November 1794 in Berlin, died 10 September 1885 in Berlin) was a German geodesist and a lieutenant-general in the Royal Prussian Army. He was the first director of the Royal Prussian Geodetic Institute and is regarded ...
Ferdinand Rudolph Hassler
Ferdinand Rudolph Hassler (October 6, 1770 – November 20, 1843) was a Swiss-American surveyor who is considered the forefather of both the National Oceanic and Atmospheric Administration (NOAA) and the National Institute of Standards and Techno ...
used for the
United States Survey of the Coast
The National Geodetic Survey (NGS) is a United States federal agency that defines and manages a national coordinate system, providing the foundation for transportation and communication; mapping and charting; and a large number of applications ...
, consisting of a single standard with lines marked on the bar and microscopic measurements. Regarding the two methods by which the effect of temperature was taken into account, Ibáñez used both the bimetallic rulers, in platinum and brass, which he first employed for the central baseline of Spain, and the simple iron ruler with inlaid mercury thermometers which was utilized in Switzerland. These devices, the first of which is referred to as either Brunner apparatus or Spanish Standard, were constructed in France by
Jean Brunner
Jean Brunner or Johann Josef Brunner (1804 in Balsthal – 1862 in Paris), was a Swiss-born, French measuring instrument maker and mechanic.Eveline Hänggi: ''Die fünf Turmuhren von Balsthal und der vergessene Balsthaler Künstler Johann Josef Bru ...
, then his sons.
Measurement traceability Traceability is the capability to trace something. In some cases, it is interpreted as the ability to verify the history, location, or application of an item by means of documented recorded identification.
Other common definitions include the capab ...
between the toise and the metre was ensured by comparison of the Spanish Standard with the standard devised by
Borda Borda may refer to:
*Qaṣīda al-Burda, a famous Sufi poem.
* Borda (building) or borde, traditional cattle farmers' buildings in the Pyrenees, a barn, sheepfold, or stable
* Places in India
** Borda, Goa, a town and suburb of the city of Margao ...
and
Lavoisier
Antoine-Laurent de Lavoisier ( , ; ; 26 August 17438 May 1794), CNRS (
meridian arc
In geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length.
The purpose of measuring meridian arcs is to de ...
connecting
Dunkirk
Dunkirk (french: Dunkerque ; vls, label=French Flemish, Duunkerke; nl, Duinkerke(n) ; , ;) is a commune in the department of Nord in northern France.Barcelona
Barcelona ( , , ) is a city on the coast of northeastern Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second most populous municipality of Spain. With a population of 1.6 million within ci ...
.
Hassler's metrological and geodetic work also had a favourable response in Russia. In 1869, the
Saint Petersburg Academy of Sciences
The Russian Academy of Sciences (RAS; russian: Росси́йская акаде́мия нау́к (РАН) ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across t ...
sent to the
French Academy of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...
a report drafted by
Otto Wilhelm von Struve
Otto Wilhelm von Struve (May 7, 1819 (Julian calendar: April 25) – April 14, 1905) was a Russian astronomer of Baltic German origins. In Russian, his name is normally given as Otto Vasil'evich Struve (Отто Васильевич Струве ...
,
Heinrich von Wild
Heinrich von Wild or Heinrich Wild I (1833–1902) was a Swiss meteorologist and physicist who established a modern meteorological system throughout the Russian empire and developed meteorological instruments.
Biography
He was born on 17 Decembe ...
and
Moritz von Jacobi
Moritz Hermann or Boris Semyonovich (von) Jacobi (russian: Борис Семёнович Якоби; 21 September 1801, Potsdam – 10 March 1874, Saint Petersburg) was a Prussian and Russian Imperial engineer and physicist of Jewish descent. Jac ...
inviting his French counterpart to undertake joint action to ensure the universal use of the
metric system
The metric system is a system of measurement that succeeded the Decimal, decimalised system based on the metre that had been introduced in French Revolution, France in the 1790s. The historical development of these systems culminated in the d ...
in all scientific work.
