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    Re: Accuracy of Lewis and Clark Observations
    From: George Huxtable
    Date: 2002 Aug 2, 23:18 +0100

    Back on 14 June, Paul Middents sent the posting, copied below, and asked
    for comments.
    
    My early version of Adobe Acrobat isn't capable of decoding the Preston
    paper, but listmember Clive Sutherland has now kindly printed it out for
    me.
    
    First, thanks to Paul for bringing this paper to our attention. I wasn't
    aware of it, and am most impressed by the clarity of Preston's description
    of lunar techniques. I wish that I could write half as lucidly. Even though
    it refers to lunars in a land-based context, any marine navigator with
    lunar inclinations would find that it repays a careful reading.
    
    Paul Middents has provided an excellent summary which I don't need to repeat.
    
    Sadly, Richard Preston has died since the paper was published. I would have
    liked to discuss with him some aspects of his paper, but alas this cannot
    be.
    
    I apologise for knowing so little about Lewis and Clark's work.
    Unfortunately, American history was seriously neglected in my schooldays,
    long ago, in England.
    
    I have some comments to make about the paper, and some questions arise
    which puzzle me, the answers to which may be well-known to many American
    list members. In response to Paul's invitation, I will list some of them
    below, numbered but in no particular order, hoping that list members can
    explain. All this will make sense only to someone who has downloaded a copy
    of the Preston paper, from-
    http://www.aps-pub.com/proceedings/jun00/Preston.pdf
    
    1. Page 169. Preston states that one of the instruments carried by the
    expedition was a chronometer, but there seems to be no mention of
    chronometer-timed observations. Did the chronometer fail?
    
    2. Page 177. Preston refers to Maskelyne's Tables Requisite, which
    "describes the calculation of Moon altitudes without explicitly
    recommending the use of calculated lunar altitudes for correcting lunar
    distances". But one wonders what else, in those days before intercepts and
    position lines, a calculated Moon altitude would have been useful for.
    Surely, those calculated altitudes must have been intended for correcting a
    lunar, in place of altitude observations. Preston's copy of Tables
    Requisite is the 2nd ed. of 1781. I have the 1st ed., 1766, in photocopy,
    and in that I can find no mention at all of calculated Moon altitudes.
    However, Maskelyne's first major work on lunars, his British Mariner's
    Guide of 1763, does explicitly describe using calculated Moon altitudes for
    that purpose, on page 57, Rule 3 of the appendix, "To compute the apparent
    Altitude of the Moon or a Star, at the Time of the Observations of the
    Distance of the Moon from the Star." I'm not intending to quibble with
    Preston's text here, but wish to show that Maskelyne was "on the ball"
    about this topic, right from the start of lunar distances.
    
    3. page 178. Preston states, about Lewis- "As he did not have the three
    sextants or octants required for three simultaneous measurements, it is
    likely that he used the Problem 4th method ..." [The "Problem 4th method"
    is a way of calculating the altitudes rather than measuring them]. I do not
    accept this as a valid argument, though the conclusion may be correct.
    Although the Navy, overstaffed with officers, might have established a
    ritual with three observers and three instruments, it is quite feasible for
    the job to be done by one man, with one sextant, measuring in a defined
    sequence. That is what Joshua Slocum had to do, single-handed, and so did
    countless merchant vessel navigators.
    
    4. I am interested in some discrepancies in the determination of latitude
    by noon measurements of the Sun. Preston says (page 186) that it was always
    the octant that was used for such measurements, and I wonder why. As the
    measured angle was always twice the altitude of the Sun (because of
    reflection in the Mercury horizon pool) then only in winter would the Sun's
    altitude be less than 45 deg. and be within range of an octant in its
    normal mode. If a sextant had been used then Sun altitudes up to 60 deg
    would have been directly usable. There is some importance in this question.
    Used in the normal mode, the index error of an octant or sextant can be
    checked and allowed for in a flash: it's the work of a moment.
    
