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
“Remarks on the Construction of Telescopes with Simple Cylindrical Glasses,“ Monthly Notices of the Astronomical Society, XV (1854–1855), pp. 223–4. The note was communicated by John Lee, future president of the Society. It discusses a lens grinding machine patented by the author, who is only referred to as Mr. Sturm. According to information provided by the patent office at the British Library, one Salomon Sturm of London, «formerly of Vienna, in the Kingdom of Austria.» applied for a patent of such a machine on November 11, 1853. The patent was granted on April 11th, 1854.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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).
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.
Bertrand, Joseph «Mémoire sur ia théorie des surfaces,» Journal de mathématiques pures et appliquées (1) 9 (1844), pp. 133–154.
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).
Chappert, André Etienne Louis Malus (1775–1812) et la Théorie Corpusculaire de la Lumière (Paris, 1977).
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.
Donders, Franciscus Cornells On the Anomalies of Accommodation and Refraction of the Eye. With a Preliminary Essay on Physiological Dioptrics (London: 1864).
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.
Elfving, Gustav The History of Mathematics in Finland, 1828–1918 (Helsinki, 1981).
Fick, Adolf De errore optico quadam asymmetria bulbi oculi effecto (Inaug.-diss. Marburg, 1851).
Gauss, Carl Friedrich «Dioptrische Untersuchungen,» Abhandlungen der königlichen Gesellschaft der Wisenschaften zu Göttingen 1 (1841), pp. 1–34.
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.
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.
Gergonne, Joseph-Diez «Recherches d’analise sur les caustiques planes,» Annales des mathématiques pures et appliquées 15 (1824–5), pp. 345–358.
Hachette, Jean «Moyen de construire par points ies caustiques,» Correspondance sur l’Ecole Polytechnique 4 (1812), 2 (Juillet), pp. 353–358.
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.
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.
Hankins, Thomas Sir William Rowan Hamilton (Baltimore: Johns Hopkins U. P., 1980).
Helmholtz, Hermann Handbuch der physiologischen Optik (Leipzig: Voss, 1857–1867).
Herschel, John «Treatise on Light,» in: Smedley, E. (ed.) Encyclopedia Metropolitana (London, 1827), pp. 341–586.
Herzberger, Max Modern Geometrical Optics (New York, 1958).
Knapp, Hermann «Ueber die Asymmetrie des Auges in seinen verschiedenen Meridianebenen,» Archiv für Ophthalmologie 8 (1862), pp. 185–241.
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.
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.
Maxwell, James Clerk «On the focal lines of a refracted pencil,» Proceedings of the London Mathematical Society (1) 4 (1871–1873), pp. 337–341.
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.
Möbins, August Ferdinand «Kurse Darstellung der Haupteigenschaften eines Systems von Linsengläsern,» Journal für die reine und angewandte Mathematik, 5 (1829), pp. 113–132.
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.
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.
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.
Prange, Georg «W-R. Hamiltons Arbeiten zur Strahlenoptik und analytischen Mechanik.» Nova. Acta Leopoldina 107 (1923), 1.
Prentice, Charles F. Dioptric Formulae for Combined Cylindrical Lenses (...) (New York, 1888).
Rive, Auguste de la. Dissertation sur la partie de l’optique qui traite des courbes dites caustiques (Genève, 1823).
Sampson, Ralph Allen «A Continuation of Gauss's Dioptrische Untersuchungen.» Proceedings of the London Mathematical Society 29 (1898), pp. 33–83.
Turner, R. Stephen «Paradigms and Productivity: The Case of Physiological Optics, 1840–1894» Social Studies of Science 17 (1987), pp. 35–68.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Birkhäuser Verlag Basel/Switzerland
About this chapter
Cite this chapter
Atzema, E.J. (2009). Charles François Sturm’s Writings on Optics. In: Pont, JC. (eds) Collected Works of Charles François Sturm. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7990-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-7643-7990-2_4
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7989-6
Online ISBN: 978-3-7643-7990-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)