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Alex,

One little request first: You listed the URL for the article in your reply.
Although it resolves to an address under "clockwk.com", it's in everybody's
best interest if you use the address I originally gave, which is
  www.HistoricalAtlas.com/lunars/ejwhite/
One of these days, clockwk.com is going to disappear, while
HistoricalAtlas.com is here to stay, so if you can remember to do so, please
use that domain when referring to files on my site(s). Thanks!

You wrote:
"1. George discusses at length the question, what is "pillar sextant". I
think it is reasonable to assume that this was a "pillar-frame" sextant,
typical for this manufacturer (Troughton), rather than a column-mounted
sextant. White emphasises all the time that his experiments are relevant for
the sea use. It would be stupid or dishonest to use a mounted sextant in
such experiments:-)"

Yep. And in addition, the expression "pillar sextant" did NOT refer to
sextants mounted on stands back then. The terminology is bound to be in flux
in the year 2007 since sextants like this have not been manufactured in
almost a hundred years, but certainly when White was writing, there would
have been no question.

Next, you wrote:
"2. Several things in White's article look very suspect to me. First of all,
what his "observations" really mean. Are these individual shots or averages
of series? Notice: he records at most ONE "observation" per day.
(In fact, one per week, in the average). While the normal practice at that
time (and in our time!) is to take series of several observations."

I agree that there is no way to be certain on this point. However he says
nothing about averaging multiple sights (except at the end when he averages
the whole lot). Considering how carefully he has spelled out other details,
I think it's unlikely that he took multiple sights. Also notice his comment
about the possibility that he mis-read the clock on one of his observations.
Would that comment make sense if he had taken multiple observations? As for
"normal practice at that time"... there was no normal practice. Lunar
observations were long dead by 1887 when White was experimenting with them.
I see him as one of the earliest lunarian hobbyists. He would have loved the
Navigation List. :-)

And:
"Taking a single lunar shot PER WEEK seems ridiculous to me
and contrary to the common practice."

See above. He was doing this for relaxation and his own amusement.

"3. On page 90, White writes that the "greatest excentric error of his
sextant was 20 seconds." Of arc, of course. Which is the maximum arc
correction from the certificate, I suppose. And then on page 91, line 1 he
says "The correction for excentricity have NOT BEEN APPLIED (!!!)" and then
states a ridiculous reason for this. Which means he NEGLECTED a known
instrumental correction of up to 20"=0.3' for his sextant!"

In a follow-up post, you decided that this wasn't so ridiculous after all,
and I agree with your logic there.

And you wrote:
"This correction is LARGER than the supposed typical accuracy
of his shots..."

Ah, but that correction is the maximum correction at only one point along
his sextant's arc. I propose that his arc error table would have read
something like this: 30d: 0", 60d: +10", 90d: 0", 120d: -20". It should
actually be possible to tease out the arc error from the sights that he has
listed. But assuming that the table has a form at least "somewhat" like the
one I've proposed, you can see that the error from ignoring arc error would
tend to cancel out if observations are taken over a wide range of angles, as
they are, and in many cases would be insignificant.

"4. Now about his results, as recorded. He obtains the "most probable error"
of his "single observation" 21 seconds of time which is roughly equivalent
to 10.5" in distance or 0'.2 in distance. I confirm this calculation from
the data of his table. But again as I wrote above, I have very strong doubts
that his "single observation" recorded in the table is indeed a "single
shot" rather than the average of a series (which would be a normal
practice)."

The standard deviation is equivalent to about 0.25 minutes of arc in the
measured distance. As I said, I agree that there is at least the possibility
that these are averaged sights, but without evidence that this is ACTUALLY
the case, you're only speculating.

And you wrote:
"5. How Frank comes with the "mean error" of 0'.1, I don't know."

Take them in sets of four and average. Yes, this is a legitimate procedure
when each sight is individually cleared to yield a longitude.

I found your point "6" amusing. You seem to be saying that you don't trust
him because he writes plainly and without pseudo-academic pretense. Oddly
enough, I like him for that.

"7. And finally I want to bring the following passage from White to your
attention:
"As observations can be taken at sea with nearly
the same ease as on shore,..."
Well, I am also mostly an armchair sailor, but I would never say such
thing:-) My very limited sea experience completely contradicts
this opinion." "

You know, they do have calm days on the oceans, Alex. :-) I have no sea
experience at all. But to your point, we have only one list member who has
been both a professional navigator and a lunarian. That's Henry Halboth.
After getting a longitude accurate to within 6 miles from a lunar distance
observation, he recently wrote, "I am not of the opinion that sea state has
a significant effect on the observer, unless a vibratory effect is present,
such as when a vessel be laboring or pounding, or when vibration is enduced
by operating machinery. It does seem usual for a vessel to have been eased
off or hove-to so as to provide more favorable conditions for observation."
...So that's ONE data point.

Finally, I would emphasize that lunars were widely used in the early
nineteenth century --so they MUST have been accurate "enough", whatever
"enough" means. There is ample evidence for them in the logbooks. For those
of you who haven't looked at them, there are dozens of scanned logbooks from
the era available on the web site of Mystic Seaport:
http://www.mysticseaport.org/library/initiative/MsList.cfm
For fun, here is an example of a worked lunar from one of those logbooks:
http://www.mysticseaport.org/library/initiative/PageImage.cfm?PageNum=48&Bib
ID=35388
Scroll down the page to see the scan. The calculation of the lunar
observation occupies the top third of the page. The rest of the page is an
unrelated tabulation of chronometer error.

 -FER


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