History of the metre
Encyclopedia
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 metric 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.
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 Constituent 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): despite the support of the Assembly, and of Great Britain and the newly independent United States, nothing came of Talleyrand's proposal.The idea of the seconds pendulum as a length standard did not die completely, and such a standard was used to define the yard
in the United Kingdom from 1843 to 1878.
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 was an avid supporter of 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
" ( of a quarter-circle) rather than degree
s, 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 existing second (as a unit of time) would not be used in the proposed decimal system of time measurement
- a system of 10 hours to the day, 100 minutes to the hour and 100 seconds to the minute - introduced in 1793.
Instead of the seconds pendulum method, 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 consideration of safe access for French surveyors, the Paris meridian
was also a sound choice for practical scientific reasons: a portion of the quadrant from Dunkirk 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 arc
fell to Pierre Méchain
and Jean-Baptiste Delambre, and took more than six years (1792–98).The technical difficulties were not the only problems the surveyors had to face in the convulsed period of the aftermath of the Revolution: Méchain and Delambre, and later Arago
, were imprisoned several times during their surveys, and Méchain died in 1804 of yellow fever, which he contracted while trying to improve his original results in northern Spain. In the meantime, the commission calculated a provisional value from older surveys of 443.44 ligne
s.All values in lignes are referred to the toise de Pérou, not to the later value in mesures usuelles
. 1 toise
= 6 pieds; 1 pied = 12 pouces; 1 pouce = 12 lignes; so 864 lignes = 1 toise. This value was set by legislation on 7 April 1795.
The project was split into two parts – the northern section of 742.7 km from the Belfry, Dunkirk to Rodez Cathederal
which was surveyed by Delambre and the southern section of 333.0 km from Rodez
to the Montjuïc Fortress
, Barcelona which was surveyed by Méchain.
Delambre used a baseline of about 10 km in length along a straight road, located close to Melun
. In an operation taking six weeks, the baseline was accurately measured using four platinum rods, each of length two toise (about 3.9 m). Thereafter he used, where possible, the triangulation points used by Cassini
in his 1744 survey of France. Méchain's baseline, of a similar length, and also on a straight section of road was in the Perpignan
area. Although Méchain's sector was half the length of Delambre, it included the Pyrenees
and hitherto unsurveyed parts of Spain. After the two surveyors met, each computed the other's baseline in order to cross-check their results and they then recomputed the kilometre. Their result came out at 0.144 lignes shorter than the provisional value, a difference of about 0.03%.
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 m or lignes.The WGS 84 reference spheroid has a semi-major axis of and a flattening of .
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 1867) 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".
The only significant international use of the meridional definition of the metre, apart from Méchain and Delambre's original survey, was the initial work conducted by the British Association for the Advancement of Science
(B.A.) on electrical units which was to lead to the International System of Electrical and Magnetic Units
. It was often claimed that the international electrical units formed a coherent set of absolute units in the "QES system", where the unit length was the quadrant of the Earth's polar circumference, the unit mass was the "eleventh-gram" or 10−11 grams and the unit time was the second
. Nevertheless, the precision of absolute electrical measurements in the late nineteenth century was not such that the 0.02% difference in the definitions of the metre had any practical significance.
The International Conference on Geodesy in 1867 called for the creation of a new, international prototype metreThe term "prototype" does not imply that it was the first in a series and that other standard metres would come after it: the "prototype" metre was the one that came first in the logical chain of comparisons, that is the metre to which all other standards were compared. and to arrange a system where national standards could be compared with it. The international prototype would also be a "line standard", that is the metre was defined as the distance between two lines marked on the bar, so avoiding the wear problems of end standards. The French government gave practical support to the creation of an International Metre Commission, which met in Paris in 1870 and again in 1872 with the participation of about thirty countries.
The international nature of the standards was ensured by a treaty – the Metre Convention – signed in Paris on 20 May 1875. This set up an international organization, the Bureau international des poids et mesures (BIPM), to conserve the prototypes (which were to be the joint property of the signatory nations) and to carry out regular comparisons with national standards. In recognition of the role of France in designing the metric system, the BIPM is based in Sèvres, just outside Paris, but it enjoys the usual privileges of an international organization and is under the ultimate control of a diplomatic conference (the Conférence générale des poids et mesures, CGPM) and not of the French government.
