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The mechanical career of Councillor Orffyreus, confidence man
1. Jorge Luis Borges, “ Ramón Llull's Thinking Machine,” in Borges: Selected Non-Fictions, edited by E. Weinberger (Penguin Books, New York, 1999), pp. 155–159. This essay was originally published in El Hogar, 15 Oct. 1937.
2. Y. I. Perelman, “ The ‘Perpetual Motion’ Machine Peter the Great Wanted to Buy,” in Physics for Entertainment, book 1, 2nd English ed. (Mir, Moscow, 1972 ), pp. 90–94.
3. R. T. Gould, “ Orffyreus' Wheel,” in Oddities: A Book of Unexplained Facts, revised ed. (Geoffrey Bles, London, 1944), pp. 89–116.
4.Gould is principally remembered for his painstaking work restoring and documenting John Harrison's chronometers, which in the 18th century had provided the first practical way to determine the longitude of a ship at sea. He is co-protagonist of the TV adaptation56 of Dava Sobel's bestselling book Longitude.57 Gould was an earnest and hard-working scholar,58 but scientifically informed readers today will probably smile at the credence that he gives in Oddities to accounts of coffins moving inside a sealed vault in a Barbados cemetery, or to the validity of Nostradamus's prophecies.
5. Claude A. Crommelin, “ La Roue d’Orffyreus,” Janus 49(1 ), 47–52 (1960).
7. Simon Werrett, “ The Schumacher Affair: Reconfiguring Academic Expertise across Dynasties in Eighteenth-Century Russia,” Osiris 25(1 ), 104–126 (2010).
8.See Lynn T. White, Jr., “ Tibet, India, and Malaya as Sources of Western Medieval Technology,” in Medieval Religion and Technology: Collected Essays (University of California Press, Berkeley, 1978), pp. 43–57. This is a reprinting of Am. Hist. Rev. 65(3), 515–526 (1960).
9.A detailed account of Stevin's reasoning is given in Ernst Mach, The Science of Mechanics: A Critical and Historical Account of its Development, 6th English ed. (Open Court, La Salle, IL, 1960 ), pp. 32–44.
10.See Ernst Mach, The Science of Mechanics: A Critical and Historical Account of its Development, 6th English ed. (Open Court, La Salle, IL, 1960 ), pp. 162–169.
In 1663, Worcester received a royal patent for a “water commanding engine.” Very little information about that device has survived, but some historians have seen in it the first practical steam engine. See Stephen K. Roberts
, “ Somerset, Edward, second marquess of Worcester (d. 1667)
,” in Oxford Dictionary of National Biography
). Online ed.
May 2006, http://www.oxforddnb.com/view/article/26006
(last accessed 21 Jan. 2013).
12. Edward Somerset, Marquess of Worcester, Century of Inventions, edited by J. Buddle (S. Hodgson, Newcastle, 1813 ), no. LVI.
14.On the debates between Leibniz and the Cartesians, see Carolyn Iltis, “ Leibniz and the Vis Viva Controversy,” Isis 62(1 ), 21–35 (1971).
15.This confusion was due in part to the use, in computing static equilibria, of what is now called the method of “virtual work,” in which only infinitesimal displacements are considered, making the work linear in the velocity of the virtual displacement. Leibniz called such virtual work vis mortua (“dead force”).
17.Leibniz argued that in an inelastic collision the missing vis viva is transferred to the imperceptible motion of the bodies' microscopic components. This is consistent with our current understanding of dissipation, but at the time it was an untestable speculation. Note that momentum conservation follows from Newton's third law of motion, whereas energy conservation requires a further assumption that forces are exact differentials of positions. This last point was later stressed in George B. Airy, “ On certain Conditions under which a Perpetual Motion is possible,” Trans. Cambridge Phil. Soc. 3(2), 369–372 (1830). Airy's argument has recently been revisited in Alejandro Jenkins, “Self-oscillation,” Phys. Rep. 525(2 ), 167–222 (2013).
18. Willem J. ’s Gravesande, “ Remarques touchant le Mouvement perpétuel,” in Œuvres philosophiques et mathématiques de Mr. G. J. ’s Gravesande, vol. I, edited by J. N. S. Allamand (Marc Michel Rey, Amsterdam, 1774), pp. 305–312.
19.’s Gravesande's argument has been modernly quoted and explained in Ref. 5.
20. Willem J. ’s Gravesande, “ Essai d’une Nouvelle Théorie du Choc des Corps,” in Œuvres philosophiques et mathématiques de Mr. G. J. ’s Gravesande, vol. I, edited by J. N. S. Allamand (Marc Michel Rey, Amsterdam, 1774), pp. 217–251. This is a reprinting of J. Lit. (La Haye) 12(1), 1–54, 190–197 (1722).
21.Similar experiments had already been conducted by Giovanni Poleni, of the University of Padua, which 's Gravesande learned about only after he had carried out his own tests. The interpretation of Poleni's and ’s Gravesande's results provoked a debate between Leibnizians and Newtonians, which from our present perspective could have been resolved by noting that a constant force F changes the momentum of a body by an amount and its energy by , where is the time interval and is the displacement over which the force acts. See Ref. 16.
