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David. Hope my math is correct, but here goes...

Bill: Did you turn the micrometer drum in same direction for
edge-to-edge observations? By that I mean NOT turning CW for one and CCW
for the other?

David: I did not attempt to systematically approach the measurement from
any one direction in other method.  As I approached a reading the
micrometer was adjusted to and fro till overlap looked as above or if
edge to edge just touching.

You may be introducing "Ghosts in the machine" with you technique.

1. Gears have slack (backlash). No matter what the tool, sextant,
radial-arm or table saw there is always some slack. Turning one way x
degrees then turning the other way x degrees will not get you back
*exactly* to your starting point. Even a pin detente has slack or you
would need a hammer to seat it. With the above tools you "play the
slack" by always making your final adjustment in the same direction.

The slack in my Astra IIIB is below my threshold of perception. It
really shows up in a plastic sextant so a good case study. See David
Burch's PDF for examples at:
https://www.starpath.com/online/celestial/plastic.pdf

You do not need a natural horizon for Burch's "touch and leave"
experiment. The center of the dip in a fine phone line etc. at any
distance will work. (We do not need an IE check now, we just need to see
how close we can come to aligning the wire images.) Done in one
direction, it gives you a good approximation of how close you can come
to alignment under ideal conditions. (Not aligned reading, first aligned
reading, last aligned reading, then not aligned reading). For me, 1.5'
to 0.2' with a 3.5x scope is about an average set if I recall. That's
the best precision I can expect with a more challenging sea horizon.

Bottom line, most folks make it a habit of turning in one direction
only, even if it means backing up a half or whole turn and starting
fresh. For me, this makes seeing the exact point of tangency when
pulling the discs apart more difficult than when bringing them together,
and is shows in my standard deviations. (I do have a method of
tightening up the tangency data).

Bill: What do you believe your IE to be from superimposing vs. edge-to-edge?

David: As indicated I adjusted side error out for the edge to edge
measurement as that would be a systematic error so I can not say that
one measurement was better than the other in terms of accuracy, we never
know that in any event.  What I can say is that the ovelap gave an IE of
on the arc 3.6 +/- .4 moa while the edge to edge gave on the arc of 3.1
+/- .7 moa and I had to make twice as many measurements for the inferior
measurement.)

Bill: Looking at you data, to my eye your train left the tracks
somewhere along the line. To determine the off-the-arc offset from 0 you
need to subtract that reading from 60. That is, if it reads 25.0'  off
the arc, it is actually 35.0' from the zero point. Now you can subtract
one from the other, then DIVIDE THE REMAINDER BY 2. That is your IE.
BTW. (32.16 - 29.05) / 2 = 1.56 (1.6 IE on the arc, not 3.1))

If the right column is off the arc before subtracting it from 60, then
your semi-diameter will be off. Subtracting it from 60 you would get
30.95' for the off-the-arc offset from 0 (60-29.05=30.95)

Subtracting 30.95 from on-the-arc 32.16 the remainder is 01.21. Divided
by 2 the IE is 0.61' (0.6'). The on-the-arc number is greater, therefore
the IE is on the arc. Your IC is -0.6.

Now lets do a sanity check. I would never use a NA SD for a 4SD check.
Worst case scenario at the crux of rounding it would be 0.05' x 4 =
0.20' off in a 4SD check even if otherwise perfect. So I'll use the SD
from Frank's site for 6/05/2015. It is 15.77.

Case 1: The right (off-the-arc) column has already been subtracted from
60. In this case the sum to the far right is correct and the divided by
4 the SD is 15.30'. That's 0.47' (0.5') low. A red flag.

Case 2: The right (off-the-arc) column has NOT already been subtracted
from 60. In this case the off-the-arc offset from 0 is 30.95'. On and
off added, 32.16' + 30.95' = 62.21'. divided by 4, 15.78' (15.8'). Not
too shabby for to and fro. Turn in the same direction and you might get
rid of that pesky 0.01' difference from 15.77' :-)

I'm no professional statistician, but I would guess your SD for on- and
off-the-arc would be an average of 0.33' and 0.48' or 40.50'. Pretty
close to your superimposed SD of 0.38'

A caveat: If I understood you adjusted the side error AFTER recording
the superimposed data, and that would change the IE. So IE wise apples
to oranges.

A side bar. Some of the members claim that with a well designed sextant
frame brought to ambient temperature the measurements (and therefore the
IE) will not vary during 20-or-so IE-check observations. Others swear
they can and often do experience changes--a drift/trend in one direction
in on and off data for example. I'm of the second camp.  A study decades
ago took several men to a mountain top in South America so
atmosphere/refraction etc. would not be a deciding variable. They did
strings of IE checks. Some were long, others short with breaks between.
In every case the IE readings of each person and each sextant changed to
a significant degree. Not clear I support all of the methodology, but...

> IC measurements	06/05/15							
> 									
> 	overlap			edge to	edge		difference	sum	
> 1	3.2	on	on	32.6	28.3	off	4.3	60.9	
> 2	3.5			31.6	28.6		3	60.2	
> 3	4.2			32.2	29		3.2	61.2	
> 4	3.3			32	29.3		2.7	61.3	
> 5	3.9			32.6	29.1		3.5	61.7	
> 6	3.2			32	28.6		3.4	60.6	
> 7	4.1			32.4	29.1		3.3	61.5	
> 8	3.8			32	29.4		2.6	61.4	
> 9	3.1			31.8	30.1		1.7	61.9	
> 10	3.5			32.1	29.2		2.9	61.3	
> 11	3.4			32.5	28.9		3.6	61.4	
> 									
> avg	3.56			32.16	29.05		3.11	61.22	Sum/4
> std	0.38			0.33	0.48		0.66	0.49	15.30
> 									
> 									
> 							Semidiameter	15.8	
>
> Fred Hebard claimed that edge to edge sun index measuremets were more
> accurate than overlapping measurements.  I don't believe the above data
> supports that claim.
>
> Two sets of measurements were made on my Astra sextant with the 3.5
> power scope.  First column is 11 overlapping measurements with about
> 1/10 sun diameter side error which I believe is helpful for overlap
> judgement but no proof for that.
>
> Then the side error was removed and I made 11 edge to edge measurements
> (22 measurements in all).
>
> Precision in all sets of primary measurements are reasonably identical
> order of .4 moa.
>
> But we see that the precision of the edge to edge values shows higher
> spread, .66 moa.  Taking the difference of two numbers increases their
> spread to square root two times the fundamental precision.  It is better
> to utilize the time taking more measurements of one thing than two
> things and taking their difference.
>
> Dave
>
> 
> 
>
>

   

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