The construction of the international prototype metre and the copies which would be national standards was at the limits of the technology of its time. The bars were to be made of a special alloy, 90% platinum
and 10% iridium
, which is significantly harder than pure platinum, and have a special X-shaped cross section (a "Tresca section", named after French engineer Henri Tresca
) to minimise the effects of torsional strain during length comparisons. The first castings proved unsatisfactory, and the job was given to the London firm of Johnson Matthey
who succeeded in producing thirty bars to the required specification: one of these (No. 6) was determined to be identical in length to the mètre des Archives, and was consecrated as the international prototype metre at the first meeting of the CGPM in 1889. The other bars, duely calibrated against the international prototype, were distributed to the signatory nations of the Metre Convention for use as national standards: for example, the United States received No. 27 with a calibrated length of (1.6 µm short of the international prototype).
The first (and only) follow-up comparison of the national standards with the international prototype was carried out between 1921 and 1936, and indicated that the definition of the metre was preserved to with 0.2 µm. At this time, it was decided that a more formal definition of the metre was required (the 1889 decision had said merely that the "prototype, at the temperature of melting ice, shall henceforth represent the metric unit of length"), and this was agreed at the 7th CGPM in 1927:
The support requirements represent the Airy points
of the prototype, that is the points, separated by of the total length of the bar, at which the bending or droop of the bar is minimized.
measurements carried out using the international prototype metre were those of Michelson and Benoît
(1892–93) and of Benoît, Fabry
and Perot
(1906), both using the red line of cadmium
. These results, which gave the wavelength
of the cadmium line (λ ≈ 644 nm), led to the definition of the angstrom
as a secondary unit of length for spectroscopic measurements, first by the International Union for Solar Research (1907) and later by the CIPM (1927).The IUSR (later to become the International Astronomical Union
) defined the angstrom such that the wavelength (in air) of the cadmium line was Å. Michelson's work in "measuring" the prototype metre to within of a wavelength ( µm) was one of the reasons for which he was awarded the Nobel Prize in Physics
in 1907.
By the 1950s, interferometry had become the method of choice for precise measurements of length but there remained a practical problem imposed by the system of units used. The natural unit for expressing a length measured by interferometry was the angstrom, but this result then had to be converted into metres using an experimental conversion factor – the wavelength of light used, but measured in metres rather than in angstroms. This added an additional measurement uncertainty
to any length result in metres, over and above the uncertainty of the actual interferometric measurement. The solution was to define the metre in the same manner as the angstrom had been defined in 1907, that is in terms of the best interferometric wavelength available.
Advances in both experimental technique and theory showed that the cadmium line was actually a cluster of closely separated lines, and that this was due to the presence of different isotope
s in natural cadmium (eight in total). To get the most precisely defined line, it was necessary to use a monoisotopic source and this source should contain an isotope with even numbers of protons and neutrons (so as to have zero nuclear spin). Several isotopes of cadmium, krypton
and mercury
both fulfil the condition of zero nuclear spin and have bright lines in the visible region of the spectrum. Krypton is a gas at room temperature, allowing for easier isotopic enrichment and lower operating temperatures for the lamp (which reduces broadening
of the line due to the Doppler effect
), and so it was decided to select the orange line of krypton-86 (λ ≈ 606 nm) as the new wavelength standard. Accordingly, the 11th CGPM in 1960 agreed a new definition of the metre:
The measurement of the wavelength of the krypton line was not made directly against the international prototype metre: instead the ratio of the wavelength of the krypton line to that of the cadmium line was determined in vacuum, and this was compared to the 1906 Fabry–Perot determination of the wavelength of the cadmium line in air (with a correction for the refractive index
of air). In this way, the new definition of the metre was traceable
to both the old prototype metre and the old definition of the angstrom.
of nitrogen
(63.14 K, −210.01 °C) was the state of the art light source for interferometry in 1960, but it was soon to be superseded by a new invention – the laser
, of which the first working version was constructed in the same year as the redefinition of the metre. Laser light is usually highly monochromatic, and is also coherent (all the light has the same phase
, unlike the light from a discharge lamp), both of which are advantageous for interferometry.
