Columbus's method of determining longitude : An analytical view

Journal of Navigation

Volumn 49, Issue 1, 1996, Pages 95-111

  Pickering, Keith A ^a  

^a NONE

Author keywords

Astronomical navigation; History

Indexed keywords

COLUMBUS; LONGITUDE; LUNAR ECLIPSE;

EID: 0029730507     PISSN: 03734633     EISSN: None     Source Type: Journal    
DOI: 10.1017/S037346330001314X     Document Type: Article

References (45)

1. West, D. C. and Kling, A. (1991). The Libro de las profecias of Christopher Columbus. University of Florida Press, Gainsville, pp. 226-227.
2. ibid.
3. Olson, D. W. (1992). Columbus and an eclipse of the Moon. Sky & Telescope (October), 437-440.
4. Ashley, R. E. (1991). The search for longitude. The American Neptune 51:4, 261-262.
5. Molander, A. B. (1992). Columbus and the method of lunar distances. Terrae Incognitae 24, 65-78.
6. Dunn, O. and Kelley, J. E. Jr (1989). The Diario of Christopher Columbus's First Voyage to America, 1492-1493. Norman and London, University of Oklahoma Press, p. 329.
7. Morison, S. E. (1942). Admiral of the Ocean Sea. Little, Brown, & Co., Boston, p. 65.
8. Jane, C. (1988). The Four Voyages of Columbus, 2 vols. Dover Publications, New York, II 34, 84.
9. Kelley, J. E. Jr. (1983). In the wake of Colombus on a Portolan chart. Terrae Incognitae 15, 102-107.
10. Marden, L. (1986). The first landfall of Columbus. National Geographic 170, 573-575.
11. McElroy, J. W. (1941). The ocean navigation of Columbus. The American Neptune 1, 209-240.
12. Richardson, P. L. and Goldsmith, R. A. (1987). The Columbus landfall: voyage track corrected for winds and currents. Oceanus 30:3, 3-10.
13. Molander (1992), 77-78.
14. Molander (1992), 75.
15. Dunn & Kelley (1989), p. 341.
16. Jane (1988), II, 26.
17. Dunn & Kelley (1989), p. 373.
18. Molander (1992), 74, fn 19.
19. Davies neglected to calculate parallax when determining the Moon's apparent position. Rawlins' corrected analysis shows that Vespucci must have been off the coast of Guinea (not Brazil as Vespucci claimed) to have made the observation described. Both Davies' paper and Rawlins' rebuttal are unpublished; but see Dennis Rawlins, 'Peary, verifiability, and altered data', D10 1:1 (1991/1/14), 29.
20. Dr Charles Kowal as quoted in The Washington Post, 11 Dec. 1990: A5.
21. Molander (1992), 68.
22. Molander (1992), 68-69.
23. have followed Molander's convention and used Columbus's daily positions as given by John W. McElroy in 'The ocean navigation of Columbus', The American Neptune I (1941), 219-239. The position on 27 February is not given by McElroy in this article, but it can be measured from the map in Morison (1942) (opposite p. 228) at 37°-7 N, 17°-6 W.
24. The conjunction occurred at 22 : 16 : 10 Universal Time on 24 September, which is 1912 hours Local Mean Solar Time for an observer at 45° 58-4′ W, McElroy's position at dawn on the 26th - which would have been dawn on the 25th after applying Molander's 24-hour shift. Molander's given time of 1907 hours LMST is therefore off by at least 5 minutes. Eliminating the 24-hour shift puts Columbus at 45° 9′.2 at dawn on the 25th, and the conjunction at 0715 hours. But we should really interpolate McElroy's dawn positions for 1915 hours the previous night, which would put Columbus at 29° 8′.4 N, 44° 47′.8 W, and the time of conjunction at 1917 hours LMST. We should also note that in this era before accurate clocks, the concept of mean time was unknown; the time used in this period was local apparent solar time, or 'sundial time'.
25. Lunar positions have been calculated from Michelle Chapront-Touze and Jean Chapront, Lunar Tables and Programs from 4000 B.C. to A.D. 8000 (Richmond: Willmann-Bell, 1991). Accuracy at this epoch is approximately 37 areseconds. Planetary positions have been calculated from Pierre Bretagnon and Jean-Louis Simon, Planetary Programs and Tables from - 4000 to + 2800 (Richmond: Willmann-Bell, 1986). Accuracy at this epoch is approximateily 7 aroeconds for Jupiter and Saturn, 23 arcseconds for Mars, 10 areseconds for Venus and Mercury, and 2 arcseconds for the Sun. I have optimistically assumed that Columbus was aware of lunar paralax and corrected for it at all times; this correction is absolutely necessary for any longitude determination, since it can alter the moon's apparent location by over a degree and the resulting position fix by as much as 30° in longitude. I must point out, however, that there is no historical evidence that Columbus was aware of lunar parallax, nor of how to correct for it.
26. Lunar positions have been calculated from Michelle Chapront-Touze and Jean Chapront, Lunar Tables and Programs from 4000 B.C. to A.D. 8000 (Richmond: Willmann-Bell, 1991). Accuracy at this epoch is approximately 37 areseconds. Planetary positions have been calculated from Pierre Bretagnon and Jean-Louis Simon, Planetary Programs and Tables from - 4000 to + 2800 (Richmond: Willmann-Bell, 1986). Accuracy at this epoch is approximateily 7 aroeconds for Jupiter and Saturn, 23 arcseconds for Mars, 10 areseconds for Venus and Mercury, and 2 arcseconds for the Sun. I have optimistically assumed that Columbus was aware of lunar paralax and corrected for it at all times; this correction is absolutely necessary for any longitude determination, since it can alter the moon's apparent location by over a degree and the resulting position fix by as much as 30° in longitude. I must point out, however, that there is no historical evidence that Columbus was aware of lunar parallax, nor of how to correct for it.
27. Dr Schaefer has contributed a letter on this subject to the ongoing Columbus Landfall Round Robin, of which both Molander and myself are contributing members. These correspondences have a wide distribution, and can be considered public, albeit unpubusned.
28. Molander (1992), 75, fn 2o.
29. By coincidence, no Mercury conjunctions are correlated to a position fix.
30. By coincidence, a probably invisible daytime conjunction with Venus is correlated to a position fix.
31. Including daytime conjunctions would have given Molander one more correlation success, on 15 February, but the large increase in P caused by including all the uncorrelated daytime conjunctions actually would have been less favourable for the alleged lottery-odds coincidence, even with the 15 February success. Thus, Molander excludes the daytime conjunctions. By coincidence, Molander also excludes the position of 15 February and so avoids a correlation failure.
32. By coincidence, two of Molandrr's correlation successes occur below the horizon
33. By coincidence, all of these errors favour a correlation between conjunctions and position fixes.
34. Molander (1992), 75, 78.
35. Molander (1992), passim.
36. Molander (1992), 77.
37. Jane (1988), II, 12.
38. Molander (1992), 77
39. Ibid.
40. Morison ( 1942), p. 68.
41. Jane (1988), II, 34, 84.
42. McElroy (1941), 219-239.
43. Chapront-Touzé & Chapront (1991).
44. William H. Beyer, CRC Standard Mathematical Tables and Formulae, 29th edition (CRC Press, Boca Raton, 1991), p. 492.
45. William H. Beyer (ed), Handbook of Tables for Probability and Statistics, 2nd Edition (Chemical Rubber Co., 1968), p. 283.