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    Re: sextants on aeroplanes
    From: George Huxtable
    Date: 2008 Dec 13, 16:27 -0000

    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  90�, one quarter of a circle,
    with an instrument having a calibrated arc of only one-half that, 45�,
    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 120� and if the arc is one-quarter of a circle then you can
    measure an angle of half of a circle, 180�, 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 90�, were 
    known as "quadrants". That applied to instruments without a mirror, which 
    then required an arc of 90�, and, also later, to Hadley's 2-mirror 
    invention, which did the same job with an arc of only 45�. It was called a 
    reflecting quadrant, a Hadley quadrant, or sometimes just a "Hadley".
    
    A bit later, the working range was extended to 120�, which required an arc 
    of 60�, 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 144�, and 
    an arc of 72�, known as "quintants")
    
    But all this was logically inconsistent with the use of the word "quadrant", 
    for an intrument measuring to 90�, 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 30� 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 125� and my SNO-T goes all the
    way to 140� 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 140�, is only 4� 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, 180�, 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 180�, 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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