Appear of the Earth and meridian of Delambre and Méchain

Measure and decimal metric system: children of the French revolution

The history of the Meter and the Metric system currently used in all the international scientific exchanges, in the same way moreover as the history of the determination of the mass of the Earth, constitutes to some extent a history in the general history of the geodesy and the determination of the Figure of the Earth. The introduction of the meter and the metric system was undoubtedly the consequence of the problems which had the geodesists of the {{S|XVIII|E}} to be had in each place of a standard sufficiently precise and reliable, and easily reproducible length in theory. The meter and the decimal metric system are with the Déclaration of the Human rights undoubtedly the most important things bequeathed by the French revolution to posteriority. It is impossible to tell in detail in this article, and a another article which constitutes the continuation of it, the enthralling history politico-économico-scientist which hides behind the metric system.

It is known that the natural laws do not depend on the choice of the measuring units. For example, the gravific Attraction will always decrease like the reverse of the square of the distance, it does not matter if one expresses the distance in Toise S or meters. It will be always proportional to the product of the Masse S of the two bodies which attract each other, that one expresses these masses in ounce S or Kilogram S. With the rigor, one could even express one of the masses in ounces, the other in grams, for example. What will change with the units chosen, they are thus not the relations between physical sizes but only the numerical values of the constants which intervene in these relations. In the example considered, it is the numerical value of the constant of attraction which will vary according to the system of unit S adopted. First of all, one cannot thus say that a system of units is better than another. It is the fact that it proved to be practical with use and especially the fact that it ended up being accepted by the majority of the civilized nations which give its superiority to the metric system. Certains States was reticent a long time to accept this system of measurement, for reasons of national prestige or quite simply for reasons of hostility in France. However, upon the departure it had been conceived in the idea of a supranational system, which does not belong to any particular nation but to the whole of humanity, in agreement with the generous ideas prevailing under revolutionary France. This is why the meter was initially defined not like any length materialized at a particular place in a particular country, but like the ten millionth part of a quarter of terrestrial meridian line . In theory, everyone had access there, but the meter did not belong to anybody in particular.

Around 1770 the work of Triangulation required by the meridian one of France was completed, if one excludes certain operators of Cassini who continued the geodetic groundwork of the chart of France, whose 1st order was published as a whole in 1783. The comparison of the measuring apparatuses used in North (Lapland), in Peru, in the Cape and in France had shown that all these measuring apparatuses were equal, in margins of error of some hundredths of line. The measuring apparatus of Peru was adopted like standard and became the measuring apparatus of the Academy . It is with this measuring apparatus that one was to bring back later measurements. Unfortunately, this did not solve the question of the unification of measurements, which in all the Kingdom of France (without speaking about the other nations) preserved their anarchistic independence savagely, in spite of several attempts at unification. This situation, which proved to be serious in its consequences with various recoveries, could not last for ever any more, but the things changed indeed only when the Constituent Assembly named in 1790 (thus a year after the beginning of the Revolution), on proposal of Charles-Maurice Talleyrand (1754 - 1838), a composite commission of Jean-Charles Borda (1733 - 1799), of the count Joseph-Louis de Lagrange (1736 - 1813), of the marquis Pierre-Simon of Laplace (1749 - 1827), of Gaspard Monge (1746 - 1818) and of Marie-Jean-Antoine Caritat, marquis de Condorcet (1743 - 1794). This one presented a report/ratio the March 19th 1791 in which she proposed a double choice to unify the measures of length: the unit would be either a pendulum beating the second with the latitude of 45° to the sea level, or the ten millionth part of the quarter of the terrestrial meridian . The March 26th 1791, the Constituent one adopted this report/ratio and King Louis XVI, still representing the Executive power at this time, charged the Academy with the nomination of the police chiefs for his implementation. The astronomer Cassini IV, the mathematician Legendre (or the Son-in-law) and the astronomer Méchain were charged to measure the meridian one. The two first were not long in being withdrawn and were replaced by the young astronomer Jean-Baptiste Delambre.