The shortcomings of the krypton standard were demonstrated by the measurement of the wavelength of the light from a methane
-stabilized helium–neon laser (λ ≈ 3.39 µm). The krypton line was found to be asymmetrical, so different wavelengths could be found for the laser light depending on which point on the krypton line was taken for reference.Taking the point of highest intensity as the reference wavelength, the methane line had a wavelength of µm; taking the intensity-weighted mean point ("centre of gravity") of the krypton line as the standard, the wavelength of the methane line is µm. The asymmetry also affected the precision to which the wavelengths could be measured.
Developments in electronics also made it possible for the first time to measure the frequency of light in or near the visible region of the spectrum, instead of inferring the frequency from the wavelength and the speed of light
. Although visible and infrared frequencies were still too high to be directly measured, it was possible to construct a "chain" of laser frequencies that, by suitable multiplication, differ from each other by only a directly measurable frequency in the microwave
region. The frequency of the light from the methane-stabilized laser was found to be THz.
Independent measurements of frequency and wavelength are, in effect, a measurement of the speed of light (c = fλ), and the results from the methane-stabilized laser gave the speed of light with an uncertainty
almost 100-times lower than previous measurements in the microwave region. Or, somewhat inconveniently, the results gave two values for the speed of light, depending on which point on the krypton line was chosen to define the metre.The measured speed of light was for the "centre-of-gravity" definition and for the maximum-intensity definition, with a relative uncertainty ur = 3.5. The ambiguity was resolved in 1975, when the 15th CGPM approved a conventional value of the speed of light as exactly .
Nevertheless, the infrared light from a methane-stabilized laser was inconvenient for use in practical interferometry. It was not until 1983 that the chain of frequency measurements reached the 633 nm line of the helium–neon laser, which can be stabilized (if necessary) against absorptions of molecular iodine
. That same year, the 17th CGPM adopted the current definition of the metre, in terms of the 1975 conventional value for the speed of light:
The concept of defining a unit of length in terms of a time received some comment, although it is similar to Wilkins'
original proposal in 1668 to define the universal unit of length in terms of the seconds pendulum. In both cases, the practical issue is that time can be measured more accurately than length (one part in 1013 for a second using a caesium clock as opposed to four parts in 109 for the metre in 1983). The definition in terms of the speed of light also means that the metre can be realized using any light source of known frequency, rather than defining a "preferred" source in advance: given that there are more than 22,000 lines in the visible spectrum of iodine, any of which could be potentially used to stabilize a laser source, the advantages of flexibility are obvious.
French livre
The livre was the currency of France until 1795. Several different livres existed, some concurrently. The livre was the name of both units of account and coins.-Etymology:...
was replaced by the decimal franc
French franc
The franc was a currency of France. Along with the Spanish peseta, it was also a de facto currency used in Andorra . Between 1360 and 1641, it was the name of coins worth 1 livre tournois and it remained in common parlance as a term for this amount of money...
, 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 metric system in France (including an official reversion to the mesures usuelles
Mesures usuelles
Mesures usuelles were a system of measurement introduced by Napoleon I in 1812 to act as compromise between the metric system and traditional measurements...
["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.
Universal measure
The standard measures of length in Europe diverged from one another following the fall of Charlemagne's 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
John Wilkins
John Wilkins FRS was an English clergyman, natural philosopher and author, as well as a founder of the Invisible College and one of the founders of the Royal Society, and Bishop of Chester from 1668 until his death....
called it) or "metro cattolico" (Italian Tito Livio Burattini
Tito Livio Burattini
Tito Livio Burattini was an inventor, architect, Egyptologist, scientist, instrument-maker, traveller, engineer, and nobleman. He was born in Agordo, Italy, and studied in Padua and Venice...
), 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
Pendulum
A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position...
with a half-period of one second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
) 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
Yard
A yard is a unit of length in several different systems including English units, Imperial units and United States customary units. It is equal to 3 feet or 36 inches...
). However, it was soon discovered that the length of a seconds pendulum varies from place to place: French astronomer Jean Richer
Jean Richer
Jean Richer was a French astronomer and assistant of Giovanni Domenico Cassini.Between 1671 and 1673 he traveled to Cayenne at the request of the French Academy of Sciences to observe Mars during its perigee...
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 Constituent 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): despite the support of the Assembly, and of Great Britain and the newly independent United States, nothing came of Talleyrand's proposal.The idea of the seconds pendulum as a length standard did not die completely, and such a standard was used to define the yard
Yard
A yard is a unit of length in several different systems including English units, Imperial units and United States customary units. It is equal to 3 feet or 36 inches...
in the United Kingdom from 1843 to 1878.
