# History of longitude

History of longitude

The history of longitude is a record of the effort, by navigators and scientists over several centuries, to discover a means of determining longitude.

The measurement of longitude is important to both cartography and navigation. Historically, the most important practical application of these was to provide safe ocean navigation. Knowledge of both latitude and longitude was required. Finding a method of determining longitude took centuries and involved some of the greatest scientific minds.

Problem of longitude

Determining longitude on land was fairly easy compared to the task at sea. A stable surface to work from, a comfortable location to live in while performing the work and the ability to repeat determinations over time made for great accuracy. Whatever could be discovered from solving the problem at sea would only improve the determination of longitude on land.

Determining latitude was relatively easy in that it could be found from the altitude of the sun at noon with the aid of a table giving the sun's declination for the day. [Latitude can also be determined from Polaris, the northern pole star. However, since Polaris is not precisely at the pole, it can only estimate the latitude unless the precise time is known or many measurements are made over time. While many measurements can be made on land, this makes it impractical for determining latitude at sea.] For longitude, early ocean navigators had to rely on dead reckoning. This was inaccurate on long voyages out of sight of land and these voyages sometimes ended in tragedy.

In order to avoid problems with not knowing one's position accurately, navigators have, where possible, relied on taking advantage of their knowledge of latitude. They would sail to the latitude of their destination, turn toward their destination and follow a line of constant latitude. This was known as "running down a westing" (if westbound, easting otherwise). ["Dutton's Navigation and Piloting", 12th edition. G.D. Dunlap and H.H. Shufeldt, eds. Naval Institute Press 1972, ISBN 0-87021-163-3] This prevented a ship from taking the most direct route (a great circle) or a route with the most favourable winds and currents, extending the voyage by days or even weeks. This increased the likelihood of short rations [As food stores ran low, the crew would be put on rations to extend the time with food. This was referred to as giving the crew "short rations", "short allowance" or "petty warrant".] , scurvy or starvation leading to poor health or even death for members of the crew and resultant risk to the ship.

Errors in navigation have also resulted in shipwrecks. Motivated by a number of maritime disasters attributable to serious errors in reckoning position at sea, particularly spectacular disasters such as that which took Admiral Cloudesley Shovell and his fleet, the British government established the Board of Longitude in 1714.

The prizes were to be awarded to the first person to demonstrate a practical method for determining the longitude of a ship at sea. Each prize, in increasing amounts, were for solutions of increasing accuracy. These prizes, worth millions of dollars in today's currency, motivated many to search for a solution.

Britain was not alone in the desire to solve the problem. France's King Louis XIV founded the Académie Royale des Sciences in 1666. It was charged with, among a range of scientific activities, the improvement of maps and sailing charts and advancement of the science of navigation. From 1715, the Académie offered one of the two "Prix Rouillés" specifically for navigation.Taylor, E.G.R., "The Haven-finding Art: A History of Navigation from Odysseus to Captain Cook", Hollis &amp; Carter, London 1971, ISBN 0 370 01347 6] Spain's Philip II offered a prize for the discovery of a solution to the problem of the longitude in 1567; Philip III increased the prize in 1598. Holland added to the effort with a prize offered in 1636. [ [http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Longitude1.html Longitude and the Académie Royale] ] Navigators and scientists in most European countries were aware of the problem and were involved in finding the solution. Due to the international effort in solving the problem and the scale of the enterprise, it represents one of the largest scientific endeavours in history.

Time equals longitude

Since the Earth rotates at a steady rate of 360° per day, or 15° per hour (in sidereal time), there is a direct relationship between time and longitude. If the navigator knew the time at a fixed reference point when some event occurred at his location, the difference between that time and his apparent local time would give him his position relative to the fixed location. For example, knowing the time at a reference location when the apparent local time the sun reached its highest point in the sky (local noon) would yield the location. [For practical reasons, establishing position by observing the maximum height of the sun (local apparent noon) is not generally done. It is more reliable to measure the height of the sun at an arbitrary point in time and determine local apparent time from that.] Finding apparent local time is relatively easy. The problem, ultimately, was to determine the time at a distant reference point while on a ship.

