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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.

George.

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contact George Huxtable by email at george@huxtable.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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