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"while the rotation of the Earth causes the stars and the Moon to appear to move from east to west across the night sky, the Moon, because of its own orbit around the Earth, fights back against this apparent motion, and seems to move eastward (or retrograde) by about 0.5 degree per hour. In other words, the Moon "moves" west only 11.5 degrees per day." I may well be misunderstanding this but it seems that the passage should end "11.5 degrees per hour." not "per day"?Catalyzer (talk)02:03, 21 May 2017 (UTC)[reply]

Huygens did make and use pendulum clocks. He also tried to use them to solve the longitude problem. Using a pendulum clock on land is the same as using them on the water - both are susceptible to motion-induced errors. He demonstrated that they could be built to be accurate but that the motion problem reduced their suitability.

I think the anonymous editor's changes are reasonable and more accurate that what was before. --Michael Daly (talk)23:30, 10 November 2008 (UTC)hello people out in the world[reply]

"It was less expensive to buy three chronometers, which could serve as checks on each other, than it was to acquire a high-quality sextant which was essential for lunar distance navigation."

This statement doesn't ring true. In order to fix his position, a navigator must in any case have an accurate sextant - the chronometer only gives him the current time so that he can calculate the co-ordinates of the object on which he is taking the sextant sight.

The sights for a position fix when GMT (or UT) is known require only a basic instrument. For this, through the middle of the 19th century, navigators used octants (usually made of wood) while the expensive, precision sextant (usually brass) was reserved for lunars. The sextant was, in fact, designed specifically for shooting lunars. Later in the 19th century, cheaper metal sextants eventually displaced the low-end octant but at the expense of accuracy. It is widely reported that sextants in the latter half of the 19th century were much lower in quality (see e.g. Lecky's "Wrinkles").

Secondly, I may well be wrong but I image a sextant, which is basically two (carefully calibrated and assembled) moving parts, two mirrors and a low-power (3x recommended) telescope, would have been cheaper to make than a chronometer.

See above. Also the parts of the sextant are not the critical components. It's the cutting and calibration of the scale as well as the centering of the index that makes a sextant accurate, and this was expensive. And it's worth remembering that this was market-driven. As lunars faded, the demand for very accurate sextants dropped. With declining demand, sextant quality. Without accurate sextants, lunars became less accurate. So lunars faded even faster... By the way, the "3x recommended" telescope is a modern perspective. In the 19th century, sextants for lunars were equipped even with 9x and 12x telescopes.

The three chronometer approach also has a fatal flaw - - if they show different times, how do you know which one is right?

You don't. So you have several options: 1) average them if the differences are small, 2) ignore one if it has suddenly deviated from the other two by a large change in rate, 3) assume that any of them might be right and navigate with an error band around your longitude that covers all three, 4) ask the first passing ship, "Hey, what is your GMT?" (this was quite common in the 19th century), 5) visit the nearest available port or known island at the earliest opportunity and compare the calculated longitudes against the charted longitude, 6) dust off the textbooks and shoot some lunars (as noted this was much less likely in the late 19th century, but it was always a last resort). And you'll note that even two chronometers would be enough to work with any of these solutions except the second. Also, three is not a magic number. Some ships carried five chronometers, or more. The point is that when you have multiple chronometers, the ensemble reveals its own errors rather than requiring an independent check by lunars (or other sources).

PS: If anyone has data on the price of chronometers and sextants at the end of the 19th century, I'd be interested.Scartboy (talk)13:52, 5 September 2009 (UTC)[reply]

Many chronometer makers entered the business by that time, driving the prices down. They could make them fairly easily with mass production techniques (albeit low volume compared to other industries). Furthermore, navigators in merchant marine or fishing could make do with deck watches instead of chronometers. They could measure the rate of the watch (how fast or slow it was) and use the rate to correct the time. If the timepieces differed, the relative times could be compared on an ongoing basis to determine which one was showing an error (as opposed to its rate).

