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    Re: Lat/Lon by "Noon Sun" & The Noon Fix PROVE IT
    From: Brad Morris
    Date: 2009 May 12, 15:14 -0400

    I inadvertently dropped the line whilst typing.  Whoops!
    I have von Littrow's paper referred to.  I have coded that method into a 
    spreadsheet for comparison to other methods and have yet to find the 
    approximation indicated, even when extending von Littrow's method far beyond 
    his stated limitations.  I think he was just being cautious, and in the end, 
    made his method obscure.
    I thought the statement quoted fairly interesting in that the folks whose very 
    lives depended on it were perfectly satisfied with an approximation, when a 
    conclusive, mathematically pure method was un-available.
    The noon fix method has been shown, even under the demanding test applied to 
    it, to be functional and provide a fix that is "within the ballpark".  Hence 
    my statement that I believe it proven.  You can obtain a fix using the method 
    shown, within practical limits of observation.  Is it perfect?  I don't think 
    so, but then it doesn't have to be so.  As you say, there are different 
    levels of precision afforded by different computations.
    This is on my list of things I really would like to play with.  It will be 
    interesting to compare it to the fixes I get by the LOP twilight "standard" 
    method.  When I get this done (and it is not too terribly embarrassing), I 
    will post to the list!
    Best Regards
    -----Original Message-----
    From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of frankreed@HistoricalAtlas.com
    Sent: Tuesday, May 12, 2009 2:43 PM
    To: NavList@fer3.com
    Subject: [NavList 8231] Re: Lat/Lon by "Noon Sun" & The Noon Fix PROVE IT
    Brad, you quoted:
    "Report of the Secretary of the Navy
    'We recognize in navigation two classes of astronomical problems; one
    possessing perfect accuracy of computation; the other uncertain, and
    approximate only in its results.  The first class is, of course, always
    employed when the weather and other circumstances are favorable.  The second
    class of problems, that which gives only approximate deductions, is never
    resorted to except from necessity.' "
    When I read this, I thought I recognized it and recalled that it was from an 
    era somewhat before the modern understanding of error in observations and 
    calculations. Sure enough, it's the report from c.1865. What's written here 
    wasn't true then, and it isn't true today.
    The text per google books is slightly different and reads:
    "We recognize in navigation two classes of astronomical problems; one 
    possessing perfect accuracy of computation, *** and admitting no other error 
    than the probable error of observation***; the other uncertain..." etc.
    That one extra phrase (between the ***'s) helps a bit since, of course, 
    there's no such thing as perfection in any observational activity, but it's 
    still misleading. There are NO problems in nautical astronomy that possess 
    "perfect accuracy of computation" though there are certainly different levels 
    of accuracy in different computations.
    The report was referring to von Littrow's method of finding apparent time 
    incidentally. Chauvenet also wrote about this in "Astronomy: Comprising 
    Instructions to Naval officers" which you can read on google books here:
    This article has some good material, some not so good. Chauvenet was a 
    land-based mathematician --influential in the U.S. Navy and highly respected, 
    but idiosyncratic in his beliefs.
    Of lat/lon by noon sun, you wrote:
    "I would like to assign the latitude and longitude by the noon sun fix to the
    second class of problems.  It can provide us with a useful figure of merit,
    albeit without perfect accuracy. Certainly, with a least squares curve fit,
    the method affords us a very reasonable fix."
    It's a fix, not different except in degree from any other fix in celestial 
    navigation. It is a running fix, and therefore it is somewhat dependent on 
    errors in estimating the vessel's true speed. It is a statistical fix, and 
    therefore there is an error ellipse around the position. But note that ALL 
    running fixes in celestial navigation are somewhat dependent on errors in 
    true speed. And ALL fixes have error ellipses around the position. ALL fixes 
    are "without perfect accuracy" to use your phrasing.
    Oh, and the other thing about this approach to getting a fix at noon is that 
    it's easy to teach, easy to learn, and, as I cannot emphasize enough, easy to 
    re-learn if that day comes when you really need celestial. "Easy" is a dirty 
    word for some fans of celestial. Some folks, equally worthy of our attention 
    as educators, are in it for the intricacy and the delight of a tricky puzzle. 
    They're a different market.
    And you concluded:
    "Proven??  A resounding YES!"
    Well, I'm glad you think so. Have you tried it out yet? :-)
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