Thearc measurement of Delambre and Méchain was ageodetic survey carried out byJean-Baptiste Delambre andPierre Méchain in 1792–1798 to measure anarc section of theParis meridian betweenDunkirk andBarcelona. Thisarc measurement served as the basis for the original definition of themetre.[2]
Until theFrench Revolution of 1789, France was particularly affected by the proliferation of length measures; the conflicts related to units helped precipitate the revolution. In addition to rejecting standards inherited fromfeudalism, linking determination of a decimal unit of length with thefigure of the Earth was an explicit goal.[3][4] This project culminated in an immense effort to measure a meridian passing through Paris in order to define themetre.
When question of measurement reform was placed in the hands of theFrench Academy of Sciences, a commission, whose members includedJean-Charles de Borda,Joseph-Louis Lagrange,Pierre-Simon Laplace,Gaspard Monge and theMarquis de 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 at thelongitude ofParis Observatory. Since this survey, thePanthéon became the central geodetic station in Paris.[4][1]
In 1791,Jean Baptiste Joseph Delambre andPierre Méchain were commissioned to lead an expedition to accurately measure the distance between a belfry inDunkerque andMontjuïc castle inBarcelona in order to calculate the length of themeridian arc through the centre ofParis Observatory.[4][1] The official length of theMètre des Archives was based on these measurements, but the definitive length of the metre required a value for thenon-spherical shape of the Earth, known as the flattening of the Earth.[5] Pierre Méchain's and Jean-Baptiste Delambre's measurements were combined with the results of theFrench Geodetic Mission to the Equator and a value of1/334 was found for the Earth's flattening.[6][7]
The distance from the North Pole to the Equator was then extrapolated from the measurement of theParis meridian arc between Dunkirk and Barcelona and the length of the metre was established, in relation to theToise de l'Académie also called toise of Peru, which had been constructed in 1735 for theFrench Geodesic Mission to Peru, as well as to Borda's double-toise N°1, one of the four twelve feet (French:pieds) long ruler, part of the baseline measuring instrument devised for this survey.[8][4] When the final result was known, theMètre des Archives a platinum 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.[4]
TheFrench Academy of Sciences, responsible for the concept and definition of the metre, was established in 1666.[4] In the 17th century it had determined the first reasonably accurate distance to theSun and organised important work ingeodesy andcartography. In the 18th century, in addition to its significance forcartography,geodesy grew in importance as a means of empirically demonstratingNewton's law of universal gravitation, whichÉmilie du Châtelet promoted in France in combination withLeibniz's mathematical work and because theradius of the Earth was the unit to which all celestial distances were to be referred.[9][10][11] Among the results that would impact the definition of the metre: Earth proved to be anoblate spheroid through geodetic surveys inEcuador andLapland.[4][5]
Galileo had discoveredgravitational acceleration explaining the fall of bodies at the surface of the Earth.[12] He had also observed the regularity of the period of swing of thependulum and that this period depended on the length of the pendulum.[13]Marin Mersenne was the central figure in the dissemination of Galileo's ideas in France, thanks to his role as a translator and commentator of Galileo's work.[14] In 1645Giovanni Battista Riccioli had been the first to determine the length of a "seconds pendulum" (apendulum with a half-period of onesecond).[15][a] In 1656,Christiaan Huygens, inspired by Galileo,[13] invented the firstpendulum clock which greatly improved the accuracy oftime measurement required forastronomical observations.[16] In 1671,Jean Picard also measured the length of aseconds pendulum atParis Observatory and proposed this unit of measurement to be called the astronomical radius (French:Rayon Astronomique).[17][18] He found the value of 36pouces and 81/2lignes of theToise ofChâtelet, which had been recently renewed.[18][6] Proposals for decimal measurement systems from scientists and mathematicians also led to proposals to base units on reproducible natural phenomena, such as the motion of a pendulum or a fraction of thecircle of latitude at theEquator.[19]
The first reasonably accurate distance to the Sun was determined in 1684 byGiovanni Domenico Cassini. Knowing that direct measurements of the solar parallax were difficult he chose to measure the Martian parallax. Having sent Jean Richer to Cayenne, part of French Guiana, for simultaneous measurements, Cassini in Paris determined the parallax of Mars when Mars was at its closest to Earth in 1672. Using the circumference distance between the two observations, Cassini calculated the Earth-Mars distance, then usedKepler's laws to determine the Earth-Sun distance. His value, about 10% smaller than modern values, was much larger than all previous estimates.[20]
Although it had been known sinceclassical antiquity that the Earth wasspherical, by the 17th century, evidence was accumulating that it was not a perfect sphere. In 1672,Jean Richer found the first evidence thatgravity was not constant over the Earth (as it would be if the Earth were a sphere); he took apendulum clock toCayenne,French Guiana and found that it lost2+1⁄2 minutes per day compared to its rate atParis.[21][22] This indicated theacceleration of gravity was less at Cayenne than at Paris. Pendulum gravimeters began to be taken on voyages to remote parts of the world, and it was slowly discovered that gravity increases smoothly with increasinglatitude,gravitational acceleration being about 0.5% greater at thegeographical poles than at theEquator.
