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Arc measurement of Delambre and Méchain

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At the time of Delambre, it served as a warehouse for all the old weights and measures which were sent by towns throughout France in anticipation of the standardisation of weights and measures by the establishment of the new decimal metric system.[1]

The arc measurement of Delambre and Méchain was a geodetic survey carried out by Jean-Baptiste Delambre and Pierre Méchain in 1792–1798 to measure an arc section of the Paris meridian between Dunkirk and Barcelona. This arc measurement served as the basis for the original definition of the metre.[2]

Until the French 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 from feudalism, linking determination of a decimal unit of length with the figure 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 the metre.

When question of measurement reform was placed in the hands of the French Academy of Sciences, a commission, whose members included Jean-Charles de Borda, Joseph-Louis Lagrange, Pierre-Simon Laplace, Gaspard Monge and the Marquis 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 the longitude of Paris Observatory. Since this survey, the Panthéon became the central geodetic station in Paris.[4][1]

In 1791, Jean Baptiste Joseph Delambre and Pierre Méchain were commissioned to lead an expedition to accurately measure the distance between a belfry in Dunkerque and Montjuïc castle in Barcelona in order to calculate the length of the meridian arc through the centre of Paris Observatory.[4][1] The official length of the Mètre des Archives was based on these measurements, but the definitive length of the metre required a value for the non-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 the French Geodetic Mission to the Equator and a value of ⁠1/334⁠ 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 the Paris meridian arc between Dunkirk and Barcelona and the length of the metre was established, in relation to the Toise de l'Académie also called toise of Peru, which had been constructed in 1735 for the French 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, the Mètre 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]

Scientific revolution in France and beginning of Greenwich arc measurement

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The French 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 the Sun and organised important work in geodesy and cartography. In the 18th century, in addition to its significance for cartography, geodesy grew in importance as a means of empirically demonstrating Newton's law of universal gravitation, which Émilie du Châtelet promoted in France in combination with Leibniz's mathematical work and because the radius 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 an oblate spheroid through geodetic surveys in Ecuador and Lapland.[4][5]

Galileo had discovered gravitational 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 the pendulum 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 1645 Giovanni Battista Riccioli had been the first to determine the length of a "seconds pendulum" (a pendulum with a half-period of one second).[15][a] In 1656, Christiaan Huygens, inspired by Galileo,[13] invented the first pendulum clock which greatly improved the accuracy of time measurement required for astronomical observations.[16] In 1671, Jean Picard also measured the length of a seconds pendulum at Paris Observatory and proposed this unit of measurement to be called the astronomical radius (French: Rayon Astronomique).[17][18] He found the value of 36 pouces and 8 ⁠1/2⁠ lignes of the Toise of Châtelet, 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 the circle of latitude at the Equator.[19]

The first reasonably accurate distance to the Sun was determined in 1684 by Giovanni Domenico Cassini. Knowing that directly 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 used Kepler'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 since classical antiquity that the Earth was spherical, by the 17th century, evidence was accumulating that it was not a perfect sphere. In 1672, Jean Richer found the first evidence that gravity was not constant over the Earth (as it would be if the Earth were a sphere); he took a pendulum clock to Cayenne, French Guiana and found that it lost 2+1⁄2 minutes per day compared to its rate at Paris.[21][22] This indicated the acceleration 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 increasing latitude, gravitational acceleration being about 0.5% greater at the geographical poles than at the Equator.

