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    Re: Coordinates on Cook's maps
    From: Alexandre Eremenko
    Date: 2007 Apr 18, 14:53 -0400

    Dear George,
    On Tue, 17 Apr 2007, George Huxtable wrote:
    > Cook had metal sextants, with large radius, and Vernier scales, so their
    > scales could be read rather precisely. But they were divided by hand,
    > machine division being a decade or two into the future, so systematic errors
    > in the scale calibration were the big problem. I suppose they could have
    > been corrected by a programme of measuring star-to-star distances, but I
    > have no idea whether that was ever done.
    These statements raise several interesting issues.
    Let me share my own experience (and I will appreciate if
    other list members add to this).
    1. Reading a vernier scale to 0.1' is a tricky business,
    especially at night. This can be very annoying and time consuming
    but this cannot be a serious additional source of errors
    I mean no more than 10"-15" if you read with maximal care,
    even on a 7 inch arc.
    2. That sextants were divided by hand. It would be very interesting
    to know how accurately were they divided. I do not see a priori reasons,
    why machine division should be more precise. Were not the dividing
    machines themselves divided by hand?
    More serious matter is that at that time they were not apparently
    "certified". (The Kew observatory certificates begin
    somewhere in XIX century). And it is not clear to me
    how those early sextant were really
    tested. And whether they were tested.
    3. Concerning the star-distance method of testing,
    I remember your own question, George, on the old list
    several years ago: "Has anyone succeded in finding the arc error
    of a modern sextant with star distances?" (I cite from memory).
    Nobody ever replied that s/he succeeded:-)
    I failed, despite my serious efforts to so this over 3 or 4 years.
    I very seriously doubt that star distances permit you
    to test your arc to 0.1' or 0.2' accuracy. I could never do this.
    Same applies to IC from stars btw. It is only the constancy of my SNO
    index error that permits me to determine it reliably by very many
    My Lunars are better than star distances.
    4. When speaking of high precision Lunars
    (I am talking of 0.2' accuracy
    or so) I see two main difficultiues:
    a) How to achieve a precise touch of the two objects in
    your field of view. This seems to require years of continuous practice.
    It took me 3 years of frequent observations to achieve the results I
    recently posted. (My sight is considered normal by doctors and I am 50+
    years old). The errors here are NOT random, and cannot be eliminated
    by averaging. The observer just has to feel how the picture should look
    then the objects really touch. And feel this under very different
    conditions of brightness, sextant position and the loo
    of the objects themselves. This is what I find hardest.
    One needs reasonably good optics. (I find the optics on my old
    sextants just terrible
    in comparison with the SNO inverting scope).
    b) Sextant rigidity. This (together with the optics)
    was probably a major
    of old sextants. Again, I find my modern SNO far superior to the
    old vernier C. Plath in this respect. There is a lot of discussion of
    rigidity in XVIII century literature, and one of Cook's associates
    complains that his sextant has unpredictably changing instrumental
    error which he cannot explain.
    Same problem I experienced for several
    years, and I still don't know whether this was an instrumental error
    or a personal error, but it looks that by now most of it is
    eliminated. Though if one looks at the distribution of my
    errors produced in a previous message by George, you see that it is
    asymmetric, it is not a normal distribution, and it is slightly
    biased to the positive side.
    U suppose that the main reason why they eventually switched to smaller
    frames (6 and 1/2 to 7 and 1/2 inches) was rigidity problems.
    It is probably impossible to make a brass frame of 9 inches radius
    rigid enough, and so that you could still lift your sextant without
    an assistant. I also suspect that modern lightweight alloys
    (duralumin) permitted to make much more rigid frames.
    Anyway, the conclusions from my limited experience are
    a) achieving 0.2 accuracy of a measurement is VERY hard
    b) averaging does not always help (because systematic personal
    and instrumental errors dominate the overall error).
    Of course, averaging helps to some extent (as seen from my statistics,
    for example)
    c) on the question whether the best XVIII sextants were better
    or not than those which are available nowadays I still have no
    definite answer. Here by "better" I mean "better ultimate accuracy".
    There is no doubt that modern sextants are much more convenient
    in use. I used to think that the old ones were better
    but now I don't think this anymore.
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