Preliminary theoretical work: spheroidic trigonometry

Before briefly describing this meridian news of France, which one calls the “meridian one of Delambre and Méchain”, it is advisable to recall that during the twenties or thirty years which preceded the French revolution, the Géodésie had proposed with sagacity scientists like Euler, Monge, Laplace and others a certain number of subjects of study: attraction of the ellipsoids, theory of the balance of the bodies in rotation, general theory of surfaces. The solutions brought to these theoretical problems were going to appear of a great interest to treat more practical geodetic applications. Thus, Euler in 1760 then Monge in 1771 defined the basic elements of the geometry of surfaces, connects which was going to become the differential Géométrie: curve, lines traced on surfaces, geodetic, lines of curve. J. Meusnier states in 1776 a theorem which will play a big role in differential geometry. In 1773, Pierre-Simon Laplace, then 24 years old, raises and protected from D' Alembert, its first report of celestial mechanics published. This one milked of the stability of the main roads of the planetary orbits.

In 1785 appears with the Academy a report into which Legendre introduces the concept of potential, which this one expressly assigns with Laplace, and founds the theory of the spherical functions, tools mathematical which became essential to theoretical geodesy. In this same year 1785 appears also a report of Laplace entitled Théorie of attractions of the spheroids and figure of the planets which will be followed in 1786 of a Mémoire on the figure of the Earth . Laplace combines various measurements of arc and obtains a flatness of 1/250 with it while the gravimetric method, expressed in the theorem of Clairaut, provides him only 1/321. Always in 1785, the astronomer Joseph de Lalande (1732 - 1807) had obtained theory of Clairaut consequently a flatness of 1/302. Two years later, in 1787, Legendre publishes its Mémoire on the trigonometrical Operations, whose results depend on the figure of the Earth , where it in particular states, without showing it, a become theorem celebrates and who bears his name. This memory studies the formulas necessary for the reduction and the calculation of the triangles on the surface of a Sphéroïde, and thus gives strong foundations to the spheroidic Trigonométrie. The latter constitutes a generalization of the spherical Trigonométrie, extension for which the need had already been felt with work of meridian of Jean Dominique and Jacques Cassini, but which had not been treated in an entirely satisfactory way in the theoretical work of Clairaut going back to 1733 and 1739, of Euler going back from 1744 and Dionis Of-Stay (1734 - 1794) going back to 1778. The formulas of Legendre are applied to the triangles formed between Dunkirk and Greenwich, during the extension of meridian of Delambre and Méchain towards the England. One finds a demonstration of the “theorem of Legendre” and the formulas to solve one of the problems opposite, in the particular case where one on the sides of the spheroid triangle is very small compared to the others, in a work of J.B. Delambre (1747 - 1822) published in 1799 and entitled analytical Methods for the determination of an arc of the Meridian line in Paris . This work contains at the beginning (pp. 1-16) a small article of Legendre in which this last exposes the Méthode to determine the exact length of the quarter of Meridian line . However, Legendre there still does not show the theorem which bears its name, but leaves this task (for the quoted particular case) to Delambre. In fact, it acts in the work in question of the first text which provides the complete theory of spheroidic trigonometry applied to the calculation of the meridian line and the eccentricity of the terrestrial ellipsoid.

The work of Delambre, of which the essential goal is to summarize the mathematical apparatus used between 1793 and 1799 for calculations of the new meter, gives explicitly, while it making operational, the theory of the arc independent of terrestrial flatness. It is a first great result which new spheroidic trigonometry offers to the geodesy, and which will have its importance in later geodetic work to found the system metric.

Under the effect of the geodetic operations which were going quickly to become extensive not only in France but also in the adjoining countries, especially because of the military successes gained by the revolutionary armies then Napoleonean, spheroidic trigonometry became a branch with whole share of theoretical geodesy, and developed in an autonomous mathematical theory. First of all, it is in 1806 that Legendre proves for the first time its theorem in any general information, and insists on the independence of its result compared to the flatness of the spheroid considered, of the latitude of the top of the studied triangle and the azimuth directions on the sides. The work in which Legendre thus solved the fundamental problems of spheroidic trigonometry carries the title Analyze of the triangles traced on the surface of a spheroid . Then, the same year 1806 sees appearing in Italy a work entitled Elementi di trigonometria sferoidica in which Barnabá Oriani (1752 - 1832), already known by beautiful geodetic work, somewhat supplemented the theory of Legendre. Oriani determines the three fundamental equations of spheroidic trigonometry, by developing them in series until an arbitrary order of approximation, and solves the opposite problem consisting in finding the latitude of a point on a spheroid starting from the latitude and of the azimuth of another point of the geodetic line, by supposing known the distance between the two points. In fact, this work of Oriani exposes the total solution of the twelve most important problems of spheroidic trigonometry. This one experienced still a little later some developments of a practical nature under the impulse of the Colonel Louis Puissant (1769 - 1843), but essentially one can consider that it constituted an already ripe discipline starting from 1806.

