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154-662: Farthest South refers to the most southerly latitudes reached by explorers before the first successful expedition to the South Pole in 1911. Significant steps on the road to the pole were the discovery of lands south of Cape Horn in 1619, Captain James Cook 's crossing of the Antarctic Circle in 1773, and the earliest confirmed sightings of the Antarctic mainland in 1820. From the late 19th century onward,

308-484: A geographic coordinate system as defined in 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

462-560: 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

616-527: A British naval officer, his contribution to Antarctic knowledge might have been better received, but "a Norwegian seaman/schoolmaster was never going to be taken seriously". The Discovery Expedition of 1901–1904 was Robert Falcon Scott 's first Antarctic command. Although according to Edward Wilson the intention was to "reach the Pole if possible, or find some new land", there is nothing in Scott's writings, nor in

770-517: A Fiji heavily indebted to foreign creditors to the United Kingdom. It became independent on 10 October 1970 and a republic on 28 September 1987. Fiji is classified as Melanesian and (less commonly) Polynesian. Beginning in the late 13th and early 14th centuries, Polynesians began to migrate in waves to New Zealand via their canoes , settling on both the North and South islands as well as

924-647: A Polynesian settlement dating back to the 13th century on Enderby Island in the Auckland Islands . According to ancient legends, around the year 650 the Polynesian traveller Ui-te-Rangiora led a fleet of Waka Tīwai south until they reached "a place of bitter cold where rock-like structures rose from a solid sea". It is unclear from the legends how far south Ui-te-Rangiora penetrated, but it appears that he observed ice in large quantities. A shard of undated, unidentified pottery, reported as found in 1886 in

1078-682: A Treaty of Friendship on 18 May 1900, when European settlers and rival Tongan chiefs tried to oust the second king. Within the British Empire , which posted no higher permanent representative on Tonga than a British Consul (1901–1970), Tonga formed part of the British Western Pacific Territories (under a High Commissioner who residing in Fiji ) from 1901 until 1952. Despite being under the protectorate, Tonga retained its monarchy without interruption. On June 4, 1970,

1232-701: A change in the movements of the Pacific Plate in relation to the Indo-Australian Plate . The Pacific plate had previously been subducted under the Australian Plate . When that changed, it had the effect of uplifting the portion of the continent that is modern-day New Zealand. The convergent plate boundary that runs northwards from New Zealand's North Island is called the Kermadec-Tonga subduction zone . This subduction zone

1386-499: A hint of the fertile continent which some still hoped lay in the south. Cook wrote that if any such continent existed it would be "a country doomed by nature", and that "no man will venture further than I have done, and the land to the South will never be explored". He concluded: "Should the impossible be achieved and the land attained, it would be wholly useless and of no benefit to the discoverer or his nation". Despite Cook's prediction,

1540-643: A longitude close to that in which Cook had made his record 47 years earlier. In 1821, the American sealing captain John Davis led a party which landed on an uncharted stretch of land beyond the South Shetlands. "I think this Southern Land to be a Continent", he wrote in his ship's log. If his landing was not on an island, his party were the first to set foot on the Antarctic continent. James Weddell

1694-543: A margin "caused some raised eyebrows", but was soon accepted. In November 1823, the American sealing captain Benjamin Morrell reached the South Sandwich Islands in the schooner Wasp . According to his own later account he then sailed south, unconsciously following the track taken by James Weddell a month previously. Morrell claimed to have reached 70°14'S, at which point he turned north because

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1848-547: A member of a party that had reached the location of the North Magnetic Pole , and he was an obvious choice as commander. The expedition left England on 30 September 1839, and after a voyage that was slowed by the many stops required to carry out work on magnetism, it reached Tasmania in August 1840. Following a three-month break imposed by the southern winter, they sailed south-east on 12 November 1840, and crossed

2002-563: A non- Polynesian language . Some of the Lau Islands to the southeast of Fiji have strong historic and cultural links with Tonga. However, in essence, Polynesia remains a cultural term referring to one of the three parts of Oceania (the others being Melanesia and Micronesia ). The following islands and island groups are either nations or overseas territories of former colonial powers. The residents are native Polynesians or contain archaeological evidence indicating Polynesian settlement in

2156-514: A possibility that the early Lapita Austronesians were direct descendants of the early colonists of the Marianas (which preceded them by about 150 years), which is also supported by pottery evidence. The most eastern site for Lapita archaeological remains recovered so far is at Mulifanua on Upolu . The Mulifanua site, where 4,288 pottery shards have been found and studied, has a "true" age of c.  1000 BC based on radiocarbon dating and

2310-642: A reasonable doubt. The impetus for what would become known as the Heroic Age of Antarctic Exploration came in 1895, when in an address to the Sixth International Geographical Congress in London, Professor Sir John Murray called for a resumption of Antarctic exploration: "a steady, continuous, laborious and systematic exploration of the whole southern region". He followed this call with an appeal to British patriotism: "Is

2464-733: A region within Polynesia and the categorization of these language groups by Green in 1966 helped to confirm that Polynesian settlement generally took place from west to east. There is a very distinct "East Polynesian" subgroup with many shared innovations not seen in other Polynesian languages. The Marquesas dialects are perhaps the source of the oldest Hawaiian speech which is overlaid by Tahitian-variety speech, as Hawaiian oral histories would suggest. The earliest varieties of New Zealand Maori speech may have had multiple sources from around central Eastern Polynesia, as Maori oral histories would suggest. The Cook Islands are made up of 15 islands comprising

2618-662: A subset of the sea-migrating Austronesian people . Tracing Polynesian languages places their prehistoric origins in Island Melanesia , Maritime Southeast Asia , and ultimately, in Taiwan . Between about 3000 and 1000 BC, speakers of Austronesian languages spread from Taiwan into Maritime Southeast Asia . There are three theories regarding the spread of humans across the Pacific to Polynesia. These are outlined well by Kayser et al. (2000) and are as follows: In

