History of longitude: Difference between revisions - Wikipedia

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The second important technical development for longitude determination was the [[pendulum clock]], patented by [[Christiaan Huygens]] in 1657.<ref name="Grimbergen">{{cite conference |last1=Grimbergen |first1=Kees |title=Huygens and the advancement of time measurements |conference=Titan - From Discovery to Encounter |editor-last=Fletcher | editor-first=Karen |location=ESTEC, Noordwijk, Netherlands |date=2004 |pages=91–102 |publisher=ESA Publications Division |isbn=92-9092-997-9 |url=https://ui.adsabs.harvard.edu/abs/2004ESASP1278...91G}}</ref> This gave an increase in accuracy of about 30 fold over prrevious mechanical clocks - the best pendulum clocks were accurate to about 10 seconds per day.<ref>{{cite journal |last1=Blumenthal |first1=Aaron S. |last2=Nosonovsky |first2=Michael |title=Friction and Dynamics of Verge and Foliot: How the Invention of the Pendulum Made Clocks Much More Accurate |journal=Applied Mechanics |date=2020 |volume=1 |issue=2 |pages=111–122 |doi=10.3390/applmech1020008}}</ref> From the start, Huygens intended his clocks to be used for determination of longitude at sea.<ref name="Huygens">{{cite journal |last1=Huygens |first1=Christiaan |title=Instructions concerning the use of pendulum-watches for finding the longitude at sea |journal=Philosophical Transactions |date=1669 |volume=4 |issue=47 |pages=937-953 |url=https://archive.org/details/jstor-100996}}</ref><ref name="Howard">{{cite journal |last1=Howard |first1=Nicole |title=Marketing Longitude: Clocks, Kings, Courtiers, and Christiaan Huygens |journal=Book History |date=2008 |volume=11 |pages=59–88}}</ref> However, pendulum clocks did not tolerate the motion of a ship sufficiently well, and after a series of trials it was concluded that other approaches would be needed. The future of pendulum clocks would be on land. Together with telescopic instruments, they would revolutionize observational astronomy and cartography in the coming years.<ref name="Olmsted">{{cite journal |last1=Olmsted |first1=J.W. |title=The Voyage of Jean Richer to Acadia in 1670: A Study in the Relations of Science and Navigation under Colbert |journal=Proceedings of the American Philosophical Society |date=1960 |volume=104 |issue=6 |pages=612–634 |url=https://www.jstor.org/stable/985537}}</ref>

==ProblemMethods of determining longitude==

The development of the telescope and accurate clocks increased the range of methods that could be used to determine longitude. They all depend on a common principle, which was to determine an absolute time from an event or measurement and to compare the corresponding local time at two different locations. (Absolute here refers to a time that is the same for an observer anywhere on earth.) Each hour of difference of local time corresponds to a 15 degrees change of longitude (360 degrees divided by 24 hours). Local noon is defined as the time at which the sun is at the highest point in the sky. This is hard to determine directly, as the apparent motion of the sun is nearly horizontal at noon. The usual approach was to take the mid-point between two times at which the sun was at the same altitude. With an unobstructed horizon, the mid-point between sunrise and sunset could be used.<ref name="Norie">{{cite book |last1=Norie |first1=John William |title=A New and Complete Epitome of Practical Navigation |date=1805 |publisher=William Heather |location=William Heather |page=219 |url=https://archive.org/details/norie-1805-a-new-and-complete-epitome-of-practical-navigation/page/n253}}</ref>

To determine the measure of absolute time, lunar eclipses continued to be used. Other proposed methods include the following

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#Sun|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.

===Lunar Distances===

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.