Meridional definition
Jean-Charles de Borda
Jean-Charles, chevalier de Borda was a French mathematician, physicist, political scientist, and sailor.-Life history:...
. Borda was an avid supporter of 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
Grad (angle)
The gradian is a unit of plane angle, equivalent to of a turn. It is also known as gon, grad, or grade . One grad equals of a degree or of a radian...
" ( of a quarter-circle) rather than degree
Degree (angle)
A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...
s, 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 existing second (as a unit of time) would not be used in the proposed decimal system of time measurement
Decimal time
Decimal time is the representation of the time of day using units which are decimally related. This term is often used to refer specifically to French Revolutionary Time, which divides the day into 10 decimal hours, each decimal hour into 100 decimal minutes and each decimal minute into 100 decimal...
- a system of 10 hours to the day, 100 minutes to the hour and 100 seconds to the minute - introduced in 1793.
Instead of the seconds pendulum method, the commission – whose members included Lagrange, Laplace
Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics. He summarized and extended the work of his predecessors in his five volume Mécanique Céleste...
, Monge
Gaspard Monge
Gaspard Monge, Comte de Péluse was a French mathematician, revolutionary, and was inventor of descriptive geometry. During the French Revolution, he was involved in the complete reorganization of the educational system, founding the École Polytechnique...
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
Meridian (geography)
A meridian is an imaginary line on the Earth's surface from the North Pole to the South Pole that connects all locations along it with a given longitude. The position of a point along the meridian is given by its latitude. Each meridian is perpendicular to all circles of latitude...
passing through Paris. Apart from the obvious consideration of safe access for French surveyors, the Paris meridian
Paris Meridian
The Paris Meridian is a meridian line running through the Paris Observatory in Paris, France—now longitude 2°20′14.025″ east. It was a long-standing rival to Greenwich as the prime meridian of the world, as was the Meridian of Antwerp in Antwerp, Belgium....
was also a sound choice for practical scientific reasons: a portion of the quadrant from Dunkirk to Barcelona
Barcelona
Barcelona is the second largest city in Spain after Madrid, and the capital of Catalonia, with a population of 1,621,537 within its administrative limits on a land area of...
(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 arc
Meridian arc
In geodesy, a meridian arc measurement is a highly accurate determination of the distance between two points with the same longitude. Two or more such determinations at different locations then specify the shape of the reference ellipsoid which best approximates the shape of the geoid. This...
fell to Pierre Méchain
Pierre Méchain
Pierre François André Méchain 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:...
and Jean-Baptiste Delambre, and took more than six years (1792–98).The technical difficulties were not the only problems the surveyors had to face in the convulsed period of the aftermath of the Revolution: Méchain and Delambre, and later Arago
François Arago
François Jean Dominique Arago , known simply as François Arago , was a French mathematician, physicist, astronomer and politician.-Early life and work:...
, were imprisoned several times during their surveys, and Méchain died in 1804 of yellow fever, which he contracted while trying to improve his original results in northern Spain. In the meantime, the commission calculated a provisional value from older surveys of 443.44 ligne
Ligne
The ligne is a unit of length that was in use prior to the French adoption of the metric system in the late 18th century, and is still used by French and Swiss wristwatch makers to measure the size of a watch movement.- Watchmakers' use :There are 12 lignes to one French inch...
s.All values in lignes are referred to the toise de Pérou, not to the later value in mesures usuelles
Mesures usuelles
Mesures usuelles were a system of measurement introduced by Napoleon I in 1812 to act as compromise between the metric system and traditional measurements...
. 1 toise
Toise
A toise 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 , and Quebec...
= 6 pieds; 1 pied = 12 pouces; 1 pouce = 12 lignes; so 864 lignes = 1 toise. This value was set by legislation on 7 April 1795.
The project was split into two parts – the northern section of 742.7 km from the Belfry, Dunkirk to Rodez Cathederal
Rodez
Rodez is a town and commune in southern France, in the Aveyron department, of which it is the capital. Its inhabitants are called Ruthénois.-History:Existing from at least the 5th century BC, Rodez was founded by the Celts...
which was surveyed by Delambre and the southern section of 333.0 km from Rodez
Rodez
Rodez is a town and commune in southern France, in the Aveyron department, of which it is the capital. Its inhabitants are called Ruthénois.-History:Existing from at least the 5th century BC, Rodez was founded by the Celts...
to the Montjuïc Fortress
Montjuïc
Montjuïc is a hill located in Barcelona, Catalonia.-Etymology:Montjuïc is translated as 'Jew Hill' in medieval Catalan, or is perhaps related to the Latin phrase Mons Jovicus . The name is found in several locations in the Catalan Countries: the Catalan cities of Girona and Barcelona both have a...
