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    Re: Index mirror adjustment with offset mirror
    From: Luc Van den Borre
    Date: 2014 Jan 17, 11:54 +0100

    On 17/01/2014 5:43, Bill Morris wrote:
     > I don't understand the references to the top surfaces of the various
     > solid objects - dice, piles of coins, pieces of Lego - in this thread
    
    The top surface allows you to more accurately determine that your eye is
    placed at the correct height, namely in the plane formed by the tops of
    these objects. The way I do this is to lower my viewing height until the
    top surface disappears. A fine edge does not allow this, since it's
    basically a 2D segment that will look more or less the same when viewed
    from slightly too high or too low.
    
    > the only requirement is for two edges of equal height above the limb,
    > very approximately of the same height as the centre of the horizon
    > mirror.
    
    (I assume you meant the index mirror.)
    No, I think any height will do - as long both objects can be observed at
    that height. There's nothing wrong with the top edges of the objects
    appearing close to the top or bottom of the index mirror. After all,
    ideally we'd use the arc itself, which is just a zero-height object (but
    we can't, since if we place our eye in the plane of the arc, we can no
    longer see its mirror image).
    
    The centre of the index mirror does make for easy viewing, so it's a
    good choice. There is, however, nothing special about it, unless you're
    assuming the index mirror isn't flat...
    
     > The index mirror is then adjusted so as to bring the direct
    > image of the edge at the lower end of the limb into line with reflected
    > image of the edge at the top end of the limb, when viewed with the eye
    > at about the same height as the top of the vanes. "Vane" seems to be the
    > best translation of "dioptre" in this context.
    
    I think this procedure is 'about right', and perhaps through your long
    experience you are intuitively doing this better than most would if they
    followed these instructions.
    What I object to is the 'about the same height'. The eye should be at
    the height of the top of the vanes _as precisely as possible_.
    
    1) on a sextant with an index mirror placed on the centre of the arc,
    the height of your eye _doesn't_ matter (and in this case you can just
    use the arc itself for alignment)
    2) the more the mirror is offset, the more getting the height correct
    will matter. Why? Because on such a sextant even with the mirror aligned
    correctly, the vanes will only line up when viewed from the correct
    height. So if you are viewing from 'about the same height' while doing
    the procedure, you'll get an 'about correct' alignment (which may well
    be good enough for all intents and purposes, I haven't looked into that).
    
    Imagine a sextant with a mirror that is perfectly aligned to the arc,
    but that has an adjustable offset. If we move the index mirror forward a
    few mm (that is, towards the eye), the image of the arc in the mirror
    will only stay unbroken when viewed from the height of the arc (which is
    not possible to view in most cases). In fact, the arc will appear more
    broken the higher we move our eye from the plane of the arc.
    
    * The more you offset the mirror, the more the arc will appear broken,
    unless your eye is in the plane of the arc.
    * The higher you move your eye above the plane of the arc, the more the
    arc will appear broken. Only at the height of the arc does it remain
    aligned.
    
    Note that this is all with a perfectly aligned mirror!
    
    So there's no use trying to align a sextant that has an offset mirror
    without the calibration objects on the arc, since you can't actually
    _see_ the arc from its own plane.
    
    Now, with the mirror offset by 4 or 5mm, if you tilt the mirror slightly
    forward (the top rotating towards your eye), a tricky situation occurs
    whereby the effect of the rotation and the effect of the offset cancel
    each other in the middle of the mirror, where you'd typically be looking
    to line up two vanes for example. The mirror offset will make the
    reflected arc appear lower, but the forward tilt will compensate and
    bring it back up higher. The misalignment will only be apparent if your
    eye is quite precisely at the height of the vanes - which will be hard
    to do with vanes.
    
    Luc
    

       
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