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Useful Notes / The Longitude Problem

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Figuring out how far north or south you are, even when at sea, is fairly easy. You just need to find the height of the sun at noon (i.e., when the sun is due north or south of your position) and apply a corrective factor based on the time of year. That is, all that's required to determine your latitude is a compass, a sextant, and a single table—all of which sailors would have had easy access to.

On the other hand, figuring out how far east or west you are is considerably more difficult, because of the rotation of the earth. If you want to determine your longitude, you have to contend with the fact that, if you're observing something in the sky now, someone several hundred miles to your east could have observed almost precisely the same thing an hour ago. On the other hand, the rotation does have an advantage: if you know what time it is in some fixed location, and know what time it is locally, you can tell how far you are east or west of that fixed location. Before a genuine solution came along, the general practice was to sail to the correct latitude then go East or West until you hit land, but that has certain drawbacks: Not only is it remarkably inefficient, it makes it difficult to avoid any nautical hazards that are at the same latitude as your desired destination.

Historically, there have been two forms of attempted solution to this problem:

  1. Observe celestial phenomena which vary rapidly and are visible simultaneously worldwide, and compare local time when you see it to the predicted time of occurrence at a fixed location. There were two practical ways of doing this: observing the eclipses of the moons of Jupiter or observing the angular distance from the Moon to some particular star:

    The moons of Jupiter eclipse behind their primary very regularly and very frequently, making this method fairly easy to use; it was used to find the longitudes of places on land more or less from the time Galileo discovered them and the pattern of their eclipses, which helped greatly in the development of accurate maps of landmasses (including coasts). Unfortunately, finding the moons from the deck of a moving ship proved to be incredibly impractical.

    Measuring the angular distances of the Moon to the fixed stars—or the Sun, when they're both up—was much easier to do, requiring only equipment that all seamen already had (i.e. a sextant and a compass), particularly when using the Sun (big giant thing in the sky that it is, seamen preferred to use it). However, this measurement was completely useless on its own. The method relies on the fact that the Moon's path across the sky moves very regularly (half a degree per hour), and that the Moon's position relative to the fixed stars is the same no matter where you're looking from. Thus, you can tell what time it is in a fixed location (e.g. in London)...if an astronomer has already done the maths and published a table predicting the position of the Moon as observed from London for each hour of each day of that year. A daunting task. And then the navigator would have to do a bit more maths to actually use the tables properly. And of course, it meant you had to be able to actually find the Moon and see the stars: not usually a problem, but it could be frustrating if you needed to fix your position on a cloudy night with a new moon. Despite all the work it took, this method was standard from the late 18th through the early 19th century, and for the early period of chronometers (see below), this method was often used to make slight corrections to the clock.
  2. Have a very accurate clock. If you carry around a clock set to some fixed time, you can compare local time to time at that fixed location, and thereby determine how different your longitude is from its longitude. On the other hand, constructing a clock that keeps good time while on a moving ship is itself a very difficult problem. The first chronometer capable of keeping sufficiently accurate time while on a ship was made by John Harrison in 1761; for quite some time, nobody actually believed that a mere clock could solve the problem astronomers had struggled with for centuriesnote  - and even once people did listen, they were prohibitively expensive for years - but eventually they became cheap enough to be the standard method of determining longitude.

Neither of these methods were viable until the middle of the 18th century; thus, any ships out of sight of land before that time would have had no good way of knowing where they were, leading to many navigational mishaps as well as wasted time at sea. For the British, this problem became intolerable and led to a massive £20,000 reward (on the order of ten million of today's U.S. dollars). The money was enough for an entire generation of bright minds to seek a solution.

Another kind of "longitude problem" that may show up as a plot device in works of fiction (as in the Tintin example below) is the fact that, for centuries, there was no universally accepted prime meridian (a meridian arbitrarily defined as the zero longitude meridian). Various conventions have been used or advocated in different regions and throughout history. Therefore, longitude coordinates that you find in old texts can be tricky if there is no mention of the prime meridian used. You could be mistaken if you infer that it was the Greenwich meridian.

For more details, see The Other Wiki, here.

Invocations of the longitude problem in media include:

Comic Books

  • In the Tintin album Red Rackham's Treasure, the protagonists originally thought that the coordinates on Francis Haddock's parchments had the Greenwich meridian as the prime meridian. Tintin correctly figures that the French naval officers under Louis XIV were using the Paris meridian as their reference point. Although they do find the shipwreck, the treasure was actually taken by Francis Haddock.

Fan Works

  • The problem with longitude - and latitude - takes on (or perhaps loses) a dimension when considering navigation on a flat earth, such as the Discworld. A.A. Pessimal suggested a way around this when he introduced a Discworld cartographer called Jocky Wilson, who had been wrestling with the problem, and getting nowhere with it, until a night when he turned out for his pub darts team and had a "Eureka!" Moment. Wilson superimposed the grid of a dartboard over the map of the Disc, placed the bullseye over the Hub at Cori Celesti, did some adjustment work to the circles, decided there should be twenty radiating lines between Hub and Rim spaced at eighteen-degree intervals... and the rest is Geography. The master line of longitude is called the Dimwell Meridian, passing through Ankh-Morpork. ("Double Seventeen" in the original schema).

Film - Live-Action

  • In The Bounty, Fletcher Christian's inability to determine how far away Pitcairn Island is (because he can't get a fix on longitude) nearly causes his crew to mutiny for a second time before they finally reach the island. (See also examples from The Bounty Trilogy listed under Literature below.)