In 1687,Isaac Newton had published in thePrincipia as a proof that the Earth was an oblatespheroid offlattening equal to1/230.[23] This was disputed by some, but not all, French scientists. A meridian arc ofJean Picard was extended to a longer arc byGiovanni Domenico Cassini and his sonJacques Cassini over the period 1684–1718.[24] The arc was measured with at least three latitude determinations, so they were able to deduce mean curvatures for the northern and southern halves of the arc, allowing a determination of the overall shape. The results indicated that the Earth was aprolate spheroid (with an equatorial radius less than the polar radius). To resolve the issue, theFrench Academy of Sciences (1735) undertookexpeditions to Peru (Bouguer,Louis Godin,de La Condamine,Antonio de Ulloa,Jorge Juan) andto Lapland (Maupertuis,Clairaut,Camus,Le Monnier,Abbe Outhier,Anders Celsius). The resulting measurements at equatorial and polar latitudes confirmed that the Earth was best modelled by an oblate spheroid, supporting Newton.[24] In the 1740s an account was published in the ParisMémoires, byCassini de Thury, of a remeasurement by himself andNicolas Louis de Lacaille of the meridian of Paris. With a view to determine more accurately the variation of the degree along the meridian, they divided the distance from Dunkirk to Collioure into four partial arcs of about two degrees each, by observing the latitude at five stations. The results previously obtained by Giovanni Domenico and Jacques Cassini were not confirmed, but, on the contrary, the length of the degree derived from these partial arcs showed on the whole an increase with increasing latitude.[11]
Geodetic surveys found practical applications inFrench cartography and in theAnglo-French Survey, which aimed to connectParis andGreenwich Observatories and led to thePrincipal Triangulation of Great Britain.[25][26] The unit of length used by the French was theToise de Paris, while the English one was theyard, which became the geodetic unit used in theBritish Empire.[27][28][29]
In 1783 the director of theParis Observatory,César-François Cassini de Thury, addressed a memoir to theRoyal Society in London, in which he expressed grave reservations about the latitude and longitude measurements undertaken at theRoyal Greenwich Observatory. He suggested that the correct values might be found by combining the Paris Observatory figures with a precisetrigonometric survey between the two observatories. This criticism was roundly rejected byNevil Maskelyne who was convinced of the accuracy of the Greenwich measurements but, at the same time, he realised that Cassini's memoir provided a means of promoting government funding for a survey which would be valuable in its own right.[30]
For thetriangulation of theAnglo-French Survey,César-François Cassini de Thury was assisted byPierre Méchain. They used therepeating circle, an instrument forgeodetic surveying, developed from thereflecting circle byÉtienne Lenoir in 1784. He invented it while an assistant ofJean-Charles de Borda, who later improved the instrument. It was notable as being the equal of thegreat theodolite created by the renowned instrument maker,Jesse Ramsden. It would later be used tomeasure themeridian arc fromDunkirk toBarcelona byJean Baptiste Delambre andPierre Méchain as improvements in the measuring device designed by Borda and used for this survey also raised hopes for a more accurate determination of the length of theFrench meridian arc.[30]
From the French revolution of 1789 came an effort to reform measurement standards, leading ultimately to remeasure the meridian passing through Paris in order to define themetre.[31]: 52 The question of measurement reform was placed in the hands of theFrench Academy of Sciences, who appointed a commission chaired byJean-Charles de Borda. Instead of the seconds pendulum method,[b] the commission of the French Academy of Sciences – whose members includedBorda,Lagrange,Laplace,Monge andCondorcet – 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 at thelongitude ofParis pantheon, which became the central geodetic station in Paris.[33][34]Jean Baptiste Joseph Delambre obtained the fundamentalco-ordinates of the Panthéon by triangulating all the geodetic stations around Paris from the Panthéon's dome.[34][35]
Apart from the obvious consideration of safe access for French surveyors, theParis meridian was also a sound choice for scientific reasons: a portion of the quadrant fromDunkirk toBarcelona (about 1000 km, or one-tenth of the total) could be surveyed with start- and end-points at sea level,[7] and that portion was roughly in the middle of the quadrant, where the effects of the Earth's oblateness were expected not to have to be accounted for.[36]
