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    Re: Preston's paper on Lewis & Clark's Navigation
    From: George Huxtable
    Date: 2003 Jun 10, 16:44 +0100

    I have looked at some of Gary Moulton's 13 volumes on Lewis and Clark's
    journey, which is a really thorough job, and am trying to make some sense
    of their observational records, starting with Moulton's vol 2, which covers
    nearly all the data that Preston considers.
    I'm concentrating first on the latitude determinations, which appear to
    show a lot of scatter. If we can't understand where that comes from,
    there's little hope of understanding the observations for longitude.
    Already, there are indications that when taking Sun declination from the
    almanac (to work out latitude from Sun altitude near noon) the tabulated
    value for Greenwich noon (which was about 6 hours earlier) was used
    unaltered. The correct procedure would be to interpolate between
    declinations at the previous Greenwich noon and the following one, to allow
    for that 6-hour time-lag. This would be particularly serious around the
    equinoxes, when Sun dec changes by about 1 minute per hour, which would
    then give rise to 6-mile discrepancy, one way or another, in latitude.
    In the meantime, I wonder if listmembers would be interested, as I was, by
    the account of the instruments that were carried on the voyage? This was
    inserted at July 22nd, 1804, page 410 in vol 2 of Moulton. Any
    interjections of mine are in square brackets.
    Here goes-
    Lewis: July 22nd 1804.
    A summary description of the apparatus employed in the following
    observations; containing also some remarks on the manner in which they have
    been employed, and the method observed in recording the observations made
    with them-
    1st.-- A brass Sextant of 10 Inches radius, graduated to 15' which by the
    assistance of the nonius [= vernier] was devisible to 15"; and half of this
    sum by means of the micrometer could readily be distinguished [I don't
    understand this reference to a "micrometer" but perhaps there was a
    fine-adjustment by an uncalibrated screw. Or does he mean a hand-lens?],
    therefore -- 7.5"of an angle was perceptible with this instrument: she [do
    others think of their sextants as feminine?] was also furnished with three
    eye-pieces, consisting of a hollow tube and two telescopes one of which
    reversed the images of observed objects. finding on experiment that the
    reversing telescope when employed as the eye-piece gave me a more full and
    perfect image than either of the others, I have most generally imployed it
    in all the observations made with this instrument; when thus prepared I
    found from a series of observations that the quantity of her index error
    was 8'45"-; this sum is therefore considered as the standing error of the
    instrument unless otherwise expressly mentioned. the altitudes of all
    objects, observed as well with this instrument as with the Octant,  were by
    means of a reflecting surface; and those stated to have been taken with the
    sextant are the degrees, minutes, etc shewn by the graduated limb of the
    instrument at the time of observation and are of course the double
    altitudes of the objects observed.
    [The "standing" index-error of 8' 45"- was taken to be constant. Either the
    sextant was remarkably stable or else nobody bothered to take on the simple
    task of reassessing it. I suspect the latter.]
    2ed-- A common Octant of 14 inches radius, graduated to 20', which by means
    of the nonius was devisible to 1', half this sum, or 30" was perceptible by
    means of a micrometer. [this sounds as though the "micrometer" was perhaps
    a lens] this instrument was prepared for both the fore and back
    observation; her error in the fore observation is 2?+, and in the back
    observation 2? 11' 40.3"+.
    [These seem big errors, and perhaps the octant provided no means of
    correcting them to near-zero, by mirror adjustment, before the start. It
    doesn't really matter how big these errors are, though, they can always be
    corrected for as long as they are known and stable. But how, I wonder, was
    the error in the back position assessed to be 2? 11' 40.3", which is stated
    to an absurd precision, and why in the fore position does it take such a
    convenient round value as 2? 0' 0"? Both these index-error values were
    taken as to be constant for at least this part of the voyage, in spite of
    the hazards and changes along the journey.]
    at the time of our departure from the River Dubois [which is, I thik, near
    present-day Saint Louis] untill the present moment, the sun's altitude at
    noon has been too great to be reached with my sextant, for this purpose I
    have therefore employed the Octant by the back observation. The degrees '
    and ", recorded for the sun's altitude by the back observation express only
    the angle given by the graduated limb of the instrument at the time of
    observation, and are the complyment of the double Altitude of the sun's
    observed limb, if therefore the angle recorded be taken from 180? the
    remainder will be the double altitude of the observed object, or that which
    would be given by the fore observation with a reflecting surface.
