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GregR asked-

On every sextant that I've ever seen, the index mirror is offset a few
degrees clockwise with respect to the index arm itself (i.e. they're
not parallel to each other). Is there a reason for that (or maybe it's
just a tradition that survives to this day)?

The only thing that I can think of offhand might have to do with the
overall design scheme of the sextant itself (i.e. maybe something I'm
not seeing here that makes the manufacturing process easier) - but the
only thing that's obvious is that would move the index arc itself more
counter-clockwise (or more to the right-hand side as you face the
instrument), and I really don't see any advantage or disadvantage in
doing that.

I realize that the actual position of the mirrors is really irrelevant
to getting an accurate reading (and any "offset" of the index mirror
could easily be taken out with a corresponding offset in the horizon
mirror), but wouldn't it be easier to just make the index mirror and
arm parallel in the first place and be done with it?

=======================

Response from George.

Well, I would throw the question back, and ask what's the problem
about having the index mirror non-parallel with the index arm. Where
would be the saving if they were made parallel?

Here are some constraints in sextant design, to think about if you
were rolling your own.

First, forget about the index arm and scale, and just consider the
mirrors and their optics.

The index mirror must be mounted in line with the pivot axis so that
its position doesn't shift as the arm turns.

The horizon mirror must reflect light coming from the index mirror
into the telescope. Or, looking the other way, horizontal light from
the telescope would reflect in the horizon mirror directly toward the
index mirror.

The two mirrors need to be vertically separated so that (depending on
their size) the index mirror doesn't get in the way of the telescope
and its light path, and the horizon mirror doesn't get in the way of
the light path seen by the index mirror when the index is set to zero.
And also, there's sufficient room for the shades. That establishes the
vertical offset between the two mirrors

The aim is to be practicably able to measure angles to 120 degrees,
without the height of the view of the index mirror shrinking
vertically into an impossibly narrow letter-box slot. Therefore, index
set at 120, we have to avoid near-grazing incidence on the index
mirror. Let's assume that under these conditions, the light comes no
closer than 10 deg to grazing incidence. At 120 deg altitude, the
incoming light is 30 degrees from the vertical, behind the observer's
head, so therefore, the index mirror needs to be 40 degrees from the
vertical, at least. In which case, the light reflected toward the
horizon mirror would be 50 deg from the vertical.

The horizon mirror needs to deflect this light to a horizontal
direction; that is, through 140 degrees. To do this, it has to be set
to 20 deg off the vertical, at which you will see that angles of
incidence and reflection are equal, as they should be, at 70 deg. So
that's fixed the horizon mirror.

Now what happens when we set the index to zero, to align the horizon
with itself? The angle of the index mirror must change by just half
the scale marking of 120, or actually 60 degrees. From being tilted 40
deg from the vertical one way, it's now 20 deg from the vertical the
other way. And notice that now both mirrors are tilted 20 deg from the
vertical, so they are exactly parallel, just as they should be when
set at zero.

So that's why all sextants look more or less the same. A few are
designed to cover a wider range of altitudes; a quintant goes to 144
deg, and its horizon mirror is a bit more upright correspondingly. And
then, to give itself enough elbow-room for its light paths, the
horizon mirror has to be shifted a bit further forward, other things
being equal. Other than that, there's little or no choice in where the
mirrors must go; the geometry is defined by the application.

===================

But none of that is really what GregR was asking. He wanted to know
about where the index arm and scale could go, and we haven't
considered that yet. The answer is- absolutely anywhere! It's designed
entirely according to user convenience.

Hadley's first octant (which is just like a sextant, but usually
wooden, with a 90 deg range) had an arm that was horizontal when set
to zero degrees, moving down to point toward the observer's collarbone
when set at 90. Presumably, navigators objected to it poking them in
the nose when making a zero-check! So his second sextant shifted the
arc, so that the index arm was roughly vertical at mid-scale, and
that's the way it has stayed ever since. In those days octants tended
to have a very long arm and scale, up to 18 inches radius, so it was
hard to find anywhere else to put it. Around 1790, sextants got much
smaller, but still, an index arm where it is on all sextants is just
in a naturally easy spot for the left hand to twiddle.

GregR can design a sextant, if he wishes, in which the index mirror is
parallel to its arm. But he could only do that by shifting the arm and
scale, from its convenient location to an inconvenient one. Not by
twisting the mirror, which is constrained by the way a sextant works.

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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