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Fred Hebard said-

>In the thread on Maskelyne's tables, George Huxtable very kindly
>provided a link to the late Richard.S.Preston's paper,"the accuracy of
>the Astronomical Observations of Lewis and Clark", downloadable from
>www.aps-pub.com/proceedings/jun00/Preston.pdf.

Don't thank me: this reference, and many others, have been made available
for the use of Fred, me, and other lunartics, by Arthur Pearson, together
with other interesting stuff, at his website www.ld-DEADLINK-com

>I read this with great interest, but have some questions.

It has raised many questions in my mind also, which I long to ask the
author. Unfortunately, Richard Preston died a couple of years ago, so is
beyond the reach even of email.

>In the table at the end of the paper, I note that the Lewis & Clark
>latitudes all seem to be out by about 5' of arc.  Is this a large
>amount of error?  It would seem those measurements could be more
>accurate.  I presume Preston used modern ephemerides to calculate the
>positions, but wonder whether the old ones were accurate enough to get
>closer than 5', which then would influence the care with which the
>observations were made.

First, to answer Fred's worry. Sun declinations had already been tied down
and understood by astronomers to a FAR greater accuracy than the nautical
tables needed. No problem there.

My own questions mostly relate to that table as well, and, like Fred, would
like to see the raw data it's based on. I am not at all familiar with the
Lewis and Clark literature, and I can't find in Preston's paper a reference
to where his initial data can be found. Can anyone help in pointing to a
way to access that data, please?

I started to look at that table with a view to understanding the longitude
calculations, but was startled by the discrepancies that showed up even in
the measurements at noon for latitude. If noon latitudes don't come right,
how on earth can we analyse the details of the longitude calculation?

The latitude discrepancies are even greater than Fred's quoted figure of 5'
suggests. On 9 June 1805, L&C give a lat of 47? 29'N, where the modern
position of that observation site (if identified correctly) is stated to be
47?55'45"N, nearly 27 minutes out. Similarly, on 10 July, L&C give 47?03'N,
but the site is stated to be at 47?27'23"N, over 24' in error. How on earth
could any competent observer get his noon altitudes so wrong?

The table also compares L&C's calculated noon Sun altitudes (without
telling us how they were calculated) with, in another column, those
calculated by "Ellicott's method of 1803" (without telling us how they were
calculated).

Navigators had been calculating latitudes from noon Sun altitudes for
hundreds of years, and there's no argument that I am aware of about how
this should be done. It's a straightforward business. Yet if you look down
the table, there are huge discrepancies in the results, between latitudes
calculated by these two methods, whatever they may be. They should agree
exactly, but they differ by (in minutes, starting at the top of the table)
4, 30, 2, 0, -32, -30, 34, 7, 1, 40, 0, -7, -3, 10, 8, 8, 14, 14, 1, 32,
35, 12. What is going on here? Neither L&C's set of latitudes, nor
Ellicott's, agrees at all well with the Bergantino list of positions of
observation site. Is there something here that I am completely
misunderstanding?

Without access to the raw-date, I don't think we have much hope of
discovering what is going wrong. Until some consistency has been achieved
in the latitudes, to my mind there's little point in attempting to take the
matter further by analysing the lunar distances for longitude.

Where might the problems lie? The discrepancies between the two methods of
calculating noon altitude must relate to a failure of understanding by L&C,
or by Ellicott, or indeed by both, of how this simple job should be done.

Observationally, we should consider this. An octant was used for all these
measurements, we're told, and an octant in normal use can measure an angle
up to 90? only (compare with 120? for a sextant). For all the observations
listed in Preston's table (except the two in February) the noon Sun
altitude is greater that 45?. Altitude measurements were made using a
liquid artificial horizon, which doubles the angle that the octant has to
measure, so in nearly all cases the angle to be measured was out of normal
octant range, above 90?. In that case an octant can be used (if
appropriately fitted-out) in "backsight" mode. In that case the observer
looks into the sextant from a peep or telescope facing in the opposite
direction from normal. and the 0 to 90 degree scale of the octant will
actually indicate 90 to 180 degrees.

Use of an octant in backsight mode has one great disadvantage, however. In
normal mode it's easy to check its index error by looking at a distant
object and aligning the two images, when the scale should show the index
error. But as far as I know, there's no way of checking index error when in
backsight mode. If anyone knows how, I would be pleased to learn. So L&C
would have to presume that their octant in  backsight mode was free of
index error and remained that way throughout the journey. Is that a
realistic assumption, for a wooden (I presume) octant subject to all the
rough usage and weather-changes of an inland expedition? I doubt it.

To summarise. Before devoting any attention to the longitudes, we have to
understand why the latitudes are so wrong. In the meantime, an interim
conclusion appears to be that Lewis and Clark were indeed hopelessly bad
celestial navigators: the Emperors had no clothes. I bet that will stir
things up. Anyone disagree?

George.

PS For anyone that wishes to follow-up "Patterson's problem 4th" and his
advice on tackling other problems that might be faced, referred to in
Preston's paper, this can be downloaded, with interspersed comments for
modern readers, from www.huxtable.u-net.com/lewis01.htm

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