Abstract
Rotating mirror and its mechanism built by Louis Breguet in 1844 for Arago. After a few modifications, it was used by Fizeau in 1850 for the comparison of the velocity of light in air and in water. Bibliothèque de l’Observatoire de Paris
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Notes
- 1.
Daumas (1987) p. 77–78; first edition in 1943.
- 2.
See for this e.g. Eisenstaedt (2005).
- 3.
Philosophical transactions (1728) 35, p. 637–661, accessible via http://www.jstor.org/stable/view/103725
- 4.
Philosophical transactions (1784) 74, p. 35–57, accessible as http://www.jstor.org/stable/106576; see p. 50. I cannot resist the pleasure to reproduce the full title: “On the Means of discovering the Distance, Magnitude, etc. of the fixed Stars, in consequence of the diminution of the Velocity of their Light, in case such a diminution should be found to take place in any of them, and such other Data should be procured from Observations, as would be farther necessary for that Purpose.”
- 5.
Such objects really exist, but their properties are quite different from those imagined by Michell: these are the black holes. The reason why light does not escape from them is due to their high gravitation, but this is a general relativity effect: the space-time is locally very deformed, the velocity of light is unchanged but its redshift is infinite. As far as “normal” stars are concerned, the effect of gravitation on light is generally small, even for the very compact white dwarf stars: for them, the gravitational redshift is conspicuous, but the velocity of light is unchanged.
- 6.
John Dollond (1706–1761) in 1757 built the first achromatic objectives for telescopes, by associating a converging lens of crown glass with a diverging lens of flint glass. He also built achromatic prisms (see Fig. 4.2).
- 7.
*Comptes rendus (1853) 36, p. 38–49; *Arago, F. Œuvres complètes t. 7, p. 548–568.
- 8.
A possible path from Michell to Arago, via Blair and Robison, is described by Eisenstaedt (2005). Robert Blair (1748–1828) had built a series of 12 achromatic prisms to make the observations, but this project did not succeed because of excessive absorption of light and insufficient correction for dispersion by the prisms.
- 9.
One often attributes to Laplace the idea that the gravitational field of some stars could slow or stop their light, a prefiguration of the black holes. But the idea is Michell’s; Laplace, who rarely cited his sources, had perhaps borrowed it from him.
- 10.
Fourth edition (1813), p. 326. Laplace concludes: “Would not it be possible to suppose that luminous bodies send an infinity of rays with different velocities, and that the only ones whose velocity is comprised between certain limits have the property to excite the sensation of light, while the others only produced an obscure heat.”
- 11.
*Arago, F. Œuvres complètes, t. 1, p. I–XXXII, see p. VI.
- 12.
*Annales de chimie et de physique (1818) 9, p. 57–66, also Fresnel (1866, 1868, 1870) t. 1, p. 627–636.
- 13.
*La vie des sciences (1989) 6, p. 327–334. Mascart (1889–1893) t. 3, chap. 15, criticizes the demonstration by Fresnel and gives another one that is not more satisfying.
- 14.
For a detailed scientific biography of Fizeau, see Lequeux (2014).
- 15.
*Comptes rendus (1851) 33 p. 349–355.
- 16.
There is a fundamental difference between the observation of Arago and of Fizeau’s experiment. In the latter, the refringent medium moves with respect to the observer, while this is not the case in the former.
- 17.
Michelson, A.A. & Morley, E.W. (1886) American journal of science 31, p. 377–86, accessible by http://en.wikisource.org/wiki/Influence_of_Motion_of_the_Medium_on_the_Velocity_of_Light
- 18.
Mascart, E. (1874) Annales scientifiques de l’École Normale Supérieure. 2e série, 3, p. 363–420, see p. 420. Accessible by http://archive.numdam.org
- 19.
This experiment seemed initially to yield a positive result, but the hopes failed after some time.
- 20.
Mascart (1889–1893) see t. 3, p. 114.
- 21.
Actually a slightly lower velocity than c because the prisms were in air. But this velocity still did not depend on the source and its motion.
- 22.
This demonstration was first published by Max von Laue (1879–1960) 2 years after Einstein’s fundamental paper: von Laue, M. (1907) Annalen der Physik 23, p. 989–90. English translation in http://en.wikisource.org/wiki/Translation:The_Entrainment_of_Light_by_Moving_Bodies_in_Accordance_with_the_Principle_of_Relativity
- 23.
See *Comptes rendus (1839) 8, p. 259–272 and 315–327.
- 24.
- 25.
Wheatstone, C. (1834) Philosophical transactions 124, p. 583–591, accessible as http://www.jstor.org/stable/108080
- 26.
