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> That's where your mind-picture is wrong, Bill. Forget about "a point on the
> index mirror (hopefully at the axis)". For a plane mirror, one point is as
> good as another; none has any special significance. If you unshipped the
> index mirror from its mountings, you could move it about IN ITS PLANE, and
> as long as it could still reflect some starlight down to the horizon
> mirror, the star images would still coincide. I think that's probably obvious.
>
> Now shift the index mirror away from the horizon mirror in a direction
> PERPENDICULAR TO ITS PLANE, moving it upwards and backwards so it can still
> reflect some incoming starlight into the index mirror. As long as the index
> mirror is kept exactly parallel with the horizon mirror, you could shift it
> is far as you wanted, many feet away if you wish, and the two star images
> will remain coincident. It's because the starlight is coming from infinity,
> and is all exactly parallel. That would not be the case if the light was
> diverging from a nearby object; indeed, that's how a rangefinder works.

George

I agree that if you move the mirror IN ITS PLANE nothing will change UNTIL
the horizon mirror can no longer see it.  Also that if you move the index
mirror away from the horizon mirror ALONG THE LINE OF SIGHT from the horizon
mirror, the only thing that changes is the apparent size of the index mirror
when viewed through the scope.

After that, I respectfully disagree (except in special cases).  When we set
our index arm to 0d on the arc and adjust our horizon mirror to make an
object or line coincide (adjusting out index error), we are adjusting it to
look a a specific point on the index mirror. (Perhaps semantics fog the
issue.  The "point" is relative to the geometric relationship, not a given
point on a given mirror.  Clearly, if I replace the index mirror, the
"point" does not remain on the removed mirror;-)  The angle we need for the
horizon mirror is predetermined by the geometry of the sextant design and
construction.  Note that the angle between the bottom of the horizon mirror
and line-of-sight through the scope is equal to the angle between the
horizon-mirror top and the spot on the index mirror--simply by the laws of
reflection.

Here is where it gets sticky.  We have been using a special case (mirrors
parallel and one object).  If the point the horizon mirror is looking at on
the index mirror is not on the axis of rotation of the index mirror, things
go to hell in a handbasket when you try to measure the angular distance
between the horizon and a body or two bodies. Note a similar loss of
precision occurs if the index-arm is eccentric.

I can easily see this with my cardboard sextant. It is initially calibrated
by rotating the index mirror until it appears as a sliver through the sight
tube when reflected by the horizon mirror.  Then, looking through the sight
tube, a horizontal marker line is placed on the front-silvered horizon
mirror (actually polished stainless steel, with air where the glass would be
on a rear-silvered horizon mirror) right in the middle of the reflected
index-mirror image.  If I line up the horizon or an object between the
horizon and air (glass) through the sight tube ON THE MARKER LINE, and then
shift the sextant up or down so the images are significantly above or below
the marker line when viewed through the site tube, they will no longer be
aligned.  Since it is a sight tube, no blame can be placed on the optics ;-)

This is why it is so important to center the objects being viewed through a
real sextant on the horizon mirror.  I also suspect the optical quality of
scopes is such that using the edges introduce distortion as well.

That being said, lets revisit refraction.  As Frank pointed out, the effect
my be insignificant for bodies at infinity.  That being noted the discussion
becomes academic.  To simplify, let's forget the whole index mirror thing
for the moment.  With no shades in place we align an object (or two).  Now
we introduce a piece of glass way off perpendicular to the line of sight
through the scope in front of the horizon glass (away from the eye and
horizon glass).  It will shift the apparent position of the object being
viewed directly, so the two images will no longer be aligned. Yes?  (This
movement my be so small as to be imperceptible to the eye.)

That's my take at the moment.

Bill

   

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