2772-538: A suitable anchorage that would have allowed the ships to over-winter, so he returned to Tasmania, arriving there in April 1841. The following season Ross returned and located an inlet in the Barrier face that enabled him, on 23 February 1842, to extend his Farthest South to 78°09'30"S, a record which would remain unchallenged for 58 years. Although Ross had not been able to land on the Antarctic continent, nor approach

2926-495: 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

3080-555: 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

3234-629: A widespread Polynesian network or confederacy (or "empire") that was prehistorically ruled by the successive Tui Manuʻa dynasties. Manuan genealogies and religious oral literature also suggest that the Tui Manuʻa had long been one of the most prestigious and powerful paramount of Samoa. Oral history suggests that the Tui Manuʻa kings governed a confederacy of far-flung islands which included Fiji , Tonga as well as smaller western Pacific chiefdoms and Polynesian outliers such as Uvea , Futuna , Tokelau , and Tuvalu . Commerce and exchange routes between

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3388-457: Is a subregion of Oceania , made up of more than 1,000 islands scattered over the central and southern Pacific Ocean . The indigenous people who inhabit the islands of Polynesia are called Polynesians . They have many things in common, including linguistic relations , cultural practices , and traditional beliefs . In centuries past, they had a strong shared tradition of sailing and using stars to navigate at night. The term Polynésie

3542-411: 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

3696-663: Is associated with the volcanism that gave rise to the Kermadec and Tongan islands. There is a transform fault that currently traverses New Zealand's South Island, known as the Alpine Fault . Zealandia's continental shelf has a total area of approximately 3,600,000 km (1,400,000 sq mi). The oldest rocks in Polynesia are found in New Zealand and are believed to be about 510 million years old. The oldest Polynesian rocks outside Zealandia are to be found in

3850-416: Is considered to have lasted roughly 1,000 years. The cause of this gap in voyaging is contentious among archaeologists with a number of competing theories presented including climate shifts, the need for the development of new voyaging techniques, and cultural shifts. After the long pause, dispersion of populations into central and eastern Polynesia began. Although the exact timing of when each island group

4004-409: Is derived. This is due to new population being established by a very small number of individuals from a larger population which also causes a loss of genetic variation. Atholl Anderson wrote that analysis of mitochondrial DNA (mtDNA, female) and Y chromosome (male) concluded that the ancestors of Polynesian women were Austronesians while those of Polynesian men were Papuans . Subsequently, it

4158-484: 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

4312-453: Is determined with the meridian altitude method. More precise measurement of latitude requires an understanding of 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

4466-746: Is no main island to be seen to the southwards but that the Atlantic Ocean and the South Sea meet." This open sea south of Cape Horn became known as the Drake Passage even though Drake himself did not traverse it. On 14 June 1615, Willem Schouten, with two ships Eendracht and Hoorn , set sail from Texel in the Netherlands in search of a western route to the Pacific. Hoorn was lost in a fire, but Eendracht continued southward. On 29 January 1616, Schouten reached what he discerned to be

4620-466: Is of great importance in accurate applications, such as 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

4774-451: Is the angle between 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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4928-469: Is the marker of Austronesian expansions. The high frequencies of mtDNA Haplogroup B in the Polynesians are the result of founder effect and represents the descendants of a few Austronesian females who intermixed with Papuan males. A genomic analysis of modern populations in Polynesia, published in 2021, provides a model of the direction and timing of Polynesian migrations from Samoa to the islands to

5082-421: 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

5236-639: Is the oldest site yet discovered in Polynesia. This is mirrored by a 2010 study also placing the beginning of the human archaeological sequences of Polynesia in Tonga at 900 BC. Within a mere three or four centuries, between 1300 and 900 BC, the Lapita archaeological culture spread 6,000 km further to the east from the Bismarck Archipelago, until reaching as far as Fiji , Tonga , and Samoa . A cultural divide began to develop between Fiji to

5390-912: Is thought that the Cook Islands were settled in two periods: the Tahitian Period, when the country was settled between 900 and 1300 AD, and the Maui Settlement, which occurred in 1600 AD, when a large contingent from Tahiti settled in Rarotonga, in the Takitumu district. The first contact between Europeans and the native inhabitants of the Cook Islands took place in 1595 with the arrival of Spanish explorer Álvaro de Mendaña in Pukapuka , who called it San Bernardo (Saint Bernard). A decade later, navigator Pedro Fernández de Quirós made

5544-522: 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

5698-570: The Antarctic Circle on 1 January 1841. On 11 January, a long mountainous coastline that stretched to the south was sighted. Ross named the land Victoria Land , and the mountains the Admiralty Range . He followed the coast southwards and passed Weddell's Farthest South point of 74°15'S on 23 January. A few days later, as they moved further eastward to avoid shore ice, they were met by the sight of twin volcanoes (one of them active), which were named Mount Erebus and Mount Terror , in honour of

5852-684: The Antipodes Islands , has been associated with this expedition. Although Portuguese by birth, Ferdinand Magellan transferred his allegiance to King Charles I of Spain , on whose behalf he left Seville on 10 August 1519, with a squadron of five ships, in search of a western route to the Spice Islands in the East Indies . Success depended on finding a strait or passage through the South American land masses, or finding

6006-681: The Atlantic Ocean and allocated all trade routes to the east of the line to Portugal. That gave Portugal dominance of the only known route to the east–via the Cape of Good Hope and Indian Ocean , which left Spain, and later other countries, to seek a western route to the Pacific . The exploration of the south began as part of the search for such a route. Unlike the Arctic , there is no evidence of human visitation or habitation in ' Antarctica ' or

6160-666: The British Crown in 1836. In 1840, Royal Navy officer William Hobson and several Māori chiefs signed the Treaty of Waitangi , which transformed New Zealand into a colony of the British Empire and granting all Māori the status of British subjects. However, tensions between Pākehā settlers and the Māori over settler encroachment on Māori lands and disputes over land sales led to the New Zealand Wars (1845–1872) between

