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Re: Suitable Sextants - Mirrors
From: George Huxtable
Date: 2005 Oct 14, 10:35 +0100

```I'm with Frank Reed when he writes-

>Just so there's no  misunderstanding, I agree with you that a sextant should
>have (or at least  potentially accept) a telescope with a relatively large
>aperture and the mirrors  should be compatible in size with that --large
>enough
>to fill the field of view.

But we differ about his statements, in an earlier posting, that-

>The horizon mirror only needs to be as big as the  aperture of the
>telescope. Navy sextants from the Second World War had small  horizon mirrors
>because their telescopes were usually small in aperture.  Naturally there is
>no reason to have a horizon mirror bigger than than the  telescope aperture.

and-

>the index mirror. This  doesn't need to be any wider
>than the horizon mirror ...

How big does a mirror have to be to meet the test; that the mirror frame
doesn't intercept any light which would otherwise be seen in the telescope,
not just at the centre, but right out to the edge of the field of view?

To the diameter of the telescope objective, you should add a quantity to
allow for that field of view. Divide the angular field-of-view of the
telescope, in degrees, by 57, to put it into radians. Then multiply by the
path length of the light, from the mirror in question to the object lens of
the telescope, in mm. That result has to be added to the diameter of the
object lens to arrive at the necessary diameter of the mirror, in mm.
Because the index mirror is further from the object lens than is the
horizon mirror, then its required diameter  is slightly greater.

If the mirror is that size, there's no point at all in making it any
bigger, except for the allowance that Frank rightly emphasises, in-

>... the index mirror ... it helps a lot if it's  longer (bigger in the
>dimension along the index arm) because it will be  foreshortened when the
>sextant
>is set to a large angle.

For a sextant which is designed with optimal geometry, the enhancemant in
the length of the index mirror should be  (1 / cos 30), or 15%, which
allows for that foreshortening over the full range of observed altitudes
from 0 to 120 degrees. Many makers expand the width of the index mirror by
that same 15% also, simply because it's easier to make a round mirror than
an elliptical one, but that extra width serves no purpose at all.

If the mirrors are sized according to those precepts, there is absolutely
no point in making them any bigger. The field of view is then determined
entirely by the telescope, and has not been degraded, in any way, by the
sextant's mirrors. Any extra mirror-area would indeed "accept more light",
in Joel's terms, but not a photon of that extra light could possibly reach
the observer's eye. It's true that a wider-angle telescope, and (in
twilight conditions) a larger telescope aperture, both make observation
easier. When telescope apertures  were increased, then indeed mirror sizes
were increased to correspond. Without that change to the telescope, there
would have been no advantage at all in enlarging the mirrors. One followed
the other.

Joel Jacobs, trying to make a case for bigger-is-better sextant mirrors, wrote-

>"Your analysis though  interesting, fails to take into account that a
>sextant's mirrors are not used in  a static state, and hence size does make a
>difference. Consider that the  platform is moving directionally, and
>rolling and
>pitching all at the same  time."

To which Frank has correctly replied-

>But since the mirrors, telescope, and other components of the  sextant are
>all experiencing the same motion, this really isn't relevant to  mirror size.
>They're either big enough to fill the field of view, or they're not  --no
>matter
>how much pitching and rolling there is.

Joel's counter was as follows-

>The idea that the boat and the crew are moving in unison to the affects of
>motion is incorrect. The centrifical forces can cause the vessel to go one
>way, and the individual the other.

That argument is entirely bogus. It wasn't suggested that the boat and crew
were moving in unison, just that the bits of the sextant were. It's simply
impossible to improve the field of view of a sextant by enlarging the
mirrors, once they are large enough to pass all the relevant light.

>The procedure of rotating the sextant is to have the celestial body
>subtend an arc in which its lowest point just kisses the horizon. At that
>moment, the sextant is perpendicular, and the reading is taken. To do that
>correctly, the object will sweep across the field of view as an arc, and
>not be centered "at all times" as he suggests.

The error is in that last sentence. I'm sure Joel has taken many more
sextant observations that I have, and subconsciously does them the "right
way", even if his explanation of how it's done is at fault. Frank's earlier
account of how to take a sight was correct, when he wrote-

>When "rocking" for perpendicularity, the sextant is  supposed to be
>rotated about an axis that points to the Sun or star. And when  this is done
>correctly, the Sun or star remains centered in the field of view.

The body should indeed remain roughly still in the centre of view, and what
changes is the view of the horizon in the horizon mirror, as the sextant is
rotated about the direct line from the observer to the body. Joel's
description is a near-equivalent to that, only for low-altitude sights. If
the body is high in the sky, it would be well-nigh impossible to put that
method into practice. It's no wonder that Joel feels such a need for a
larger field of view. It's just a pity that an over-large mirror will do
nothing to help him.

It seems important to contradict "Joel's method" for taking sights;
textbook, and do the job the other way.

George.

===============================================================
Contact George at george@huxtable.u-net.com ,or by phone +44 1865 820222,
or from within UK 01865 820222.
Or by post- George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13
5HX, UK.

```
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