This is the earliest proposal having been first suggested in a letter by [[Amerigo Vespucci]] referring to observations he made in 1499<ref name="Arciniegas">Cited in: {{cite book |last1=Arciniegas |first1=German |title=Amerigo And The New World The Life & Times Of Amerigo Vespucci |date=1955 |publisher=Alfred A. Knopf |location=New York |page=192 |url=https://archive.org/details/amerigonewworld00arci}}</ref>. The method was published by [[Johannes Werner]] in 1514<ref name="Werner">{{cite book |last1=Werner |first1=Johann |author-link=Johannes Werner|title=In hoc opere haec continentur Noua translatio primi libri Geographiae Cl. Ptolomaei |language=la |date=1514 |publisher=Ioanne Stuchs |location=Nurembergae |url=https://archive.org/details/ARes04201}}</ref>, and discussed in detail by [[Petrus Apianus]] in 1524<ref name="Apianus">{{cite book |last1=Apianus |first1=Petrus |author-link=Petrus Apianus|title=Cosmographicus liber Petri Apiani mathematici, iam denuo integritati restitutus per Gemmam Phrysium. |language=la|date=1533 |publisher=vaeneunt in pingui gallina per Arnoldum Birckman |location=Landshut |url=https://archive.org/details/bub_gb_Y5VRORXjoZ8C}}</ref>. The [[Lunar distance (navigation)|method]] depends on the motion of the moon relative to the "fixed" stars, which completes a 360° circuit in 27.3 days on average (a lunar month), giving an observed movement of just over 0.5°/hour. Thus an accurate measurement of the angle is required, since a 2' of arc (1/30°) difference in the angle between the moon and the selected star corresponds to a 1° difference in the longitude - 60 nautical miles at the equator<ref name="Halley 1731">{{cite journal |last1=Halley |first1=Edmund |author-link=Edmond Halley |title=A Proposal of a Method for Finding the Longitude at Sea within a Degree, or Twenty Leagues. |journal=Philosophical Transactions |date=1731 |volume=37 |issue=417-426 |pages=185-195 |url=http://rstl.royalsocietypublishing.org/content/37/417-426/185.short}}</ref>. The method also required accurate tables, which were complex to construct, since they had to take into account parallax and the various sources of irregularity in the orbit of the moon. Neither measuring instruments nor astronomical tables were accurate enough in the early 16th-century. Vespucci's attempt to use the method placed him at 82° east of Cadiz, when he was actually less than 40° east of Cadiz, on the north coast of Brazil<ref name="Arciniegas"/>.

===Satellites of Jupiter===

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).<ref>''Dutton's Navigation and Piloting'', 12th edition. G.D. Dunlap and H.H. Shufeldt, eds. Naval Institute Press 1972, {{ISBN|0-87021-163-3}}</ref> 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,<ref>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''.</ref> 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.▼

In 1612, having determined the orbital periods of Jupiter's four brightest satellites ([[Galilean moons|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, thisThe method required thea observationtelescope, ofas the moons fromare thenot deckvisible ofto athe movingnaked shipeye. For Touse thisin marine endnavigation, 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.<ref>[http://brunelleschi.imss.fi.it/museum/esim.asp?c=500174 Celatone]</ref> 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 [[gimbal]]led platform. To provide for the determination of time from the observed moons' positions, a [[Jovilabe]] was offered &mdash; this was an analogue computer that calculated time from the positions and that got its name from its similarities to an [[astrolabe]].<ref>[http://brunelleschi.imss.fi.it/museum/esim.asp?c=404003 Jovilabe]</ref> The practical problems were severe and the method was never used at sea. However, it was used for longitude determination on land.▼

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 [[Cloudesley Shovell|Admiral Sir Cloudesley Shovell]] and his fleet, the British government established the [[Board of Longitude]] in 1714:

On land, this method proved useful and accurate. An early example was the measurement of the longitude of the site of [[Tycho Brahe]]'s former observatory on the Island of [[Ven |Hven]]. [[Jean Picard]] on Hven and [[Giovanni Domenico Cassini|Cassini]] in Paris made observations during 1671 and 1672, and obtained a value of 42 minutes 10 seconds (time) east of Paris, corresponding to 10° 32' 30", about 12' (1/5°) of arc higher than the modern value.<ref name="Picard">{{cite journal |last1=Picard |first1=Jean |title=Voyage D'Uranibourg ou Observations Astronomiques faites en Dannemarck |language=fr |journal=Memoires de l'Academie Royale des Sciences |date=1729 |volume=7 |issue=1 |pages=223-264 |url=https://archive.org/details/picard-mmoiresdelacad-07pari}}</ref>

{{quote|"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 rewards|Longitude Prize]]] "for such person or persons as shall discover the Longitude."}}

===Appulses and Occultations===

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.

