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    Re: accuracy of Cook's lunars
    From: Alexandre Eremenko
    Date: 2013 Jan 9, 18:15 -0500

    I can conclude from this message that your student understands what
    she is doing, and that was a serious research.
    If she continues her research in this direction
    (is not clear from her message whether she intends to), I would like to be
    on her mailing list. Please pass her this message and my e-mail:
    > Alex (et. al.) -
    > Here are some answers from my student regarding her project on Cook's
    > lunars.
    > I tend to agree with her that a lot of work on this kind of thing is one
    > of
    > successive approximation.   You try to fit the data, the fits raise
    > questions, you look at the data in another way, etc etc.   (I omit my
    > questions, but they're along the lines of what we've discussed).
    > Begin clip
    > ------------------------------------------------------------
    > As much as I would like to duck behind bravado, I have to say I'm pretty
    > stumped. You've raised many good questions, and I'm not sure I have
    > satisfactory answers. But here's a try.
    > Most of Cook's coordinates were taken at sea, but he is careful to make
    > distinctions. The journals are useful in that they do not merely log data,
    > but flesh-out measurements within the context of a narrative. For example,
    > Thursday 12/14 (1769): In the evening, having split the shore and mizen
    > (?)
    >> topsails, we brought the ship under her courses; and at midnight, we
    >> wore,
    >> and stood to the southward till five in the morning ... we discovered
    >> that
    >> we had fallen much to the leeward since yesterday morning. At noon, our
    >> latitude by observation was 34 degrees 6 minutes south ... and at noon
    >> the
    >> next day we were in latitude 34 degress 10', longitude 185 degrees 45' W
    >> and by estimation about seventeen leagues from the land.
    > Being a sponsored scientific expedition, Cook and his crew made conscious
    > efforts to be precise about their measurements. Most (though not all)
    > longitude & latitude sightings were described in relation (or lack
    > thereof)
    > to land. It's for instance clear that the coordinate readings in the above
    > excerpt were not made on land, but in the middle of sea. Others, however,
    > were recorded and refined on land:
    > Monday 12/11 (1769): Early in the morning, we stood in with the land,
    > seven
    >> leagues to the westward of Doubless Bay, the bottom of which is not far
    >> distant from the bottom of another large bay, which the shore ... being
    >> separated only by a low neck of land, which juts out into a peninsula
    >> that
    >> I have called Knuckle Point. About the middle of this bay, which we
    >> called
    >> Sandy Bay, is a high mountain, standing upon a distant shore, to which I
    >> gave the name of Mount Camel. The latitude here is 34 degrees 51' S and
    >> longitude 186 degrees 5'.
    > I also read in a secondary source that the majority of lunar readings were
    > made by Charles Green, assistant to Astronomer Royal Nevil Maskelyne (the
    > lunar guy himself). To be precise, he recorded hundreds of sets of lunar
    > observations for locations to be incorporated into new maps. This would
    > not
    > have been possible in mid-ocean ship conditions (I think?).
    > In other words, most of the time, Cook was clear about location:
    > observations at sea meant observations at sea, those referring to capes or
    > beaches or islands are usually accompanied by descriptions of local flora
    > &
    > fauna, meaning that the ship made a stop on land. Cook is also very good
    > at
    > being specific about the layout of the land itself: islands often have
    > western and eastern extremities, as does beaches and even inland sea
    > routes
    > (e.g. entrance to Queen Charlotte's Sound). And of course, much of this
    > coordinates were meant to be incorporated into new maps, and so maps made
    > immediately after the expedition are good sources for location.
    > Nonetheless, the question about precision still remains: exactly how
    > precisely can we assign modern/accurate coordinates to Cook's coordinates,
    > so that the error calculation actually mean something. Admittedly, this
    > problem made me break out in cold sweat throughout the project--especially
    > when dealing with measurements based on dastardly vague "cape-this" and
    > "cape-that". Here I assume that "cape", "bay", "point" refer to shores
    > where Cook's ships harbored and where observations were made. I threw out
    > locations when such "cape" "bay" or "point" referred to a wide stretch of
    > land. For the locations I worked with,  "north" vs "south" of a "bay" or
    > "beach" is significant only in seconds of longitude. However, because
    > Cook's measures were almost always precise only to minutes of longitude, I
    > decided to allow this imprecision in seconds of longitude. This means I
    > had
    > to round all error calculations to minutes of longitude rather than
    > seconds
    > (unfortunately, not sure if this is acceptable methodology).
    > The problematic nature of historical data demands careful handling. My
    > experience with Cook's journals is definitely a learning process, and
    > frustratingly layered by multiple attempts to redo things. To be honest,
    > the "final turned-in" product is still not good, and the data could
    > benefit
    > from additional cleaning and scrutiny. But I do believe that there is
    > enough resources and primary documents out there to render this sort of
    > error analysis meaningful. It just requires a lot of research and care.
    > On Tue, Jan 8, 2013 at 1:11 AM, Geoffrey Kolbe > wrote:
    >> I seem to recall that Cook's survey of the coast of the Northern Island
    >> of
    >> New Zealand was amazingly accurate in latitude, but that was offset by
    >> some
    >> 25 miles (from memory) in longitude. I recall that he landed at least
    >> once
    >> to make astronomical observations. No doubt somebody will be better
    >> informed than I on this subject..
    >> Geoffrey
    >> At 15:24 07/01/2013, you wrote:
    >>  I have a more general question:
    >>> What observations of Cook's expedition from known places on land
    >>> are available?
    >>> Except Point Venus, Thaiti, that I know.
    >>> Alex.
    > View and reply to this message: http://fer3.com/arc/m2.aspx?i=121820

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