Sextants remained expensive and a high quality one quite expensive. While octants had dropped out of production by about 1880 or so (IIRC), they were adequate for use with a timepiece while inadequate for lunars. Hence, that sets the standard for what sort of sextant quality is required for lunars. --Michael Daly (talk)03:14, 7 September 2009 (UTC)[reply]

Leibniz also claimed to have solved the longitude problem at the end of the 17th century....though I don't know the details, nor whether his insights had any merit worthy of including on this page.—Precedingunsigned comment added by71.167.58.167 (talk)17:33, 24 June 2010 (UTC)[reply]

The article's section "Lunars or chronometers?" includes the phrase, "gradually but rapidly." Could someone replace this self-contradiction with something unambiguous and meaningful?

During the mid- to late-19th century, affordable, reliable marine chronometers became available,gradually but rapidly replacing the method of lunar distance calculation. It became possible to buy three relatively inexpensive chronometers, serving as checks on each other, rather than acquiring a single (and expensive) sextant of sufficient quality for lunar distance navigation.

--Humanist Geek (talk)19:36, 23 August 2010 (UTC)[reply]

Fixed.—Precedingunsigned comment added by24.148.18.151 (talk)06:35, 11 October 2010 (UTC)[reply]

I`m in search for data on the accuracy of astronomic derived longitude (land based, I assume lunar eclipse or occulation) before the time of telescopes and marine dead reckoning accuracy (all times, all ships) --Portolanero (talk)14:35, 16 June 2011 (UTC)[reply]

One instance you may find interesting is theIslas de las Velas (Islands of the Sails) (now the Marianas Islands) mentioned in the Treaty of Zaragoza (1529) as being 17° east of the Mollucca Islands, but are actually about 17°21' east, which I thought was remarkably close by 16th-century standards. This longitude was determined by dead reckoning and solar observation by the navigators aboard Magellan's ships. See my discussion atTreaty of Tordesillas#Antimeridian: Moluccas and Treaty of Zaragoza. A source of raw data is Magellan's navigator's log book (1519) published by Lord Stanley of Alderley in hisThe first voyage round the world, by Magellan, London: Hakluyt, 1874, pp. 211–234. —Joe Kress (talk)06:27, 17 June 2011 (UTC)[reply]

Thank you! I thought about this treaties too. The WP article is interesting. I see a big diference at the north of what the Cantino map shows as meridian and the modern map. That may be a result of AD 1500 dead reckoning. I found a source that modern DR systems on motorships had an error of 5 %. I expect much worse in 1500. I can not read your ref to Magellan's Voyage. This issue is not on the net. Andthis one seems to have another pagination. But anyway I`m not sure I could destill the DR error from this account. I`m not an expert here.

Just because of such treaties I expect they had some astronomical way in development or use. Lunar distance I estimate to +- 6°. Lunar eclipse to +- 1.5°. Lunar occulation could be better but its hard to estimate it. May depend on the stars magnitude. Thats why I look for real observations. There is evidence they did something but neither the method nor the results were much accepted. May be it was held secret. I assume they did at least lunar eclipse. But where is any direct record? Even a modern reenactment may help. To bad history of science has no much lobby. --Portolanero (talk)09:48, 18 June 2011 (UTC)[reply]

Most publications of Magellan's voyage only include Pigafetta's prose account. Virtually none except that by Lord Stanley of Alderley have the rather dry log book. You are probably a victim of Google Books' "selective geographic availibility" which limits views of a book to a single country or region such as North America or Europe, even for books in the public domain such as this one. Several other Google Books editions of the log book (one or more of which you may have access to) are:1874,1874,2005,2010.

The oldest coordinates are inPtolemy'sGeography, most of which were determined by pacing the distances. Muslim geographers improved these. During his fourth voyage, Columbus used a lunar eclipse predicted byRegiomontanus in hisEphemerides astronomicae to impress the natives of Jamaica[1]. —Joe Kress (talk)03:28, 19 June 2011 (UTC)[reply]

Thanks a lot! Your suspicion on Google was right. I was not aware of this trick. I got advertisments to buy it from antiquarians. But the last two versions worked and I even found a full texthere. It is very detailed and not easy to analyse. During the search I noted a paper"Magellan's Route in the Pacific" by George E. Nunn (1934) seems based on Alderley. I respect Nunn and he mentions maps but I can only see the first page. Maybe he already did it.

