Abstract
Biot and Arago’s triangulation in Spain. Bibliothèque de l’Observatoire de Paris
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Notes
- 1.
In France, the lengths were measured in toises of approximately 1.95 m. The toise was divided into 6 pieds of 12 pouces each. The French pouce, of 27.07 mm, is larger than the inch of 25.4 mm.
- 2.
*Cassini de Thury (1740) Suite des Mémoires de l’Académie royale des sciences, published in 1744.
- 3.
The theodolite was well developed in England, but appeared only slowly in France. The first French one was built by Étienne Lenoir around 1800, with a single, horizontal graduated circle. Theodolites with two perpendicular circles, which allowed the measurement of azimuths and elevations, were constructed later by Gambey. They very progressively replaced the repeating circles, which wore down rapidly because of the large number of rotations they experienced.
- 4.
It was also foreseen that the meter would have been the length of a seconds pendulum at 45° latitude; but this idea was not retained because of the difficulties of practical realization.
- 5.
- 6.
The rulers are preserved at the Paris Observatory. Two of the circles are at the Marseilles observatory and at the National Geographic Institute at Saint-Mandé, near Paris.
- 7.
Laplace, who made the first mathematical estimates of measurement errors, considered that the altitude of Paris obtained during the operations of Delambre had a probable error of 8 m.
- 8.
There are 864 lignes in a toise, so that the length of the toise was 1.94904 m.
- 9.
*Connaissance des temps for 1816, p. 345–358. See also *Biot (1843) Comptes rendus 16, 1019–1032.
- 10.
Nicollet was not well respected by Arago. He was ruined by hazardous speculations and emigrated in 1830 to the United States.
- 11.
Bibliothèque universelle de Genève (1828) 38, p. 165–179 and 250–263, accessible via Google books.
- 12.
*Arago, F., Œuvres complètes t. 11, p. 115–137 and 138–139.
- 13.
* Arago, F., Œuvres complètes, t.11, p. 55–114.
- 14.
The measurements had to be done by night, with light signals produced by oil lamps at the focus of parabolic mirrors. Coordination must have been a problem, due to the slowness of communications.
- 15.
* Arago, F., Œuvres complètes t. 1, p. 1–102.
- 16.
Biot and Arago were virtuosos of the repeating circle. They succeeded in making more than 100 measurements of the zenith distance of a star in 1 h, while Cassini IV could make only 10 in 12 min.
- 17.
*Connaissance des temps for 1822, p. 346–348.
- 18.
*Connaissance des temps for 1810, p. 485–488; also *Annuaire du Bureau des longitudes for 1809, p. 81–87.
- 19.
*Comptes rendus (1836) 3, p. 428–433, 450–453 and 483–486, and *Connaissance des temps for 1844, supplément, p. 123–131.
- 20.
See *Arago, F., Œuvres complètes 3, p. 603.
- 21.
Philosophical transactions (1828) 118, p. 153–239, accessible via http://www.jstor.org/stable/107842: see p. 192.
- 22.
Bigourdan (1928–1932, see 1932) p. A65–A66, and following him Levallois (1988) p. 131 write that the results of the operations, given to captain Ketter (in fact Kater) were lost after his death “soon after” the end of these operations. We know that this is not true.
- 23.
Philosophical Transactions (1826) 116, p. 77–126, accessible via http://www.jstor.org/stable/107803
- 24.
The complex operations are described in detail in *Picard (1684), p. 140–175.
References
*Méchain, P.F.A. & Delambre, J.B.J. (1806-1810) Base du Système métrique décimal, ou mesure de l’arc du méridien compris entre les parallèles de Dunkerque et Barcelone, exécutée en 1792 et années suivantes, 3 vol., Baudouin [Paris].
*Picard, J. (1684) Traité du Nivellement, Michallet, Paris.
Adler, K. (2002) The Measure of all Things. The seven-year odyssey and hidden error that transformed the world, Free Press, New York.
Guedj, D. (2001) The Measure of the World: a novel, University of Chicago Press.
Levallois, J.-J. (1988) Mesurer la Terre – 300 ans de géodésie française, École des Ponts et Chaussées/Association Française de Topographie, Paris.
Murdin, P. (2009) Full Meridian of Glory: Perilous Adventures in the Competition to Measure the Earth, Springer, New York.
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Lequeux, J. (2016). Measuring the Earth. In: François Arago. Astrophysics and Space Science Library, vol 421. Springer, Cham. https://doi.org/10.1007/978-3-319-20723-0_6
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