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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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