In the 1870s and in light of modern precision, a series of international conferences was held to devise new metric standards. When a conflict broke out regarding the presence of impurities in the metre-alloy of 1874, a member of the Preparatory Committee since 1870 and Spanish representative at the Paris Conference in 1875, Carlos Ibáñez e Ibáñez de Ibero intervened with the
French Academy of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...
to rally France to the project to create an
International Bureau of Weights and Measures
The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation, through which its 59 member-states act together on measurement standards in four areas: chemistry, ...
equipped with the scientific means necessary to redefine the units of the
metric system
The metric system is a system of measurement that succeeded the Decimal, decimalised system based on the metre that had been introduced in French Revolution, France in the 1790s. The historical development of these systems culminated in the d ...
according to the progress of sciences.
The
Metre Convention
The Metre Convention (french: link=no, Convention du Mètre), also known as the Treaty of the Metre, is an international treaty that was signed in Paris on 20 May 1875 by representatives of 17 nations (Argentina, Austria-Hungary, Belgium, Brazi ...
(''Convention du Mètre'') of 1875 mandated the establishment of a permanent
International Bureau of Weights and Measures
The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation, through which its 59 member-states act together on measurement standards in four areas: chemistry, ...
(BIPM: ') to be located in
Sèvres
Sèvres (, ) is a commune in the southwestern suburbs of Paris, France. It is located from the centre of Paris, in the Hauts-de-Seine department, Île-de-France region. The commune, which had a population of 23,251 as of 2018, is known for i ...
, France. This new organisation was to construct and preserve a prototype metre bar, distribute national metric prototypes, and maintain comparisons between them and non-metric measurement standards. The organisation distributed such bars in 1889 at the first
General Conference on Weights and Measures
The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established i ...
(CGPM: '), establishing the ''
International Prototype Metre
The history of the metre starts with the Scientific Revolution that is considered to have begun with Nicolaus Copernicus's publication of ''De revolutionibus orbium coelestium'' in 1543. Increasingly accurate measurements were required, and sc ...
'' as the distance between two lines on a standard bar composed of an alloy of 90%
platinum
Platinum is a chemical element with the symbol Pt and atomic number 78. It is a dense, malleable, ductile, highly unreactive, precious, silverish-white transition metal. Its name originates from Spanish , a diminutive of "silver".
Platinu ...
and 10%
iridium
Iridium is a chemical element with the symbol Ir and atomic number 77. A very hard, brittle, silvery-white transition metal of the platinum group, it is considered the second-densest naturally occurring metal (after osmium) with a density of ...
Mètre des Archives
The history of the metre starts with the Scientific Revolution that is considered to have begun with Nicolaus Copernicus's publication of ''De revolutionibus orbium coelestium'' in 1543. Increasingly accurate measurements were required, and sc ...
'') involved the development of special measuring equipment and the definition of a reproducible temperature scale. The BIPM's
thermometry
Temperature measurement (also known as thermometry) describes the process of measuring a current local temperature for immediate or later evaluation. Datasets consisting of repeated standardized measurements can be used to assess temperature tren ...
work led to the discovery of special alloys of iron-nickel, in particular
invar
Invar, also known generically as FeNi36 (64FeNi in the US), is a nickel–iron alloy notable for its uniquely low coefficient of thermal expansion (CTE or α). The name ''Invar'' comes from the word ''invariable'', referring to its relative lac ...
Nobel Prize for physics
)
, image = Nobel Prize.png
, alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
metrology
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 Fran ...
combined with those of
gravimetry
Gravimetry is the measurement of the strength of a gravitational field. Gravimetry may be used when either the magnitude of a gravitational field or the properties of matter responsible for its creation are of interest.
Units of measurement
Gr ...
through improvement of
Kater's pendulum
A Kater's pendulum is a reversible free swinging pendulum invented by British physicist and army captain Henry Kater in 1817 for use as a gravimeter instrument to measure the local acceleration of gravity. Its advantage is that, unlike previous ...
led to a new era of
geodesy
Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivale ...
