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Still more on George's August 2nd posting:

The last part of it concerns Lewis and Clark's noon latitudes. Here is an
excerpt:

George: >What on earth is going on here? An on-land measurement of noon
altitude
using an artificial horizon was a standard technique for geographers, who
would expect to achieve a precision of a minute or so. I find it hard to
understand the earlier discrepancies of -5 and then +4 minutes, but the
subsequent errors of -21 to -29 minutes are simply unbelievable! Does
anyone have a clue about the origin of these huge discrepancies? Could it
perhaps relate to refraction in the glass (or talc) wind-shield over the
Mercury, if that's what was used? If Lewis and Clark's latitudes are so
greatly in error, what hope is there of using such a faulty observation
technique for lunar longitudes?<

Me: George probably has answers to his questions by now, but since nothing
has been said on the List, here are things to consider. First let's talk
about the comparatively SMALL errors.

The talc (isinglass) roof over the artificial horizon may have been part of
the problem. I have no idea how they worked the talc. But with glass, getting
the two surfaces of the sheet perfect and parallel to each other was not easy.

The octant was wood, mortised and glued with what we'd call "biodegradable"
glue. It seems reasonable to suppose it could have measured differently after
weeks of hot, dry weather than it did after long periods of rain and humid
weather, and perhaps a swim in the river with the other baggage.

But I expect a large part of the problem was that the frame of the instrument
was not always precisely in line with the sun's azimuth when the sun crossed
the meridian. Large angles measure too great if the frame of the instrument
is not parallel to the plane of the observation. That plane is formed by the
observer, the sun, and the sun's reflection in the water. It's a vertical
plane, of course, and bringing the sun and its reflection together puts the
instrument in a vertical plane. But there are as many vertical planes as
there are azimuths. The observation is in just one of them.

The HUGE errors in latitude are a separate question. They probably came from
the captains copying the instrument errors from one part of their journals to
another. It was mentioned in data Professor Bergantino sent me a while back,
but I must not have registered it. A bad number in the Journals was hardly a
surprise.

Later, working some observations taken in the Rocky Mountains, I ran aground
on the problem. The altitude azimuths, worked as time sights, wouldn't agree
with the equal altitudes. Fortunately, one of the equal altitudes was enough
out of the prime vertical to be worth working for latitude. With the latitude
found that way, things fell into place.

Then I remembered, from the Bald-pated Prairie observations of the previous
year, that the quadrant's back observation correction had been given to the
fraction of a second of arc. Here it was to the whole minute. Digging back, I
found that what was given as 2� 40' in this part of the Journal had once been
2� 11' 40.3". Reverting to the old correction produced a latitude close to
the one I'd found the hard way.

As George and other list members will know, the usual way of finding a
quadrant's back observation error is to bring the sea horizon behind you to
the sea horizon ahead of you. Correct for dip, and what's left over is index
error. On land you could measure a long lunar if you knew your longitude or
Greenwich time. Otherwise you'd have to measure between two stars, clear the
measurement for refraction, and then calculate the true distance between the
stars for comparison. Lewis and Clark were not familiar with such
calculations.

Had they chosen to, they might have gotten a fair idea by comparing back
sight measurements to the same measurements made with the sextant. But I'm
not sure they even bothered to check the sextant's index error.

Bruce

   

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