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    Re: Puzzle
    From: George Huxtable
    Date: 2000 Sep 09, 1:49 PM

    In respect of Richard B Emerson's puzzle about an 80-mile discrepancy in
    position lines obtained from sextant observations of Betelgeuse, Barrie
    Hudson commented-
    >Possibly put this down to excessive refraction on the eastern horizon
    >due to proximity of land and I notice in the
    >093034 sight sunrise was not to far away. Bellatrix was the only star
    >close by and its magnitude would not have
    >confused. Also no planets close by. It has to be refraction.
    >Barrie Hudson
    Here I have to disagree with Barrie. An error in position of 80 miles,
    corresponding to a difference in horizon refraction of 80 minutes from its
    nominal value, is implausible to say the least. It would create a world
    record in observed deviation of the horizon.
    A survey was made of horizon dip and its variations, in ocean cruises by
    the American research vessels "Carnegie" and "Galilee", and reported by W J
    Peters in the journal "Terrestrial Magnetism and Atmospheric Electricity",
    vol 23, pages 47-60, (1918). Although Peters concedes that accounts exist
    of observed deviations of the horizon of 15 minutes above and 3 minutes
    below its normal position, and quotes the Bowditch of the day as stating
    that "reliable observations have frequently placed it 10 minutes above, and
    values as high as 32 minutes have been recorded", Peters himself says-
    "In all the observations taken first on the Galilee, then continued on the
    Carnegie, amounting to 3,031 determinations, the refraction has not raised
    the horizon more than 2.4 minutes nor depressed it below 2.0 minutes below
    the position in which it would be seen if no refraction existed."
    Barrie Hudson's suggestion is that the horizon at 110 degrees azimuth was
    subject to refraction errors of 80 minutes, while 20 minutes later
    Emerson's observations of Jupiter at an azimuth of 125 degrees were
    completely unaffected by refraction. Such a notion is literally beyond
    belief. I wonder whether some extreme values of refraction recorded in the
    past may have resulted from a similar attitude of "If it doesn't add up,
    blame horizontal refraction".
    Additionally, the observed altitudes reported by Richard Emerson for
    Betelgeuse are 80 minutes too great, so to explain them by refraction at
    the horizon would require a depression of the apparent horizon from its
    expected value by that amount. In the extreme cases reported above, the
    greatest divergence was always an elevation, not a depression, of the
    apparent horizon.
    There are other possible explanations for the discrepancy. Emerson hinself
    has raised the possibility of timing error or star identification error.
    Here's another suggestion. Star sights, of necessity, have to be taken in
    the dim twilight of dawn or dusk when the star can still be seen in the
    half-light and there is sufficient light for the horizon to be clearly
    seen. If there happens to be a shallow patch of mist close to the sea
    surface, this could obscure the true horizon, and it might not be obvious
    that the mist is present. It's unlikely that such mist would obscure the
    high-angle view of Betelgeuse, If it's going to be misty, early morning is
    the ideal time for it. It can happen that in the half-light a horizontal
    dividing line between the sea surface and the mist above (at the limit of
    visibility, which could be much closer than the true horizon distance)
    might be mistaken for the level of the real horizon. This false "horizon"
    would be depressed below the real horizon, so observed altitudes would be
    too great, as appears to have happened with Emerson's Betelgeuse sights.
    However, the plausibility of this explanation too suffers when the
    magnitude of the error observed by Emerson, 80-odd minutes, is taken into
    account. The depression of the observed horizon caused by mistaking a
    nearby mist-water interface, at a short distance, for the true horizon is
    tabulated in "dip of shore horizon" tables in, say, Norie, intended for
    solving a similar problem. For a height of eye of 5 ft the maximum
    depression in these tables is given as 28 minutes at 0.1 miles distance. To
    obtain a depression large enough to explain Emerson's 80-minute error would
    require the false "horizon" to be as close as 200 ft. It's hard to imagine
    such a situation occurring, even in half-light, without the observer being
    aware that something was wrong, and that mist was in the way. Unlikely
    though this might be, I think it is a lot more plausible than Barrie
    Hudson's suggestion of horizon refraction.
    I do not wish to give the impression that the effects of variable horizon
    refraction are entirely negligible. Indeed, they are not. In good observing
    conditions of clear sky, calm sea, sharp horizon, well-calibrated sextant,
    I suggest that biggest remaining uncertainty in a sextant altitude
    observation is that of the unknown refraction in the light path from when
    the ray skims past the horizon to when it enters the observer's eye. This
    uncertainty is of the order of a minute or perhaps two, and is irreducible
    unless the observer carries a special instrument to measure the actual dip
    at that moment. For this reason, there is no great virtue in requiring a
    much greater accuracy of the sextant itself.
    George Huxtable
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.

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