# meter

Physical unit
Unit name meter
Unit symbol ${\ displaystyle \ mathrm {m}}$
Physical quantity (s) length
Formula symbol ${\ displaystyle l, s, b, h, d, r}$ Etc.
dimension ${\ displaystyle {\ mathsf {L}}}$
system International system of units , technical measurement system
In SI units Base unit
In CGS units ${\ displaystyle \ mathrm {1 \, m = 10 ^ {2} \, cm}}$ (Centimeter is the basic unit)
Named after ancient Greek μέτρον métron , German 'measure, length'

The meter is the basic unit of length in the International System of Units (SI) and in other metric systems of units . One meter is defined as the length of the distance that light travels in a vacuum over a period of 1/299 792 458 seconds . The unit symbol for the meter is the lowercase letter "m". The international prefixes for units of measurement are used for decimal multiples and parts of the meter .

The meter was defined in 1799 as the length of the original meter , a prototype made of platinum . According to the measurements carried out at that time, its length corresponded to ten millionth part of the distance from the North Pole to the equator . The current definition has been in force since 1983.

## definition

The meter is defined by the speed of light in vacuum c is a fixed value has been allocated and the second (s) is also a natural constant, the oscillation frequency .DELTA v Cs is defined .

${\ displaystyle c = 299 \, 792 \, 458 \, {\ frac {\ mathrm {m}} {\ mathrm {s}}}}$
${\ displaystyle 1 \, \ mathrm {m} = {\ frac {1} {299 \, 792 \, 458}} \ cdot c \ cdot \ mathrm {s} = {\ frac {9 \, 192 \, 631 \, 770} {299 \, 792 \, 458}} \ cdot {\ frac {c} {\ Delta \ nu _ {\ mathrm {Cs}}}}}$

This definition has been in force since 1983 (the current wording since 2019).

## History of definition

Standard Meter, Rue de Vaugirard , Paris (marble)

The meter as a unit of length has been in use since the end of the 18th century. The origin of this unit of length goes back to a decision by the French National Assembly to define a uniform measure of length. This was preceded by a number of suggestions for defining a unit of length that, unlike traditional length measures, was not derived from the length of human limbs ( finger width , inch , hand width , hand span , cubit , foot , crotch, and fathom ) . In 1668 , the Abbé Jean Picard suggested the second pendulum as the unit of length - i.e. the length of a pendulum that has half a period of one second. In the gravitational field of Europe, such a pendulum would have a length of about 0.994 m and would come pretty close to the current definition of the meter.

### Earth figure

The meter was originally one ten-millionth of the distance between the north pole and the equator on the meridian through Paris be

However, it was not the seconds pendulum that was decisive for the new unit of length, but the figure of the earth . In 1735 the Paris Academy of Sciences sent two expeditions to measure degrees in what is now Ecuador and Lapland to determine the exact dimensions of the earth. In 1793, the French National Convention set - in addition to a new calendar - a new measure of length: the meter should be the 10 millionth part of the earth quadrant on the meridian of Paris - that is, the ten millionth part of the distance from the North Pole via Paris to the equator . A prototype of this meter was cast in brass in 1795.

### Standard meter

Copy number 27 of the original meter made of platinum-iridium, which was made in 1889. It was in use in the USA from 1893 to 1960 as a measuring standard for the unit of length meters.

Between 1792 and 1799 Delambre and Méchain redefined the length of the meridian arc between Dunkirk and Barcelona . A combination with the Ecuador-Lapland results resulted in a new value of 443.296 Paris lines, which was declared binding in 1799 and implemented as a platinum rod, the original meter. In the 19th century, however, more precise measurements of the earth came to the conclusion that the original meter was about 0.02% too short. Nevertheless, the meter defined in 1799 was retained - with the result that the earth meridian quadrant is not 10,000 km, but 10,001.966 km long. This length applies to the meridian of Paris, other meridians can have different lengths. A side effect was that it was recognized that the earth is not an exact ellipsoid of revolution, but has an irregular shape. The earth had thus proven to be unsuitable for defining the meter. Until 1960, the meter was therefore defined as the length of a specific object - first the original meter, then since 1889 the international meter prototype (see below). All later definitions aimed to match this length as closely as possible.

In 1889 the International Bureau of Weights and Measures (BIPM) introduced the International Meter Prototype as a prototype for the unit meter. It was a rod with a cross-shaped cross-section. As the material was a platinum iridium - alloy selected in the ratio 90:10. The length of the meter was determined as the distance between the middle lines of two groups of lines on the stick kept at a constant temperature of 0  ° C. 30 copies of this prototype were made and handed over to national calibration institutes.

### wavelength

A Krypton-86 lamp whose vermilion spectral line (wavelength approx. 606 nm) was used between 1960 and 1983 to define the meter

Although great importance was attached to durability and immutability in the manufacture of the meter prototypes, it was clear that these are fundamentally impermanent. The making of copies inevitably led to deviations and - as well as regular comparisons of the copies with each other and with the original - the risk of damage.