The expedition would take place after theAnglo-French Survey, thus the French meridian arc, which would extend northwards across theUnited Kingdom, would also extend southwards toBarcelona, later toBalearic Islands.Jean-Baptiste Biot andFrançois Arago would publish in 1821 their observations completing those of Delambre and Mechain. It was an account of the length's variations of portions of one degree of amplitude of the meridian arc along theParis meridian as well as the account of the variation of theseconds pendulum's length along the same meridian betweenShetland and theBalearc Islands.[37][38]
The task of surveying the meridian arc fell toPierre Méchain andJean-Baptiste Delambre, and took more than six years (1792–1798). 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 laterFrançois Arago, were imprisoned several times during their surveys, and Méchain died in 1804 ofyellow fever, which he contracted while trying to improve his original results in northern Spain.[39]
The project was split into two parts – the northern section of 742.7 km from the belfry of theChurch of Saint-Éloi, Dunkirk toRodez Cathedral which was surveyed by Delambre and the southern section of 333.0 km fromRodez to theMontjuïc Fortress, Barcelona which was surveyed by Méchain. Although Méchain's sector was half the length of Delambre, it included thePyrenees and hitherto unsurveyed parts of Spain.[40]
Delambre measured a baseline of about 10 km (6,075.90toises) in length along a straight road betweenMelun andLieusaint. In an operation taking six weeks, the baseline was accurately measured using four platinum rods, each of length twotoises (atoise being about 1.949 m).[40][8] These measuring devices consisted of bimetallic rulers in platinum and brass fixed together at one extremity to assess the variations in length produced by any change in temperature.[41][42]Borda's double-toise N°1, which had been compared to the Toise of Peru,[43] became the main reference for measuring all geodetic bases in France.[4] Intercomparisons of baseline measuring devices were essential formetrological traceability. Moreover, because ofthermal expansion, geodesists tried to accurately assesstemperature of standards in the field in order to avoidobservational errors.[44] Thereafter he used, where possible, thetriangulation points used byNicolas Louis de Lacaille in his 1739-1740arc measurement.[45][46] Méchain's baseline was of a similar length (6,006.25toises), and also on a straight section of road between Vernet (in thePerpignan area) and Salces (nowSalses-le-Chateau).[47]
To put into practice the decision taken by theNational Convention, on 1 August 1793, to disseminate the new units of the decimalmetric system,[50] it was decided to establish the length of the metre based on a fraction of the meridian in the process of being measured. The decision was taken to fix the length of a provisional metre (French:mètre provisoire) determined by the French meridian arc measurement, which had been carried out fromDunkirk toPerpignan byNicolas Louis de Lacaille andCesar-François Cassini de Thury and published by the latter in 1744.[46] The length of the metre was established, in relation to the toise of the academy also called toise of Peru, at 3 feet 11.44 lines, taken at 13 degrees of the temperature scale ofRené-Antoine Ferchault de Réaumur in use at the time. This value was set by legislation on 7 April 1795.[50][6] It was therefore metal bars of 443.44 lignes that were distributed in France in 1795–1796.[39] This was the metre installed under the arcades of therue de Vaugirard, almost opposite the entrance to theSenate.[45]
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End of November 1798, Delambre and Méchain returned to Paris with their data, having completed the survey to meet a foreign commission composed of representatives ofBatavian Republic:Henricus Aeneae andJean Henri van Swinden,Cisalpine Republic:Lorenzo Mascheroni,Kingdom of Denmark:Thomas Bugge,Kingdom of Spain: Gabriel Císcar and Agustín de Pedrayes,Helvetic Republic:Johann Georg Tralles,Ligurian Republic: Ambrogio Multedo,Kingdom of Sardinia: Prospero Balbo, Antonio Vassali Eandi,Roman Republic: Pietro Franchini,Tuscan Republic:Giovanni Fabbroni who had been invited byTalleyrand. The French commission comprisedJean-Charles de Borda,Barnabé Brisson,Charles-Augustin de Coulomb,Jean Darcet,René Just Haüy,Joseph-Louis Lagrange,Pierre- Simon Laplace,Louis Lefèvre-Ginneau, Pierre Méchain andGaspar de Prony.[51][6][52]
