History of longitude
The history of longitude is a record of the effort, by astronomers, cartographers and navigators over several centuries, to discover a means of determining longitude.
The measurement of longitude is important to both cartography and navigation, in particular to provide safe ocean navigation. Knowledge of both latitude and longitude was required. Finding an accurate and reliable method of determining longitude took centuries of study, and involved some of the greatest scientific minds in human history.
- 1 Ancient history
- 2 Problem of longitude
- 3 Time equals longitude
- 4 Proposed methods of determining time
- 5 Lunars or chronometers?
- 6 Modern solutions
- 7 Further refinements for longitude on land
- 8 Notable scientific contributions
- 9 See also
- 10 References
- 11 External links
Eratosthenes in the 3rd century BC first proposed a system of latitude and longitude for a map of the world. By the 2nd century BC Hipparchus was the first to use such a system to uniquely specify places on Earth. He also proposed a system of determining longitude by comparing the local time of a place with an absolute time. This is the first recognition that longitude can be determined by accurate knowledge of time. 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.
Problem of longitude
Determining latitude was relatively easy in that it could be found from the altitude of the sun at noon (i.e. at its highest point) with the aid of a table giving the sun's declination for the day, or from many stars at night. 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 as a result.
Determining longitude at sea was also much harder than on land. 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 various astronomical techniques possible on land (such as the observation of eclipses) that were unfortunately impractical at sea. Whatever could be discovered from solving the problem at sea would only improve the determination of longitude on land.
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). 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, which could lead to poor health or even death for members of the crew due to scurvy or starvation, with 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 such spectacular disasters as the Scilly naval disaster of 1707, which took Admiral Sir Cloudesley Shovell and his fleet, the British government established the Board of Longitude in 1714:
The Discovery of the Longitude is of such Consequence to Great Britain for the safety of the Navy and Merchant Ships as well as for the improvement of Trade that for want thereof many Ships have been retarded in their voyages, and many lost..." [and there will be a Longitude Prize] "for such person or persons as shall discover the Longitude.
The prizes were to be awarded for the discovery and demonstration of a practical method for determining the longitude of a ship at sea. Prizes were offered in graduated amounts for solutions of increasing accuracy. These prizes, worth the equivalent of millions of pounds 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 other scientific activities, advancement of the science of navigation and the improvement of maps and sailing charts. From 1715, the Académie offered one of the two Prix Rouillés specifically for navigation. 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. Navigators and scientists in most European countries were aware of the problem and were involved in finding a solution. The international effort in solving the problem and the scale of the enterprise represented one of the largest scientific endeavours in history.
Time equals longitude
Since at any instant in time, local solar time at a location varies by one hour for every 15 degrees change of longitude (360 degrees divided by 24 hours), 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 the ship's location, the difference between the reference time and the apparent local time would give the ship's position relative to the fixed location. Finding apparent local time is relatively easy. The problem, ultimately, was how to determine the time at a distant reference point while on a ship.
Proposed methods of determining time
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 Nuremberg in 1514. The method was discussed in detail by Petrus Apianus in his Cosmographicus liber (Landshut 1524).
It appears that Johannes Werner had been inspired by Amerigo Vespucci's letter written in 1502 where he wrote: "...I maintain that I learned [my longitude] ... by the eclipses and conjunctions of the Moon with the planets; and I have lost many nights of sleep in reconciling my calculations with the precepts of those sages who have devised the manuals and written of the movements, conjunctions, aspects, and eclipses of the two luminaries and of the wandering stars, such as the wise King Don Alfonso in his Tables, Johannes Regiomontanus in his Almanac, and Blanchinus, and the Rabbi Zacuto in his almanac, which is perpetual; and these were composed in different meridians: King Don Alfonso's book in the meridian of Toledo, and Johannes Regiomontanus's in that of Ferrara, and the other two in that of Salamanca."2 The best "clock" to use for reference, is the stars. In the roughly 27.3 solar days of a lunar orbit, the Moon moves a full 360 degrees around the sky, returning to its old position among the stars. This is 13 degrees per day, or just over 0.5 degree per hour. So, 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."
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, which 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, this method 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. 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 that got its name from its similarities to an astrolabe. 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.
