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Frank Reed noted-

>Of lunars set B, George H wrote:
>"Here is a discrepancy of 4.9', which would make sense only if the longitude
>was about 92.5 deg rather than 90deg. Again, this is a serious discrepancy "
>
>Serious, yes. But seems to be about as good as Lewis & Clark were capable of
>doing from the evidence of the later parts of the trip. I assume you've read
>Preston's article about the lunar observations in 1804 and 1805. Probably there
>are people on the list who don't know about this though, so here's a link:
>   http://www.aps-pub.com/proceedings/jun00/Preston.pdf
>
>In Preston's table comparing calculated longitudes with known longitudes,
>it's clear that the lunars they took were frequently off by two or three
>degrees
>in longitude. Further, the error is systematic --it's almost always in one
>direction. Preston speculates on causes. Here's one to consider: bad
>eyesight. If
>an oberver is nearsighted, bringing a star to the edge of the Moon's limb is
>tricky since the star appears to have a large "disk". Even within any given
>set (the sets A, B, C in yout post), the lunars jump around by 2 or 3 minutes
>around the distances that one would expect.

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

I thank Frank for his useful comments.

Yes, I've read Preston's paper, which was one cause of my being drawn in to
investigating Lewis and Clark.

But since he wrote that paper, several errors in Lewis and Clark's methods
have come to light, of which Preston may have been unaware..

Particularly this one. To calculate a lunar, it's necessary to know the
latitude to some degree of accuracy. L&C didn't know how to calculate it
from their equal-altitude observations, in the way that was shown in a
previous earlier posting. Instead, they would measure Sun meridian
altitudes, using reflection in an artificial horizon..

As mentioned in that earlier posting, L&C invariably miscalculated the
index correction of their sextant altitudes, first halving for the
reflection, and then adding/subtracting index correction, rather than doing
it in the opposite order, as they should have. That meant that their
meridian altitudes were ALWAYS out by half the index correction.

That was bad enough in Winter, when Sun noon altitudes were low enough that
the doubled altitude could be measured with their sextant, for which the
correction was nearly 9 arc-minutes.

But in Summer the doubled Sun noon altitude exceeded the 120deg angular
range of the sextant, so they had to revert to their wooden octant, which
had been adapted for back observation. This meant that in that mode it
could measure angles between 90deg and 180deg. Unfortunately, that octant,
in back-observation mode, is stated to require an immense index correction
of 2deg 41'. And because they got the correction method wrong, their
deduced latitudes were therefore always in error by 1deg 20'! Worse still,
being a wooden instrument, an octant is likely to show significant changes
in its index error with changes in weather, but in back-observation mode
there's no easy way (that I'm aware of) to check for such changes.

The above problem was considered in some detail by Rudner and Heynau in
"Revisiting Fort Mandan's Latitude", in "We Proceeded On", vol 27, No 4.

An additional error is this, brought to my attention by Hans Heynau-

In the early stages of the journey at least, L&C frequently got mixed up as
to whether they were measuring the altitude of an upper-limb or a lower one
when they were observing the Sun by reflection. I have found that in their
first few weeks, although they labelled some observations as upper-limb,
and some as lower-limb, every one without exception must have been an
upper-limb measurement! Whether this continued into the voyage, I don't yet
know.

Another paper, in the same issue of "We Proceeded On", by Bergantino,
"Revisiting Fort Mandan's Longitude", details several errors made by L&C in
assessing their clock-times.

Add in the chronometer misreadings that were described in my earlier
posting, and it's clear that there's no alternative to thoroughly unpicking
and correcting every detectable known mistake. That's what I am trying to
do. Then the Preston information can be re-evaluated.

I can say, however, that until I have come up against this lunar-distance
problem, after recalculating their positions and correcting known (or
suspected) errors, over the first few weeks of the journey, their
measurements seem to be within an arc-minute or two of the truth, and you
can't ask for much better than that.

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

Frank continues-

>Even within any given
>set (the sets A, B, C in yout post), the lunars jump around by 2 or 3 minutes
>around the distances that one would expect.

Yes, it's true that they jump around by 2 or 3 minutes, but how do we know
what lunar distances to expect? Their lunar observations are nowhere near
as precise as those of that expert inland Lunarian, Gregory, in Australia,
50 years later. But remember, this was their first recorded shot at lunars,
perhaps their first attempt ever.

After averaging a set-of-six such measurements, one might perhaps expect
the scatter to average out with an accuracy of 1 arc-minute or so. The
discrepancies that appear to occur are of a much greater magnitude than
that.

George

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