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    Re: David Thompson's Navigational Technique
    From: George Huxtable
    Date: 2004 May 29, 22:41 +0100

    Congratulations to Ken Muldrew for a masterly account of David Thompson's
    navigation. It qualifies him for full membership of the Band of Lunartics.
    I have a few comments and questions about this Thompson paper.
    1. Ken said-
    >This article is intended as a supplement to the lengthy and
    >informative discussion of David Thompson's navigational technique
    >written by Jeff Gottfred and published in the Northwest Journal
    >(Gottfred, Jeff. How David Thompson Navigated. Northwest Journal Vol.
    >9. ISSN 1206-4203. Available at:
    >http://www.northwestjournal.ca/dtnav.html). Although Gottfred covers
    >almost the entire subject in this excellent article, there are a few
    >minor points that can be clarified for completeness.
    I agree that Gottfred's series about Thompson makes really informative
    reading, but I have found aspects of the relevant chapter (chapter 7) to be
    somewhat confusing. In particular, his use of the same symbols m and s to
    represent both the apparent altitudes of Moon and Sun, and also the "corner
    angles" of the lunar triangle. The diagram showing that lunar triangle is
    so deformed as to confuse rather than clarify. And I calculate the "corner
    angle" s, at the Sun, to be 60.3625deg, not, as Gottfred does, 62.4644deg
    (not that it makes much difference to the end-result).
    2. In Ken's transcript, a capital-pi symbol sometimes appears, which
    presumably indicates some fraction of a mile, as in-
    "Our Co to the crossing Place of the Clear Water River may be about SEbE 2
    ? M."  Is this a symbol for "1/2"? In other places, "1/2" is spelled out,
    and comes over correctly.
    Ken, please clarify this. Just for interest, would these be magnetic
    courses? and if so, is the variation measured and stated, anywhere?
    3. Thompson's lunar distance sequences are very closely spaced in time and
    very smoothly varying in lunar distance. Clearly, he was a highly skilled
    observer; much more so than Lewis & Clark.
    4. Ken wrote-
    >Right ascension and declination for both the sun and moon are reduced
    >from the Greenwich time that results from adding the longitude by
    >account (converted to h:m:s) to the local time (as well as the
    >equation of time if the nautical almanac used mean time in 1800,
    >although perhaps they still used sun time then).
    They still used Sun time. The argument of the Nautical Almanac remained as
    Apparent Time until 1834, when it switched to Mean Time.
    5. >The true altitudes
    >of both the sun and the moon are then calculated (the following
    >method comes from Patterson's notebook that Lewis & Clark carried):
    My transcription of that manuscript notebook (with commentary) is available at-
    6. Ken wrote-
    >Thompson then subtracts the cleared distance (71?13'30") from the
    >true distance that he obtained from the almanac (71?13'54") to get a
    >difference of 24" (D by account being greater than the cleared,
    >measured distance). 24" in distance corresponds to 12" in time which
    >converts to 3 minutes of longitude. He then subtracts 3' from his
    >longitude by account (subtract because his D by account was greater)
    >to get a corrected longitude of 114?45'.
    I'm a bit worried by this procedure, as Ken describes it, in two respects.
    To start with, the "nominal" speed of the Moon across the sky background is
    something like 30 arc-minutes per hour (but note the qualification below),
    which allows it to go right around the sky in a month. But at that rate,
    wouldn't an angle of 24" in lunar-distance convert to 48" (not 12") in
    time, which would convert to 12 minutes (not 3 minutes) of longitude? Am I
    misunderstanding something here? Or was Thompson? Or is there a
    transcription error?
    But, leaving that matter aside, there's a weakness in this procedure, as I
    see it. It appears to assume that the lunar distance changes at a
    reasonably constant rate (of 30 arc-minutes per hour). That is only very
    approximately true. The effects of our old friend "parallactic retardation"
    can, under some circumstances when the Moon is high in the sky, cause the
    speed of the Moon with respect to the Sun or stars to drop to somewhere
    near half that value. If measuring to a star which is badly out of line
    with the Moon's direction of travel, it could reduce even further.
    In such an extreme case, correcting the longitude, even by the amended
    recipe I have suggested above, would only provide about half the change
    that's needed.
    Proceeding by iteration would overcome this problem, but that's not how
    Thompson worked, according to Ken's account.
    7. Thompson uses a curious procedure for establishing Sun altitude for his
    time-sight of the Sun, that I haven't seen before. He makes a series of
    timed measurements of Sun lower-limb altitudes, and then another series, of
    upper-limb altitudes, and processes each set separately to obtain two
    values of clock error, which is then averaged. It works, but I wonder why
    he does it that way?
    contact George Huxtable by email at george---.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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