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    Re: Suitable Sextants - Mirrors
    From: Joel Jacobs
    Date: 2005 Oct 14, 15:57 +0000
    Thank you George,
    I always get a chuckle out of your efforts to be througough and scholarly. 
    First you  say that  my argument that bigger mirrors are better is entirely bogus because " It wasn't suggested (by Frank) 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."
    What you and Frank are missing is that the viewer's eye is not always centered in the ocular lens of the scope due to the motion of the vessel. If it  were attached to the sextant as your comments presuppose, then what you say would be correct. But it isn't. The sextant and the hand holding it and the eye viewing are independent from one another. What the viewer sees is not in the laboratory setting upon which your argument is based. Nothing that you or Frank have offered changes my opinion.
    Second, you say  "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."
    You also amuse me when you quote unnamed texts to prove a point, and will declare later that you never do such things
    George, here is a link to photographs of page 108, Figure 6-4 of Bauer's " The Sextant Handbook". I would like you to publish some illustrtions from other texts that show a different picture from that which I discribed. For those interested, Bauer goes into great detail in the methodology of swining an arc on pages 105-108 which are the same as my own.
    Since I think you have a sincere interest in "knowledge" and enjoy sharing your opinions in great detail with others, what I would like to learn from you is whether contemporary sextant's mirror size and scopes are optimized. So you need not search for the dimensions which are typical of most major brands they are:
    Scope 4 x 40
    Index mirror, 57 x 42mm
    Horizon Mirror, 57mm dia.
    Thanks George,
    Joel Jacobs
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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.
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