As a remedy, Albert A. Michelson suggested at the beginning of the 20th century to define the meter based on the wavelength of spectral lines. In 1951 Ernst Engelhard and Wilhelm Kösters developed the Krypton-86 spectral lamp at the Physikalisch-Technische Bundesanstalt in Braunschweig , which produced orange-red light with the most stable and reproducible wavelength at the time and which exceeded the accuracy of the original meter. In 1960 the meter was officially redefined: One meter was now 1,650,763.73 times the wavelength of the radiation emitted by atoms of the nuclide 86 Kr during the transition from state 5d 5 to state 2p 10 and spreading in a vacuum . The numerical value was chosen so that the result corresponded to the meter valid until 1960 within the measurement uncertainty of that time. Understanding this definition only required knowledge of atomic physics . If this and the necessary equipment were available, the length of a meter could be reproduced at any location. The meter was the first basic unit that was based on a natural constant and that could be implemented independently of measuring standards and measuring regulations.

### Speed ​​of Light

With the krypton lamp , the meter could be defined with an accuracy of 10 −8 . With the discovery of the laser, however, more and more stable light sources and measurement methods were developed in the following years. In particular, the speed of light could be determined with an accuracy of 1 m / s, and the definition of the meter became the limiting factor. For this reason, at the 15th General Conference on Weights and Measures (CGPM) in 1975, it was  recommended that the numerical value of the speed of light should no longer be measured, but that the unit of length should be defined using the speed of light. The 17th CGPM adopted this definition on October 20, 1983. The meter was defined as the distance that the light travels in a vacuum within the time interval of 1/299 792 458  seconds . With the redefinition of the SI in 2019 by the 26th General Conference on Weights and Measures, only the wording of the definition was adapted to that of the other SI base units.

## Common decimal multiples

The unit meter is used with various decimal multiples, which are designated with the respective SI prefixes , for example:

designation symbol factor As a multiple Notes , for examples of such lengths see order of magnitude (length)
kilometre km 10 3-0 1000 m
Hectometer Hm 10 2-0 0100 m Mainly used by artillery and navy, hectometer stone on roads and hectometer boards on tracks
Decameter dam 10 1-0 0010 m until 1884 also chain
meter m 10 0 0010 dm until 1884 also staff
decimeter dm 10 −1 0010 centimeters obsolete decimeter (around 1900)
centimeter cm 10 −2 0010 mm until 1884 also Neuzoll
millimeter mm 10 −3 1000 µm until 1884 also dash
Micrometer μm 10 −60 1000 nm until 1967 also micron (symbol: μ , simplified designation [myː])
Nanometer nm 10 −90 1000 pm obsolete: Millimicrons , commonly used today for the wavelength of light and in nanotechnology
Ångström Å 10 -10 0100 pm Commonly used today in physical chemistry and molecular thermodynamics, not SI-compliant
Picometer pm 10 −12 1000 fm Commonly used in chemistry for specifying bond lengths
Femtometer fm 10 -15 in nuclear and particle physics as Fermi

Compositions with additional prefixes are not used. In the past, the (non-SI conform) was myriameter(M yr ) in use, 1 M yr = 10 km, see Myriameter stone .

## Relationship to other common units of length

Meters expressed in non-SI units Non-SI units expressed in meters
1 meter ≈ 03.2808 feet0 1 foot = 0000.3048 meters
1 meter ≈ 00.00062 miles (international) 1 mile (international) = 1,609,344 0meters
1 meter ≈ 00.00054 nautical miles 1 nautical mile = 1852.0 000meters
1 meter ≈ 01.0936 yards0 1 yard = 0000.9144 meters
1 meter ≈ 39.370 inches00 1 inch = 0000.0254 meters

Note: The "=" sign means an exact match that is defined by definition; the "≈" symbol indicates a rounded value.

## Introduction of the metric system in Germany

The North German Confederation decided on 17 August 1868, the North German weights and measures regulations (in the law Maaß- and weight of Procedure for the North German Confederation), the introduction of the French meter system . It came into force in the German Empire on January 1, 1872. In 1875 Germany was one of the twelve founding members of the Meter Convention .

## Use of language

The German unit name meter goes back to the French mètre [from Latin metrum , Greek métron = (verse) measure, syllable measure].

The unit name meter was neuter (the meter) according to DIN 1301-1: 2002-10 , analogous to the original languages. With DIN 1301-1: 2010-10, however, masculine (the meter) was defined as the norm. With this, the technical language was adapted to the general usage, where masculine predominates. “The” meter, on the other hand, is used to mean a measuring instrument, for example: the thermometer .

