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Central European Arc Measurement

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The Central European Arc Measurement (German: Mitteleuropäische Gradmessung) was established in Berlin in October 1864, after the creation of the Swiss Geodetic Commission in 1861 and following a preliminary consultation between representatives of Prussia, Austria, and Saxony in April 1862.[1][2] It became the European Arc Measurement (Europäische Gradmessung) in 1867 and the International Geodetic Association (German: Internationale Erdmessung) in 1886.[3][2] At the first General Assembly of the International Geodetic and Geophysical Union in Rome in 1922, it became the Geodesy Section, one of the five constituent parts of the International Union of Geodesy and Geophysics.[4] It officially adopted its current name, the International Association of Geodesy (IAG), in 1946.[2][5]

Implementation of new scientific methods

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Portrait of the mathematician and philosopher Carl Friedrich Gauss nicknamed the Prince of mathematicians.

The creation of the Central European Arc Measurement marked, following the examples of Friedrich Wilhelm Bessel and Friedrich Georg Wilhelm von Struve,[6] the systematic adoption of more rigorous scientific methods, including the application of the least squares method in geodesy.[7][8]

In 1809 Carl Friedrich Gauss published his method of calculating the orbits of celestial bodies. In that work he claimed to have been in possession of the method of least squares since 1795. This naturally led to a priority dispute with Adrien-Marie Legendre. However, to Gauss's credit, he went beyond Legendre and succeeded in connecting the method of least squares with the principles of probability and to the normal distribution. He had managed to complete Laplace's program of specifying a mathematical form of the probability density for the observations, depending on a finite number of unknown parameters, and define a method of estimation that minimises the error of estimation. Gauss showed that the arithmetic mean is indeed the best estimate of the location parameter by changing both the probability density and the method of estimation. He then turned the problem around by asking what form the density should have and what method of estimation should be used to get the arithmetic mean as estimate of the location parameter. In this attempt, he invented the normal distribution.[9]

Like numerous astronomers of his time Bessel dealt on the field of geodesy, too,[10] first theoretically, when he published a method for solving the main geodetic problem.[11] In 1830 he got the royal order for the survey of East Prussia with the purpose to connect the yet existing Prussian and Russian triangulation networks. This work was carried out in cooperation with Johann Jacob Baeyer, then major of the Prussian army; the final report was published in 1838.[12] He also obtained an estimate of increased accuracy for the Earth's ellipsoid, nowadays called the Bessel ellipsoid, based on several arc measurements.[13][14]

Struve Geodetic Arc.

The Scandinavian-Russian meridian arc or Struve Geodetic Arc, named after the German astronomer Friedrich Georg Wilhelm von Struve, was a degree measurement that consisted of a nearly 3000 km long network of geodetic survey points. The Struve Geodetic Arc was one of the most precise and largest projects of Earth measurement at that time. In 1860 Friedrich Georg Wilhelm Struve published his Arc du méridien de 25° 20′ entre le Danube et la Mer Glaciale mesuré depuis 1816 jusqu’en 1855. The flattening of the Earth was estimated at 1/294.26 and the Earth's equatorial radius was estimated at 6378360.7 metres.[15] Struve's arc measurement spanned a period of forty years and initiated an international scientific collaboration between the Russian Empire and the Swedish-Norwegian Union, involving prominent astronomers such as Friedrich Georg Wilhelm von Struve, Friedrich Wilhelm Bessel, Carl Friedrich Gauss and George Biddell Airy.[16]

Many measurements of degrees of longitudes along central parallels in Europe were projected and partly carried out as early as the first half of the 19th century; these, however, only became of importance after the introduction of the electrical telegraph, through which calculations of astronomical longitudes obtained a much higher degree of accuracy. Of the greatest moment is the measurement near the parallel of 52° lat., which extended from Valentia in Ireland to Orsk in the southern Ural mountains over 69 degrees of longitude. F. G. W. Struve, who is to be regarded as the father of the Russo-Scandinavian latitude-degree measurements, was the originator of this investigation. Having made the requisite arrangements with the governments in 1857, he transferred them to his son Otto, who, in 1860, secured the co-operation of England.[15]

After the Struve Geodetic Arc measurement, it was resolved in the 1860s to remeasure the arc of meridian from Dunkirk to Formentera and to extend it from Shetland to the Sahara.[17] Since the arc measurement of Delambre and Méchain, Friedrich Wilhelm Bessel using the method of least squares had calculated from several arc measurements a new value for the flattening of the Earth, which he determined as ⁠1/299.15⁠.[18][10][a] Seventeen years after Bessel calculated his ellipsoid of reference, some of the meridian arcs the German astronomer had used for his calculation had been enlarged. This was a very important circumstance because the influence of random errors due to vertical deflections was minimized in proportion to the length of the meridian arcs: the longer the meridian arcs, the more precise the image of the Earth ellipsoid would be.[18]

In 1859, Friedrich von Schubert demonstrated that several meridians had not the same length, confirming an hypothesis of Jean Le Rond d'Alembert. He also proposed an ellipsoid with three unequal axes.[25][26] In 1860, Elie Ritter, a mathematician from Geneva, using Schubert's data computed that the Earth ellipsoid could rather be a spheroid of revolution accordingly to Adrien-Marie Legendre's model.[27] However, the following year, resuming his calculation on the basis of all the data available at the time, Ritter came to the conclusion that the problem was only resolved in an approximate manner, the data appearing too scant, and for some affected by vertical deflections, in particular the latitude of Montjuïc in the French meridian arc which determination had also been affected in a lesser proportion by systematic errors of the repeating circle.[28][29][30][b]

Johann Jacob Baeyer (1794–1885)

As early as 1861, Johann Jacob Baeyer sent a memorandum to the King of Prussia recommending international collaboration in Central Europe with the aim of determining the shape and dimensions of the Earth. On July 7, 1861, the Prussian delegation in Bern submitted Baeyer's project to the Federal Council. The Federal Department of the Interior submitted it to Guillaume Henri Dufour, head of the Swiss Federal Office of Topography. At the 1861 session of the Swiss Society of Natural Sciences in Lausanne, the project discussed by the physics section of the Society was strongly supported by Élie Ritter and Adolphe Hirsch. On their proposal, the Society decided to give a favorable opinion on Switzerland's accession to the Central European Arc Measurement and to establish the Swiss Geodetic Commission. Its founding members were Rudolf Wolf, president (canton of Zurich), Guillaume Henri Dufour, honorary president and Élie Ritter, soon replaced by Émile Plantamour (canton of Geneva), Adolphe Hirsch (canton of Neuchâtel) and Hans Heinrich Denzler (canton of Bern).[1] A founding member of the International Committee of the Red Cross and forerunner of metrication in Switzerland,[37][38][c] Guillaume Henri Dufour contributed to the creation of the Central European Arc Measurement as a member of the Swiss Geodetic Commission from 1861.[43][d] Guillaume-Henri Dufour, cantonal engineer in Geneva since 1817 and commissioned by the Federal Diet to superintend land surveying of Switzerland,[46][47] founded in 1838 in Carouge (canton of Geneva) a topographic office (the future Federal Office of topography),[48] which published under his direction, from 1845 to 1864, the first official map of Switzerland, on the basis of new cantonal measurements.[49] 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.[50][51] However, the baselines for this map were measured in 1834 with three toises long measuring rods calibrated on a toise made in 1821 by Jean Nicolas Fortin for Friedrich Georg Wilhelm von Struve.[52][53]

