Edmund Halley, an astronomer, predicted that on June 3, 1769, the planet Venus would cross in front of the sun. When this happened the distance from the Sun to the Earth could be calculated by timing the transit of Venus across the face of the Sun. The Royal Geographic Society had proposed that observers should be sent to three places around the world for further study and better calculation of this distance. Observers would be sent to the north of Norway, to Hudson Bay and to an island in the Pacific. Cook was chosen to lead the official British expedition to this last destination. This was a little surprising to some, but Cook and those in hierarchy of the navy knew of his capabilities, even if some thought him inexperienced and without a long distance journey.

Cook led the expedition with his new ship, the Endeavour. The Endeavour was a Whitby collier with a crew of about 80 and a team of 11 scientists, including: Charles Green, Assistant to the Astronomer Royal, and Sir Joseph Banks, a young man of the Royal Geographic Society who supplied numerous scientific instruments of his own. The Endeavour weighed 368 tons, was 106 feet long, 29 feet wide, 29 feet 3 inches in the beam and was specially fitted for the voyage. She could make seven or eight knots at the most, but could keep a good pace for a long voyage. One of the important things was that she was sturdy. She had a relatively low draught, fourteen feet, and carried twelve swivel guns, which were important for safety from natives. Cook and his crew left Plymouth on August 25, 1768 (Beaglehole). The Endeavour sailed first to Madeira and then, in November, reached Rio de Janeiro, where a delay occurred because the ship was mistaken for a pirate vessel. By January 1769 the misunderstanding was dealt with and the Endeavour was on the way to Cape Horn. She rounded the Cape with good weather and no troubles with wind.

Cook and the crew often grew quite weary and we can only imagine what a voyage of this type on a sailing ship would be like. Cook took excellent care of his ship and crew when on the voyage. They did their work along with catching of sharks and dolphins shooting of birds and dealing with the storms that came along their way. The crew ate extremely well even having a little fresh milk from a very famous goat on board. The goat had already sailed with Wallis, a British sailor, who discovered Tahiti not long before Cook would visit. When celebrations came around they had wine and maybe slaughtered a pig or cow that they brought with them. The basic diet however was salted pork and a biscuit. This did not seem to be a favorite since it was served continuously and often had weevils crawling and scavenging around inside. Since Cook was very strict about keeping his men free of scurvy he forced the men to eat vegetables, usually found in sauerkraut and made them keep their quarters clean and aired out.

There were some complaints on board, but only the usual for such a voyage. There was often punishment for work not done, and to keep the presence of order and command on the ship. Most problems were very minor as the men were still quite young, most men under thirty, and their main goal was still for a bit of adventure.

Cook journeyed to the recently discovered George III Island, by way of the Straits of Magellan. George III Island was discovered by Wallis and later re-named Tahiti. Tahiti was seen from the topmast on the 11th of April. The men spent the next two days arduously trying to get their beaten ship to the beautiful shores of Tahiti. The men landed in Matavai Bay on the morning of April 13 of the same year. The crew was greeted by the native's and soon felt dry immobile ground after eight months with only the touch of cold seawater in the morning and a swaying base to sleep on at night. The crew found that the Tahitian natives were a little weary upon their coming. However, soon after landing the native chief recognized Lieutenant Gore, as he had recently sailed to this land with Wallis, and the Europeans were then welcomed onto the island. In the next few months Cook and his crew experienced many things and learned much more than any other previous voyage to Tahiti. They were one of the first to see, (and feel) such things as tattoos. This is probably where sailors first received their trademark sign, the tattoo on their upper arm. The crew would find that the Tahitians were also very clever people and they outnumbered the small crew of the Endeavour and there were many incidents of pickpocketing and robbery during the visit. On one occasion a very important piece of equipment was stolen, the main piece of the observatory. This was the whole reason that the men had come to Tahiti and now it had been stolen leaving everyone in a bit of chaos. Cook sent out a warning and with help and a chase to the other side of the island the natives returned the disassembled pieces of the instrument. With the help of Banks' repairing skills the eclipse of Venus, Earth, and the Sun was successfully observed on June 3. Cook stayed for three months and not only observed the eclipse, but also mapped the Tahitian coast before leaving on the second half of his voyage. This half of the voyage's instructions were sealed, and even though hinted at by the public, Cook did not know exactly what his second orders were. Cook's instructions from the Royal Society were to prove the long contemplated question: Does the continent of Terra Australis Incognita exist, or is there only ocean in the unexplored part of the Southern Hemisphere? He was to proceed southward as far as the 40th latitude. If this course resulted in nothing found, he was to turn west and search between latitudes 40 and 35 until he discovered the unknown land or came to the eastern side of the land discovered by the Tasman.' (Blumberg, 1991) Cook did not sail south at once as the crew that he had kept so clean from scurvy had become ill with a form of venereal disease instead, and he gave them time to partially recover. Cook says in his diary that the crew was not to blame for bringing the disease to Tahiti.

Cook sailed south in the middle of August, but severe weather forced him to turn northwest at the beginning of September. No sight of the supposed Terra Australis was found so he moved as ordered to New Zealand.

Cook came to Poverty Bay in New Zealand around October and here the native Maoris people became hostile. Cook fired in self-defense and killed two or three people. From there he turned north again and Cook circumnavigated the two islands. He discovered the South Island and all the way, accurately charted the coast.

No European had yet visited the eastern coast of the recently discovered New Holland (Australia). Lieutenant Hicks made the first sighting of this land. Cook was notorious of duly naming places and this situation was no different. He named the bay that Hicks had found, Cape Hicks (later renamed Cape Everard). From here they sailed north, and anchored on April 29, 1770 in what Cook originally called Stingray Bay. After the group of scientists found huge numbers of unknown plant specimens, Cook renamed it to Botany Bay. Two Aborigines resisted their landing and fired darts, which Joseph Banks feared might be poisoned. Cook eventually scared them off with musket fire and they went without harm from Aborigines during the week they explored the area around the bay.

On May 7, Cook sailed again traveling north and seeing an approach to the later named, Sydney harbor. They had no luck investigating it and instead landed at Bustard Bay. A few days later they suffered a near shipwreck on a piece of the Great Barrier Reef. Despite a leaky hull the Endeavour was still afloat and the crew brought her into Cook Harbor, staying near today's Cooktown. Cook decided on a two-month stay here, giving time to repair the hull with what few resources they had and observing and shooting kangaroos. Cook was now to sail one of the longest and most dangerous stretches of water in the world and with a still leaky ship. By the middle of August they had come in sight of the tip of Australia's northeastern tip, which Cook named Cape York. Turning westward, the crew discovered and named the Endeavour Strait between the mainland and today's Prince of Wales Island. The next day he claimed all of Eastern Australia for Britain after quite a lengthy expedition and named the new territory, New South Wales. Cook then continued westward and proved a new sea route between Australia and New Guinea.

Another shipwreck forced the broken Endeavour to dock at Jakarta. The ship underwent repairs, but still could not leave until the end of December. Cook's efforts to keep a "clean" crew failed here and some of the crew became sick. Cook blamed the climate for this sickness and despite his efforts, many died before the Endeavour ever reached England. Cook and his Endeavour crew made their way to England slowly and landed on July 13, 1771.