When it comes to the question of whether meters are inflected after number and case, according to the Duden editorial team, the following cases can be distinguished:

• If the one whose measurement is specified is directly behind the unit of measurement, the endless form is used: at a height of 2 meters or 100 meters away
• If the measure is not directly after the unit of measurement, the form with an inflected ending is usually used ( -s in the genitive singular, -n in the dative plural). It does not matter whether the measured data is not mentioned at all (at 100 meters) or in a different place in the sentence (at a distance of 100 meters) .
• The inflected ending is also used when there is an article before the number and unit of measure: with the 150 meters walk or neglecting one meter .

## Derived units of measure

The area unit square meter and the volume unit cubic meter (and thus also the liter ) are derived from the meter . Originally defined by the mass of a liter of water, the kilogram was also derived from the meter.

## literature

• Hans-Joachim v. Alberti: Measure and Weight. Historical and tabular representations from the beginning to the present. Akademie-Verlag, Berlin 1957.
• Johannes Hoppe-Blank: From the metric system to the international system of units . Physikalisch-Technische Bundesanstalt, Braunschweig 1975 (report PTB-ATWD-5).
• Reinhard Kreutzfeldt: The archive meter - on the foundation of the metric system 200 years ago. In: The surveyor. 3/99, Verlag Chmielorz, 1999, pp. 156-158.
• Bettina Schütze, Andreas Engler, Harald Weber: Textbook Surveying - Basic Knowledge. 2nd Edition. Self-published, Dresden 2007, ISBN 978-3-936203-07-3 .
• Harald Schnatz: Length - The SI base unit, the meter. In: PTB-Mitteilungen. 1/2012, pp. 7-22. (on-line)

Commons : Meter  - collection of images, videos and audio files
Wiktionary: Meter  - explanations of meanings, word origins, synonyms, translations

## Individual evidence

1. a b New definitions in the International System of Units (SI). (pdf) PTB , accessed on September 28, 2019 .
2. “The meter, unit symbol m, is the SI unit of length. It is defined by specifying the numerical value 299 792 458 for the speed of light in vacuum c , expressed in the unit m / s, with the second being defined by means of Δν Cs . " Directive (EU) 2019/1258 (PDF) - official German Translation from: Le Système international d'unités . 9e édition, 2019 (the so-called "SI Brochure").
3. Isaac Asimov: Michelson. In: Encyclopædia Britannica . Retrieved July 28, 2019 .
4. ^ Resolution 6 of the 11th CGPM (1960). In: bipm.org. Bureau International des Poids et Mesures, accessed June 22, 2019 .
5. Johannes Kaufmann: The meter turns 30th Phyikalisch-Technische Bundesanstalt, October 16, 2013, accessed on June 19, 2019 .
6. Recommended value for the speed of light Resolution 2 of the 15th meeting of the CGPM (1975) .
7. ^ Resolution 1 of the 17th CGPM (1983). In: bipm.org. Bureau International des Poids et Mesures, accessed June 18, 2019 .
8. 26th CGPM (2018) - Resolutions adopted / Résolutions adoptées. (PDF; 1.2 MB) Versailles 13–16 November 2018. In: bipm.org. Bureau International des Poids et Mesures, November 19, 2018, pp. 2–5 , accessed on May 6, 2019 (English, French).
9. a b c d On the German terms chain, rod, Neuzoll and Strich:
Strich, Maßbezeichnung . In: Brockhaus Konversations-Lexikon 1894-1896, Volume 15, p. 436.
H. Balsam: Guide to planimetry along with a collection of doctrines and tasks. Reprint of the 1st edition from 1872, Salzwasser Verlag, Paderborn, ISBN 978-3-8460-4629-6 , limited preview in the Google book search.
Adam Freiherr v. Burg: The pendulum as a measure of time and length with the transition to the metric measure and weight. In: Association for the dissemination of scientific knowledge in Vienna (ed.): Popular lectures from all subjects of natural science. 16. Cyclus, Vienna 1876, p. 509, scan (PDF; 1.4 MB) accessed April 15, 2018.
10. ^ Resolution 7 of the 13th CGPM (1967). In: bipm.org. Bureau International des Poids et Mesures, accessed December 28, 2019 .
11. K. Rauschert, J. Voigt, I. Wilke, K-Th. Wilke: Chemical tables and calculation tables for analytical practice . 11th edition. Europa-Lehrmittel, 2000, ISBN 978-3-8085-5450-0 , p. 20 .
12. Grossh. Badisches Centralbureau for Meteorology and Hydrography: The Rhine River and its most important tributaries . Ernst & Korn, Berlin 1889.
13. a b DUDEN - The large dictionary of the German language . Bibliographisches Institut & FA Brockhaus, Mannheim 2000, ISBN 3-411-71001-2 .
14. DIN 1301-1: 2010-10 units - Part 1: Unit names, unit symbols, October 2010.
15. Duden, Volume 9: Correct and good German , then briefly summarized Juliane Topka: Meter or Meter?