¹ Hakluyt, Richard (ed.), De orbe novo Petri martyris anglerii mediolanensis, Paris, 1587Google Scholar, preface. For a detailed history of navigation in this period see Waters, D. W., The art of navigation in England in Elizabethan and early Stuart times, London, 1958.Google Scholar

² See Pepper, Jon V., ‘Harriot's calculation of the meridional parts as logarithmic tangents’, Archive for history of exact sciences, 1968, 4, 359–413CrossRefGoogle Scholar, and idem, ‘Harriot's earlier work on mathematical navigation’, in Shirley, John W. (ed.), Thomas Harriot, renaissance scientist, Oxford, 1974, pp. 54–90.Google Scholar

³ British Museum (hereafter BM) Add.MS 6788, ff. 476, 485; see below, pp. 246, 257.

⁴ Shirley, John W., ‘Sir Walter Ralegh and Thomas Harriot’, in his op. cit. (2), pp. 21, 33.Google Scholar

⁵ Quinn, David B., ‘Thomas Harriot and the New World’Google Scholar, in ibid., p. 43.

⁶ Harriot, Thomas, A briefe and true report of the new found land of Virginia, London, 1588.Google Scholar

⁷ ‘The Will of Thomas Harriot’, in Tanner, R. C. H., ‘Thomas Harriot as mathematician’, Pysis, 1967, 9, 247Google Scholar; Latham, A., ‘Sir Walter Ralegh's Will’, Review of English studies, 1971, 22, 129–36.CrossRefGoogle Scholar

⁸ See Historical Manuscripts Commission (hereafter HMC), Calendar of the manuscripts of… the Marquis of Salisbury, London, 1895, vi, 256–7.Google Scholar

⁹ See SirRalegh, W., The discoverie of the large, rich and beautiful empire of Guiana, London, 1596.Google Scholar

¹⁰ Rowse, A. L., Ralegh and the Throckmortons, London, 1962, p. 160 and facing plates.CrossRefGoogle Scholar

¹¹ Lefranc, Pierre, Sir Walter Ralegh, écrivain, Paris, 1968, pp. 137–8, n. 10.Google Scholar

¹² This house still stands as part of the present Sherborne castle; Royal Commission on Historical Monuments, England: Dorset, vol. i: West, London, 1952, pp. 64–9.Google Scholar

¹³ See Taylor, E. G. R., ‘Harriot's instructions for Ralegh's voyage to Guianay’, Journal of the Institute of Navigation, 1952, 5, 345–50.CrossRefGoogle Scholar

¹⁴ Ralegh, , op. cit. (9), p. 1.Google Scholar

¹⁵ Shirley, John W., ‘Sir Walter Raleigh's Guiana finances’, Huntingdon Library quarterly, 1949–1950, 13, 55–69.CrossRefGoogle Scholar

¹⁶ BM Add.MS 6788. ff. 211^v–220^v

¹⁷ ibid., f. 423.

¹⁸ ibid., f. 488.

¹⁹ ibid., ff. 485, 486. The mode of address and other circumstances mentioned above show clearly that the latter are addressed.

²⁰ SirRalegh, W., The discovery… of Guiana (ed. by Schomburgk, R. H.), London, 1848, p. lxviii.Google Scholar

²¹ BM Add.MS 6788, ff. 484, 486, 487.

²² ibid., ff. 485–9.

²³ See, however, Roche, J., ‘Thomas Harriot's Astronomy’, University of Oxford D Phil thesis, 1977, pp. 187–9.Google Scholar

²⁴ . Nuñez, P., De arte atque ratione navigandi, Coimbra, 1573, book I, pp. 45–6.Google Scholar

²⁵ BM Add.MS 6788, ff. 484, 485. The topic referred to here is discussed in Latin in Nuñez’ De arte…, and in the edition of the latter which appeared in Nuñez, Opera, Basel, 1592.

²⁶ ibid., f. 485.

²⁷ Ralegh, , op. cit. (9), sig. A 3^v.Google Scholar; Latham, A. (ed.), Sir Walter Raleigh: selected prose and poetry, London, 1965, p. 113.Google Scholar

²⁸ BM Add.MS 6788, f. 485.

²⁹ ibid., ff. 485–9; Petworth House IIMC 241/VIb, p. 32.

³⁰ See below, pp. 255–8.

³¹ French, Peter, John Dee, London, 1972, p. 125.Google Scholar

³² Roche, , op. cit. (23), pp. 87–8.Google Scholar

³³ BM Add.MS 6788, ff. 469, 480.