Baeyer's goal was a new determination of anomalies in the shape of the Earth using precise triangulations, combined with gravity measurements. This involved determining the geoid by means of gravimetric and leveling measurements, in order to deduce the exact knowledge of the terrestrial spheroid while taking into account local variations. To resolve this problem, it was necessary to carefully study considerable areas of land in all directions. Baeyer developed a plan to coordinate geodetic surveys in the space between the parallels of Palermo and Christiana (Oslo) and the meridians of Bonn and Trunz (German name for Milejewo in Poland). This territory was covered by a triangle network and included more than thirty observatories or stations whose position was determined astronomically. Bayer proposed to remeasure ten arcs of meridians and a larger number of arcs of parallels, to compare the curvature of the meridian arcs on the two slopes of the Alps, in order to determine the influence of this mountain range on vertical deflection. Baeyer also planned to determine the curvature of the seas, the Mediterranean Sea and Adriatic Sea in the south, the North Sea and the Baltic Sea in the north. In his mind, the cooperation of all the States of Central Europe could open the field to scientific research of the highest interest, research that each State, taken in isolation, was not able to undertake.[54][55] Following a preliminary consultation between representatives of Prussia, Austria and Saxony in April 1862, in which August von Fligely, Karl Ludwig Littrow, Josef Philipp Herr, Julius Ludwig Weisbach, Christian August Nagel and Karl Christian Bruhns took part, the Central European Arc Measurement (German: Mitteleuropäische Gradmessung) was established in Berlin in October 1864.[56] At the time of its creation, the association had sixteen member countries: Austrian Empire, Kingdom of Belgium, Denmark, seven German states (Grand Duchy of Baden, Kingdom of Bavaria, Kingdom of Hanover, Mecklenburg, Kingdom of Prussia, Kingdom of Saxony, Saxe-Coburg and Gotha), Kingdom of Italy, Netherlands, Russian Empire (for Poland), United Kingdoms of Sweden and Norway, as well as Switzerland.[e] The Central European Arc Measurement created a Central Office, located at the Prussian Geodetic Institute, whose management was entrusted to Johann Jacob Baeyer.[60][56] As early as 1864, the Association appointed a Permanent Commission with administrative powers which supervised the Central Bureau and became the supreme scientific body of the geodetic association.[8][60] This Commission was chaired by Peter Andreas Hansen from 1864 to 1868, by the Austro-Hungarian general August von Fligely from 1869 to 1874 and by the Spanish general Carlos Ibáñez e Ibáñez de Ibero from 1874 to 1886.[56][2]

Carlos Ibáñez e Ibáñez de Ibero (1825-1891).

In 1866, in Neuchâtel, Carlos Ibáñez e Ibáñez de Ibero proposed the membership of Spain in the geodetic association.[61][f] In 1867, at its second general conference in Berlin and after the admission of Spain and Portugal, the geodetic association became the Europäische Gradmessung (European Arc Measurement).[2][67] France, the initiator of arc measurement efforts, remained largely stagnant while other nations covered their land with triangulations, employing superior instruments and methods of observation and calculation. It even hesitated for a long time before yielding to the European Arc Measurement's requests to participate in its work. It was only in 1871 that France began to join, appointing Charles-Eugène Delaunay to represent it at the Congress in Vienna. In 1874, Hervé Faye was appointed a member of the Permanent Commission. He would succed Carlos Ibáñez e Ibáñez de Ibero as president of the International Geodetic Association after the latter's death in 1891.[8][2]

To encompass all measurements made outside Europe, the European Arc Measurement was reorganized after the death of its founder, Baeyer. The Prussian government initiated the reform. At a conference held in Berlin in October 1886, delegates from the major European countries (excluding England) and from several other parts of the world decided that the International Geodetic Association would aim arc measurements across the entire Earth; that it would have a central Bureau of Calculations in Berlin; that a Permanent Commission of 11 members would meet annually in a city of the associated states; and that the Association would hold a plenary meeting every three years at which half of the Permanent Commission would be renewed. Carlos Ibáñez e Ibáñez de Ibero was then appointed president of this Commission, and Friedrich Robert Helmert director of the Central Bureau of Calculations. A new international convention was ratified by 20 European states, which conferred intergovernmental status upon the Association.The 1886 Convention entrusted the execution of the decisions of the General Conference and the management of administrative affairs to the Bureau of the association, composed of the president and vice-president of the association, the permanent secretary, and the director of the Central Bureau.[8][60] Adolphe Hirsch, one of the two secretaries of the Central European Arc Measurement since its creation, became its first permanent secretary until 1900.[68][69]

In Rome, in 1887, the International Geodetic Association and the International Committee for Weights and Measures were represented at the first session of the International Statistical Institute (ISI) by their president, Carlos Ibáñez de Ibero,[70] first director of the Geographic and Statistical Institute, member of the Royal Academy of Exact, Physical and Natural Sciences, honorary member of the National Academy of Sciences of Córdoba, correspondent of the French Academy of Sciences, associate of the Royal Academy of Belgium and honorary member of the Prussian Academy of Sciences.[71][72][g] In the second half of the 19th century, this scientific undertaking, whose objective was precise mapping, took on a global dimension. It accompanied German unification and the return of democracy in France, marked the beginning of the Second Industrial Revolution, and led to the Metre Convention,[h] the adoption of Greenwich meridian as Prime meridian and a new definition of the metre.[i][j] In 1858, an Egyptian Technical Commission had been set up to continue, by adopting the procedures instituted in Europe, the cadastre work, inaugurated by means of the cassaba (Qaṣbah قصبة an ancient Arabic unit of measurement),[87] under Muhammad Ali. This Commission suggested to Viceroy Mohammed Sa'id Pasha the idea of building geodetic devices which were ordered in France. The Khedive entrusted to Ismail Mustafa al-Falaki the study, in Europe, of the precision apparatus calibrated against the metre intended to measure the geodetic baselines and already built by Jean Brunner in Paris. Ismail Mustafa had the task to carry out the experiments necessary for determining the expansion coefficients of the two platinum and brass rulers, and to compare Egyptian standard with a known standard. The Spanish standard designed by Carlos Ibáñez e Ibáñez de Ibero and Frutos Saavedra Meneses was chosen for this purpose, as it had served as a model for the construction of the Egyptian standard. In addition, the Spanish standard had been compared with Borda's double-toise N° 1, which served as a comparison module for the measurement of all geodetic baselines in France.[88][89][k] The Struve Geodetic Arc would become part of the longest meridian arc of the Old World. In 1954, the connection of the southerly extension of the Struve Arc with an arc running north from South Africa through Egypt would bring the course of a major meridian arc back to land where Eratosthenes had founded geodesy.[16]

