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Ken Gebhart wrote:
"it seems to me that you  are neglecting the effect of drum eccentricity.  The
readings of the  micrometer drum itself can be in error by as much as 20 or
30" of arc all by  itself. This is caused by any microscopic deformation of
the drum shaft, or  errors in machining (or damage to) the worm gear. This
can be added (plus or  minus) to any errors determined on the arc.  This will
pretty much make  a mess of any attempts to calibrate the arc unless all
measurements are made  at the same drum reading (not likely when measuring
stellar  distances).

It seems to me that a way to get a handle on your own drum  eccentricity
might be to measure a moon- star distance over a period of about  2 hours."

Fascinating suggestion and fodder for an indoor project now  that we're
buried in snow. I set up a simple means of measuring this "micrometer  error" and
indeed found that this is a significant source of error for one  sextant that
has always given me puzzling errors on the order of 0.7 minutes of  arc but
with no discernible pattern.

The setup:
I wrote a very simple  piece of software that displays two vertical white
lines, one above the other,  which can be separated at regular pixel intervals (I
used 40 pixel jumps). I set  this up and ran it on my laptop which I placed
at the far end of a room about 25  feet away (so that I could focus the
telescope). I placed my sextant on its side  and carefully measured the angle between
the upper and lower line, repeating at  each interval. The angles ranged in
roughly 5 minute of arc steps from 0 to 2  degrees (two minutes or so for each
observation and the walk across the room to  move the line over one step so
over three-quarters of an hour of work for each  run). Then I compared two runs
of these measurements with the linear increase  that I would predict if the
sextant has no micrometer error. Sure enough, there  was a nearly sinusoidal,
cyclic difference between the actual observations and  the linear prediction.
The amplitude from top to bottom was 0.7 minutes of arc  --exactly the same
magnitude as the mysterious errors I had seen previously. I  have not yet had the
opportunity to try correcting real observations, of lunar  distances e.g.,
with my new micrometer correction table, but I'm optimistic that  this will
render this instrument essentially perfect (*after* correcting for arc  error and
micrometer error). Lots of fun! I highly recommend trying this.

By the way, as a bonus, this is an easy, extremely accurate way to test  for
backlash error. With the same sextant, I found zero backlash error every  time
I checked for it. It was also interesting how repeatable these measurements
turned out to be. Ninety percent of the time the angles between the lines were
 the same to 0.1 minute of arc accuracy when re-measured, and over 95% were
no  more than 0.2 minutes different when re-measured.

And don't forget to  test your sextant's telescope collimation! --Also a nice
indoor project for the  winter months.

-FER
42.0N 87.7W, or 41.4N  72.1W.
www.HistoricalAtlas.com/lunars

   

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