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    Re: sextant index error measurement
    From: Bill B
    Date: 2006 Nov 03, 14:27 -0500

    Some excellent thoughts George.  The problems I ran into was when trying to
    use the sextant as a range finder.  As you proved at that time, the
    reflected image on the index mirror does not have to be at the axis of
    rotation. Assuming the distance of the reflected image to the scope's sight
    line did not change when the index arm/mirror were moved was my downfall
    when trying the use geometry to predict distances based on one sighting.
    In this case of determining the distance from index mirror point to scope
    sight line at one setting, it seems to have promise.
    > 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.
    George responded
    > 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.
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