The metre, or meter,, is the fundamental unit

of length in the International System of Units. Originally intended to be one ten-millionth

of the distance from the Earth’s equator to the North Pole, its definition has been periodically

refined to reflect growing knowledge of metrology. Since 1983, it has been defined as “the length

of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.”

The US yard is defined so as to be exactly 0.9144 metres. History A decimal-based unit of length, the universal

measure or standard was proposed in an essay of 1668 by the English cleric and philosopher

John Wilkins. In 1670 Gabriel Mouton, Bishop of Lyon, also suggested a universal length

standard with decimal multiples and divisions, to be based on a one minute angle of the Earth’s

meridian arc or on a pendulum with a one second period. In 1675, the Italian scientist Tito

Livio Burattini, in his work Misura Universale, used the phrase metro cattolico, derived from

the Greek μέτρον καθολικόν, to denote the standard unit of length derived

from a pendulum. In the wake of the French Revolution, a commission organised by the

French Academy of Sciences and charged with determining a single scale for all measures,

advised the adoption of a decimal system and suggested a basic unit of length equal to

one ten-millionth of the distance between the North Pole and the Equator, to be called

mètre. The National Convention adopted the proposal in 1793. The first occurrence of

metre in this sense in English dates to 1797. Meridional definition

In 1668, Wilkins proposed using Christopher Wren’s suggestion of a pendulum with a half-period

of one second to measure a standard length that Christiaan Huygens had observed to be

38 Rijnland inches or 39 1⁄4 English inches in length. In the 18th century, there were

two favoured approaches to the definition of the standard unit of length. One approach

followed Wilkins in defining the metre as the length of a pendulum with a half-period

of one second, a ‘seconds pendulum’. The other approach suggested defining the metre as one

ten-millionth of the length of the Earth’s meridian along a quadrant; that is, the distance

from the Equator to the North Pole. In 1791, the French Academy of Sciences selected the

meridional definition over the pendular definition because the force of gravity varies slightly

over the surface of the Earth, which affects the period of a pendulum.

To establish a universally accepted foundation for the definition of the metre, more accurate

measurements of this meridian would have to be made. The French Academy of Sciences commissioned

an expedition led by Jean Baptiste Joseph Delambre and Pierre Méchain, lasting from

1792 to 1799, which measured the distance between a belfry in Dunkerque and Montjuïc

castle in Barcelona to estimate the length of the meridian arc through Dunkerque. This

portion of the meridian, assumed to be the same length as the Paris meridian, was to

serve as the basis for the length of the half meridian connecting the North Pole with the

Equator. The exact shape of the Earth is not a simple

mathematical shape at the level of precision required for defining a standard of length.

The irregular and particular shape of the Earth is called a geoid, which means “Earth-shaped”.

Despite this fact, and based on provisional results from the expedition, France adopted

the metre as its official unit of length in 1793. Although it was later determined that

the first prototype metre bar was short by a fifth of a millimetre because of miscalculation

of the flattening of the Earth, this length became the standard. The circumference of

the Earth through the poles is therefore slightly more than forty million metres.

Prototype metre bar In the 1870s and in light of modern precision,

a series of international conferences was held to devise new metric standards. The Metre

Convention of 1875 mandated the establishment of a permanent International Bureau of Weights

and Measures to be located in Sèvres, France. This new organisation would preserve the new

prototype metre and kilogram standards when constructed, distribute national metric prototypes,

and maintain comparisons between them and non-metric measurement standards. The organisation

created a new prototype bar in 1889 at the first General Conference on Weights and Measures,

establishing the International Prototype Metre as the distance between two lines on a standard

bar composed of an alloy of ninety percent platinum and ten percent iridium, measured

at the melting point of ice. The original international prototype of the

metre is still kept at the BIPM under the conditions specified in 1889. A discussion

of measurements of a standard metre bar and the errors encountered in making the measurements

is found in a NIST document. Standard wavelength of krypton-86 emission

In 1893, the standard metre was first measured with an interferometer by Albert A. Michelson,

the inventor of the device and an advocate of using some particular wavelength of light

as a standard of length. By 1925, interferometry 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 as equal to 1,650,763.73 wavelengths

of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum.

