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    Re: Cross Staff in use, 1574 image
    From: George Huxtable
    Date: 2009 Oct 18, 11:03 +0100

    Wolfgang and Nicolas have provided authoritative answers to some of Brad's
    questions about the cross-staff, but there's a bit more to add.
    
    Brad wrote- "From the recommendations of "A Regiment for the Sea", Bourne;
    the mariner was advised to align the upper limb of the sun with the upper
    edge of the cross staff, but only when above 60 degrees.  Below 60 degrees,
    and the mariner is informed to align the center of the sun with the upper
    edge."
    
    Not the way I read his tract. Though that text may run without paragraph
    separations, there are section-headings in the margins. The previous section
    had been headed ""The astrolobe is best to take the heigth of the Sunne at
    .60. 70. or .80 degrees in heigth". But then he goes on to discuss what to
    do when your staff is not provided with dark glasses, marginal note "How to
    preserve your eyes when you touch the Sunne with your crosse staffe and have
    no glasses. The diameter of the Sunne is 30. or .31. minuts". No longer,
    there, is he referring to the 60-degrees-and-over situation, as I read it.
    He is providing a general rule for observing the Sun at any altitude, if you
    have no dark glass at the tip of the transom. He recommends that then you
    should protect your eyes by covering the complete Sun disc with the top of
    the transom, and subtract 15 minutes from the result. Not much chance of
    doing that in a rolling vessel!
    
    However, I don't see any great instrumental difficulty about the procedure,
    using a dark glass, of putting the Sun's mid-point at the tip of the
    transom, by eye estimation. To my mind, anyone should be able to bisect the
    Sun disc, by eye, to put its centre within a couple of minutes of the truth;
    an error that's small in comparison with the imprecision of a any
    cross-staff.
    
    ================================
    
    Brad and Wolfgang referred to the illustration Brad gave from Apian, at
    http://www.fer3.com/arc/imgx/COSMOGRAPHIA-PETRI-APIANI-1574.doc
    
    Unfortunately, the top of that picture was cut off, but as it's rather
    interesting. I attach a complete, slightly-different engraving from another
    edition.
    The picture on the left shows the geometrical construction required to
    divide the stick of a cross-staff. The bottom picture shows a portly
    observer measuring a lunar distance. He is aligning the centre of the Moon
    with the end of the transom; more difficult to estimate than for the Sun,
    especially with a crescent Moon.
    
    But look at the top picture, which Wolfgang points out is intended to show
    parallax. Or is it?
    
    It shows two observers, 30 degrees apart on the Earth's surface, seeing the
    Moon at two different positions in the sky, against the star background,
    that are also 30 degrees apart! But that's not how parallax works: if it
    was, lunar distance navigation would be simple. Moon parallax can never be
    more than a degree-or-so. It's only because the distances of Moon and sky
    are so grotesquely distorted that the engraving has come out as it has. Such
    a picture would mislead any reader's understanding, and indeed raises the
    question as to whether the designer of the engraving, or the author of the
    text, really understood the nature of parallax. Of course, at that date Moon
    and star distances were not precisely known, but even Ptolemy and Hipparchus
    knew much better than that, as did Kepler.
    
    ===================
    
    Anyway, the whole notion of lunar distance measurement of longitude was then
    nonsense, for two reasons. First, the precision of a cross-staff was nowhere
    near good enough for a lunar. Second, the predictions of the Moon's motion
    were nowhere near good enough either. It was an interesting idea, that could
    not be fulfilled until two centuries later.
    
    But no question about it, the cross-staff (or Jacob's staff, ot Balestilla)
    was a worthwhile and useful instrument for measuring latitude, widely used
    by mariners over several centuries.
    
    George.
    
    contact George Huxtable, at  george{at}hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
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