6314-597: The Chatham Islands . Over the course of several centuries, the Polynesian settlers formed distinct cultures that became known as the Māori on the New Zealand mainland, while those who settled in the Chatham Islands became the Moriori people . Beginning the 17th century, the arrival of Europeans to New Zealand drastically impacted Māori culture. Settlers from Europe (known as " Pākehā ") began to colonize New Zealand in

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6468-769: The German Empire and the United States. The German-controlled Western portion of Samoa (consisting of the bulk of Samoan territory – Savaiʻi, Apolima, Manono and Upolu) was occupied by New Zealand in WWI, and administered by it under a Class C League of Nations mandate . After repeated efforts by the Samoan independence movement, the New Zealand Western Samoa Act of 24 November 1961 granted Samoa independence, effective on January 1, 1962, upon which

6622-563: The Kingdom of Tonga became independent from the British Empire. The reef islands and atolls of Tuvalu are identified as being part of West Polynesia. During pre-European-contact times there was frequent canoe voyaging between the islands as Polynesian navigation skills are recognised to have allowed deliberate journeys on double-hull sailing canoes or outrigger canoes . Eight of the nine islands of Tuvalu were inhabited; thus

6776-615: The Magellan Strait to a point where the crew thought they saw a headland, and water beyond it, which indicated the southern extremity of the continent. There is speculation as to which headland they saw; conceivably it was Cape Horn . In parts of the Spanish-speaking world it is believed that de Hoces may have discovered the strait later known as the Drake Passage more than 50 years before Sir Francis Drake,

6930-593: The Solomon Islands . The Tongan influence brought Polynesian customs and language throughout most of Polynesia. The empire began to decline in the 13th century. After a bloody civil war, political power in Tonga eventually fell under the Tuʻi Kanokupolu dynasty in the 16th century. In 1845, the ambitious young warrior, strategist, and orator Tāufaʻāhau united Tonga into a more Western-style kingdom. He held

7084-460: The Tovata confederacy of Fiji. This is where most Fijian-Polynesian linguistic interactions occurred. In the chronology of the exploration and first populating of Polynesia, there is a gap commonly referred to as the long pause between the first populating of Fiji ( Melanesia ), Western Polynesia of Tonga and Samoa among others and the settlement of the rest of the region. In general this gap

7238-525: The colonial government and the Māori. In response to the conflict, the colonial government initiated a series of land confiscations from the Māori. This social upheaval, combined with epidemics of infectious diseases from Europe, devastated both the Māori population and their social standing in New Zealand. In the 20th and 21st centuries, the Maori population began to recover, and efforts were made to redress social, economic, political and economic issues facing

7392-580: 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

7546-453: The ' Australo-Papuans ' of New Guinea and the Solomon Islands . The preliminary analysis of skulls found at the Teouma and Talasiu Lapita sites is that they lack Australian or Papuan affinities and instead have affinities to mainland Asian populations. A 2017 DNA analysis of modern Polynesians indicates that there has been intermarriage resulting in a mixed Austronesian-Papuan ancestry of

7700-526: The 19th century, leading to tension with the indigenous Māori. On October 28, 1835, a group of Māori tribesmen issued a declaration of independence (drafted by Scottish businessman James Busby ) as the " United Tribes of New Zealand ", in order to resist potential efforts at colonizing New Zealand by the French and prevent merchant ships and their cargo which belonged to Māori merchants from being seized at foreign ports. The new state received recognition from

7854-472: The Antarctic, led by Henryk Bull . In January 1895 Borchgrevink was one of a group from that expedition that claimed the first confirmed landing on the Antarctic continent, at Cape Adare . Borchgrevink determined to return with his own expedition, which would overwinter and explore inland, with the location of the South Magnetic Pole as an objective. Borchgrevink then went to England, where he

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8008-520: The Bismarck Archipelago. The modern Polynesians still show human genetic results of a Melanesian culture which allowed indigenous men, but not women, to "marry in" – useful evidence for matrilocality. Although matrilocality and matrilineality receded at some early time, Polynesians and most other Austronesian speakers in the Pacific Islands were and are still highly "matricentric" in their traditional jurisprudence. The Lapita pottery for which

8162-570: The British privateer . Sir Francis Drake sailed from Plymouth on 15 November 1577, in command of a fleet of five ships under his flagship Pelican , later renamed the Golden Hinde . His principal objective was plunder, not exploration; his initial targets were the unfortified Spanish towns on the Pacific coasts of Chile and Peru. Following Magellan's route, Drake reached Puerto San Julian on 20 June. After nearly two months in harbour, Drake left

8316-542: The Drake Passage. The next recorded navigation of the Drake Passage was achieved in February 1619, by the brothers Bartolome and Gonzalo Garcia de Nodal. The Garcia de Nodal expedition discovered a small group of islands about 60 nautical miles (100 km; 70 mi) south-west of Cape Horn, at latitude 56°30'S. They named these the Diego Ramirez Islands after the expedition's pilot. The islands remained

8470-467: The Earth had been broadly mapped, the lure for mercantile adventurers was the great fertile continent of " Terra Australis " which, according to myth, lay hidden in the south. Belief in the existence of this supposed land of plenty persisted well into the 18th century; explorers were reluctant to accept the truth that slowly emerged, of a cold, harsh environment in the lands of the Southern Ocean . James Cook's voyages of 1772–1775 demonstrated conclusively

8624-401: 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

8778-534: The Frenchman Jean-Baptiste Bouvet de Lozier discovered the remote Bouvet Island , and in 1772, his compatriot, Yves-Joseph de Kerguelen de Trémarec , found the Kerguelen Islands . The second of James Cook 's historic voyages, 1772–1775, was primarily a search for the elusive Terra Australis Incognita that was still believed to lie somewhere in the unexplored latitudes below 40°S . Cook left England in September 1772 with two ships, HMS Resolution and HMS Adventure . After pausing at Cape Town, on 22 November

