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Douglas Denny, you wrote:
"I note you are an afficionado of 'Lunars' and you have on more than one 
occasion I note, made a very strong reaction to any challenge to their 
validity in navigation."

Yes, it's fair to call me an "afficionado" of lunars. You're incorrect to say 
that I oppose any challenges to their "validity in navigation". For example, 
I do not anywhere suggest that navigators should have continued using them 
longer than they did in the 19th century, BUT THEY DID USE THEM for 75 years 
after the first true chronometer was completed and tested. The expression 
"Longitude by lunar" is found throughout many logbooks from late 18th and 
early 19th century vessels. Even in the latter half of the 19th century, 
there was a rapidly-declining, but still active group of navigators, who 
insisted on using lunars at sea to verify their chronometer longitudes. That 
usage (after 1850), however, is interesting because it is so exceptional, not 
because it represented common practice.

[an aside: so that there is no confusion, I have also suggested an entirely 
different use for lunars today: you can get a position fix in both latitude 
and longitude from two lunar sights without a visible horizon. But this is 
mostly for amusement since vessels at sea are no longer navigated by 
celestial except in extraordinary circumstances (some sailing races, a few 
rare emergencies, instances of personal challenge).]

And you wrote:
"I can cite a number of references made from various sources, contemporaneous 
and modern, to how useless they are in practical navigation terms."

And no doubt your resources would be secondary sources like the one you posted 
previously which erroneously claimed that it took an hour to do the math for 
a lunars sight. As for "contemporaneous" sources, one potential error that 
may well trip you up is to treat sources from decades after lunars were 
commonly used at sea as if they are describing current practice. If you cite, 
for example, a source from 1895, that's much too late. But I agree that you 
can EASILY find sources from the latter half of the 20th century repeating a 
long list of myths about these sights (impossible to use, four hours of 
terrible math, loved only by astronomers, immediately obsolete after 
Harrison's chronometer, and so on). This standardized history had been handed 
down from one author to another for decades.

And you wrote:
"As far as I am concerned, my understanding is they were promoted, developed 
and made into a _just_ practical method by the astronomers because there was 
nothing else possible - until the chronometer - that is all.  They remain an 
astronomical and navigational curiosity.  It took a genius English carpenter 
to remove them from their undeserved place of astronomical and maritime 
prominence.  Some astronomers have never got over it I guess."

There's some truth to that. The astronomical community could only see what 
they understood themselves, and they did not devote as much attention as they 
perhaps should have to "clockwork" solutions. Of course, we have the 
advantage of hindsight here. As for lunars, they were made practical at a 
time when there was only ONE functioning chronometer in the world. They were 
actively employed by real navigators at sea for 75 years after they were 
first practically introduced, and they were also used in land exploration and 
mapping for another 50 years after that. The idea that lunars were dropped as 
soon as Harrison demonstrated his chronometer H4 is incorrect.

And you wrote:
"My opinion is Lunars are inherently flawed because of the very thing which 
has been discussed here under star distances - practical measurement to 
sufficient accuracy  under 'normal' conditions of bouncing around in the 
briny."

Lunars were what they were: a medium-accuracy method for determining 
longitude. A lot of folks operate under the assumption that if lunars weren't 
exactly equivalent to a chronometer in practical terms, then they would have 
been useless. But this theory is over-turned by the real evidence we have 
today. I've personally slogged through around a hundred logbooks from this 
period of time looking for evidence of how navigation was actually done (as 
opposed to how we imagine it may have been done based on armchair 
speculation). And as I've noted in many posts over the past few years, lunars 
were never the primary means of determining longitude. The logbooks I've 
examined were primarily from American merchant vessels, and there is abundant 
evidence in them of lunars being used on long-distance voyages through about 
1850. That period can be divided in two, very roughly, at about 1835. In the 
period up to 1835, dead reckoning was the principal means of determining 
longitude (chronometers were relatively rare on American merchant vessels 
before this turning point). After 1835 (I emphasize, very roughly), the 
longitude was determined primarily by chronometers. And all through this 
period, from at least the 1790s through 1850, lunars were widely used as a 
check on the primary means of determining longitude. Lunar distances are not 
available every day, and lunars taken using the Sun as the other body around 
First Quarter and Last Quarter were popular for a variety of reasons. So for 
several days, every two weeks, lunar observations were made and compared with 
the primary longitude. If they disagreed substantially (and this depended on 
the individual) then the navigator would worry about it in his logbook. 

You also wrote:
"That is ignoring the difficult calculations - which they _are_ to most people 
excepting scientists like yourself. I accept in modern times the calculations 
which were formidable to pre-calculator sailors can be done more easily, but 
the fact remains they are impractical for sailors at sea - even now."

That's just not true. Clearing lunars was no more difficult than an ordinary 
time sight (which every navigator worked every day), and in fact there is a 
considerable similarity geometrically in the bulk of the calculation. Many 
commentators on lunars in later decades (AFTER they had fallen out of common 
use at sea) mistakenly claimed that it must have been the "difficult math" 
that kept mariners from using lunars. This claim is belied by the logbooks. 
Lunars were actively used when there was a reason to use them. The 
calculations took longer than anything else a navigator might choose to do, 
but that amounted to no more than twenty minutes of work. And using some 
short tables, the work could take as little as ten minutes. The calculations 
were NOT unusually difficult.