Proposed methods of determining time

Galileo's proposal - Jovian moons

In 1612, having determined the orbital periods of Jupiter's four brightest satellites (Io, Europa, Ganymede and Callisto), Galileo proposed that with sufficiently accurate knowledge of their orbits one could use their positions as a universal clock and this would make possible the determination of longitude. He worked on this problem from time to time during the remainder of his life.

To be successful, it required the observation of the moons from the deck of a moving ship. To this end, Galileo proposed the celatone, a device in the form of a helmet with a telescope mounted so as to accommodate the motion of the observer on the ship. [ [http://brunelleschi.imss.fi.it/museum/esim.asp?c=500174 Celatone] ] This was later replaced with the idea of a pair of nested hemispheric shells separated by a bath of oil. This would provide a platform that would allow the observer to remain stationary as the ship rolled beneath him, in the manner of a gimballed platform. To provide for the determination of time from the observed moons' positions, a Jovilabe was offered - this was an analogue computer that calculated time from the positions and gets its name by its similarities to an astrolabe. [ [http://brunelleschi.imss.fi.it/museum/esim.asp?c=404003 Jovilabe] ] The practical problems were severe and the method was never used at sea. However, it was used for longitude determination on land.

Halley's proposals - lunar occultations and appulses, magnetic deviation

Around 1683, Edmund Halley proposed using a telescope to observe the time of occultations or appulses of a star by the moon as a means of determining time while at sea. He had accumulated observations of the moon's position and of certain stars to this end and had deduced the means of correcting errors in predictions of the moon's position.

Following John Flamsteed's death, as new Astronomer Royal, he had undertaken the task of observing both stellar positions and the path of the moon, with the intention of supplementing existing knowledge and advancing his proposal for determining longitude at sea.Halley, Edmund, "A Proposal of a Method for Finding the Longitude at Sea Within a Degree, or Twenty Leagues.", Philosophical Transactions of the Royal Society, Vol. 37, 1731-1732, pp 185-195] By this time, he had abandoned the use of occultations in preference for appulses exclusively. No reason was given by Halley for abandoning occultations, however, there are few bright stars occulted by the moon and the task of documenting the dim stars' positions and training navigators to recognize them would be daunting. Appulses with brighter stars would be more practical.

While he had tested the method at sea, it was never widely used or considered as a viable method. His observations did contribute to the lunar distance method.

Halley also hoped that careful observations of magnetic deviations could provide a determination of longitude. The magnetic field of the Earth was not well understood at the time. Mariners had observed that magnetic north deviated from geographic north in many locations. Halley and others hoped that the pattern of deviation, if consistent, could be used to determine longitude. If the measured deviation matched that recorded on a chart, the position would be known. Halley used his voyages on the pink "Paramour" to study the magnetic variance and was able to provide maps showing the "halleyan" or "isogonic" lines. This method was eventually to fail as the localized variations from general magnetic trends make the method unreliable.

Maskelyne's proposal - lunar distance method

The first publication of a method of determining time by observing the position of the Earth's moon was by Johannes Werner in his "In hoc opere haec continentur Nova translatio primi libri geographiae Cl. Ptolomaei", published at Nürnberg in 1514. The method was discussed in detail by Petrus Apianus in his "Cosmographicus liber" (Landshut 1524).

A Frenchman, the Sieur de St. Pierre, brought the technique to the attention of King Charles II of England in 1674. [Forbes, Eric G., " [http://adsabs.harvard.edu/abs/1977VA.....20...39F The origins of the Greenwich observatory] ", "Vistas in Astronomy", vol. 20, Issue 1, pp.39-50] Being enthusiastic for the proposed technique, the king contacted his royal commissioners who included Robert Hooke. They in turn consulted the astronomer John Flamsteed. Flamsteed supported the feasibility of the method but lamented the lack of detailed knowledge of the stellar positions and the moon's movement. King Charles responded by accepting Flamsteed's suggestion of the establishment of an observatory and appointed Flamsteed as the first astronomer royal. With the creation of the Royal Observatory, Greenwich and a program for measuring the positions of the stars with high precision, the process of developing a working method of lunar distances was under way.Sobel, Dava, "Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time", Walker and Company, New York, 1995 ISBN 0-8027-1312-2] To further the astronomers' ability to predict the moon's motion, Isaac Newton's theory of gravitation could be applied to the motion of the moon.

