Sailing away with this device, which reduced the leaking of the ship to only about 15 inches of water an hour, easily kept at bay by the pumps, Cook passed close to two small islands, which at one time had seemed almost unattainable, and which out of gratitude he called Hope Islands. "In all the joy of our unexpected deliverance we had not forgotten that there was nothing but a lock of wool between us and destruction." At last they managed to reach the right kind of harbour at the place where the great town of Cooktown now stands. Here the ship was run up against a steep part of the shore, the stores, provisions, and the men were all transferred to the beach, where a camp was made and tents were put up for the sick; for, in addition to their other troubles, scurvy had broken out. Amongst other people thus affected was Tupia, the invaluable Polynesian interpreter, who, however, no sooner got on shore than he caught plenty of fresh fish and obtained herbs which cured his scurvy. Banks explored the country in all directions. There were many traces of the natives, but none of these people were visible. In his walks he met with vast flocks of pigeons and crows[86], and the pigeons (the plumage of which was exceedingly beautiful) proved most welcome as stores of fresh food.

On examining the main leak of the ship it was found that the coral rocks had pierced through four planks even into the timbers of her construction. There was not a splinter to be seen, but all was as smooth as though it had been cut by sharp instruments. The vessel would have been inevitably swamped but that a portion of the leak was filled up by fragments of rock broken off the spikes of coral.

On shore, palms yielding "cabbages" were found, which proved to be a grateful supply of vegetable food, and they even met with clumps of wild bananas yielding small fruit with nice-tasting pulp, but full of hard black seeds. "As I was walking this morning at a little distance from the ship", wrote Cook in his journal, "I saw myself one of the animals which had been so often described. It was of a light mouse colour, and in size and shape very much resembled a greyhound. It had a long tail also.... I should have taken it for a wild dog if instead of running it had not leapt like a hare or bird." It was, in fact, a kangaru. They also saw two animals like dogs (dingoes), of a straw colour. There were very large fruit-eating bats, "as big as a partridge", with wide-stretching black wings.

At last, after they had been many days on shore, they succeeded in getting into touch with the natives, who were more amenable to reason than the savages farther south. Their skin was dark chocolate, the hair was black, in some cases lank and in others curly, but never woolly like the Papuans. Their bodies were painted with streaks of red and white, the features of their faces were agreeable, and their voices were soft and tuneful. One of them wore the bone of a bird 5 or 6 inches long thrust through the gristle between the nostrils. However, the kindness shown them led these people on to acts of great presumption. They began to pester the party on land with requests for food, and, when this was denied them, gave way to transports of rage, and finally, seizing brands from a fire, set light to the dry grass. Having in this way nearly succeeded in destroying the camp, it was necessary to shoot at them with muskets. With great difficulty peace was made, which was perhaps fortunate, for the seamen, straying out in all directions in search of food, encountered parties of native Australians who might otherwise have killed them had they not been reassured as to the intentions of the white men. In one such instance a seaman found himself alone in a little camp of four natives, who had kindled a fire and were broiling a bird over it together with part of a kangaru. The seaman, being unarmed, was very much alarmed, but had the presence of mind to assume a placid demeanour. He sat down with the people and offered them his knife, but after examining it they returned it to him politely. They examined his hands and face and clothes with the greatest attention, and then made signs that he could go away if he wished, a leave which he hastened to take. It was invariably found, however, that presents given to these people, whether cloth, beads, trinkets, or iron, were thrown away as useless lumber. The expedition also obtained a specimen of phalanger, a marsupial often misnamed the Australian opossum.[87] These phalangers or cuscuses had already been sent home to European collections from the Dutch East Indies, and had been described and named by Buffon, the great eighteenth-century French zoologist. Among the birds seen at Endeavour Harbour, where the ship was laid up for repairs, and where the chief fresh food of the crew was the green turtle, were Australian crows, kites, hawks, black cockatoos and white cockatoos, many beautiful parrots and parrakeets, a variety of pigeons, tree-ducks (noted for their whistling cry), geese, and curlews. On the islands off the coast which they touched at as they sailed northwards there were large Monitor lizards; and the nests of great eagles could be seen, mostly built on the ground. In their passage northward they were again and again within a few yards of destruction amongst the shoals, the coral reefs, the sudden storms, and the holes of unfathomable water. The dangers of navigating the unknown parts of the vast Pacific Ocean were greatly increased by having a crazy ship and by being short of provisions, "yet the first adventures of a first discoverer made us cheerfully encounter every danger".

