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I have been wrestling with a problem similar to what beset Arthur
Pearson in his Grenadine lunars, namely that the precision of my
sights has been higher than their accuracy, implying the existence of
a systematic error.  This problem became evident after upgrading from
a Davis Mark 3 to a Husun Mate sextant,

All the sights were taken on dry land, using an artificial horizon.
I determined accuracy by comparing observed altitudes, corrected for
refraction, semidiameter, index and instrument error, as appropriate,
to calculated altitudes for my location.  Precision was assessed by
taking multiple measurements around the same time and computing the
standard deviation of the difference between observed and computed
altitudes; usually I would make three measurements, sometimes four or
five.

Typically, for a good sight, the mean of the difference between
computed and observed altitudes was around -0.4' to -0.7' and the
standard deviation around 0.2' or 0.3'.  (I should note that not all
my sights are that good).

I then noticed in a series of sun sights over the course of a day
that the systematic error dropped to close to zero around local
apparent noon, while it had been -1.3' in the morning, although the
precision remained constant at a standard deviation of 0.33'.  Around
noon, the sun wasn't moving much, whereas it was moving quite fast in
the morning, which implied that the lack of error at noon was due to
the lack of motion.  I looked over my data and found that negative
errors tended to occur in sights of rising objects while positive
errors tended to occur in sights of setting objects (the overall
negative error was associated with a higher frequency for sights of
rising than setting objects).  This suggested that I was not timing
the sights accurately, lagging between the time of perfecting the
sight and noting the time.

I then have endeavored to close this gap between perfecting the sight
and noting the time, and my results have improved considerably.
Today, I took three sets of observations of the sun while it was
moving, taking five measurements around 10 am, yielding a mean error
of 0.2' plus or minus 0.32'.  At 2 pm, four measurements yielded a
mean error of -0.2' plus or minus 0.23', and four measurements at 3
pm yielded a mean error of 0.0' plus or minus 0.31.

I expect that the mean error could be reduced further by still better
technique, and the the standard deviation could approach 0.1',
routinely.  I would appreciate it if others could comment on my
experience, share their experiences, or point to archived collections
of data.

Thanks

Fred

   

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