, Barcelona which was surveyed by Méchain.
Delambre used a baseline of about 10 km in length along a straight road, located close to Melun
Melun
Melun is a commune in the Seine-et-Marne department in the Île-de-France region in north-central France. Located in the south-eastern suburbs of Paris, Melun is the capital of the department, as the seat of an arrondissement...
. In an operation taking six weeks, the baseline was accurately measured using four platinum rods, each of length two toise (about 3.9 m). Thereafter he used, where possible, the triangulation points used by Cassini
César-François Cassini de Thury
César-François Cassini de Thury , also called Cassini III or Cassini de Thury, was a French astronomer and cartographer.- Biography :...
in his 1744 survey of France. Méchain's baseline, of a similar length, and also on a straight section of road was in the Perpignan
Perpignan
-Sport:Perpignan is a rugby stronghold: their rugby union side, USA Perpignan, is a regular competitor in the Heineken Cup and seven times champion of the Top 14 , while their rugby league side plays in the engage Super League under the name Catalans Dragons.-Culture:Since 2004, every year in the...
area. Although Méchain's sector was half the length of Delambre, it included the Pyrenees
Pyrenees
The Pyrenees is a range of mountains in southwest Europe that forms a natural border between France and Spain...
and hitherto unsurveyed parts of Spain. After the two surveyors met, each computed the other's baseline in order to cross-check their results and they then recomputed the kilometre. Their result came out at 0.144 lignes shorter than the provisional value, a difference of about 0.03%.
Mètre des Archives
While Méchain and Delambre were completing their survey, the commission had ordered a series of platinumPlatinum
Platinum is a chemical element with the chemical symbol Pt and an atomic number of 78. Its name is derived from the Spanish term platina del Pinto, which is literally translated into "little silver of the Pinto River." It is a dense, malleable, ductile, precious, gray-white transition metal...
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
French Republican Calendar
The French Republican Calendar or French Revolutionary Calendar was a calendar created and implemented during the French Revolution, and used by the French government for about 12 years from late 1793 to 1805, and for 18 days by the Paris Commune in 1871...
) as a permanent record of the result: this standard metre bar became known as the mètre des Archives.
The metric system
Metric system
The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...
, 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
Mesures usuelles
Mesures usuelles were a system of measurement introduced by Napoleon I in 1812 to act as compromise between the metric system and traditional measurements...
, 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
François Arago
François Jean Dominique Arago , known simply as François Arago , was a French mathematician, physicist, astronomer and politician.-Early life and work:...
and Biot
Jean-Baptiste Biot
Jean-Baptiste Biot was a French physicist, astronomer, and mathematician who established the reality of meteorites, made an early balloon flight, and studied the polarization of light.- Biography :...
extended the survey to the island of Formentera
Formentera
Formentera is the smaller and more southerly island of the Pine Islands group , which belongs to the Balearic Islands autonomous community .-Geography:...
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 m or lignes.The WGS 84 reference spheroid has a semi-major axis of and a flattening of .
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 1867) 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".
The only significant international use of the meridional definition of the metre, apart from Méchain and Delambre's original survey, was the initial work conducted by the British Association for the Advancement of Science
British Association for the Advancement of Science
frame|right|"The BA" logoThe British Association for the Advancement of Science or the British Science Association, formerly known as the BA, is a learned society with the object of promoting science, directing general attention to scientific matters, and facilitating interaction between...
(B.A.) on electrical units which was to lead to the International System of Electrical and Magnetic Units
International System of Electrical and Magnetic Units
The International System of Electrical and Magnetic Units is an obsolete system of units used solely for measuring electrical and magnetic quantities. It was introduced by the Fourth International Electrical Congress and modified in 1908...
. It was often claimed that the international electrical units formed a coherent set of absolute units in the "QES system", where the unit length was the quadrant of the Earth's polar circumference, the unit mass was the "eleventh-gram" or 10−11 grams and the unit time was the second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
. Nevertheless, the precision of absolute electrical measurements in the late nineteenth century was not such that the 0.02% difference in the definitions of the metre had any practical significance.
