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72-626: The line of longitude running through El Hierro (Ferro), the westernmost of the Canary Islands , was known in European history as the prime meridian in common use outside of the future British Empire . Already in the 2nd century A.D., Ptolemy considered a definition of the zero meridian based on the westernmost position of the known world, giving maps with only positive (eastern) longitudes. In 1634, France ruled by Louis XIII and Richelieu decided that Ferro's meridian should be used as

144-539: A Global Positioning System (GPS), but in common usage, where high accuracy is not required, the reference ellipsoid is not usually stated. In English texts, the latitude angle, defined below, is usually denoted by the Greek lower-case letter phi ( ϕ or φ ). It is measured in degrees , minutes and seconds or decimal degrees , north or south of the equator. For navigational purposes positions are given in degrees and decimal minutes. For instance, The Needles lighthouse

216-400: A graticule on the reference surface. The latitude of a point on the actual surface is that of the corresponding point on the reference surface, the correspondence being along the normal to the reference surface, which passes through the point on the physical surface. Latitude and longitude together with some specification of height constitute a geographic coordinate system as defined in

288-413: A prime meridian , is mathematically related to time differences up to 12 hours by a factor of 15. Thus, a time differential (in hours) between two points is multiplied by 15 to obtain a longitudinal difference (in degrees). Historically, times used for calculating longitude have included apparent solar time , local mean time , and ephemeris time , with mean time being the one most used for navigation of

360-560: A 300-by-300-pixel sphere, so illustrations usually exaggerate the flattening. The graticule on the ellipsoid is constructed in exactly the same way as on the sphere. The normal at a point on the surface of an ellipsoid does not pass through the centre, except for points on the equator or at the poles, but the definition of latitude remains unchanged as the angle between the normal and the equatorial plane. The terminology for latitude must be made more precise by distinguishing: Geographic latitude must be used with care, as some authors use it as

432-510: A common grid with Paris degrees at the top and Ferro degrees offset by 20 at the bottom. Louis Feuillée also worked on this problem in 1724. It was later found that the actual island of El Hierro itself is in fact 20° 23' 9" west of Paris, but the Ferro meridian was still defined as 20 degrees west of Paris. According to the European longitude adjustment of Carl Theodor Albrecht (ca. 1890)

504-637: A few of the more prevalent ones. Longitude is given as an angular measurement with 0° at the Prime Meridian , ranging from −180° westward to +180° eastward. The Greek letter λ (lambda) is used to denote the location of a place on Earth east or west of the Prime Meridian. Each degree of longitude is sub-divided into 60 minutes , each of which is divided into 60 seconds . A longitude is thus specified in sexagesimal notation as, for example, 23° 27′ 30″ E. For higher precision,

576-474: A method of determining longitude by comparing the local time of a lunar eclipse at two different places, thus demonstrating an understanding of the relationship between longitude and time. Claudius Ptolemy (2nd century CE) developed a mapping system using curved parallels that reduced distortion. He also collected data for many locations, from Britain to the Middle East. He used a prime meridian through

648-476: A one-hour difference in local time, due to the differing position in relation to the Sun. Comparing local time to an absolute measure of time allows longitude to be determined. Depending on the era, the absolute time might be obtained from a celestial event visible from both locations, such as a lunar eclipse, or from a time signal transmitted by telegraph or radio. The principle is straightforward, but in practice finding

720-462: A reliable method of determining longitude took centuries and required the effort of some of the greatest scientific minds. A location's north–south position along a meridian is given by its latitude , which is approximately the angle between the equatorial plane and the normal from the ground at that location. Longitude is generally given using the geodetic normal or the gravity direction . The astronomical longitude can differ slightly from

792-495: A survey but, with the advent of GPS , it has become natural to use reference ellipsoids (such as WGS84 ) with centre at the centre of mass of the Earth and minor axis aligned to the rotation axis of the Earth. These geocentric ellipsoids are usually within 100 m (330 ft) of the geoid. Since latitude is defined with respect to an ellipsoid, the position of a given point is different on each ellipsoid: one cannot exactly specify

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864-555: A synonym for geodetic latitude whilst others use it as an alternative to the astronomical latitude . "Latitude" (unqualified) should normally refer to the geodetic latitude. The importance of specifying the reference datum may be illustrated by a simple example. On the reference ellipsoid for WGS84, the centre of the Eiffel Tower has a geodetic latitude of 48° 51′ 29″ N, or 48.8583° N and longitude of 2° 17′ 40″ E or 2.2944°E. The same coordinates on

