A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: What were the Lunar Distances for?
From: George Huxtable
Date: 2002 Dec 27, 16:27 +0000
From: George Huxtable
Date: 2002 Dec 27, 16:27 +0000
I think Jan Kalivoda is a new name to the Nav-L list, and (if I decode his email address correctly) perhaps our first contributor from the land-locked Czech Republic. He has done his homework well, thoroughly understood our discussions, and asked interesting and pertinent questions. He has no need to apologise for raising lunar-distances again, from a new perspective. I would like to welcome him on-board and hope to see more from his pen. Now to deal with his questions. First, I have to agree that he is factually correct. Longitudes from lunar-distances were (and still are) just about as inaccurate as Jan claims. For example, on Cook's first circumnavigation (with no chronometer on that voyage) he recorded in 1770 the longitude of the island of Savu, in the Arafura Sea, to be E 122� 29'. In 1811 James Horsbrugh noted, in "Directions for sailing to and from the East Indies", part 2, page 444, that more recent chronometer measurements indicated a long of 122� 00', adding- "Captain Cook ... made it 30 miles more to the Eastward, but after his arrival... the lunar tables were found to require a correction of 2 minutes [of time, or 1 minute of arc] or 30 miles Westerly, at the time the observations were taken at Savu.". This is quoted from a footnote in JC Beaglehole's Voyages of Captain James Cook, vol 1, page cclxxv. Cook himself (on page 392 of that same volume) refers to lunar distances as "a method that we have generally found may be depended on to within half a degree, which is a degree of accuracy more than sufficient for all Nautical Purposes". That quotation gives one answer to Jan's question. Cook had made several transatlantic voyages, with nothing more than dead reckoning to inform him of his longitude. Anything was better than that! Cook couldn't conceive of any navigator requiring a longitude accuracy of better then 30 arc-minutes. Nowadays we complain if GPS is out by a few metres. Cook's comments above presumably referred to his errors of measurement only: he may not have been aware of inaccuracies in the Almanac itself, which quoted lunar distances to the arc-second, though achieving accuracies of 1 arc-minute. Even though his astronomer, Green, was proficient in lunars from the start, and so was Cook by the time he reached Tahiti, and even though he had both lat. and long. for Tahiti from Dolphin's previous voyage, he still searched for that island by running down the latitude in the old familiar way. Partly this was because he knew his latitude measurements were much more trustworthy and precise than his longitudes, and partly because he was riding the Easterly trade winds anyway. I use Cook as an example because his voyages were so well-documented, and because he was one of the first to use the lunar distances, that were first tabulated by Maskelyne in the Nautical Almanac for 1767. Jan goes on to say- "I can imagine only two modes of using lunars for navigation in the past - firstly, the check of D.R. position before a landfall when finishing a long deep-see passage. But even then, owing to inaccuracy of lunars, so called "easting/westing" from the target and the final latitude sailing would be necessary, only the initial amount of this deliberate longitude deflection could be smaller." Here I disagree. There were many ocean passages which required a turning-point to round a cape or avoid a danger in mid-voyage, and where passing close enough to get a visual fix would only add to the danger. Let me suggest a few examples- European navigators have long known that the best sailing-vessel route to the China seas took them well South of the Cape of Good Hope into the Westerly trades at S40� until reaching the rocky islands of Amsterdam or St Pauls, from which they could head Northeast toward Sunda Strait, between Sumatra and Java. They would try to pass close enough to sight one of those unlit islands as a turning-point, without striking them. This wasn't easy if the visibility was poor, as they rose out of deep water, so soundings didn't help. If neither island had been sighted, at some point the navigator had to take his chance and steer Northeast anyway, with the risk that one of the islands might still lie in his path. Those islands became graveyards for ships. Even a rough figure for longitude would give the navigator confidence that he had left those rocks behind and could safely steer for the Sunda Strait. A navigator heading from the Atlantic around Cape Horn would first have to pass the Falklands and then head Southward for Le Maire Strait, inside Staten Island, off the end of a long peninsula jutting Eastward. Until he could see that land and identify that strait he had no knowlege of whether he was heading in the right direction. Only longitude, from a lunar distance (or later, a chronometer) could help. Another graveyard of ships. Later in that passage round the Horn he would want to know if he was clear West of Diego Ramirez, another dangerous unmarked rock right in the middle of the Passage, after which he could safely make some Northing. If he got a glimpse of clear sky at the right time, a lunar could inform his decision. Nearer home, sailing vessels from ports in Western Norway, heading South into the Atlantic, would choose the passage between Orkney