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    Re: Lewis & Clark
    From: George Huxtable
    Date: 2004 May 29, 22:41 +0100

    I have been following, with great interest, the exchanges between Bruce
    Stark and Ken Muldrew about Lewis & Clark's navigation.
    >On 25 May 2004 at 18:49, Bruce Stark wrote:
    >Re. Lewis & Clark's observations:
    >> It's my view, though, that they weren't entirely sure what they should
    >> have been doing. All too often they would spend a great deal of time
    >> taking observations, then leave out a critical piece of information.
    >> And none of us can argue that the numbers they brought back, or that
    >> have survived, are immaculate.
    >> Jefferson had wisely advised Lewis not to bother with calculation.
    >> Just take observations and bring the numbers back in understandable
    >> form.
    and Ken Muldrew responded-
    >Though well intentioned, I think this advice from Jefferson was
    >seriously in error. Had L&C worked their observations, they would
    >have immediately gained an understanding of what information was
    >required. Even if an expert had been assigned to re-work all their
    >observations upon their return, the effort of doing the calculations
    >in the field would still have been worthwhile. I think it would have
    >been the difference between observations that could have been used to
    >construct a map immediately upon their return vs. observations that
    >became mere historical curiosities.
    I agree with both.
    There are lots of things that are missing in L&C's account, that would have
    been useful to their own navigation. I will give two examples-
    1. Magnetic Variation.
    I am still wading through the Mississippi part of their journey. For each
    reach of the river, they recorded a magnetic course and distance. The
    course was measured using a "circumferenter", an accurate azimuth compass,
    presumably with sighting vanes. How the distances were estimated along each
    leg, I can't even guess. At two points along that river they recorded
    celestial observations to determine magnetic variation.
    If we analyse those observations we get these results-
    Near Cairo, 7.3deg East.
    At Kaskasia, 7.6deg East, and 7.4deg East.
    We can conclude, then, that the magnetic variation in that part of the
    journey was 7.4 degrees East, roughly speaking. This can be used to convert
    all their magnetic courses to true, along that stretch. Only by doing so
    can we hope to relate their "dead reckoning" observations, with any
    precision, to their celestial observations of latitude and longitude.
    And yet: they never even bothered to do that! They do not seem to have
    derived magnetic variation at all, in that part of their journey (or at
    least, I haven't noticed any such mention in Moulton vol 2; if anyone is
    aware of any mention of variation, please let me know). A rough estimate,
    from a magnetic bearing of Polaris, would have given the variation within a
    couple of degrees without any serious calculation at all. Although the
    expedition spent several winter months in close contact with the city of St
    Louis, I'm not aware that they noted a local value of magnetic variation at
    that city.
    As the expedition proceeded on their immense journey Westward, then
    presumably the variation would be expected to change significantly. A map
    constructed only on the basis of their magnetic dead-reckoning would have
    shown different amounts of tilt from North. The resulting distortions would
    somehow have to be reconciled with lat and long coordinates. Did L&C deduce
    and apply magnetic variation ANYWHERE along their great journey? Others
    more familiar with the journal texts than I am may have the answer.
    2. Checking Clock Rate and Error.
    The day-to-day changes in longitude were estimated from their
    dead-reckoning, backed up, on occasional lay-days, by a comparison of
    watch-time with local apparent time, using Sun equal-altitudes.
    Unfortunately, because the watch rate wasn't trustworthily constant, it was
    necessary to compare its time, at intervals, with time-by-lunar. That was
    the intention, anyway.
    When the expedition stopped for a few days or more, then the clock rate
    could be checked,
    by making comparisons with local time, a few days apart. That was done,
    during a pause at the mouth of the Ohio, but it was impossible to do when
    the expedition was moving on each day, because then the local time also
    changed because of their inaccurately-known Westward shift in longitude.
    The expedition arrived at their Winter camp at the mouth of River Dubois on
    12 Dec 1803. By 17 Dec they had checked the chronometer against local
    apparent time, by equal altitudes. That was sensible, even if two of their
    timings slipped by a whole minute (L&C's timings were often a whole-minute
    out). They were to remain at that camp for 5 months, and in all that time,
    there's no record in the journals of any further check on clock error, even
    though the watch had stopped and was somehow restarted at "noon" on 20 Dec.
    At departure, on May 14th, two accurate values for longitude were noted;
    one dependent on that 17 Dec equal-altitude observation, taken with earlier
    lunars. The other is stated as being derived from four sets of lunar
    distance observations, with the Sun, Aldebaran, and Spica, which must have
    been made on separated occasions. It's not stated on which dates those
    observations had been made, no readings are given, and no calculations are
    offered: just a resulting longitude. For L&C, this is odd. On other
    occasions, they have quoted all the lunar readings, but failed to deduce a
    longitude. Here, it's the other way round. Might they, I wonder, have
    actually transferred the coordinates of St Louis (if known), just a few
    miles downstream across the river, adjusted for the displacement to their
    campsite, without admitting it, rather than observe and calculate for
    themselves? Is it just my sceptical nature that arouses my suspicions?
    So, as they left Dubois Camp (which they defined as the expedition's "point
    of departure") on 14 May, there appears to be no recent record of clock
    error on apparent time. That was put right on 16th May, a few miles up the
    Missouri, when an equal-altitude measurement was recorded; the first we can
    find since the previous December.
    It seems to me that L&C were extraordinarily lackadaisical about making
    (or, at least, recording) chronometer checks during that long period in
    camp when it would have been easy to do so. They just don't seem to have
    appreciated which aspects of their observations would be important.
    In a later message, referring to the lunars of June 2 and 3 1804, Bruce wrote-
    >Is anyone
    >else working them? Does anyone have a better handle on where they were than I
    >do, so we can know how well they did? I've already posted my results for the
    >June 2nd lunars and am starting on June 3d.
    Well, I plan to get round to them eventually, but am lagging badly behind
    L&C at present, so I wish Bruce well. Those observations look very
    complete, and being between Moon and Sun, L&C can hardly manage to
    misidentify them, as we suspect they did with those stars. The
    equal-altitude observations made around noon on 2 June should provide
    apparent time for all those lunars on both days, and this set shows no sign
    of contamination by their frequent 1-minute timing errors.
    I haven't seen the posted results for June 2nd that Bruce mentions, but
    would welcome a copy if somehow I have missed out.
    As for "where were they?", Paul Hirose has kindly determined for me the
    positions of all L&C's camps within and around the State of Missouri, as
    deduced by Harlan & Denny in their recent "Atlas of Lewis & Clark in
    Missouri". An interactive website exists via
     which shows the
    Harlan and Denny mapping and their presumed campsites and waypoints marked
    on. If you have a sufficiently versatile browser (I don't but Paul does)
    then you can read off the coodinates by pointing a mouse at them.
    Presuming Harlan and Denny have got things right (and I can't vouch for
    that, but it may become clearer as we generate more celestial positions),
    then the coordinates for the campsite from 1 to 3 June are-
    38.5618N, 92.0250W.
    Perhaps Paul will be willing to download that complete set of State of
    Missouri campsites to the list, or allow me to do so.
    contact George Huxtable by email at george---.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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