936-553: Is cos φ decreases from 1 at the equator to 0 at the poles, which measures how circles of latitude shrink from the equator to a point at the pole, so the length of a degree of longitude decreases likewise. This contrasts with the small (1%) increase in the length of a degree of latitude (north–south distance), equator to pole. The table shows both for the WGS84 ellipsoid with a = 6 378 137 .0 m and b = 6 356 752 .3142 m . The distance between two points 1 degree apart on

1008-411: Is also used in the current literature. The parametric latitude is related to the geodetic latitude by: The alternative name arises from the parameterization of the equation of the ellipse describing a meridian section. In terms of Cartesian coordinates p , the distance from the minor axis, and z , the distance above the equatorial plane, the equation of the ellipse is: The Cartesian coordinates of

1080-504: Is at 50°39.734′ N 001°35.500′ W. This article relates to coordinate systems for the Earth: it may be adapted to cover the Moon, planets and other celestial objects ( planetographic latitude ). For a brief history, see History of latitude . In celestial navigation , latitude is determined with the meridian altitude method. More precise measurement of latitude requires an understanding of

1152-484: Is determined by the shape of the ellipse which is rotated about its minor (shorter) axis. Two parameters are required. One is invariably the equatorial radius, which is the semi-major axis , a . The other parameter is usually (1) the polar radius or semi-minor axis , b ; or (2) the (first) flattening , f ; or (3) the eccentricity , e . These parameters are not independent: they are related by Many other parameters (see ellipse , ellipsoid ) appear in

1224-421: Is the meridional radius of curvature . The quarter meridian distance from the equator to the pole is For WGS84 this distance is 10 001 .965 729  km . The evaluation of the meridian distance integral is central to many studies in geodesy and map projection. It can be evaluated by expanding the integral by the binomial series and integrating term by term: see Meridian arc for details. The length of

1296-522: The Philosophiæ Naturalis Principia Mathematica , in which he proved that a rotating self-gravitating fluid body in equilibrium takes the form of an oblate ellipsoid. (This article uses the term ellipsoid in preference to the older term spheroid .) Newton's result was confirmed by geodetic measurements in the 18th century. (See Meridian arc .) An oblate ellipsoid is the three-dimensional surface generated by

1368-615: The east – west position of a point on the surface of the Earth , or another celestial body. It is an angular measurement , usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians are imaginary semicircular lines running from pole to pole that connect points with the same longitude. The prime meridian defines 0° longitude; by convention the International Reference Meridian for

1440-419: The poles where the axis of rotation of the Earth intersects the reference surface. Planes which contain the rotation axis intersect the surface at the meridians ; and the angle between any one meridian plane and that through Greenwich (the Prime Meridian ) defines the longitude: meridians are lines of constant longitude. The plane through the centre of the Earth and perpendicular to the rotation axis intersects

1512-580: The zenith ). On map projections there is no universal rule as to how meridians and parallels should appear. The examples below show the named parallels (as red lines) on the commonly used Mercator projection and the Transverse Mercator projection . On the former the parallels are horizontal and the meridians are vertical, whereas on the latter there is no exact relationship of parallels and meridians with horizontal and vertical: both are complicated curves. \ In 1687 Isaac Newton published

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1584-542: The 12th century, astronomical tables were prepared for a number of European cities, based on the work of al-Zarqālī in Toledo . The lunar eclipse of September 12, 1178 was used to establish the longitude differences between Toledo, Marseilles , and Hereford . Christopher Columbus made two attempts to use lunar eclipses to discover his longitude, the first in Saona Island , on 14 September 1494 (second voyage), and

1656-655: The British parliament in 1714. It offered two levels of rewards, for solutions within 1° and 0.5°. Rewards were given for two solutions: lunar distances, made practicable by the tables of Tobias Mayer developed into an nautical almanac by the Astronomer Royal Nevil Maskelyne ; and for the chronometers developed by the Yorkshire carpenter and clock-maker John Harrison . Harrison built five chronometers over more than three decades. This work