³⁴ Roche, J. J., ‘The radius astronomicus in England’, Annals of science, 1981, 38, 1–32.CrossRefGoogle Scholar

³⁵ Crossley, J. (ed.), Autobiographical tracts of Dr. John Dee, London, 1851, p. 28.Google Scholar

³⁶ Digges, Leonard, A boke named Tectonicon, London, 1556, sig. f. 1^v.Google Scholar

³⁷ Digges, Thomas, Alae seu scalae mathematicae, London, 1573, sigs. I₁–L₃v.Google Scholar

³⁸ Roche, , op. cit. (34), pp. 19–23.Google Scholar

³⁹ Brahe, Tycho, Astronomiae instauratae mechanica, Wandesbeck, 1598, f. 28^vGoogle Scholar; and Roche, , op. cit. (34), pp. 21–2, 28, 31–2.Google Scholar

⁴⁰ Horrox, Jeremiah, Opera posthuma (ed. by Wallis, John), London, 1672–3, pp. 252, 255, 298–9, 304–5.Google Scholar

⁴¹ Birch, Thomas (ed.), Miscellaneous works of Mr. John Greaves, 2 vols., London, 1737, i, pp. ix, 92, ii, p. 508Google Scholar; Oxford, Bodleian Library, MS Smith, 93 f. 161.

⁴² Zinner, E., Astronomischen Instrumente, Munich, 1956, plate 16.2Google Scholar; Roche, , op. cit. (34), pp. 28–32.Google Scholar

⁴³ BM Add.MS 6788, ff. 486–9; HMC 241/VIb, p. 31; HMC 241/VII, ff. 1–7.

⁴⁴ Halliwell, J. O., Letters illustrative of the progress of science, London, 1841, pp. 32–3.Google Scholar

⁴⁵ HMC 24 I/II, p. 87. We do not know when this transcription was made.

⁴⁶ BM Add.MS 6788, f. 480; see also Pepper, J. V., ‘Studies of some of Thomas Harriot's unpublished mathematical and scientific manuscripts’, University of London PhD thesis, 1978, pp. 137–257.Google Scholar

⁴⁷ ibid., ff. 468–9.

⁴⁸ ‘Durham place’, Survey of London, London, 1937, xviii, chapter XII.Google Scholar

⁴⁹ ibid., p. 89.

⁵⁰ Rowse, , op. cit. (10), p. 233.Google Scholar

⁵¹ Survey, op. cit. (48), pp. 93, 94.Google Scholar

⁵² ibid., p. 92, and plate 2, p. 164; Van den Wyngaerde, A., London, c. 1542Google Scholar; Marks, S. P., The map of mid-sixteenth-century London, London, 1964, plate VGoogle Scholar; Glanville, Philippa, London in maps, London, 1972, plate 3, p. 76, and plate 4, p. 79Google Scholar; Norden, John, Speculum Britanniae London, 1593.Google Scholar

⁵³ E.g., Sinobas, Rico Y. (ed.), Libros del saber de astronomia, Madrid, 1866, ii, 71Google Scholar; iv, 6; see also 55, below.

⁵⁴ This is 11.2 minutes. See Smart, W. M., Spherical astronomy, Cambridge, 1962, p. 420.Google Scholar

⁵⁵ de Albuquerque, Lúis, ‘Astronomical navigation’, in Cortesão, Armando, A history of Portuguese cartography, Coimbra, 1971, pp. 290–4.Google Scholar

⁵⁶ Zacuto, A., Almanach perpetuum, facsmile edn. by Bensaude, J., Munich, 1915.Google Scholar

⁵⁷ Obliquity of the ecliptic, ε = 23°27′ 8.26″–46″. 84T. Where T is measured in Julian centuries from 1900; Smart, , op. cit. (54), p. 420.Google Scholar

⁵⁸ de Medina, Peter, The arte of navigation (tr. by Frampton, John), London, 1581, p. 46.Google Scholar

⁵⁹ Zacuto, , op. cit. (56), pp. 33–42.Google Scholar

⁶⁰ Bourne, William, An almanacke and prognostication for three yeares, London, 1571, sig. DviiGoogle Scholar; see also n. 102, below.

⁶¹ Regimento do estrolabio e do quadrante, facsmile edn. by Besaude, J., Munich, 1914.Google Scholar

⁶² The book of Francisco Rodrigues (tr. and ed. by Cortesão, Armando), London, 1944, pp. 313–18.Google Scholar

⁶³ Regimento do estrolabio Evora, facsimile edn. by Bensaude, J., Munich, 1914 or 1915, pp. 61ff.Google Scholar

⁶⁴ Nuñez, P., Tratado da esphera, 1537, facsimile edn. by Bensaude, J., Munich, 1915, pp. 171–15.Google Scholar

⁶⁵ Joannes de Regiomonte, Tabula directionum profectionum…. Augsburg, 1490, sig. d. 7^v; and Nuñez, , op. cit. (24), p. 35Google Scholar, where he refers to Regiomontanus's value of the obliquity.

