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Re: Sextants, vernier and micrometer.
From: George Huxtable
Date: 2006 Nov 1, 09:57 -0000

```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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