In 1799, a commission includingJohann Georg Tralles,Jean Henri van Swinden,Adrien-Marie Legendre,Pierre-Simon Laplace, Gabriel Císcar, Pierre Méchain and Jean-Baptiste Delambre calculated the distance from Dunkirk to Barcelona using the data of thetriangulation between these two towns and determined the portion of the distance from the North Pole to the Equator it represented.Pierre-Simon Laplace originally hoped to figure out theEarth ellipsoid problem from the sole measurement of the arc from Dunkirk to Barcelona. However, when, about 1804, he would calculate it using theleast squares method, this portion of the meridian arc led for the flattening to the value of1/150 considered as unacceptable.[49][6][35] This value was the result of a conjecture based on too limited data. Another flattening of the Earth would be calculated by Delambre, who would exclude the results of theFrench Geodetic Mission to Lapland and would found a value close to1/300 combining the results of Delambre and Méchain arc measurement with those of theSpanish-French Geodetic Mission taking in account a correction of the astronomic arc.[53][6][54]
Eventually, the distance from the North Pole to the Equator was extrapolated from the measurement of theParis meridian arc between Dunkirk and Barcelona and was determined as5130740 toises assuming anEarth flattening of1/334. The Weights and Measures Commission adopted, in 1799, this value for the flattening based on an analysis byPierre-Simon Laplace who combined theFrench Geodesic Mission to the Equator and the data of the arc measurement of Delambre and Méchain.[55] Combining these two data sets Laplace succeeded to estimate theflattening of theEarth ellipsoid and was happy to find that it also fitted well with his estimate 1/336 based on 15 pendulum measurements.[55][5]
As the length of the metre had been set by legislation to be equal to one ten-millionth of this distance, it was defined as 0.513074 toise or 3 feet and 11.296 lines of the Toise of Peru, which had been constructed in 1735 for theFrench Geodesic Mission to Peru.[51][7] When the final result was known, a bar whose length was closest to the definition of the legal 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.[45] Another platinum metre, calibrated against theMètre des Archives, and twelve iron ones were made as secondary standards.[56] One of the iron metre standards was brought to the United States in 1805.[57] It became known as the Committee Meter in the United States and served as a standard of length in theUnited States Coast Survey until 1890.[58][57][28][59]
However,Louis Puissant declared in 1836 to theFrench Academy of Sciences thatJean Baptiste Joseph Delambre and Pierre Méchain had made errors in the triangulation of the meridian arc, which had been used for determining the length of the metre.[60][61] This is why Antoine Yvon Villarceau verified the geodetic operations at eight points of theParis meridian arc from 1861 to 1866. Some of the errors in the operations of Delambre and Méchain were then corrected.[62]
In his 2002 bookThe measure of all things, Ken Alder recalled that the legal metre is about 0.2 millimetres shorter than it should be according to its original proposed definition.[63] Since long, the length of the legal metre has been questioned because of an uncertainty in Méchain's determination of the latitude of the southern end of the arc measurement besides other problems in the publication of his results.[64] This 2 km error in the Earth quadrant appeared toAdrien-Marie Legendre when he compared5130740 toises obtained for the length of the definitive metre with5132430 toises deduced from the distance measured byNicolas-Louis de Lacaille of a meridian arc of one degree at 45° of latitude which was used to fix the length of the provisional metre.[6][63] He suspected a deviation ofplumb-line due togravity anomaly that geodesists now callvertical deflection. Indeed, 95% of the missing length of the legal metre was due to not taking the effect of vertical deflection into account, while wrong assumption of flattening of the Earth ellipsoid accounted for 3% of the error and the length of the meridian arc as measured by Delambre and Méchain contributed for less than 2% of the total error. Despite the precision of their survey, the definition of the metre was beyond Delambre and Méchain's reach asgravity anomalies had not yet been studied.[63] Indeed, thegeoid is a ball which can be approximately assimilated to an ellipsoid, however meridians have such differencies from one another in shape and length that any extrapolation is impossible from only one arc measurement.[35]
