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Here's the general observing procedure:
You observe an "absolute" event in a lunar eclipse, like the beginning or end of totality. On the way into totality, this is the moment when the last "bright white" bit of the Moon (actually dull grey, but by contrast it looks white) disappears into the dusky, reddish eclipse. Coming out of totality, this would be the moment when the Moon becomes rapidly brighter and a "bright white" small crescent appears on the limb leaving the Earth's shadow. At the same time, you perform some observation for local time like measuring the altitude of a star, or you measure the elapsed time by a clock or watch until some observable event for local time is available. Then you compare notes with an observer in a different part of the world.

For example, you're in England, and your cousin is in New England. You observe the end of lunar totality. This is an absolute event the time of it does not depend on your location in any way. It's happening on the Moon. An astronaut standing on the Moon in that zone that has just emerged from totality would see a sliver of the Sun's disk emerge from behind the disk of the Earth. Local conditions for that observer on the Moon matter; the lunar latitude and longitude of that observer matter. Only an observer standing on the edge of the zone separating "bright white" lunar surface from "dusky red" lunar surface will see this event --the emergence of the Sun from behind the Earth. But observers on the Earth all see almost exactly the same view of the Moon all at once. If we had giant telescopes, we could all see that astronaut standing on the Moon and watch him quickly brightening as the Sun emerges at his location on the Moon. For all observers on the Earth this emergence from totality is an absolute-time event. It occurs at some (perhaps unknown) instant of Universal Time (UT or UTC or GMT, the distinctions don't matter). Since the shadow of the Earth on the Moon is "fuzzy", these events can be timed by earthbound observers to the nearest minute or so, but no better.

Quite similar to real "lunars" or "lunar distances", the Moon during a lunar eclipse becomes a "chronometer in the sky". Unlike lunars, there's almost no work involved in the determination of this absolute time event. Also like real lunars, to convert this determination of absolute time into a determination of longitude, we also need an observation for local time. Note first that this assumes that the goal of the observation is to go all the way to longitude itself and not simply "check" a clock that's reading GMT/UT. If I'm only checking the Greenwich time, I can look up the GMT of the eclipse event that I've just observed, compare with my clock, and I'm done. But assuming it's a pre-chronometer historical era or assuming we have an observer with no functioning chronometer, we need the local time of the absolute-time event. Compare two observers, one in northwest Europe and another in the eastern US. We both observe the end of totality. For the observer in Europe, the end of totality occurs at, let's say, 07:30 local time. For the observer in the US it occurs at 02:42 local time. Since we have observed the same absolute event, almost like a firework going off on the lunar surface, the difference in local time is exactly the same as our difference in longitude. In the example here, it's 4h48m longitude difference. It's customary to convert that to degrees (this wasn't always the case) by multiplying by 15° per hour, and the result is a longitude difference of 72°W.

A book arrived in the mail a couple of days ago (relevance in a minute). In the book there was a description of a lunar eclipse observed in June 1638 in the colony of Rhode Island in a place called Aquidneck. This was almost certainly the island that I can see out my window today though in the modern era it's just called Newport. The observer timed the interval from the end of totality to the moment of sunrise and sent that result, 65 minutes, back to England in a letter. How good was this observation? Did they determine the longitude accurately? Turns out, yes, quite accurately, but the result was ignored and forgotten. We can test the accuracy by simulation in "Stellarium" or some equivalent tool. 

On the modern calendar the eclipse occurred early on the morning of 26 June 1638. We can simulate the eclipse in Stellarium. The Moon was low in the southwestern sky that morning just above the handle of the "teapot" in Sagittarius. The Moon first showed a thin bright edge emerging from total eclipse at about 8:05-8:07 UT which we know from Stellarium was around 03:20 Local Apparent Time (to check L.App.Time, do a ctrl-F to find the Sun and read off its "hour angle" and after subtracting twelve hours, that hour angle is identical to Local Apparent Time). Advancing the clock in Stellarium, we find that sunrise did indeed occur 65 minutes later, plus or minus a minute or two (*). So that's quite impressive. If this observation had been compared with other reliable observations, or if it had been computed with a good eclipse model, it would have given the longitude of this spot in Rhode Island accurate to +/- a quarter of a degree of longitude which is about 11 nautical miles east/west offset in this latitude.

Unfortunately, when these numbers arrived in England the observer's cousin compared them with a rather mediocre lunar eclipse prediction which gave the time wrong by about half an hour. Thus the supposed longitude was in error by about 7.5° which is thirty times worse than it could have been. The astronomer who did this eclipse comparison was Jeremiah Horrocks and the observer in New England, 375 years ago just a few miles east of where I live now was apparently his cousin Christopher Horrocks, but the family details are less certain than the reported astronomical details.

Horrocks?? Yes, Horrocks. I've been looking through academic articles trying to get some handle on this guy's work that is not tainted by the author's own hopes and dreams. This is problematic. I'm starting to see Jeremiah Horrocks as a human Rorschach test. Since he died young and his papers are fragmented, different readers look at the "inkblot" of his life and find whatever value they seek. His "star" has risen and fallen repeatedly over the centuries. Of course I'm interested in his coverage in "pop culture", too, which, while very limited is still significant since he continues to be re-discovered, especially by British astronomy fans. In that lighter zone of scientific history, I saw a reference to a book the other day and bought a copy --cheap, just $5 shipping included. It's "The Transit of Venus" by Peter Aughton, subtitled "The brief, brilliant life of Jeremiah Horrocks, father of British astronomy". I had very low expectations, but it's actually quite good. It arrived on Friday, and on the third page-opening of a quick browsing, not even five minutes after I grabbed it from the mailbox, I came across this wonderful story I've re-told about a lunar eclipse observed with the hope of determining longitude by my "neighbors" here in Rhode Island almost four centuries ago. 

That's enough about Horrocks for this topic. His lunar "theory" (in modern terms, a "model" or "algorithm") can wait for another day.

Aughton's book, "The Transit of Venus", was published in 2004, just in time for the first of the 2004/2012 pair of transits of Venus in our century. The blurb on the back cover explicitly calls out "John Harrison, the clockmaker" and like so many pop science books in that period, its publishers were clearly trying to duplicate the massive success of Dava Sobel's "Longitude". Unfortunately it seems that Aughton's "Transit of Venus" did not perform as hoped commercially. I've read a third of it so far. The book is quite good, as I say, but it's not difficult to find flaws. Aughton has some details of that 1638 lunar eclipse wrong (here's a later account). I haven't seen any analysis that recoginzes how good the longitude derived from it should have been. I've said before that it's a shame this business was so misunderstood four centuries ago. Longitudes could have been determined far earlier and with considerable accuracy a century earlier if the astronomers, nautical and otherwise, back then had focused on what was possible and practical at the time instead of chasing an idealized solution.

Frank Reed
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA

* I suggested above that the time until sunrise was correct to "plus or minus a minute or two". But there's a catch: what is sunrise? what was it considered to be in 1638?? From Aquidneck Island itself, there's no sea horizon to the east or northeast (sunrise in this latitude in late June occurs around azimuth 57°) but the hills across the bay are low so perhaps the reported time would have been close enough. There's no way to know for sure.