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² Gellibrand, H., A Discourse Mathematical on the Variation of the Magnetic Needle, London, 1635Google Scholar, reprinted in Hellman, G., (ed.), Neudrucke von Schriften und Karten uber Meteorologie and Erdmagnetismus, Berlin, 1897, pp. 16–17.Google Scholar

³ Waters, , op. cit. (1), Navigation, p. 161.Google Scholar

⁴ The concept is put to use in an historical dispute in Shapin, S. and Schaffer, S., Leviathan and the Air Pump. Hobbes, Boyle and the Experimental Life, Princeton, 1985Google Scholar, especially chapters I and II.

⁵ See Barnes, B., Interests and the Growth of Knowledge, London, 1977.Google Scholar

⁶ Collins, H.M., Changing Order. Replication and Induction in Scientific Practice, London, 1985, Chapter IV.Google Scholar

⁷ Collins, , op. cit. (6)Google Scholar, Changing Order, makes this point, p. 27, n. 18.Google Scholar

⁸ Collins, , op. cit. (6), Changing Order, chapter III.Google Scholar

⁹ This is discussed in detail in Section VI below.

¹⁰ Singer, C. et al. , (eds), A History of Technology, vol. iii, Oxford, 1957, p. 450.Google Scholar

¹¹ Digges, T., A Perfit Description of the Celestiall Orbs, London, 1576. signature Pl_r.Google Scholar

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¹³ For Borough see Waters, , op. cit. (1)Google Scholar, Navigation, p. 161Google Scholar; Observation from Wright (1610), p. Ppv. Mariner's attitudes are discussed in Waters, , op. cit. (1), Navigation, pp. 58f.Google Scholar

¹⁴ de Medina, P., Arte de Navegar, Valladolid, 1545.Google Scholar The English translation, by John Frompton, did not supplant Matin Cortes's work of the same title, translated by Richard Eden (London, 1561). Cortes attributed variation to some ‘motive force beyond the heavens’, according to Gilbert. See Gilbert, W., De Magnete trs. Mottelay, P. Fleury (1893; reprint edn, New York, 1957), p.232.Google Scholar All references to De Magnete are to this edition.

¹⁵ This is discussed in the second part of section VII below.

¹⁶ Waters, , op. cit. (1), Navigation, p. 292.Google Scholar

¹⁷ Ibid.., p. 307.

¹⁸ See the second part of Section VII below.

¹⁹ Seen. 16.

²⁰ He claimed that only Henry Wynne's needles were good enough, in the London Gazette of September 1677. See Schaffer, S., ‘Henry Bond and the Problem of Longitude’ (B.A. dissertation, Univ. of Cambridge, 1975), p. 32.Google Scholar

²¹ Or so Descartes thought. I discuss this in the second part of Section VII.

²² Pumfrey, S., ‘Mechanizing Magnetism in Restoration England—the Decline of Magnetic Philosophy’, Annals of Science (1987), 44, pp. 1–22.CrossRefGoogle Scholar

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²⁴ Polter, R., The Pathway to Perfect Sailing, London, 1605.Google Scholar No copies of this survive. For information see Taylor, , op. cit. (1), Mathematical Practitioners, p. 338Google Scholar, and Waters, , op. cit. (1), Navigation, vol i, p. 232.Google Scholar

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²⁶ Taylor, , op. cit. (12), Havenfinding Art, p. 205.Google Scholar

²⁷ ‘[Experimentum] factum est, ut prudenter hanc quaestionem ipse declinarit, ne causam quaereret effectus, qui nusquam esset; et potuit suspicari ipse triginta ab hinc annis, aut quadraginta, quo tempore magnetum exercebat, ne ubique semper eodem modo declinaret gradibus 5 ad orientem.’ Cabeo, N., Philosophia Magnetica, Ferrara, 1629, p. 56.Google Scholar

²⁸ Petit, P., Dissertatio de Latitudine Parisiensis eaque in urbe magnetica declinatione, adductis pluribus argumentis, quibus suspicari licet utram subinde variareGoogle Scholar, published as an appendix to du Hamel, J. B., Astronomia Physica, Paris, 1660.Google Scholar See Petit's Appendix, p. 30, ‘neque ulla declinationis diversitas apparuit.’

²⁹ For economics see Hill, C., The Century of Revolution, 2nd edn, Walton-on-Thames, pp. 29–33, 133–136.Google Scholar For relation to navigation see Merton, R. K., Science, Technology and Society in Seventeenth-Century England, 1938 (reprint edn, New York, 1970)Google Scholar, chapter VII passim, especially pp. 165–175.

