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    Re: Coordinates on Cook's maps
    From: Alexandre Eremenko
    Date: 2007 Apr 19, 15:50 -0400

    > I agree that it would, but I don't know if that has ever been studied. I
    > could try to get an answer to that question from my contacts at Greenwich.
    I read several long papers on the subject of "circle division",
    in particular on Bird (who was famous for his accurate division
    by hand), and on Ramsden and other inventors of the dividing
    engins. I was very
    disappointed that NONE of these papers
    even raised the question: just how accurate this division was?!
    To me this seems the very first question to ask if you study
    this matter. But apparently the logic of the authors of these
    papers is different...
    So I study the question myself using the information available
    to me: I examine certificates of the sextants sold on e-bay:-)
    Unfortunately, they did not supply certificates in the first
    half of the XIX century, so I can only study recent history of
    Interestingly, many mid XX century sextants have quite large
    corrections in their certificates (30" to 45").
    Which means of course that the manufactures simply DO NOT CARE
    to make a perfect arc. There is no doubt that in XX century there
    is such a technical possibility: the arcs of theodolites, for
    example are divided to much greater precision than sextant arcs
    (good theodolites measure to 1" and some to 0.1")
    > No, it was an "automatic" process, though a very time-consuming one, to make
    > a master wormwheel.
    I agree that machine-divided sextants probably shouldB have smaller
    arc irregularities than hand-divided.
    > Dividing by hand called for the sort of construction we used in geometry
    > classes at school,
    Maybe in XIX century school. Not in a modern one:-(
    > How you got an absolute calibration right, in the first place, is a
    > mystery to me.
    By high school geometry and a pair of compasses,
    as you explained before:-)
    This is the only primary source of "absolute calibration".
    Even with star distances: before you use them to calibrate
    your instrument, you have to measure them with some other instrument
    and make a star catalog.
    So I am afraid everything goes back to hand-divided scales
    of large astronomical instruments in the observatories.
    They had a standard of a meter and of a kilogram but they
    never had a standard of a degree!
    Because in principle, you can reproduce a given angle with
    arbitrary precision anywhere "from nothing" just by pure geometry.
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