Tobias Mayer, the German astronomer, had been working on the lunar distance method in order to determine accurately positions on land. He had corresponded with Leonard Euler, who contributed information and equations to describe the motions of the moon.Landes, David S., "Revolution in Time", Belknap Press of Harvard University Press, Cambridge Mass., 1983, ISBN 0-674-76800-0] With these studies, Mayer had produced a set of tables predicting the position of the Moon more accurately than ever before. These were sent to the Board of Longitude for evaluation and consideration for the Longitude Prize. With these tables and after his own experiments at sea trying out the lunar distance method, Nevil Maskelyne proposed annual publication of lunar distance predictions in an official nautical almanac for the purpose of finding longitude at sea to within half a degree.

Being very enthusiastic for the lunar distance method, Maskelyne and his team of human computers worked feverishly through the year 1766 preparing tables for the new Nautical Almanac and Astronomical Ephemeris. Published first with data for the year 1767, it included daily tables of the positions of the Sun, Moon, and planets and other astronomical data as well as tables of lunar distances giving the distance of the Moon from the Sun and nine stars suitable for lunar observations (ten stars for the first few years).cite web
title =The History of HM Nautical Almanac Office
publisher =HM Nautical Almanac Office
url = http://www.nao.rl.ac.uk/nao/history/
doi =
accessdate = 2007-07-31
] cite web
title =Nautical Almanac History
publisher=US Naval Observatory
url=http://aa.usno.navy.mil/publications/docs/NewAsAHistory.htm
accessdate = 2007-07-31
] This publication later became the standard almanac for mariners worldwide, and since it was based on the Royal Observatory, led to the international adoption of Greenwich Mean Time as an international standard.

Harrison's proposal - marine chronometer

Another proposed solution was to use a mechanical timepiece to maintain the correct time at a reference location while being carried on the ship. The concept of using a clock can be attributed to Gemma Frisius and attempts had been made on land with some success using pendulum clocks. However, many including Isaac Newton, were pessimistic that a clock of required accuracy could ever be developed. At that time, there were no clocks that could maintain accurate time while being subjected to the conditions experienced on a moving ship. The rolling, pitching and yawing, coupled with the pounding of wind and waves would knock existing clocks out of time.

In spite of this pessimism a small group felt that the answer lay in chronometry--developing a time piece that would work, even on extended voyages at sea. A suitable timepiece was eventually built by John Harrison, a humble Yorkshire carpenter, with his marine chronometer; the timepiece in question was the one later known as "H-4".

Harrison built five chronometers and two were tested at sea. His first, "H-1", was not tested under the conditions that were required by the Board of Longitude. Instead, Admiralty required that it travel to Lisbon and back. It performed excellently but the perfectionist in Harrison prevented him from sending it on the trial to the West Indies and instead embarked on the construction of "H-2". This never went to sea and was immediately followed by "H-3". Still not satisfied with his own work, he produced "H-4" which did get its sea trial and satisfied all the requirements for the Longitude Prize. However, he was not awarded the prize and was forced to fight for his reward.

Though the British Parliament rewarded John Harrison for his marine chronometer in 1773, his chronometers were not to become the standard design. Chronometers, such as those by Thomas Earnshaw were suitable for general nautical use by the end of the 18th century. However, they remained very expensive and the lunar distance method continued to be used for some decades.

Lunars or chronometers?

