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    Re: Lunars
    From: Frank Reed
    Date: 2007 Sep 24, 22:13 -0400

    Fred H, you wrote:
    "I fail to understand what the date of invention of the quadrant has
    to do with the accuracy set for the longitude prize."
    Ok, Fred. Consider: how would those folks who recommended the prize have
    known back in 1714 that there would be a device invented, twenty years in
    their future, that could reliably measure angles to about 1' of arc?
    "It would seem
    that John Karl's explanation may be correct, in that the advisors to
    Parliament may have recommended setting the accuracy to 30' because
    they figured that lunars would be the method chosen and that 1' of
    arc was about the limit of accuracy for such a measurement,
    regardless of the instrument."
    Hmmm. Who in the world suggested that 1' of arc was the limit of accuracy
    for such measurements?
    The 30' level for longitude determination was chosen because "30 minutes
    accuracy in longitude is as good as anyone would ever need" (today that
    sounds a bit like saying "no one would ever need more than 640k of computer
    memory"). If you can sail from Europe to the Indies and arrive with your
    longitude known within 30', from the masthead you will be able to see all
    but the most insignificant, low-lying islands. It gets you there. Once
    you've arrived, greater accuracy in longitude is little more than a luxury
    since you're in piloting waters. That close you're going to sail with
    soundings and an excellent chart or with the aid of a local pilot. At least
    that's how it would have seemed in 1714.
    Additionally, the limits for the prize were not "pre-set" so that lunar
    distances would win. In fact, the prize was probably arranged so that
    Whiston and Ditton could win. They were the ones promoting the cause, and
    they suggested that Newton (and others) should set the rules. Isaac Newton
    was at least somewhat sympathetic to Whiston, his successor as Lucasian
    Professor of Mathematics at Cambridge (a chair now occupied by Stephen
    Hawking), after Whiston was booted out of Cambridge on the quaint old charge
    of religious heresy. Intentions aside, by the time the prize was finally
    approved, the proposal of Whiston and Ditton was already the subject of
    scathing satire. It was Jonathan Swift of Gulliver fame who noticed that
    "Whiston and Ditton" rhymed with the scatalogical "p--sed on and s--t on".
    And thus the first longitude drinking song was born.
    A random thought on sextant accuracy:
    Something that's hard to notice from our perspective in the year 2007 is
    that sextants stopped getting better over 200 years ago. Sure, there were
    modest improvements, neat little features like the micrometer that made them
    easier to use, but fundamentally the best sextants today can measure angles
    with about the same accuracy, about a quarter of a minute of arc, as the
    best sextants from 200 years ago. And who could have guessed that?! With
    significant, continual impovement in angle-measuring devices during the 18th
    century, surely the logical prediction would have been continued
    improvement. One of Chauvenet's stated reasons for developing a novel method
    for clearing lunars c.1850 was his belief that better instruments for
    measuring angles might be developed one day soon. But that didn't happen...
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