In other words, he had reached the southern point of the strait named after Torres.
To this immense line of coast Cook gave the name of New South Wales, from some resemblance that he saw to the coast about Swansea.

By this first voyage Cook had proved that neither New Holland nor Staaten Land belonged to the great Antarctic continent, which remained the sole myth bequeathed by the ancients which had not yet been definitely removed from the maps.

In his second voyage, starting in 1772, he was directed to settle finally this problem.

He went at once to the Cape of Good Hope, and from there started out on a zigzag journey round the Southern Pole, poking the nose of his vessel in all directions as far south as he could reach, only pulling up when he touched ice.

In whatever direction he advanced he failed to find any trace of extensive land corresponding to the supposed Antarctic continent, which he thus definitely proved to be non-existent.
He spent the remainder of this voyage in rediscovering various sets of archipelagos which preceding Spanish, Dutch, and English navigators had touched, but had never accurately surveyed.