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Re: accuracy of Cook's lunars
From: Alexandre Eremenko
Date: 2013 Jan 9, 18:15 -0500
From: Alexandre Eremenko
Date: 2013 Jan 9, 18:15 -0500
John, 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: eremenko@math.purdue.edu Alex. > 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. >>> >> >> >> >> >> > > > > > : http://fer3.com/arc/m2.aspx?i=121820 > > >