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.