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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: David Thompson's Navigational Technique
From: Frank Reed CT
Date: 2004 May 31, 22:24 EDT
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
"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
