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    Re: David Thompson's Navigational Technique
    From: Frank Reed CT
    Date: 2004 May 31, 22:24 EDT
    From Ken M's quotation of Witchell's Method:
    "Fifth, in table X [Moore's table numbering], look for this last
    corrected distance in the top column, and the correction of the
    moon's altitude in the left-hand side column; take out the number of
    seconds that stand under the former and opposite to the latter. Look
    again in the same table for the corrected distance in the top column,
    and the principal effect of the moon's parallax in the left hand side
    column, and take out the number of seconds that stand under the
    former and opposite the latter. The difference between these 2
    numbers must be added to the corrected distance if less than 90°, but
    subtracted from it if more than 90°; the sum or difference will be
    the true distance."

    In case anyone's interested in the "mathy" side of this, this is the quadratic or "Q" correction that I talked about a few weeks back under 'Easy Lunars'. Moore's table 10 lists the quantity (1/2)*x^2*cot(d) where x is any angle and d is the lunar distance. The quadratic term "Q" in the series expansion is (1/2)*(dh_moon)^2*(1-A^2)*cot(d) where dh_moon is the Moon's altitude correction and A is the Moon's "corner cosine" (the percentage that tells us how much of the Moon's altitude correction acts along the arc of th measured lunar). By multiplying this out, you get
        (1/2)*dh_moon^2*cot(d)  -  (1/2)*(dh_moon*A)^2*cot(d)
    so by entering table 10 twice, first with the Moon's altitude correction and then with the correction multiplied by A (which we've already calculated!), you get the complete quadratic correction.

    Frank R
    [ ] Mystic, Connecticut
    [X] Chicago, Illinois
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