³⁰ Norwood, R., The Sea-Mans Practice, London, 1637Google Scholar; Cortes, M., Arte de Navegar, Seville, 1557.Google Scholar The latter was known throughout Europe. For the various editions, translations and adaptations see Taylor, , op. cit. (1), Mathematical Practitioners, pp. 32–33, 318, 322.Google Scholar

³¹ As Hooke recalled. See Hooke, R., Posthumous Works, London, 1705 (reprint edn, London, 1971), p. 486.Google Scholar

³² Major, R.H., The Life of Prince Henry, surnamed the Navigator, and its Results, 1868 (reprint edn, London, 1967), p. 423.Google Scholar

³³ Prestage, C., The Portuguese Pioneers, 1932 (reprint edn, London. 1966), pp. 305–306.Google Scholar

³⁴ The view dates back at least to Peregrinus, 's Letter on the MagnetGoogle Scholar (1269) and reappeared in the plagiarism of Taisnier, J., Opusculum … de Natura Magnetis et eius EffectibusGoogle Scholar (1562), and in the rough translation of it by Eden, Richard, A very Necessarie and Profitable Booke Concerning Navigation, London, 1579?, pp. 6–7Google Scholar, although it should be noted that other regions of heaven were also allowed an effect.

³⁵ Cardan, J., De Subtilitate Libri XXI, Basle, 1554, p. 215.Google Scholar

³⁶ Gilbert, , op. cit. (14), De Magnete, pp. 231–232.Google Scholar

³⁷ de Nautonnier, G. (Nautonier), Mécometrie de leymant cest a dire la manière de mesurer les longitudes par le moyen de l'eymant, Venes, Toulouse, 1602–1604, pp. 79–80.Google Scholar

³⁸ Taylor, , op. cit. (1), Mathematical Practitioners, p. 332.Google Scholar

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⁴⁰ Bourne, W., A Regiment for the Sea, LondonGoogle Scholar, 1574, chapter IX. The quotation from the 1576 (2nd) edition is taken from Waters, p. 142.

⁴¹ Digges, T., A Perfit Description of the Celestiall Orbs (LondonGoogle Scholar, 1576), signature 04r–v.

⁴² Quoted from Waters, , p. 146.Google Scholar For Bourne see Taylor, , op. cit. (1), Mathematical Practitioners, p. 33Google Scholar; For Borough see Waters, , p. 96.Google Scholar

⁴³ Barlow, W., The Navigators Supply, LondonGoogle Scholar, 1597, signature A4.

⁴⁴ Borough, W., A Discours of the Variation of the Cumpas (London, 1581), chapter VIII.Google Scholar

⁴⁵ Wright, E., Certaine Errors in Navigation (London, 1599), pp. M_V–N1_V.Google Scholar

⁴⁶ Ibid.., p. 205.

⁴⁷ De Magnete, p. 67.Google Scholar

⁴⁸ Ibid.., pp. 247–248.

⁴⁹ Gilbert, , op. cit. (14), De Magnete, p. 241.Google Scholar Interestingly, Gilbert, didGoogle Scholar believe that the earth underwent continuous and major geological changes of the kind that would alter variation. One such was the disappearance of Atlantis. See Gilbert, W., De Mundo nostro Sublunari, Amsterdam, 1651 (reprint edn, Amsterdam, 1965), pp. 282–283 and 292–293 especially.Google Scholar

⁵⁰ Gilbert, , op. cit. (14), De Magnete, p. 247.Google Scholar

⁵¹ Ibid.., Book 4, chapter IX, pp. 251–254.

⁵² Ibid.., Book 4, chapter XIII, pp. 265–267.

⁵³ Ibid.., pp. 234–5, 254–5, 269.

⁵⁴ Zilsel, E., ‘The Origins of William Gilbert's Scientific Method’, Journal for the History of Ideas, 1941, 2, pp. 1–31CrossRefGoogle Scholar; Bennett, J. A., ‘The Mechanics' Philosophy and the Mechanical Philosophy’, History of Science, (1986), 24, pp. 1–28.CrossRefGoogle Scholar

⁵⁵ Gilbert, , op. cit. (14), De Magnete, pp. 14, 181.Google Scholar

⁵⁶ Pumfrey, S., ‘William Gilbert's Magnetic Philosophy 1580–1684: the Creation and Dissolution of a Discipline’ (Ph.D. dissertation, University of London, 1987), pp. 60–66.Google Scholar

⁵⁷ See notes 45, 46.

⁵⁸ Wright, , Certaine Errors (1599), p. M_v; 2nd edn (1610), p. 9.Google Scholar

⁵⁹ I have used the British Library copy, shelf mark 533.k.9. This is in French and bears the date 1603 on the title page but other parts e.g. Books III and IV are dated 1604. According to Waters, , op. cit. (1), Navigation, p.275Google Scholar, other versions existed dated 1602 and written partly in Scots.

⁶⁰ Nautonnier, , op. cit. (59), Mécometrie, Definitions 6 and 7, pp. 21–36, 37–44.Google Scholar

⁶¹ Ibid.., pp. 21,37.

