Before 1789 there are various types of the units of measurement, especially in the Europe, which made inconvenience among countries. So people wanted to create a kind of universal measure that can be used internationally. In the aftermath of the French Revolution (1789), the old units of measure that were associated with the ancien régime were replaced by new units. The livre was replaced by the decimal franc, and a new unit of length was introduced which became known as the metre. Although there was initially considerable resistance to the adoption of the new decimal system in France (including an official reversion to the mesures usuelles ["normal units"] for a period), the metre gained following in continental Europe during the mid nineteenth century, particularly in scientific usage, and was officially adopted as an international measurement unit by the Metre Convention of 1875. Now metre is a base unit in SI, which is used all over the world.
Metre is defined originally my the meridian, and now it is defined by light speed in vacuum.
Meridional definition
In 1668, John Wilkins,an English cleric and philosopher, 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 39¼ English inches (997 mm) 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 quarter meridian connecting the North Pole with the Equator.
The exact shape of the Earth is not a simple mathematical shape (sphere or oblate spheroid) at the level of precision required for defining a standard of length. The irregular and particular shape of the Earth (smoothed to sea level) 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 (40007863 m).
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 (Convention du Mètre) of 1875 mandated the establishment of a permanent International Bureau of Weights and Measures (BIPM: Bureau International des Poids et Mesures) 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 (CGPM: Conférence Générale des Poids et Mesures), 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 (SI) as equal to 1650763.73 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 1/299792458 of a second.
This definition fixed the speed of light in vacuum at exactly 299792458 m/s. 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 (U) of 2.1E−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 (U = 5E-16). Consequently, a realisation of the metre is usually delineated (not defined) today in labs as 1579800.762042(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 1579800.762042(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.
Timeline of definition
- 8 May 1790 - 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.
- 30 March 1791 - 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 (a standard French unit of length from 1747).
- 10 December 1799 - 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.
- 28 September 1889 - The 1st General Conference on Weights and Measures (CGPM) 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.
- 6 October 1927 - The 7th CGPM redefines the metre as the distance, at 0 °C (273.15 K), 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 mm from each other.
- 14 October 1960 - The 11th CGPM defines the metre as 1650763.73 wavelengths in a vacuum of the radiation corresponding to the transition between the 2p10 and 5d5 quantum levels of the krypton-86 atom.
- 21 October 1983 - The 17th CGPM defines the metre as the length of the path travelled by light in a vacuum during a time interval of 1/299792458 of a second.
- 2002 - The International Committee for Weights and Measures (CIPM) 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 realization".
Now metre is one of the base unit in SI, which is used by everyone in the world. In the next post we will talk about the origin of the SI mass unit - kg.
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