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    Floating mirror correction
    From: Frank Reed
    Date: 2015 Apr 22, 18:52 -0700

    Someone may have already mentioned this. Apologies if I'm treading worn ground...

    While I was driving to the market today to buy more breadfruit for my plantation, it occurred to me that Greg's averaging trick to get rid of the tilt error in a nearly level mirror is identical to the process for measuring a small angle when the index correction is unknown or uncertain. For exammple, you can measure the diameter of the Sun by bringing together the two images first on-arc and then again off-arc. You get angles Don and Doff and then the actual measured diameter of the Sun is D = (Don + Doff)/2, no matter what the index correction is. Of course we rarely need to measure the angular diameter of the Sun, and instead we use this pair of measured angles to get the index error, which is I.E. = (Don - Doff)/2 --the difference instead of the sum. See the analogy? We can do the same thing with angles measured off some nearly level mirror that is mounted on some rotatable surface (including floating on water). We can directly get an average angle from A = (Adirect + Areversed)/2, or we can get a "mirror error angle" from M.E. = (Adirect - Areversed)/2 so long as we are measuring an angle which is not changing, like any altitude within a couple of minutes of meridian passage, especially the Sun at local noon. Then, if the system is relatively stable, which is an important issue to investigate, we can use this mirror error, M.E., to correct any subsequent sights without having to shoot pairs and average them. If the system is, in fact, reasonably stable, then the M.E. is just a fixed correction, just like index error, that applies whenever the mirror is oriented with its axis in the same direction relative to the altitude being taken. Does that make sense?

    Frank Reed
    Conanicut Island USA

    PS: No, I wasn't buying breadfruit for my plantation. I was buying cat food. 

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