8932-409: The Hawaiian Emperor Seamount Chain and are 80 million years old. Polynesia is generally defined as the islands within the Polynesian Triangle , although some islands inhabited by Polynesians are situated outside the Polynesian Triangle. Geographically, the Polynesian Triangle is drawn by connecting the points of Hawaii , New Zealand , and Easter Island . The other main island groups located within

9086-525: The Kingdom of Fiji by 1871. In around 1855 a Tongan prince, Enele Ma'afu , proclaimed the Lau islands as his kingdom, and took the title Tui Lau . Fiji had been ruled by numerous divided chieftains until Cakobau unified the landmass. The Lapita culture, the ancestors of the Polynesians, existed in Fiji from about 3500 BC until they were displaced by the Melanesians about a thousand years later. (Both Samoans and subsequent Polynesian cultures adopted Melanesian painting and tattoo methods.) In 1873, Cakobau ceded

9240-482: The Māori in wider New Zealand society. Beginning in the 1960s, a protest movement emerged seeking redress for historical grievances . In the 2013 New Zealand census , roughly 600,000 people in New Zealand identified as being Māori. In the 9th century, the Tui Manuʻa controlled a vast maritime empire comprising most of the settled islands of Polynesia. The Tui Manuʻa is one of the oldest Samoan titles in Samoa. Traditional oral literature of Samoa and Manu'a talks of

9394-410: The Nimrod Expedition, 1907–1909. This was the first expedition to set the definite objective of reaching the South Pole, and to have a specific strategy for doing so. To assist his endeavour, Shackleton adopted a mixed transport strategy, involving the use of Manchurian ponies as pack animals, as well as the more traditional dog-sledges. A specially adapted motor car was also taken. Although the dogs and

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9548-399: The Northern and Southern groups. The islands are spread out across many kilometers of a vast ocean. The largest of these islands is called Rarotonga, which is also the political and economic capital of the nation. The Cook Islands were formerly known as the Hervey Islands, but this name refers only to the Northern Groups. It is unknown when this name was changed to reflect the current name. It

9702-401: The Norwegian explorer Roald Amundsen , who had been developing plans for a North Pole expedition, changed his mind when, in September 1909, the North Pole was claimed in quick succession by the Americans Frederick Cook and Robert Peary . Amundsen resolved to go south instead. Amundsen concealed his revised intentions until his ship, Fram , was in the Atlantic and beyond communication. Scott

9856-457: The Polynesian Triangle are Samoa , Tonga , the Cook Islands , Tuvalu , Tokelau , Niue , Wallis and Futuna , and French Polynesia . Also, small Polynesian settlements are in Papua New Guinea , the Solomon Islands , the Caroline Islands , and Vanuatu . An island group with strong Polynesian cultural traits outside of this great triangle is Rotuma , situated north of Fiji . The people of Rotuma have many common Polynesian traits, but speak

10010-419: The Polynesians (as with other modern Austronesians, with the exception of Taiwanese aborigines ). Research at the Teouma and Talasiu Lapita sites implies that the migration and intermarriage, which resulted in the mixed Austronesian-Papuan ancestry of the Polynesians, occurred after the first initial migration to Vanuatu and Tonga. A complete mtDNA and genome-wide SNP comparison (Pugach et al. , 2021) of

10164-422: The Russian captain Fabian von Bellingshausen , in another Antarctic sector, had come within sight of the coast of what is now known as Queen Maud Land . He is thus credited as the first person to see the continent's mainland, although he did not make this claim himself. Bellingshausen made two circumnavigations mainly in latitudes between 60 and 67°S, and in January 1821, reached his most southerly point at 70°S, in

10318-404: The South Sea Islands because of their relative proximity to the southern Pacific islands, even though they are in fact located in the North Pacific . Another term in use, which avoids this inconsistency, is "the Polynesian Triangle " (from the shape created by the layout of the islands in the Pacific Ocean). This term makes clear that the grouping includes the Hawaiian Islands, which are located at

10472-575: The Spanish ship Aurora in 1762. He failed to discover this non-existent land, but his sealing activities showed a handsome profit. In 1822, Weddell, again in command of Jane and this time accompanied by a smaller ship, the cutter Beaufoy , set sail for the south with instructions from his employers that, should the sealing prove barren, he was to "investigate beyond the track of former navigators". This suited Weddell's exploring instincts, and he equipped his vessel with chronometers, thermometers, compasses, barometers and charts. In January 1823 he probed

10626-406: 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

10780-443: The Teouma Lapita site ( Efate Island , Vanuatu ) and the Talasiu Lapita site (near Nuku'alofa , Tonga ) published in 2016 supports the Express Train model; although with the qualification that the migration bypassed New Guinea and Island Melanesia . The conclusion from research published in 2016 is that the initial population of those two sites appears to come directly from Taiwan or the northern Philippines and did not mix with

10934-427: The Trusteeship Agreement terminated. The new Independent State of Samoa was not a monarchy, though the Malietoa titleholder remained very influential. It effectively ended however with the death of Malietoa Tanumafili II , the country's head of state, on May 11, 2007. In the 10th century, the Tuʻi Tonga Empire was established in Tonga, and most of the Western Pacific came within its sphere of influence, up to parts of

11088-571: 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

11242-581: The anchorage was 57°S . However, there is no island at that latitude. The as yet undiscovered Diego Ramírez Islands , at 56°30'S, are treeless and cannot have been the islands where Drake's crew collected wood. This indicates that the navigational calculation was faulty, and that Drake landed at or near the then unnamed Cape Horn , possibly on Horn Island itself. His final southern latitude can only be speculated as that of Cape Horn, at 55°59'S. In his report, Drake wrote: "The Uttermost Cape or headland of all these islands stands near 56 degrees, without which there