. If precision metrology had needed the help of geodesy, the latter could not continue to prosper without the help of metrology. It was then necessary to define a single unit to express all the measurements of terrestrial arcs and all determinations of the
force of gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong ...
by the mean of pendulum. Metrology had to create a common unit, adopted and respected by all civilized nations.
Moreover, at that time,
statistician
A statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors.
It is common to combine statistical knowledge with expertise in other subjects, and statisticians may wor ...
s knew that scientific observations are marred by two distinct types of errors, constant errors on the one hand, and fortuitous errors, on the other hand. The effects of the latters can be mitigated by the
least-squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...
method. Constant or regular errors on the contrary must be carefully avoided, because they arise from one or more causes that constantly act in the same way and have the effect of always altering the result of the experiment in the same direction. They therefore deprive of any value the observations that they impinge. However, the distinction between systematic and random errors is far from being as sharp as one might think at first assessment. In reality, there are no or very few random errors. As science progresses, the causes of certain errors are sought out, studied, their laws discovered. These errors pass from the class of random errors into that of systematic errors. The ability of the observer consists in discovering the greatest possible number of systematic errors in order to be able, once he has become acquainted with their laws, to free his results from them using a method or appropriate corrections.
For metrology the matter of expansibility was fundamental; as a matter of fact the
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
measuring
error
An error (from the Latin ''error'', meaning "wandering") is an action which is inaccurate or incorrect. In some usages, an error is synonymous with a mistake. The etymology derives from the Latin term 'errare', meaning 'to stray'.
In statistics ...
related to the length measurement in proportion to the expansibility of the standard and the constantly renewed efforts of metrologists to protect their measuring instruments against the interfering influence of temperature revealed clearly the importance they attached to the expansion-induced errors. It was thus crucial to compare at controlled temperatures with great precision and to the same unit all the standards for measuring geodetic baselines and all the pendulum rods. Only when this series of metrological comparisons would be finished with a probable error of a thousandth of a millimetre would geodesy be able to link the works of the different nations with one another, and then proclaim the result of the measurement of the Globe.
As the
figure of the Earth
Figure of the Earth is a Jargon, term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. A Spherical Earth, sphere is a well-k ...
could be inferred from variations of the
seconds pendulum
A seconds pendulum is a pendulum whose period is precisely two seconds; one second for a swing in one direction and one second for the return swing, a frequency of 0.5 Hz.
Pendulum
A pendulum is a weight suspended from a pivot so that ...
length with
latitude
In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...
, the
United States Coast Survey
United may refer to:
Places
* United, Pennsylvania, an unincorporated community
* United, West Virginia, an unincorporated community
Arts and entertainment Films
* ''United'' (2003 film), a Norwegian film
* ''United'' (2011 film), a BBC Two fi ...
instructed
Charles Sanders Peirce
Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism".
Educated as a chemist and employed as a scientist for t ...
in the spring of 1875 to proceed to Europe for the purpose of making pendulum experiments to chief initial stations for operations of this sort, in order to bring the determinations of the forces of gravity in America into communication with those of other parts of the world; and also for the purpose of making a careful study of the methods of pursuing these researches in the different countries of Europe. In 1886 the association of geodesy changed name for the
International Geodetic Association )
, merged =
, successor =
, formation =
, founder =
, founding_location =
, extinction =
, merger =
, type = scholarly society
, tax_id ...
International Geodetic Association )
, merged =
, successor =
, formation =
, founder =
, founding_location =
, extinction =
, merger =
, type = scholarly society
, tax_id ...
(German: ''Internationale Erdmessung'') gained worldwide importance with the joining of
United States
The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...
,
Mexico
Mexico (Spanish: México), officially the United Mexican States, is a country in the southern portion of North America. It is bordered to the north by the United States; to the south and west by the Pacific Ocean; to the southeast by Guatema ...
,
Chile
Chile, officially the Republic of Chile, is a country in the western part of South America. It is the southernmost country in the world, and the closest to Antarctica, occupying a long and narrow strip of land between the Andes to the east a ...
,
Argentina
Argentina (), officially the Argentine Republic ( es, link=no, República Argentina), is a country in the southern half of South America. Argentina covers an area of , making it the second-largest country in South America after Brazil, th ...
and
Japan
Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the north ...
