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    Re: Quadrants, was: Preston's paper on Lewis & Clark's Navigation
    From: George Huxtable
    Date: 2003 Jun 9, 09:22 +0100

    Trevor Kenchington wrote-
    I have seen at least one quadrant/octant with
    >dual peep holes. (The particular example that I recall is in the
    >Peabody-Essex museum in Salem, Massachusetts.) Using the second eye
    >position would still confine the instrument to a 90-degree arc but it
    >would not be the arc from 0 to 90, more like 30 to 120.
    >I have never read anything about such an instrument, nor how one might
    >be used, but it may be unsafe to simply assume that any quadrant was
    >incapable of measuring altitudes greater than 90 degrees.
    George responds-
    That's an interesting variation. Presumably, the peep was mounted on the
    right arm of the octant's A-frame, looking across it to the left, rather
    like the normal peep, but somewhat shifted in direction. Can Trevor recall
    whather that was the arrangement? I have never seen, or read about, such an
    A common arrangement was an octant fitted for "back observation", with a
    peep mounted on the left arm. This looked rightwards, into a additional
    horizon mirror which was below the usual horizon mirror, angled in a
    different direction so the observer could see past the original horizon
    mirror into the index mirror. This allowed the scale readings on the arc,
    marked as 0 to 90 degrees, to correspond instead with the supplement, 180
    to 90 degrees respectively. In this mode, the observer's sight-line was
    much lower down the frame than normal, to allow the observer to view
    backward over his head, when the instrument was set to read 180 deg. The
    arrangement was only practical because of the long legs of an octant frame.
    This, clearly, is not the variation that Trevor speaks of.
    The big problem with any such arrangement, which didn't allow the scale to
    be set to read 0 deg, was in determining the index error. What an observer
    could do, with a back-observation instrument, was to set it to read 180
    deg, then align his direct view of the horizon ahead, with his view through
    the octant of the horizon behind his back. It wasn't very precise, because
    the observer had to estimate and allow for twice the dip (the angle between
    those opposite horizons is 180 - 2*dip). It could only be checked that way
    at sea, or on land if a suitable promontory could be found, which had a
    long horizon-view over water in opposite directions, so life was difficult
    for a land-explorer using such an instrument. This method wasn't available
    for finding the index error of the Salem instrument, in its "alternative"
    mode, if its scale then corresponded to altitudes of 30deg to 120 deg, so
    neither fore horizons at 0 deg nor back horizons at 180 deg were available.
    An alternative arrangement, which could be used for the Salem instrument as
    well as the back-observation instrument, would be to measure the
    angle-in-the-sky between two known stars that come within its working
    range, rather like taking a lunar. This angle is, roughly-speaking,
    constant. Any discrepancy, after a complex correction for refractions,
    would be the index error. It would need a lot of astronomical knowledge and
    Alternatively, altitudes of an object such as the Sun, when it was in a
    range where it could be measured in either mode (which would be a nice wide
    band of 30 to 90 degrees in the Salem instrument) could be taken
    alternately in the two modes, and a bit of graph-plotting would show the
    index error. A sea-horizon wasn't necessary; a flattish land-horizon would
    suffice. This would be a lot more difficult in the back-observation
    instrument because there was little such overlap between its ranges. A few
    scale markings were often provided past 90 degrees, so a star passing near
    the zenith could be plotted, but measuring altitudes when straight-above is
    notoriously difficult. It would be easier to use a reflecting horizon, with
    a body near 45deg.
    Perhaps another option was available to the land-explorer, that the
    sea-navigator lacked. If he was on clear ground, with some distant
    landmarks such as prominent trees, he could measure a horixontal angle
    between two trees, and walk until he found a place where they subtended
    90deg, and then compare that angle, measured directly and measured by
    back-observation. I've not read of such a measurement being made, but
    perhaps it was a possibility to an intelligent explorer. Can anyone see any
    snags in that procedure: has anyone read of it being used?
    contact George Huxtable by email at george@huxtable.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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