Longitude

1. Longitude and latitude

People split the Earth into lines of latitude and longitude in order to help with navigation. Longitude lines, or meridians, circle the Earth from east to west, and a person's longitude determines how far east or west they are in degrees. The meridian that passes through Greenwich, in London, is set at 0° longitude for historical reasons. Latitude lines circle the Earth from north to south.

Globes of the Earth. Latitude lines run from north to south, and longitude lines run from west to east.

Latitude and Longitude. Image credit: Djexplo/Public domain.

2. Measuring longitude

Longitude is much harder to calculate than latitude. The Earth rotates 360° per day, or 15° per hour, and so there's a direct relationship between longitude and the time that the Sun rises and sets.

The Greenwich meridian is designated 0° longitude. The Sun sets an hour earlier every 15° east of this, and will set one hour later every 15° west.

Diagram showing that the time on Earth depends on where you are relative to the Sun.

Time zones. Image credit: modified by Helen Klus, original images by NASA & Dnu72: 12:00, 3:00, 6:00, and 9:00/CC-SA.

If you know the difference between the time of the sunset in your location and another known location, then you can work out how far east or west you are from there.

Ancient Greek astronomer Hipparchus was the first to suggest that longitude could be calculated by comparing the time of a lunar eclipses at different locations in about 127 BCE, but the inaccuracy of timekeeping devices meant that longitude measurements were often wrong[1].

Painting of clocks in a circle. The middle clock states the time at Washington, and the other clocks show the time elsewhere.

Diagram showing the difference in time between the places shown and Washington, 1860 (click to enlarge). Image credit: A.J. Johnson/Public domain.

2.1 The first clocks

Early clocks included sundials, which measure the movement of the Sun across the sky by marking where a shadow falls, and sand clocks, candles, incense sticks, and water clocks, which were all used to measure constant time durations.

Water clocks measure how long it takes for water to flow from one place to another, and existed in Ancient Egypt, Babylon, India, and China.

Mechanical clocks were first built in 13th century Europe. These used an escapement mechanism, which was first designed by Chinese polymath Su Song in 1088. An escapement is a device that supplies energy to the timekeeping element and allows each cycle to be counted. In Song's clock, it was driven by water[2].

In medieval clocks, the escapement mechanism was composed of a verge and foliot, where verge refers to a vertical rod connecting a wheel, shaped like a crown, to the foliot. The foliot is a horizontal beam with weights attached to either side. The rod has two metal plates, the pallets, placed at the top and bottom of the wheel.

As the wheel rotates, one of the pallets is caught by one of the wheel's teeth. This rotates the verge and foliot in one direction until the second pallet hits another tooth, turning it the other way. Each time the foliot turns, the wheel moves, and so the hands on the clock move too.

Labelled diagram of a verge and foliot escapement mechanism.

Verge and foliot escapement mechanism. Image credit: modified by Helen Klus, original image by Pierre Dubois/Public domain.

Animation of a verge and foliot escapement mechanism.

Animation of a verge escapement mechanism. Image credit: AlienAtSystem/CC-SA.

Ottoman Turkish polymath Taqi al-Din invented the first known alarm clock, the first watch, and the first clocks that measure time in minutes and seconds. In 1551, he invented a rudimentary steam engine[3].

Al-Din was also an astronomer, and his stellar observations may have been even more precise than Danish astronomer Tycho Brahe's[4].

2.2 Pendulum clocks

Italian natural philosopher Galileo Galilei became the first person to suggest using a pendulum to measure time in 1602.

Galileo discovered that the time it takes for a pendulum to swing back and forth, its period, does not depend on how far it swings or how massive the pendulum is. The time it takes is, however, proportional to the square root of the length of the pendulum[5a].

Dutch natural philosopher Christiaan Huygens built the first pendulum clock in 1656[6].

Diagram of a pendulum clock.

Christiaan Huygens' pendulum clock, 1673. Image credit: Christiaan Huygens/Harold C. Kelly/Public domain.

Animation of a gravity escapement mechanism.

Animation of a gravity escapement mechanism. Image credit: Hugh Hunt, Trinity College Cambridge/Public domain.

The pendulum was the first harmonic oscillator to be studied scientifically. A harmonic oscillator is a system that, when moved from equilibrium, experiences a force that restores it back to its original position. If the restoration force is the only force involved, then it is called a simple harmonic oscillator.

In 1660, English natural philosopher Robert Hooke showed that a spring acts the same way, where the force needed to compress a spring is proportional to the length you compress.

Hooke used a pendulum to model the orbits of the planets and, in about 1666, he suggested that the pendulum could be used to measure acceleration due to gravity. In 1671, French astronomer Jean Richer noticed that his pendulum clock was over two minutes slower per day when he was in Cayenne, in South America, than when he was in Paris, France. He deduced that the force of gravity must be lower in Cayenne, allowing the pendulum to swing further[7].