In 1891, at the meeting of the Permanent Commission of the International Geodetic Association in Florence, Wilhelm Foerster referred to the discovery by Seth Carlo Chandler of the polar motion predicted by Leonhard Euler in 1765 and his impact on the determination latitudes.[96] He proposed that the International Geodetic Association implement a systematic study of this important phenomenon.[97] In 1895, the creation of the International Latitude Service was decided by the International Geodesic Association. Its central office was based in Potsdam and headed by Friedrich Robert Helmert. Regular observations began in 1899.[98][99] The distinction between systematic and random errors is far from being as sharp as one might think at first glance. In reality, there are no or very few random errors. As science progresses, the causes of certain errors are sought out, studied, their laws discovered. These errors pass from the class of random errors into that of systematic errors. The ability of the observer consists in discovering the greatest possible number of systematic errors to be able, once he has become acquainted with their laws, to free his results from them using a method or appropriate corrections. It was the experimental study of causes of errors that has led to most of the great astronomical discoveries (precession, nutation, aberration).[100]

The International Geodetic Association gained global importance with the accession of Chile, Mexico and Japan in 1888; Argentina and United-States in 1889; and British Empire in 1898. From 1903 to 1917, Jean-Antonin-Léon Bassot succeded Hervé Faye as president of the International Geodetic Association.[2] The convention of the International Geodetic Association expired at the end of 1916. It was not renewed due to the First World War. However, the activities of the International Latitude Service were continued through an Association Géodesique réduite entre États neutres thanks to the efforts of H.G. van de Sande Bakhuyzen and Raoul Gautier, respectively directors of Leiden Observatory and Geneva Observatory.[2][56] During the war, many scientists were concerned with the means to be considered for resuming, at the end of hostilities, international scientific work. An essentially American and British idea was to group together the scientific unions relating to various disciplines under the authority of a Supreme Council. An international conference, which brought together in Brussels in July 1919 the scientists of the countries allied or associated in the fight against Germany and of a certain number of neutral states, created an International Science Council and various unions dependent on this Council; but, Geodesy, instead of being free and independent as before, was associated with the Geophysical Sciences in the International Union of Geodesy and Geophysics which first president was Charles Jean-Pierre Lallemand.[101]

The mètre and dynamic geodesy

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From geodesists point of view, the Mètre des Archives was a secondary standard deduced from the Toise of Peru.[102] When, in 1799, the results necessary for the practical and definitive realization of the metre were available, the commission in charge of the matter decided to fully utilize the precision of the comparator developed by the engineer Étienne Lenoir. It fixed the length of the definitive metre at 3 feet 11.296 lines (or 443.296 lines). The law of 18 Germinal, Year III (April 7, 1795) stipulated that the metre should be drawn on a platinum ruler. Lenoir therefore constructed the prototype of the standard metre according to these criteria. Another platinum standard, as well as twelve other iron standards, were also produced in 1799.[103]

Bessel's apparatus at the Museum of Instruments of the Military Geographic Institute of Florence.

At the first general meeting of the Central European Arc Measurement held in Berlin in 1864, it was decided to adopt the Bessel Toise, a copy of the Toise of Peru made in 1923 by Jean-Nicolas Fortin in Paris,[52] as the international standard.[104] 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.[105]These comparisons were essential. Indeed, thermal expansion, which corresponds to the increase in volume of a body caused by heating, was already well known at the time. Pierre Bouguer had demonstrated it to a large audience at the Hôtel des Invalides. This problem has consistently dominated all thinking regarding the measurement of geodetic standards. Geodesists were preoccupied with the constant concern of accurately determining the temperature of the length standards used in the field. Determining this variable, on which the length of measuring instruments depends, has always been considered so complex and so important that one could almost say that the history of geodetic standards corresponds to the history of the precautions taken to avoid temperature errors.[106][107]

In the 19th century, statisticians knew that scientific observations were subject to two types of error: constant errors and random errors. The effects of the latter could be corrected using the least squares method. Constant errors, on the other hand, had to be carefully avoided, as they were caused by various factors that consistently altered the results of observations in the same direction. These errors thus tended to render the results they affected worthless. Consider, for example, measuring a straight line to determine its length in metres. If a metal ruler is used for this measurement, and an error is made in determining the temperature at which its length corresponds to that of a metre, all observations will be affected by a consistent error stemming from this error, and no matter how many times the operation is repeated, it will be impossible to obtain an accurate result. If, on the contrary, we know exactly the temperature at which the ruler is equivalent to the metre and if the error affects the actual temperature of the ruler in the different observations, each observation will be affected by a random error, but these errors will occur sometimes in one direction and sometimes in the other, and by repeating the operation a large number of times we can hope to eliminate their effect by compensating for them.[108]

In the absence of a standard temperature scale, inconsistencies arose when attempting to link geodetic surveys from different countries to create a European geodetic network.[52] It was thus crucial to compare at controlled temperatures with great precision and to the same unit all the standards for measuring geodetic baselines.[109] 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.[52] 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.[110] 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.[111][97] 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.[112]

Closeup of National Prototype Metre Bar No. 27, made in 1889 by the International Bureau of Weights and Measures (BIPM) in collaboration with Johnson Mattey and given to the United States,[102] which served as the standard for American cartography from 1890 replacing the Committee Meter, an authentic copy of the Mètre des Archives produced in 1799 in Paris, which Ferdinand Rudolph Hassler had brought to the United States in 1805.[113]

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,[114] or approximately 0.013 millimetres. By contrast, in 2007, a comparison of the American Committee meter and its Swiss counterpart was carried out at NIST and METAS. The two metre standards can be considered perfectly equivalent, with a difference of only (0.96 ±3.0) micrometres. The poor quality of the measuring surfaces explained the significant uncertainty in the measurements compared to today's standards. Assuming a linear thermal expansion coefficient of 11.6·10−6 °C-1 for steel,[115] the difference between the legal metre (defined as 443.296 lines of the Toise of Peru) and the international metre (defined as the length of the Mètre des Archives) must be related to a temperature error of approximately 1.3 °C during the manufacturing of Borda apparatus, which was used for baseline measurements of the Arc measurement of Delambre and Méchain.[103] 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. However, the error in measuring the length of Paris meridian represented less than 2% of the total error, and the error due to a flawed assumption about the shape of the Earth contributed to approximately 3% of the total error. If the meticulous work of Pierre Méchain and Jean Baptiste Delambre were the only source of error, the current metre would be too long by less than 4 μm instead of being too short by 197 μm. The 95% of the missing length of the legal metre is due to the failure to account for vertical deflections; this was beyond the scope of Delambre and Méchain because the Earth's gravitational field had not yet been studied.[116][30]

Gravimeter with variant of Repsold-Bessel pendulum.

