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    Re: Reliable Index Correction to a Tenth Minute of Arc
    From: Frank Reed
    Date: 2010 Feb 17, 17:41 -0800

    Brad, You wrote:

    "My method is one of super-imposition, using the sun’s image on top of its reflected image, whilst paying attention to the edges or margins of the sun."

    Everything you've described in the first couple of sentences in your description is really just adjustment for mirror perpendicularity, which is important of course, but separate from I.E. tests.

    You wrote:
    "The next day, actually use the index arm to bring the sun’s two images in contact for both the upper and lower limbs. Create the difference to find the standard IE correction. This readily gets me well below 0.5 arc minute, and typically in the 10 seconds to zero IE. This method can be performed solely on a star image, but I have not found the same degree of success."

    I agree with you that, of the standard methods, this is among the best for testing index error. It's old, too. Maskelyne recommended it in one of his earliest contributions on lunar distance observations back in the 18th century. I also agree that one does not get the same quality of results when using a star image. In my own experience, when I use the Sun's image limb-to-limb to get the index error, I have found standard deviations on individual trials around 0.5 minutes of arc. This is not as good as what I find for individual lunar distance observations (for those I find 0.25 minutes of arc, s.d.). Of course, the index correction is halved so that's getting close. Repeat four times and average, and you have an excellent result. And yet, even so, I have spoken to people who have tried this who get strangely different results under different conditions. Part of the problem is probably slight prismatic effects in the shades. To do this test with the Sun, we need full shades in front of the horizon glass, but this is really the only observation when you would have full shades there. It wouldn't be surprising to find a couple of tenths of a minute of arc error there.

    You wrote:
    "This CAN be done at sea, no reason why not."

    Yes, the limb-to-limb I.E. test can be done at sea, and many people use it as sea. But even when they do, they still find strange discrepancies, perhaps related to prismatic error, as above.

    "As to the recalled difficulty with different telescopes, I would suggest that this implies a lack of parallelism between the plane of the arc of the instrument and the long axis of the telescope."

    It doesn't work. Telescope collimation error goes to zero at zero degrees on the arc. You can try this out easily. Set your sextant up for an I.E. test. Get everything aligned right. Then, without making any other adjustments, tilt the telescope a bit. Even if the instrument is a modern one and includes no adjustment screws for telescope collimation, you can just get the same result with a paper shim in the yoke.

    You wrote:
    "Some sextants do have an adjustment for parallelism. Pick out two bright objects about 90 degrees apart. Assuming stars for a moment, superimpose them. With a vibratory motion (to quote 1856 Bowditch!) see that they maintain contact on both sides (toward and away from the plane of the arc) of the telescope. If your telescope has the sighting wires, use them! Adjust the telescope’s parallelism until the images remain in contact on both sides."

    That's also some very old advice (long before Bowditch!). Have you tried it? It's fairly tough to adjust this out using that old method. It's much easier to adjust this using table-top tests. Place your sextant on its side on a table where you can see twenty feet or so down a hallway. Next place a sighting tube or a good carpenter's laser on two equal-height supports placed on the frame of the instrument. You aim the sighting tube or laser parallel to the axis of the telescope. You peek through the sighting tube and note what you see at its exact center. Or if you're using a laser, you just observe the dot on the wall. Draw a horizontal line on the wall at that level (in your head is usually sufficient) Next look through the telescope. The center of the telescope's field of view should be very close to the horizontal line. If not, adjust.

    -FER
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