On Tuesday, 21 August, 1770, Cook rounded Cape York and realized that he was quitting the shores of Australia and had found a passage between that island continent and New Guinea—the straits through which the Spaniard, Torres, had sailed in 1607, the existence of which had been entirely overlooked or forgotten. Cook, believing that he had at last found a passage into the Indian Ocean, landed on a little islet, climbed its highest hill, and hoisted the British flag, taking possession of the whole eastern coast of Australia (by the name of "New South Wales") on behalf of His Majesty King George III, "with all the bays, harbours, rivers, and islands situated upon it".

No clue is given in Cook's journals to his reason for giving the very inappropriate name of New South Wales to the eastern side of the Australian continent.

Almost unconsciously they rounded the northernmost extremity of Australia, feeling their way between islands, sandbanks, and shoals. On 23 August, 1770, they saw an open sea to the westward and realized that they were passing Tasman's Gulf of Carpentaria, and that they had discovered (in reality, rediscovered) the important strait between New Guinea and Australia, proving that the last-named (which they knew as "New Holland"), though continental in size, was in reality a separate island, and not connected with New Guinea.

New South Wales and much of Queensland was found by Cook to be fairly well watered, with innumerable small brooks and springs, but no great rivers. Access to the coast was much obstructed by the dense mangrove thickets. Eucalyptus was the most prominent type of tree in the forests. Cook observed two sorts of this "gum tree", with its "narrow leaves not much unlike those of a willow", and its gum of a deep-red colour. The pine trees[88] he mentions were probably species of Araucaria and Frenela (miscalled Callitris). They found three different kinds of palm[89], that which grew in the southern part of New South Wales had fan-shaped fronds, and the heart of the palm (namely, the undeveloped fronds—the cabbage, as it was called by the mariners in those days, who depended on it so much for vegetable food) was exceedingly sweet to the taste. The nuts which it bore in great abundance were good food for pigs. The second palm, also producing an edible cabbage, had large pinnated fronds like those of the coconut; and the third kind, which, like the second, was found only in northern Queensland, was seldom more than 10 feet high, with fronds resembling those of a large fern. It bore no cabbage, but a plentiful crop of nuts the size of a large chestnut only rounder, nuts that were probably roasted and eaten by the aborigines. Nevertheless, when eaten by Europeans, they proved almost poisonous, causing them to vomit and to be purged with great violence.

The conclusions at which Cook arrived in regard to the aborigines of Australia were singularly accurate, considering that he had only landed about five times on the coast of New South Wales and Queensland, and had in addition only the scanty records of Dampier and the Dutch seamen regarding the western coast of Australia. He argues from the utter savagery of these coast natives, and from the Dutch accounts of the desolate, parched nature of the south and west coasts of Australia, that the interior is probably mainly desert and uninhabitable. Their houses, which were seen at their best at Botany Bay, were just high enough for a man to sit upright in, and not large enough for him to lie down at full length. They were built with pliable rods as thick as a man's finger, in the form of an oven, the two ends being stuck into the ground. These withes were then covered with palm leaves and broad pieces of bark, and the door was nothing but a large hole at one end. In other words, they were precisely like the houses built by the pygmies in some parts of the Congo Forest. Inside these huts they slept three or four in number, coiled up. Their only implements seemed to be made of bark or netted fibre. Pieces of bark were tied at the two ends with some lithe twig which served as a handle, and these bark basins or buckets would then hold water. In addition the natives roughly knitted together long fibres into bags, which they slung by a string over the head. But their fish hooks were very neatly made of shell, and some exceedingly small. For striking turtle they had a barbed wooden harpoon, the detachable end of which was fastened into a staff of light wood, to which was tied a line of fibrous string, while the other end of the bush rope was fastened to the harpoon. After striking the turtle the barbed end of this weapon would become detached in the animal's body, while the staff, being of light wood, rose to the surface and served as a float by which the victim could be traced, and also as a drag on his speed. They were able to make string from some fibre which ranged from the thickness of a half-inch rope to the fineness of a hair, and argued some skill on their part. Their cooking was done by broiling on coals or baking in a hole with the help of hot stones. They had no nets for catching fish, though they used a hook and line and also the harpoon. The boomerang was almost their only weapon for bringing down birds. They produced fire by whirling a drilling-stick into a piece of soft wood, getting a spark in less than two minutes. "We have often seen one of them running along the shore, to all appearance with nothing in his hand, who, stooping down for a moment at the distance of every 50 or 100 yards, left fire behind him, as we could see first by the smoke and then by the flame amongst the driftwood and other litter. We had the curiosity to examine one of these planters of fire when he set off, and we saw him wrap up a small spark in dry grass, which when he had run a little way, having been fanned by the air that his motion produced, began to blaze. He then laid it down in a place convenient for his purpose, enclosing a spark of it in another quantity of grass, and so continued his course."

By setting fire to the bush the natives managed to surround and kill a number of animals—kangarus, emus, lizards, &c.