The Bélidor Bascule Bridge Design

Notes

• Deakin M, Fraser D, ‘Curved-tracked Bascule Bridges in New South Wales and their Relationship to the Cardioid’, Transactions of Multi-Disciplinary Engineering, GE18(2) (1994), 163–71; M. Deakin, ‘Henry Harvey Dare and the New South Wales cardioids’, Australian Mathematical Society Gazette 22(5) (1995), pp. 232–241.
   Google Scholar
• l’Hôpital G, Solutio problematis physicomathematicii ab erudition quodam geometra propositi’, Acta Eruditorum Lipsius. Reprinted in Johann I Bernoulli’s Opera Omnia 1, (Lausanne: Bosquet & Sociorum, 1742) (1695), pp. 129–131.
   Google Scholar
• Bernoulli J, l’Hôpital G, Correspondence. Briefwechsel von Johann I Bernoulli 1, (Basel: Birkhäuser, 1988) (1694), p. 244–257. J. Bernoulli, ‘Animadversi Præcendentum Solutionem Illustris Marchionis Hospitalii; Demonstratio identitatis curvæ equilibrationis sum Cycloide descripta ex circumductione rota super rota æquali’, Acta Eruditorum Lipsius 25 (1695). Reprinted in Johann I. Bernoulli’s Opera Omnia 1, (Lausanne: Bosquet & Sociorum, 1742), pp. 132–8.
   Google Scholar
• de Bélidor B, La Science des Ingénieurs dans la Conduite des Travaux de Fortification et d’Architecture Civile, Jombert, Paris (1729). Subsequent editions with notes by C.L.M.H. Navier (Paris, Didot, 1813 and 1830).
   Google Scholar
• Bernoulli.
   Google Scholar
• Varignon P, Letter to Johann I. Bernoulli. Briefwechsel von Johann I Bernoulli 2, (Basel: Birkhäuser, 1988), (1695), pp. 84–90.
   Google Scholar
• Scarambone L, Intorno a’ Ponti Levatoi delle Piazze di Guerra, Reale Tipografia della Guerra, Napoli (1839), M. Cundy, The bascule bridge — an unexpected cardioid, Mathematical Gazette 74 (1990), pp. 124–7, O.E. Hovey, Movable Bridges, Vol. 1: Superstructure (New York: Wiley, 1926).
   Google Scholar
• l’Hôpital.
   Google Scholar
• Ibid.
   Google Scholar
• Treitz K, Apfelmännchen auf dem Königstein, Mathematik in der Schule 37 (1999), pp.30–33. Edited English translation, Function — A School Mathematics Magazine 25 (2001), pp. 134–140.
   Google Scholar
• Fraser D, Deakin M, Curved track bascule bridges: From castle drawbridge to modern applications, in Proceedings of the 7th Historic Bridges Conference (Cleveland: Watson Bridge Book Collection, 2001), pp. 28–36.
   Google Scholar
• Williams M, ‘The coasts of Corsica’, National Geographic 44(3) (1923), pp. 221–312. See especially p. 307.
   Google Scholar
• Treitz.
   Google Scholar
• Ferrara A, Analisi di ponti basculanti di tipo ‘Bélidor’, Tesi di Laurea [Master’s thesis], Politecnico di Torino (2010).
   Google Scholar
• Deakin and Fraser (1994) and Deakin (1995).
   Google Scholar
• Deakin and Fraser.
   Google Scholar
• Glimmer Glass Bridge 2011, http://en. wikipedia.org/wiki/Glimmer_Glass_Bridge
   Google Scholar
• Fraser and Deakin.
   Google Scholar
• Bernoulli; de Bélidor, see the title of his book.
   Google Scholar
• Ferrara.
   Google Scholar
• Fort of Exilles 2011. http://www.fortediexilles. it/
   Google Scholar
• Fort l’Écluse 2011a. http://www.cc-pays-de-gex.fr/fortlecluse/-Francais-.h%tml; Fort l’Écluse 2011b. http://en.wikipedia.org/wiki/Fort_l\%27Ecluse.
   Google Scholar
• Fort Marie Christine. http://www.fort-marie christine.com/
   Google Scholar
• Fraser D, ‘Darlington Point bridge reconstruction’, Proc. 5th Nat. Conf. on Engineering Heritage, Institution of Engineers, Aust. (1990), pp. 81–7.
   Google Scholar
• For more details on the Australian bridges and these American ones, see Deakin and Fraser (1994), and Fraser and Deakin.
   Google Scholar
• Dare HH, ‘Recent Road-Bridge Practice in New South Wales’, Min. Proc. Inst. C. Eng., 155 (1904), 382–400 and pls 2–4; reproduced in edited form by L. Coltheart and D. Fraser, Landmarks in Public Works (Sydney: Hale and Ironmonger, 1987), pp. 62–70.
   Google Scholar
• From Deakin and Fraser (2001).
   Google Scholar
• Anon., ‘The Morison Lift Bridge over the Chicago River’, Railroad Gazette, 31 (2 June 1899), 382–83.
   Google Scholar
• Railroad Gazette, 28 (27 November 1896), 819–22; Scientific American, 80·22 (28 November 1896); Deakin and Fraser (1994).
   Google Scholar
• Anon., ‘Report on the Buffalo Bridge’, Engineering News, ii (1897), 125; cited by Hovey, pp. 8–9; Anon., ‘The Michigan Avenue Bascule Bridge, Buffalo’, The Engineering Record, 36·12 (21 August 1897), 246–47.
   Google Scholar
• Anon., ‘The Harway Avenue Bascule Bridge’, The Engineering Record, 49·18 (30 April 1904), 562–63.
   Google Scholar
• Anon., ‘Report on the Rhode Island Bridge’, ibid., 57 (29 February 1908), 237, cited by Hovey.
   Google Scholar
• See all the previous references of either or both of Deakin and Fraser.
   Google Scholar
• Glimmer Glass Bridge.
   Google Scholar
• Scientific American lxxv, 28 November 1896.
   Google Scholar
• Bennett Engineering Design Consultants 2011, <http://www.bennettmg.co.uk/Project_ MS_Forton.aspx>. See also the Wikipedia entry: <http://en.wikipedia.org/wiki/File:Forton_ Bridge.jpg>
   Google Scholar
• Cundy.
   Google Scholar
• Fraser and Deakin.
   Google Scholar
• Wikipedia entry: ‘Cardioid’, <http://en. wikipedia.org/wiki/Cardioid>. Eric W. Weisstein, ‘Cardioid’, from MathWorld — A Wolfram Web Resource, <http://mathworld. wolfram.com/Cardioid.html>; E. Lockwood, A Book of Curves (Cambridge University Press, 1961), ch. 4.
   Google Scholar