Nevertheless, in 1855, the Dufour map (French:Carte Dufour), the firsttopographic map of Switzerland for which the metre was adopted as the unit of length, won the gold medal at the Exposition Universelle.[65][66] On the sidelines of theExposition Universelle (1855) and the secondCongress of Statistics held in Paris, an association with a view to obtaining a uniform decimal system of measures, weights and currencies was created.[67] At the initiative of this association, a Committee for Weights and Measures and Monies (French:Comité des poids, mesures et monnaies) was created during theExposition Universelle (1867) in Paris and called for the international adoption of the metric system.[68][67] In the United States, theMetric Act of 1866 allowed the use of the metre,[69] and in 1867 the General Conference of theEuropean Arc Measurement (German:Europäische Gradmessung) proposed the establishment of theInternational Bureau of Weights and Measures.[70][71]
The destruction of the standard measurements during theburning of parliament led to an overhaul of the British weights and measures system.[72] This also led to the abandonment of the idea of dematerializing the definition of units of length by means of the pendulum, as this method proved less reliable than artefacts.[73][74] The destroyed weights and measures were recast byWilliam Simms, the scientific instrument maker, who produced the replacements after "countless hours of tests and experiments to determine the best metal, the best shape of bar, and the corrections for temperature".[72][75] The creation of the newyard standard inaugurated the principle, which was taken up byHenri Tresca, of marking lines indicating the length of the unit on theneutral plane of the standard.[74]
In 1875 a number of American, Asian, African and European states concluded theMetre Convention,[c] and the International Bureau of Weights and Measures (BIPM) was established at thePavillon de Breteuil. Until this time the metre was determined by the end-surfaces of a platinum rod (Mètre des archives); subsequently, rods of platinum-iridium, of cross-section X, were constructed, having engraved lines at both ends of the bridge, which determined the distance of a metre.[11] The representation of the unit of length by means of the distance between two fine lines on the surface of a bar of metal at a certain temperature is never itself free from uncertainty and probable error, owing to the difficulty of knowing at any moment the precise temperature of the bar; and the transference of this unit, or a multiple of it, to a measuring bar will be affected not only with errors of observation, but with errors arising from uncertainty of temperature of both bars. If the measuring bar be not self-compensating for temperature, its expansion must be determined by very careful experiments. The thermometers required for this purpose must be very carefully studied, and their errors of division and index error determined.[76]
The standards used by geodesists were compared with a known reference standard.[43] In order to maintainmeasurement traceability it was important to control the temperature during these intercomparisons in order to avoidsystematic errors.[77] In 1886,Adolphe Hisch, secretary of theInternational Committee for Weights and Measures (CIPM) and of theInternational Geodetic Association, proposed that all the toises that had served as geodetic standards in Europe during the 19th century be compared at the BIPM with the Toise of Peru and with the newinternational metre so that the measurements made until then could be used to measure the Earth.[43] The result of these comparisons made it possible to reduce the arcs measured in Germany to the metre. The discordance of1/66 000 which remained between the triangles common to the German and French networks could be reduced to1/600 000 which was at the limit ofaccuracy of geodetic surveys at the time.[78] In fact, the length of Bessel's Toise, which according to the then legal ratio between the metre and the Toise of Peru, should be equal to 1.9490348 m, would be found to be 26.2·10−6 m greater during measurements carried out byJean-René Benoît at the BIPM. It was the consideration of the divergences between the different toises used by geodesists that led theEuropean Arc Measurement (German:Europäische Gradmessung ) to consider, at the meeting of its Permanent Commission inNeuchâtel in 1866, the founding of a World Institute for the Comparison of Geodetic Standards, the first step towards the creation of the BIPM.[79][80] Careful comparisons with several standard toises showed that the international metre calibrated on theMètre des Archives was not exactly equal to the legal metre or 443.296 lines of the toise, but, in round numbers,1/75 000 of the length smaller,[11] or approximately 0.013 millimetres.