Two proposed methods depend on the relative motions of the moon and a star or planet. An [[appulse]] is the least apparent distance between the two objects, an [[occultation]] occurs when the star or planet passes behind a moon -- essentially a type of eclipse. The times of either of these events can be used as the measure of absolute time in the same way as with a lunar eclipse. [[Edmond Halley]] described the use of this method to determine the longitude of [[Balasore]], using observations of the star [[Aldebaran]] (the Bull's Eye) in 1680, with an error of just over half a degree<ref name="Halley 1682">{{cite journal |last1=Halley |first1=Edmund |title=An account of some very considerable observations made at Ballasore in India, serving to find the longitude of that place, and rectifying very great errours in some famous modern geographers |journal=Philosophical Collections of the Royal Society of London |date=1682 |volume=5 |issue=1 |pages=124-126 |doi=10.1098/rscl.1682.0012}}</ref>. He published a more detailed account of the method in 1717<ref name="Halley 1717">{{cite journal |last1=Halley |first1=Edmund |title=An advertisement to astronomers, of the advantages that may accrue from the observation of the moon's frequent appulses to the Hyades, during the next three ensuing years |journal=Philosophical Transactions |date=1717 |volume=30 |issue=354 |pages=692-694 |url=https://archive.org/details/halley-1717-philosophicaltra-3017roya}}</ref>. A longitude determination using the occultation of a planet, [[Jupiter]], was described by [[James Pound]] in 1714<ref name="Pound">{{cite journal |last1=Pound |first1=James |title=Some late curious astronomical observations communicated by the Reverend and learned Mr. James Pound, Rector of Wansted |journal=Philosophical Transactions of the Royal Society of London |date=1714 |volume=29 |issue=347 |pages=401-405 |url=https://archive.org/details/jstor-103078}}</ref>.

===Chronometers===

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.<ref name="egrtaylor">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}}</ref> Spain's [[Philip II of Spain|Philip II]] offered a prize for the discovery of a solution to the problem of the longitude in 1567; [[Philip III of Spain|Philip III]] increased the prize in 1598. Holland added to the effort with a prize offered in 1636.<ref name="Académie Royale">[http://www-groups.dcs.st-and.ac.uk/~history/PrintHT/Longitude1.html Longitude and the Académie Royale]</ref> 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.

The first to suggest travelling with a clock to determine longitude was [[Gemma Frisius]], a physician, mathematician, cartographer, philosopher, and instrument maker from the Netherlands. The clock would be set to the local time of a starting point whose longitude was known, and longitude of any other place could be determined by comparing its local time with the clock time.<ref name="Pogo">{{cite journal |last1=Pogo |first1=A |title=Gemma Frisius, His Method of Determining Differences of Longitude by Transporting Timepieces (1530), and His Treatise on Triangulation (1533) |journal=Isis |date=1935 |volume=22 |issue=2 |pages=469-506 |doi=10.1086/346920}}</ref><ref name="Meskens 1992">{{cite journal |last1=Meskens |first1=Ad |title=Michiel Coignet's Nautical Instruction |journal=The Mariner's Mirror |date=1992 |volume=78 |issue=3 |pages=257-276 |doi=10.1080/00253359.1992.10656406}}</ref>{{rp|259}} While the method is perfectly sound, and was partly stimulated by recent improvements in the accuracy of mechanical clocks, it still requires far more accurate time-keeping than was available in Frisius day. The term [[chronometer]] was not used until the following century<ref name="Koberer">{{cite journal |last1=Koberer |first1=Wolfgang |title=On the First Use of the Term "Chronometer" |journal=The Mariner's Mirror |date=2016 |volume=102 |issue=2 |pages=203-206 |doi=10.1080/00253359.2016.1167400}}</ref>, and it would be over two centuries before this became the standard method for determining longitude at sea<ref name="Gould 1921">{{cite journal |last1=Gould |first1=Rupert T |title=The History of the Chronometer |journal=The Geographical Journal |date=1921 |volume=57 |issue=4 |pages=253-268 |jstor=1780557}}</ref>.

===Magnetic Declination===

==Time equals longitude==

This method is based on the observation that a compass needle does not in general point exactly north. The angle between true north and the direction of the compass needle (magnetic north) is called the [[magnetic declination]] or variation, and its value varies from place to place. Several writers proposed that the size of magnetic declination could be used to determine longitude. Mercator suggested that the magnetic north pole was an island in the longitude of the Azores, where magnetic declination was, at that time close to zero. These ideas were supported by [[Michiel Coignet]] in his ''Nautical Instruction''<ref name="Meskens 1992"/>.

Halley made extensive studies of magnetic variation during his voyages on the [[pink (ship)|pink]] [[HMS Paramour (1694)|''Paramour'']]. He published the first chart showing ''[[Isogon (geomagnetism)|isogonic]] lines'' - lines of equal magnetic declination - in 1701<ref name="Halley 1701">{{cite book |last1=Halley |first1=Edm. |title=A New and Correct Chart Shewing the Variations of the Compass in the Western & Southern Oceans as Observed in ye Year 1700 by his Ma[jes]ties Command |date=1701 |publisher=Mount and Page |location=London |url=https://digitalcollections.nypl.org/items/510d47da-ef24-a3d9-e040-e00a18064a99}}</ref>. One of the purposes of the chart was to aid in determining longitude, but the method was eventually to fail as changes in magnetic declination over time proved too large and too unreliable to provide a basis for navigation.

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.