I should add that my mathematical and scientific background does give me some 
advantage in being able to re-derive and reverse-engineer the various methods 
that were used for clearing lunars. But let's be clear here: this ain't 
rocket science. There's nothing more difficult than standard spherical 
trigonometry and some very basic calculus (not to clear the sights, but to 
derive the clearing methods).

And you wrote:
"They were never really accurate enough to make practical use a full reality, 
and the fact the chronometer spelt their death knell almost as soon as they 
were invented was because of the convenience, practical use and consistent 
results more accurate than 'lunars'. "

See above. Lunars were WIDELY used at sea through about 1850, but they were 
not used in the same fashion as chronometers.

And you wrote:
"If 'Lunars' were an easy, practical and sufficiently accurate method - it 
would have carried on into the twentieth century as saiors are notoriously 
slow to change methods. It did not. It was ditched immediately the cost of a 
chronometer could be bourne by the shipping companies."

Yes, that's mostly correct. Lunars were no longer used much after 1850, and 
that's because chronometers had become cheap and reliable. It was easier to 
buy two chronometers than to pay for the high-quality sextant required for 
lunar observations. And by the way, I've mentioned the dates 1835 and 1850 
above. Those dates are based on the American merchant fleets. For British 
mariners, subtract roughly 25 years from each. So in the Royal Navy, you can 
assume that lunars were over and done with by about 1825 --but note that this 
is still SIXTY years after Harrison's H4 was considered successful.

For an entertaining example of the use of lunars in the early period, you 
might enjoy the story of young Basil Hall put in command of a captured 
American topsail schooner, the Erin, back in 1807. This vessel was suspected 
of breaking the British blockade of Napoleonic France and was taken to 
Bermuda for processing. Along the way, Hall became uncertain of his longitude 
and he shot some lunars to test his longitude. To his dismay, the lunars 
indicated that the small, fast vessel he was commanding had overshot Bermuda 
and against his "seat-of-the-pants" instincts, he trusted his lunars and 
turned back to the west. Sure enough, Bermuda was sighted at dawn.
Here's the full story:
  http://fer3.com/arc/m2.aspx?i=102871
I think you'll like it.

And you suggested:
"and it is unlikely to change until and unless you have hard evidence to show 
it is not so - such as going out onto a small boat in force 3"

Such an experiment might well prove that lunars cannot be done at all in a 
small boat in force 3 winds. But so what? Lunars were widely used at sea 
through about 1850, and they were widely used in land exploration for decades 
after that. And in addition, I should say that there are around a dozen 
current NavList members who have done lunars, for their amusement or for 
historical understanding, in real practical conditions. That is, it's not 
just me.

And you wrote:
"using your sextant about fifty times doing 'Lunars' then with an analysis 
of the results .... as Gordon did with the 1964 report I sent in.
Then I might take more interest in your hearsay statements about accuracy of lunars and star distances."

Labeling my analyses as "hearsay statements" speaks volumes about you but says nothing about me. 

I have shot hundreds and hundreds of lunars for my own entertainment (such as 
it is), but experiments like this are only marginally relevant to a practice 
that is purely historical. If you want to understand how and when lunars were 
used (and when they were not used), how accurate they were (or were not), how 
difficult they were (or were not), then you need to go to the hard data, the 
extant logbooks from the era, as I have done.

And you wrote:
"Finally; I note you have completely ignored the main aspect of my submissions 
about star distances and sextant observational accuracy - namely the 
resolving power of the eye itself."

Not so. I have been discussing this for years and years. The normal resolution 
(for standard resolving tasks) of the human eye is around 1 minute of arc, 
somewhat better under excellent conditions. Do you recognize now that when 
you look through a telescope (a GOOD telescope) that angles on the sky are 
magnified? And therefore if the eye can normally see details of one minute of 
arc without magnification then using a 3x or a 7x telescope, the observer can 
see details of 0.33 and 0.14 minutes of arc respectively? I should emphasize 
that the standard deviation for my lunar observations with a 7x telescope is 
about 0.25 minutes of arc which implies that there are other sources of error 
in addition to the limiting resolution of the eye-telescope system.

And you wrote:
"curiously, very close to the ultimate practical accuracy of a single 
observation with a sextant. This I have noted with practical observations I 
have made myself, in discussion about  accuracy to friends who use sextants, 
(including one master mariner who used them 'for real') and is confirmed in 
the 1964 report by Gordon."

It appears to me that you are confusing a couple of things here. The 
resolution of what we can see through the telescope of a sextant (which 
depends on the resolution of the eye and the magnification of the telescope) 
is not the same thing as the final effective accuracy of a celestial 
navigation sight. Standard LOP sights are strongly influenced by 
uncertainties in the horizon and those uncertainties appear to be the 
limiting factor in standard cel nav sights. When you do sights which do not 
involve the horizon, such as lunars, that particular uncertainty is removed. 
Adding magnification to sights which have intrinsic variability on the order 
of 0.5-1.0 minute of arc (like standard LOPs off a sea horizon) does not 
offer significant improvement, as is well-known. But when you add 
magnification to sights which do not involve the horizon, there is 
significant improvement in direct proportion to the magnification as long as 
the optics of the telescope are reasonably good.

-FER






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