TheMètre des Archives and its copies such as theCommittee Meter were replaced from 1889 by thirtyplatinum-iridium bars kept across the globe.[81] A betterstandardisation of the new prototypes of the metre and their comparison with each other and with the historical standard involved the development of specialised measuring equipment and the definition of a reproducible temperature scale.[82]
In 1901, thanks to the work initiated inSwitzerland byÉmile Plantamour under the auspices of theInternational Geodetic Association,[83]Friedrich Robert Helmert would find, essentially throughgravimetry, parameters of theEarth ellipsoid remarkably close to reality, namely asemi-major axis equal to 6 378 200 metres and a flattening of1/298.3 . This last value would be set at1/298.25 by the analysis of the first results from satellite measurements.[84] At theExposition Universelle (1889), theBrunner frères company exhibited a reversible pendulum designed by Gilbert Étienne Defforges.[85] In 1892, he measured the value ofgravitational acceleration at the BIPM.[86] In 1901, the thirdGeneral Conference on Weights and Measures (CGPM) confirmed a value of 980.665 cm/s2 for thestandard gravity.[87]
In collaboration with the International Geodetic Association created to measure the Earth, the International Bureau of Weights and Measures became the world reference center for the measurement of geodetic bases thanks toCharles Édouard Guillaume's discovery ofinvar, an alloy of nickel and iron with a coefficient ofthermal expansion close to zero.[68][88]
TheBIPM, based inSèvres, not far from Paris, was originally responsible, under the supervision of theCIPM, for the conservation of international prototypes of measurement standards, as well as their comparison and calibration with national prototypes. However, the BIPM gradually reoriented itself towards the study ofphysical constants,[89] which are the basis of2019 revision of the SI.
In 1834,Ferdinand Rudolph Hassler measured atFire Island the firstbaseline of theSurvey of the Coast.[90] Ferdinand Rudolph Hassler's use of the metre and the creation of the Office of Standard Weights and Measures as an office within the Coast Survey contributed to the introduction of theMetric Act of 1866 allowing the use of the metre in the United States,[91] and preceded the choice of the metre as international scientific unit of length and the proposal by the 1867 General Conference of theEuropean Arc Measurement (German:Europäische Gradmessung) to establish theInternational Bureau of Weights and Measures.[92]
Ferdinand Rudolph Hassler was a Swiss-Americansurveyor who is considered the forefather of both theNational Oceanic and Atmospheric Administration (NOAA) and theNational Institute of Standards and Technology (NIST) for his achievements as the first Superintendent of the U.S. Survey of the Coast and the first U.S. Superintendent of Weights and Measures.[93][94] The foundation of theUnited States Coast and Geodetic Survey led to the actual definition of the metre, withCharles Sanders Peirce being the first to experimentally link the metre to the wavelength of a spectral line. Charles Sanders Peirce's work promoted the advent of American science at the forefront of global metrology. Alongside his intercomparisons of artifacts of the metre and contributions to gravimetry through improvement of reversible pendulum, Peirce was the first to tie experimentally the metre to the wave length of a spectral line. According to him the standard length might be compared with that of a wave of light identified by a line in thesolar spectrum.Albert Abraham Michelson soon took up the idea and improved it.[95][96]
Progress in science finally allowed the definition of the metre to be dematerialised; thus in 1960 a new definition based on a specific number of wavelengths of light from a specific transition inkrypton-86 allowed the standard to be universally available by measurement. In 1983 this was updated to a length defined in terms of thespeed of light; this definition was reworded in 2019:[97]
The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of thespeed of light in vacuumc to be299792458 when expressed in the unit m⋅s−1, where the second is defined in terms of the caesium frequencyΔνCs.