Significant improvements in gravity measuring instruments must be attributed to Friedrich Wilhelm Bessel. He devised a gravimeter constructed by Adolf Repsold which was first used in Switzerland by Emile Plantamour, Charles Sanders Peirce and Isaac-Charles Élisée Cellérier (1818–1889), a Genevan mathematician soon independently discovered a mathematical formula to correct systematic errors of this device which had been noticed by Plantamour and Adolphe Hirsch.[109][117] As the figure of the Earth could be inferred from variations of gravitational field, the United States Coast Survey's direction instructed Charles Sanders Peirce in the spring of 1875 to proceed to Europe for the purpose of making pendulum experiments to chief initial stations for operations of this sort, to bring the determinations of gravitational acceleration in America into communication with those of other parts of the world; and also for the purpose of making a careful study of the methods of pursuing these researches in the different countries of Europe.[118]

The progresses of metrology combined with those of gravimetry through gravimeters with variant of Repsold-Bessel pendulum led to a new era of geodesy. If precision metrology had needed the help of geodesy, it could not continue to prosper without the help of metrology. It was then necessary to define a single unit to express all the measurements of terrestrial arcs, and all determinations of the gravitational acceleration by the means of pendulum. Metrology had to create a common unit.[109] The 1875 Conference of the International Association of Geodesy also dealt with the best instrument to be used for the determination of gravitational acceleration. After an in-depth discussion in which Charles Sanders Peirce took part, the association decided in favor of the reversion pendulum, which was used in Switzerland, and it was resolved to redo in Berlin, in the station where Friedrich Wilhelm Bessel made his famous measurements, the determination of gravity by means of devices of various kinds employed in different countries, to compare them and thus to have the equation of their scales.[119] In 1901, Friedrich Robert Helmert found, mainly by gravimetry, parameters of the ellipsoid remarkably close to reality. Although marked by the concern to correct vertical deflections, taking into account the contributions of gravimetry, research between 1910 and 1950 remained practically limited to large continental triangulations. The most significant work would be that by John Fillmore Hayford, which relied mainly on the North American national network. His ellipsoid was adopted in 1924 by the International Union of Geodesy and Geophysics.[120]

Notes

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  1. ↑ Errors in the method of calculating the length of the arc measurement of Delambre and Méchain were taken into account by Bessel when he proposed his reference ellipsoid in 1841.[10] The definitive length of the Mètre des Archives had required a value for the non-spherical shape of the Earth, known as the flattening of the Earth. The Weights and Measures Commission adopted, in 1799, a flattening of ⁠1/334⁠ based on analysis by Pierre-Simon Laplace who combined the arc of Peru and the data of the meridian arc of Delambre and Méchain.[19] Combining these two data sets Laplace succeeded to estimate the flattening anew and was happy to find the suitable value ⁠1/334⁠. It also fitted well with his estimate ⁠1/336⁠ based on 15 pendulum measurements[20] Bessel's reference ellipsoid would long be used by geodesists. An even more accurate value was proposed in 1901 by Friedrich Robert Helmert according to gravity measurements performed under the auspices of the International Geodetic Association.[21][22][23][18][24]
  2. ↑ It was well known that by measuring the latitude of two stations in Barcelona, Méchain had found that the difference between these latitudes was greater than predicted by direct measurement of distance by triangulation and that he did not dare to admit this inaccuracy.[31][32][33] This was later explained by clearance in the central axis of the repeating circle causing wear and consequently the zenith measurements contained significant systematic errors.[29] Polar motion predicted by Leonhard Euler and later discovered by Seth Carlo Chandler also had an impact on accuracy of latitudes' determinations.[34][21][35][20] Among all these sources of error, it was mainly an unfavourable vertical deflection that gave an inaccurate determination of Barcelona's latitude and a metre "too short" compared to a more general definition taken from the average of a large number of arcs.[36]
  3. ↑ 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.[39][40] 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 in 1855.[41] 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.[42][41]
  4. ↑ Following the Act of Mediation of 1803, Swiss cartography was entrusted to French geographical engineers. Geneva, which was part of France, was not affected by this issue. However, Ferdinand Rudolph Hassler, a former magistrate from Aargau in the Helvetic Republic, saw his prospects of creating a map of Switzerland dashed. He therefore emigrated to the United States of America where Albert Gallatin, then Secretary of the Treasury, was lauching a call for tenders for heading the geodetic survey of East Coast of the United States. Hassler was appointed, with the endorsement of the American Philosophical Society, Superintendent of the United States Survey of the Coast, which would become the first civilian scientific agency of the federal government. At the time, geodesists incorporated reference points into a network of triangles. The relative positions of these points were determined by the angles of the triangles formed by the triangulation stations, and also by astronomical observations. Finally, the dimensions of the network of triangles were determined by measuring the length of one side of some of the triangles in the field using metal rulers. For measuring the baselines of the map survey of the American coast, Hassler designed a ruler equipped with microscopes, which he calibrated to the Committee Meter.[44][45]
  5. ↑ Spain and Portugal joined the European Arc Measurement in 1866. French Empire hesitated for a long time before giving in to the demands of the Association, which asked the French geodesists to take part in its work. It was only after the Franco-Prussian War, that Charles-Eugène Delaunay represented France at the Congress of Vienna in 1871. In 1874, Hervé Faye was appointed member of the Permanent Commission which was presided by Carlos Ibáñez e Ibáñez de Ibero.[57][58][59]
  6. ↑ 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.[62] When Carlos Ibáñez e Ibáñez de Ibero took part to the extension of the arc measurement of Delambre and Méchain, mathematicians like Legendre and Gauss had developed new methods for processing data, including the least squares method which allowed to compare experimental data tainted with observational errors to a mathematical model.[63] Until the Hayford ellipsoid would be introduced in 1910, vertical deflections would be considered as random errors.[64] The Earth measurements thus underscored the importance of the scientific method at a time when statistics were implemented in geodesy. As a leading scientist of his time, Ibáñez was one of the 81 initial members of the International Statistical Institute (ISI) and delegate of Spain to the first ISI session (now called World Statistic Congress) in Rome in 1887.[65][66]
  7. ↑ The International Statistical Institute (ISI) was founded in 1885 during the jubilee of the Royal Statistical Society, and coinciding with the 25th anniversary of the Société statistique de Paris.[73] Its origins can be traced back to a series of International Statistical Congresses, the first of which was chaired by Adolphe Quetelet and held in Brussels in 1853 after the Great Exhibition held in London at the initiative of Prince Albert of Saxe-Coburg and Gotha.[74][75] The 81 founding members of the ISI constituted the elite of statisticians of this era within government administrations and scientific academies.[74]
  8. ↑ In 1834, Ferdinand Rudolph Hassler measured at Fire Island the first baseline of the Survey of the Coast.[76] 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,[77] 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.[78]
  9. ↑ In 1875 a number of American, Asian, African and European states concluded the Metre Convention, and in 1877 an international weights-and-measures bureau was established at 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 H, were constructed, having engraved lines at both ends of the bridge, which determine the distance of a metre. As bar lengths vary with temperature, precise measurements required known and stable temperatures and could even be affected by a scientist's body heat,[79] so standard metres were provided with precise thermometers.[80] The thermometers required for this purpose must be very carefully studied, and their errors of division and index error determined.[81] 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. Careful comparisons with several standard toises showed that the Mètre des Archives was not exactly equal to the legal metre or 443.296 lines of the toise of Peru, but, in round numbers, ⁠⁠1/75 000⁠⁠ of the length smaller, or approximately 0.013 millimetres. The metre according to the older relation is called the “legal metre,” according to the new relation the “international metre.”[82]
  10. ↑ The creation 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.[83][84] 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:[85]
    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.[86]
  11. ↑ Egypt was, after the United States of America and Spain in Europe, the first country in Africa to use a geodetic standard calibrated against the metre. The history of the metre reveals that it was then chosen as an international scientific unit of length by the European Arc Measurement which would later become the International Association of Geodesy. The inspiration for the creation of this association came to Johann Jacob Baeyer following the measurement of the geodetic arc of Struve. In 1867 at the second General Conference of the International Association of Geodesy held in Berlin, the question of an international standard unit of length was discussed in order to combine the measurements made in different countries to determine the size and shape of the Earth. According to a preliminary proposal made in Neuchâtel the precedent year,[90] the General Conference of the European Arc Measurement recommended the adoption of the metre in replacement of the toise of Bessel.[91][92] In 1869, the Saint Petersburg Academy of Sciences sent to the French Academy of Sciences a report drafted by Otto Wilhelm von Struve, Heinrich von Wild, and Moritz von Jacobi inviting his French counterpart to undertake joint action to ensure the universal use of the metric system in all scientific work.[93] In 1954, the connection of the southerly extension of the Struve Geodetic Arc with an arc running north from South Africa through Egypt brought the course of a major meridian arc back to land where Eratosthenes had founded geodesy.[94][95]