In 1687, Isaac Newton had published in the Principia as a proof that the Earth was an oblate spheroid of flattening equal to ⁠1/230⁠.[23] This was disputed by some, but not all, French scientists. A meridian arc of Jean Picard was extended to a longer arc by Giovanni Domenico Cassini and his son Jacques 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 a prolate spheroid (with an equatorial radius less than the polar radius). To resolve the issue, the French Academy of Sciences (1735) undertook expeditions to Peru (Bouguer, Louis Godin, de La Condamine, Antonio de Ulloa, Jorge Juan) and to 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 Paris Mémoires, by Cassini de Thury, of a remeasurement by himself and Nicolas 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]

The triangulation mesh of the Anglo-French Survey (1784–1790).
Repeating circle devised by Jean-Charles de Borda and constructed by Étienne Lenoir

Geodetic surveys found practical applications in French cartography and in the Anglo-French Survey, which aimed to connect Paris and Greenwich Observatories and led to the Principal Triangulation of Great Britain.[25][26] The unit of length used by the French was the Toise de Paris, while the English one was the yard, which became the geodetic unit used in the British Empire.[27][28][29]

In 1783 the director of the Paris Observatory, César-François Cassini de Thury, addressed a memoir to the Royal Society in London, in which he expressed grave reservations about the latitude and longitude measurements undertaken at the Royal Greenwich Observatory. He suggested that the correct values might be found by combining the Paris Observatory figures with a precise trigonometric survey between the two observatories. This criticism was roundly rejected by Nevil 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 the triangulation of the Anglo-French Survey, César-François Cassini de Thury was assisted by Pierre Méchain. They used the repeating circle, an instrument for geodetic surveying, developed from the reflecting circle by Étienne Lenoir in 1784. He invented it while an assistant of Jean-Charles de Borda, who later improved the instrument. It was notable as being the equal of the great theodolite created by the renowned instrument maker, Jesse Ramsden. It would later be used to measure the meridian arc from Dunkirk to Barcelona by Jean Baptiste Delambre and Pierre 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 the French meridian arc.[30]

Invention and international adoption of the metre as scientific unit of length

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The free-standing belfry – the northerly end of meridianal survey of 1792–9

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 the metre.[31]: 52  The question of measurement reform was placed in the hands of the French Academy of Sciences, who appointed a commission chaired by Jean-Charles de Borda. Instead of the seconds pendulum method, the commission of the French Academy of Sciences – whose members included Borda, 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 at the longitude of Paris pantheon, which became the central geodetic station in Paris.[32][33] Jean Baptiste Joseph Delambre obtained the fundamental co-ordinates of the Panthéon by triangulating all the geodetic stations around Paris from the Panthéon's dome.[33][34]

Apart from the obvious consideration of safe access for French surveyors, the Paris meridian was also a sound choice for 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,[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.[35]

The expedition would take place after the Anglo-French Survey, thus the French meridian arc, which would extend northwards across the United Kingdom, would also extend southwards to Barcelona, later to Balearic Islands. Jean-Baptiste Biot and François 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 the Paris meridian as well as the account of the variation of the seconds pendulum's length along the same meridian between Shetland and the Balearc Islands.[36][37]

The task of surveying the meridian arc fell to Pierre Méchain and Jean-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 later François 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.[38]

The north and south sections of the meridinal survey met at Rodez Cathedral, seen here dominating the Rodez skyline at left.

The project was split into two parts – the northern section of 742.7 km from the belfry of the Church of Saint-Éloi, Dunkirk to Rodez Cathedral 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. Although Méchain's sector was half the length of Delambre, it included the Pyrenees and hitherto unsurveyed parts of Spain.[39]

Delambre measured a baseline of about 10 km (6,075.90 toises) in length along a straight road between Melun and Lieusaint. In an operation taking six weeks, the baseline was accurately measured using four platinum rods, each of length two toises (a toise being about 1.949 m).[39][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.[40][41] Borda's double-toise N°1, which had been compared to the Toise of Peru,[42] became the main reference for measuring all geodetic bases in France.[4] Intercomparisons of baseline measuring devices were essential for metrological traceability. Moreover, because of thermal expansion, geodesists tried to accurately assess temperature of standards in the field in order to avoid observational errors.[43] Thereafter he used, where possible, the triangulation points used by Nicolas Louis de Lacaille in his 1739-1740 arc measurement.[44][45] Méchain's baseline was of a similar length (6,006.25 toises), and also on a straight section of road between Vernet (in the Perpignan area) and Salces (now Salses-le-Chateau).[46]