Where older traditional length measures are still used, they are now defined in terms of the metre – for example theyard has since 1959 officially been defined as exactly 0.9144 metre.[98]
In 1870,Carlos Ibáñez e Ibáñez de Ibero founded the SpanishNational Geographic Institute which he then directed until 1889.[99][100] At the time it was the world's biggest geographic institute.[101] It encompassed geodesy, general topography, leveling, cartography, statistics and the general service of weights and measures.[101] Spain had adopted the metric system in 1849. The Government was urged by theSpanish Royal Academy of Sciences to approve the creation of a large-scale map of Spain in 1852.[102] In 1858, Spain's central geodetic base of triangulation was measured inMadridejos (Toledo) with exceptional precision for the time thanks to the Spanish Standard.[101] The four-metre-long Spanish measuring instrument was compared with Borda's double-toise N°1 which was the main reference for measuring all geodetic bases in France and whose length was by definition 3.8980732 metres at a specified temperature.[103][28] From 1865 to 1868 Ibáñez added the survey of the Balearic Islands with that of the Iberian Peninsula. For this work, he devised a new instrument, which allowed much faster measurements.[104] Regarding the two methods by which the effect of temperature was taken into account, Ibáñez used both the bimetallic rulers, in platinum and brass, which he first employed for the central base of Spain, and the simple iron ruler with inlaid mercury thermometers which was used in Switzerland.[101]
In order to avoid the difficulty in exactly determining the temperature of a bar by the mercury thermometer,Friedrich Wilhelm Bessel, inspired byJean-Charles de Borda, introduced in 1834 nearKönigsberg a compound bar which constituted a metallic thermometer. Azinc bar was laid on aniron bar two toises long, both bars being perfectly planed and in free contact, the zinc bar being slightly shorter and the two bars rigidly united at one end. As the temperature varied, the difference of the lengths of the bars, as perceived by the other end, also varied, and afforded a quantitative correction for temperature variations, which was applied to reduce the length to standard temperature. During the measurement of the base line the bars were not allowed to come into contact, the interval being measured by the insertion of glass wedges. The results of the comparisons of four measuring rods with one another and with the standards were elaborately computed by the method ofleast-squares.[76] Indeed, beforeinvar's discovery, geodesists tried to assess temperature effect on measuring devices in order to avoidobservational errors.[44][24]
Carlos Ibáñez e Ibáñez de Ibero recognized that the end standards with which the most perfect devices of the eighteenth century and those of the first half of the nineteenth century were still equipped, thatBorda orBessel simply joined measuring the intervals by means ofvernier calipers or glass wedges, would be replaced advantageously for accuracy by microscopic measurements, a system designed inSwitzerland byFerdinand Rudolph Hassler andJohann Georg Tralles,[106] and which Ibáñez ameliorated using a standard with lines marked on the bar.[101][28] Suppose A, B, C three micrometer microscopes very firmly supported at intervals of 4 metres with their axes vertical, and aligned in the plane of the base line by means of a transit instrument, their micrometer screws being in the line of measurement. The measuring bar was brought under say A and B, and those micrometers read; the bar was then shifted and brought under B and C. By repetition of this process, the reading of a micrometer indicating the end of each position of the bar, the measurement was made.[76]
Ibañez employed in 1858–1879, for the measurement of nine base lines in Spain, two apparatus similar to the apparatus previously employed by Hassler in the United States;[58] one is complicated, the other simplified. The first, an apparatus ofJean Brunner of Paris,[107] was a thermometric combination of two bars, one of platinum and one of brass, in length 4 metres. Since, however, it only permitted a distance of about 300 m. to be measured daily, Ibañez introduced a simplification; the measuring rod being made simply of steel, and provided with inlaid mercury thermometers. This apparatus was used in Switzerland for the measurement of three base lines. The accuracy is shown by the estimated probable errors: ±0.2 μ to ±0.8 μ. The distance measured daily amounts at least to 800 m. In 1869, Ibáñez brought it along toSouthampton whereAlexander Ross Clarke was making the necessary measurements to compare the geodetic standards of length used in the World.[28][29]
