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Douglas Denny, you wrote:
"A x7 telescope does NOT improve sextant accuracy of results by seven times."

It does imrove accuracy when the limiting factor in observations is 
resolution. But if there are other larger sources of error, then 
magnification cannot eliminate those. In standard altitudes (as for LOPs) off 
a sea horizon, you can expect a standard deviation in observations of about 
0.5 minutes of arc under good conditions. The limiting factor here is 
generally acknowledged to be the uncertainty in the horizon --the dip can 
only be estimated. Magnification cannot change that. By contrast, when you 
shoot angles between clearly-defined terrestrial objects, like distant 
vertical antennas for example, or reliable lunar pairings like the angle 
between the Moon and Jupiter, the limiting factor is the overall quality of 
the instrument and this can be much less than half a minute of arc. In those 
cases, adding magnification helps significantly. If you get around to trying 
some lunars, you will find that with a 7x scope you can clearly see the small 
disk of Jupiter and place it cleanly bisected on the limb of the Moon. This 
cannot be done with the same accuracy using lower power optics. There are 
good opportunities to try this during the next few days --if you feel like 
playing with a sextant at 2:00 in the morning, that is.

And you wrote:
"It is not surprising that lunars therefore were in use for an interim period 
of say fifty years until large-scale production made costs low enough for 
shipping companies to adopt them."

Actually, as I have noted already, it was more like 75 years in the US 
merchant fleets. Aboard the whaling vessels which sailed in their hundreds 
from New England ports to the Pacific whaling grounds, lunars were used on a 
regular basis (in the fashion that I described in my previous post) right up 
to 1850 with rapidly-diminishing frequency around that date. I must emphasize 
that a navigational method which was in active use for seventy-five years is 
no mere "stop-gap". But, as in my previous post, I very much agree with you 
that when the price for chronometers came down low enough, lunars were 
finished.

And you wrote:
"The point you cannot escape however is that as soon as chronometers were a 
viable financial proposition - lunars were ditched like a hot potato."

Douglas, I AGREED WITH YOU generally on this point in my previous post. I 
think your description here is a bit over-the-top. They were not dropped like 
a "hot potato". Lunars were used for a couple of decades longer even aboard 
vessels carrying chronometers because a single chronometer could not be 
trusted. And this isn't just theory or speculation: it's what we find in 
actual logbooks from the era. On the voyage of the Sabina from Long Island in 
New York to San Francisco during the gold rush in 1849, the captain shoots 
lunars on a fairly regular basis and discovers in mid-Atlantic that his 
chronometer is wrong by some two degrees of longitude. You can read a more 
thorough account of this logbook which I wrote up for NavList four years ago 
here:
http://fer3.com/arc/m2.aspx?i=024812&y=200507


And you wrote:
"Why? if lunars were so 'easily used' with "calculations done in ten minutes"  
etc? Answer - because they were difficult to take under practical conditions, 

inaccurate despite great care, and calculations were a pain."

Accuracy: longitudes by lunars were roughly three to five times less accurate 
than longitudes by chronometers using a properly-functioning chronometer. 
That's very true. So as long as you're SURE that your chronometer is working 
perfectly, there's no reason to use lunars. And just how sure are you? Lecky 
in his Wrinkles makes the very good point that steamships have greatly 
reduced the length of ocean voyages (writing well after lunars had stopped 
being commonly used at sea) and also the individual legs of such voyages were 
much shorter (since they needed to stop for coal regularly) and he says that 
this is a major reason why lunars are no longer needed to check the 
chronometers (you can check them in port as you go). The logic here is that 
you can much more easily trust a chronometer on short voyages than on very 
long voyages. And that's an excellent point.

Ease-of-use: lunars are (and were) not difficult to shoot with even a little 
practice, but there's something else here that's related to this issue. 
Lunars require clear skies (more so than sights for longitude by chronometers 
since you need both bodies in a lunar sight continuously visible), and lunars 
are limited by the visibility of the Moon during the lunar month. For a 
minimum of four days every month, the Moon cannot be seen clearly, if at all. 
And for a variety of reasons, lunars were prefered for a few days around 
First and Last Quarter. So as I said previously, this implies that lunars 
never served as the primary means of finding longitude. They were a check on 
the primary means which was dead reckoning in the early period and longitude 
by chronometer (time sights) in the later period. Here's a post from me back 
in December of 2004 with the subject "No Lunars Era" which will demonstrate 
some of my thoughts on this back then: 
http://fer3.com/arc/m2.aspx?y=200412&i=020586.

Calculations: this is simply a bit of mythology. The idea that clearing a 
lunar required "four hours" of hard work or that it was mathematically 
painful is due to two unrelated issues at opposite ends of the history of the 
method of lunar distances. First, at the beginning of the history of lunars, 
there was no Nautical Almanac, so the would-be lunarian had to generate his 
own ephemerides --very difficult work indeed! And even after the Nautical 
Almanac began to be published (containing lunar distances from its very first 
issue in 1767), there were easy methods that were widely available for doing 
the calculations, but there were also some un-necessarily complicated 
methods. Quite ordinary people could learn to do the calculations for lunars 
using some of these methods, but the advanced methods could be devilishly 
difficult (and they offered no real benefit). At the other extreme of the 
history of lunars, after they had fallen into obsolescence in the latter half 
of the 19th century, the calculations for lunars were still taught as a 
"rite-of-passage" for navigation students. Naturally, slogging through 
calculations that they all knew would probably never be used at sea generated 
considerable antipathy. As late as 1900, many navigation certifications 
required that the student know how to clear lunars and work various arcane 
details that never mattered in real ocean navigation.

And you wrote:
"I do not understand why you shoud want to dispute this. It is the received wisdom from many sources."

Have you known cases where 'received wisdom' in history is wrong??

You concluded:
"You also confuse the issue by making land use (surveying) as a supportive reason for using them."

Why did this confuse you, Douglas? That's real history. They were used in land 
explorations, and this usage lasted decades after they had generally fallen 
out of favor at sea. This doesn't "support" their use. It simply describes 
their use. Many of the great British explorers of Africa, for example, shot 
lunars on a regular basis.  

By the way, for a fun bit of trivia, one of the earliest correct longitudes 
for the muslim holy city of Mecca was determined by lunar distances in about 
1807 by the Spanish "spy" Ali Bey al-Abbasi. It's entertaining to picture him 
secretly shooting lunars to get the longitude of that "forbidden city" at 
about the same time that Basil Hall was shooting his lunars off Bermuda to 
get his prize to port.

And you wrote:
"The reason this persisted is because chronometers are still liable to unknown 
rate changes especially when carried overland"

Yes. Quite correct.

And:
"and making accurate sights with a theodolite (much better than at sea) made 
reasonable accuracy attainable with plenty of time to to do all the 
calculations and careful observations."

No, you can't use a theodolite for lunars. The land-based lunars shot by 
explorers were done with the same instruments and the same techniques used by 
mariners at sea in the first half of the nineteenth century. They used 
sextants.

-FER




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