FOOTNOTES:
[1] This traditional view is expressed by almost every history of horology. An ultimate source for many of these has been the following two classic treatments: J. Beckmann, A history of inventions and discoveries, 4th ed., London, 1846, vol. 1, pp. 340 ff. A. P. Usher, A history of mechanical inventions, 2nd ed., Harvard University Press. 1954, pp. 191 ff., 304 ff.
[2] There is a considerable literature dealing with the later evolution of perpetual motion devices. The most comprehensive treatment is H. Dircks, Perpetuum mobile, London, 1861; 2nd ser., London, 1870. So far as I know there has not previously been much discussion of the history of such devices before the renaissance.
[3] For the early history of gearing in the West see C. Matschoss, Geschichte des Zahnrades, Berlin, 1940. Also F. M. Feldhaus, Die geschichtliche Entwicklung des Zahnrades in Theorie und Praxis, Berlin, 1911.
[4] A general account of these important archaeological objects will be published by J. Needham, Science and civilisation in China, Cambridge, 1959(?), vol. 4. The original publications (in Chinese) are as follows: Wang Chen-to, "Investigations and reproduction in model form of the south-pointing carriage and hodometer," National Peiping Academy Historical Journal, 1937, vol. 3, p. 1. Liu Hsien-chou, "Chinese inventions in horological engineering," Ch'ing-Hua University Engineering Journal, 1956, vol. 4, p. 1.
[5] For illustrations of intermeshing worms in Indian cotton mills, see Matschoss, op. cit. (footnote [3]), figs. 5, 6, 7, p. 7.
[6] It is interesting to note that the Chinese hodometer was contemporary with that of Hero and Vitruvius and very similar in design. There is no evidence whatsoever upon which to decide whether there may have been a specific transmission of this invention or even a "stimulus diffusion."
[7] A summary of the content of the manuscript sources, illustrated by the original drawings, has been published by H. Alan Lloyd, Giovanni de Dondi's horological masterpiece, 1364, without date or imprint (?Lausanne, 1955), 23 pp. It should be remarked that de Dondi declines to describe the workings of his crown and foliot escapement (though it is well illustrated) saying that this is of the "common" variety and if the reader does not understand such simple things he need not hope to comprehend the complexities of this mighty clock. But this may be bravado to quite a large degree.
[8] See, for example, the chronological tables of the 14th century and the later mentions of clocks in E. Zinner, Aus der Frühzeit der Räderuhr, Munich, 1954, p. 29 ff. Unfortunately this very complete treatment tends to confuse the factual and legendary sources prior to the clock of de Dondi; it also accepts the very doubtful evidence of the "escapement" drawn by Villard of Honnecourt (see p. [107]). An excellent and fully illustrated account of monumental astronomical clocks throughout the world is given by Alfred Ungerer, Les horloges astronomiques, Strasbourg, 1931, 514 pp. Available accounts of the development of the planetarium since the middle ages are very brief and especially weak on the early history: Helmut Werner, From the Aratus globe to the Zeiss planetarium, Stuttgart, 1957; C. A. Crommelin, "Planetaria, a historical survey," Antiquarian Horology, 1955, vol. 1, pp. 70-75.
[9] Derek J. Price, "Clockwork before the clock," Horological Journal, 1955, vol. 97, p. 810, and 1956, vol. 98, p. 31.
[10] For the use of this material I am indebted to my co-authors. I must also acknowledge thanks to the Cambridge University Press, which in the near future will be publishing our monograph, "Heavenly Clockwork." Some of the findings of this paper are included in shorter form as background material for that monograph. A brief account of the discovery of this material has been published by J. Needham, Wang Ling, and Derek J. Price, "Chinese astronomical clockwork," Nature, 1956, vol. 177, pp. 600-602.
[11] For these translations from classical authors I am indebted to Professor Loren MacKinney and Miss Harriet Lattin, who had collected them for a history, now abandoned, of planetariums. I am grateful for the opportunity of giving them here the mention they deserve.
[12] A. G. Drachmann, "The plane astrolabe and the anaphoric clock," Centaurus, 1954, vol. 3, pp. 183-189.
[13] A fuller description of the anaphoric clock and cognate water-clocks is given by A. G. Drachmann, "Ktesibios, Philon and Heron," Acta Historica Scientiarum Naturalium et Medicinalium, Copenhagen, 1948, vol. 4.
[14] First published by O. Benndorf, E. Weiss, and A. Rehm, Jahreshefte des österreichischen archäologischen Institut in Wien, 1903, vol. 6, pp. 32-49. I have given further details of its construction in A history of technology, ed. Singer, Holmyard, and Hall, 1957, vol. 3, pp. 604-605.
[15] L. Maxe-Werly, Mémoires de la Société Nationale des Antiquaires de France, 1887, vol. 48, pp. 170-178.
[16] The first definitive account of the Antikythera machine was given by Perikles Rediadis in J. Svoronos, Das Athener Nationalmuseum, Athens, 1908, Textband I, pp. 43-51. Since then, other photographs (mostly very poor) have appeared, and an attempt at a reconstruction has been made by Rear Admiral Jean Theophanidis, Praktika tes Akademias Athenon, Athens, 1934, vol. 9, pp. 140-149 (in French). I am deeply grateful to the Director of the Athens National Museum, M. Karouzos, for providing me with an excellent new set of photos, from which figures 6-8 are now taken.
[17] H. Diels Über die von Prokop beschriebene Kunstuhr von Gaza, Abhandlungen, Akademie der Wissenschaften, Berlin, Philos.-Hist. Klasse, 1917, No. 7.
[18] L. A. Mayer, Islamic astrolabists and their works, Geneva, 1956, p. 62.