==Land and Sea==

==Proposed methods of determining time==

[[File:Moll World Map 1719 master-gmd-gmd3-g3200-g3200-mf000001Z Atlantic.jpg|thumb|Modern outline map (blue) superimposed on Herman Moll's. 1718 World Map. The southern part of South America is much too far west, but the west coast of the Americas is generally within 3° longitude]]On land, the period from the development of telescopes and pendulum clocks until the mid 18th-Century saw a steady increase in the number of places whose longitude had been determined with reasonable accuracy, often with errors of less than a degree, and nearly always within 2-3°. By the 1720s errors were consistently less than 1°<ref>See, for example, Port Royal, Jamaica: {{cite journal |last1=Halley |first1=Edmond |title=Observations on the Eclipse of the Moon, June 18, 1722. and the Longitude of Port Royal in Jamaica |journal=Philosophical Transactions |date=1722 |volume=32 |issue=370-380 |pages=235-236 |url=https://archive.org/details/jstor-103607}}; Buenos Aires: {{cite journal |last1=Halley |first1=Edm. |title=The Longitude of Buenos Aires, Determin'd from an Observation Made There by Père Feuillée |journal=Philosophical Transactions |date=1722 |volume=32 |issue=370-380 |pages=2-4 |url=https://archive.org/details/jstor-103565}}Santa Catarina, Brazil: {{cite journal |last1=Legge |first1=Edward |last2=Atwell |first2=Joseph |title=Extract of a letter from the Honble Edward Legge, Esq; F. R. S. Captain of his Majesty's ship the Severn, containing an observation of the eclipse of the moon, Dec. 21. 1740. at the Island of St. Catharine on the Coast of Brasil |journal=Philosophical Transactions |date=1743 |volume=42 |issue=462 |pages=18-19 |url=https://archive.org/details/jstor-104132}}</ref>.

At sea during the same period, the situation was very different. Two problems proved intractable. The first was the need for immediate results. On land, an astronomer at, say, Cambridge Massachusetts could wait for the next lunar eclipse that would be visible both at Cambridge and in London; set a pendulum clock to local time in the few days before the eclipse; time the events of the eclipse; send the details across the Atlantic and wait weeks or months to compare the results with a London colleague who had made similar observations; calculate the longitude of Cambridge; then send the results for publication, which might be a year or two after the eclipse<ref name="Brattle">{{cite journal |last1=Brattle |first1=Tho. |last2=Hodgson |first2=J. |title=An Account of Some Eclipses of the Sun and Moon, Observed by Mr Tho. Brattle, at Cambridge, about Four Miles from Boston in New-England, Whence the Difference of Longitude between Cambridge and London is Determin'd, from an Observation Made of One of Them at London |journal=Philosophical Transactions |date=1704 |volume=24 |pages=1630-1638 |url=https://archive.org/details/philtrans09445181}}</ref>. And if either Cambridge of London had no visibility because of cloud, wait for the next eclipse. The marine navigator needed the results quickly. The second problem was the marine environment. Making accurate observations in an ocean swell is much harder than on land, and pendulum clocks do not work well in these conditions. Thus longitude at sea could only be estimated from [[dead reckoning]] (DR) - by using estimations of speed and course from a known starting position - at a time when longitude determination on land was becoming increasingly accurate.

The first publication of a method of determining time by observing the position of the Earth's moon was by [[Johannes Werner]] in his {{lang|la|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).

▲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).<ref>''Dutton's Navigation and Piloting'', 12th edition. G.D. Dunlap and H.H. Shufeldt, eds. Naval Institute Press 1972, {{ISBN|0-87021-163-3}}</ref> 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,<ref>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''.</ref> 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.

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 [[Abraham Zacuto|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."

A famous longitude error that had disastrous consequences occurred in April 1741. [[George Anson, 1st Baron Anson|George Anson]], commanding H.M.S. Centurion, was rounding [[Cape Horn]] from east to west. Believing himself past the Cape, he headed north, only to find the land straight ahead. A particularly strong easterly current had put him well to the east of his DR position, and he had to resume his westerly course for several days. When finally past the Horn, he headed north for Juan Fernandez, to take on supplies, and to relieve his crew, many of whom were sick with scurvy. On reaching the latitude of Juan Fernandez, he did not know whether the Island was to the east or West, and spent 10 days sailing first eastwards and then westwards before finally reaching the island. During this time over half of the ship's company died of scurvy<ref name="Gould 1935">{{cite journal |last1=Gould |first1=R.T. |title=John Harrison and his timekeepers |journal=The Mariner's Mirror |date=1935 |volume=21 |issue=2 |pages=115-139}}</ref>.