International prototype metre
With increasing international adoption of the metre, the short-comings of the mètre des Archives as a standard became ever more apparent. Countries which adopted the metre as a legal measure purchased standard metre bars that were intended to be equal in length to the mètre des Archives, but there was no systematic way of ensuring that the countries were actually working to the same standard. The meridional definition, which had been intended to ensure international reproducibility, quickly proved so impractical that is was all but abandoned in favour of the artefact standards, but the mètre des Archives (and most of its copies) were "end standards": such standards (bars which are exactly one metre in length) are prone to wear with use, and different standard bars could be expected to wear at different rates.The International Conference on Geodesy in 1867 called for the creation of a new, international prototype metreThe term "prototype" does not imply that it was the first in a series and that other standard metres would come after it: the "prototype" metre was the one that came first in the logical chain of comparisons, that is the metre to which all other standards were compared. and to arrange a system where national standards could be compared with it. The international prototype would also be a "line standard", that is the metre was defined as the distance between two lines marked on the bar, so avoiding the wear problems of end standards. The French government gave practical support to the creation of an International Metre Commission, which met in Paris in 1870 and again in 1872 with the participation of about thirty countries.
The international nature of the standards was ensured by a treaty – the Metre Convention – signed in Paris on 20 May 1875. This set up an international organization, the Bureau international des poids et mesures (BIPM), to conserve the prototypes (which were to be the joint property of the signatory nations) and to carry out regular comparisons with national standards. In recognition of the role of France in designing the metric system, the BIPM is based in Sèvres, just outside Paris, but it enjoys the usual privileges of an international organization and is under the ultimate control of a diplomatic conference (the Conférence générale des poids et mesures, CGPM) and not of the French government.
Platinum
Platinum is a chemical element with the chemical symbol Pt and an atomic number of 78. Its name is derived from the Spanish term platina del Pinto, which is literally translated into "little silver of the Pinto River." It is a dense, malleable, ductile, precious, gray-white transition metal...
and 10% iridium
Iridium
Iridium is the chemical element with atomic number 77, and is represented by the symbol Ir. A very hard, brittle, silvery-white transition metal of the platinum family, iridium is the second-densest element and is the most corrosion-resistant metal, even at temperatures as high as 2000 °C...
, which is significantly harder than pure platinum, and have a special X-shaped cross section (a "Tresca section", named after French engineer Henri Tresca
Henri Tresca
Henri Édouard Tresca was a French mechanical engineer, and a professor at the Conservatoire National des Arts et Métiers in Paris....
) to minimise the effects of torsional strain during length comparisons. The first castings proved unsatisfactory, and the job was given to the London firm of Johnson Matthey
Johnson Matthey
Johnson Matthey plc is multinational chemicals and precious metals company headquartered in London, United Kingdom.It is listed on the London Stock Exchange and is a constituent of the FTSE 100 Index.-History:...
who succeeded in producing thirty bars to the required specification: one of these (No. 6) was determined to be identical in length to the mètre des Archives, and was consecrated as the international prototype metre at the first meeting of the CGPM in 1889. The other bars, duely calibrated against the international prototype, were distributed to the signatory nations of the Metre Convention for use as national standards: for example, the United States received No. 27 with a calibrated length of (1.6 µm short of the international prototype).
The first (and only) follow-up comparison of the national standards with the international prototype was carried out between 1921 and 1936, and indicated that the definition of the metre was preserved to with 0.2 µm. At this time, it was decided that a more formal definition of the metre was required (the 1889 decision had said merely that the "prototype, at the temperature of melting ice, shall henceforth represent the metric unit of length"), and this was agreed at the 7th CGPM in 1927:
The support requirements represent the Airy points
Airy Points
Airy Points are used for precision measurement to support a length standard in such a way as to minimise bending or droop. The points are symmetrically arranged around the centre of the length standard and are separated by a distance equal to...
of the prototype, that is the points, separated by of the total length of the bar, at which the bending or droop of the bar is minimized.
Krypton standard
The first interferometricInterferometry
Interferometry refers to a family of techniques in which electromagnetic waves are superimposed in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy,...
measurements carried out using the international prototype metre were those of Michelson and Benoît
Benoit
Benoit may refer to:*Benoit , a surname and male given name*Benoit, Mississippi, a United States town*Benoit, Wisconsin, a United States unincorporated community...