The lunar distance method was initially labour intensive, due to the complexity of the calculations (early trials of the method could involve four hours of effort). However, the tables in the nautical almanacs contained more of the pre-calculated information and the process became usable (time for calculations was reduced to less than 30 minutes ["The Nautical Almanac and Astronomical Ephemeris, for the year 1767", London: W. Richardson and S. Clark, 1766] ). Lunar distances were widely used at sea during the period from 1767 to about 1850. Lunar distance tables last appeared in the USNO Nautical Almanac for 1912 and an appendix explaining how to generate single values of lunar distances was published as late as the early 1930s. Similarly, the British Nautical Almanac published the tables until 1906 and the instructions until 1924. [Message from Catherine Hohenkerk of HM Nautical Almanac Office as posted in [http://www.fer3.com/arc/m2.aspx?i=103183&y=200709 NavList Google group.] ] The presence of these tables does not imply common usage. Expert navigators learned lunars as late as 1905 since they were a requirement for certain licenses. However, by this late date, the vast majority of navigators had ceased using the method of lunar distances because affordable, reliable marine chronometers had been available for decades. 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.cite book
first=Frederick James
last=Britten
title = Former Clock & Watchmakers and Their Work
pages=p228
date = 1894
publisher=Spon & Chamberlain
location = New York
quote=In the early part of the present century the reliability of the chronometer was established, and since then the chronometer method has gradually superseded the lunars.
accessdate=2007-08-08
]

The combination of the availability of marine chronometers and wireless telegraph time signals put an end to the use of lunars in the 20th century.

Modern solutions

Time signals were first broadcast by wireless telegraphy by the US Navy from Navy Yard in Boston in 1904. Another regular broadcast began in Halifax, Nova Scotia in 1907 and the more widely used time signals were broadcast from the Eiffel Tower in 1910. [Lombardi, Michael A., PDFlink| [http://tf.nist.gov/timefreq/general/pdf/1877.pdf "Radio Controlled Clocks"] |983 KiB , "Proceedings of the 2003 National Conference of Standards Laboratories International", Aug 17, 2003] As ships adopted radio telegraph sets for communication, these time signals could be used to correct the chronometer. This reduced the importance of lunars as a means of verifying chronometers.

Today a sailor has a number of choices for determining accurate positional information, including radar and GPS, the satellite navigation system. With modern technical refinements that make position fixes accurate to within meters, the radio-based LORAN system is also regaining popularity. Combining independent methods also improves the accuracy of position fixes. Even with all these modern methods of determining longitude, a marine chronometer and sextant are normally carried as a backup.

Further refinements for longitude on land

For the determination of longitude on land, the preferred method became exchanges of chronometers between observatories to accurately determine the differences in local times in conjunction with observation of the transit of stars across the meridian.

An alternative method was the simultaneous observation of occultations of stars at different observatories. Since the event occurred at a known time, it provided an accurate means of determining longitude. In some cases, special expeditions were mounted to observe a special occultation or eclipse to determine the longitude of a location without a permanent observatory.

From the mid 19th century, telegraph signalling allowed more precisely synchronization of star observations. This significantly improved longitude measurement accuracy. The Royal Observatory in Greenwich and the U.S. Coast Survey coordinated European and North American longitude measurement campaigns in the 1850s and 1860s resulting in improved map accuracy and navigation safety. Synchronization by radio followed in the early 20th century. Satellites were used to more precisely measure geographic coordinates from the 1970s and 1980s - see GPS.

Notable scientific contributions

In the process of searching for the solution to the problem of the longitude, many scientists added to our knowledge of astronomy and physics.
*Galileo - detailed studies of Jupiter's moons reinforcing the argument that not all celestial objects orbited the Earth as stated by Ptolemy
*Robert Hooke - determination of the relationship between forces and displacements in springs, laying the foundations for the theory of elasticity.
*Jacob Bernoulli, with refinements by Leonhard Euler - invention of the calculus of variations for Bernoulli's solution of the brachistochrone problem. This problem was to find the shape of the path for a pendulum with a period that did not vary with degree of lateral displacement. This refinement created greater accuracy in pendulum clocks.
*John Flamsteed and many others - formalization of observational astronomy with established astronomical observatories, further progressing modern astronomy as a science.
*John Harrison - invention of the gridiron pendulum and bimetallic strip along with further studies in the thermal behavior of materials. This contributed to the evolving science of the Solid mechanics. Invention of caged roller bearings contributed to refinements in mechanical engineering designs.

References

* [http://www.pbs.org/wgbh/nova/longitude/ PBS Nova Online: "Lost at Sea, the Search for Longitude"]

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