22.A work that has played a major role in sustaining the myth of Orffyreus as a maligned genius is the biography of 's Gravesande published in 1774 by his successor to the chair of mathematics at Leiden: Jean N. S. Allamand, “ Histoire de la vie et des ouvrages de Mr. ’s Gravesande,” in Œuvres philosophiques et mathématiques de Mr. G. J. ’s Gravesande, vol. I (Marc Michel Rey, Amsterdam, 1774), pp. ix–lix.
23.For a modern account of 's Gravesande’s life and work see A. Rupert Hall, “ ’s Gravesande, Willem Jacob,” in Complete Dictionary of Scientific Biography (Charles Scribner's Sons, Detroit, 2008), Vol. 5, pp. 509–511.
24. Friedrich W. Strieder, “ Orffyreus, Orffyre (Johann Ernst Elias),” in Grundlage zu einer Hessischen Gelehrten- und Schriftsteller- Geschichte (J. H. G. Griesbach, Kassel, 1795), Vol. X, pp. 150–174.
25. Richard Roos (Karl A. Engelhardt), “ Joh. Ernst Elias Orffyreus oder Orffyré, ein mechanischer Charlatan,” in Curiositäten der physisch- literarisch- artistisch- historischen Vor- und Mitwelt, edited by C. A. Vulpius (Landes-Industrie-Comptoirs, Weimar, 1813), Vol. III, pp. 53–69.
26. Friedrich Bülau, “ Bessler-Orffyré,” in Geheime Geschichten und räthselhafte Menschen, 2nd ed. (F. A. Brodhaus, Leipzig, 1864), Vol. XI, pp. 251–265.
27.Today this procedure is called a ROT13 cipher.
28.The possible connections of Orffyreus's career to the social context of Annaberg have recently been explored in an unpublished thesis: Gabor Rychlak, Hexenfieber im Erzgebirge: Die Annaberger Krankheit 1712–1720, doctoral dissertation, University of Mainz (2009). It is difficult for me to evaluate the reliability of the author's research and conclusions.
29. Kurt Müller and Gisela Krönert, Leben und Werk von G. W. Leibniz: Eine Chronik (Vittorio Klostermann, Frankfurt am Main, 1969), p. 249.
30. Gottfried W. Leibniz, letter to Robert Erskine (known in Russia as Areskine) dated 3 Aug. 1716, published in Leibniz in seinen Beziehungen zu Russland und Peter dem Grossen, edited by W. Guerrier (Imperial St. Petersburg Academy of Sciences, St. Petersburg and Leipzig, 1873), pp–361.
31.Leibniz’s involvement goes unmentioned in most scholarly accounts of the Orffyreus affair. On Peter the Great's interest in Orffyreus's wheel, the surrounding negotiations, and the need for competent scientific advice that led to the founding of the St. Petersburg Academy of Sciences, see Ref. 7.
33.See Henry Dircks, “ Inventions of the Marquis of Worcester and Councillor Orffyreus,” in Perpetuum mobile; or, Search for self-motive power, during the 17th, 18th, and 19th centuries, second series (E. & F. N. Spon, London, 1870), pp. 90–116.
34. Joseph E. Fischer von Erlach, letter to John Desaguliers dated Aug. 1721. A translation is given in Ref. 33, pp. 110–112.
35.The most substantial of those pamphlets is Orffyreus (Johann E. E. Bessler), Triumphans perpetuum mobile Orffyreanum (Kassel, 1719). On the principle of the wheel's design, see the passage translated in Ref. 33, p. 103.
36. Willem J. ’s Gravesande, letter to Isaac Newton dated 7 Aug. 1721, published in The Correspondence of Isaac Newton, vol. VII, edited by A. R. Hall and L. Tilling (Cambridge U.P., Cambridge, 1977), pp. 143–147.
38.For an alternative explanation of the non-operation of Worcester's wheel (Fig. 1) in terms of an explicit computation of the torques, see Maurice B. Stewart, “ The Marquess of Worcester's perpetual motion machine,” Phys. Teach. 19(1 ), 37 (1981).
39.Journal Book of the Royal Society of London 12(158), 161–162 (1721).
40. Willem J. ’s Gravesande, letter to Jean-Pierre de Crousaz in response to a communication dated 3 Feb. 1729. Quoted in Ref. 22, pp. xxv–xxvi. A translation is included in Ref. 33, pp. 113–114.
41.’s Gravesande recalled in Ref. 40 that it had been his examination of the Weissenstein machine's bearings that threw Orffyreus into such a rage that he smashed the device, but this did not arouse in the professor any suspicion that Orffyreus might have feared too close a scrutiny of the axle and its supports. The cumbersome three-bobbed pendula shown in Fig. 2, ostensibly needed to regulate the turning speed, might have helped divert attention during examinations of the axle.
