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. It became the European Arc Measurement (Europäische Gradmessung) in 1867 and the International Geodetic Association (German: Internationale Erdmessung) in 1886. 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.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 It officially adopted its current name, the International Association of Geodesy (IAG), in 1946.
Implementation of new scientific methods
The creation of the Central European Arc Measurement marked, following the examples of Friedrich Wilhelm Bessel and Friedrich Georg Wilhelm von Struve, the systematic adoption of more rigorous scientific methods, including the application of the least squares method in geodesy.
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.
Like numerous astronomers of his time Bessel dealt on the field of geodesy, too, first theoretically, when he published a method for solving the main geodetic problem. Errata. 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. He also obtained an estimate of increased accuracy for the Earth's ellipsoid, nowadays called the Bessel ellipsoid, based on several arc measurements.
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. 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.
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.
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.J. M. López de Azcona, "Ibáñez e Ibáñez de Ibero, Carlos", Dictionary of Scientific Biography, vol. VII, 1–2, Scribner's, New York, 1981. 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 . 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.
In 1859, Friedrich von Schubert demonstrated that several meridians had not the same length, confirming an hypothesis of Georges-Louis Leclerc, Comte de Buffon. He also proposed an ellipsoid with three unequal axes. 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. 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. 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). A founding member of the International Committee of the Red Cross and forerunner of metrication in Switzerland, Guillaume Henri Dufour contributed to the creation of the Central European Arc Measurement as a member of the Swiss Geodetic Commission from 1861. Guillaume-Henri Dufour, cantonal engineer in Geneva since 1817 and commissioned by the Federal Diet to superintend land surveying of Switzerland, founded in 1838 in Carouge (canton of Geneva) a topographic office (the future Federal Office of topography), which published under his direction, from 1845 to 1864, the first official map of Switzerland, on the basis of new cantonal measurements. 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. 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.
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. 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. 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. The Central European Arc Measurement created a Central Office, located at the Prussian Geodetic Institute, whose management was entrusted to Johann Jacob Baeyer. 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. 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.