.
Efforts to supplement the various national
surveying
Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is ca ...
systems, which began in the 19th century with the foundation of the '' Mitteleuropäische Gradmessung'', resulted in a series of global
ellipsoid
An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.
An ellipsoid is a quadric surface; that is, a surface that may be defined as the ...
s of the Earth (e.g.,
Helmert
Friedrich Robert Helmert (31 July 1843 – 15 June 1917) was a German geodesist and statistician with important contributions to the theory of errors.
Career
Helmert was born in Freiberg, Kingdom of Saxony. After schooling in Freiberg and D ...
1906, Hayford 1910 and 1924) which would later lead to develop the
World Geodetic System
The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS. The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also descri ...
. Nowadays the practical realisation of the metre is possible everywhere thanks to the
atomic clock
An atomic clock is a clock that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different energy levels. Electron states in an atom are associated with different energy levels, and in transitions betwee ...
s embedded in
GPS satellites
GPS satellite blocks are the various production generations of the Global Positioning System (GPS) used for satellite navigation. The first satellite in the system, Navstar 1, was launched on 22 February 1978. The GPS satellite constellatio ...
.
Wavelength definition
In 1873,
James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and ligh ...
suggested that light emitted by an element be used as the standard both for the metre and for the second. These two quantities could then be used to define the unit of mass.
In 1893, the standard metre was first measured with an
interferometer
Interferometry is a technique which uses the ''interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber op ...
by
Albert A. Michelson
Albert Abraham Michelson Royal Society of London, FFRS HFRSE (surname pronunciation anglicized as "Michael-son", December 19, 1852 – May 9, 1931) was a German-born American physicist of Polish/Jewish origin, known for his work on measuring the ...
, the inventor of the device and an advocate of using some particular
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
of
light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
as a standard of length. By 1925,
interferometry
Interferometry is a technique which uses the ''interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber opt ...
was in regular use at the BIPM. However, the International Prototype Metre remained the standard until 1960, when the eleventh CGPM defined the metre in the new
International System of Units
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(SI) as equal to
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
s of the
orange
Orange most often refers to:
*Orange (fruit), the fruit of the tree species '' Citrus'' × ''sinensis''
** Orange blossom, its fragrant flower
*Orange (colour), from the color of an orange, occurs between red and yellow in the visible spectrum
* ...
-
red
Red is the color at the long wavelength end of the visible spectrum of light, next to orange and opposite violet. It has a dominant wavelength of approximately 625–740 nanometres. It is a primary color in the RGB color model and a secondar ...
emission line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to iden ...
in the
electromagnetic spectrum
The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies.
The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from ...
of the
krypton-86
There are 34 known isotopes of krypton (36Kr) with atomic mass numbers from 69 through 102. Naturally occurring krypton is made of five stable isotopes and one () which is slightly radioactive with an extremely long half-life, plus traces of radi ...
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, and ...
in a
vacuum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
.
Speed of light definition
To further reduce uncertainty, the 17th CGPM in 1983 replaced the definition of the metre with its current definition, thus fixing the length of the metre in terms of the
second
The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ...
and the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
:
::The metre is the length of the path travelled by light in vacuum during a time interval of of a second.
This definition fixed the speed of light in
vacuum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
at exactly metres per second (≈ or ≈1.079 billion km/hour). An intended by-product of the 17th CGPM's definition was that it enabled scientists to compare lasers accurately using frequency, resulting in wavelengths with one-fifth the uncertainty involved in the direct comparison of wavelengths, because interferometer errors were eliminated. To further facilitate reproducibility from lab to lab, the 17th CGPM also made the iodine-stabilised
helium–neon laser
A helium–neon laser or He-Ne laser, is a type of gas laser whose high energetic medium gain medium consists of a mixture of 10:1 ratio of helium and neon at a total pressure of about 1 torr inside of a small electrical discharge. The best ...