References

edit
  1. 1 2 Gautier, Raoul (1892–1893). "Exposé historique des travaux de la commission géodésique suisse de 1862 à 1892". Bulletin de la Société des Sciences Naturelles de Neuchâtel. 21: 33. doi:10.5169/seals-88335. ISSN 0366-3469.
  2. 1 2 3 4 5 6 7 8 Drewes, Hermann; Kuglitsch, Franz; Adám, József; Rózsa, Szabolcs (2016-10-01). "The Geodesist's Handbook 2016". Journal of Geodesy. 90 (10): 907–1205. doi:10.1007/s00190-016-0948-z. ISSN 1432-1394.
  3. ↑ Soler, T. (1997-02-01). "A profile of General Carlos Ibáñez e Ibáñez de Ibero: first president of the International Geodetic Association". Journal of Geodesy. 71 (3): 176–188. doi:10.1007/s001900050086. ISSN 1432-1394.
  4. ↑ IUGG Yearbook 2023, International Union of Geodesy and Geophysics, p. 26, Potsdam, 2023. Available at: https://iugg.org/wp-content/uploads/2022/12/yearbook2023.pdf
  5. ↑ Letroye, Armand (1963). "Centenaire de l'Association Internationale de Géodésie, à Munich. Rapport". Bulletins de l'Académie Royale de Belgique. 49 (1): 71–74.
  6. ↑ "Geodesy" . Encyclopædia Britannica. Vol. 11 (11th ed.). 1911. pp. 607–615.
  7. ↑ "Mesure du 1er mètre : une erreur qui changea le monde". Techniques de l'Ingénieur (in French). Retrieved 2026-05-06.
  8. 1 2 3 4 Lebon, Ernest (1899). Histoire abrégée de l'astronomie [A Short History of Astronomy] (in French). Paris: Gauthier-Villars. pp. 168–173.
  9. ↑ Plackett, R.L. (1972). "The discovery of the method of least squares" (PDF). Biometrika. 59 (2): 239–251. doi:10.2307/2334569. JSTOR 2334569.
  10. 1 2 3 Viik, T. (2006). F.W. Bessel and Geodesy (PDF). Struve Geodetic Arc 2006 International Conference: The Struve Arc and Extensions in Space and Time. 13–15 August 2006. Haparanda and Pajala, Sweden: Lantmäteriet, Gävle, Sweden, 2006. pp. 53–63. Archived from the original (PDF) on 9 November 2013. Retrieved 9 November 2013.
  11. ↑ Bessel, F. W. (1825). "Ueber die Berechnungen der geographischen Länge und Breite aus geodätischen Vermessungen". Astronomische Nachrichten (in German). 4 (16): 241–254. arXiv:0908.1823. doi:10.1002/asna.18260041601. S2CID 118630614.
  12. ↑ Bessel, F. W.; Baeyer, J. J. (1838). Gradmessung in Ostpreussen und ihre Verbindung mit Preussischen und Russischen Dreiecksketten [The East Prussian Survey and its connection with the Prussian and Russian networks] (in German). Berlin: Dümmler.
  13. ↑ Bessel, F. W. (1837). "Bestimmung der Axen des elliptischen Rotationssphäroids, welches den vorhandenen Messungen von Meridianbögen der Erde am meisten entspricht" [Determination of the axes of ellipsoid that fits best to the existing measurements of meridian arcs]. Astronomische Nachrichten (in German). 14 (333): 333–346. Bibcode:1837AN.....14..333B. doi:10.1002/asna.18370142301.
  14. ↑ Bessel, F. W. (1841). "Ueber einen Fehler in der Berechnung der französischen Gradmessung und seinen Einfluß auf die Bestimmung der Figur der Erde" [Concerning an error in the calculation of the French survey and its influence on the determination of the figure of the Earth]. Astronomische Nachrichten (in German). 19 (438): 97–116. Bibcode:1841AN.....19...97B. doi:10.1002/asna.18420190702.
  15. 1 2 "Earth, Figure of the" . Encyclopædia Britannica. Vol. 8 (11th ed.). 1911. pp. 801–813.
  16. 1 2 "Nomination of the STRUVE GEODETIC ARC for inscription on the WORLD HERITAGE LIST" (PDF). whc.unesco.org. pp. 38, 122, 143–144.
  17. ↑ J. M. López de Azcona, "Ibáñez e Ibáñez de Ibero, Carlos", Dictionary of Scientific Biography, vol. VII, 1–2, Scribner's, New York, 1981.
  18. 1 2 3 von Struve, Friedrich Georg Wilhelm (July 1857). "Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels". Gallica (in French). p. 509. Retrieved 2021-08-30.
  19. ↑ Nyblom, Jukka (2023-04-25). "How did the meter acquire its definitive length?". GEM - International Journal on Geomathematics. 14 (1): 10. doi:10.1007/s13137-023-00218-9. ISSN 1869-2680.
  20. 1 2 Torge, Wolfgang (2016). Rizos, Chris; Willis, Pascal (eds.). "From a Regional Project to an International Organization: The "Baeyer-Helmert-Era" of the International Association of Geodesy 1862–1916". IAG 150 Years. International Association of Geodesy Symposia. 143. Cham: Springer International Publishing: 3–18. doi:10.1007/1345_2015_42. ISBN 978-3-319-30895-1.
  21. 1 2 Perrier, Général (1935). "Historique Sommaire De La Geodesie". Thalès. 2: 117–129, p. 128. ISSN 0398-7817. JSTOR 43861533.
  22. ↑ Delambre, Jean-Baptiste; Méchain, Pierre (1806–1810). Base du système métrique décimal, ou Mesure de l'arc du méridien compris entre les parallèles de Dunkerque et Barcelone. T. 1 /, exécutée en 1792 et années suivantes, par MM. Méchain et Delambre, rédigée par M. Delambre,... p. 10.
  23. ↑ Chisholm, Hugh, ed. (1911). "Earth, Figure of the" . Encyclopædia Britannica. Vol. 08 (11th ed.). Cambridge University Press. pp. 801–813.
  24. ↑ Rath, Geheimen; Ritter (January 1842). "Ueber einen Fehler in der Berechnung der französischen Gradmessung und seinen Einfluss auf die Bestimmung der Figur der Erde". Astronomische Nachrichten. 19 (7–8): 97–116. doi:10.1002/asna.18420190702. ISSN 0004-6337.
  25. ↑ Historische Commission bei der königl. Akademie der Wissenschaften (1908), "Schubert, Theodor von", Allgemeine Deutsche Biographie, Bd. 54, Allgemeine Deutsche Biographie (1. ed.), München/Leipzig: Duncker & Humblot, p. 231, retrieved 2023-10-01
  26. ↑ D'Alembert, Jean Le Rond. "Figure de la Terre, in Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, par une Société de Gens de lettres". artflsrv04.uchicago.edu. Retrieved 2023-10-01.