⁶² See Fournier, G., Hydrographie, Paris, 1643, pp. 542, 607Google Scholar; Balmer, H., Beitrage zur geschichte der Erkenntnis des Erdmagnetismus, Zurich, 1956, pp. 461–462.Google Scholar

⁶³ By Jean Le Tellier in 1631. See Taylor, , op. cit. (12), Havenfinding Art, p. 220.Google Scholar

⁶⁴ See Nautonnier, , op. cit. (59)Google Scholar, Mécotnetrie, ‘Au Lecteur’, for his self-proclaimed breadth of reading.

⁶⁵ ‘… les observations de plus grans Pilotes qui ayent este au monde durant le siècle passé’, ibid.., p. 11.

⁶⁶ Ibid.., p. 14.

⁶⁷ Ibid.., Au lecteur, p. 1.

⁶⁸ Ibid.., pp. 66–68, 95–98.

⁶⁹ ‘si quelqu'un veut dire, que le defaut de rondeur en la terre, est cause de la variation de l'eymant, je dy que … il est tout certain et indubitablement resolu, que la terre est ronde … la profondeur de la mer et la hauteur des montaignes est si petite, eu esgard a ceste grand machine, que sa rondeur n'en pas difformee.’ Ibid.., pp. 95–6.

⁷⁰ ‘ne sont presque rien eu esgard au rest d'icelle, ce qui est monstre par Guillaume Gilbert au dernier chapitre du premier livre de l'eymant,’ Ibid.., p. 96.

⁷¹ Gilbert, , op. cit. (14), De Magnete, p. 235.Google Scholar

⁷² Cabeo, N.Philosophia Magnetica, Ferrara, 1629, p. 76.Google Scholar Although Cabeo's description might appear to be a thought experiment, he instructed the reader ‘tum vero caera, aut alia simile re reple cavitates, quas fecisti:’

⁷³ Gilbert, op. cit. (14), De Magnete, p. 232.Google Scholar

⁷⁴ Gilbert, , op. cit. (14), De Magnate, p. xli.Google Scholar

⁷⁵ An appendix to Blundeville, T., The Theoriques of the Seven Planets, London, 1602.Google Scholar In ‘A short Appendix annexed to the former Treatise by Edward Wright, at the motion of the right Worshipful M. Doctor Gilbert’ Wright wrote ‘that (according to M. Blundeviles earnest request) this table following should be hereunto adjoined, which M. Henry Briggs … calculated.’ See p. 29.

⁷⁶ London, 1609.

⁷⁷ Taylor, , op. cit. (1), Mathematical Practitioners, p. 339.Google Scholar

⁷⁸ Linton, , op. cit. (76), Newes, p. 15.Google Scholar

⁷⁹ Ibid.., p. 12.

⁸⁰ Barlow first circulated his Magnetical Advertisments as a manuscript in 1609. Ridley later commented that the Dedicatory Epistle said that Barlow's stimulus had been the desire to refute a French work called ‘Niccometria Magnetica [sic]’ by one Gulielmus Nantonierus [sic].

⁸¹ Taylor, , op. cit. (1), Mathematical Practitioners, p. 176.Google Scholar

⁸² Linton, , op. cit. (76), Neives, p. ii.Google Scholar

⁸³ Wright, , op. cit. (58), Errors (2nd edn, 1610), p. 8.Google Scholar

⁸⁴ Ibid.., signature Ppr.

⁸⁵ Waters, , op. cit. (1), Navigation, p. 282. See pp. 282–284.Google Scholar

⁸⁶ Waters, , op. cit. (1) Navigation, pp. 288, 499.Google Scholar

⁸⁷ See the third part of Section VII below.

⁸⁸ Carpenter, N., Geography Delineated Forth in Two Bookes. Oxford, 1625, pp. 59–63.Google Scholar On p. 63 Carpenter supported Gilbert and considered that pole theorists ‘laboured with more hope than successe,’ echoing Ridley's taunt.

⁸⁹ Purchas, S., Purchas His Pilgrims, (2nd edn) London, 1625, Book II, pp. 3–4.Google Scholar On variation ‘most laborious have beene the paines, most probable (perhaps) the reasons of our Countryman Doctor Gilbert.’

⁹⁰ See the first two parts of Section VII below.

⁹¹ For Alleaume (Aleaume) see Mersenne, M., Correspondence du P. Marin Mersenne Religieux Minime ed. de Waard, C. (15 vols, Paris, 1945–1983), vol. i, p. 315, and p. 617.Google Scholar

⁹² Paris, 1611.