    For octant measurements with Sun altitudes above 45 deg., and reflected
    angles above 90 deg., then a special octant has to be used provided with a
    backsight mirror, which can then measure angles 90 to 180 deg. The trouble
    with an octant used in this way is that there's no obvious way (not obvious
    to me, anyway) of checking the index error, so as I see it the readings
    must be taken at face value with no opportunity to correct for any index
    error. On page 186, Preston does refer to the possibility of index error,
    but I would maintain that index error will only be a serious matter when
    the sextant is used in backsight mode, with altitudes above 45 deg. But
    then index error could indeed be a major source of error
    
    Now we come to those discrepancies in the stated noon-Sun latitudes in the
    table on pages 185-6. Preston states (page 186)- "except for the first
    three readings in 1805, the latitudes he calculated from the noon altitudes
    of the sun (third column) are consistently low by about 5'." That is, low
    compared with modern latitudes of those same sites, presuming that those
    sites have been correctly identified (by R. Bergantino). But inspection of
    the table doesn't support this claim. It shows that up to the beginning of
    1805 the Lewis and Clark latitudes are consistently low by amounts that
    hover around 5', as Preston claims. Then in those first three 1805
    measurements, Lewis and Clark measure higher latitudes than modern values,
    by 4'. But then, these discrepancies in latitude become, successively: 26'
    low, 24' low, 21' low, 29' low!
    
    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?
    
    =============================
    
    I have a few further questions and comments, but these should do for now.
    
    I have said little about the general validity of the technique of
    calculating a lunar altitude as opposed to measuring it, because I am still
    struggling somewhat, in my own mind, about that matter. In that, I have
    been helped greatly by the ideas of fellow list-members, and also by what
    Preston had to say about it.
    
    Please do not think I am in any way knowledgeable about land-navigation in
    general, or Lewis and Clark in particular, because I'm not, and have no
    wish to sail under false colours.
    
    George Huxtable
    
    
    Paul Middents' mailing of 14 June follows-
    =============================
    
    >I have just found a very interesting article which addresses Lewis and
    >Clark's observational methods: "The Accuracy of the Astronomical
    >Observations of Lewis and Clark", Richard S. Preston, Proceedings of the
    >American Philosophical Society, Vol 144, No. 2, June 2000
    >
    >http://www.aps-pub.com/proceedings/jun00/Preston.pdf
    >
    >I am still absorbing the details but in summary, Preston determines why
    >simultaneous altitudes were not measured in conjunction with the lunar
    >distances. These altitudes were to be calculated from an assumed
    >longitude and then used to clear the lunar distance of the effects of
    >refraction and parallax. He finds that this method as recommended by
    >Andrew Ellicott and Robert Patterson is technically correct. It should
    >yield reasonable results with a single iteration for most cases.  Had
    >Lewis and Clark's results been calculated, Most would have been
    >reasonable.
    >
    >He speculates why F.R. Hassler (Mathematics professor at West Point)
    >might have given up in despair when trying to calculate from Lewis and
    >Clark's data. I was most surprised to find out that the data had never
    >been computed.
    >
    >Preston developed computer programs based on a method developed by
    >Robert Bergantino of Montana, to calculate positions and finds that
    >Lewis' data supports positions within about 30 minutes of arc in
    >longitude.
    >
    >I find this article extremely interesting. It seems to solve a long
    >standing mystery concerning Lewis and Clark's methods and somewhat
    >vindicates their observational ability.
    >
    >I have followed the thread between George Huxtable and Bruce Stark on
    >the question of calculated altitudes. Bruce is acknowledged by Preston
    >in the article so I know he is familiar with this. I find no other
    >reference to either Preston or Bergantino in the Navigation-L archives.
    >
    >I would appreciate the opinion of the "lunarians" on this list of
    >Preston's work.
    >
    >I would also like to express my appreciation and admiration for George
    >Huxtable's series, "About Lunars".
    >
    >Paul Middents
    
    ================================
    
    
    ------------------------------
    
    george---.u-net.com
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.
    ------------------------------
    
    
    

       
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