Portable Meter

[Meinard Hartmann]

Themetre was originally defined in 1791 by the French National Assembly as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's polar circumference is approximately 40000 km.

Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations, the exceptions being the United States[3][4][5][6] and the Philippines[7] which use meter.

Galileo discovered gravitational acceleration to explain the fall of bodies at the surface of the Earth.[14] He also observed the regularity of the period of swing of the pendulum and that this period depended on the length of the pendulum.[15]

Kepler's laws of planetary motion served both to the discovery of Newton's law of universal gravitation and to the determination of the distance from Earth to the Sun by Giovanni Domenico Cassini.[16][17] They both also used a determination of the size of the Earth, then considered as a sphere, by Jean Picard through triangulation of Paris meridian.[18][19] 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).[20][21] In 1675, Tito Livio Burattini suggested the term metro cattolico meaning universal measure for this unit of length, but then it was discovered that the length of a seconds pendulum varies from place to place.[22][23][24][25]

Christiaan Huygens found out the centrifugal force which explained variations of gravitational acceleration depending on latitude.[26][27] He also mathematically formulated the link between the length of the simple pendulum and gravitational acceleration.[28] According to Alexis Clairaut, the study of variations in gravitational acceleration was a way to determine the figure of the Earth, whose crucial parameter was the flattening of the Earth ellipsoid. In the 18th century, in addition of its significance for cartography, geodesy grew in importance as a means of empirically demonstrating the theory of gravity, which milie du Chtelet 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. Indeed, Earth proved to be an oblate spheroid through geodetic surveys in Ecuador and Lapland and this new data called into question the value of Earth radius as Picard had calculated it.[28][29][30][22][19]

In 1790, one year before it was ultimately decided that the metre would be based on the Earth quadrant (a quarter of the Earth's circumference through its poles), Talleyrand proposed that the metre be the length of the seconds pendulum at a latitude of 45. This option, with one-third of this length defining the foot, was also considered by Thomas Jefferson and others for redefining the yard in the United States shortly after gaining independence from the British Crown.[48][49]

In 1816, Ferdinand Rudolph Hassler was appointed first Superintendent of the Survey of the Coast. Trained in geodesy in Switzerland, France and Germany, Hassler had brought a standard metre made in Paris to the United States in 1805. He designed a baseline apparatus which instead of bringing different bars in actual contact during measurements, used only one bar calibrated on the metre and optical contact. Thus the metre became the unit of length for geodesy in the United States.[60][61][46]

In 1830, Hassler became head of the Office of Weights and Measures, which became a part of the Survey of the Coast. He compared various units of length used in the United States at that time and measured coefficients of expansion to assess temperature effects on the measurements.[62]

In 1832, Carl Friedrich Gauss studied the Earth's magnetic field and proposed adding the second to the basic units of the metre and the kilogram in the form of the CGS system (centimetre, gram, second). In 1836, he founded the Magnetischer Verein, the first international scientific association, in collaboration with Alexander von Humboldt and Wilhelm Edouard Weber. The coordination of the observation of geophysical phenomena such as the Earth's magnetic field, lightning and gravity in different points of the globe stimulated the creation of the first international scientific associations. The foundation of the Magnetischer Verein would be followed by that of the Central European Arc Measurement (German: Mitteleuropasche Gradmessung) on the initiative of Johann Jacob Baeyer in 1863, and by that of the International Meteorological Organisation whose president, the Swiss meteorologist and physicist, Heinrich von Wild would represent Russia at the International Committee for Weights and Measures (CIPM).[58][41][63][64][65][66]

In 1834, Hassler, measured at Fire Island the first baseline of the Survey of the Coast, shortly before Louis Puissant declared to the French Academy of Sciences in 1836 that Jean Baptiste Joseph Delambre and Pierre Mchain had made errors in the meridian arc measurement, which had been used to determine the length of the metre. Errors in the method of calculating the length of the Paris meridian were taken into account by Bessel when he proposed his reference ellipsoid in 1841.[67][68][69][37][38]

Egyptian astronomy has ancient roots which were revived in the 19th century by the modernist impetus of Muhammad Ali who founded in Sabtieh, Boulaq district, in Cairo an Observatory which he was keen to keep in harmony with the progress of this science still in progress. In 1858, a Technical Commission was set up to continue, by adopting the procedures instituted in Europe, the cadastre work inaugurated under Muhammad Ali. This Commission suggested to Viceroy Mohammed Sa'id Pasha the idea of buying geodetic devices which were ordered in France. While Mahmud Ahmad Hamdi al-Falaki was in charge, in Egypt, of the direction of the work of the general map, the viceroy entrusted to Ismail Mustafa al-Falaki the study, in Europe, of the precision apparatus calibrated against the metre intended to measure the geodesic bases 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 bars, and to compare the Egyptian standard with a known standard. The Spanish standard designed by Carlos Ibez e Ibez 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 geodesic bases in France, and was also to be compared to the Ibez apparatus. In 1954, the connection of the southerly extension of the Struve Geodetic Arc with an arc running northwards from South Africa through Egypt would bring the course of a major meridian arc back to land where Eratosthenes had founded geodesy.[70][71][72][73][74]

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 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.[36] After Struve Geodetic Arc measurement, it was resolved in the 1860s, at the initiative of Carlos Ibez e Ibez de Ibero who would become the first president of both the International Geodetic Association and the International Committee for Weights and Measure, to remeasure the arc of meridian from Dunkirk to Formentera and to extend it from Shetland to the Sahara.[75][76][77][74] This did not pave the way to a new definition of the metre because it was known that the theoretical definition of the metre had been inaccessible and misleading at the time of Delambre and Mechain arc measurement, as the geoid is a ball, which on the whole can be assimilated to an oblate spheroid, but which in detail differs from it so as to prohibit any generalization and any extrapolation from the measurement of a single meridian arc.[34] 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.[78][79] 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.[80] 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 Montjuc in the French meridian arc which determination had also been affected in a lesser proportion by systematic errors of the repeating circle.[81][82][34].mw-parser-output .templatequoteoverflow:hidden;margin:1em 0;padding:0 32px.mw-parser-output .templatequote .templatequoteciteline-height:1.5em;text-align:left;padding-left:1.6em;margin-top:0

It was well known that by measuring the latitude of two stations in Barcelona, Mchain 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.[83][84][54] 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.[82] Polar motion predicted by Leonhard Euler and later discovered by Seth Carlo Chandler also had an impact on accuracy of latitudes' determinations.[85][28][86][87] 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.[34]

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