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    Re: Accuracy of Lewis and Clark Observations
    From: Bruce Stark
    Date: 2002 Aug 20, 10:58 EDT

    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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