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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
suspicion..]

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
midnight.

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.

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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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