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Thanks to Bruce Stark for referring us back to our earlier discussions on
Nav-L, about navigation discrepancies of the Lewis and Clark expedition.
The postings he refers to are indeed relevant.

I've gone back to read some off-list discussions I had last summer with Bob
Bergantino (who isn't a member of this list, but is referred to in the
Preston paper).

Here's a relevant part of what he said-

"Lewis made a consistent error in his reductions while in Montana that put
all his calculated latitudes too far south by an average of about 28
minutes. The given index error for the octant was 2*11'40.3" (actually, this
was half error, for Lewis applied it AFTER he had halved the observed
altitude). On 12 April 1805, at the mouth of the Little Missouri River we
discover Lewis's mistake. He writes that the octant's error is 2*40'--" and
must have used that all summer. While Lewis was at Fort Clatsop (see Fort
Clatsop Miscellany) he discovered his error and made a few recalculations,
but seems never to have told Clark about it."

This is the same immense index discrepancy that Bruce mentions in his
postings of last year: a transcription error, by the explorers, of over 28
arc-minutes!

Beside that error, there are some interesting facts to glean from
Bergantino's note.

1. Lewis was noting as "index error" what was actually HALF the index
error, but because he applied it to the observed angle after halving that
angle, that would not cause an error.

2. The index error of his octant in back-observation mode was immense, at
4deg 23' 20.6", or thereabouts. The instrument must have been very badly
constructed for that to be the case. I presume that its mirrors had been
adjusted at some time, to give a small value of index error in normal
fore-observation mode. When switching to back-observations, there was no
way for the navigators to readjust the index error, without a sea-horizon
to view, and they would have to preserve their mirror-adjustments strictly
unaltered. Perhaps they might have had a go at determining the backwards
index error when they came to a big-enough lake or a long slow-running
reach of the river. Or as Bruce suggests, from measuring a known angle
between two stars that's greater than 90 degrees: but he doesn't think the
explorers were up to this, and I tend to agree. How, and when, I wonder,
did they arrive at that figure for half-index-error of 2deg 11' 40.3",
which they later garbled so badly to 2deg 40'?

3. It appears from what Bergantino says, that having settled on an index
error the explorers would stick to it, through all the rough-and tumble of
their inland journey. Those with expensive metal sextants may find that the
index error doesn't alter, but it's asking for trouble to assume the same
for a wooden octant in an inland journey. I have read that a brass sextant
was carried, but the wooden octant was used for all these altitudes.
Perhaps the reason for this might be that only the octant, not the sextant,
was fitted out for back-observations. Through most of the summer, the
doubled sun altitudes were beyond the 120 deg range of a normal sextant.

At Oxford University, there's now an American Institute, and I've learned
that its library holds, on open shelf, the Gary Moulton volumes of Lewis
and Clark. When I can, I will do a bit of investigation.

George Huxtable.



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