A copy of the "provisional" metre located in the wall of a building, 15 rue de Vaugirard, Paris. These metres were provisional (French: provisoire) because the expedition and the calculations to determine the definitive length of metre were not completed until 1799.[47][48]

To put into practice the decision taken by the National Convention, on 1 August 1793, to disseminate the new units of the decimal metric system,[49] 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 from Dunkirk to Perpignan by Nicolas Louis de Lacaille and Cesar-François Cassini de Thury and published by the latter in 1744.[45] 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 of René-Antoine Ferchault de Réaumur in use at the time. This value was set by legislation on 7 April 1795.[49][6] It was therefore metal bars of 443.44 lignes that were distributed in France in 1795–1796.[38] This was the metre installed under the arcades of the rue de Vaugirard, almost opposite the entrance to the Senate.[44]

Montjuïc Castle in Barcelona, Spain – the southern end of the meridian arc

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 of Batavian Republic: Henricus Aeneae and Jean 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 by Talleyrand. The French commission comprised Jean-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 and Gaspar de Prony.[50][6][51]

In 1799, a commission including Johann 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 the triangulation 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 the Earth ellipsoid problem from the sole measurement of the arc from Dunkirk to Barcelona. However, when, about 1804, he would calculate it using the least squares method, this portion of the meridian arc led for the flattening to the value of ⁠1/150⁠ considered as unacceptable.[48][6][34] 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 the French Geodetic Mission to Lapland and would found a value close to ⁠1/300⁠ combining the results of Delambre and Méchain arc measurement with those of the Spanish-French Geodetic Mission taking in account a correction of the astronomic arc.[52][6][53]

Eventually, the distance from the North Pole to the Equator was extrapolated from the measurement of the Paris meridian arc between Dunkirk and Barcelona and was determined as 5130740 toises assuming an Earth flattening of ⁠1/334⁠. The Weights and Measures Commission adopted, in 1799, this value for the flattening based on an analysis by Pierre-Simon Laplace who combined the French Geodesic Mission to the Equator and the data of the arc measurement of Delambre and Méchain.[54] Combining these two data sets Laplace succeeded to estimate the flattening of the Earth ellipsoid and was happy to find that it also fitted well with his estimate ⁠⁠1/336⁠⁠ based on 15 pendulum measurements.[54][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 the French Geodesic Mission to Peru.[50][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.[44] Another platinum metre, calibrated against the Mètre des Archives, and twelve iron ones were made as secondary standards.[55] One of the iron metre standards was brought to the United States in 1805.[56] It became known as the Committee Meter in the United States and served as a standard of length in the United States Coast Survey until 1890.[57][56][28][58]

However, Louis Puissant declared in 1836 to the French Academy of Sciences that Jean 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.[59][60] This is why Antoine Yvon Villarceau verified the geodetic operations at eight points of the Paris meridian arc from 1861 to 1866. Some of the errors in the operations of Delambre and Méchain were then corrected.[61]

In his 2002 book The 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.[62] 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.[63] This 2 km error in the Earth quadrant appeared to Adrien-Marie Legendre when he compared 5130740 toises obtained for the length of the definitive metre with 5132430 toises deduced from the distance measured by Nicolas-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][62] He suspected a deviation of plumb-line due to gravity anomaly that geodesists now call vertical 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 as gravity anomalies had not yet been studied.[62] Indeed, the geoid is a ball wich 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.[34]

Nevertheless, in 1855, the Dufour map (French: Carte Dufour), the first topographic map of Switzerland for which the metre was adopted as the unit of length, won the gold medal at the Exposition Universelle.[64][65] On the sidelines of the Exposition Universelle (1855) and the second Congress of Statistics held in Paris, an association with a view to obtaining a uniform decimal system of measures, weights and currencies was created.[66] At the initiative of this association, a Committee for Weights and Measures and Monies (French: Comité des poids, mesures et monnaies) was created during the Exposition Universelle (1867) in Paris and called for the international adoption of the metric system.[67][66] In the United States, the Metric Act of 1866 allowed the use of the metre,[68] and in 1867 the General Conference of the European Arc Measurement (German: Europäische Gradmessung) proposed the establishment of the International Bureau of Weights and Measures.[69][70]

