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    Re: Reducing back sights
    From: George Huxtable
    Date: 2004 Aug 11, 14:47 +0100

    Jim Thompson asked-
    >Neither Dutton's nor Bowditch explain back sight reduction in sufficient
    >detail for me to be confident about the process.  My understanding is this:
    >1. Raw altitude = back sight.
    >2. Corrected raw altitude: apply Index Correction and dip.
    >3. Corrected hs = 180d minus corrected raw altitude.
    >4. Then reduce the corrected hs as usual.
    >True, or bungled?
    This is a deeper question than it appears, and it has puzzled me too. I
    don't know of any text which explains it properly.
    Not, perhaps, for Jim's benefit, but for others, perhaps I should explain
    that the Hadley quadrant, (otherwise known as an octant), had an arc of
    only 45deg (or perhaps a little more) so it was unable to measure angles
    much greater than 90deg. The sextant was a later development, which allowed
    measurement of angles up to 120deg, perhaps slightly more, mainly to use
    for lunar distances.
    Some octants had an additional fitting, which allowed them to measure
    angles from 90deg to 180deg. This was an additional peep and horizon
    mirror, fitted low down to the left arm of the A-frame. The horizon mirror
    was angled so as to give a view to the observer (who was now looking from
    the left, having turned the instrument about a vertical axis) of both the
    horizon and the index mirror. The index mirror would then collect light
    from over, or behind, the observer's head. This was possible because the
    arms of the octant were so long, and the backsight peep was mounted so low,
    that light from the horizon behind the observer could pass clear over the
    top of his head, and reach his eye via the two mirrors.
    In back-sight mode, an object overhead would correspond to a scale reading
    of 90deg, and then objects increasingly further from the observer's forward
    horizon would give scale readings reducing from 90deg, until an object on
    the horizon, right behind his back, would correspond to a scale reading of
    zero. That's why, in backsight mode, the scale reading was subtracted from
    180deg to get the required angle.
    In normal, forward mode, it's easy to check the index error of an octant,
    or sextant, by aligning the distant views of, say, the horizon, or a
    celestial body, direct and via the mirrors. When they align, the near-zero
    scale reading is the index error, by which all observations should be
    But there's no such simple way to allow for index error in back-sight mode,
    as there's no way to align an object with its reflected image.
    A further question now arises: what does Jim Thompson wish to use an octant
    backsight FOR? I can think of four applications.
    1. He wishes to measure a lunar distance greater than 90deg. (at sea or on land)
    2. He wishes to measure a horizontal angle (for surveying purposes) greater
    than 90deg. (at sea or on land)
    3. On land, he wishes to measure the altitude (greater than 45deg) of a
    body seen by looking down into the reflecting pool surface of an artificial
    horizon, which doubles the angle.
    4. At sea,He wishes to measure the altitude of a body above a horizon which
    is obscured by nearby land or by mist, though the horizon in the opposite
    direction is clear.
    In cases 1, 2, and 3, dip doesn't enter the question at all, because angles
    aren't being measured from the horizon.
    Whatever purpose he wishes to use the back-sight quadrant for, Jim has to
    decide just how he is going to determine its index correction, on land or
    at sea. Only then can we say how the observation should be reduced.
    Over to you, Jim.
    contact George Huxtable by email at george---.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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