⁶⁶ Stoeflerus, Joannes, Ephemeridum …, Tübingen, 1531, sigs L2^v–S5^v.Google Scholar

⁶⁷ Cortes, Martin, Breve compendio de la sphera y de la arte de navegar, Seville, 1556 (1st edn., Seville, 1551).Google Scholar Cortes used the same table of solar declinations as Nuñez at f.30^v, and Zacuto's form of solar longitude tables at ff. 28^v–29.

⁶⁸ Cortes, Martin, The arte of navigation, englished by Eden, Richard, London, 1561, f.xxvi.Google Scholar

⁶⁹ Bourne, William, A regiment for the sea, London, 1577 (1st edn., London, 1574), ff. 17^v–25.Google Scholar

⁷⁰ Norman, Robert, The newe attractive, London, 1581, sigs. Fiii–Giv^v.Google Scholar

⁷¹ BM Add.MS 6788, ff. 205–210*.

⁷² Wright, Edward, Certaine errors in navigation, London, 1599, sigs. Mm4-O01^v.Google Scholar

⁷³ BM Add.MS 6788, f. 469.

⁷⁴ Reinhold, Erasmus, Tabulae prutenicae, Tübingen, 1551.Google Scholar

⁷⁵ Copernicus, , On the revolutions of the heavenly spheres (tr. introduction, and notes by Duncan, A. M.), Newton Abbot, 1976, p. 155.Google Scholar

⁷⁶ Bourne, , op. cit. (60), sigs. Dviii–Eiiii.Google Scholar

⁷⁷ Bourne, , op. cit. (70).Google Scholar

⁷⁸ Çamorano, Rodrigo, Compendio de la arte de navegar, Seville, 1581, f. 17^v.Google Scholar

⁷⁹ Waghenaer, Lucas, Spieghel der Zeevaerdt, Leyden, 1584, p. 12.Google Scholar

⁸⁰ Blundeville, Thomas, His exercises, London, 1594, p. 344.Google Scholar

⁸¹ Cyprianus Leovitius, Ephemeridum novum… Augsburg, 1557.

⁸² Stadius, Joannes, Ephemerides… 1554 usque ad… 1600, Cologne, 1570Google Scholar; Magini, Joannes, Ephemerides… (1581–1620), Venice, 1582.Google Scholar

⁸³ See p. 250 above.

⁸⁴ For 1593 the maximum errors in Stadius's and Leovitus's tables were ⅔ and ⅓ respectively; see n. 127, below.

⁸⁵ BM Add.MS 6788, ff. 468–9.

⁸⁶ See below, p. 257.

⁸⁷ ibid.

⁸⁸ BM Add.MS 6788, f. 469.

⁸⁹ ibid.

⁹⁰ See n. 57, above.

⁹¹ HMC 241/11, pp. 2–3. In fact the maximum solar parallax is only about 9″: Smart, , op. cit. (54), p. 420.Google Scholar

⁹² The calculation of this value has had to be omitted due to cost and lack of space. Full details are available from the author.

⁹³ Bm Add.MS 6788, f. 489.

⁹⁴ In practice it was usually too small for navigators to bother about; see BM Add.MS 6788, f. 489.

⁹⁵ Brahe, Tycho, De mandi aethereii recentioribus phaenomenis, Uraniburg, 1588, 74.Google Scholar

⁹⁶ Wright, , op. cit. (72), sig. G.g.2.Google Scholar

⁹⁷ BM Add.MS 6788, f. 489.

⁹⁸ Lohne, J. A., ‘Harriot’, in Gillispie, C. C. (ed.), Dictionary of scientific biography, New York, 1972, vi, 124–9 (125).Google Scholar

⁹⁹ Copernicus, , op. cit. (75), book III, chapter XVI, p. 173.Google Scholar

¹⁰⁰ Dreyer, J. L. E., Tycho Brahe, New York, 1963, p. 333.Google Scholar

¹⁰¹ Wright, , op. cit. (72), sigs. Hh3^v-Mm2^v.Google Scholar

¹⁰² Bourne, William, A regiment for the sea, 1574 (ed. by Taylor, E. G. R.), Cambridge, 1963, p. 189.Google Scholar

¹⁰³ Roche, , op. cit. (23), pp. 104–5.Google Scholar

¹⁰⁴ Table 1, below.