"a recommended radiation" for realising the metre. For the purpose of delineating the metre, the BIPM currently considers the HeNe laser wavelength, , to be with an estimated relative standard uncertainty (''U'') of .The term "relative standard uncertainty" is explained by NIST on their web site: This uncertainty is currently one limiting factor in laboratory realisations of the metre, and it is several orders of magnitude poorer than that of the second, based upon the caesium fountain
atomic clock
An atomic clock is a clock that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different energy levels. Electron states in an atom are associated with different energy levels, and in transitions betwee ...
(). Consequently, a realisation of the metre is usually delineated (not defined) today in labs as wavelengths of helium-neon laser light in a vacuum, the error stated being only that of frequency determination. This bracket notation expressing the error is explained in the article on
measurement uncertainty
In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a measured quantity. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by ...
.
Practical realisation of the metre is subject to uncertainties in characterising the medium, to various uncertainties of interferometry, and to uncertainties in measuring the frequency of the source. A commonly used medium is air, and the
National Institute of Standards and Technology
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
(NIST) has set up an online calculator to convert wavelengths in vacuum to wavelengths in air.The formulas used in the calculator and the documentation behind them are found at The choice is offered to use either th modified Edlén equation or th Ciddor equation The documentation provide a discussion of how to choose between the two possibilities. As described by NIST, in air, the uncertainties in characterising the medium are dominated by errors in measuring temperature and pressure. Errors in the theoretical formulas used are secondary. By implementing a refractive index correction such as this, an approximate realisation of the metre can be implemented in air, for example, using the formulation of the metre as wavelengths of helium–neon laser light in a vacuum, and converting the wavelengths in a vacuum to wavelengths in air. Air is only one possible medium to use in a realisation of the metre, and any
partial vacuum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
can be used, or some inert atmosphere like helium gas, provided the appropriate corrections for refractive index are implemented.
The metre is ''defined'' as the path length travelled by light in a given time, and practical laboratory length measurements in metres are determined by counting the number of wavelengths of laser light of one of the standard types that fit into the length, and converting the selected unit of wavelength to metres. Three major factors limit the accuracy attainable with laser interferometers for a length measurement:
A more detailed listing of errors can be found in
Zagar, 1999, pp. 6–65''ff''.
* uncertainty in vacuum wavelength of the source,
* uncertainty in the refractive index of the medium,
*
least count {{Short description, Smallest value a measuring instrument can measure
In the science of measurement, the least count of a measuring instrument is the smallest value in the measured quantity that can be resolved on the instrument's scale. William ...
resolution of the interferometer.
Of these, the last is peculiar to the interferometer itself. The conversion of a length in wavelengths to a length in metres is based upon the relation
:
which converts the unit of wavelength ''λ'' to metres using ''c'', the speed of light in vacuum in m/s. Here ''n'' is the
refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
of the medium in which the measurement is made, and ''f'' is the measured frequency of the source. Although conversion from wavelengths to metres introduces an additional error in the overall length due to measurement error in determining the refractive index and the frequency, the measurement of frequency is one of the most accurate measurements available.
The CIPM issued a clarification in 2002:
Timeline
Early adoptions of the metre internationally
In France, the metre was adopted as an exclusive measure in 1801 under the
Consulate
A consulate is the office of a consul. A type of diplomatic mission, it is usually subordinate to the state's main representation in the capital of that foreign country (host state), usually an embassy (or, only between two Commonwealth coun ...
. This continued under the
First French Empire
The First French Empire, officially the French Republic, then the French Empire (; Latin: ) after 1809, also known as Napoleonic France, was the empire ruled by Napoleon Bonaparte, who established French hegemony over much of continental Eu ...
until 1812, when
Napoleon
Napoleon Bonaparte ; it, Napoleone Bonaparte, ; co, Napulione Buonaparte. (born Napoleone Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French military commander and political leader who ...
decreed the introduction of the non-decimal ''
mesures usuelles Mesures usuelles (, ''customary measurements'') were a French system of measurement introduced by Napoleon I in 1812 to act as compromise between the metric system and traditional measurements. The system was restricted to use in the retail indust ...
