Metre

The metre (symbol: m), spelled meter in the United States, is the SI unit of length and one of the seven base units in the International System of Units. The name is derived from the Greek μέτρον (metron) meaning "measure", and gives rise to the term "metric system", a system of units of which the metre is one.

The metre was conceived in the aftermath of the French Revolution (1789) as a replacement for the old units of length that were associated with the ancien régime. Although there was initially considerable resistance to the adoption of the new units 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 consacrated as an international measurement unit by the Metre Convention of 1875.

Definition

The current definition of the metre was agreed at the 17th General Conference on Weights and Measures (CGPM) in 1983:

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 has the effect that the speed of light in vacuum has an exact, defined value in SI units: 299 792 458 m s⁻¹.

Relativity

The metre is considered to be a unit of proper length. As such, the definition is only adequate in itself for measurements in an area where the local gravitational field can be considered to be uniform, a condition which is met by almost all measurements on the surface of the Earth (the Earth's gravitational field varies by about one part in 10¹⁶ per vertical metre, which is far less than the measurement uncertainty in Earth-based length measurements). For astronomical measurements, the effects of general relativity cannot be ignored and the definition of the metre must be completed with a description of the metric tensor which defines the gravitational field.

Realization

The metre can be realized either directly, by measuring the time taken for light to travel a certain distance, or by interferometry.

Interferometry

Source	Stabilizing line (127I2)	Frequency THz	Wavelength nm	ur
Helium–neon laser	a16 component, R(127) 11-5 transition	473.612 353 604(10)	632.991 212 579(13)	2.1 × 10−11
Nd:YAG laser	a10 component, R(56) 32-0 transition	563.260 223 513(5)	532.245 036 104(5)	8.9 × 10−12

For an unstabilized helium–neon laser (Ne 3s₂→2p₄ transition):

f = 473.612 7 THz

λ = 632.990 8 nm

u_r = 1.5 × 10⁻⁶

History

Universal measure

The standard measures of length in Europe diverged from one another following the fall of the Roman Empire: while measures could be standardized within a given jurisdiction (which was often little more than a single market town), they were numerous varieties of measure between regions. Indeed, as the measures were often used as the basis for taxation (of cloth, for example), the use of a certain measure was associated with the sovereignty of a given ruler and often dictated by law.

Nevertheless, with the increasing scientific activity of the seventeenth century came calls for the institution of a "universal measure" (as Englishman John Wilkins called it) or "metro cattolico" (Italian Tito Livio Burattini), which would be based on a natural phenomenon rather than royal decree, and would also be decimal rather than the various systems of multipliers, often duodecimal, that coexisted at the time.

Wilkins' idea was to choose the length of a "seconds pendulum" (a pendulum with a half-period of one second) as the unit length: such pendulums had recently been demonstrated by Christiaan Huygens, and their length is very close to one modern metre (as well as to length units which were then in use, such as the yard). However, it was soon discovered that the length of a seconds pendulum varies from place to place: French astronomer Jean Richer had measured the 0.3% difference in length between Cayenne (in French Guiana) and Paris.

Little practical progress was made towards the establishment of the "universal measure" until the French Revolution of 1789. France was particularly affected by the proliferation of length measures, and the need for reform was widely accepted across all political viewpoints, even if needed the push of revolution to bring it about. Talleyrand resurrected the idea of the seconds pendulum before the Constituant Assembly in 1790, suggesting that the new measure be defined at 45°N (a latitude that, in France, runs just north of Bordeaux and just south of Grenoble): dispite the support of the Assembly, and of Great Britain and the newly independent United States, nothing came of Talleyrand's proposal.

Meridional definition

The question of measurement reform was placed in the hands of the Academy of Sciences who appointed a commission chaired by Jean-Charles de Borda. Borda could be said to have been a fanatic for decimalization: he had invented the "repeating circle", a surveying instrument which allowed a much-improved precision in the measurement of angles between landmarks, but insisted that it be calibrated in "grades" (¹⁄₁₀₀ of a quarter-circle) rather than degrees, with 100 minutes to a grade and 100 seconds to a minute. For Borda, the seconds pendulum was a poor choice for a standard because the second (as a unit of time) was insufficiently decimal: he preferred a system of 10 hours to the day, 100 minutes to the hour and 100 seconds to the minute…

Instead, the commission – whose members included Lagrange, Laplace, Monge and Condorcet – decided that the new measure should be equal to one ten-millionth of the distance from the North Pole to the Equator (the quadrant of the Earth's circumference), measured along the meridian passing through Paris. Apart from the obvious nationalistic considerations, the Paris meridian was also a sound choice for practical scientific reasons: a portion of the quadrant from Dunkerque to Barcelona (about 1000 km, or one-tenth of the total) could be surveyed with start- and end-points at sea level, and that portion was roughly in the middle of the quadrant, where the effects of the Earth's oblateness were expected to be the largest.

The task of surveying the meridian fell to Pierre Méchain and Jean-Baptiste Delambre, and took more than six years (1792–98). In the meantime, the commission calculated a provisional value from older surveys of 443.44 lignes. Méchain and Delambre's result came out at 0.144 lignes shorter than this, a difference of about 0.03%.

Mètre des Archives

While Méchain and Delambre were completing their survey, the comission had ordered a series of platinum bars to be made based on the provisional metre. When the final result was known, the bar whose length was closest to the meridional definition of the metre was selected and placed in the National Archives on 22 June 1799 (4 messidor An VII in the Republican calendar) as a permanent record of the result: this standard metre bar became known as the mètre des Archives.

The metric system, that is the system of units based on the metre, was officially adopted in France on 10 December 1799 (19 frimaire An VIII) and became the sole legal system of weights and measures from 1801. After the instauration of the Empire, in 1812, the old names for units of length were revived but the units redefined in terms of the metre: this system was known as mesures usuelles, and lasted until 1840 when the decimal metric system was again made the sole legal measure. In the meantime, the Netherlands had adopted the metric system from 1816, the first of several countries to follow the French lead.

It soon became apparent that Méchain and Delambre's result (443.296 lignes) was slightly too short for the meridional definition of the metre. Arago and Biot extended the survey to the island of Formentera in the western Mediterranean Sea in 1806–9, and found that one ten-millionth of the Earth's quadrant should be 443.31 lignes: later work increased the value to 443.39 lignes. The modern value, for the WGS 84 reference spheroid, is 1.000 196 57 m or 443.383 08 lignes.

Nevertheless, the mètre des Archives remained the legal and practical standard for the metre in France, even once it was known that it did not exactly correspond to the meridional definition. When it was decided (in 1875) to create a new international standard metre, the length was taken to be that of the mètre des Archives "in the state in which it shall be found".

External links

• meter (metre) at Sizes.com