  27. ↑ Société de physique et d'histoire naturelle de Genève.; Genève, Société de physique et d'histoire naturelle de (1859). Memoires de la Société de physique et d'histoire naturelle de Genève. Vol. 15. Geneve: Georg [etc.] pp. 441–444, 484–485.
  28. ↑ Société de physique et d'histoire naturelle de Genève.; Genève, Société de physique et d'histoire naturelle de (1861). Memoires de la Société de physique et d'histoire naturelle de Genève. Vol. 16. Geneve: Georg [etc.] pp. 165–196.
  29. 1 2 Martina Schiavon. La geodesia y la investigación científica en la Francia del siglo XIX : la medida del arco de meridiano franco-argelino (1870–1895). Revista Colombiana de Sociología, 2004, Estudios sociales de la ciencia y la tecnologia, 23, pp. 11–30.
  30. 1 2 Levallois, J.J. (1991). "La méridienne de Dunkerque à Barcelone et la déterminiation du mètre (1792-1799)". Vermessung, Photogrammetrie, Kulturtechnik: VPK = Mensuration, photogrammétrie, génie rural. 89 (7): 375. doi:10.5169/seals-234595. ISSN 0252-9424.
  31. ↑ "c à Paris; vitesse de la lumière ..." expositions.obspm.fr. Retrieved 2021-10-12.
  32. ↑ Jouffroy, Achille de (1852–1853). Dictionnaire des inventions et découvertes anciennes et modernes, dans les sciences, les arts et l'industrie.... 2. H–Z / recueillis et mis en ordre par M. le marquis de Jouffroy; publié par l'abbé Migne,... p. 419.
  33. ↑ Comité Interational des Poids et Mesures. Procès-Verbaux des Séances. Deuxième Série. Tome II. Session de 1903. Paris: Gauthier-Villars. pp. 5–7.
  34. ↑ Yokoyama, Koichi; Manabe, Seiji; Sakai, Satoshi (2000). "History of the International Polar Motion Service/International Latitude Service". International Astronomical Union Colloquium. 178: 147–162. doi:10.1017/S0252921100061285. ISSN 0252-9211.
  35. ↑ "Polar motion | Earth's axis, wobble, precession | Britannica". www.britannica.com. Retrieved 2023-08-27.
  36. ↑ "La méridienne de Dunkerque à Barcelone et la déterminiation du mètre (1972–1799)". Vermessung, Photogrammetrie, Kulturtechnik (in French). 89 (7): 377–378. 1991. doi:10.5169/seals-234595.
  37. ↑ "Journal de Genève - 22.03.1854 - Page 1". www.letempsarchives.ch. Retrieved 2026-02-28.
  38. ↑ "Journal de Genève - 14.02.1852 - Page 4". www.letempsarchives.ch. Retrieved 2026-02-28.
  39. ↑ Abplanalp, Andrej (2019-07-14). "Henri Dufour et la carte de la Suisse". Musée national - Blog sur l'histoire suisse (in German). Archived from the original on 25 December 2024. Retrieved 2025-01-25.
  40. ↑ Dufour, G.-H. (1861). "Notice sur la carte de la Suisse dressée par l'État Major Fédéral". Le Globe. Revue genevoise de géographie. 2 (1): 5–22. doi:10.3406/globe.1861.7582.
  41. 1 2 Quinn, T. J. (2012). From artefacts to atoms: the BIPM and the search for ultimate measurement standards. Oxford: Oxford University Press. pp. 12–14, 8–12, 49–72, 106–108, 144–147. ISBN 978-0-19-990991-9. OCLC 861693071.
  42. ↑ "History – The BIPM 150". Retrieved 2025-01-24.
  43. ↑ Gautier, Raoul (October 1893). "Exposé historique des travaux de la commission géodésique suisse de 1862 à 1892". Bulletin de la Société des Sciences Naturelles de Neuchâtel. 21: 33. doi:10.5169/seals-88335. ISSN 0366-3469.
  44. ↑ "Un Suisse cartographe aux USA". Tribune de Genève (in French). 2022-12-13. Retrieved 2026-03-20.
  45. ↑ "Ce qu'il faut savoir de Gallatin". Tribune de Genève (in French). 2022-12-03. Retrieved 2026-03-21.
  46. ↑ "Dufour, Guillaume Henri". hls-dhs-dss.ch (in French). Retrieved 2025-08-02.
  47. ↑ Chisholm, Hugh, ed. (1911). "Dufour, Wilhelm Heinrich" . Encyclopædia Britannica (11th ed.). Cambridge University Press.
  48. ↑ "Le Bureau topographique fédéral créé par Dufour était logé à Carouge, mais certaines sources indiquent que c'était plutôt à la Porte Neuve, qu'en est-il ? | Ville de Genève - Site officiel". www.geneve.ch (in French). Retrieved 2025-07-29.
  49. ↑ "Carte Dufour 1845-1865". Genève à la carte (in French). 12 March 2014. Retrieved 30 July 2025.
  50. ↑ Abplanalp, Andrej (14 July 2019). "Henri Dufour et la carte de la Suisse". Musée national - Blog sur l'histoire suisse (in German). Archived from the original on 25 December 2024. Retrieved 25 January 2025.
  51. ↑ Dufour, G.-H. (1861). "Notice sur la carte de la Suisse dressée par l'État Major Fédéral". Le Globe. Revue genevoise de géographie. 2 (1): 5–22. doi:10.3406/globe.1861.7582.
  52. 1 2 3 4 Seligmann, A. E. M. (1923). "La Toise de Belgique". Ciel et Terre, Bulletin of the Société Belge d'Astronomie. 39: 25. Bibcode:1923C&T....39...25S.
  53. ↑ Clarke, Alexander Ross; James, Henry (January 1997). "X. Abstract of the results of the comparisons of the standards of length of England, France, Belgium, Prussia, Russia, India, Australia, made at the ordnance Survey Office, Southampton". Philosophical Transactions of the Royal Society of London. 157 (157): 161–180. doi:10.1098/rstl.1867.0010.
  54. ↑ Zuerich, ETH-Bibliothek (1892). "Exposé historique des travaux de la commission géodésique suisse de 1862 à 1892". Bulletin de la Société des Sciences Naturelles de Neuchâtel (in French). 21: 33. doi:10.5169/seals-88335.
  55. ↑ Quinn, Terry (2019). "Wilhelm Foerster's Role in the Metre Convention of 1875 and in the Early Years of the International Committee for Weights and Measures". Annalen der Physik. 531 (5) 1800355. doi:10.1002/andp.201800355. ISSN 1521-3889.