In 1875 a number of American, Asian, African and European states concluded the Metre Convention,[b] and the International Bureau of Weights and Measures (BIPM) was established at the Pavillon 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.[71]

The standards used by geodesists were compared with a known reference standard.[42] In order to maintain measurement traceability it was important to control the temperature during these intercomparisons in order to avoid systematic errors.[72] In 1886, Adolphe Hisch, secretary of the International Committee for Weights and Measures (CIPM) and of the International 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 new international metre so that the measurements made until then could be used to measure the Earth.[42] The result of these comparisons made it possible to reduce the arcs measured in Germany to the metre. The discordance of ⁠1/66 000⁠ which remained between the triangles common to the German and French networks could be reduced to ⁠1/600 000⁠ which was at the limit of accuracy of geodetic surveys at the time.[73] 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 by Jean-René Benoît at the BIPM. It was the consideration of the divergences between the different toises used by geodesists that led the European Arc Measurement (German: Europäische Gradmessung ) to consider, at the meeting of its Permanent Commission in Neuchâtel in 1866, the founding of a World Institute for the Comparison of Geodetic Standards, the first step towards the creation of the BIPM.[74][75] Careful comparisons with several standard toises showed that the international metre calibrated on the Mètre 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.

The Mètre des Archives and its copies such as the Committee Meter were replaced from 1889 by thirty platinum-iridium bars kept across the globe.[76] A better standardisation 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.[77] 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 to Charles Édouard Guillaume's discovery of invar, an alloy of nickel and iron with a coefficient of thermal expansion close to zero.[78][79]

In 1901, thanks to the work initiated in Switzerland by Émile Plantamour under the auspices of the International Geodetic Association,[80] Friedrich Robert Helmert would find, essentially through gravimetry, parameters of the Earth ellipsoid remarkably close to reality, namely a semi-major axis equal to 6 378 200 metres and a flattening of ⁠1/298.3⁠ . This last value would be set at ⁠1/298.25⁠ by the analysis of the first results from satellite measurements.[81] At the Exposition Universelle (1889), The Brunner frères company exhibited a reversible pendulum designed by Gilbert Étienne Defforges.[82] In 1892, he measured the value of gravitational acceleration at the BIPM.[83] In 1901, the third General Conference on Weights and Measures (CGPM) confirmed a value of 980.665 cm/s2 for the standard gravity.[84]

The BIPM, based in Sèvres, not far from Paris, was originally responsible, under the supervision of the CIPM, 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 of physical constants,[85] which are the basis of 2019 revision of the SI.

American cartography and the metre

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In 1834, Ferdinand Rudolph Hassler measured at Fire Island the first baseline of the Survey of the Coast.[86] 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 the Metric Act of 1866 allowing the use of the metre in the United States,[87] and preceded the choice of the metre as international scientific unit of length and the proposal by the 1867 General Conference of the European Arc Measurement (German: Europäische Gradmessung) to establish the International Bureau of Weights and Measures.[88]

Ferdinand Rudolph Hassler was a Swiss-American surveyor who is considered the forefather of both the National Oceanic and Atmospheric Administration (NOAA) and the National 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.[89][90] The foundation of the United States Coast and Geodetic Survey led to the actual definition of the metre, with Charles 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 the solar spectrum. Albert Abraham Michelson soon took up the idea and improved it.[91][92]

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 in krypton-86 allowed the standard to be universally available by measurement. In 1983 this was updated to a length defined in terms of the speed of light; this definition was reworded in 2019:[93]

The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299792458 when expressed in the unit m⋅s−1, where the second is defined in terms of the caesium frequency ΔνCs.