Upon succeeding John Flamsteed in the post of Astronomer Royal, Halley 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. 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.
Mayer's proposal—lunar distance method
A Frenchman, the Sieur de St. Pierre, brought Werner's technique to the attention of King Charles II of England in 1674. 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. At the same time, Sir Jonas Moore had suggested to King Charles the establishment of an observatory and proposed 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 gathering the data for a working method of lunar distances was under way. To further the astronomers' ability to predict the moon's motion, Isaac Newton soon published his theory of gravitation, which could be applied to the motion of the moon.
In 1755, Tobias Mayer, the German astronomer and superintendent of the observatory at Göttingen, who had been working on a method to determine accurately positions on land based on lunar distances, sent a proposal to the Admiralty. He had corresponded with Leonhard Euler, who contributed information and equations to describe the motions of the moon. Based on this work, Mayer had produced a set of tables predicting the position of the Moon more accurately than ever before. The Admiralty passed them on to the Board of Longitude for evaluation and consideration for the Longitude Prize. James Bradley, the Astronomer Royal at that time, evaluated the tables, and found their predictions to be accurate to within half a degree. The calculations themselves, however, were extremely laborious and time-consuming.
A decade later, Nevil Maskelyne, who as the newly appointed Astronomer Royal was on the Board of Longitude, armed with Mayer's tables and after his own experiments at sea trying out the lunar distance method, proposed annual publication of pre-calculated lunar distance predictions in an official nautical almanac for the purpose of finding longitude at sea.
Being very enthusiastic for the lunar distance method, Maskelyne and his team of 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).  This publication later became the standard almanac for mariners worldwide. Since it was based on the Royal Observatory, it helped lead to the international adoption a century later of the Greenwich Meridian as an international standard.
Harrison's proposal—marine chronometer
Another proposed solution was to use a mechanical timepiece, to be carried on a ship, that would maintain the correct time at a reference location. The concept of using a clock can be attributed to Gemma Frisius. Attempts had been made on land using pendulum clocks, with some success. In particular, Huygens had made accurate pendulum clocks that made it possible to determine longitude on land. He also proposed the use of a balance spring to regulate clocks. There is some dispute as to whether he or Robert Hooke first proposed this idea. However, many, including Isaac Newton, were pessimistic that a clock of the required accuracy could ever be developed. At that time, there were no clocks that could maintain accurate time while being subjected to the conditions of a moving ship. The rolling, pitching, and yawing, coupled with the pounding of wind and waves, would knock existing clocks out of the correct time.
In spite of this pessimism, a group felt that the answer lay in chronometry—developing an improved time piece that would work even on extended voyages at sea. A suitable timepiece was eventually built by John Harrison, a Yorkshire carpenter, with his marine chronometer; that timepiece was later known as H-4.
Harrison built five, two of which were tested at sea. His first, H-1, was not tested under the conditions that were required by the Board of Longitude. Instead, the Admiralty required that it travel to Lisbon and back. It lost considerable time on the outward voyage but performed excellently on the return leg, which was not part of the official trial. The perfectionist in Harrison prevented him from sending it on the required trial to the West Indies (and in any case it was regarded as too large and impractical for service use). He instead embarked on the construction of H-2. This chronometer never went to sea, and was immediately followed by H-3. During construction of H-3, Harrison realised that the loss of time of the H-1 on the Lisbon outward voyage was due to the mechanism losing time every time the ship came about while tacking down the English Channel. Harrison produced H-4, with a completely different mechanism 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 standard. Chronometers such as those by Thomas Earnshaw were suitable for general nautical use by the middle of the 19th century (1836). 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 because of the time-consuming complexity of the calculations for the Moon's position. Early trials of the method could involve four hours of effort. However, the publication of the Nautical Almanac starting in 1767 provided tables of pre-calculated distances of the Moon from various celestial objects at three-hour intervals for every day of the year, making the process practical by reducing the time for calculations to less than 30 minutes and as little as ten minutes with some efficient tabular methods. Lunar distances were widely used at sea from 1767 to about 1905. With the new tables with Haversines from Josef de Mendoza y Ríos (1805), computation time was reduced to a few minutes.