  56. 1 2 3 4 Torge, Wolfgang (2016). Rizos, Chris; Willis, Pascal (eds.). "From a Regional Project to an International Organization: The "Baeyer-Helmert-Era" of the International Association of Geodesy 1862–1916". IAG 150 Years. Cham: Springer International Publishing: 3–18. doi:10.1007/1345_2015_42. ISBN 978-3-319-30895-1.
  57. ↑ Lebon, Ernest (1899). Histoire abrégée de l'astronomie / par Ernest Lebon,... pp. 168–171.
  58. ↑ Drewes, Hermann; Kuglitsch, Franz; Adám, József; Rózsa, Szabolcs (2016). "The Geodesist's Handbook 2016". Journal of Geodesy. 90 (10): 914. Bibcode:2016JGeod..90..907D. doi:10.1007/s00190-016-0948-z. ISSN 0949-7714. S2CID 125925505.
  59. ↑ "El General Ibáñez e Ibáñez de Ibero, Marqués de Mulhacén".
  60. 1 2 3 Levallois, J. J. (1980-09-01). "Notice historique". Bulletin géodésique (in French). 54 (3): 248–313. Bibcode:1980BGeod..54..248L. doi:10.1007/BF02521470. ISSN 1432-1394. S2CID 198204435.
  61. ↑ Sánchez Tello, José L. (March 2025). "General Ibáñez e Ibáñez de Ibero: CIENTÍFICO TOTAL" (PDF). Revista Española de Defensa: 62.
  62. ↑ Debarbat, Suzanne (2011). "FROM OLD WEIGHTS AND MEASURES TO THE SI AS A NUMERICAL STANDARD FOR THE WORLD" (PDF). ui.adsabs.harvard.edu. Retrieved December 30, 2020.
  63. ↑ "Mesure du 1er mètre: une erreur qui changea le monde". Techniques de l'Ingénieur (in French). Retrieved December 30, 2020.
  64. ↑ Géodésie in Encyclopedia Universalis. Encyclopedia Universalis. 1996. pp. Vol 10, p. 302. ISBN 978-2-85229-290-1. OCLC 36747385.
  65. ↑ Appell, Paul (1925). "Le centenaire du général Ibañez de Ibéro". Revue internationale de l'enseignement. 79 (1): 208–211.
  66. ↑ [webmastergep@unav.es], Izaskun Martínez. "Carlos Ibáñez e Ibáñez de Ibero (Grupo de Estudios Peirceanos)". www.unav.es. Archived from the original on 2025-07-02. Retrieved 2026-03-21.
  67. ↑ Hirsch, Adolphe (1868). Bericht über die Verhandlungen der vom 30. September bis 7. October 1867 zu BERLIN abgehaltenen allgemeinen Conferenz der Europäischen Gradmessung [Report on the proceedings of the general conference of the European Arc Measurement held in Berlin from September 30 to October 7, 1867.] (PDF) (in German). Berlin: Central-Bureau der Europäischen Gradmessung. p. 14.
  68. ↑ "Hirsch, Adolphe". hls-dhs-dss.ch (in French). Retrieved 2026-05-08.
  69. ↑ Gautier, R. (1901). "Mémoires et observations. Notice nécrologique sur Hirsch". Bulletin Astronomique, Serie I. 18: 209–211.
  70. ↑ Appell, Paul (1925). "Le centenaire du général Ibañez de Ibéro". Revue internationale de l'enseignement. 79 (1): 208–211.
  71. ↑ "Académicos Históricos - Real Academia de Ciencias Exactas, Físicas y Naturales". rac.es. Retrieved 2026-03-25.
  72. ↑ Proyectos, HI Iberia Ingeniería y. "Real Academia de la Historia | Historia Hispánica". historia-hispanica.rah.es (in Spanish). Retrieved 2026-03-25.
  73. ↑ Bodin, Jean-Louis (2020-06-09). "A view on 50 years of life of the ISI: With a focus on ISI relations with official statistics1". Statistical Journal of the IAOS. 36 (2): 303–308. doi:10.3233/SJI-190608.
  74. 1 2 "The History of the ISI | ISI". isi-web.org. Retrieved 2026-03-25.
  75. ↑ Droesbeke, Jean-Jacques (2003). "1841-1853 : une période faste pour la statistique belge ?". Journal de la Société française de statistique (in French). 144 (1–2): 35–73. ISSN 1625-7421.
  76. ↑ Hassler, Harriet; Burroughs, Charles A. (2007). Ferdinand Rudolph Hassler (1770–1843). NIST Research Library. pp. 51–52.
  77. ↑ "Metric Act of 1866 – US Metric Association". usma.org. Retrieved 2021-03-15.
  78. ↑ Bericht über die Verhandlungen der vom 30. September bis 7. October 1867 zu BERLIN abgehaltenen allgemeinen Conferenz der Europäischen Gradmessung (PDF) (in German). Berlin: Central-Bureau der Europäischen Gradmessung. 1868. pp. 123–134.
  79. ↑ Guillaume, Charles-Édouard (11 December 1920). "Nobel lecture: Invar and Elinvar". NobelPrize.org. p. 445. Retrieved 21 May 2020.
  80. ↑ Comptes rendus des séances de la ... Conférence générale des poids et mesures (in French). Gauthier-Villars. 1890. p. 25.
  81. ↑ Clarke, Alexander Ross; Helmert, Friedrich Robert (1911). "Geodesy" . Encyclopædia Britannica. Vol. 11 (11th ed.). pp. 607–615.
  82. ↑ "Earth, Figure of the" . Encyclopædia Britannica. Vol. 8 (11th ed.). 1911. pp. 801–813.
  83. ↑ Crease, Robert P. (2009-12-01). "Charles Sanders Peirce and the first absolute measurement standard". Physics Today. 62 (12): 39–44. Bibcode:2009PhT....62l..39C. doi:10.1063/1.3273015. ISSN 0031-9228.
  84. ↑ Lenzen, Victor F. (1965). "The Contributions of Charles S. Peirce to Metrology". Proceedings of the American Philosophical Society. 109 (1): 29–46. ISSN 0003-049X. JSTOR 985776.
  85. ↑ 9th edition of the SI Brochure, BIPM, 2019, p. 131
  86. ↑ Nelson, Robert A. (December 1981). "Foundations of the international system of units (SI)" (PDF). The Physics Teacher. 19 (9): 596–613. Bibcode:1981PhTea..19..596N. doi:10.1119/1.2340901.
  87. ↑ "Définition de cassaba | Dictionnaire français". La langue française (in French). 2024-08-11. Retrieved 2026-03-22.
  88. ↑ Jamʻīyah al-Jughrāfīyah al-Miṣrīyah (1876). Bulletin de la Société de géographie d'Égypte. University of Michigan. [Le Caire]. pp. 7–8.
  89. ↑ Ismail Mustafa al-Falaki (1864). Recherche des coefficients de dilatation et étalonnage de l'appareil à mesurer les bases géodésiques appartenant au gouvernement égyptien / par Ismaïl-Effendi-Moustapha, ... (in French).
  90. ↑ Hirsch, Adolphe (1892). Comptes-rendus des séances de la Commission permanente de l'Association géodésique internationale réunie à Florence du 8 au 17 octobre 1891 (in French). De Gruyter, Incorporated. pp. 101–109.
