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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
Brad





-----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:
http://books.google.com/books?id=KWUpAAAAYAAJ
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? :-)

-FER







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