11396-425: 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

11550-900: The archaeological record, there are well-defined traces of this expansion which allow the path it took to be followed and dated with some certainty. It is thought that by roughly 1400 BC, " Lapita peoples", so-named after their pottery tradition, appeared in the Bismarck Archipelago of northwest Melanesia . This culture is seen as having adapted and evolved through time and space since its emergence "Out of Taiwan ". They had given up rice production, for instance, which required paddy field agriculture unsuitable for small islands. However, they still cultivated other ancestral Austronesian staple cultigens like Dioscorea yams and taro (the latter are still grown with smaller-scale paddy field technology), as well as adopting new ones like breadfruit and sweet potato . The results of research at

11704-401: The artifacts—two arrowheads—were later found to have been planted, possibly to reinforce Chilean claims to the area. While the natives of Tierra del Fuego were not capable of true oceanic travel, there is some evidence of Polynesian visits to some of the sub antarctic islands to the south of New Zealand , although these are further from Antarctica than South America. There are also remains of

11858-504: The car were used during the expedition for a number of purposes, the task of assisting the group that would undertake the march to the pole fell to the ponies. The size of Shackleton's four-man polar party was dictated by the number of surviving ponies; of the ten that were embarked in New Zealand, only four had survived the 1908 winter. Ernest Shackleton and three companions ( Frank Wild , Eric Marshall and Jameson Adams ) began their march on 29 October 1908. On 26 November, they surpassed

12012-580: The centre of the Earth and perpendicular to the rotation axis intersects 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

12166-426: The chiefly title of Tuʻi Kanokupolu, but had been baptised with the name Jiaoji ("George") in 1831. In 1875, with the help of the missionary Shirley Waldemar Baker , he declared Tonga a constitutional monarchy, formally adopted the western royal style, emancipated the "serfs", enshrined a code of law, land tenure, and freedom of the press, and limited the power of the chiefs. Tonga became a British protectorate under

12320-408: 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

12474-550: The days of Ross. A party consisting of Borchgrevink, William Colbeck and a Sami named Per Savio landed with sledges and dogs. This party ascended the Barrier and made the first sledge journey on the barrier surface; on 16 February 1900 they extended the Farthest South record to 78°50'S. On its return to England later in 1900, Borchgrevink's expedition was received without enthusiasm, despite its new southern record. Historian David Crane commented that if Borchgrevink had been

12628-401: The decline of the Tui Manuʻa's power, with the western isles of Savaiʻi and Upolu rising to prominence in the post-Tongan occupation period and the establishment of the tafaʻifa system that dominated Samoan politics well into the 20th century. This was disrupted in the early 1900s due to colonial intervention, with east–west division by Tripartite Convention (1899) and subsequent annexation by

12782-529: 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 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

12936-549: The early 19th century saw numerous attempts to penetrate southward, and to discover new lands. In 1819, William Smith , in command of the brigantine Williams , discovered the South Shetland Islands , and in the following year Edward Bransfield , in the same ship, sighted the Trinity Peninsula at the northern extremity of Graham Land . A few days before Bransfield's discovery, on 27 January 1820,

13090-608: The east. This model presents consistencies and inconsistencies with models of Polynesian migration that are based on archaeology and linguistic analysis. The 2021 genomic model presents a migration pathway from Samoa to the Cook Islands (Rarotonga), then to the Society Islands (Tōtaiete mā) in the 11th century AD, the western Austral Islands (Tuha'a Pae) and the Tuāmotu Archipelago in the 12th century AD, with

13244-402: 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 ) ,

13398-517: The equator. For navigational purposes positions are given in degrees and decimal minutes. For instance, The Needles lighthouse 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

13552-608: The expedition ship Southern Cross left London for the Ross Sea , reaching Cape Adare on 17 February 1899. Here a shore party was landed and was the first to over-winter on the Antarctic mainland, in a prefabricated hut. In January 1900, Southern Cross returned, picked up the shore party and, following the route which Ross had taken 60 years previously, sailed southward to the Great Ice Barrier, which they discovered had retreated some 30 miles (48 km) south since

13706-414: The expedition's ships. The Great Ice Barrier (later to be called the "Ross Ice Shelf") stretched away east of these mountains, forming an impassable obstacle to further southward progress. In his search for a strait or inlet, Ross explored 300 nautical miles (560 km; 350 mi) along the edge of the barrier, and reached an approximate latitude of 78°S on or about 8 February 1841. He failed to find

13860-504: The farthest point reached by Scott's 1902 party. "A day to remember", wrote Shackleton in his journal, noting that they had reached this point in far less time than on the previous march with Scott. Shackleton's group continued southward, discovering and ascending the Beardmore Glacier to the polar plateau, and then marching on to reach their Farthest South point at 88°23'S, a mere 97 nautical miles (180 km; 112 mi) from

14014-595: The farthest southern penetration by man; the position was north of the Tierra del Fuego archipelago, where there is evidence of human settlement dating back thousands of years. The first sighting of an ocean passage to the Pacific south of Tierra del Fuego is sometimes attributed to Francisco de Hoces of the Loaisa Expedition . In January 1526, his ship San Lesmes was blown south from the Atlantic entrance of

14168-424: The first European landing in the islands when he set foot on Rakahanga in 1606, calling it Gente Hermosa (Beautiful People). Cook Islanders are ethnically Polynesians or Eastern Polynesia. They are culturally associated with Tahiti, Eastern Islands, NZ Maori and Hawaii. The Lau Islands were subject to periods of Tongan rulership and then Fijian control until their eventual conquest by Seru Epenisa Cakobau of

14322-407: The first party to reach the pole overland since Scott. Latitude On its own, the term "latitude" normally refers to the geodetic latitude as defined below. Briefly, 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

14476-402: The first ships to do so. Further progress was barred by ice, and the ships turned north-eastwards and headed for New Zealand, which they reached on 26 March. During the ensuing months, the expedition explored the southern Pacific Ocean before Cook took Resolution south again— Adventure had retired back to South Africa after a confrontation with the New Zealand native population. This time Cook

14630-438: The following sections. Lines of constant latitude and longitude together constitute 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

