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Fred H, you wrote:
"For those without access to a theodolite, the church steeple method
may be the quickest.  An advantage of the star-star or lunars methods
are that you improve your technique while trying."

I don't know if anyone has spelled this out in detail in this latest thread,
but the "church steeple method" that Fred and Alex mentioned was something I
brought up last Spring. The only printed reference I kow that mentions this
technique is the "Tratado de Navegacion" by Jose de Mendoza y Rios from way
back in 1785. It does work. I've tried it in practice, and the results are
really excellent. The catch is that you need a location with a fairly clear,
level horizon with a lot of well-defined points or vertical lines at
considerable distance. In the 18th century, a city on a level plain with
numerous church steeples would fit the bill. Today, lighthouses or other
navigational beacons around a relatively enclosed body of water work just as
well. The principle is simple enough: suppose I have four fixed objects ,
call them A,B,C,D, which are roughly 90 degrees apart spaced around the
horizon. I measure the angles between them in pairs: AB, BC, CD, DA. Then I
correct each for index error, and add them up. The total MUST be 360 degrees
(or very close --the objects will be slightly out of a great circle but it
makes no serious difference). Suppose I make my measurements and get a total
of 360d 16'. Then the arc error of my instrument must be +4' for angles near
90 degrees. That is now a known quantity. It doesn't mean my sextant is
"bad" since I can now correct every observation near 90 degrees by
subtracting 4 minutes of arc. I can then repeat the process for other angles
by using this established error at 90 degrees and measurements of other
objects more closely spaced around the horizon. No theodolite required. No
almanac data for star-to-star angles. No special equipment! And as long as
no one tears down your favorite lighthouses, you have a permanent sextant
calibration observatory at no cost. Note that your "lighthouses" have to be
far enough away so that sextant parallax and slight errors in placement of
the instrument don't matter. The typical lengths for these issues is about
four inches. To get angular measurements accurate to 1.0 minute of arc, the
distant reference points have to be farther away than about 3438*4 inches,
call it 1200 feet (you could set it up in a small corn field). For angular
measurement accurate to 0.1 minutes of arc, clearly the reference objects
should be ten times farther away, call it two miles.

 -FER


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