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Alex,

I also thought Frank had an excellent suggestion, both for drum
eccentricity and backlash.

One point about detecting backlash when measuring star-to-star
distances or using one star as an IC check  is that, as you know,
it's hard to see the stars because of flare and their extreme point
source.  Thus it might take more practice to merge two stars
correctly coming from both directions than to merge two lines.
Therefore, there may be apparent eccentricity with stars but none
with lines.

Fred

On Dec 9, 2005, at 4:20 PM, Alexandre E Eremenko wrote:

> I tried Frank's interesting suggestion,
> but I have some doubt that it works.
> Frank: did you test it with a good sextant as well?
> Does the test with a good sextant show no excentricity?
>
> My doubt is based on the following observation: if you have two
> vertical lines on your screen, say 3 inches appart, and look
> through your
> sextant at them, when the straight and reflected image of the first
> line
> coincide perfectly, the straight and reflected images
> of the second line do not coincide.
> They are about 1/2 min apart, and this is apparently due to the
> difference in parallax when you look at one line and when you look
> at another one.
>
> I found this while trying to "improve" Frank's test, by saving time
> on walking to and from the computer:-)
> I drew several vertical lines in the upper half of the screen, approx
> 1 inch apart, and 4 vertical lines in the lower part of the screen,
> 1/4 inch apart. So I hoped to make many measurements without having to
> changle the picture. For the reason explained above this does not
> work.
>
> But it is still possible that the method works if one of the lines
> used is the same all the time...
>
> The results indeed are highly reproducible (better than with my
> average
> IC tests with Sun, not speaking of the stars). In two runs
> (rotating the drum in the same direction) the results of the
> measurements differed no more than by 0.1'.
>
> But if the test is sound indeed, I still don't see why not
> to save time by having one line whose straight image will be used and,
> say, 10 lines of which the reflected image will be used.
> I can even label those 10 with the numbers on the screen:-)
>
> Alex.
>
> On Fri, 9 Dec 2005, Frank Reed wrote:
>
>> 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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