14784-524: The following years gave particular weight to the achievement of new Farthest South records, and began to develop the character of a race for the South Pole. The Norwegian-born Carsten Egeberg Borchgrevink had emigrated to Australia in 1888, where he worked on survey teams in Queensland and New South Wales before accepting a school teaching post. In 1894 he joined a sealing and whaling expedition to

14938-559: The general archaeological complex of the earliest "Oceanic" Austronesian speakers in the Pacific Islands are named also lapsed in Western Polynesia. Language, social life and material culture were very distinctly "Polynesian" by 1000 BC. Early European observers detected theocratic elements in traditional Polynesian government. Linguistically, there are five sub-groups of the Polynesian language group . Each represents

15092-399: 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

15246-481: The initial settlement of individual islands; although Professor Matisoo-Smith of the Otago study said that the founding Māori population of New Zealand must have been in the hundreds, much larger than previously thought. The Polynesian population experienced a founder effect and genetic drift. The Polynesian may be distinctively different both genotypically and phenotypically from the parent population from which it

15400-647: The islands around it prior to European exploration . However, the most southerly parts of South America were already inhabited by tribes such as the Selk'nam/Ona , the Yagán/Yámana , the Alacaluf and the Haush . The Haush in particular made regular trips to Isla de los Estados , which was 29 kilometres (18 mi) from the main island of Tierra del Fuego , suggesting that some of them may have been capable of reaching

15554-549: The islands near Cape Horn . Fuegian Indian artefacts and canoe remnants have also been discovered on the Falkland Islands , suggesting the capacity for even longer sea journeys. Chilean scientists have claimed that Amerinds visited the South Shetland Islands , due to stone artifacts recovered from bottom-sampling operations in Admiralty Bay , King George Island , and Discovery Bay, Greenwich Island ; however,

15708-655: The known route to the polar plateau via the Beardmore Glacier, Amundsen led his party of five due south, reaching the Transantarctic Mountains on 16 November. They discovered the Axel Heiberg Glacier , which provided them with a direct route to the polar plateau and on to the pole. Shackleton's Farthest South mark was passed on 7 December, and the South Pole was reached on 14 December 1911. The Norwegian party's greater skills with

15862-494: The last great piece of maritime exploration on the surface of our Earth to be undertaken by Britons, or is it to be left to those who may be destined to succeed or supplant us on the Ocean?" During the following quarter-century, fifteen expeditions from eight different nations rose to this challenge. In the patriotic spirit engendered by Murray's call, and under the influence of RGS president Sir Clements Markham , British endeavours in

16016-451: 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

16170-442: The likely hostile nature of any hidden lands. This caused a shift of emphasis in the first half of the 19th century, away from trade and towards sealing and whaling, and then exploration and discovery. After the first overwintering on continental Antarctica in 1898–99 ( Adrien de Gerlache ), the prospect of reaching the South Pole appeared realistic, and the race for the pole began. The British were pre-eminent in this endeavour, which

16324-472: The location of the South Magnetic Pole, on his return to England in 1843 he was knighted for his achievements in geographical and scientific exploration. The oceanographic research voyage known as the Challenger Expedition , 1872–1876, explored Antarctic waters for several weeks, but did not approach the land itself; its research, however, proved the existence of an Antarctic continent beyond

16478-538: 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

16632-477: The migrant pathway branching to the north to the Marquesas (Te Henua 'Enana), to Raivavae in the south, and to the easternmost destination on Easter Island (Rapa Nui), which was settled in approximately 1200 AD via Mangareva . The Polynesians were matrilineal and matrilocal Stone Age societies upon their arrival in Tonga , Samoa and the surrounding islands, after having spent at least some time in

16786-647: The most southerly known land on earth until Captain James Cook's discovery of the South Sandwich Islands in 1775. Other voyages brought further discoveries in the southern oceans; in August 1592, the English seaman John Davis had taken shelter "among certain Isles never before discovered"—presumed to be the Falkland Islands . In 1675, the English merchant voyager Anthony de la Roché visited South Georgia (the first Antarctic land discovered); in 1739

16940-484: The northern vertex of the referenced "triangle". Polynesia is characterized by a small amount of land spread over a very large portion of the mid- and southern Pacific Ocean . It comprises approximately 300,000 to 310,000 square kilometres (117,000 to 118,000 sq mi) of land, of which more than 270,000 km (103,000 sq mi) are within New Zealand . The Hawaiian archipelago comprises about half

17094-826: The official objectives of the expedition, to indicate that the pole was a definite goal. However, a southern journey towards the pole was within Scott's formal remit to "explore the ice barrier of Sir James Ross ... and to endeavour to solve the very important physical and geographical questions connected with this remarkable ice formation". The southern journey was undertaken by Scott, Wilson and Ernest Shackleton . The party set out on 1 November 1902 with various teams in support, and one of these, led by Michael Barne , passed Borchgrevink's Farthest South mark on 11 November, an event recorded with great high spirits in Wilson's diary. The march continued, initially in favourable weather conditions, but encountered increasing difficulties caused by

17248-457: The party's lack of ice travelling experience and the loss of all its dogs through a combination of poor diet and overwork. The 80°S mark was passed on 2 December, and four weeks later, on 30 December 1902, Wilson and Scott took a short ski trip from their southern camp to set a new Farthest South at (according to their measurements) 82°17'S. Modern maps, correlated with Shackleton's photograph and Wilson's drawing, put their final camp at 82°6'S, and

17402-688: The past. Some islands of Polynesian origin are outside the general triangle that geographically defines the region. The Line Islands and the Phoenix Islands , most of which are parts of Kiribati , had no permanent settlements until European colonization, but are often considered to be parts of the Polynesian Triangle . Polynesians once inhabited the Auckland Islands , the Kermadec Islands , and Norfolk Island in pre-colonial times, but these islands were uninhabited by

17556-422: The pinnace was lost later. The gales persisted for more than seven weeks. The Golden Hinde was driven far to the west and south, before clawing its way back towards land. On 22 October, the ship anchored off an island which Drake named " Elizabeth Island ", where wood for the galley fires was collected and seals and penguins captured for food. According to Drake's Portuguese pilot, Nuno da Silva, their position at

