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Alex Eremenko wrote-

>I propose the following procedure for Index correction
>for back sights on land. It seems simpler, and independent
>of the index correction for the fore sights.
>
>Choose two distant objects in opposite directions.
>They don's have to be too distant. Horizontal edges
>of roofs of the buildings
>will be OK. Or two assistants holding some poles.
>
>The difference in bearings should be 180d.
>Now measure the vertical angle between the directions
>on these two objects by a back sight.
>Then do the same with your quadrant upside down.
>One angle will be negative, another positive.
>Their algebraic sum, divided by 2 is your index correction
>for back sights.
>
>Remark. Taking a back sight with your quadrant upside down
>may be somewhat tricky: you have to incline your head
>to horizontal position. Not to obscure your back sight
>with your body. You may need another assistant for this
>(to hold your body from falling:-)

=======================
from George-

Yes, I think that method would work well; but I have one reservation. It
depends on a question I have asked about before: whether the octant was
subject to any flexure due to the different direction of gravity as the
instrument was inverted. I suspect that because of its larger size and
rather flimsier construction, it may not resist flexure so well as does the
modern small-and-sturdy metal sextant.

I don't know that is the case; it's just a speculation. Does anyone own an
octant to try that out?

The flexure problem can't be that serious, because I have a reprint from a
Maskelyne contribution to the Nautical Almanac which is undated, but I
suspect went with the 1774 edition. This recommends the use of direct and
inverted octant, in a similar way.
=======================

Alex, in another posting, quoted from a letter from Dollond drawing
attention to the difficulties of determining index error in backsight mode
using the fore and aft horizons (presumably because allowing for dip).

>George,
>
>"The method hitherto practiced for adjusting that
>part of the instrument, by means of the opposite
>horisons at sea, has been attended with so many
>difficulties that it has scarce ever been used;
>for so little dependance could be made on the observations taken
>this way, that the best Hadley sextants made
>for the purposes of observing the distances of the Moon
>from the Sun or fixed stars, have been always made without
>the horizon
>glass for the back observation; for want of which,
>many valuable observations of the Sun and Moon have been
>lost, when their distance exceeded 120 degrees."
>
>This is from
>"A letter from Mr. Peter Dollond, to Nevil Maskelyne, FRS etc.
>read on March 29 1772
>(Trans Royal Soc., you said you have easy access to this).
>
>Alex.

Response from George.

This was a sales-pitch for Peter Dollond's new sextant, with modifications
that had been suggested by Maskelyne. Already, a sextant was capable of
measuring to 120 deg, but this would allow greater angles still, by adding
a back-sight to it.

Dollond's gimmick was to put the back-horizon mirror on a turntable which
could be shifted between two stops through an angle of precisely 90
degrees. Then one could determine and correct index-error in the forward
direction, as observed through that mirror in its shifted-clockwise
position, viewed from the right by a telescope (which had to be displaced
from its normal position). Then the two mirrors would be parallel. And
then, Dollond argued, having moved the back-horizon mirror back again
through exactly 90 degrees anticlockwise, a measured angle of 180 degrees
must then correspond to that same scale reading.

The flaw in that argument, as I see it, was that it relied on the exactness
of that 90-degree shift, over long periods, and any mechanical derangement
would result in errors for all back observations.

One of these instruments was taken on Cook's second voyage. Bayly and Wales
(Cook's astronomers) are reported to have measured Sun-Moon lunars as great
as 155 degrees. However the almanac left off predicting lunar distances
when they increased beyond 120, so to make use of that observation they
would have had to do a lot of arithmetic. Perhaps for that reason, the
backsight-modified sextant never caught on.

A picture and (partial) description is available in a modern publication,
"The Charts and Views of Captain Cook's Voyages", vol 2, ed. Andrew David
(Hakluyt Society, London,1992), on page xx of the introduction.

As well as the paper in Phil. Trans. 1772 that Alex refers to, Dollond also
wrote "Directions for using the new improved Hadley's Quadrant; with the
new method  of adjusting the glasses for the Back Observation", which was
undated, and which I haven't seen, but I understand there's a copy in the
National Maritime Museum at Greenwich. Maskelyne also describes it in the
Nautical Almanac for 1774.

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

A different proposal for correcting back-sight index error was made by
Robert Blain in the Nautical Almanac, but I don't know for which year. It
was in "Selections from the additions that have been occasionally annexed
to the Nautical Almanac from its commencement to the year 1812", published
in 1815 by the Commissioners for Longitude. Unfortunately, that publication
doesn't identify the year that each selection was annexed to.

The paper is "A description of an accurate and simple method of adjusting
Hadley's Quadrant for the back observation". Blain proposes that the index
mirror should have its lower edge made visible and polished to be at
EXACTLY 90 degrees to the normal reflecting surface of that mirror. Then,
when the forward horizon could be seen, via the back-horizon mirror and the
edge of the index mirror, aligned exactly with the fore horizon as seen
directly, then at that scale reading the back-horizon mirror and the edge
of the index mirror must have been parallel. At that setting the normal
reflecting face of the index mirror must then have been exactly
perpendicular to the back-horizon mirror, assuming that the reflecting
faces of the index mirror were exactly 90 degrees apart. And in that case,
light from behind the observer will have been bent through exactly twice
that angle, or 180 degrees. So that same index position must correspond to
180 degrees of measured angle.

Blain doesn't give a value for the accuracy with which the two faces of the
index mirror may be made exactly perpendicular, and that's the weakness
that I see in his proposal. But he does make the reasonable claim that once
measured, any discrepancy from 90 degrees will always remain constant.

====================
Alex informs us-

>the following paper addresses most issues
>that are permanent topics on this list:
>
>A Letter from the Rev. Nevil Maskelyne, MA, FRS to the
>Rev. Thomas Birch, DD. etc., containing the Results of
>Observations of the distance of the Moon from the Sun
>and fixed Stars, made in a voyage from England to the Island
>of St Helena, in order to determine the Longitude of the Ship,
>from Time to Time; together with the whole Process of
>Computation used on this Occasion,
>read on June 24 and July 1, 1762.

For anyone that can get access to it, Maskelyne's "British Mariner's Guide"
(London, 1763) has a detailed account of the lunar distance measurements of
that voyage, together with an explanation of the wickedly complicated
procedure for determining the position of the Moon and predicting lunar
distances. 135 pages of solid text and 35 tables.

And I agree with Alex that the volumes of Phil. Trans (Philosophical
Transactions of the Royal Society) provide a goldmine of fascinating
information about the current thinking of the real experts of the day.
Among some dreadful dross, of course. Longitude, and navigation generally,
was a major preoccupation.

George




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