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    Re: Reliable Index Correction to a Tenth Minute of Arc
    From: Bill Morris
    Date: 2010 Feb 25, 18:27 -0800

    On 17 February (g11914) you wrote:

    "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."

    This led me to investigate prismacity of mirrors and shades. I can dismiss mirrors quickly. In a collection of fourteen sextant mirrors that I stripped prior to re-silvering, only one had prismacity exceeding 1 second and that was a horizon mirror, where prismacity is of no account, as the angle of the rays striking and leaving it is always the same.

    In 1883, G M Whipple communicated to the Royal Society of London "A Description of an Apparatus...for the Examination of the Dark Glasses...of Sextants" (Proc. Roy. Soc. Lond., 35 (1885), pp.42 - 44). In a paper written in 18 years previously, in 1867 on sextant calibration, Balfour Stewart had written as a concluding paragraph:

    " In conclusion, it ought to be mentioned that perhaps no artificial light easily obtainable is sufficiently powerful to allow of the darkest glasses of a sextant being examined, and for that purpose, we may ultimately have to resort to other means." (Proc. Roy. Soc. Lond., 16 (1868), p.6)

    Whipple did resort to other means, using a heliostat to direct the sun's rays into his apparatus. I used a 40 watt halogen bulb in a desk lamp to illuminate the cross wires of a collimator and focussed on the wires using a Watts Microptic autocollimator as a micrometer telescope. It allowed me to examine all but the darkest of the "dark glasses" of a selection of sextants, by interposing them between the collimator and the telescope and noting the maximum displacement of the cross wire image.

    In Whipple's time, if the shade caused no more than 20 seconds deviation, it was marked K.O.1, if no more than 40 seconds, it was marked K.O.2; and if more than 40 seconds, it was rejected. This gives us some insight as to why nineteenth century writers dwelled on prismacity and steps to eliminate its effects, but none on why "K.O." was chosen. In a time when ancient Greek was widely studied, perhaps it was "ola kala" (everything correct) reversed.

    I was able to get results for six out of seven shades for each of the sextants I looked at.

    Bronze octant in the style of Spencer, Browning and Co., ca 1850:
    Average deviation 7.0 seconds. Worst deviation 14 seconds.

    Hughes and Son sextant, 1920
    Average deviation 2.2 seconds. Worst deviation 4 seconds.

    Tamaya sextant 1957
    Average deviation 2.0 seconds. Worst deviation 6 seconds.

    Freiberger sextant ca 1964
    Average deviation 2.8 seconds. Worst deviation 5 seconds.

    It seems clear that things improved between 1850 and 1920, but little progress was made after that. Six seconds is of course a tenth of a minute and may indeed account for the "strangely different results" obtained.

    To obtain index error using the sun, an eyepiece shade can be used (it is one of the reasons why they were provided) and this will eliminate errors from prismacity of the shades, though only "lunartics" will need to do so. However, they will still have to use shades when obtaining the distance between the sun and moon and the height of the sun.

    Bill Morris
    New Zealand

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