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    Re: A noon sight conundrum
    From: Wolfgang K�berer
    Date: 2004 Mar 3, 15:32 +0100

    Dear George,
    I am following my tendency to make nitpicking remarks again. In December you
    commented on early declination tables as follows:
    "Early navigators went by a set of declination tables that were the same for
    each year, and accepted the inaccuracy. It was Pedro Nunez in about 1530
    who recognised that he could make a more accurate declination table for
    leap years, another for leap years +1, leap years +2, and leap years +3,
    and that would be all that was needed, for many years. They became
    This is not historically correct: Although the earliest printed navigation
    manual that we know, the "Regimento do Astrolabio" ( ca.
    1509) contains tables for the declination of the sun only for one year, the
    next manual, the "Tractado da Spera" ( ca. 1516) has tables
    for the leap year and the following 3 years which were probably prepared for
    the circumnavigation of Magellan. The fact that one has to take into
    consideration the fact that a solar year does not have exactly 365 days was
    therefore well known before Nunez to the anonymous author that constructed
    these tables on the basis of Zacuto`s "Almanach Perpetuum" (Leiria 1496).
    The most thorough study of the Portuguese manuals can be found in Luis de
    Albuquerque`s "Guia N?utico de Munique e Guia N?utico de Evora" (Lisboa
    1991) and "Astronomical Navigation" (Lisboa 1988).
    In comparison to these manuals Nunez` works are of a purely theoretical
    nature; their tables do not contain solar declinations for every day but
    positions of the sun in the zodiac; one then has to consult a separate table
    "Tavoa das declinacoes" to find the declination of the sun (cf. Nunez
    "Tratado da sphera..." Lisboa 1537 fol. E IIII). This was standard
    astronomical practice for some time by then - Zacuto uses it as well as
    Early last month you remarked in another post:
    "I have a modern reprint of Matthew Bourne's "A Regiment for the Sea",
    which, two centuries before the Nautical Almanac, provided Sun declination
    tables for each day at noon over a four-year cycle starting
    1574: taken, I suppose, from Pedro Nunez."
    William (not: Matthew) Bourne`s "Regiment for the Sea" does contain
    declination tables for the sun over a four-year cycle as does about every
    navigation manual in Portuguese, Spanish, French, Dutch, German and English
    as well as almost all Portuguese Portolan Atlases produced after 1520. It is
    highly unlikely, though, that Bourne`s tables were derived from Nunez;
    Bourne certainly knew the English translation of Matin Cortes` "Arte de
    Navegar", but there is no indication that he read or even knew the works of
    Nunez - they were printed in Latin and Portuguese. Apart from that Nunez
    gives as the maximum of the sun`s declination a value of 23 degrees 30
    minutes (Nunez "Tratado da sphera..." Lisboa 1537 fol. E IIII), whereas the
    tables of Bourne`s "Almanacke for three yeares" (London 1571) and "Regiment
    for the Sea" give a maximum declination of 23 degrees and 28 minutes. It
    should be fun to compare the values of the different tables to develop some
    kind of lineage; I have done this for the oldest German navigation manual of
    1578 and found out that they are derived from the Portuguese "Tractado da
    spera" of ca. 1516.
    Best regards,
    Wolfgang Koeberer
    Life member of
    TINSTAARG (There is no such thing as a responsible gun)
    TOTTCHAIAUITPOBIAGW (The only thing that Charlton Heston and I agree upon is
    that Patrick O`Brian is a great writer)
    CSSTHOBIEMAATNCTKA (Can`t somebody stop this habit of broadcasting in
    e-mails memberships and allegiances that nobody cares to know about)

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