Extrait of a [second] memoir on double refraction

References (22)

1. Académie des Sciences, Procès-verbaux des séances de l'Académie tenues depuis la fondation de l'Institut jusqu'au mois d'août 1835, vol. 7 (for 1820-23), Hendaye, Basses Pyrénées: Imprimerie de l'Observatoire d'Abbadia, 1916.
2. J.-B. Biot, "Extrait d'un Mémoire sur les lois de la double réfraction et de la polarisation dans les corps régulièrement cristallisés" ("Extrait of a Memoir on the laws of double refraction and of polarization in regularly crystallized bodies"; memoir read 29 March 1819), Bulletin des Sciences par la Société Philomatique de Paris, vol. 7, pp. 12-16 (1820); archive.org/details/bulletindesscien79plas/page/n23. This paragraph and the next do not seem to have any parallels in the First Memoir and Supplements, but reappear with only small changes in the Second Memoir [11, p.330].
3. In the Second Memoir [11, p. 330], Fresnel deletes "for example", leaving only one version of the hypothesis, which is indeed the one refuted by his next argument. Huygens supposed the existence of "two different kinds of matter which serve for the two species of refraction" [15, p.94], but then could not explain to his own satisfaction why one ray (ordinary or extraordinary) emerging from one crystal could move either kind or both kinds of matter in a second crystal, according to the relative orientations of the crystals [15, pp. 92-4]. That is, in optically isotropic media. Second Supplement to the First Memoir [12, vol. 2, pp. 379-83], and Second Memoir [11, pp. 299-300]; cf. [13, p.892].
4. First Memoir [12, vol. 2, pp. 287-9], First Supplement [12, vol. 2, pp. 353-5], and Second Memoir [11, pp. 288-91];
5. Literally "crystal of rock". Fresnel's memoir on the circular birefringence of quartz is now available in English [10].
6. Second Supplement to the First Memoir [12, vol. 2, pp. 370, 379]; cf. Second Memoir [11, p.273].
7. D. Brewster, "On the laws of polarisation and double refraction in regularly crystallized bodies" (read 15 Jan. 1818), Philosophical Transactions of the Royal Society, vol. 108 (1818), pp. 199-273; rstl.royalsocietypublishing.org/content/108/199.
8. J. Z. Buchwald, The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century, University of Chicago Press, 1989.
9. O. Darrigol, A History of Optics: From Greek Antiquity to the Nineteenth Century, Oxford, 2012.
10. A. Fresnel, "Note sur le calcul des teintes que la polarisation développe dans les lames cristallisées" et seq., Annales de Chimie et de Physique, Ser. 2, vol. 17, pp. 102-11 (May 1821), 167-96 (June 1821), 312-15 ("Postscript", July 1821); reprinted (adding section nos.) in [12], vol. 1, pp. 609-48; translated by G.R. Putland as "On the calculation of the tints that polarization develops in crystalline plates, & postscript", doi.org/10.5281/zenodo.4058004 (2021).
11. A. Fresnel, Letter to D.F. J. Arago, 21 September 1821, in [12], vol. 2, pp. 257-9; translated by G.R. Putland as "Letter to Arago on biaxial birefringence", en.wikisource.org/wiki/Translation:Letter_to_Arago_on_biaxial_birefringence (2021).
12. A. Fresnel, "Extrait du Supplément au Mémoire sur la double réfraction" (read 13 Jan. 1822?), printed in [12], vol. 2, pp. 335-42; translated by G.R. Putland as "Extrait of the Supplement to the Memoir on double refraction", doi.org/10.5281/zenodo.5886692 (2022).
13. A. Fresnel, "Extrait d'un Mémoire sur la double réfraction", Bulletin des Sciences par la Société Philomatique de Paris, vol. 9, pp. 63-71 (May 1822); archive.org/details/bulletindesscien79plas/page/63.
14. A. Fresnel, "Mémoire sur la double réfraction que les rayons lumineux éprouvent en traversant les aiguilles de cristal de roche suivant les directions parallèles à l'axe", read 9 Dec. 1822; in [12], vol. 1, pp. 731-51; translated by G.R. Putland as "Memoir on the double refraction that light rays undergo in traversing the needles of quartz in the directions parallel to the axis", doi.org/10.5281/zenodo.4745976 (2021).
15. A. Fresnel, "Mémoire sur la double réfraction", Mémoires de l'Académie Royale des Sciences de l'Institut de France, vol. VII (nominally for 1824, printed 1827), pp. 45-176; reprinted as "Second mémoire..." in [12], vol. 2, pp. 479-596; translated by A.W. Hobson as "Memoir on double refraction" in R. Taylor (ed.), Scientific Memoirs, vol. V (London: Taylor & Francis, 1852), pp. 238-333, archive.org/details/scientificmemoir05memo/page/238. Cited page numbers are from the translation. For notable errata in the original printing, and consequently in the translation, see [12], vol. 2, p.596 .
16. A. Fresnel (ed. H. de Sénarmont, E. Verdet, & L. Fresnel), Oeuvres complètes d'Augustin Fresnel (3 vols.), Paris: Imprimerie Impériale, 1866, 1868, 1870.
17. I. Grattan-Guinness, Convolutions in French Mathematics, 1800-1840, Basel: Birkhäuser, 1990, vol. 2, chapter 13 (pp. 852-915, "The entry of Fresnel: Physical optics, 1815-1824").
18. W. R. Hamilton, "Third supplement to an essay on the theory of systems of rays", Transactions of the Royal Irish Academy, vol. 17, pp. v-x, 1-144, read 23 Jan. and 22 Oct., 1832 (author's introduction dated June 1833; volume started 1831, completed 1837); jstor.org/stable/30078785.
19. C. Huygens, Traité de la Lumière (Leiden: Van der Aa, 1690), tr. by S.P. Thompson as Treatise on Light, University of Chicago Press, 1912; Project Gutenberg, 2005, gutenberg.org/ebooks/14725. Cited page numbers match the Chicago edition and the Gutenberg HTML edition. See also "Errata in various editions of Huygens' Treatise on Light" at www.grputland.com or grputland.blogspot.com, June 2016.
20. H. Lloyd, "Report on the progress and present state of physical optics", Report of the Fourth Meeting of the British Association for the Advancement of Science (Edinburgh, 1834), London: J. Murray, 1835, pp. 295-413; books.google.com/books?id=mtU4AAAAMAAJ&pg=PA295.
21. J. MacCullagh, "On the double refraction of light in a crystallized medium, according to the principles of Fresnel", Transactions of the Royal Irish Academy, vol. 16 (1830), pp. 65-78; jstor.org/stable/30079025.
22. G.R. Putland, Wave Foundations of Ray Optics, doi.org/10.5281/zenodo.3901935, 2021 (in progress).