(1892–93) and of Benoît, Fabry
Charles Fabry
Maurice Paul Auguste Charles Fabry FMRS was a French physicist.-Life:Fabry graduated from the Ecole Polytechnique in Paris and received his doctorate from the University of Paris in 1892, for his work on interference fringes, which established him as an authority in the field of optics and...
and Perot
Alfred Pérot
Jean-Baptiste Alfred Perot was a French physicist.Together with his colleague Charles Fabry he developed the Fabry–Pérot interferometer.-Spelling:...
(1906), both using the red line of cadmium
Cadmium
Cadmium is a chemical element with the symbol Cd and atomic number 48. This soft, bluish-white metal is chemically similar to the two other stable metals in group 12, zinc and mercury. Similar to zinc, it prefers oxidation state +2 in most of its compounds and similar to mercury it shows a low...
. These results, which gave the wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
of the cadmium line (λ ≈ 644 nm), led to the definition of the angstrom
Ångström
The angstrom or ångström, is a unit of length equal to 1/10,000,000,000 of a meter . Its symbol is the Swedish letter Å....
as a secondary unit of length for spectroscopic measurements, first by the International Union for Solar Research (1907) and later by the CIPM (1927).The IUSR (later to become the International Astronomical Union
International Astronomical Union
The International Astronomical Union IAU is a collection of professional astronomers, at the Ph.D. level and beyond, active in professional research and education in astronomy...
) defined the angstrom such that the wavelength (in air) of the cadmium line was Å. Michelson's work in "measuring" the prototype metre to within of a wavelength ( µm) was one of the reasons for which he was awarded the Nobel Prize in Physics
Nobel Prize in Physics
The Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...
in 1907.
By the 1950s, interferometry had become the method of choice for precise measurements of length but there remained a practical problem imposed by the system of units used. The natural unit for expressing a length measured by interferometry was the angstrom, but this result then had to be converted into metres using an experimental conversion factor – the wavelength of light used, but measured in metres rather than in angstroms. This added an additional measurement uncertainty
Measurement uncertainty
In metrology, measurement uncertainty is a non-negative parameter characterizing the dispersion of the values attributed to a measured quantity. The uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity. All measurements are subject to uncertainty and a measured...
to any length result in metres, over and above the uncertainty of the actual interferometric measurement. The solution was to define the metre in the same manner as the angstrom had been defined in 1907, that is in terms of the best interferometric wavelength available.
Advances in both experimental technique and theory showed that the cadmium line was actually a cluster of closely separated lines, and that this was due to the presence of different isotope
Isotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...
s in natural cadmium (eight in total). To get the most precisely defined line, it was necessary to use a monoisotopic source and this source should contain an isotope with even numbers of protons and neutrons (so as to have zero nuclear spin). Several isotopes of cadmium, krypton
Krypton
Krypton is a chemical element with the symbol Kr and atomic number 36. It is a member of Group 18 and Period 4 elements. A colorless, odorless, tasteless noble gas, krypton occurs in trace amounts in the atmosphere, is isolated by fractionally distilling liquified air, and is often used with other...
and mercury
Mercury (element)
Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...
both fulfil the condition of zero nuclear spin and have bright lines in the visible region of the spectrum. Krypton is a gas at room temperature, allowing for easier isotopic enrichment and lower operating temperatures for the lamp (which reduces broadening
Doppler broadening
In atomic physics, Doppler broadening is the broadening of spectral lines due to the Doppler effect caused by a distribution of velocities of atoms or molecules. Different velocities of the emitting particles result in different shifts, the cumulative effect of which is the line broadening.The...
of the line due to the Doppler effect
Doppler effect
The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...
), and so it was decided to select the orange line of krypton-86 (λ ≈ 606 nm) as the new wavelength standard. Accordingly, the 11th CGPM in 1960 agreed a new definition of the metre:
The measurement of the wavelength of the krypton line was not made directly against the international prototype metre: instead the ratio of the wavelength of the krypton line to that of the cadmium line was determined in vacuum, and this was compared to the 1906 Fabry–Perot determination of the wavelength of the cadmium line in air (with a correction for the refractive index
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
of air). In this way, the new definition of the metre was traceable
Traceability
Traceability refers to the completeness of the information about every step in a process chain.The formal definition: Traceability is the ability to chronologically interrelate uniquely identifiable entities in a way that is verifiable....
to both the old prototype metre and the old definition of the angstrom.
