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    Re: Plot of my lunar errors
    From: Frank Reed
    Date: 2013 Jul 31, 09:29 -0700

    Hi Peter,

    If we drop your first group, which you say had problems, and also drop the sets with only two or three individual sights, and then look at the scatter in the later groups near 20, 60, 80, 100, it looks to me like you've got about two-thirds in each batch within about +/-0.3 minutes of arc of the middle of the group. So that's quite good, and about what I would expect for excellent observations with a 6x scope (the "two-thirds" measure corresponds roughly to one standard deviation). I find that I can get 0.25' for the standard deviation in individual lunars with a 7x scope, and that ratio corresponds nearly to the ratio of the magnifications (0.3/0.25 is about the same as 7x/6x), as it probably should, all other things being equal. The remaining problem then is the substantial offset from zero in each set. This is (more or less by definition) either index error or "arc error". You said you plotted these errors against actual angle (lunar distance, that is) and you saw no pattern. This is, of course, worth re-visiting, but that would appear to exclude arc error, leaving index error as the prime suspect. It really is notoriously difficult in my experience to estimate index error repeatably to within a half a minute of arc with the usual methods.

    Over the years I have experimented with many methods for determining index error. A few years ago I came up with a method that is very accurate, relatively easy to test, and shows high repeatability. On the negative side, it requires a separate small telescope and it may be a bit laborious if we're going to test the IE before every set of sights.

    My "best test" for index error:
    Find yourself a "spotting scope". This would be a small telescope, typically intended for bird-watching or similar, with a magnification of 25-50x. Place your sextant on its side on a table where you can see a very distant vertical mast of some sort. Remove the standard sextant scope. Put the spotting scope on a tripod (or possibly just resting on the table with the sextant if it can sit that way) so that it is in-line with the normal position of the sextant scope. It should be roughly aligned correctly to look at the horizon mirror just as the normal scope must be aligned, but note that collimation does not matter for index error tests, so you don't need to make any special adjustments here. Now follow the normal procedure for testing index error. The high magnification is key. At 30x magnification, with corrected focus, you can now see changes in angular adjustment as small as two seconds of arc. You should find that you can reliably and repeatably get the index error to a tenth of a minute of arc. You can also easily experiment with various procedures like making the final adjustment of the micrometer "always clockwise" and perhaps other tricks. You can also try this under various environmental conditions to see if there is a simple temperature dependence to any variation in the instrument's index correction.

    By the way, you do not need to worry so much about collimation. The error due to lack of collimation is observable. Bring the Moon and other body together at the center of the field of view. Now swing the sextant so that the two bodies remain in contact but they are in different points within the field of view. If you do not see any separation, then there is no observable collimation issue. If you find that they do separate, then you just look for the minimum which MAY NOT be at the center of the field of view. That minimum is the correct collimation axis regardless of other tests. But again, if you can't detect any separation, then you have nothing to worry about. And since collimation error is proportional to tan(LD/2), it grows nearly linearly with the observed angle. For relatively short lunars, it's completely insignificant.

    -FER

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