¹⁰⁵ See n. 92, above.

¹⁰⁶ In 3½ hours the sun moves approximately 9′ in longitude.

¹⁰⁷ See table 1, below and n. 92, above.

¹⁰⁸ BM Add.MS 6788, f. 206.

¹⁰⁹ From Table 1, the errors in the equinoxes in 1593 are —3^h 29′ and +2^h42′ respectively. Half the difference is 23½ minutes.

¹¹⁰ BM Add.MS f. 207^v, and plate 2.

¹¹¹ See nn. 99, 100, 101, above.

¹¹² Roche, , op. cit. (23), p. 35.Google Scholar

¹¹³ HMC 241/11, pp. 18, 19, 20.

¹¹⁴ BM Add.MS 6788, f. 469.

¹¹⁵ The sun takes only four minutes of time to move one degree of terrestrial longitude. The effect on declination is negligible.

¹¹⁶ Harriot was actively engaged in theoretical as well as in practical cartography; see Shirley, John W. (ed.), op. cit. (2), pp. 48, 54–90Google Scholar; Salisbury MSs, op. cit. (8), pp. 256–7.Google Scholar

¹¹⁷ Saxton, Christopher, Chartae geographicae comitatum Angliae et Walliae, London, 1579.Google Scholar

¹¹⁸ Tuckerman, Bryant, Planetary, lunar, and solar positions, 601 BC to AD 1649, 2 vols., Philadelphia, 1962, p. 64.Google Scholar

¹¹⁹ Julian year—tropical year = 11.25 minutes; cf. Smart, , op. cit. (54), p. 420.Google Scholar

¹²⁰ The other possible starting date is the spring equinox of 1590. Harriot would hardly have chosen this as his most accurate equinox since he was then only just beginning, if he had begun at all.

¹²¹ See n. 92, above. As was mentioned earlier, it is most unlikely that Harriot calculated the orbital parameters from actual observations of the solstices. However, the accuracy of his predicted times for the solstices of 1593 derived from the accuracy of these parameters. Harriot's declination table was sensitive to a change of 1° in the position of the apogee.

¹²² Brahe, Tycho, Astronomiae instauratae progymnasmata, Uraniburg and Prague, 1602, pp. 57, 60.Google Scholar

¹²³ Wright, , op. cit. (72), sig. Kk 1^v.Google Scholar

¹²⁴ Again using Tuckerman's Tables, op. cit. (118), and reducing to a meridian 4° W of Greenwich, noon longitudes at 10-day intervals were determined. The solar declination was then calculated using Smart's formular for the obliquity of the ecliptic, op. cit. (57). The results were rounded oft to the nearest minute.

¹²⁵ Wagenar, Luke, The mariner's mirrour, englished by Ashley, Anthony, London, 1588, sig. A4^v.Google Scholar

¹²⁶ Norman, , op. cit. (70), sig. F iv.Google Scholar

¹²⁷ For the Alphonsine Tables the maximum error in longitude is 20′ (Leovitius (1557), op. cit. (81), sig. PP3^v), therefore the maximum error in declination would be: 20′ x sin 23°33′ + 2′ (parallax) ≈ 10′. For Stadius's Ephemerides (1570), op. cit. (82), sig. Bbbbbbb 3^v, the maximum longitude error is 39′ and the corresponding error in declination is ≈ 18′.

¹²⁸ BM Add.MS 6788, f. 469. A latitude error of one degree is an error of 60 nautical miles, or 111 kilometres. One nautical mile= 1.85 kilometres.

¹²⁹ See next paragraph.

¹³⁰ P. 264, above.

¹³¹ HMC 241/V1b, pp. 31–2.

¹³² BM Add.MS 6788, ff. 423, 476^v, 480–484°; Roche, , op. cit. (23), pp. 116–38.Google Scholar

¹³³ Pepper, , ‘Harriot's earlier work’, op. cit. (2).Google Scholar

¹³⁴ BM Add.MS 6788, ff. 485–9; HMC 241/V1b, p. 32.

¹³⁵ ibid., f. 475.

¹³⁶ ibid., f. 469.

¹³⁷ Nuñez had earlier drawn attention to this error; op. cit. (24), p. 29.Google Scholar

¹³⁸ Near the equinoxes the declination varies by about 24′ per day (BM Add.MS 6788, f. 206). At a geographic longitude 180° away from the meridian of the ‘Regiment’ there would be a difference of 12′ in the noon declination on the same day.

¹³⁹ BM Add.MS 6788, ff. 470–1.

¹⁴⁰ Roche, , op. cit. (23), p. 145.Google Scholar