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On 19 March 1791 the metre, the base of the new metric system, was theoretically defined as being equal to the ten millionth part of one quarter of the terrestrial meridian. Practically, the length of the meridian still had to be set up, however.

In its "report on the choice of units of measure", the Academy of Science defined the various steps that this work would involve: the length of the meridian would be determined by triangulation, from an arc of 9 and a half degrees between Dunkirk and Barcelona.

Already in 1718, Jacques Cassini used this method to measure the meridian between Dunkirk and Collioure. Triangulation consists of marking a route by a network of highly visible landmarks: tower, peak, church spire, etc., these points representing a series of connected triangles. The method involves trigonometry calculations. Knowing all the angles formed by two adjacent triangles and at least one of the lengths in one of these triangles, we can determine the lengths of all sides in both triangles.

Juvisy Pyramid (picture)

The triangulation and determination of the latitudes were to be carried out by Cassini ( the son of Jacques Cassini), Legendre and Méchain.

Monge and Meusnier were to measure the bases. In June 1791, Cassini simply visited with Méchain the base of Villejuif at Juvisy, Paris (the obelisk is currently known as the *Pyramide de Juvisy*). Although Cassini expected to be able to use this old base, which had already been used by his father in 1739, his grandfather in 1701, and Abbot Picard in 1670 when they carried out their triangulation calculations ; he was unable to do so. Cassini then stayed in Paris to help Borda. Monge and Legendre did very little in fact. Meusnier left to join the Rhine army and was killed in 1793. Delambre, who had just joined the Academy of Science was then nominated to replace them.

Measurement of the meridian arc involved the use of precision instruments and was partly justified by improvements to these instruments. Of much greater precision, these measurements would replace the previous ones taken fifty years before.

To determine the angles, our two geodesists were going to use the new Borda repeating circle. Using this innovation, angles could be measured to the nearest second, whereas with the quadrants used so far it had only been possible to obtain accuracy to the nearest 15 seconds. The ground measurements, in *Toise du Pérou* units, were to be made with copper-platinum bimetal rulers. Obviously, any other unit would have been suitable, since once the length of the quarter of the meridian is determined, dividing it by 10 000 000 would give the length of a metre. In this case, the length of the first metre was therefore expressed in *Toise du Pérou* units; in 1747, La Contamine had brought back this measurement unit from his expedition to the equator, but it only became a national standard on 16 May 1766 after a royal declaration.

Cercle répétiteur

(St Mandé, IGN)

Delambre's team included the Frenchmen Lalande and Bellet; Tranchot and Esteveny accompanied Méchain. The Academy of Science distributed the work involved in measurement of the meridian arc as follows: the two upper thirds, from Dunkirk to Rodez, were assigned to Delambre; the last third, from Rodez to Barcelona, was assigned to Méchain. This difference could be explained by the fact that Delambre's route would theoretically follow close to the points of the former triangulation, whereas Méchain would explore territory where no geodesic measurements had yet been taken.

In practice, the earlier triangulation landmarks turned out to be unusable: during the turmoil of the revolution, some spires had disappeared or were about to collapse. Peak after peak, Delambre discovered that it was impossible to use Cassini's previous landmarks: the old spires had been rebuilt differently after being burnt down.

More than one hundred triangles were required to mark out the meridian arc; our two geodesists were to experience numerous mishaps during their expedition: arrests, temporary revocations, damaged or destroyed geodesic equipment. The marker signals they used for their observations aroused the distrust of the population; the material attached at the end of their signals was white, the colour of royalty, and therefore a counter-revolutionary colour. In spite of their passes, passports and other authorisations, our two scientists were still not safe from arrest, since the authorities which had issued these documents disappeared, making them outlaws. For instance, following the abolition of the Academies (in 1793), Delambre found that he had been excluded from the temporary commission of weights and measures (in 1794) and therefore prohibited from continuing his work, until June 1795. Méchain also experienced numerous setbacks.

Landmarks to establish, mountains to cross, not forgetting the historical events :

War broke out on 7 March 1793 between France and Spain, where some of his measurements had to be taken. From 1793 to 1795 therefore, the Terror regime was to delay his triangulation calculations. At the same time, the metre was temporarily fixed by the law of 1 August 1793 according to the results of measuring the French meridian, published by Lacaille in the 1758 *Mémoires de l'Académie*. Moreover, the decimal subdivisions of the metre were to be the decimetre, the centimetre and the millimetre. This temporary standard metre did not correspond to the work carried out by Méchain and Delambre, but to the results of Cassini's earlier triangulation.

In 1795, with the improvement of the political situation, the triangulation work was able to resume. It continued for a further three years, before the length of the quarter of the meridian could be accurately determined and a new platinum metre standard dedicated to "all times and all men " was deposited in 1799, in the archives of the republic.

pictures extracted from the book *"L'épopée du mètre"* (published by the French Ministry in charge of Industry and Regional Planning)