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Charles François Sturm’s Writings on Optics

  • Eisso J. Atzema

Abstract

Sturm’s writings on geometrical optics consist of only four papers in all, their publication evenly spread over the span of his career. The first two, published in 1824 and 1826, discuss the theory of plane caustics. The third paper, an extension of his work on plane caustics to spatial caustics was published in 1838. Finally, a paper on the physiology of the eye appeared in 1845. It is in this paper that Sturm introduces the description of the so-called infinitely thin pencil often associated with his name. The same publication also contains a much simplified derivation of the formulas he had obtained in his third paper. The Royal Society Catalogue of Scientific Papers also lists a publication in English on cylindrical lenses of 1854 among Sturm’s papers. Most likely, however, this note was written by a namesake.1

Keywords

Geometrical Optic Transition Formula Ciliary Muscle Focal Line Physiological Optic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Atzema, Eisso J. The Structure of Systems of Lines in 19th Century Geometrical Optics: Malus’ Theorem and the Description of the Infinitely Thin Pencil (Ph.D. Utrecht, 1993).Google Scholar
  2. [2]
    Atzema, Eisso J. «A Theory of Caustics — The Contribution of Dupin, Quetelet, and Gergonne to Geometrical Optics,» In: A. von Gotstedter (ed.), Ad Radices. IGN Jubiläumsband (Steiner Verlag Stuttgart. 1995), pp. 331–354.Google Scholar
  3. [3]
    Bertrand, Joseph «Mémoire sur ia théorie des surfaces,» Journal de mathématiques pures et appliquées (1) 9 (1844), pp. 133–154.Google Scholar
  4. [4]
    Bösser, Ferdinand Die Theorie der caustischen Linien und Flächen in ihrer geschichtlichen Erdwickelung (Inaug.-Dissertation Kiel, 1869) (= Zeitschrift für Mathematik und Physik (1) 15 (1870), pp. 170–206).Google Scholar
  5. [5]
    Chappert, André Etienne Louis Malus (1775–1812) et la Théorie Corpusculaire de la Lumière (Paris, 1977).Google Scholar
  6. [6]
    Crahey, Jacques-Guillaume «Notice sur une nouvelle théorie de la vision,» Bulle-Un de l’Académie Royale des Sciences et Belles-Lettres de Bruxelles 12(2) (1845), pp. 311–318.Google Scholar
  7. [7]
    Donders, Franciscus Cornells On the Anomalies of Accommodation and Refraction of the Eye. With a Preliminary Essay on Physiological Dioptrics (London: 1864).Google Scholar
  8. [8]
    Dupin, Charles «Sur les routes suivis par la lumière (...) dans les phénomènes de la réflexion et de ia réfraction.» In: Applications de géométrie et de méchanique (Paris, 1822), pp. 187–245.Google Scholar
  9. [9]
    Elfving, Gustav The History of Mathematics in Finland, 1828–1918 (Helsinki, 1981).Google Scholar
  10. [10]
    Fick, Adolf De errore optico quadam asymmetria bulbi oculi effecto (Inaug.-diss. Marburg, 1851).Google Scholar
  11. [11]
    Gauss, Carl Friedrich «Dioptrische Untersuchungen,» Abhandlungen der königlichen Gesellschaft der Wisenschaften zu Göttingen 1 (1841), pp. 1–34.Google Scholar
  12. [12]
    Gergonne, Joseph-Dies «De la multiplicité des images d’un même objet, consideré à travers une glace posée obliquement, ou refléchi par un miroir plan, non métallique,» Annales des mathématiques pures et appliquées 5 (1814–5), pp. 283–295.Google Scholar
  13. [13]
    Gergonne, Joseph-Diez «Recherches de dioptrique, renfermant la solution du dernier des deux problèmes proposés à la page 288 du Xième volume de ce recueil,» Annales des mathématiques pures et appliquées 11 (1820–1), pp. 229–269.Google Scholar
  14. [14]
    Gergonne, Joseph-Diez «Recherches d’analise sur les caustiques planes,» Annales des mathématiques pures et appliquées 15 (1824–5), pp. 345–358.Google Scholar
  15. [15]
    Hachette, Jean «Moyen de construire par points ies caustiques,» Correspondance sur l’Ecole Polytechnique 4 (1812), 2 (Juillet), pp. 353–358.Google Scholar