'', which remained in use in France up to 1840 in the reign of
Louis Philippe
Louis Philippe (6 October 1773 – 26 August 1850) was King of the French from 1830 to 1848, and the penultimate monarch of France.
As Louis Philippe, Duke of Chartres, he distinguished himself commanding troops during the Revolutionary War ...
. Meanwhile, the metre was adopted by the Republic of Geneva. After the joining of the
canton of Geneva
The Canton of Geneva, officially the Republic and Canton of Geneva (french: link=no, République et canton de Genève; frp, Rèpublica et canton de Geneva; german: Republik und Kanton Genf; it, Repubblica e Cantone di Ginevra; rm, Republica e ...
to
Switzerland
). Swiss law does not designate a ''capital'' as such, but the federal parliament and government are installed in Bern, while other federal institutions, such as the federal courts, are in other cities (Bellinzona, Lausanne, Luzern, Neuchâtel ...
in 1815,
Guillaume Henri Dufour
Guillaume Henri Dufour (15 September 178714 July 1875) was a Swiss military officer, structural engineer and topographer. He served under Napoleon I and held the Swiss office of General four times in his career, firstly in 1847 when he led the ...
published the first official Swiss map, for which the metre was adopted as the unit of length.
Louis Napoléon Bonaparte
Napoleon III (Charles Louis Napoléon Bonaparte; 20 April 18089 January 1873) was the first President of France (as Louis-Napoléon Bonaparte) from 1848 to 1852 and the last monarch of France as Emperor of the French from 1852 to 1870. A nephew ...
, a Swiss–French binational officer, was present when a baseline was measured near
Zürich
Zürich () is the list of cities in Switzerland, largest city in Switzerland and the capital of the canton of Zürich. It is located in north-central Switzerland, at the northwestern tip of Lake Zürich. As of January 2020, the municipality has 43 ...
for the
Dufour map
Dufour or ''variant'', may refer to:
*Dufour (surname)
Places
*Dufourspitze or Dufour's peak, in the Swiss Alps
*Julia Dufour, a village and municipality in Santa Cruz Province, Argentina
Other uses
*1961 Dufour, main-belt asteroid
*Dufour Audit ...
, which would win the gold medal for a national map at the Exposition Universelle of 1855. Among the scientific instruments calibrated on the metre that were displayed at the Exposition Universelle, was
Brunner Brunner may refer to:
Places
* Brunner, New Zealand
* Lake Brunner, New Zealand
* Brunner Mine, New Zealand
* Brunner, Houston, United States
* Brunner (crater), lunar crater
Other uses
* Brunner (surname)
* Brunner the Bounty Hunter, a character ...
's apparatus, a geodetic instrument devised for measuring the central baseline of Spain, whose designer, Carlos Ibáñez e Ibáñez de Ibero would represent Spain at the
International Statistical Institute
The International Statistical Institute (ISI) is a professional association of statisticians. It was founded in 1885, although there had been international statistical congresses since 1853. The institute has about 4,000 elected members from gov ...
. In 1885, in addition to the Exposition Universelle and the second Statistical Congress held in Paris, an International Association for Obtaining a Uniform Decimal System of Measures, Weights, and Coins was created there. Copies of the Spanish standard were made for Egypt, France and Germany. These standards were compared to each other and with the Borda apparatus, which was the main reference for measuring all geodetic bases in France. In 1869, Napoleon III convened the International Metre Commission, which was to meet in Paris in 1870. The Franco-Prussian War broke out, the
Second French Empire
The Second French Empire (; officially the French Empire, ), was the 18-year Empire, Imperial Bonapartist regime of Napoleon III from 14 January 1852 to 27 October 1870, between the French Second Republic, Second and the French Third Republic ...
collapsed, but the metre survived.
Metre adoption dates by country
*
France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...
: 1801 - 1812, then 1840,
*
Republic of Geneva
The Canton of Geneva, officially the Republic and Canton of Geneva (french: link=no, République et canton de Genève; frp, Rèpublica et canton de Geneva; german: Republik und Kanton Genf; it, Repubblica e Cantone di Ginevra; rm, Republica e ...
