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    An "alternative" sextant?
    From: George Huxtable
    Date: 2008 Dec 15, 00:15 -0000

    The following idea may be a bit daft, and if it is I hope Navlist members
    will identify the snags and point them out.
    
    What follows is an alternative way to reassemble the basic components of a
    sextant in a new geometry, which will give it different characteristics from
    the standard instrument. It's difficult to illustrate the notion without
    making a perspective drawing (at which I am hopelessly bad), so instead I'll
    try to paint a word-picture.
    
    Start by taking a normal sextant and rebuild it. I'm not asking you to
    demolish your favourite instrument; just imagine it in your head, which is
    all I've done, so far.
    
    The angling of the index mirror has to change. Instead of its plane being
    perpendicular to the frame, it's now placed at exactly 45� to the frame, in
    such a way that incoming light from the observed body is now reflected to
    travel along the pivot line of the arm. The horizon mirror is shifted and
    fixed to a bracket that places it so that the pivot line passes through its
    centre, with a few centimetres spacing between the two mirrors. The horizon
    mirror, too, is angled by exactly 45� to the plane of the frame (about a
    vertical axis). In that way light from the observed body, travelling along
    the pivot line, is reflected into the telescope, which is aligned to point
    to the horizon as normal, and relocated to centralise the horizon mirror in
    its view. The horizon mirror is half silvered, as normal, so the observer
    sees, in the telescope, a direct view of the horizon and superimposed, a
    view of the celestial object, reflected via both mirrors, just as with a
    sextant.
    
    The essential feature of the Hadley 2-mirror invention is then retained;
    that after two reflections the image of the observed body will shift about
    in the view exactly the same as the direct view does, so that motion of the
    instrument in a seaway will not cause any relative motion between the two
    views.
    
    At the index-arm position when the two mirrors become exactly parallel, it
    should be at its zero mark, and the two images of any distant object should
    coincide, allowing checking of index zero-error as with the usual sextant.
    
    However, there's another "essential" feature of the normal sextant that will
    no longer apply. Normally, as the angle of the index mirror changes, the
    deflection of light changes by twice that angle. But that law is only true
    when all light paths are kept in the same plane. With this alternative
    instrument, the light paths are in very different planes (except at the
    zero-check position), such that the deflection of light becomes equal to,
    not double, the angling of the mirrors. (If anyone can offer disproof,
    please do so).
    
    Horizon shades will be placed in the direct view line through the horizon
    glass, as usual. Index shades will go into the space between the two
    mirrors.
    
    What would be the consequences of the new geometry? Most obvious is the
    doubling of the angular motion of the arm, that's called for to achieve the
    same angular range. A standard sextant frame, only 60 � wide, would only be
    able to measure up to 60� of arc, not 120� as with the standard sextant, so
    this would clearly be insufficient. The arc length would need to be doubled
    to subtend 120�, or even (for reasons we will see) 180�. That would lead to
    a large, clumsy instrument, except for the following...
    
    Because each measured degree now corresponds to a whole degree subtended on
    the engraved arc, and not half a degree as with the normal sextant, the
    degree markings, and the teeth of the rack,  now become twice as far apart
    as they were. Or, to put it another way, the same precision as before can
    now be achieved by halving the radius of the arc. So a standard sextant with
    a 60� arc and 18cm. radius could be replaced by one of 180� arc and 9 cm
    radius, which would be no less compact.
    
    There would be a few advantages, if only minor ones. Because each mirror
    always reflects through 90�, there's no shrinkage in the view to a
    letter-box shape, as you get with a sextant at large angles. That implies
    you could use the instrument right up to 180�, wall-to-wall between
    horizons. to measure dip, as long as one proviso has been met. That is, that
    the sideways displacement between the two sight-lines is enough to allow
    incoming light from astern to miss the ear of even the most jug-eared
    navigator. That's why there has to be a certain minimum spacing between the
    two mirrors.
    
    Another minor advantage would be that there's no vertical offset between the
    two view-lines, only a horizontal one instead. So instead of calling for a
    distant horizon to zero-check on, to avoid parallax errors, that job could
    be done with something quite close-up. Also, it means the same instrument
    could be used for on-land close-up angular measurements for surveying
    purposes, which presently call for a theodolite because of the parallax
    error that offset causes..
    
    I haven't yet discovered any major drawbacks to such a redesign, and hope
    that Navlist members will point out any there may be. For example, is its
    calibration unduly sensitive to the exactness of those 45� twists? Drawbacks
    there must
    be, I presume, if in all the years of sextant development, nobody has tried,
    or even proposed, such an alternative construction. Perhaps someone has,
    that I'm unaware of; dicovered the snags, and dropped the notion.
    
    The era of the sextant has been and gone; now is not the moment to be
    proposing a redesign, and that's not what I am doing. I am just asking the
    question; could sextants have been made in quite a different way, and if
    not, why not?
    
    If no serious objections emerge to the principles of what's been suggested,
    I can proceed to the practical details of how such a very-different
    instrument might have been constructed, which I've been pondering on, a bit.
    
    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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