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    Re: sextants on aeroplanes
    From: Gary LaPook
    Date: 2008 Dec 13, 17:00 -0800
    You're right George, I didn't think that one thru, I just extended the idea of octant-sextant to quadrant to get to the 180º range. Thinking about it it becomes obvious that you can't get to that with a double reflecting instrument. As you measure greater and greater angles your view of the index mirror gets thinner and thinner in height and if you ever got all the way to 180º you would be looking at the index mirror edge on which obviously wouldn't work. Thanks for the correction.

    gl

    --- On Sat, 12/13/08, George Huxtable <george@hux.me.uk> wrote:
    From: George Huxtable <george@hux.me.uk>
    Subject: [NavList 6728] Re: sextants on aeroplanes
    To: NavList@fer3.com
    Date: Saturday, December 13, 2008, 8:27 AM

    Gary LaPook wrote in [6658]-

    "There is a distinction between sextants, octants and quadrants. Because
    of the double reflection operating principle of the marine instruments
    it is possible to measure an angle of 90º, one quarter of a circle,
    with an instrument having a calibrated arc of only one-half that, 45º,
    one-eight of a circle, an instrument called an octant.
    If the arc is one-sixth of a circle, a sextant, you can measure angles
    up to 120º and if the arc is one-quarter of a circle then you can
    measure an angle of half of a circle, 180º, and you then have an
    instrument called a quadrant."

    ========================

    In trying to resolve these matters, I fear that Gary has added to the
    confusion. Historically, instruments which could measure up to 90º, were
    known as "quadrants". That applied to instruments without a mirror,
    which
    then required an arc of 90º, and, also later, to Hadley's 2-mirror
    invention, which did the same job with an arc of only 45º. It was called a
    reflecting quadrant, a Hadley quadrant, or sometimes just a "Hadley".

    A bit later, the working range was extended to 120º, which required an arc
    of 60º, and that being a sixth of a circle, it was christened a
    "sextant".

    (Later still, a few instruments were made with a range extended to 144º, and
    an arc of 72º, known as "quintants")

    But all this was logically inconsistent with the use of the word
    "quadrant",
    for an intrument measuring to 90º, so those instead became known as
    "octants", because their arc was an eightth of a circle. There is no
    difference at all between a reflecting quadrant and an octant; they are two
    names for the same thing.

    So Gary is wrong when he writes-

    "Quadrants must be made larger than sextants which are larger than
    octants. An octant is sufficient to measure any angle from horizontal to
    straight up so can be use for normal celestial navigation and this is
    how they are used in aircraft. Sextants and quadrants allow a greater
    range of measurement which might be useful for lunar distance
    measurements, horizontal sextant angles for coast wise navigation and in
    the rare case of a body within 30º of the zenith with an obstructed
    horizon below it but a clear horizon in the opposite direction in which
    case the navigator could turn his back to the star and use the opposing
    horizon for the sight. (I don't know if this was ever actually done in
    real life.) Since these types of sights are never taken from an aircraft
    it is never necessary to have more than an octant on an aircraft. My
    tamaya sextant actually measures up to 125º and my SNO-T goes all the
    way to 140º but these are both sextants."

    The first account I have read of that trick of measuring up from the
    opposite horizon was on the Malaspina exploration, near Callao, in 1790,
    when the morning Sun was visible to the West, but the horizon beneath it
    couldn't be seen because of the nearby coast (a dip-short situation,
    really). Usually, if you're close to visible land, celestial navigation
    isn't called for: except when, as here, surveying an unknown coast.
    Malaspina was pleased to have, in his kit, an early quintant, perfect for
    such a task.

    Gary's SNO-T sextant, measuring up to 140º, is only 4º short of being a
    true
    quintant. Quintants were mostly used by hydrographic surveyors, to measure
    wide horizontal angles. Lecky, in his "Wrinkles", was keen to push
    quintants
    for navigators, but I've never really understood why. I wonder if, when
    Gary
    wrote "Quadrants must be made larger than sextants which are larger than
    octants.", he was thinking of quintants rather than quadrants.

    However, in writing "if the arc is one-quarter of a circle then you can
    measure an angle of half of a circle, 180º, and you then have an instrument
    called a quadrant", he was describing a device which, as far as I know,
    has
    never existed. Not that it's impossible, necessarily. I've been
    pondering a
    scheme which might allow a two-mirror reflecting instrument to measure
    angles up to 180º, which would allow wall-to-wall observations from one
    horizon to the opposite one, and so allow dip to be measured. More about
    that later, unless it turns out to be nonsense.

    George.

    contact George Huxtable, now at george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.






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