, Switzerland: 1813,
*
Kingdom of the Netherlands
, national_anthem = )
, image_map = Kingdom of the Netherlands (orthographic projection).svg
, map_width = 250px
, image_map2 = File:KonDerNed-10-10-10.png
, map_caption2 = Map of the four constituent countries shown to scale
, capital = ...
: 1820,
* Kingdom of
Belgium
Belgium, ; french: Belgique ; german: Belgien officially the Kingdom of Belgium, is a country in Northwestern Europe. The country is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeast, France to th ...
: 1830,
*
Chile
Chile, officially the Republic of Chile, is a country in the western part of South America. It is the southernmost country in the world, and the closest to Antarctica, occupying a long and narrow strip of land between the Andes to the east a ...
: 1848,
*
Kingdom of Sardinia
The Kingdom of Sardinia,The name of the state was originally Latin: , or when the kingdom was still considered to include Corsica. In Italian it is , in French , in Sardinian , and in Piedmontese . also referred to as the Kingdom of Savoy-S ...
, Italy: 1850,
*
Spain
, image_flag = Bandera de España.svg
, image_coat = Escudo de España (mazonado).svg
, national_motto = ''Plus ultra'' (Latin)(English: "Further Beyond")
, national_anthem = (English: "Royal March")
, i ...
: 1852,
*
Portugal
Portugal, officially the Portuguese Republic ( pt, República Portuguesa, links=yes ), is a country whose mainland is located on the Iberian Peninsula of Southwestern Europe, and whose territory also includes the Atlantic archipelagos of ...
: 1852,
*
Colombia
Colombia (, ; ), officially the Republic of Colombia, is a country in South America with insular regions in North America—near Nicaragua's Caribbean coast—as well as in the Pacific Ocean. The Colombian mainland is bordered by the Car ...
: 1853,
*
Ecuador
Ecuador ( ; ; Quechua: ''Ikwayur''; Shuar: ''Ecuador'' or ''Ekuatur''), officially the Republic of Ecuador ( es, República del Ecuador, which literally translates as "Republic of the Equator"; Quechua: ''Ikwadur Ripuwlika''; Shuar: ''Eku ...
: 1856,
*
Mexico
Mexico (Spanish: México), officially the United Mexican States, is a country in the southern portion of North America. It is bordered to the north by the United States; to the south and west by the Pacific Ocean; to the southeast by Guatema ...
: 1857,
*
Brazil
Brazil ( pt, Brasil; ), officially the Federative Republic of Brazil (Portuguese: ), is the largest country in both South America and Latin America. At and with over 217 million people, Brazil is the world's fifth-largest country by area ...
: 1862,
*
Argentina
Argentina (), officially the Argentine Republic ( es, link=no, República Argentina), is a country in the southern half of South America. Argentina covers an area of , making it the second-largest country in South America after Brazil, th ...
: 1863,
*
Italy
Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical re ...
: 1863,
*
German Empire
The German Empire (),Herbert Tuttle wrote in September 1881 that the term "Reich" does not literally connote an empire as has been commonly assumed by English-speaking people. The term literally denotes an empire – particularly a hereditary ...
,
Germany
Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...
: 1872,
*
Austria
Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous ...
, 1875,
*
Switzerland
). Swiss law does not designate a ''capital'' as such, but the federal parliament and government are installed in Bern, while other federal institutions, such as the federal courts, are in other cities (Bellinzona, Lausanne, Luzern, Neuchâtel ...
: 1877.
SI prefixed forms of metre
SI prefix
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
es can be used to denote decimal multiples and submultiples of the metre, as shown in the table below. Long distances are usually expressed in km,
astronomical unit
The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits t ...
s (149.6 Gm),
light-year
A light-year, alternatively spelled light year, is a large unit of length used to express astronomical distances and is equivalent to about 9.46 trillion kilometers (), or 5.88 trillion miles ().One trillion here is taken to be 1012 ...
s (10 Pm), or
parsec
The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, and ...
s (31 Pm), rather than in Mm, Gm, Tm, Pm, Em, Zm or Ym; "30 cm", "30 m", and "300 m" are more common than "3 dm", "3 dam", and "3 hm", respectively.
