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-------------- Original message from george huxtable <george@HUXTABLE.U-NET.COM>: --------------


> 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 thoug! h 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.
>
> Joel adds the remarkable statement-
>
> >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 explanat! ion 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;
> otherwise novices might be tempted to follow it. Instead, read any
> 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.