Where older traditional length measures are still used, they are now defined in terms of the metre – for example the yard has since 1959 officially been defined as exactly 0.9144 metre.[94]

Extension of Greenwich arc measurement through Spain

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In 1870, Carlos Ibáñez e Ibáñez de Ibero founded the Spanish National Geographic Institute which he then directed until 1889.[95][96] At the time it was the world's biggest geographic institute.[97] It encompassed geodesy, general topography, leveling, cartography, statistics and the general service of weights and measures.[97] Spain had adopted the metric system in 1849. The Government was urged by the Spanish Royal Academy of Sciences to approve the creation of a large-scale map of Spain in 1852.[98] In 1858, Spain's central geodetic base of triangulation was measured in Madridejos (Toledo) with exceptional precision for the time thanks to the Spanish Standard.[97] 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.[99][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.[100] 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.[97]

Ibáñez apparatus calibrated on the metric Spanish standard and used at Aarberg, in canton of Bern, Switzerland in 1880.[101]

In order to avoid the difficulty in exactly determining the temperature of a bar by the mercury thermometer, Friedrich Wilhelm Bessel, inspired by Jean-Charles de Borda, introduced in 1834 near Königsberg a compound bar which constituted a metallic thermometer. A zinc bar was laid on an iron 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 of least-squares.[71] Indeed, before invar's discovery, geodesists tried to assess temperature effect on standards in order to avoid observational errors.[43][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, that Borda or Bessel simply joined measuring the intervals by means of vernier calipers or glass wedges, would be replaced advantageously for accuracy by microscopic measurements, a system designed in Switzerland by Ferdinand Rudolph Hassler and Johann Georg Tralles,[102] and which Ibáñez ameliorated using a standard with lines marked on the bar.[97][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.[71]

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;[57] one is complicated, the other simplified. The first, an apparatus of Jean Brunner of Paris,[103] 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 to Southampton where Alexander Ross Clarke was making the necessary measurements to compare the geodetic standards of length used in the World.[28][29]

The West Europe-Africa Meridian-arc shown extending from the Shetland Islands at the top of the map, through Great Britain, France and Spain to El Aghuat in Algeria, whose parameters were calculated from surveys carried out in the mid to late 19th century. The Greenwich meridian is depicted rather than the Paris meridian.[104]

In 1865 the triangulation of Spain was connected with that of Portugal and France.[105][106] In 1866 at the conference of the Association of Geodesy in Neuchâtel, Ibáñez announced that Spain would collaborate in remeasuring and extending the French meridian arc.[97][107] From 1870 to 1894, François Perrier, then Jean-Antonin-Léon Bassot proceeded to a new survey.[61][108] In 1879 Ibáñez and François Perrier completed the junction between the geodetic networks of Spain and Algeria and thus completed the measurement of a meridian arc which extended from Shetland to the Sahara.[109] This connection was a remarkable enterprise where triangles with a maximum length of 270 km were observed from mountain stations (Mulhacén, Tetica, Filahoussen, M'Sabiha) over the Mediterranean Sea.[110][109][111][108]

This meridian arc was named West Europe-Africa Meridian-arc by Alexander Ross Clarke and Friedrich Robert Helmert. It yielded a value for the equatorial radius of the earth a = 6 377 935 metres, the ellipticity being assumed as ⁠1/299.15⁠ according to Bessel ellipsoid.[112][113] 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.[104] 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, the meridian of Greenwich is nearer the mean than that of Paris.[104]

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. The International 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.[114] 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.[115] 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 by Carlos 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.[115] 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.[116] 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 the Metre Convention.[117]

See also

[edit]

Notes

[edit]
  1. ^ At the time the second was defined as a fraction of the Earth's rotation time and determined by clocks whose precision was checked by astronomical observations. In 1936 French and German astronomers found that Earth rotation's speed is irregular. Since 1967 atomic clocks define the second. For further information see atomic time.
  2. ^ convention members were Argentina, Austria-Hungary, Belgium, Brazil, Denmark, France, German Empire, Italy, Peru, Portugal, Russia, Spain, Sweden and Norway, Switzerland, Ottoman Empire, United States and Venezuela.

References

[edit]
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Sources

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