:: Measuring the quadrant by triangulation ::

The quadrant of the earth was divided in two areas for the measurement processes. Delambre was responsible for the north area, from Dunkirk to Rodez, and Méchain was in charge of the South area, from Rodez to Barcelona.

The two astronomers used the triangulation process, whose principle is:
• On the strip of area in which you have to measure the quadrant, you choose on the east and on the west of the quadrant a certain number of points - for example steeples - that are visible from one another at least in threes; these points make a network of triangles that cover the quadrant;
• from each triangle top, you measure the viewing angles on the other tops, which definites all triangles by its angles;
• you choose in the network a "base" that you measure directly. It corresponds to one of the triangles side and is a roughly horizontal ground, whose length is nearly ten kilometers;
• You measure one of the triangles side azimuth thanks to astronomic view, the azimuth being the angle the side produces with the meridian, which makes possible a network orientation. Then you measure the latitude of the two ends of the quadrant, which determines its amplitude.
• the triangulation enables a step by step calculation from the base of the length of the triangles sides and from their projections over the meridian at sea level. In other words, it is the quadrant length from which you deduct the quarter of meridian length.

Delambre and Méchain used a tool named "repeating circle" to measure angles. This instrument was developped by Borda and Lenoir, and it makes possible a one second of an arc accuracy.

Repeating circle
(Paris, Conservatoire National des Arts et Métiers)

The initial base, which is nearly 6,000 toises (11.7 km), was measured near Melun; as an ascertaining, a second base was measured in Perpignan.

For these measures, Delambre and Laplace used "Borda rulers" made by Lenoir and adapted to the Toise de l'Académie; each twelve-foot ruler was a couple of two shafts, one platinum-made and the other brass-made, placed one upon the other. They were united by one of their ends, and ended by verniers, which could accurately take into account the expansion due to temperature. They were successively transferred in a straight line all along the base.

This thorough work, which was done in a revolutionary period, was interrupted by numerous incidents such as equipment breakings or destruction, arrests, etc. Although it started in June 1792, it was only finished in the late 1798.

Scientists also had to take into account the flattening-out of the earth ellipsoid to get the final result. For this purpose, they used the information garnered when measuring the quadrant on the equator from 1735 to 1744.

The distance value from the North pole to the equator was reckoned to be 5,130,740 toises - the value that was used for the determination of the provisional metre was 5,132,430 toises.

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