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Brad's diagram, of light paths for fore and back observations in an octant,
is most persuasive. I think he has it right, that it would be quite
possible to arrange the light paths to be parallel, in the way he has
shown, and some octants may indeed be designed in just that way.

His diagram implies that it would be necessary, in that case, to use a
particularly long horizon mirror, and certain illustrations of back-sighted
octants, in Peter Ifland's "Taking the stars", seem to show exactly that.
I'm thinking particularly of the Spencer, Browning, Rust octant in fig.50.

In which case, I was quite wrong, when considering the light paths between
the two mirrors, to insist that there simply had to be an angular
difference between those paths, between fore and back observations. In some
instruments, the paths may well be designed to be parallel, as shown in
Brad's diagram, so I should not have tried to lay down the law in arguing
otherwise.

However, it's also a perfectly valid design, to have those light paths
non-parallel, which was what Bill Noyce was pointing out could be the case.
All that that implies is that the sextant frame may be required to nod at a
different angle, in the two cases. That diverging geometry was indicated by
the diagrams in the Heynau article, that Bill drew to our attention, even
if the details in that diagram had not been fully followed-through. In that
design, it would be possible to get away with a perfectly ordinary-sized
index mirror. In my view, that's how many, perhaps most, backsighted
octants were arranged. That view is based only on pictures; not on personal
experience, as I haven't handled a backsight octant.

So, I suggest that Brad was wrong, if he was suggesting that those two
light paths had to be parallel, just as I was wrong, in insisting they
couldn't be. Can we agree about that?

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
----- Original Message -----
From: "Brad Morris" 
To: 
Sent: Thursday, March 25, 2010 7:03 PM
Subject: [NavList] Re: Back sights


Hi George

You requested that I sketch an octant for myself, showing the paths.

Linked, find just that image.  To be clear about the sketch, here are some
considerations

1) I made no attempt to optimize for index mirror size.  Clearly, I could
do so
2) The angles were arbitrarily selected, again, no optimization
3) The horizon, foresight view to horizon and backsight view to horizon are
all parallel
4) The view to the zenith for the foresight and backsight paths are
parallel.
5) All of the normals are shown, as well as, angles. (this is a sketch,
don't expect arc-second accuracy).

Conclusion #1:  The arrangement I have sketched can be made to work by
optimizing angles for index mirror size.
Conclusion #2:  The paths are indeed parallel.
Conclusion #3:  I am not "wrong", with all due respect to your opinion.

This may be an unusual circumstance in which multiple folks are right
without actually agreeing on the details!  How?  There are many
arrangements which can
be made to work.  There is no one definition of an octant and how the
mirrors are arranged.

I believe that the main difference is that you required the beam from the
object to strike the index mirror in the same spot, and with a differing
angle to each horizon mirror.  This is not a requirement with a planar
mirror, as can be seen in my sketch.

Best Regards
Brad


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