42.On this period of Leibniz's life see, e.g., Maria R. Antognazza, Leibniz: An Intellectual Biography (Cambridge U.P., Cambridge, 2009), chap. 9.
43.In an appendix to his 1690 medical dissertation59 Bernoulli had proposed a perpetual fountain driven by the difference in density of two miscible liquids. A similar idea was rediscovered much later in Octave Levenspiel and Noel de Nevers, “ The Osmotic Pump,” Science 183(4121 ), 157–160 (1974), where the authors explain that, because of osmosis, continued operation depends on an external power keeping the liquid mixture homogenous.
44.For an overview of the correspondence between Bernoulli and Leibniz on perpetual motion, see pp. 58–67 of Alan Gabbey, “ The Mechanical Philosophy and its Problems: Mechanical Explanations, Impenetrability, and Perpetual Motion,” in Change and Progress in Modern Science, edited by J. C. Pitt (D. Reidel, Dordrecht, 1985), pp. 9–84. Bernoulli's and Leibniz's concern with the relation between macroscopic mechanical processes and microscopic “natural” phenomena could be interpreted as distantly anticipating the investigations into the mechanical equivalent of heat that would lead, in the 19th century, to the formulation of the laws of thermodynamics.
45. Johann Bernoulli, letter to Willem 's Gravesande dated 31 Oct. 1722, quoted in Ref. 22, pp. xxxvi–xlv.
46. Isaac Newton, “ Query 31,” in Opticks, 4th ed. (Dover, New York, 1979 ), pp. 376–406. See especially the discussion of planetary orbits on p. 402, which first appeared in the Latin edition of 1706. The portion of the query relevant to the controversy with Leibniz is quoted and annotated in The Leibniz-Clarke Correspondence, edited by H. G. Alexander, (Manchester U. P., Manchester and New York, 1956), pp. 175–183.
47. Gottfried W. Leibniz, letter to Caroline, Princess of Wales, dated Nov. 1715. Quoted in The Leibniz-Clarke Correspondence, edited by H. G. Alexander (Manchester U.P., Manchester, New York, 1956), pp. 11–12.
48.See especially Steven Shapin, “ Of Gods and Kings: Natural Philosophy and Politics in the Leibniz-Clarke Disputes,” Isis 72(2 ), 187–215 (1981).
Leibniz’s motivations, and the genesis of his dispute with Clarke, have recently been explored in Gregory Brown
, “‘[…] et je serai tousjours la même pour vous': Personal, Political, and Philosophical Dimensions of the Leibniz-Caroline Correspondence
,” in Leibniz and His Correspondents
, edited by P. Lodge
), pp. 262
; “The Theodicy
and the Leibniz-Clarke Correspondence,” talk delivered at the conference Leibniz's Theodicy
: Context and Content, University of Notre Dame, 16–18 Sep. 2010. http://philreligion.nd.edu/research-initiatives/problem-of-evil/early-modern/conferences/context-and-content/
51. “Nova literaria Mathematica de perpetuo mobili, Longitudine Maris & Quadratura Circuli,” Acta Erudit. 4(1), 46–48 (1715);
51.Review of Christian Wolff's Mathematisches Lexikon, Acta Erudit. 6(2), 88–92 (1717);
51.“Relatio de perpetuo mobili Joh. Ernesti Eliæ Orffyrei,” Acta Erudit. 7(11), 497–499 (1718). These are cited and quoted in translation in Ref. 33, pp. 95–96.
52. Christian Wolff, “ Perpetuum Mobile,” in Mathematisches Lexicon (Bey Joh. Friedrich Gleditschens seel. Sohn, Leipzig, 1716), columns 1037–1043.
53.The 1734 version of Wolff's article in Ref. 52 is translated in Henry Dircks, Perpetuum mobile; or, Search for self-motive power, during the 17th, 18th, and 19th centuries, second series (E. & F. N. Spon, London, 1870), pp. 155–157.
54. Christian Wolff, “ Num. XXIII: Nova literaria Mathematica de perpetuo mobili, Longitudine Maris & Quadratura Circuli,” in Meletemata mathematico-philosophica (Bibliopoleo Rengeriano, Halle and Magdeburg, 1755), pp. 69–72.
55.See, e.g., James Randi, Flim-Flam! Psychics, ESP, Unicorns, and Other Delusions (Prometheus Books, Amherst, NY, 1982), p. 7.
56. Longitude, directed by Charles Sturridge, with Jeremy Irons, William Gambon and Ian Hart (Granada Film Productions, UK, 2000).
57. Dava Sobel, Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time (Walker & Co., New York, 2005 ).
58.On Gould's life and work, see Jonathan Betts, Time Restored: The Harrison Timekeepers and R. T. Gould, The Man Who Knew (Almost) Everything (Oxford U.P., Oxford, 2006).
59. Johann Bernoulli, “ On the Mechanics of Effervescence and Fermentation,” in Dissertations, edited by P. Maquet, A. Ziggelaar and T. Kardel (American Philosophical Society, Philadelphia, 1997 ), pp. 35–97.
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