[19] The translation which follows is quoted from J. Beckmann, op. cit. (footnote [1]), p. 349.
[20] E. Wiedemann, "Ein Instrument das die Bewegung von Sonne und Mond darstellt, nach al Biruni," Der Islam, 1913, vol. 4, p. 5.
[21] I acknowledge with thanks to the Curator of that museum the permission to reproduce photographs of this instrument. It is item 5 in R. T. Gunther, Astrolabes of the world, Oxford, 1932.
[22] Abulcacim Abnacahm, Libros del saber, edition by Rico y Sinobas, Madrid, 1866, vol. 3, pp. 241-271. The design of the instrument has been very fully discussed by A. Wegener, "Die astronomischen Werke Alfons X," Bibliotheca Mathematica, 1905, pp. 129-189. A more complete discussion of the historical evolution of the equatorium is given in Derek J. Price, The equatorie of the planetis, Cambridge (Eng.), 1955, pp. 119-133.
[23] E. Wiedemann, and F. Hauser, "Uber die Uhren im Bereich d. islamischen Kultur," Nova Acta; Abhandlungen der königliche Leopoldinisch-Carolinische Deutsche Akademie der Naturforscher zu Halle, 1915, vol. 100, no. 5.
[24] E. Wiedemann, and F. Hauser, Die Uhr des Archimedes und zwei andere Vorrichtungen, Halle, 1918.
[25] The manuscripts in question are as follows: Gotha, Kat. v. Pertsch. 3, 18, no. 1348; Oxford, Cod. 954; Leiden, Kat. 3, 288, no. 1414, Cod. 499 Warn; and another similar, Kat. 3, 291, no. 1415, Cod. 93 Gol.
[26] H. Schmeller, Beiträge zur Geschichte der Technik in der Antike und bei den Arabern, Erlangen, 1922 (Abhandlungen zur Geschichte der Naturwissenschaften und der Medizin no. 6).
[27] Once more I am indebted to Professor Loren MacKinney and Miss Harriet Lattin (see footnote [11]) for making their collections on Gerbert available to me.
[28] Item 198 in Gunther, op. cit. (footnote [21]). I am grateful to the authorities of that museum for permission to reproduce photographs of this instrument.
[29] Sotheby and Co., London, sale of March 14, 1957, lot 154. The outer rim of the rete has 120 teeth.
[30] The Latin text of the treatise on the Albion, has been transcribed by Rev. H. Salter and published in R. T. Gunther, Early science in Oxford, Oxford, 1923, vol. 2, pp. 349-370. An analysis of its design is given in Price, op. cit. (footnote [22]), pp. 127-130.
[31] Such evidence as there is for the existence and form of the clock is collected by Gunther, op. cit. (footnote [30]), p. 49.
[32] I have discussed this new manuscript source in "Two medieval texts on astronomical clocks," Antiquarian Horology, 1956, vol. 1, no. 10, p. 156. The manuscript in question is ms. 230/116, Gonville and Caius College, Cambridge, folios 11v-14v = pp. 31-36.
[33] The Chronicle of Jocelin of Brakelond ..., H. E. Butler (ed.), London, 1949, p. 106.
[34] C. B. Drover, "A medieval monastic water-clock," Antiquarian Horology, 1954, vol. 1, no. 5, pp. 54-58, 63. Because this water clock uses wheels and strikes bells one must reject the evidence of literary reference, such as by Dante, from which the mention of wheels and bells have been taken as positive proof of the existence of mechanical clocks with mechanical escapements. The to-and-fro motion of the mechanical clock escapement is quite an impressive feature, but there seems to be no literary reference to it before the time of de Dondi.
[35] Annales de la Société Royale d'Archéologie de Bruxelles, 1896, vol. 1/8, pp. 203-215, 404-451. The translation here is cited from Drover, op. cit., (footnote [34]), p. 56.
[36] L. Thorndike, The sphere of Sacrobosco and its commentators, Chicago, 1949, pp. 180, 230.
[37] The album was published with facsimiles by J. B. A. Lassus, 1858. An English edition with facsimiles of 33 of the 41 folios was published by Rev. Robert Willis, Oxford, 1859. An extensive summary of this section is given, with illustrations, by J. Drummond Robertson, The evolution of clockwork, London, 1931, pp. 11-15.
[38] M. Jules Quicherat, Revue Archèologique, 1849, vol. 6.
[39] M. C. Frémont. Origine de l'horloge à poids, Paris, 1915.
[40] For this, I have used and quoted from the very beautiful edition in English, prepared by Silvanus P. Thompson, London, Chiswick Press, 1902.
[41] See E. G. R. Taylor, "The South-pointing needle," Imago Mundi, Leiden, 1951, vol. 8, pp. 1-7 (especially pp. 1, 2).
[42] I have wondered whether the medieval interest in perpetual motion could be connected with the use of the "Wheel of Fortune" in churches as a substitute for bell-ringing on Good Friday. Unfortunately I can find no evidence for or against the conjecture.
[43] W. E. May, "Alexander Neckham and the pivoted compass needle," Journal of the Institute of Navigation, 1955, vol. 8, no. 3, pp. 283-284.
[44] W. E. May, "Hugues de Berze and the mariner's compass," The Mariner's Mirror, 1953, vol. 39, no. 2, pp. 103-106.
[45] H. Balmer, Beiträge zur Geschichte der Erkenntnis des Erdmagnetismus, Aarau, 1956, p. 52.
[46] The collection is the Gami 'al Hikajat; the relevant passage being given in German translation in Balmer. op. cit. (footnote [45]), p. 54.
[47] Balmer, op. cit. (footnote [45]), p. 53.