1728-775: The Canary Islands, so that all longitude values would be positive. While Ptolemy's system was sound, the data he used were often poor, leading to a gross over-estimate (by about 70%) of the length of the Mediterranean. After the fall of the Roman Empire, interest in geography greatly declined in Europe. Hindu and Muslim astronomers continued to develop these ideas, adding many new locations and often improving on Ptolemy's data. For example al-Battānī used simultaneous observations of two lunar eclipses to determine

1800-526: The Earth passes near the Royal Observatory in Greenwich , south-east London on the island of Great Britain . Positive longitudes are east of the prime meridian, and negative ones are west. Because of the Earth's rotation , there is a close connection between longitude and time measurement . Scientifically precise local time varies with longitude: a difference of 15° longitude corresponds to

1872-401: The Earth's orbit about the Sun is called the ecliptic , and the plane perpendicular to the rotation axis of the Earth is the equatorial plane. The angle between the ecliptic and the equatorial plane is called variously the axial tilt, the obliquity, or the inclination of the ecliptic, and it is conventionally denoted by i . The latitude of the tropical circles is equal to i and the latitude of

1944-457: The Ferro meridian is 17° 39ʹ 46.02ʺ west of the Greenwich meridian. But for the geodetic networks of Austria , Germany and Czechoslovakia , the value 17° 40ʹ 00ʺ was adopted in the 1920s, not only for practical reasons but also as it was discovered that the longitude of the Berlin ( Rauenberg ) fundamental point was miscalculated by 13.39ʺ. For the geodetic networks of Hungary and Yugoslavia ,

2016-493: The Poles. Also the discontinuity at the ± 180° meridian must be handled with care in calculations. An example is a calculation of east displacement by subtracting two longitudes, which gives the wrong answer if the two positions are on either side of this meridian. To avoid these complexities, some applications use another horizontal position representation . The length of a degree of longitude (east–west distance) depends only on

2088-691: The Sun is overhead at some point of the Tropic of Capricorn . The south polar latitudes below the Antarctic Circle are in daylight, whilst the north polar latitudes above the Arctic Circle are in night. The situation is reversed at the June solstice, when the Sun is overhead at the Tropic of Cancer. Only at latitudes in between the two tropics is it possible for the Sun to be directly overhead (at

2160-571: The WGS84 spheroid is The variation of this distance with latitude (on WGS84 ) is shown in the table along with the length of a degree of longitude (east–west distance): A calculator for any latitude is provided by the U.S. Government's National Geospatial-Intelligence Agency (NGA). The following graph illustrates the variation of both a degree of latitude and a degree of longitude with latitude. There are six auxiliary latitudes that have applications to special problems in geodesy, geophysics and

2232-471: The West Indies, and as far as Japan and China in the years 1874–90. This contributed greatly to the accurate mapping of these areas. While mariners benefited from the accurate charts, they could not receive telegraph signals while under way, and so could not use the method for navigation. This changed when wireless telegraphy (radio) became available in the early 20th century. Wireless time signals for

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2304-556: The advantages that both the observations and the calculations were simpler, and as they became cheaper in the early 19th century they started to replace lunars, which were seldom used after 1850. The first working telegraphs were established in Britain by Wheatstone and Cooke in 1839, and in the US by Morse in 1844. It was quickly realised that the telegraph could be used to transmit a time signal for longitude determination. The method

2376-425: The angle subtended at the centre by the meridian arc from the equator to the point concerned. If the meridian distance is denoted by m ( ϕ ) then where R denotes the mean radius of the Earth. R is equal to 6,371 km or 3,959 miles. No higher accuracy is appropriate for R since higher-precision results necessitate an ellipsoid model. With this value for R the meridian length of 1 degree of latitude on

2448-757: The convention of negative for east is also sometimes seen, most commonly in the United States ; the Earth System Research Laboratories used it on an older version of one of their pages, in order "to make coordinate entry less awkward" for applications confined to the Western Hemisphere . They have since shifted to the standard approach. The longitude is singular at the Poles and calculations that are sufficiently accurate for other positions may be inaccurate at or near

2520-408: The datum ED50 define a point on the ground which is 140 metres (460 feet) distant from the tower. A web search may produce several different values for the latitude of the tower; the reference ellipsoid is rarely specified. The length of a degree of latitude depends on the figure of the Earth assumed. On the sphere the normal passes through the centre and the latitude ( ϕ ) is therefore equal to