and Shetland, North or South about Fair Isle, to avoid the constricted and congested waters of the English Channel. Having passed through that gap by latitude sailing, it was then necessary to delay turning South until the navigator could be certain of clearing the Outer Isles (Rona, St Kilda). If landmarks had been sighted, no real problem. But otherwise a lunar distance could establish the safe longitude to make his left-hand turn. When a lunar distance was used near the end of an East-West passage, simply to indicate the distance-to-go, that information could be vital, if the approaching coast was low (so invisible at a distance), or was being approached at night, or was strewn with offshore underwater hazards. Latitude sailing, in ignorance of the longitude, was of little help in those circumstances. What I've been listing above was the uses a navigator could give to a lunar distance, once he had an accurate sextant and a set of lunar distance tables, but not yet a chronometer. There were ways of improving accuracy. A "circle", rather than a sextant, could be used to accumulate the results of several lunar observations, without accumulating instrumental errors. These were employed by Continental navigators but not much by the British, who had taken an early lead in accurate scale-division by machine. Lunar distances of stars, both East and West of the Moon, could be measured in the same set of observations, which would help to cancel certain errors. Cook improved accuracy by taking many sets of Sun-lunars, by several observers, closely spaced, and averaging. When chronometers became available, and affordable, things got better. Jan asks- "What could a sailor achieve on the basis of this piece of information? He could not rate his chronometer by lunars regularly, as the rate acquired would be too irregular (if intervals had been short) or not reliable (if intervals had been long, according to the varying temperature influence on the chronometer rate) or both (between)." This is quite correct. There was no hope of RATING (establishing the rate of gaining or losing) a chronometer, except if its rate became grossly in error due to a speck of dust in the wrong place, in which case a lunar distance should show that up. To establish the rate of a chronometer with any precision, this needs to done on land, with two posts in the ground to provide a North-South line, and the interval between passages of the same star across that line compared with a sidereal day. What a lunar could provide, to some extent, is the integrated error that had built up in the elapsed time since the ship's departure, or since a previous lunar or landfall. That is, how much the chronometer was actually fast or slow on Greenwich Time, but not at what rate it was gaining or losing on Greenwich Time. However, the lunar couldn't measure that error to a high accuracy, only to a couple of minutes of time or thereabouts. If lunar and chronometer agree within a minute or so, the navigator can relax. His check on the chronometer has found no fault, and he can continue to use chronometer-time with some confidence. If a check on the chronometer by a lunar showed up a discrepancy of a couple of minutes or slightly more, what should the navigator do about it? Very little, I suggest. Note it down, certainly. Readjust the chronometer, never! Keep on using the chronometer as the time reference, but bear in mind that discrepancy. And measure another lunar as soon as possible. However, if a series of such time-checks by lunar shows an error significantly greater than 2 minutes, and more important, a divergence that grows with time, then chronometer error is strongly indicated. In such a case, a prudent navigator will establish two different reckonings, one based on each of his diverging time-scales, and presume (in the lack of any other information) that the one that puts him closest to danger is the truer. At this point, he should be adopting latitude-sailing techniques to minimise reliance on his longitude. Finally, Jan asks- "Even so, I wonder if many captains in the merchant sailing fleet used the lunars regularly." Well, I can't offer any statistics. The numbers must have dwindled rapidly from the 1850s, as accurate chronometers became affordable. Remember that ocean passages were frequently being made by small trading vessels, schooners of 100 tons or less, which dominated ocean trading in terms of vessel numbers, if not in cargoes carried. There were far more trading vessels at sea than there are today. The cost of a chronometer (or more than one) must have been a great deterrent for masters of such vessels. In terms of the many textbooks written and sold in the mid-1800s, one gets the impression that lunars were still, then, an important part of the navigator's toolbox. However, that may reflect what skills a navigator needed to pass examinations in that era, rather than the skills he would actually use. Joshua Slocum, who sailed around the world single-handed at the very end of the 1800s, used lunars to do so (with much latitude-sailing), and his familiarity with lunar-distances techniques stemmed from recent experience as master in the merchant service, when he regularly kept a check on his chronometers by lunars. George Huxtable. ------------------------------ email@example.com George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. Tel. 01865 820222 or (int.) +44 1865 820222. ------------------------------