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    Re: sextant index error measurement
    From: George Huxtable
    Date: 2006 Nov 3, 11:19 -0000

    
    Paul Hirose wrote about his interesting suggestion for placing stripes
    on a distant board for testing index error
    | > From the vertical distance
    | > between the telescope and index mirror, and the distance to the
    target,
    | > you can compute the parallax. Add parallax to the sextant reading
    to
    | > obtain index error.
    
    and Bill responded-
    
    | This is where I have failed in the past.  How does one know the
    vertical
    | distance between a moving point on the index mirror and the central
    axis of
    | the scope?  It seems quite the reverse.  If you know the angle the
    sextant
    | is set to, the distance to the target (from what point of the
    system?) AND
    | the *exact* IE/IC you could compute the vertical distance.
    
    It's clear what angle the sextant should be set to; to zero, or very
    nearly so. Because it'a a check of the index error that is being made.
    
    If you have a peep-tube, to show roughly the line of collimation of
    the sextant, it's a very simple matter to determine the offset between
    these two incoming sight directions, which are ideally parallel, or
    very nearly so. Use whatever specs are needed to give you a clear view
    at a foot or so distance. Put some sort of boldly-marked ruler at a
    convenient (short; a few inches perhaps) distance in view of the
    sextant, so that two views of it can be seen, one through the index
    mirror, one through the horizon glass, and record the offset between
    them. The ruler has to be roughly at right angles to the line of view,
    but that's very uncritical. I used a dressmaking tape that my wife
    has. It's dead easy to get the answer to a millimetre or so. For my
    sextant, it was 50 mm, give or take a mm.
    
    Or you can do it by geometry. For that, you will need the effective
    distance d between the parallel reflecting surfaces of the two
    mirrors. You can measure this between the upper part of the horizon
    glass and the lower part of the index glass, where there will usually
    be some overlap between those parallels. If they are front-silvered,
    that's easy. Otherwise, if you want to be precise, you will have to
    add two-thirds of the combined thickness of the two glasses; the
    two-thirds factor allowing for the refractive index of glass.
    
    And you need the angle A by which the horizon mirror is tilted from
    the plane that's at right angles to the collimation line of the
    telescope. You should be able to estimate this using some sort of
    protractor (or course plotter). Then the spacing between the
    sightlines is then d x cos 2A.
    
    If the sextant has been designed properly, and most are, it will be
    the same as the perpendicular distance between the pivot of the index
    arm and the centre-line of the scope; but in fact, the placing of the
    pivot has no direct influence on the offset between the sightlines.
    
    That sightline offset, having been obtained once for a sextant to a mm
    or so, won't change, and it might be useful to write it on a slip of
    paper tacked to the inside of the box. It will vary, between one
    sextant and another, but not by much.
    
    Then a nice white board could be made up, with a few black lines
    inscribed on it at just the right spacing for your sextant, as Paul
    suggests. Insulation tape would be a convenient method of marking.
    Perhaps one black line could be cut a bit shorter than the others, to
    avoid any miscounting. It needs to be stood up roughly vertical, at a
    convenient height.
    
    Because those spacings closely match the sextant's offsets, there's no
    longer a requirement for that board to be placed a very long way off.
    If the offset matches within a millimetre, then a board placed 30
    metres away would would allow alignment within 0.1 arc-minute; all
    that's necessary for normal marine navigation.
    
    It's an idea that could do with trying out, but I haven't tried it in
    practice, yet.
    
    George.
    
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
    
    
    
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