The coordinates of Ptolemy are somewhat odd. But he already mentions lunar eclipses. He only mentioned one, a very old and poor one. His book had such obvious poor data that it was almost a call for observations. --Portolanero (talk)10:51, 19 June 2011 (UTC)[reply]

Soory to be a pain but I'm having trouble reconciling just about everything in the "Ancient History" section with what is now known about the Antikythera mechanism. Bearing in mind the mechanism can hardly have sprung unbidden from the soil, those dates must be wrong. Furthermore, someone cleverer than I will have to explain how all the observations inherent in the mechanism's design were made without any form of telescope, surely.Drg40 (talk)10:33, 14 May 2012 (UTC)[reply]

Longitude on Earth is totally different from the motion of Solar System bodies displayed by theAntikythera mechanism. Konwledge of that motion was developed by the Babylonians during the 1st millennium BC and transferred to the Greeks no later than 150 BC because that knowledge was used byHipparchus. The only thing added by the Greeks was a geometrical model containingdeferents and epicycles to the purely mathematical model used by the Babylonians. What is surprising about the device is that it mechanized this knowledge. It is an astronomical clock similar tothose made during the Rennaisance (also before the telescope) but using a crank instead of a internal drive mechanism and one and a half millennia earlier. As such it simplifies complex astronomical motions now known because of the telescope to only those visible to the naked eye, although requiring hundreds of years of observation to quantify. The Babylonians began recording the positions of the Sun, Moon, and planets during the reign of Nabonassar about 750 BC. As such, the knowledge of Hipparchus as summarized byPtolemy in hisAlmagest about AD 140 is highly complex. Conversely, the knowledge of the location of places on Earth contained inPtolemy's Geography is quite rudimentary. —Joe Kress (talk)07:42, 15 May 2012 (UTC)[reply]

"It became possible to buy two or more relatively inexpensive chronometers, serving as checks on each other"Never take two chronometers. One or three, but never two!— Precedingunsigned comment added by174.6.176.106 (talk)01:12, 6 October 2011 (UTC)[reply]

Calling this section Maskelyne's Proposal, although it fits with the sequence, makes it sound as though it was Maskelyne who proposed using the lunar method to determine longitude. In fact it was Mayer who suggested this in 1755, and sent the relevant tables and instructions to the Admiralty, who passed them to the Board of Longitude, who then sent them to Bradley in Greenwich for verification. Maskelyne would never have claimed this for himself. By virtue of his position as Astronomer Royal, he was on the Board of Longitude when it awarded £3,000 to Frau Mayer for her husband's invention. What Maskelyne did, and God bless him, was the maths, and publish the Almanac, but that's all.

There is also one major omission: Sir Jonas Moore is not mentioned, and, according to the Wikipedia article, it was he who persuaded King Charles of the need for an observatory, who paid for most of the instruments and equipment, and got John Flamsteed his job, not Flamsteed himself.

A minor point: in the last paragraph, the fact that the Almanac showed longitude in relation to Greenwich led to the adoption of the GreenwichMeridian as an international standard, not Greenwich Mean Time, although the two are inextricably linkedOsmNacht (talk)10:49, 31 August 2014 (UTC)[reply]

creditsWilliam Baffin with reckoning longitude by lunar observation decades before the first mention of it on this page. Emend his page with citations, corrections, and mentions of the error if they're wrong; kindly emend this page if they're right. It's quite possible he was using an earlier technique, but still notable if it was really the first surviving account of the practice. — LlywelynII12:53, 4 December 2015 (UTC)[reply]

Can you white guys be more shameless?. Have any entire article without crediting the original inventors of the longitude - the Indians. You guys didn't even have the Math to calculate this accurately till the 17th century. The origininal prime meridian ran through the Indian city of Ujjain because that was the global epicentre of MAthematics in the ancient times. You guys didn't have to develop shit. We had already done all the hard work for centuries befeor you just came and copied us and credited yourselves with itThis article might better be called "This history of methods for determining longitude" than it's current title.

There is no discussion of the actual system of longitude we are all familiar with, as printed on almost every map in the world.

If you read the article on the meter, for instance, it explains how the meter was created and evolved. (Another system of measurement), not merely the various tools and methods used to measure a meter.

Why does 0* run though Greenwich, England and not Greenwich, Connecticut or Lagos, Nigeria?

