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George H, you wrote:

"White refers at one point to Dudley Observatory. Is that the local
observatory in Melbourne, from where he made his observations? Does it still
exist?"

I don't know, but he says he kept his sextant at his quarters and mostly
used it outside of work hours, so I assume that means he was actually making
his sextant observations from his home near the observatory.

And:
"White uses a Troughton "pillar-sextant" from the early 1800s. That term has
been used elsewhere in two different contexts."

Just to reiterate, the term "pillar sextant" was ONLY used for the
double-frame instrument. Of course a sextant can also be mounted on a stand
and sometimes those stands were termed "pillar stands". But a sextant on a
stand is NOT a "pillar sextant". Obviously, this is confusing terminology
today, but it wasn't back then, and there is no evidence that White's
sextant was mounted on a stand.

And:
"It's also interesting to note that he was taking lunar distances that
frequently exceeded 120 degrees, the greatest being just over 130."

You note that these are more difficult than shorter angles. That's true, but
they're only a little more difficult. They're certainly less fun, in my
personal opinion.

And:
"The telescope on his sextant was mounted on a "rising-piece", to alter its
spacing from the frame, while keeping it parallel, and White explains how he
used this to equalise the brightness of the images of the two bodies, so
that he never needed to change shades."

Yes, that struck me as excellent advice. Since most sextants today have the
same ability to slide the scope in and out from the frame, this is
definitely the way to go.

And you wrote:
"What I would like to question, however, is Frank Reed's treatment of
White's scatter in longitudes, in writing- "If we take his lunars in sets of
four and average them (which I consider the best approach with lunars), the
results are generally within 0.1 minutes of arc. I would note that these
results are very similar to my own experience." "
And followed by:
"It seems to me that these are numbers that Alex would recognise as being
very similar in scatter to those that he reports from his own balcony. But
in grouping that set of four into one, and averaging, Frank has reduced them
to a mean error of 0.1', and in doing so he has discarded the baby with the
bathwater, and the relevant information on the real scatter has been quite
lost."

George, how is this 'throwing out the baby with the bathwater'? For a rather
long time, I have said that you can expect to get +/-0.25 minute of arc
accuracy (in a standard deviation sense) in lunars with a good sextant for
single observations, and that by averaging sets of four, you can expect
double that accuracy. This article confirms that, so what's the problem???

And:
"As evidence, those details support Alex's view of achievable precision."

If Alex's view, which has been a moving target, matches what I have written
in the previous paragraph, then I guess we're all in agreement.

And, referring to E.J. White, you wrote:
"Here is a professional astronomer"

The fact that he is an astronomer is not particularly relevant except that
it means he is a very good judge of the sources of error in his
observations. The fact that he is a professional astronomer and enjoys
shooting lunars after work for relaxation does, however, tell us something
about his personality. :-)

Of his sextant, you wrote:
"the best of its kind that existed (from the early 19th century)"

Right. And this is a CRITICAL point. Accuracy in lunars depends far more on
the instrument than the observer. The sextant has to be high-quality and
properly adjusted. But for the hobbyist lunarians on this list, that would
seem to be the correct target. Also, in many ways, this is White's point. He
writes at length about the poor quality of many late 19th century sextants
(Lecky agrees with him). Of course, instruments only need to be sufficiently
accurate for the intended observations. Since almost no one at sea was
shooting lunars by this late date, the sextants only needed to be accurate
enough for standard time sights, meridian sights, etc. A couple of minutes
of arc error was no big deal for those observations.

And you added:
"correcting carefully for his index error, and even the temperature."

It's always worth repeating that the index correction is the most important
observational limitation on accuracy in fine sights like lunars. You have to
get the I.C. correct first. As for temperature correction, well that's
hardly impressive. It was known and emphasized in all the manuals from the
earliest period that a navigator would get better results by correcting for
temperature, and it takes only a few extra steps to do so.

And you wrote:
"And yet from one observation, to the next on another day, he records
differences of a large fraction of an arc-minute."

Large fraction? The standard deviation is 0.25 minutes of arc. Is that a
large fraction? This is an almost perfect match for my accounts of expected
lunar distance accuracy.

And:
"In my view, it does not support Frank's contention, which I paraphrase,
perhaps unfairly, that he can pull in anyone from the street, present them
with a sextant to throw up, to achieve lunar distances to a tenth of a
minute."

Are you suggesting that I have stretched the truth? I know you wouldn't
question my intellectual integrity, so I would only say that I have indeed
done this, with the single caveat that I don't drag in random people and
force them to shoot lunars until I say they can leave. Naturally, only
people with an interest choose to participate, and these people often turns
out to be folks with interest and experience in other "geeky" optical
fields, like photography and backyard astronomy. And also just a reminder:
what I see is not "tenth of a minute" accuracy on individual sights, but
that level on sets of four averaged.

And:
"Of course, these matters are relevant only to the question of the precision
achievable in measuring a lunar distance from on land, in perfect conditions
with precise instrumentation and a firm footing from an already-known
position. That's a rather academic question, of interest to sextant
enthusiasts who wish to test their prowess."

Very true.

And:
"But it bears little relation to the difficulties that would have been faced
by a real mariner, in a rolling, pitching, vessel, often doused with salt
spray, with much of the sky obscured by square sails, and when his
corrections depended on measured altitudes, not those deduced from a known
position. We need to keep those differences in mind."

Yes, but we also need to be careful not over-emphasize those difficulties.
Historically, lunars were required perhaps once a week. That leaves plenty
of opportunity to wait for better weather. As for the sails obscuring the
sky, in fact, this is not a real issue. Spars and lines and other "features"
in the sky over your head (think branches and power lines on land) make it
easier to keep an eye on the Moon in daylight, which is when most lunars
were done. Once you've found the Moon, which can remarkably difficult even
when the Moon is bright, you note its position relative to the nearest spar
(or branch) and then you can get back to it easily whenever you want.
Finally, why do you think the observation of altitudes would consitute
another "difficulty"? Those navigators back then measured the altitudes for
lunar observations because it was EASY to do so and because measured
altitudes were generally LESS suspect than calculated altitudes.

 -FER

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