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Alex,

The index error derived from measuring the semi-diameter of the sun is
independent of the actual semi-diameter.  In your first set of
measurements, for example, with an off' measurement of 32.4' and an on'
of 32.6', the index error is equal to (32.6-32.4)/2 = +0.1'.  The
average index error across all six measurements is +0.34' of arc.
Since it's on the arc, that correction should be subtracted from the
reading to make the index correction, "When it's on, take it off."

Your average measured semi-diameter (=radius) of the sun is 16.2', as
you calculated correctly, and this is large by a factor of 0.2' from
the value given in the almanac.  The virtue of knowing the
semi-diameter of the sun is to compare the accuracy of your measurement
to a known value, but it has no bearing on the index error; the
semi-diameter of the sun as measured in this way is independent of the
index error.  It appears that you are judging the two images to be in
contact when they actually are separated by 0.4' of arc.

Because of the fairly large variation in the measurements from one to
another, I would not put much stock in the average index error of
+0.3'.  I expect this variation would decrease with practice.  Your
altitude shots of the sun also had less variation than your
semi-diameter measurements, which is good!

 From your sun sight and your star-to-star measurements, it appears that
your sextant is quite accurate, although the star-to-star measurements
don't extend beyond 60 degrees.  Frequently, the sextant errors get
larger at larger distances, based on my casual inspection of the
correction certificates posted on Ebay for Husun sextants, rather than
a systematic analysis of same.

I started out as you did with the same purpose, but have switched to
trying to perfect my altitude shots in the artificial horizon.  When I
get those down, I intend to go back to a few star-to-star shots; based
on my latest results, I'm getting pretty close.  I also take lunar
measurements when the moon is conveniently located.  I started out with
inferior equipment to what you have, and still do not have a good 6x or
7x telescope, so my path has been more crooked than yours.

Fred

On Oct 4, 2004, at 4:36 PM, Alexandre Eremenko wrote:

> Dear Fred,
> Here are some of my recent observations.
> The purpose was to estimate my sextant accuracy,
> to determine its index correction,
> and simultaneously to learn how to make observations
> of maximal precision under the ideal conditions.
> All observations were made from my second floor balcony,
> under the perfect weather conditions.
> The sextant was SNO-T, made in 1990,
> with two scopes.
> I used the standard refraction table (did not measure
> air temperature and pressure).
>
> 1. Index error tests by the Sun
> Oct. 3, LT 13:20
>            off'        on'
>            32.4        32.6
>            31.6        33.2
>            31.7        32.6
>            32.4        33.0
>            32.3        32.9
>            32.2        32.4
>
> Aver:      32.1        32.78
> SD          0.3'        0.1'
> Average Observed sun radius: 16.22. Value from Almanac: 16.0
> Correction: -0.2'.
>
> 2. Index error tests by stars: 0.0'
> I mean that with stars of 2-nd magnitude I did repeated tests
> of the star-to-itself distance and the stable result is always
> less than 0.1'. So I read it from the drum as 0.
> I made 20-30 such measurements.
>
> 3. Star-to star distances.
>
> Oct. 2, LT 0:30
> Altair-Deneb (Galileo scope)
> Sextant distance: 38d00.0', 38d00.4', 37d59.9'.
> Average: 38d00.15', SD 0.3'
> Calculated distance: 38d00.1'
> Correction: 0.0'
>
> Oct. 2 LT 0:45
> Vega-Deneb (Galileo scope)
> Sextant distance: 23d50.3', 23d50.8', 23d50.5'.
> Average: 23d50.5' SD 0.2'
> Calculated distance: 38d00.1'
> Correction: -0.4
>
> Sept. 29 LT
> Arctur-Vega (Inverting scope)
> Sextant distance: 59d05.8', 59d06', 59d06', 59d05.8', 59d05.8
> Average: 59d05.9' SD 0.1'
> Calculated distance 59d05.9
> Correction: 0.
>
> 4. Sun altitudes with artificial horizon (Davis, vegetable oil).
> Assumed position: N 40d27.2', W 86d55.8'
>
> Oct 3. LT 15:10
> GMT            SEXTANT            DEVIATION          SCOPE
> 20:28:27       60d19.1'           +0.0               Galileo
> 20:30:34       59d42.1'           -0.6               Galileo
> 20:32:36       59d04.5'           -0.2               Galileo
> 20:34:07       58d35.8'           +0.2               Galileo
> 20:35:35       58d09.8'           -0.2               Galileo
> 20:38:51       57d09.2'           -0.1               Galileo
> 20:44:30       55d23.5'           +0.1              Inverting
>
> 5. Some conclusions.
> It seems from these data that the sextant "has no instrumental
> error for
> practical purposes", and that the index correction
> is 0. (The "correction" is always less than SD.)
> The star test for the index error seems to be more accurate
> than the Sun test.
> The inverting scope seems to be more accurate for stars.
>
> Further conclusions.
> All reductions in the tables presented above were made
> with the Nautical Almanac and computations with
> exact formulas (using my computer).
> The "Complete on board Celestial Navigator" which I also
> tried gave errors about
> 0.4' in its almanac part, and up to 3' because of rounding
> in its sight reduction tables.
>
> Alex
>

   

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