2592-421: 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° to 3°. By the 1720s errors were consistently less than 1°. At sea during the same period, the situation was very different. Two problems proved intractable. The first

2664-509: The difference in longitude between Antakya and Raqqa with an error of less than 1°. This is considered to be the best that can be achieved with the methods then available: observation of the eclipse with the naked eye, and determination of local time using an astrolabe to measure the altitude of a suitable "clock star". In the later Middle Ages, interest in geography revived in the west, as travel increased, and Arab scholarship began to be known through contact with Spain and North Africa. In

2736-409: The early 17th century. Initially an observation device, developments over the next half century transformed it into an accurate measurement tool. The pendulum clock was patented by Christiaan Huygens in 1657 and gave an increase in accuracy of about 30 fold over previous mechanical clocks. These two inventions would revolutionise observational astronomy and cartography. On land, the period from

2808-402: The ellipsoid to that point Q on the surrounding sphere (of radius a ) which is the projection parallel to the Earth's axis of a point P on the ellipsoid at latitude ϕ . It was introduced by Legendre and Bessel who solved problems for geodesics on the ellipsoid by transforming them to an equivalent problem for spherical geodesics by using this smaller latitude. Bessel's notation, u ( ϕ ) ,

2880-429: The equator is exactly 60 geographical miles or 111.3 kilometers, as there are 60 minutes in a degree. The length of 1 minute of longitude along the equator is 1 geographical mile or 1.855 km or 1.153 miles, while the length of 1 second of it is 0.016 geographical mile or 30.916 m or 101.43 feet. Latitude On its own, the term "latitude" normally refers to the geodetic latitude as defined below. Briefly,

2952-430: The equatorial plane and the normal to the surface at that point: the normal to the surface of the sphere is along the radial vector. The latitude, as defined in this way for the sphere, is often termed the spherical latitude, to avoid ambiguity with the geodetic latitude and the auxiliary latitudes defined in subsequent sections of this article. Besides the equator, four other parallels are of significance: The plane of

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3024-408: The established method for commercial shipping until replaced by GPS in the early 1990s. The main conventional methods for determining longitude are listed below. With one exception (magnetic declination), they all depend on a common principle, which is to determine the time for an event or measurement and to compare it with the time at a different location. Longitude, being up to 180° east or west of

3096-399: The geocentric latitude ( θ ) and the geodetic latitude ( ϕ ) is: For points not on the surface of the ellipsoid, the relationship involves additionally the ellipsoidal height h : where N is the prime vertical radius of curvature. The geodetic and geocentric latitudes are equal at the equator and at the poles but at other latitudes they differ by a few minutes of arc. Taking the value of

3168-422: The geodetic latitude of a point is the angle formed between the vector perpendicular (or normal ) to the ellipsoidal surface from the point, and the plane of the equator . Two levels of abstraction are employed in the definitions of latitude and longitude. In the first step the physical surface is modeled by the geoid , a surface which approximates the mean sea level over the oceans and its continuation under

3240-401: The gravitational field of the Earth, either to set up theodolites or to determine GPS satellite orbits. The study of the figure of the Earth together with its gravitational field is the science of geodesy . The graticule is formed by the lines of constant latitude and constant longitude, which are constructed with reference to the rotation axis of the Earth. The primary reference points are

3312-412: The land masses. The second step is to approximate the geoid by a mathematically simpler reference surface. The simplest choice for the reference surface is a sphere , but the geoid is more accurately modeled by an ellipsoid of revolution . The definitions of latitude and longitude on such reference surfaces are detailed in the following sections. Lines of constant latitude and longitude together constitute

3384-451: The latitude and longitude of a geographical feature without specifying the ellipsoid used. Many maps maintained by national agencies are based on older ellipsoids, so one must know how the latitude and longitude values are transformed from one ellipsoid to another. GPS handsets include software to carry out datum transformations which link WGS84 to the local reference ellipsoid with its associated grid. The shape of an ellipsoid of revolution

3456-538: The meridian arc between two given latitudes is given by replacing the limits of the integral by the latitudes concerned. The length of a small meridian arc is given by When the latitude difference is 1 degree, corresponding to ⁠ π / 180 ⁠ radians, the arc distance is about The distance in metres (correct to 0.01 metre) between latitudes ϕ {\displaystyle \phi }  − 0.5 degrees and ϕ {\displaystyle \phi }  + 0.5 degrees on