    [In that last sentence, there's no mention of the index correction and at
    what point that correction was introduced, which leaves me rather puzzled].
    3rd-- An Artificial Horizon on the construction recommended and practiced
    by Mr Andrew Ellicott of Lancaster, Pensyla., in which water is used as the
    reflecting surface; believing this artificial Horizon liable to less error
    than any other in my possession, I have uniformly used it when the object
    observed was sufficiently bright to reflect a distinct immage; but as much
    light is lost by reflection from water I found it inconvenient in most
    cases to take the altitude of the moon with this horizon, and that of a
    star impracticable with any degree of accuracy.
    4th-- An Artificial Horizon constructed in the manner recommended by Mr
    Patterson of Philadelphia; glass is here used as the reflecting surface.
    this horizon consists of a glass plane with a single reflecting surface,
    cemented to the flat side of the larger segment of a wooden ball; adjusted
    by means of a sperit-level and a triangular stand with a triangular mortice
    cut through it's centre sufficiently large to admit of the wooden ball
    partially; the stand rests on three screws inserted near it's angles, which
    serve as feet for it to rest on while they assist also in the adjustment.
    this horizon I have employed in taking the altitude of the sun when his
    image has been rather too dull to allow for a perfect reflection from
    water; I have used it generally in taking the altitude of the moon, and in
    some cases of the stars also; it gives the moon's image very perfectly, and
    when carefully adjusted I consider it is liable to but little error.
    5th-- An Artificial Horizon formed of the index specula [i.e. the index
    mirror] of a Sextant cemented to a flat board, adjusted by means of a
    sperit level and the triangular stand before described. as this glass
    reflects from both surfaces it gives the images of all objects much more
    bright that either of the other horizons, I have therefore most generally
    observed it in observing the altitudes of stars.
    [note: instruments 4 and 5 depend on the availability of a very sensitive
    spirit level. It also needs to be very light, and the adjustable support of
    the mirror needs to be VERY rigid, to ensure that when the weight of the
    level is removed after levelling, NO flexure results to alter the angle of
    the glass.
    Lewis doesn't indicate in the text which of his three levels he is using on
    any occasion. I would trust no 3, but would treat 4 and 5 with some
    6th-- A Chronometer, her ballance wheel and escapement were on the most
    improved construction. she rested on her back in a small case prepared for
    her, suspended by a universal joint. she was carefully wound up every day
    at 12 o'clock. Her rate of going as asscertained by a series of
    observations made by myself for that purpose was found to be 15 seconds and
    a 5 tenths of a second too slow in twenty four hours on Mean Solar time.
    This is nearly the same result as that found by Mr Andrew Ellicott who was
    so obliging as to examine her rate of going for the space of fourteen days,
    in the summer 1803. her rate of going as ascertained by that gentleman was
    15.6s too slow M.T. in 24 h. and that she went from 3 to 4 s slower the
    last 12h, than she did the first 12h. after being wound up.-
    At 12 o'ck on the 14th day of May 1804 (being the day on which the
    detachment left the mouth of the River Dubois) the Chronometer was too fat
    M, T. 6m. 32s. and 2/10- This time-piece was regulated ton mean time, and
    the time entered in the following observations is that shewn by her at the
    place of observation. the day recconed on Civil time, (ie) commencing at
    7th-- A Circumferentor, circle 8 inches diameter, on the common
    construction, by means of this instrument adjusted with the sperit level, I
    have taken the magnetic azimuth of the sun and pole Star. It has also been
    employed in taking the traverse of the river:- from the courses thus
    obtained, together with the distances estimated from point to point, the
    chart of the Missouri has been formed which now accompanys these
    observations. the several points of observation are marked with a cross of
    red ink, and numbered in such manner as to correspond with the celestial
    observations made at those points respectively.
    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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