⁹³ Grandami, J., Nova Demonstratio Immobilitatis Terrae La Flèche, 1645, p. 80.Google Scholar

⁹⁴ Mersenne, , Quaestione celeberrimae in Genesim … ‘Paris, 1623, columns 549–550.Google Scholar

⁹⁵ Mersenne, , Le Vérité des Sciences. Contre les Sceptiques ou Pyrrhoniens, Paris, 1625 (reprint edn, Stuttgart, 1969), pp. 910–929.Google Scholar

⁹⁶ See Lenoble, R., Mersenne, ou la naissance du mécanisme, Paris, 1935, chapter IV.Google Scholar

⁹⁷ Mersenne, , op. cit. (95), Verite, p. 911.Google Scholar ‘on donne un pole particulier a l'aymant, vers lequel il dresse tousiours sa pointe, que plusieurs pensent estre à 23 desgrez, et demy du pole arctique, pres du point ou le circle arctique entrecoupe le premier meridian.’

⁹⁸ ‘Puisque vous mettez de nouveaux pole pour l'aimant, on pourroit ce semble, inventer quelque nouvelle Geographie, …’ ‘Plusieurs ont en cette pensee, car outre l'essieu, les poles et l'equateur de la guidaymant, Castel-franc a voulu, des demi-circles, des paralleles, un cercle d'attouchement, un autre du Nort, et du sudaymant.’ Ibid.., pp. 916–917.

⁹⁹ Ibid.., pp. 912–915.

¹⁰⁰ ‘Or je vous conseille de ne vous assurer pas tellement sur les tables mecometriques que vous n'observiez vous meme quelle declinaison vous trouverez en chaque lieu.’ Ibid.., p. 929.

¹⁰¹ In his notes on Grandami's magnetic position finding scheme, which employed inclination and declination, he remarked that ‘probandum esset 1 has variari secundum variationem locorum et adhuc sensibiliter, quod falsum jam saepe comperimus.’ Grandami's publication meant that ‘error Castel-franci jam dudum cognitus et amandatus vim de novo recipiet et intensum habebit;’ Mersenne, op. cit. (91), Correspondance, vol. xiii, p. 576.Google Scholar

¹⁰² La Charlonye, to Mersenne, , 9 09 1634Google Scholar, Mersenne, , op. cit. (91)Google Scholar, Correspondance, vol. iv, p. 358.Google Scholar

¹⁰³ Ibid.., vol. ix, p. 252.

¹⁰⁴ See Waters, , op. cit. (1), Navigation, p. 422.Google Scholar

¹⁰⁵ Taylor, , op. cit. (1), Mathematical Practitioners, p. 203.Google Scholar

¹⁰⁶ Johnson, F., Journal of the History of Ideas, 1940, 1, p. 429.CrossRefGoogle Scholar

¹⁰⁷ Gellibrand, , op. cit. (2), Discourse, p. 16.Google Scholar

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¹⁰⁹ ‘ie crus que les auteurs avoient mal observe, et que leur peu d'exactitude ou sur la ligne meridienne, ou sur leurs Cercles, estoit la cause de ce manquement.’ Petit, to Oldenberg, , 5 05, 1667.Google ScholarOldenburg, H., The Correspondence of Henry Oldenburg, ed. and trs A.R. and Hall, M.B. (11 vols, Madison and London, 1965–1977), vol. iii, p. 378.Google Scholar

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¹¹¹ Idem.

¹¹² Ibid.., pp. 16–17.

¹¹³ Ibid., p. 17.

¹¹⁴ It is clear from Borough's Discourse and Gunter's Description and Use of the Sector that a basic equal altitude method was used, involving just one needle.

¹¹⁵ See the first and third part of Section VII, and Section VIII.

¹¹⁶ For careful definitions of this and other analytical concepts, see Collins, Harry, ‘The Place of the Core Set in Modern Science: Social Contingency with Methodological Propriety in Science,’ History of Science, (1981), 19, pp. 6–19.CrossRefGoogle Scholar

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¹¹⁸ Quoted from Webster, C., The Great Instauration; Science, Medicine and Reform in England, 1626–1660, London, 1975, p. 358.Google Scholar

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¹²¹ Norwood, R., The Sea-Mans Practice, London, 1637 (reprint edn Amsterdam), 1985, p. 108.Google Scholar

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¹²⁴ Bond, H., The Longitude Found: or, a Treatise shewing an easie and Speedie way, as well by night as by day, to find the Longitude, privately printed, London?, 1676.Google Scholar

¹²⁵ Moxon, in Wright, , Certaine Errors, 3rd edn, London, 1657, p. A3_vGoogle Scholar. Moxon was alluding to the secretive Bond and ‘wished that this knowledge had bin revealed to our Author Mr Wright, or some other so publique spirited as he.’

¹²⁶ See Mersenne, , op. cit. (91), Correspondance, vol. viii, p. 754 and pp. 755–761.Google Scholar

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¹²⁹ Ibid., p. 685; vol. ix, p. 59.

¹³⁰ Ibid., vol. viii, p. 690.

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