3528-418: The ordinary longitude because of vertical deflection , small variations in Earth's gravitational field (see astronomical latitude ). The concept of longitude was first developed by ancient Greek astronomers. Hipparchus (2nd century BCE) used a coordinate system that assumed a spherical Earth, and divided it into 360° as we still do today. His prime meridian passed through Alexandria . He also proposed

3600-463: The polar circles is its complement (90° - i ). The axis of rotation varies slowly over time and the values given here are those for the current epoch . The time variation is discussed more fully in the article on axial tilt . The figure shows the geometry of a cross-section of the plane perpendicular to the ecliptic and through the centres of the Earth and the Sun at the December solstice when

3672-454: The radius of a circle of latitude. For a sphere of radius a that radius at latitude φ is a cos φ , and the length of a one-degree (or ⁠ π / 180 ⁠ radian ) arc along a circle of latitude is When the Earth is modelled by an ellipsoid this arc length becomes where e , the eccentricity of the ellipsoid, is related to the major and minor axes (the equatorial and polar radii respectively) by An alternative formula

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3744-509: The reference ellipsoid to the plane or in calculations of geodesics on the ellipsoid. Their numerical values are not of interest. For example, no one would need to calculate the authalic latitude of the Eiffel Tower. The expressions below give the auxiliary latitudes in terms of the geodetic latitude, the semi-major axis, a , and the eccentricity, e . (For inverses see below .) The forms given are, apart from notational variants, those in

3816-673: The reference on maps, since this island was considered the most western position of the Old World . Flores Island lies further west, but the Azores were not discovered by Europeans until the early 15th century, and their identification as part of the Old World is uncertain. It was thought to be exactly 20 degrees west of the Paris meridian , so indeed the exact position of Ferro was never considered. Old maps (outside of Anglo-America) often have

3888-417: The rotation of an ellipse about its shorter axis (minor axis). "Oblate ellipsoid of revolution" is abbreviated to 'ellipsoid' in the remainder of this article. (Ellipsoids which do not have an axis of symmetry are termed triaxial .) Many different reference ellipsoids have been used in the history of geodesy . In pre-satellite days they were devised to give a good fit to the geoid over the limited area of

3960-414: The same circle of latitude, measured along that circle of latitude, is slightly more than the shortest ( geodesic ) distance between those points (unless on the equator, where these are equal); the difference is less than 0.6 m (2 ft). A geographical mile is defined to be the length of one minute of arc along the equator (one equatorial minute of longitude) therefore a degree of longitude along

4032-428: The sea. See also the equation of time for details on the differences. With the exception of magnetic declination, all proved practicable methods. Developments on land and sea, however, were very different. Several newer methods for navigation, location finding, and the determination of longitude exist. Radio navigation , satellite navigation , and Inertial navigation systems , along with celestial navigation , are

4104-568: The second in Jamaica on 29 February 1504 (fourth voyage). It is assumed that he used astronomical tables for reference. His determinations of longitude showed large errors of 13° and 38° W respectively. Randles (1985) documents longitude measurement by the Portuguese and Spanish between 1514 and 1627 both in the Americas and Asia. Errors ranged from 2° to 25°. The telescope was invented in

4176-473: The seconds are specified with a decimal fraction . An alternative representation uses degrees and minutes, and parts of a minute are expressed in decimal notation, thus: 23° 27.5′ E. Degrees may also be expressed as a decimal fraction: 23.45833° E. For calculations, the angular measure may be converted to radians , so longitude may also be expressed in this manner as a signed fraction of π ( pi ), or an unsigned fraction of 2 π . For calculations,

4248-468: The semi-major axis and the inverse flattening, ⁠ 1 / f ⁠ . For example, the defining values for the WGS84 ellipsoid, used by all GPS devices, are from which are derived The difference between the semi-major and semi-minor axes is about 21 km (13 miles) and as fraction of the semi-major axis it equals the flattening; on a computer monitor the ellipsoid could be sized as 300 by 299 pixels. This would barely be distinguishable from

4320-494: The specification of the ISO 19111 standard. Since there are many different reference ellipsoids , the precise latitude of a feature on the surface is not unique: this is stressed in the ISO standard which states that "without the full specification of the coordinate reference system, coordinates (that is latitude and longitude) are ambiguous at best and meaningless at worst". This is of great importance in accurate applications, such as