Photograph of the Earth from space. The polar diameter is labelled 12,720 km, and the equatorial diameter 12,756 km.

Oblate Earth. Image credit: modified by Helen Klus, original image by NASA/Public domain.

When English natural philosopher Isaac Newton published his theory of gravitation in 1687, he showed that this is because the Earth, and all other rotating spheres, are slightly elongated at their equator. This happens because the centrifugal force, the outwards force caused by rotation, is stronger there. Gravity maps of the Earth could then be made by taking pendulums around the world.

2.3 The Royal Observatory at Greenwich

In 1514, German mathematician Johannes Werner suggested that time could be measured by observing the position of the Moon[8]. He may have been inspired by Italian explorer Amerigo Vespucci who wrote, in 1502, that the Moon moves west at about 11.5° per hour, which is slightly less than the movement of the stars[9]. This is because the Moon is also orbiting the Earth, completing one full orbit a month.

Once an observer knew the position of the Moon, they could determine the time at Greenwich using a prepared table of lunar distances and times, and then compare this to the local time.

French explorer Jean-Paul Le Gardeur informed King Charles II of England of Werner's technique in 1674. The King consulted his royal commissioners, who included Hooke, and they turned to English astronomer John Flamsteed.

Flamsteed stated that they didn't have the means to measure the positions of the stars and Moon accurately enough to determine longitude in this way, and so King Charles II established the Royal Observatory at Greenwich and appointed Flamsteed the first Astronomer Royal[10].

2.4 The Board of Longitude

Werner's method was modified to account for Newton's theory of gravity, but errors in navigation led to so many shipwrecks that, in 1714, the British government established the Board of Longitude.

The Board promised to reward the first person who showed how longitude could be accurately calculated, following similar schemes in France, Spain, and Holland.

German astronomer Tobias Mayer and Swiss mathematician Leonhard Euler created a set of tables that predicted the position of the Moon more accurately than ever before, and allowed people to calculate their longitude to within half a degree.

Mayer and Euler submitted these to the Board of Longitude in 1755 and British astronomer Nevil Maskelyne, the fifth Astronomer Royal, suggested that tables like these should be published annually in an official book known as a nautical almanac.

The nautical almanac was ready for 1767, and became the standard set of tables used worldwide[11]. The Greenwich meridian was designated 0° longitude, and this was accepted internationally in 1884[12].

2.5 The marine chronometer

People were able to measure longitude more accurately after English clockmaker John Harrison devised a clock that would work at sea. This was known as a marine chronometer. Harrison made a number of attempts before he solved the problem in 1759. Harrison's fourth design, known as H4, was only 13 cm in diameter, and looked like a large pocket watch[5b].

Photograph of Harrison's chronometer.

Harrison's H4 chronometer. Image credit: Colonel Warden/CC-SA.

Harrison had to fight to win the prize offered by the Board of Longitude, eventually gaining recognition, and prize money, in 1773, after appealing to King George III.

Harrison's clocks were used by explorers like Captain James Cook, but were expensive, and so did not become standard for another few decades[5c].

The British Nautical Almanac published lunar distance tables until 1906, two years after the time in any particular location was first broadcast by radio.

3. References

  1. School of Mathematics and Statistics, University of St Andrews, 'Hipparchus of Rhodes', last accessed 15-02-16.

  2. Yan, H. S., 2007, 'Reconstruction Designs of Lost Ancient Chinese Machinery', Springer Science & Business Media.

  3. Al-Hassani, S., 'The Astronomical Clock of Taqi Al-Din: Virtual Reconstruction', Muslim Heritage, last accessed 15-02-16.

  4. Ayduz, S., 'Taqi al-Din Ibn Ma’ruf: A Bio-Bibliographical Essay', Muslim Heritage, last accessed 15-02-16.

  5. (a, b, c) Matthews, M. R., 2012, 'Time for Science Education: How Teaching the History and Philosophy of Pendulum Motion can Contribute to Science Literacy', Springer Science & Business Media.

  6. Macey, S. L., 2013, 'Encyclopedia of Time', Routledge.

  7. Good, G., 1998, 'Sciences of the Earth', Psychology Press.

  8. Mörzer Bruyns, W. F. J. and Dunn, R., 2009, 'Sextants at Greenwich', OUP Oxford.

  9. Sanders, R., 2001, 'Ancient Navigators Could Have Measured Longitude!', 21st Century Science & Technology, 14, pp.58-60.

  10. Couper, H. and Henbest, N., 2011, 'The Story of Astronomy: How the universe revealed its secrets', Hachette UK.

  11. Reidy, M. S. and Kroll, G. R. and Conway, E. M., 2007, 'Exploration and Science: Social Impact and Interaction', ABC-CLIO.

  12. Various, 1884, 'International Conference Held at Washington for the Purpose of Fixing a Prime Meridian and a Universal Day. October, 1884. Protocols of the Proceedings.', Gibson Bros., Printers and Bookbinders.

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