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    Re: Sextants, vernier and micrometer.
    From: Henry Halboth
    Date: 2006 Nov 1, 21:53 -0500

    George is certainly correct; the expanded or double spaced vernier came
    into use on later sextants/octants and was actually quite common. The
    thing that appears somewhat unusual to me is the 12-second vernier. To
    the best of my knowledge, and that may not be so great, the conventional
    sextant vernier was graduated throughout comparably to the arc, i.e., if
    the arc was graduated in 10-minute intervals, the vernier extent was of
    course 10-minutes, but the second intervals were also in 10-second
    intervals, and the same convention appears on instruments graduated
    numerically in units of 15 or 20. I cannot say other than it appears a
    bit strange to me that Alex's sextant does not follow this convention.
    With respect to the previous list comments regarding lighting for
    reading-off a vernier, it probably should be said that accuracy is much
    dependent upon that lighting. A little experimentation will readily
    demonstrate that varying the angle at which the light employed strikes
    the arc/vernier interface may well result in a read-off value variation
    of 10-seconds, or even more. It has further been said, and I believe
    referenced in Lecky, that the radius at which the magnifier is placed
    also affects accuracy, being directly proportional to the length of that
    radius along the index arm; for maximum accuracy the use if a separate
    more powerful magnifier has been advocated by some.
    At sea, many of these niceties of accuracy become somewhat irrelevant as,
    except possibly when discussing Lunars, an accuracy to within 0.5-minutes
    is quite acceptable in practical navigation
    On Wed, 1 Nov 2006 09:57:24 -0000 "George Huxtable"
    > Alex wrote, about the scale on the sextant he has been considering,
    > and which he showed at-
    > http://www.math.purdue.edu/~eremenko/pic1.jpg
    > | It is indeed a very strange vernier,
    > | and it took me some time to understand it.
    > |
    > | The peculiar feature (from my point of view)
    > | is that vernier divisions are much bigger than the
    > | main arc divisions.
    > |
    > | On all verniers I've seen before, those
    > | are approximately equal.
    > | (Not exactly equal, of course, but of the same
    > | order of magnitude).
    > ===================
    > Really, that shouldn't be such a surprise. This is an "expanded
    > Vernier", as described by Peter Ifland, in "Taking the Stars", in
    > the
    > following terms-
    > ""Expanded" verniers came into use toward the end of the eighteenth
    > century.In this design the distance between divisions on the vernier
    > is twice the distance between divisions on the main scale. Thus, an
    > expanded vernier provides enhanced precision compared to the
    > conventional vernier."
    > I think that last sentence could be grounds for some argument. But
    > whether or not it increases precision, it provides a less-cluttered
    > Vernier scale, allowing more room for its divisions to be properly
    > numbered and marked.
    > Alex is likely to discover that almost any sextant he considers will
    > be marked in a similar way on the Vernier; it was very common. In
    > terms of it being an expanded Vernier, I mean, not in the
    > decimal-minutes division. It is read in exactly the same way as the
    > older Vernier, looking for exact coincidence between markings on the
    > Vernier and markings on the main scale, though depending on the
    > details of the angle setting, only alternate markings on the main
    > scale will be "in play" with the Vernier divisions at any time. That
    > doesn't matter a bit.
    > My own instrument, divided to 10 seconds, has just such an expanded
    > Vernier scale. Its Vernier, covering 10 minutes (to correspond with
    > the 10 minute separation between main-scale markings) has each
    > minute
    > split into 6, that is, to 10 seconds. So it has 60 divisions. Thase
    > are speced (very nearly) twice as far apart as the main-arc
    > divisions,
    > so it spans nearly 120 divisions on the main arc. Exactly 119
    > divisions, actually, for the Vernier principle to work. Therefore,
    > it
    > covers a span of nearly 20 degrees on the main arc. That implies
    > that,
    > for an instrument to measure to 120 degrees, an extra 20 degrees
    > must
    > be added to the main-arc divisions; that is, to 140 degrees.
    > Actually,
    > that sextant can work up to 128 degrees, before the index arm
    > collides
    > with the mirror mounting, so would need the main arc to go up to 148
    > to cover it; in fact, it is marked up to 155. However, at altitudes
    > approaching 128, the view of the index mirror is reduced to such a
    > narrow slot that observations would be getting impractical.
    > In the instrument that Alex is considering, vith a 12-second
    > Vernier,
    > there are 50 divisions on the Vernier, and these will coincide with
    > nearly 100 divisions of the main arc; actually, just 99. That is
    > why,
    > on that sextant, the Vernier has a rather smaller span, across 16
    > and-a-bit degrees of the main arc.
    > In the end, no matter how the instrument is marked, the overall
    > precision boils down th the accuracy with which the coincidence of a
    > pair of fine lines can be judged by the human eye, and the precision
    > with which every one of those many lines can be marked on a metal
    > arc.
    > George.
    > contact George Huxtable at george@huxtable.u-net.com
    > or at +44 1865 820222 (from UK, 01865 820222)
    > or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    > >
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