  16. [16]
    Hamilton, William Rowan «Sur l’emploi d’une formule générale propre à. résoudre ies différentes questions d’optique.» In: Herschel, De La Lumière (Bruxelles, 1829–31), 2, pp. 456–468.Google Scholar
  17. [17]
    Hamilton, William Rowan «Sur une méthode générale pour exprimer ies trajectoires de la lumière et des planètes, au moyen des coefficiens d’une fonction charactéristique,» Correspondance Mathématique et Physique, 8 (1834), pp.69–89, 200–11, 256.Google Scholar
  18. [18]
    Hankins, Thomas Sir William Rowan Hamilton (Baltimore: Johns Hopkins U. P., 1980).MATHGoogle Scholar
  19. [19]
    Helmholtz, Hermann Handbuch der physiologischen Optik (Leipzig: Voss, 1857–1867).Google Scholar
  20. [20]
    Herschel, John «Treatise on Light,» in: Smedley, E. (ed.) Encyclopedia Metropolitana (London, 1827), pp. 341–586.Google Scholar
  21. [21]
    Herzberger, Max Modern Geometrical Optics (New York, 1958).Google Scholar
  22. [22]
    Knapp, Hermann «Ueber die Asymmetrie des Auges in seinen verschiedenen Meridianebenen,» Archiv für Ophthalmologie 8 (1862), pp. 185–241.CrossRefGoogle Scholar
  23. [23]
    Levene, John «Sir George Bidell Airy, F. R. S. (1801–1892) and the Discovery and Correction of Astigmatism,» Notes and Records of the Royal Society of London 21 (1966), pp. 180–199.CrossRefGoogle Scholar
  24. [24]
    Mareska, Daniel «responsio ad questionem ab ordine nobillisimo mathematicarum disciplinarum in academia gandavensi propositam, Investigationes mere mathematicas de causticis per reflexionem et refractionem a tempore Tschirnhausen usque ad nostram aetatem factas enarrari.» Annales Academiae Gandavensis (1824–5) s. p.Google Scholar
  25. [25]
    Maxwell, James Clerk «On the focal lines of a refracted pencil,» Proceedings of the London Mathematical Society (1) 4 (1871–1873), pp. 337–341.CrossRefGoogle Scholar
  26. [26]
    Maxwell, James Clerk «On Hamilton’s characteristic function for a. narrow beam of light,» Proceedings of the London Mathematical Society (1) 6 (1873–1875), pp. 182–190.CrossRefGoogle Scholar
  27. [27]
    Möbins, August Ferdinand «Kurse Darstellung der Haupteigenschaften eines Systems von Linsengläsern,» Journal für die reine und angewandte Mathematik, 5 (1829), pp. 113–132.Google Scholar
  28. [28]
    Möbius, August Ferdinand «Beiträge zu der Lehre von den Kettenbrüchen nebst einem Anhange dioptrischen Inhalts,» Journal für reine und angewandte Mathematik 5 (1829), pp. 113–132.Google Scholar
  29. [29]
    Möbius, August Ferdinand «Geometrische Entwickelungen der Eigenschaften unendlich dünner Strahlenbündel,» Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Mathematisch-physische Classe 14 (1862), pp. 1–16.Google Scholar
  30. [30]
    Neumann, Carl «Ueber die Brechung eines unendlich dünnen regulären Strahlen-bündels,» Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Mathematisch-physische Classe 32 (1880), pp. 42–64.Google Scholar
  31. [31]
    Prange, Georg «W-R. Hamiltons Arbeiten zur Strahlenoptik und analytischen Mechanik.» Nova. Acta Leopoldina 107 (1923), 1.Google Scholar
  32. [32]
    Prentice, Charles F. Dioptric Formulae for Combined Cylindrical Lenses (...) (New York, 1888).Google Scholar
  33. [33]
    Rive, Auguste de la. Dissertation sur la partie de l’optique qui traite des courbes dites caustiques (Genève, 1823).Google Scholar
  34. [34]
    Sampson, Ralph Allen «A Continuation of Gauss's Dioptrische UntersuchungenProceedings of the London Mathematical Society 29 (1898), pp. 33–83.CrossRefGoogle Scholar
  35. [35]
    Turner, R. Stephen «Paradigms and Productivity: The Case of Physiological Optics, 1840–1894» Social Studies of Science 17 (1987), pp. 35–68.CrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Eisso J. Atzema
    • 1
  1. 1.Dept. of MathematicsUniversity of MaineOronoUSA

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