17710-622: The point are parameterized by Cayley suggested the term parametric latitude because of the form of these equations. The parametric latitude is not used in the theory of map projections. Its most important application is in the theory of ellipsoid geodesics, ( Vincenty , Karney ). The rectifying latitude , μ , is the meridian distance scaled so that its value at the poles is equal to 90 degrees or ⁠ π / 2 ⁠ radians: Polynesia Polynesia ( UK : / ˌ p ɒ l ɪ ˈ n iː z i ə / POL -in- EE -zee-ə , US : /- ˈ n iː ʒ ə / -⁠ EE -zhə )

17864-539: The point reached by Scott and Wilson at 82°11'S, 200 nautical miles (370 km; 230 mi) beyond Borchgrevink's mark. After his share in the Farthest South achievement of the Discovery Expedition, Ernest Shackleton suffered a physical collapse on the return journey, and was sent home with the expedition's relief vessel on orders from Scott; he bitterly resented it, and the two became rivals. Four years later, Shackleton organised his own polar venture,

18018-512: 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

18172-494: The pole in January 1912, the location remained unvisited for nearly 18 years. On 28 November 1929, US Navy Commander (later Rear-Admiral ) Richard E. Byrd and three others completed the first aircraft flight over the South Pole. Twenty-seven years later, Rear-Admiral George J. Dufek became the first person to set foot on the pole since Scott, when on 31 October 1956, he and the crew of R4D-5 Skytrain "Que Sera Sera" landed at

18326-575: The pole, on 9 January 1909. Here, they planted the Union Jack presented to them by Queen Alexandra , and took possession of the plateau in the name of King Edward VII , before shortages of food and supplies forced them to turn back north. This was, at the time, the closest convergence on either pole. The increase of more than six degrees south from Scott's previous record was the greatest extension of Farthest South since Captain Cook's 1773 mark. Shackleton

18480-654: The pole. Between November 1956 and February 1957, the first permanent South Pole research station was erected and christened the Amundsen–Scott South Pole Station in honour of the pioneer explorers. Since then the station had been substantially extended, and in 2008 was housing up to 150 scientific staff and support personnel. Dufek gave considerable assistance to the Commonwealth Trans-Antarctic Expedition , 1955–1958, led by Vivian Fuchs , which on 19 January 1958, became

18634-587: The port with a reduced fleet of three ships and a small pinnace . His ships entered the Magellan Strait on 23 August and emerged in the Pacific Ocean on 6 September. Drake set a course to the north-west, but on the following day, a gale scattered the ships. The Marigold was sunk by a giant wave; the Elizabeth managed to return into the Magellan Strait, later sailing eastwards back to England;

18788-541: The quest for Farthest South latitudes became a race to reach the pole, which culminated in Roald Amundsen 's success in December 1911. In the years before reaching the pole was a realistic objective, other motives drew adventurers southward. Initially, the driving force was the discovery of new trade routes between Europe and the Far East. After such routes had been established and the main geographical features of

18942-509: 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

19096-568: The remainder. Most Polynesian islands and archipelagos , including the Hawaiian Islands and Samoa , are composed of volcanic islands built by hotspots (volcanoes). The other land masses in Polynesia — New Zealand , Norfolk Island , and Ouvéa , the Polynesian outlier near New Caledonia — are the unsubmerged portions of the largely sunken continent of Zealandia . Zealandia is believed to have mostly sunk below sea level 23 million years ago, and recently partially resurfaced due to

19250-554: The remains of early settlers of the Mariana Islands and early Lapita individuals from Vanuatu and Tonga also suggest that both migrations originated directly from the same ancient Austronesian source population from the Philippines . The complete absence of "Papuan" admixture in the early samples indicates that these early voyages bypassed eastern Indonesia and the rest of New Guinea . The authors have also suggested

19404-473: The rotation axis of the Earth. The primary reference points are 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

19558-417: 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

19712-519: 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

19866-604: The ship's stoves were running short of fuel—otherwise, he says, he could have "reached 85° without the least doubt". After turning, he claimed to have encountered land which he described in some detail, and which he named New South Greenland . This land proved not to exist. Morrell's reputation as a liar and a fraud means that most of his geographical claims have been dismissed by scholars, although attempts have been made to rationalise his assertions. James Clark Ross's 1839–1843 Antarctic expedition in HMS Erebus and HMS Terror

20020-414: The southern tip of the continent and sailing around it. The South American coast was sighted on 6 December 1519, and Magellan moved cautiously southward, following the coast to reach latitude 49°S on 31 March 1520. Little if anything was known of the coast south of this point, so Magellan decided to wait out the southern winter here, and established the settlement of Puerto San Julian . In September 1520,

20174-468: The southernmost cape of the South American continent; he named this point Kaap Hoorn (Cape Horn) after his hometown and his lost ship. Schouten's navigational readings are inaccurate—he placed Cape Horn at 57°48' south, when its actual position is 55°58'. His claim to have reached 58° south is unverified, although he sailed on westward to become the first European navigator to reach the Pacific via

20328-420: 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 )

20482-403: 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

20636-458: 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

20790-472: 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

20944-477: The techniques of ice travel, using ski and dogs, had proved decisive in their success. Scott's five-man team reached the same point 33 days later, and perished during their return journey. Since Cook's journeys, every expedition that had held the Farthest South record before Amundsen's conquest had been British; however, the final triumph indisputably belonged to the Norwegians. After Scott's retreat from

21098-407: 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

21252-671: The time European explorers arrived. The oceanic islands to the east of Easter Island, such as Clipperton Island , the Galápagos Islands , and the Juan Fernández Islands , were in the past formerly categorized on rare occasion as part of Polynesia. No evidence of prehistoric contact with either Polynesians or the indigenous peoples of the Americas has been found. The Polynesian people are considered, by linguistic, archaeological, and human genetic evidence,