Speed of light standard
The krypton-86 discharge lamp operating at the triple pointTriple point
In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases of that substance coexist in thermodynamic equilibrium...
of nitrogen
Nitrogen
Nitrogen is a chemical element that has the symbol N, atomic number of 7 and atomic mass 14.00674 u. Elemental nitrogen is a colorless, odorless, tasteless, and mostly inert diatomic gas at standard conditions, constituting 78.08% by volume of Earth's atmosphere...
(63.14 K, −210.01 °C) was the state of the art light source for interferometry in 1960, but it was soon to be superseded by a new invention – the laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...
, of which the first working version was constructed in the same year as the redefinition of the metre. Laser light is usually highly monochromatic, and is also coherent (all the light has the same phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
, unlike the light from a discharge lamp), both of which are advantageous for interferometry.
The shortcomings of the krypton standard were demonstrated by the measurement of the wavelength of the light from a methane
Methane
Methane is a chemical compound with the chemical formula . It is the simplest alkane, the principal component of natural gas, and probably the most abundant organic compound on earth. The relative abundance of methane makes it an attractive fuel...
-stabilized helium–neon laser (λ ≈ 3.39 µm). The krypton line was found to be asymmetrical, so different wavelengths could be found for the laser light depending on which point on the krypton line was taken for reference.Taking the point of highest intensity as the reference wavelength, the methane line had a wavelength of µm; taking the intensity-weighted mean point ("centre of gravity") of the krypton line as the standard, the wavelength of the methane line is µm. The asymmetry also affected the precision to which the wavelengths could be measured.
Developments in electronics also made it possible for the first time to measure the frequency of light in or near the visible region of the spectrum, instead of inferring the frequency from the wavelength and the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
. Although visible and infrared frequencies were still too high to be directly measured, it was possible to construct a "chain" of laser frequencies that, by suitable multiplication, differ from each other by only a directly measurable frequency in the microwave
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
region. The frequency of the light from the methane-stabilized laser was found to be THz.
Independent measurements of frequency and wavelength are, in effect, a measurement of the speed of light (c = fλ), and the results from the methane-stabilized laser gave the speed of light with an uncertainty
Measurement uncertainty
In metrology, measurement uncertainty is a non-negative parameter characterizing the dispersion of the values attributed to a measured quantity. The uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity. All measurements are subject to uncertainty and a measured...
almost 100-times lower than previous measurements in the microwave region. Or, somewhat inconveniently, the results gave two values for the speed of light, depending on which point on the krypton line was chosen to define the metre.The measured speed of light was for the "centre-of-gravity" definition and for the maximum-intensity definition, with a relative uncertainty ur = 3.5. The ambiguity was resolved in 1975, when the 15th CGPM approved a conventional value of the speed of light as exactly .
Nevertheless, the infrared light from a methane-stabilized laser was inconvenient for use in practical interferometry. It was not until 1983 that the chain of frequency measurements reached the 633 nm line of the helium–neon laser, which can be stabilized (if necessary) against absorptions of molecular iodine
Iodine
Iodine is a chemical element with the symbol I and atomic number 53. The name is pronounced , , or . The name is from the , meaning violet or purple, due to the color of elemental iodine vapor....
. That same year, the 17th CGPM adopted the current definition of the metre, in terms of the 1975 conventional value for the speed of light:
The concept of defining a unit of length in terms of a time received some comment, although it is similar to Wilkins'
John Wilkins
John Wilkins FRS was an English clergyman, natural philosopher and author, as well as a founder of the Invisible College and one of the founders of the Royal Society, and Bishop of Chester from 1668 until his death....
original proposal in 1668 to define the universal unit of length in terms of the seconds pendulum. In both cases, the practical issue is that time can be measured more accurately than length (one part in 1013 for a second using a caesium clock as opposed to four parts in 109 for the metre in 1983). The definition in terms of the speed of light also means that the metre can be realized using any light source of known frequency, rather than defining a "preferred" source in advance: given that there are more than 22,000 lines in the visible spectrum of iodine, any of which could be potentially used to stabilize a laser source, the advantages of flexibility are obvious.
External links
- meter (metre) at Sizes.com