  91. ↑ Hirsch, Adolphe (1867). "Procès-verbaux de la Conférence géodésique internationale pour la mesure des degrés en Europe, réunie à Berlin du 30 septembre au 7 octobre 1867". HathiTrust (in French). p. 22. Retrieved 3 February 2025.
  92. ↑ Levallois, J. J. (1 September 1980). "Notice historique". Bulletin géodésique (in French). 54 (3): 248–313. Bibcode:1980BGeod..54..248L. doi:10.1007/BF02521470. ISSN 1432-1394. S2CID 198204435.
  93. ↑ Guillaume, Ed. (1 January 1916). "Le Systeme Metrique est-il en Peril?". L'Astronomie. 30: 244–245. Bibcode:1916LAstr..30..242G. ISSN 0004-6302.
  94. ↑ Clarke, Alexander Ross; James, Henry (1873-01-01). "XIII. Results of the comparisons of the standards of length of England, Austria, Spain, United States, Cape of Good Hope, and of a second Russian standard, made at the Ordnance Survey Office, Southampton. With a preface and notes on the Greek and Egyptian measures of length by Sir Henry James". Philosophical Transactions of the Royal Society of London. 163 (163): 445–469. doi:10.1098/rstl.1873.0014.
  95. ↑ "Struve Geodetic Arc - Nomination file 1187". UNESCO World Heritage Centre. pp. 143, 144. Retrieved 2020-09-27.
  96. ↑ "Polar motion | Earth's axis, wobble, precession | Britannica". www.britannica.com. Retrieved 2023-08-28.
  97. 1 2 Hirsch, Adolphe (1892). Comptes-rendus des séances de la Commission permanente de l'Association géodésique internationale réunie à Florence du 8 au 17 octobre 1891 (in French). De Gruyter, Incorporated. pp. 23–25, 101–147.
  98. ↑ Yokoyama, Koichi; Manabe, Seiji; Sakai, Satoshi (January 2000). "History of the International Polar Motion Service/International Latitude Service". International Astronomical Union Colloquium. 178: 147–162. doi:10.1017/S0252921100061285. ISSN 0252-9211.
  99. ↑ Perrier, Général (1935). "Historique Sommaire De La Geodesie". Thalès. 2: 117–129. ISSN 0398-7817.
  100. ↑ Perrier (1872–1946), Georges (1933). Cours de géodésie et d'astronomie / par G. Perrier. pp. 17–18.{{cite book}}: CS1 maint: numeric names: authors list (link)
  101. ↑ Discours sur Charles Lallemand par Georges Perrier, lu lors de ses funérailles, le 3 février 1938, Paris, Académie des Sciences Notices et Discours, 241-242
  102. 1 2 Quinn, T. J. (2012). From artefacts to atoms: the BIPM and the search for ultimate measurement standards. Oxford: Oxford University Press. pp. 3–12, 14, 90–92, 56–57, 72, 108, 56–57. ISBN 978-0-19-990991-9. OCLC 861693071.
  103. 1 2 Bigourdan, Guillaume (1901). Le système métrique des poids et mesures ; son établissement et sa propagation graduelle, avec l'histoire des opérations qui ont servi à déterminer le mètre et le kilogramme. University of Ottawa. Paris : Gauthier-Villars. pp. 147, 154–159.
  104. ↑ [s.n.] (1864–1865). "Rapport à la commission géodésique suisse sur la conférence géodésique internationale de Berlin". Bulletin de la Société des Sciences Naturelles de Neuchâtel. 7: 3. doi:10.5169/seals-88011. ISSN 0366-3469.
  105. ↑ "Geodesy" . Encyclopædia Britannica. Vol. 11 (11th ed.). 1911. pp. 607–615.
  106. ↑ Guillaume, Charles Édouard. "Nobel Prize in Physics 1920". NobelPrize.org. p. 445. Retrieved 27 March 2025.
  107. ↑ Guillaume, C.-H.-Ed (1 January 1906). "La mesure rapide des bases géodésiques". Journal de Physique Théorique et Appliquée. 5: 242–263. doi:10.1051/jphystap:019060050024200.
  108. ↑ Ritter, Elie (1858). Manuel théorique et pratique de l'application de la méthode des moindres carrés au calcul des observations (in French). Mallet-Bachelier. pp. 7–8.
  109. 1 2 3 Public Domain This article incorporates text from this source, which is in the public 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.
  110. ↑ Pérard, Albert (1957). "Carlos Ibáñez e Ibáñez de Ibero (14 avril 1825 – 29 janvier 1891), par Albert Pérard (inauguration d'un monument élevé à sa mémoire)" (PDF). Institut de France – Académie des sciences. pp. 26–28.
  111. ↑ Charles-Édouard Guillaume, La création du Bureau international des poids et mesures et son œuvre, Paris, Gauthier-Villars, 1927, 321 p., p. 130
  112. ↑ Guillaume, Ed. (1 January 1916). "Le Systeme Metrique est-il en Peril?". L'Astronomie. 30: 244–245. Bibcode:1916LAstr..30..242G. ISSN 0004-6302.
  113. ↑ NIST Special Publication. U.S. Government Printing Office. 1966. p. 529.
  114. ↑ "Earth, Figure of the" . Encyclopædia Britannica. Vol. 8 (11th ed.). 1911. pp. 801–813.
  115. ↑ "Key comparison of the Committee Meter" (PDF). e-expo: Ferdinand Rudolf Hassler. 2007.
  116. ↑ Vaníček, Petr; Foroughi, Ismael (2019-09-01). "How gravity field shortened our metre". Journal of Geodesy. 93 (9): 1821–1827. doi:10.1007/s00190-019-01257-7. ISSN 1432-1394.
  117. ↑ "Rapport de M. Faye sur un Mémoire de M. Peirce concernant la constance de la pesanteur à Paris et les corrections exigées par les anciennes déterminations de Borda et de Biot". Comptes rendus hebdomadaires des séances de l'Académie des sciences. 90: 1463–1466. 1880. Retrieved 2018-10-10 – via Gallica.
  118. ↑ "Report from Charles S. Peirce on his second European trip for the Anual Report of the Superintendent of the U. S. Coast Survey, New York, 18.05.1877". Retrieved August 25, 2019 – via Universidad de Navarra.
  119. ↑ Hirsch, Adolphe. "Bulletin de la Société des Sciences Naturelles de Neuchâtel". E-Periodica (in German). pp. 255–256. Retrieved 2026-05-03.
  120. ↑ Géodésie in Encyclopedia Universalis. Encyclopedia Universalis. 1996. pp. Vol 10, p. 302. ISBN 978-2-85229-290-1. OCLC 36747385.
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