This velocity is that of propagation of a disturbance in an electric circuit, not that of electrons in the conductor. It depends on the properties in the environment of the conductor. Fizeau and Gounelle (1850, Comptes rendus 30, p. 437–440) measured more reasonable velocities of 100,000 and 180,000 km/s in long telegraphic lines.
- 27.
*Comptes rendus (1850) 30, p. 489–495; also *Arago, F., Œuvres complètes t. 7, p. 569–599.
- 28.
*Foucault, L. (1850) Comptes rendus 30, p. 551–60.
- 29.
*Fizeau, H. & Breguet, L. (1850) Comptes rendus 30, p. 771–4.
- 30.
See note 27.
- 31.
Lissajous, Notice historique …, in Foucault (1878), vol. Plates, p. 1–18, see p. 5.
- 32.
Galileo Galilei (1638) Discorsi e dimostrazioni matematiche intorno à due nuove scienze, Leiden, Elsevier, English translation in http://oll.libertyfund.org/titles/753, see p. 48 of the Ebook PDF version.
- 33.
This is a complex story, reported in detail by Bobis & Lequeux (2008) Journal of astronomical history and heritage 11, p. 97–105, available freely via http://cdsads.u-strasbg.fr
- 34.
*Journal des sçavans, (1676) p. 233–236. Poor and arranged translation in English in Philosophical transactions (1677) 12, p. 893–894, accessible via http://www.jstor.org/stable/101779
- 35.
Many physics treatises, even famous ones, give values of the velocity of light that they attribute to Rømer but are different from each other, and they often give wrong dates for the discovery of the finite nature of this velocity; see Wroblewski (1985) American Journal of Physics 53, p. 620–630.
- 36.
Delambre (1817) Tables écliptiques des Satellites de Jupiter d’après la Théorie de M le Marquis de Laplace, et la totalité des observations faites depuis 1662 jusqu’à l’an 1802, Paris, Courcier.
- 37.
*Comptes rendus (1849) 29, p. 90–92. The original apparatus has disappeared because Fizeau used some of its elements for other experiments. A replica can be seen in the museum of the École Polytechnique. For a detailed analysis of the experiment, see Frercks J. (2000) Centaurus 42, p. 249–287, accessible freely via http://onlinelibrary.wiley.com/doi/10.1034/j.1600-0498.2000.420401.x/abstract
- 38.
The metric system was not yet fully used in practice, even by scientists, half a century after its promulgation, although its use was declared compulsory in 1840.
- 39.
Mainly from Tobin, W. (1993) Vistas in Astronomy 36, p. 253–294 and Tobin (2003).
- 40.
*Le Verrier (1858) Annales de l’Observatoire de Paris—Mémoires 4, p. 1–262.
- 41.
*Foucault, L. (1850) Comptes rendus 30, p. 551–60.
- 42.
It was one of the first times a physicist gave the uncertainty on his measurement.
- 43.
Cornu’s results are detailed in a very long Memoir: Annales de l’Observatoire de Paris-Mémoires (1876) 13, p. 1–317, accessible via http://adsabs.harvard.edu/historical.html
- 44.
For a history of these measurements, which caused a controversy between Cornu and Perrotin, see Bogaert, G. & Blanc, W. (2011) Reflets de la Physique n 26, p. 20–22 accessible as http://www.refletsdelaphysique.fr/articles/refdp/pdf/2011/04/refdp201126p20.pdf
References
Daumas, M. (1987) Arago, La jeunesse de la science, 2e édition, Paris, Belin, Collection Un savant, une époque.
Foucault, L. (1878) Recueil des travaux scientifiques de Léon Foucault, ed. par Gariel C.-M., Gauthier-Villars, Paris, accessible via http://jubilotheque.upmc.fr/ead.html?id=PC_000326_001.
Fresnel, A. (1866, 1868, 1870) Œuvres complètes d’Augustin Fresnel, publiées par MM. Henri de Senarmont, Verdet et Léonor Fresnel, Paris, Imprimerie impériale, 3 tomes. T. 1 accessible via Google books, t. 2 by Gallica.
*Mascart, E. (1889-1893) Traité d’Optique, 3 t., Gauthier-Villars, Paris.
Eisenstaedt; J. (2005) Avant Einstein: Relativité, lumière, gravitation, Ed. du Seuil, Paris.
Lequeux, J., (2014) Hippolyte Fizeau, physicien de la lumière, EDP Sciences, Les Ulis.
Tobin, W. (2003) The Life and Science of Léon Foucault, Cambridge University Press.
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Lequeux, J. (2016). The Velocity of Light. In: François Arago. Astrophysics and Space Science Library, vol 421. Springer, Cham. https://doi.org/10.1007/978-3-319-20723-0_4
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