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    Re: Preston's paper on Lewis & Clark's Navigation
    From: George Huxtable
    Date: 2003 Jun 8, 17:21 +0100

    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
    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.
    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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