21406-477: The two ships sailed due south, but were driven to the east by heavy gales. They managed to edge further south, encountering their first pack ice on 10 December. This soon became a solid barrier, which tested Cook's seamanship as he manoeuvered for a passage through. Eventually, he found open water, and was able to continue south; on 17 January 1773, the expedition reached the Antarctic Circle at 66°20'S,

21560-458: The voyage continued down the uncharted coast, and on 21 October reached 52°S . Here Magellan found a deep inlet which proved to be the strait he was seeking , later to be known by his name. Early in November 1520, as the squadron navigated through the strait, they reached its most southerly point at approximate latitude 54°S . This was a record Farthest South for a European navigator, though not

21714-513: The waters between the South Sandwich Islands and the South Orkney Islands, looking for new land. Finding none, he turned southward down the 40°W meridian , deep into the sea that now bears his name. The season was unusually calm, and Weddell reported that "not a particle of ice of any description was to be seen". On 20 February 1823, he reached a new Farthest South of 74°15'S, three degrees beyond Cook's former record. Unaware that he

21868-489: The west, and the distinctive Polynesian language and culture emerging on Tonga and Samoa to the east. Where there was once faint evidence of uniquely shared developments in Fijian and Polynesian speech, most of this is now called "borrowing" and is thought to have occurred in those and later years more than as a result of continuing unity of their earliest dialects on those far-flung lands. Contacts were mediated especially through

22022-467: The western Polynesian societies are well documented and it is speculated that the Tui Manuʻa dynasty grew through its success in obtaining control over the oceanic trade of currency goods such as finely woven ceremonial mats, whale ivory " tabua ", obsidian and basalt tools, chiefly red feathers, and seashells reserved for royalty (such as polished nautilus and the egg cowry ). Samoa's long history of various ruling families continued until well after

22176-771: Was a full-scale Royal Naval enterprise, the principal function of which was to test current theories on magnetism , and to try to locate the South Magnetic Pole . The expedition had first been proposed by leading astronomer Sir John Herschel , and was supported by the Royal Society and the British Association for the Advancement of Science . Ross had considerable past experience in magnetic observation and Arctic exploration; in May 1831 he had been

22330-402: Was able to penetrate deep beyond the Antarctic Circle, and on 30 January 1774 reached 71°10'S, his Farthest South, but the state of the ice made further southward travel impossible. This southern record would hold for 49 years. In the course of his voyages in Antarctic waters, Cook had encircled the world at latitudes generally above 60°S , and saw nothing but bleak inhospitable islands, without

22484-456: Was able to persuade the publishing magnate Sir George Newnes to finance him to the extent of £40,000, equivalent to £5.44 million in 2023, with the sole stipulation that, despite the shortage of British participants, the venture be styled the "British Antarctic Expedition". This was by no means the grand British expedition envisaged by Markham and the geographical establishment, who were hostile and dismissive of Borchgrevink. On 23 August 1898

22638-508: Was an Anglo-Scottish seaman who saw service in both the Royal Navy and the merchant marine before undertaking his first voyages to Antarctic waters. In 1819, in command of the 160-ton brigantine Jane which had been adapted for whaling, he set sail for the newly discovered whaling grounds of the South Sandwich Islands. His chief interest on this voyage was in finding the " Aurora Islands ", which had been reported at 53°S , 48°W by

22792-590: Was characterised by the rivalry between Robert Falcon Scott and Ernest Shackleton during the Heroic Age of Antarctic Exploration . Shackleton's efforts fell short; Scott reached the pole in January 1912 only to find that he had been beaten by the Norwegian Amundsen. In 1494, the principal maritime powers, Portugal and Spain, signed a treaty which drew the Tordesillas line down the middle of

22946-519: Was close to land, Weddell decided to return northward from this point, convinced that the sea continued as far as the South Pole. Another two days' sailing would likely have brought him within sight of Coats Land , which was not discovered until 1904, by William Speirs Bruce during the Scottish National Antarctic Expedition , 1902–1904. On his return to England, Weddell's claim to have exceeded Cook's record by such

23100-663: Was first used in 1756 by the French writer Charles de Brosses , who originally applied it to all the islands of the Pacific . In 1831, Jules Dumont d'Urville proposed a narrower definition during a lecture at the Société de Géographie of Paris. By tradition, the islands located in the southern Pacific have also often been called the South Sea Islands , and their inhabitants have been called South Sea Islanders . The Hawaiian Islands have often been considered to be part of

23254-459: Was found that 96% (or 93.8%) of Polynesian mtDNA has an Asian origin, as does one-third of Polynesian Y chromosomes; the remaining two-thirds from New Guinea and nearby islands; this is consistent with matrilocal residence patterns. Polynesians existed from the intermixing of few ancient Austronesian-Melanesian founders, genetically they belong almost entirely to the Haplogroup B (mtDNA), which

23408-533: Was notified by telegram that a rival was in the field, but had little choice other than to continue with his own plans. Meanwhile, Fram arrived at the Ross Ice Shelf on 11 January 1911, and by 14 January had found the inlet, or " Bay of Whales ", where Borchgrevink had made his landing eleven years earlier. This became the location of Amundsen's base camp, Framheim . After nine months' preparation, Amundsen's polar journey began on 20 October 1911. Avoiding

23562-409: Was settled is debated, it is widely accepted that the island groups in the geographic center of the region (i.e. the Cook Islands , Society Islands , Marquesas Islands , etc.) were settled initially between 1000 and 1150 AD, and ending with more far flung island groups such as Hawaii , New Zealand , and Easter Island settled between 1200 and 1300 AD. Tiny populations may have been involved in

23716-524: Was treated as a hero on his return to England. His record was to stand for less than three years, being passed by Amundsen on 7 December 1911. In the wake of Shackleton's near miss, Robert Scott organised the Terra Nova Expedition, 1910–1913, in which securing the South Pole for the British Empire was an explicitly stated prime objective. As he planned his expedition, Scott saw no reason to believe that his effort would be contested. However,

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