The terms ''micron'' and ''millimicron'' can be used instead of ''micrometre'' (μm) and ''nanometre'' (nm), but this practice may be discouraged.
Equivalents in other units
Within this table, "inch" and "yard" mean "international inch" and "international yard" respectively, though approximate conversions in the left column hold for both international and survey units.
: "≈" means "is approximately equal to";
: "=" means "is exactly equal to".
One metre is exactly equivalent to inches and to yards.
A simple
mnemonic
A mnemonic ( ) device, or memory device, is any learning technique that aids information retention or retrieval (remembering) in the human memory for better understanding.
Mnemonics make use of elaborative encoding, retrieval cues, and imag ...
aid exists to assist with conversion, as three "3"s:
: 1 metre is nearly equivalent to 3
feet
The foot ( : feet) is an anatomical structure found in many vertebrates. It is the terminal portion of a limb which bears weight and allows locomotion. In many animals with feet, the foot is a separate organ at the terminal part of the leg made ...
inches. This gives an overestimate of 0.125mm; however, the practice of memorising such conversion formulas has been discouraged in favour of practice and visualisation of metric units.
The ancient Egyptian
cubit
The cubit is an ancient unit of length based on the distance from the elbow to the tip of the middle finger. It was primarily associated with the Sumerians, Egyptians, and Israelites. The term ''cubit'' is found in the Bible regarding No ...
was about 0.5m (surviving rods are 523–529mm). Scottish and English definitions of the ell (two cubits) were 941mm (0.941m) and 1143mm (1.143m) respectively. The ancient Parisian ''toise'' (fathom) was slightly shorter than 2m and was standardised at exactly 2m in the
mesures usuelles Mesures usuelles (, ''customary measurements'') were a French system of measurement introduced by Napoleon I in 1812 to act as compromise between the metric system and traditional measurements. The system was restricted to use in the retail indust ...
system, such that 1m was exactly toise. The Russian
verst
A verst (russian: верста, ) is an obsolete Russian unit of length defined as 500 sazhen. This makes a verst equal to .
Plurals and variants
In the English language, ''verst'' is singular with the normal plural ''versts''. In Russian, the no ...
was 1.0668km. The
Swedish mil
A Scandinavian mile (Norwegian and sv, mil, [], like "meal") is a unit of length common in Norway and Sweden, but not Denmark. Today, it is standardised as 1 being , but it had different values in the past.
The word is derived from the same ...
was 10.688km, but was changed to 10km when Sweden converted to metric units.
See also
*
Conversion of units
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects.
Overview
The process ...
for comparisons with other units
*
International System of Units
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
* ISO 1standard reference temperature for length measurements
*
Length measurement
Length measurement, distance measurement, or range measurement (ranging) refers to the many ways in which length, distance, or range can be measured. The most commonly used approaches are the rulers, followed by transit-time methods and the ...
*
Metre Convention
The Metre Convention (french: link=no, Convention du Mètre), also known as the Treaty of the Metre, is an international treaty that was signed in Paris on 20 May 1875 by representatives of 17 nations (Argentina, Austria-Hungary, Belgium, Brazi ...
*
Metric system
The metric system is a system of measurement that succeeded the Decimal, decimalised system based on the metre that had been introduced in French Revolution, France in the 1790s. The historical development of these systems culminated in the d ...
*
Metric prefix
A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pre ...
*
Metrication
Metrication or metrification is the act or process of converting to the metric system of measurement. All over the world, countries have transitioned from local and traditional units of measurement to the metric system. This process began in F ...
*
Orders of magnitude (length)
The following are examples of orders of magnitude for different lengths.
__TOC__
Overview
Detailed list
To help compare different orders of magnitude, the following list describes various lengths between 1.6 \times 10^ metres and 10^ ...
*
SI prefix
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
*
Speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
*
Vertical metre
Vertical position or vertical location, also known as vertical level or simply level, is a position along a vertical direction above or below a given vertical datum (reference level).
Vertical distance or vertical separation is the distance betwe ...