From Wikipedia

Captain Cook

Part Two

The First voyage of James Cook was a combined Royal Navy and Royal Society expedition to the south Pacific ocean aboard HMS Endeavour, from 1768 to 1771. The aims of the expedition were to observe the 1769 transit of Venus across the Sun, and to seek evidence of the postulated Terra Australis Incognita or "unknown southern land."

The voyage was commissioned by King George III and commanded by Lieutenant James Cook, a junior naval officer with skills in cartography and mathematics. Departing Plymouth in August 1768, the expedition crossed the Atlantic, rounded Cape Horn and reached Tahiti in time to observe the transit of Venus. Cook then set sail into the largely uncharted ocean to the south, stopping at the Pacific islands of Huahine, Borabora and Raiatea to claim them for Great Britain, and unsuccessfully attempting to land at Rurutu. In September 1769, the expedition reached New Zealand, the first to do so since Abel Tasman 127 years earlier. Cook and his crew spent the following six months charting the New Zealand coast, before resuming their voyage westward across open sea. In April 1770, they became the first Europeans to reach the east coast of Australia, making landfall on the shore of what is now known as Botany Bay.

The expedition continued northward along the Australian coastline, narrowly avoiding shipwreck on the Great Barrier Reef. In October 1770, a badly damaged Endeavour limped into port in Batavia in the Dutch East Indies, her crew sworn to secrecy about the lands they had discovered. They resumed their journey on 26 December, rounded the Cape of Good Hope on 13 March 1771, and reached the English port of Deal on 12 July, having been at sea for nearly three years.