Speed of light 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 and the speed of light: The metre is the length of the path travelled

by light in vacuum during a time interval of 1/299,792,458 of a second. This definition fixed the speed of light in

vacuum at exactly 299,792,458 metres per second. An intended by-product of the 17th CGPM’s

definition was that it enabled scientists to compare their 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 recommended

radiation” for realising the metre. For the purpose of delineating the metre, the BIPM

currently considers the HeNe laser wavelength, λHeNe, to be 632.99121258 nm with an estimated

relative standard uncertainty of 2.1×10−11. 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. Consequently, a realisation

of the metre is usually delineated today in labs as 1,579,800.762042(33) 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. 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 has set up an online calculator

to convert wavelengths in vacuum to wavelengths in air. 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 1,579,800.762042(33) wavelengths

of helium-neon laser light in vacuum, and converting the wavelengths in a vacuum to

wavelengths in air. Of course, air is only one possible medium to use in a realisation

of the metre, and any partial vacuum can be used, or some inert atmosphere like helium

gas, provided the appropriate corrections for refractive index are implemented.

Length measurement in metres Although the metre is now defined as the path

length travelled by light in a given time, the 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: Uncertainty in vacuum wavelength of the source

Uncertainty in the refractive index of the medium

Least count 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 a vacuum in m/s. Here n is the refractive index 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.

Timeline of definition 1790 May 8 – The French National Assembly

decides that the length of the new metre would be equal to the length of a pendulum with

a half-period of one second. 1791 March 30 – The French National Assembly

accepts the proposal by the French Academy of Sciences that the new definition for the

metre be equal to one ten-millionth of the length of the Earth’s meridian along a quadrant

through Paris, that is the distance from the equator to the north pole.

1795 – Provisional metre bar constructed of brass. Based on Bessel’s ellipsoid and

legally equal to 443.44 lines on the toise du Pérou.

1799 December 10 – The French National Assembly specifies the platinum metre bar,

constructed on 23 June 1799 and deposited in the National Archives, as the final standard.

Legally equal to 443.296 lines on the toise du Pérou.

1889 September 28 – The 1st General Conference on Weights and Measures defines the metre

as the distance between two lines on a standard bar of an alloy of platinum with 10% iridium,

measured at the melting point of ice. 1927 October 6 – The 7th CGPM redefines

the metre as the distance, at 0 °C, between the axes of the two central lines marked on

the prototype bar of platinum-iridium, this bar being subject to one standard atmosphere

of pressure and supported on two cylinders of at least 1 cm diameter, symmetrically

placed in the same horizontal plane at a distance of 571 millimetres from each other.

1960 October 14 – The 11th CGPM defines the metre as 1,650,763.73 wavelengths in a

vacuum of the radiation corresponding to the transition between the 2p10 and 5d5 quantum

levels of the krypton-86 atom. 1983 October 21 – The 17th CGPM defines

the metre as the length of the path travelled by light in a vacuum during a time interval

of 1/299,792,458 of a second. 2002 – The International Committee for

Weights and Measures considers the metre to be a unit of proper length and thus recommends

this definition be restricted to “lengths ℓ which are sufficiently short for the effects

predicted by general relativity to be negligible with respect to the uncertainties of realisation”.

SI prefixed forms of metre SI prefixes are often employed to denote decimal

multiples and submultiples of the metre, as shown in the table below. As indicated in

the table, some are commonly used, while others are not. Long distances are usually expressed

in km, astronomical units, light-years, or parsecs, 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 term micron is often used instead of micrometre,

but this practice is officially discouraged. Spelling

Metre is used as the standard spelling of the metric unit for length in all English-speaking

nations except the USA, which uses meter. The most recent official brochure, written

in 2006, about the International System of Units, Bureau international des poids et mesures,

was written in French by the International Bureau of Weights and Measures. An English

translation is included to make the SI standard “more widely accessible”.

In 2008, the U.S. English translation published by the U.S. National Institute of Standards

and Technology chose to use meter in accordance with the United States Government Printing

Office Style Manual. Measuring devices are spelt “-meter” in all

countries. The word “meter”, signifying any such device, has the same derivation as the

word “metre”, denoting the unit of length. Equivalents in other units

Within this table, “inch” and “yard” mean “international inch” and “international yard”,

respectively, though approximate conversions in the left-hand column hold for both international

and survey units. “≈” means “is approximately equal to”;

“≡” means “equal by definition” or “is exactly equal to.”

One metre is exactly equivalent to 10,000/254 inches and to 10,000/9,144 yards.

A simple mnemonic aid exists to assist with conversion, as three “3”:

1 metre is nearly equivalent to 3 feet–3 3⁄8 inches. This gives an overestimate of 0.125 mm.

