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    Re: Almanac errors
    From: Frank Reed
    Date: 2008 Mar 09, 18:59 -0400

    George H, you wrote:
    "Thanks to Frank Reed for some really useful information on Almanac
    accuracy, much of which was quite new to me."
    Sure thing.
    And you asked:
    "He provided as a reference Souchon's "Treatise on Practical Astronomy",
    Paris 1883, which I had never even heard of before. Frank, is that in
    English tramslation, as the given title might imply, or is it in French? My
    own French is very halting, but even so, I might give it a try if I can find
    a copy."
    Alas, the "Traite d'astronomie pratique" is in the Frankish tongue. Speaking
    frankly, as I always do, it's probably not worth the trouble to slog through
    gallically. If you want to give it an essai, you can download the complete
    book from Google Books here:
    (click "Download PDF". It's ten megabytes).
    If you really want to brush up on your technical French and read a fine book
    on the history of navigation, rather than Souchon, I would strongly
    recommend "Histoire Generale de la Navigation du XVe au XXe Siecle" (General
    History of Navigation from the 15th to the 20th Century) by F. Marguet. I
    originally learned of this book in a post by Wolfgang almost four years ago.
    Back then, it was available online, but it appears someone realized that it
    was still under copyright protection, especially under the strong terms of
    French law, and it is no longer online. If you ask around, you may find
    someone with a digital copy that they're willing to let you pirate. I ended
    up buying a hard-copy of the book for $75 --which should give you a sense of
    how much I enjoy it.
    You wrote:
    "Right at the start of the Nautical Almanac, for 1767, Maskelyne employed a
    team of human "computers", who were to make the complex calculations"
    I've been meaning to try and pin down the date when the word "computer" no
    longer refers to a human. I sometimes tell people that an 18th century
    phrase like "the computers used formulae" really has to be translated into
    21st century English. The nearest equivalent today might be "the accountants
    used forms".
    You mentioned a source which:
    "analysed 4000 observations that had been made of the Moon's position over
    the previous 36 years, and compared them with predictions. Will those
    minutes contain any detailed infomation? Probably not, but I live in hope."
    You don't need them! The position of the Moon in that era is now known to
    the nearest second of arc and sometimes better. The best that they could do
    back then was compare the predicted (published) positions with contemporary
    observations. But today, we can compare the known positions (which are
    available digitally and are based on physical models as well as the best
    contemporary observations) with any published positions you might wish to
    And you wrote:
    "One puzzle is that Forbes, and Frank, both refer to "mean error", as well
    as "greatest error". The divergence can be positive or negative, and one
    might hope that its mean would be about zero, which is why root-mean-square
    error, or standard deviation, is a more useful quantity today.."
    Yeah, it's mean absolute error. This is nearly the same as standard
    deviation for this sample. Of course, these "errors" are not like
    observational errors --they're not distributed normally. They are bounded.
    That's why it's also meaningful to quote a maximum error. As I noted in
    another post today, for a sample of twenty LDs from the 1803 Nautical
    Almanac, the mean absolute error is 33 arcseconds, the maximum is 67
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