4392-420: The sphere is 111.2 km (69.1 statute miles) (60.0 nautical miles). The length of one minute of latitude is 1.853 km (1.151 statute miles) (1.00 nautical miles), while the length of 1 second of latitude is 30.8 m or 101 feet (see nautical mile ). In Meridian arc and standard texts it is shown that the distance along a meridian from latitude ϕ to the equator is given by ( ϕ in radians) where M ( ϕ )

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4464-403: The squared eccentricity as 0.0067 (it depends on the choice of ellipsoid) the maximum difference of ϕ − θ {\displaystyle \phi {-}\theta } may be shown to be about 11.5 minutes of arc at a geodetic latitude of approximately 45° 6′. The parametric latitude or reduced latitude , β , is defined by the radius drawn from the centre of

4536-458: The standard reference for map projections, namely "Map projections: a working manual" by J. P. Snyder. Derivations of these expressions may be found in Adams and online publications by Osborne and Rapp. The geocentric latitude is the angle between the equatorial plane and the radius from the centre to a point of interest. When the point is on the surface of the ellipsoid, the relation between

4608-472: The study of geodesy, geophysics and map projections but they can all be expressed in terms of one or two members of the set a , b , f and e . Both f and e are small and often appear in series expansions in calculations; they are of the order ⁠ 1 / 298 ⁠ and 0.0818 respectively. Values for a number of ellipsoids are given in Figure of the Earth . Reference ellipsoids are usually defined by

4680-585: The surface at a great circle called the Equator . Planes parallel to the equatorial plane intersect the surface in circles of constant latitude; these are the parallels. The Equator has a latitude of 0°, the North Pole has a latitude of 90° North (written 90° N or +90°), and the South Pole has a latitude of 90° South (written 90° S or −90°). The latitude of an arbitrary point is the angle between

4752-407: The theory of map projections: The definitions given in this section all relate to locations on the reference ellipsoid but the first two auxiliary latitudes, like the geodetic latitude, can be extended to define a three-dimensional geographic coordinate system as discussed below . The remaining latitudes are not used in this way; they are used only as intermediate constructs in map projections of

4824-598: The use of ships were transmitted from Halifax, Nova Scotia , starting in 1907 and from the Eiffel Tower in Paris from 1910. These signals allowed navigators to check and adjust their chronometers frequently. Radio navigation systems came into general use after World War II . The systems all depended on transmissions from fixed navigational beacons. A ship-board receiver calculated the vessel's position from these transmissions. They allowed accurate navigation when poor visibility prevented astronomical observations, and became

4896-407: The value of Albrecht was used prior to the switch to the Greenwich prime meridian. The island of El Hierro spans more than a quarter of a degree of longitude, from Ensenada de Juanil at 17° 52ʹ 59ʺ W to Roque del Guincho at 18° 9ʹ 41ʺ W. Longitude Longitude ( / ˈ l ɒ n dʒ ɪ tj uː d / , AU and UK also / ˈ l ɒ ŋ ɡ ɪ -/ ) is a geographic coordinate that specifies

4968-472: The west/east suffix is replaced by a negative sign in the western hemisphere . The international standard convention ( ISO 6709 )—that east is positive—is consistent with a right-handed Cartesian coordinate system , with the North Pole up. A specific longitude may then be combined with a specific latitude (positive in the northern hemisphere ) to give a precise position on the Earth's surface. Confusingly,

5040-685: Was soon in practical use for longitude determination, especially in North America, and over longer and longer distances as the telegraph network expanded, including western Europe with the completion of transatlantic cables. The United States Coast Survey, renamed the United States Coast and Geodetic Survey in 1878, was particularly active in this development, and not just in the United States. The Survey established chains of mapped locations through Central and South America, and

5112-569: Was supported and rewarded with thousands of pounds from the Board of Longitude, but he fought to receive money up to the top reward of £20,000, finally receiving an additional payment in 1773 after the intervention of parliament. It was some while before either method became widely used in navigation. In the early years, chronometers were very expensive, and the calculations required for lunar distances were still complex and time-consuming. Lunar distances came into general use after 1790. Chronometers had

5184-483: Was the need of a navigator for immediate results. The second 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. In response to the problems of navigation, a number of European maritime powers offered prizes for a method to determine longitude at sea. The best-known of these is the Longitude Act passed by

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