  • In The Baroque Cycle, the problem is brought up a number of times, with the English government offering a cash prize if the problem can be solved. A number of natural philosophers take up the challenge, but the problem remains unsolved by the end of the series.
  • The Island of the Day Before by Umberto Eco contains a number of different attempts to solve the longitude problem, including one that uses Sympathetic Magic. The theory is that a wounded dog is taken on the ship; the sympathetic magic (heating up the knife used to wound the dog) is performed on the dog every night at midnight in Paris; by watching the dog's reaction (who'd been treated with "weapon salve", a balm that supposedly heals wounds caused by the weapon it's applied to) and noting the local time, you can figure out your longitude much as with the "clock" method.
  • In Devil of a Fix by Paliser Marcus, the MacGuffin is a secret almanac containing a solution to the longitude problem.
  • The Medici Emerald by Martin Woodhouse and Robert Ross has Leonardo da Vinci investigate the death of a friend of his, a merchant captain renowned for getting where he wanted to go at unheard-of speed. The captain had done a favor for an Arab mathematician who built a very accurate clock ... in the 1460s or '70s.
  • Shows up occasionally (as to be expected) in the Wooden Ships and Iron Men Aubrey-Maturin series of novels by Patrick O'Brian, usually when one of the ship's clocks has some kind of breakdown and makes navigation very difficult. Watches and clocks are rightly shown as being extremely important for any maritime venture, though not only for navigation.
    • It was to the point that no ship carried only one chronometer onboard; mention is made of Jack consulting three to get the average.
  • In Sten Nadolny's The Discovery of Slowness, Sir John Franklin notes at one point that when abandoning ship, the first thing the officers need to secure are the logs, charts and chronometers, in order to have a record of what happened and find their way to safety. The explorer ships carry at least three chronometers to derive an average time, and it's mentioned that the navigators get to know each clock as though it were a crewmember, knowing which run faster, or slower, or lose time quicker.
  • The focus of the book Longitude by Dava Sobel, who traces the various attempts to solve the problem but primarily focuses on clockmaker John Harrison.
    • Adapted into a television mini-series staring Michael Gambon as Harrison, shown on A&E in North America, and Channel 4 in the United Kingdom.
  • The novel Mason & Dixon by Thomas Pynchon talks a lot about the Longitude Problem. This is reasonable when your protagonists are surveyor-astronomers tooling around the British Empire in the 18th century. Mason and Dixon test chronometers and work out moon-observation tables in the course of their careers.
  • The gamebook Sail With Pirates has the reader stranded on a small island in the Caribbean with some sailors. There's an argument when the sailors try to determine their latitude and the reader suggests figuring out their longitude. This is immediately shot down as impossible. Which is decidedly odd, because figuring a longitude of a fixed place, instead of moving ship, is relatively easy, if a somewhat long process. They may have meant that none of them knew how to do it, or were missing the necessary tables/equipment.
  • Gulliver's Travels: When he's in Laputa fantasizing about what he could do if he were immortal, one of the problems he imagines being able to solve is "the discovery of the longitude". He meant, of course, the quick discovery. Discovering longitude on land wasn't a major problem in his time — sure, it required several careful astronomic observations and complicated calculations, but with some time it could be done very precisely. Sailors simply hadn't the time to do so, because their ship would certainly change its place between observations, and they needed a quick, even if somewhat less precise, way of figuring the longitude, instead of a very precise one that took a week to complete.
  • In Ut mine Stromtid, a 19th-century novel set in a small town in Mecklenburg and written in a mix of High and Low German by Fritz Reuter, there is a sequence during the Revolution of 1848 where a man enjoys himself by pretending to read out "new" (which he in fact made up) to the simple townfolk. One of the stories he tells them is that of a rebellion breaking out the Canary island of Ferro (El Hierro) because of the threatened abolition of the Ferro Meridian, which was the meridian most commonly used in continental Europe until the late 19th century.
  • The Bounty Trilogy:
    • In Mutiny on the Bounty, Roger Byam gets a posting as a midshipman on the Bounty despite having no sailing experience thanks to his father's work on determining longitude.
    • In Pitcairn's Island a frustrated Fletcher Christian remarks that the fellow who discovered Pitcairn's Island in 1769 had an inaccurate clock, which is why the Bounty is by Christian's reckoning a good 100 miles past the point where they should have found the island.

Live-Action TV

  • Discussed in the original Cosmos, in which Carl Sagan explains the problem and the need for a good clock when navigating.
  • The drama/documentary Longitude (see Literature above) is all about this problem; it mentions the "sympathetic magic" thing, together with other crackpot schemes like having dozens of ships anchored at fixed longitudes to provide reference points. Even after John Harrison builds several accurate chronometers, he finds himself opposed by Obstructive Bureaucrats who prefer the lunar method.
  • In the second episode of James May's Man Lab, James tests the 'sympathetic magic' theory described above by attempting to sail to France using a dog as a navigational aid. Not surprisingly, it fails.

Tabletop Games

  • 7th Sea incorporates this problem into the game setting. There's one country that's solved it - the country with teleportation magic among its nobility. Nobody's invented a clock that's accurate and robust enough to survive a sea voyage, but by bringing a noble aboard, having him teleport home, and then having him come back with the time, Montaigne has developed the most accurate charts in all of Theah.


Video Games

  • In the original Sid Meier's Pirates! from 1987, you could examine the position of the sun to determine your ship's latitude... but the longitude would just show up as "???". Since the original version had no in-game map at all, this made it more challenging to navigate.


Real Life

  • When you have two accurate clocks or watches it's very easy to figure out your longitude when one is set to a reference time and the other is set to the local time. As it happens, the same theory underlies how GPS works; by comparing the timing signals (transmitted from the GPS satellites) that your receiver can pick up, it's a relatively simple calculation to work out the co-ordinates of where you are in the world. Cross-reference that with a digital map and some other data (e.g. your heading and speed, if you're in motion) and voila; Sat Nav.note