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    Re: Lunar distance accuracy
    From: Alexandre Eremenko
    Date: 2007 Oct 27, 22:59 -0400

    
    Frank,
    
    > One of these days, clockwk.com is going to disappear,
    
    OK.
    
    > Considering how carefully he has spelled out other
    
    I disagree with this. He even did not care to mention
    his scope power:-)
    And I continue to maintain that taking one shot per week
    with the purpose of investigation of lunars accuracy
    is ridiculous. All books on the lunars strongly insist
    on averaging at least 5 shots. And I suppose White read the
    books he cites.
    
    > In a follow-up post, you decided that
    > this wasn't so ridiculous after all,
    > and I agree with your logic there.
    
    There is a logic in not applying excentricity error.
    But this makes his results highly suspicious.
    Especially if we interpret them as single shots.
    
    > I propose that his arc error table would have read
    > something like this:
    > 30d: 0", 60d: +10", 90d: 0", 120d: -20". It should
    
    Highly improbable. Especially on a good sextant.
    See Simms theoretical formula for the arc error.
    By the way, one may conclude from the article that this
    very formula was used to determine his arc excentricity
    correction:-)
    
    > "5. How Frank comes with the "mean error" of 0'.1, I don't know."
    
    > Take them in sets of four and average.
    
    Averaging observations taken a week or more apart
    has nothing to do with sea practice. Or even with
    land travel. It only makes sense when you determine
    longitude of a fixed observatory.
    
    > I found your point "6" amusing.
    > You seem to be saying that you don't trust
    > him because he writes plainly and without
    > pseudo-academic pretense. Oddly
    > enough, I like him for that.
    
    You misunderstood what I said.
    I did not say anything of the language. I was talking
    about the whole approach, "philosophy".
    There is one approach: to find what the truth is.
    For example, to evaluate the lunar method accuracy.
    And another approach: to convince people in something
    which you already know or believe.
    To promote some agenda.
    He seems to be using the second approach.
    I call the first approach "scientific".
    It has nothing to do with "language".
    
    > You know, they do have calm days on the oceans, Alex :-)
    
    Yes, they do. Have you seen
    www.math.purdue.edu/~eremenko/accuracy.html ?
    where the results of various observers are
    represented graphically?
    
    > That's Henry Halboth.
    > After getting a longitude accurate to within
    > 6 miles from a lunar distance
    
    I also have one or two lunars taken from sea with
    this accuracy. I even have a shot with a POCKET sextant
    from sea with this accuracy! I posted it 2 years ago.
    So what? I do not conclude from this that one can
    use a pocket sextant at sea to determine longitude
    within 6 miles:-)
    
    Henry, if by chance you are reading this,
    could you please tell us, how many times (perhaps in
    a certain definite period) did you make lunar
    observations at sea, and how many of those gave you
    longitude within 6 miles?
    
    > ...So that's ONE data point.
    
    Yes, exactly.
    
    
    > Finally, I would emphasize that lunars
    > were widely used in the early
    > nineteenth century --so they MUST
    > have been accurate "enough", whatever
    > "enough" means.
    
    For those British officials who made the longitude
    prize "enough" was 1/2 degree in longitude if I
    remember correctly.
    
    > There is ample evidence
    > for them in the logbooks.
    
    Evidence of WHAT? That lunars were widely practiced?
    Nobody seems to deny this.
    Or that "lunars can give you your position reliably
    to 6 or to 15 miles" ?
    
    Alex.
    
    
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