The ancient Egyptian cubit was about 1⁄2 m Scottish and English definitions of ell were

0.941 m and 1.143 m, respectively. The ancient Paris toise was slightly shorter than 2 m,

and was standardised at exactly 2 m in the mesures usuelles system, such that 1 m was

exactly 1⁄2 toise. The Russian versta was 1.0668 km. The Swedish mil was 10.688 km,

but was changed to 10 km when Sweden converted to metric units.

See also Conversion of units for comparisons with other

units International System of Units

Introduction to the metric system ISO 1 – standard reference temperature

for length measurements Length measurement

Metre Convention Metric system

Metric prefix Metrication

Orders of magnitude SI prefix

Speed of light Notes References

17th General Conference on Weights and Measures.. Resolution 1. International Bureau of Weights

and Measures. Astin, A. V. & Karo, H. Arnold,, Refinement

of values for the yard and the pound, Washington DC: National Bureau of Standards, republished

on National Geodetic Survey web site and the Federal Register

Barbrow, Louis E. & Judson, Lewis V.. Weights and Measures Standards of the United States:

A brief history.. National Institute of Standards and Technology.

Beers, J.S. & Penzes, W. B.. NIST Length Scale Interferometer Measurement Assurance.. National

Institute of Standards and Technology. “The International System of Units”. Bureau

International des Poids et Mesures. 2006. Retrieved 18 August 2008.

HTML version. Retrieved 24 August 2008. Bureau International des Poids et Mesures..

Resolutions of the CGPM. Retrieved 3 June 2006.

Bureau International des Poids et Mesures.. The BIPM and the evolution of the definition

of the metre. Retrieved 3 June 2006. Cardarelli, Francois. Encydopaedia of scientific

units, weights, and measures: their SI equivalences and origins, Springer-Verlag London Limited,

ISBN 1-85233-682-X, page 5, table 2.1, data from Giacomo, P., Du platine a la lumiere,

Bull. Bur. Nat. Metrologie, 102 5–14. Humerfelt, Sigurd.. How WGS 84 defines Earth.

Retrieved 29 April 2011. Layer, H.P.. Length—Evolution from Measurement

Standard to a Fundamental Constant. Gaithersburg, MD: National Institute of Standards and Technology.

Retrieved 18 August 2008. Mohr, P., Taylor, B.N., and David B. Newell,

D.. CODATA Recommended Values of the Fundamental Physical Constants: 2006. Gaithersburg, MD:

National Institute of Standards and Technology. Retrieved 18 August 2008.

National Institute of Standards and Technology.. The NIST Reference on Constants, Units, and

Uncertainty: International System of Units: SI base units. Retrieved 18 August 2008.

Definitions of the SI base units. Retrieved 18 August 2008.

Historical context of the SI: Meter. Retrieved 26 May 2010. National Institute of Standards and Technology..

NIST-F1 Cesium Fountain Atomic Clock. Author. National Physical Laboratory.. Iodine-Stabilised

Lasers. Author. National Research Council Canada.. Maintaining

the SI unit of length. Retrieved 4 December 2010.

Naughtin, Pat.. Spelling metre or meter. Author. Penzes, W.. Time Line for the Definition of

the Meter. Gaithersburg, MD: National Institute of Standards and Technology – Precision

Engineering Division. Retrieved 4 December 2010.

Taylor, B.N. and Thompson, A… The International System of Units. United States version of

the English text of the eighth edition of the International Bureau of Weights and Measures

publication Le Système International d’ Unités. Gaithersburg, MD: National Institute

of Standards and Technology. Retrieved 18 August 2008.

Taylor, B.N. and Thompson, A.. Guide for the Use of the International System of Units.

Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 23 August 2008.

Tibo Qorl. The History of the Meter. Retrieved 18 August 2008.

Turner, J…”Interpretation of the International System of Units for the United States”. Federal

Register Vol. 73, No. 96, p. 28432-3. Wilkins, J.. An essay towards a real character,

and a philosophical language.[Also available without images of original.] Metrication Matters.

Zagar, B.G.. Laser interferometer displacement sensors in J.G. Webster. The Measurement,

Instrumentation, and Sensors Handbook. CRC Press. isbn=0-8493-8347-1.

Further reading Alder, Ken.. The Measure of All Things :

The Seven-Year Odyssey and Hidden Error That Transformed the World. Free Press, New York

ISBN 0-7432-1675-X