From reading this article one will never know.— Precedingunsigned comment added by2601:1C2:4C00:9CBD:7DDB:5630:D8CC:F45A (talk)20:14, 20 March 2017 (UTC)[reply]

It first mentions "the Board of Longitude in 1714", followed by "the Académie Royale des Sciences in 1666" and which is mentioned again in 1715. Then it mentions a prize by Spain's King Philip II offered in 1567 and increased in 1598, and then mentions a prize by Holland in 1636. There's no logical order for these things, if there's no other order that stands out as important then it should be chronological. As it stands this is just confusing.StarkRG (talk)14:25, 7 November 2018 (UTC)[reply]

I've added material on the medieval period, including Hindu and Arabic work. I now want to trace more of the detail for the subsequent period, which it seems to me is too biased towards maritime navigation. An immense amount of work was done in the 17th and 18th centuries to determine longitudes of places on land, and this should be covered in more detail IMHO. While I'm working on this I'll try and fix some of the issues mentioned above.Kognos (talk)12:58, 13 June 2020 (UTC)[reply]

"In the 11th century Al-Biruni believed the earth rotated on its axis and this forms our modern notion of how time and longitude are related". I've left this sentence hanging for the moment. I have a good source on al-Biruni/Beruni, and will try to integrate this better into the main narrative. There were also Greek scholars who held that the earth rotated. But the connection between time and longitude also works for a stationary earth with everything else rotating abut it.Kognos (talk)21:37, 15 June 2020 (UTC)[reply]

I've taken out this reference. Aristarachus of Samos suggested this in the 4th Century BCE. Al-Birunu certainly discussed this idea but that was 14 or 15 centuries later. But as I said above, longitude and its measurement does not depend on whether the earth is stationary or rotating.Kognos (talk)20:54, 17 June 2020 (UTC)[reply]

I've renamed the initial historical section "Longitude before the telescope". I think this is sensible, as trying to connect to Medieval, Renaissance etc. seems less helpful. It was really the telescope, in the early 17th century, along with the pendulum clock, a little later, that transformed astronomy, and that seems a natural break-point in the narrative.Kognos (talk)21:05, 17 June 2020 (UTC)[reply]

I've inadvertently duplicated a section heading that's already been used. I hope this doesn't cause any problems!Kognos (talk)21:52, 17 June 2020 (UTC)[reply]

I'm re-organising the material, which I hope will make the chronology more logical. There's still thematic organisation, so it can't be strictly chronological, but I hope folks find it easier to follow. I've clarified the distinction between land and sea, and plan to add more on land-based determination, particularly the first French map completed in 1744. I've arranged the methods section by methods, rather than grouping them by originator. There's still a bit of overlap between the old and new - I'll work on this.Kognos (talk)15:15, 30 June 2020 (UTC)[reply]

Telegraphy by wire gets one short paragraph at the moment, but it's an interesting story which deserves a section (and has at least one book devoted to it). I'm starting on that now.Kognos (talk)22:18, 6 July 2020 (UTC)[reply]

That's it added. I think the section "Further refinements for longitude on land" in now mostly redundant, I'll check everything is covered elsewhere before I delete it.Kognos (talk)19:21, 7 July 2020 (UTC)[reply]

This section reads oddly. For example It makes it sound as though Galileo discovered the moons of Jupiter as a by-product of his search for a solution to longitude. Hardly likely! One option is to simply list the contributions in their place in the main article (as Galileo's already is), and remove this section. I'll work on this.Kognos (talk)09:01, 10 July 2020 (UTC)[reply]

Here it is claimed that it was Amerigo Vespucci who "first suggested" the method. The point is that this is in a letter that became public only in 1745, and that has unclear authenticity. Actually, he not only suggested it, but in the letter it is claimed that he used it. Over atAmerigo Vespucci, at the moment the situation is represented as if all the letters were authentic, but this is really not clear, I would say. I would suggest to move this claim to the end of the paragraph and note that it is disputed, after all Werner and Apian really do discuss the method thoroughly, do not reference prior work, and were not contradicted during their lifetimes.Seattle Jörg (talk)17:33, 21 February 2022 (UTC)[reply]

@Seattle Jörg: Do you have a reference to a source where these issues are discussed? If so, I would be happy to edit the article along the lines you suggestKognos (talk)19:04, 1 August 2022 (UTC)[reply]

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