In 1865 the triangulation of Spain was connected with that ofPortugal and France.[109][110] In 1866 at the conference of the Association of Geodesy inNeuchâtel, Ibáñez announced that Spain would collaborate in remeasuring and extending theFrench meridian arc.[101][111] From 1870 to 1894,François Perrier, then Jean-Antonin-Léon Bassot proceeded to a new survey.[62][112] In 1879 Ibáñez andFrançois Perrier completed the junction between the geodetic networks of Spain andAlgeria and thus completed the measurement of a meridian arc which extended fromShetland to theSahara.[113] This connection was a remarkable enterprise where triangles with a maximum length of 270 km were observed at night, with the aid of electric light-signals,[11] from mountain stations (Mulhacén, Tetica, Filahoussen, M'Sabiha) over theMediterranean Sea.[114][113][115][112]
This meridian arc was named West Europe-Africa Meridian-arc byAlexander Ross Clarke andFriedrich Robert Helmert. It yielded a value for the equatorial radius of the eartha = 6 377 935 metres, the ellipticity being assumed as1/299.15 according toBessel ellipsoid.[116][117] The radius of curvature of this arc is not uniform, being, in the mean, about 600 metres greater in the northern than in the southern part.[108] According to the calculations made at the central bureau of the International Geodetic Association, the net does not follow the meridian exactly, but deviates both to the west and to the east; actually, themeridian of Greenwich is nearer the mean than that of Paris.[108]
In the 19th century, astronomers and geodesists were concerned with questions of longitude and time, because they were responsible for determining them scientifically and used them continually in their studies. TheInternational Geodetic Association, which had covered Europe with a network of fundamental longitudes, took an interest in the question of an internationally accepted prime meridian at its seventh general conference in Rome in 1883.[118] Indeed, the Association was already providing administrations with the bases for topographical surveys, and engineers with the fundamental benchmarks for their levelling. It seemed natural that it should contribute to the achievement of significant progress in navigation, cartography and geography, as well as in the service of major communications institutions, railways and telegraphs.[119] From a scientific point of view, to be a candidate for the status of international prime meridian, the proponent needed to satisfy three important criteria. According to the report byCarlos Ibáñez e Ibáñez de Ibero, it must have a first-rate astronomical observatory, be directly linked by astronomical observations to other nearby observatories, and be attached to a network of first-rate triangles in the surrounding country.[119] Four major observatories could satisfy these requirements: Greenwich,Paris,Berlin and Washington. The conference concluded that Greenwich Observatory best corresponded to the geographical, nautical, astronomical and cartographic conditions that guided the choice of an international prime meridian, and recommended the governments should adopt it as the world standard.[120] The Conference further hoped that, if the whole world agreed on the unification of longitudes and times by the Association's choosing the Greenwich meridian, Great Britain might respond in favour of the unification of weights and measures, by adhering to theMetre Convention.[121]
Since the metre was originally defined, each time a new measurement is made, with more accurate instruments, methods or techniques, it is said that the metre is based on some error, from calculations or measurements.[122] When Ibáñez took part to the measurement of the West Europe-Africa Meridian-arc,[11] mathematicians likeLegendre andGauss had developed new methods for processing data, including theleast squares method which allowed to compare experimental data tainted withobservational errors to a mathematical model.[123] The publication in 1838 of Friedrich Wilhelm Bessel’sGradmessung in Ostpreussen had marked an era in the science of geodesy. Here was found the method of least squares applied to the calculation of a network of triangles and the reduction of the observations generally. The systematic manner in which all the observations were taken with the view of securing final results of extreme accuracy was admirable.[11] Furthermore, until theHayford ellipsoid would be introduced in 1910,vertical deflections would be considered asrandom errors.[124] The Earth measurements thus underscored the importance of thescientific method at a time whenstatistics were implemented in geodesy. As a leading scientist of his time, Ibáñez was one of the 81 initial members of theInternational Statistical Institute (ISI) and delegate of Spain to the first ISI session (now called World Statistic Congress) in Rome in 1887.[125][126][127]
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Larousse, Pierre, ed. (1874), "Métrique",Grand dictionnaire universel du XIXe siècle, vol. 11, Paris: Pierre Larousse, pp. 163–164{{cite book}}: CS1 maint: numeric names: authors list (link){{cite book}}: CS1 maint: numeric names: authors list (link) This article incorporates text from this source, which is in thepublic domain:Ibáñez e Ibáñez de Ibero, Carlos (1881).Discursos leidos ante la Real Academia de Ciencias Exactas Fisicas y Naturales en la recepcion pública de Don Joaquin Barraquer y Rovira(PDF). Madrid: Imprenta de la Viuda e Hijo de D.E. Aguado. pp. 70–78.{{cite book}}:ISBN / Date incompatibility (help)