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Jim Thompson asked-

>Neither Dutton's nor Bowditch explain back sight reduction in sufficient
>detail for me to be confident about the process.  My understanding is this:
>
>1. Raw altitude = back sight.
>2. Corrected raw altitude: apply Index Correction and dip.
>3. Corrected hs = 180d minus corrected raw altitude.
>4. Then reduce the corrected hs as usual.
>
>True, or bungled?

This is a deeper question than it appears, and it has puzzled me too. I
don't know of any text which explains it properly.

Not, perhaps, for Jim's benefit, but for others, perhaps I should explain
that the Hadley quadrant, (otherwise known as an octant), had an arc of
only 45deg (or perhaps a little more) so it was unable to measure angles
much greater than 90deg. The sextant was a later development, which allowed
measurement of angles up to 120deg, perhaps slightly more, mainly to use
for lunar distances.

Some octants had an additional fitting, which allowed them to measure
angles from 90deg to 180deg. This was an additional peep and horizon
mirror, fitted low down to the left arm of the A-frame. The horizon mirror
was angled so as to give a view to the observer (who was now looking from
the left, having turned the instrument about a vertical axis) of both the
horizon and the index mirror. The index mirror would then collect light
from over, or behind, the observer's head. This was possible because the
arms of the octant were so long, and the backsight peep was mounted so low,
that light from the horizon behind the observer could pass clear over the
top of his head, and reach his eye via the two mirrors.

In back-sight mode, an object overhead would correspond to a scale reading
of 90deg, and then objects increasingly further from the observer's forward
horizon would give scale readings reducing from 90deg, until an object on
the horizon, right behind his back, would correspond to a scale reading of
zero. That's why, in backsight mode, the scale reading was subtracted from
180deg to get the required angle.

In normal, forward mode, it's easy to check the index error of an octant,
or sextant, by aligning the distant views of, say, the horizon, or a
celestial body, direct and via the mirrors. When they align, the near-zero
scale reading is the index error, by which all observations should be
corrected.

But there's no such simple way to allow for index error in back-sight mode,
as there's no way to align an object with its reflected image.

A further question now arises: what does Jim Thompson wish to use an octant
backsight FOR? I can think of four applications.

1. He wishes to measure a lunar distance greater than 90deg. (at sea or on land)

2. He wishes to measure a horizontal angle (for surveying purposes) greater
than 90deg. (at sea or on land)

3. On land, he wishes to measure the altitude (greater than 45deg) of a
body seen by looking down into the reflecting pool surface of an artificial
horizon, which doubles the angle.

4. At sea,He wishes to measure the altitude of a body above a horizon which
is obscured by nearby land or by mist, though the horizon in the opposite
direction is clear.

In cases 1, 2, and 3, dip doesn't enter the question at all, because angles
aren't being measured from the horizon.

Whatever purpose he wishes to use the back-sight quadrant for, Jim has to
decide just how he is going to determine its index correction, on land or
at sea. Only then can we say how the observation should be reduced.

Over to you, Jim.

George.

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contact George Huxtable by email at george@huxtable.u-net.com, by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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