===Galileo's proposal—Jovian moons===

==Government Initiatives==

▲In 1612, having determined the orbital periods of Jupiter's four brightest satellites ([[Galilean moons|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.

In response to the problems of navigation, a number of European maritime powers offered prizes for a method to determine longitude at sea. Spain was the first, offering a reward for a solution in 1567, and this was increased to a permanent pension in 1598. Holland offered 30,000 florins in the the early 17th-Century. Neither of these prizes produced a solution.<ref name="Siegel">{{cite journal |last1=Siegel |first1=Jonathan R. |title=Law and Longitude |journal=Tulane Law Review |date=2009 |volume=84 |pages=1-66}}</ref>{{rp|9}}

▲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.<ref>[http://brunelleschi.imss.fi.it/museum/esim.asp?c=500174 Celatone]</ref> 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 [[gimbal]]led platform. To provide for the determination of time from the observed moons' positions, a [[Jovilabe]] was offered &mdash; this was an analogue computer that calculated time from the positions and that got its name from its similarities to an [[astrolabe]].<ref>[http://brunelleschi.imss.fi.it/museum/esim.asp?c=404003 Jovilabe]</ref> 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 [[occultation]]s or [[appulse]]s of a star by the moon as a means of determining time while at sea.<ref name="halley"/> 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.<ref name="halley">{{cite journal|last=Halley |first=Edmund| title=A Proposal of a Method for Finding the Longitude at Sea Within a Degree, or Twenty Leagues. |journal=Philosophical Transactions of the Royal Society |volume=37 |date=1731 |pages=185–195 |url=http://rstl.royalsocietypublishing.org/content/37/417-426/185.short }}</ref> 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 deviation]]s 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 (ship)|pink]] [[HMS Paramour (1694)|''Paramour'']] to study the magnetic variance and was able to provide maps showing the ''halleyan'' or ''[[Isogon (geomagnetism)|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===

{{For|details on the use of the lunar distance method|Method of lunar distances}}

A Frenchman, the Sieur de St. Pierre, brought Werner's technique to the attention of [[King Charles II of England]] in 1674.<ref>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</ref> 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.<ref name="sobel">[[Dava Sobel|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}}</ref> 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.<ref name="Landes">Landes, David S., ''Revolution in Time'', Belknap Press of Harvard University Press, Cambridge Mass., 1983, {{ISBN|0-674-76800-0}}</ref> 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.

The British Parliament passed “An Act for providing a publick Reward for such Person or Persons as shall discover the Longitude at Sea,” in 1714, and set up a Board to administer the award. The rewards depended on the accuracy of the method: from £10,000 for an accuracy within one degree of latitude (60 nautical miles at the equator) to £20,000 for accuracy within one-half of a degree.{{r|"Siegel"|p=9}}

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.

This prize in due course produced two workable solutions. The first was lunar distances, which required careful observation, accurate tables, and rather lengthy calculations. [[Nevil Maskelyne]],the newly appointed Astronomer Royal was on the Board of Longitude, started 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 [[human computer|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).<ref name="HMNAO history">{{cite web

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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===

{{main|John Harrison|Marine chronometer}}

[[File:Chronometer of Jeremy Thacker.jpg|thumb|Chronometer of [[Jeremy Thacker]].]]

The second method was the use of [[Marine chronometer|chronometer]]. Many, including Isaac Newton, were pessimistic that a clock of the required accuracy could ever be developed. Half a degree of longitude is equivalent to two minutes of time, so the required accuracy is a few seconds a day. At that time, there were no clocks that could come close to maintaining such accurate time while being subjected to the conditions of a moving ship. [[John Harrison]], a Yorkshire carpenter and clock-maker believed it could be done, and spent over three decades proving it.{{r|"Siegel"|pp=14-27}}

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.<ref>"The Man Who Knew Too Much", The Strange and Inventive Life of Robert Hooke, Stephen Inwood, Pan Books 2003 {{ISBN|0-330-48829-5}}</ref> 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 [[Flight dynamics|rolling]], [[Flight dynamics|pitching]], and [[Yaw angle|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 [[Marine chronometer|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 chronometers, 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.

A French expedition under [[Charles-François-César Le Tellier de Montmirail|Le Tellier]] performed the first measurement of longitude using marine chronometers aboard [[French corvette Aurore (1766)|''Aurore'']] in 1767.<ref name=ancre>{{Cite web|url=https://ancre.fr/en/monograph/64-monographie-de-l-aurore-corvette-1766.html|title=MONOGRAPHIE DE L'AURORE - Corvette -1766|website=Ancre|language=en|access-date=2019-12-05}}</ref>