Meridian of Delambre and Méchain and scientific progresses at the same time

Meanwhile, whereas this progress was achieved in theoretical Géodésie, the geodesy of observation did not remain inactive. First of all let us recall the experiments in 1775 of Nevil Maskelyne to the MT. Schiehallion to determine the Mass of the Earth. In addition, even it is not a question itself of a geodetic observation strictly speaking but of a major astronomical discovery, it is advisable to quote the observation, the March 13rd 1781, of the new planet Uranus. This one was done by William Herschel using a Télescope of its own manufacture. At the time, it was undoubtedly the best in the world. Herschel was not at the beginning not an astronomer, but a musician enthusiast of optics and scientific culture. Like its compatriot, the large musician G.F. Haendel, it had been born in the Hanover and had emigrated in England following the king George III. One owes him of others important astronomical discoveries, in particular the systems of double stars discovered in 1782, and the movement of the Solar system towards the Apex located in the constellation of Hercules. Later, in 1802, W. Herschel will still notice which the solar spectrum extends towards frequencies lower than radiations from red light, thus discovering the infra-red radiation.

In 1783, Pilâtre de Rozier carried out a first rise in balloon. In 1787, Jean-Charles Borda described the improvements which it was advisable to bring to the instruments geodesy and this same year one started to proceed with the new repeating circle of Bordered with the prolongations of meridian of France. First of all, on a former proposal of Cassini de Thury, operations of connection between the Observatory of Paris and the royal Observatoire of Greenwich in the suburbs of London were undertaken. This junction was carried out in concert by the British general William Roy (1726 - 1790) for the England, by Cassini IV, Méchain and Legendre for the France. The meridian one of the Ruail, prolonged until Calais, the White Cape Nose and Montlambert close to Boulogne allowed the connection with the English coast on Dover and Fairlight Down. A chain of triangulation of a score of triangles connected English side these tops to Greenwich.

At the end of June 1792, Delambre and Méchain and their operators began the completion of the work of measurement of meridian line of which they had been given the responsability by the decree with 1791 in order to determine exactly the length Q of a quarter of meridian line, with an aim of fixing the value of the meter by the relation

1 meter = 10^-7 Q.

Of 1792 with 1793, Delambre had many contentions with local national guards and could hardly work effectively. Méchain, as for him, had left for Spain. Enjoying exceptional climatic conditions and visibilities, it had made in two months of measurements in nine stations and had begun the astronomical observations necessary to the Fort of Montjuich, in the surroundings of Barcelona. He thought moreover of connecting the Balearic Islands to the continent when he was victim of a serious accident which immobilized it during nearly one year. He could finally turn over to France to take part in last work of meridian the Dunkirk - Perpignan and was named at the position of director of the Observatory of Paris, then placed under the responsibility of the Bureau of longitudes. But the project of the prolongation of meridian of France to the Balearic Islands remained with the day order, and Méchain again attacked starting from 1803. Unfortunately, it could not complete it, because it died suddenly of “third fever” with Castellon of Plana the September 20th 1804. Completion was entrusted by it, on proposal of Laplace, with Jean-Baptiste Biot (1776 - 1862) and with François Arago (1786 - 1853). Work started again in 1807 and was completed in 1808.

Meanwhile, Lagrange had published in 1788 the first edition of its Analytical mechanics , work entirely innovating which was going to exert a deep influence on the evolution of the Theoretical physics and, of course, of the Mécanique and the tributary disciplines. Always in 1788, Charles-Augustin of Coulomb (1736 - 1806) publishes his law of electrostatic attraction established with the torsion balance that he had invented in 1784. The invention of the Battery by Alessandro Volta date of 1800.

Of 1801 with 1803, Jöns Svanberg (1771 - 1851) remade measurements of Maupertuis and Clairaut in Lapland; it leads to 57196 measuring apparatuses for the degree of Lapland, against the 57436 measuring apparatuses found by Maupertuis. In addition, Legendre publishes in 1805 its New method for determination of the orbits of comets and in the appendix describes its new method of least squares, which plays a crucial role in the reduction of the geodetic data. There exists a litigation concerning the priority of the invention of this method. Indeed, Carl Friedrich Gauss (1777 - 1855) affirms on its side to have invented and have used the method of least squares about 1795; it publishes of it essence in its work Theoria motus corporum celestium in sectionibus conicis solem ambientium , which appears in 1809.

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