Between 1800 and 1850 (earlier in British and French navigation practice, later in American, Russian, and other maritime countries), affordable, reliable marine chronometers became available, with a trend to replace the method of lunars as soon as they could reach the market in large numbers. It became possible to buy three or more chronometers, serving for checking on each other (redundancy), although according to Nathaniel Bowditch, their use was precluded because they were very expensive,  obviously much higher than a single sextant of sufficient quality for lunar distance navigation which continued in use until 1906.
Two chronometers provided dual modular redundancy, allowing a backup if one should cease to work, but not allowing any error correction if the two displayed a different time, since in case of contradiction between the two chronometers, it would be impossible to know which one was wrong (the error detection obtained would be the same of having only one chronometer and checking it periodically: every day at noon against dead reckoning). Three chronometers provided triple modular redundancy, allowing error correction if one of the three was wrong, so the pilot would take the average of the two with closer readings (average precision vote). There is an old adage to this effect, stating: "Never go to sea with two chronometers; take one or three." At one time this observation or rule was an expensive one as the cost of three sufficiently accurate chronometers was more than the cost of many types of smaller merchant vessels. Some vessels carried more than three chronometers – for example, HMS Beagle carried 22 chronometers.
By 1850, the vast majority of ocean-going navigators worldwide had ceased using the method of lunar distances. Nonetheless, expert navigators continued to learn lunars as late as 1905, though for most this was a textbook exercise since they were a requirement for certain licenses. They also continued in use in land exploration and mapping where chronometers could not be kept secure in harsh conditions. The British Nautical Almanac published lunar distance tables until 1906 and the instructions until 1924. Such tables last appeared in the 1912 USNO Nautical Almanac, though an appendix explaining how to generate single values of lunar distances was published as late as the early 1930s. The presence of lunar distance tables in these publications until the early 20th century does not imply common usage until that time period but was simply a necessity due to a few remaining (soon to be obsolete) licensing requirements. The development of wireless telegraph time signals in the early 20th century, used in combination with marine chronometers, put a final end to the use of lunar distance tables.
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Telegraph signals were used regularly for time coordination by the United States Naval Observatory starting in 1865. These were used, for example, by astronomers during the Solar eclipse of July 29, 1878 to calibrate the longitude of their observations.
Time signals were first broadcast by wireless telegraphy in 1904, by the US Navy from Navy Yard in Boston. Another regular broadcast began in Halifax, Nova Scotia in 1907, and time signals that became more widely used were broadcast from the Eiffel Tower starting in 1910. As ships adopted radio telegraph sets for communication, such time signals were used to correct chronometers. This method drastically reduced the importance of lunars as a means of verifying chronometers.
Modern sailors have a number of choices for determining accurate positional information, including radar and the Global Positioning System, commonly known as GPS, a satellite navigation system. With technical refinements that make position fixes accurate to within meters, the radio-based LORAN system was used in the late 20th Century but has been discontinued in North America. Combining independent methods is used as a way to improve the accuracy of position fixes. Even with the availability of multiple modern methods of determining longitude, a marine chronometer and sextant are routinely carried as a backup system.
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. In the 1970s, the use of satellites was developed to more precisely measure geographic coordinates (GPS).
Notable scientific contributions
In the process of searching for a solution to the problem of determining longitude, many scientists added to the knowledge of astronomy and physics.
- Galileo - detailed studies of Jupiter's moons, which proved Ptolemy's assertion that not all celestial objects orbit the Earth
- Robert Hooke - determination of the relationship between forces and displacements in springs, laying the foundations for the theory of elasticity.
- Christiaan Huygens - invention of pendulum clock and a spring balance for pocket watch.
- Jacob Bernoulli, with refinements by Leonhard Euler - invention of the calculus of variations for Bernoulli's solution of the brachistochrone problem (finding the shape of the path of a pendulum with a period that does not vary with degree of lateral displacement). This refinement created greater accuracy in pendulum clocks.
- John Flamsteed and many others - formalization of observational astronomy by means of astronomical observatory facilities, further advancing 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 solid mechanics. His invention of caged roller bearings contributed to refinements in mechanical engineering designs.
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