Background:
Tierra del Fuego Spanish for Land of Fire is an archipelago off the southernmost tip of the South American mainland, across the Strait of Magellan. The archipelago consists of the main island, Isla Grande de Tierra del Fuego, with an area of 48,100 km2 and a group of many islands, including Cape Horn and Diego Ramírez Islands. Tierra del Fuego is divided between Chile and Argentina, with the latter controlling the eastern half of the main island and the former the western half plus the islands south of Beagle Channel.
The name Tierra del Fuego derives from the Portuguese explorer Ferdinand Magellan sailing for the Spanish Crown, in 1520 he was the first European to visit these lands. He believed he was seeing the many fires (fuego in Spanish) of the Yaghan, which were visible from the sea, and that the Indians were waiting in the forests to ambush his armada.
In 1525 Francisco de Hoces was the first to speculate that Tierra del Fuego was one or more islands rather than part of what was then called Terra Australis. Francis Drake in 1578 and a Dutch VOC expedition in 1616 learned more about the geography. The latter expedition named Cape Horn.

Cooks Second Voyage (1772–75)
Shortly after his return from the first voyage, Cook was promoted in August 1771, to the rank of commander. In 1772 he was commissioned to lead another scientific expedition on behalf of the Royal Society, to search for the hypothetical Terra Australis. On his first voyage, Cook had demonstrated by circumnavigating New Zealand that it was not attached to a larger landmass to the south. Although he charted almost the entire eastern coastline of Australia, showing it to be continental in size, the Terra Australis was believed to lie further south. Despite this evidence to the contrary, Alexander Dalrymple and others of the Royal Society still believed that a massive southern continent should exist.
Cook commanded HMS Resolution on this voyage, while Tobias Furneaux commanded its companion ship, HMS Adventure. Cook\\\\\\\'s expedition circumnavigated the globe at an extreme southern latitude, becoming one of the first to cross the Antarctic Circle (17 January 1773). In the Antarctic fog, Resolution and Adventure became separated. Furneaux made his way to New Zealand, where he lost some of his men during an encounter with Māori, and eventually sailed back to Britain, while Cook continued to explore the Antarctic, reaching 71°10S on 31 January 1774.
Cook almost encountered the mainland of Antarctica, but turned towards Tahiti to resupply his ship. He then resumed his southward course in a second fruitless attempt to find the supposed continent. On this leg of the voyage he brought a young Tahitian named Omai, who proved to be somewhat less knowledgeable about the Pacific than Tupaia had been on the first voyage. On his return voyage to New Zealand in 1774, Cook landed at the Friendly Islands, Easter Island, Norfolk Island, New Caledonia, and Vanuatu.
Before returning to England, Cook made a final sweep across the South Atlantic from Cape Horn and surveyed, mapped and took possession for Britain of South Georgia, which had been explored by Anthony de la Roché in 1675. Cook also discovered and named Clerke Rocks and the South Sandwich Islands (Sandwich Land). He then turned north to South Africa, and from there continued back to England. His reports upon his return home put to rest the popular myth of Terra Australis.
Cooks second voyage marked a successful employment of Larcum Kendalls K1 copy of John Harrisons H4 marine chronometer, which enabled Cook to calculate his longitudinal position with much greater accuracy. Cooks log was full of praise for this time-piece which he used to make charts of the southern Pacific Ocean that were so remarkably accurate that copies of them were still in use in the mid-20th century.
Upon his return, Cook was promoted to the rank of post-captain and given an honorary retirement from the Royal Navy, with a posting as an officer of the Greenwich Hospital. He reluctantly accepted, insisting that he be allowed to quit the post if an opportunity for active duty should arise. His fame extended beyond the Admiralty; he was made a Fellow of the Royal Society, and awarded the Copley Gold Medal for completing his second voyage without losing a man to scurvy. Nathaniel Dance-Holland painted his portrait; he dined with James Boswell; he was described in the House of Lords as the first navigator in Europe. But he could not be kept away from the sea. A third voyage was planned and Cook volunteered to find the Northwest Passage. He traveled to the Pacific and hoped to travel east to the Atlantic, while a simultaneous voyage traveled the opposite route.

Anderson, George William
A New, Authentic, and Complete Account of Voyages Round the World, Undertaken and Performed by Royal Authority. Containing a New, Authentic, Entertaining, Instructive, Full and Complete History of Captain Cooks First, Second, Third and Last Voyages. The Whole of these Voyages of Capt. James Cook, &c. being Newly written by the Editors from the Authentic Journals of Several Principal Officers and other Gentlemen of the most Distinguished Naval and Philosophical Abilities, who sailed in the Various Ships, and now publishing. Assisted, Very Materially, by a Principal Officer who sailed in the Resolution Sloop, and by Many Other Gentlemen of the Royal Navy. published by Alex. Hogg, 1784.

This publication by Anderson is a richly illustrated account of Captain James Cook, the first really scientific navigator, containing 124 magnificent full-page plates of elevations, views, inhabitants, utensils, flora and fauna, and 31 maps and charts—including a large folding map of the world.
Facing challenges surpassed only by modern space flight, Captain James Cook embodied the spirit of the great age of maritime discovery. The only 18th-century explorer to lead more than one Pacific voyage, he embarked on three circumnavigations between 1768 and 1776, essentially transforming into their modern form the dangerously unreliable maps of the Pacifics expanse and the New Worlds western coast. In three great voyages Cook did more to clarify the geographical knowledge of the Southern Hemisphere than all his predecessors had done together. He was the first really scientific navigator and his voyages made great contributions to many fields of knowledge. Accounts of these three famous voyages, with their remarkable engravings, found an eager public, and today form the basis for any collection of exploration. In addition to Cooks voyages, this important compilation of English voyages includes accounts of the voyages of Sir Francis Drake, Lord Anson, Philip Carteret, Samuel Wallis, John Byron and Lord Mulgrave. Anderson sometimes gives the original accounts, others are edited or abridged versions, and frequently additional materials, from other sources, are added to give scope and depth to the narratives.