After rounding Cape York, Cook claimed the entire coastline he had just explored as British territory at Possession Island on 22 August. From there, satisfied that New Guinea and the coast he had named New South Wales were separate entities, he sailed for Batavia.
He arrived in the Dutch headquarters in the East Indies on 11 October and while further repairs and refitting kept him there until 26 December. Having made his way that far without losing a single member of his crew to scurvy, two months in Batavia was more than enough time for malaria, other mosquito-borne fevers and dysentery to take their toll.
Once the repairs were complete, the voyage continued via Cape Town and Saint Helena and the Endeavour was back in England on 13 July 1771.
Cook had charted more than eight thousand kilometres of new coastline with incredible accuracy but had failed to find the presumed southern continent.
By circumnavigating New Zealand Cook had established that it was not attached to a continental landmass to the south, and despite emerging evidence to the contrary, significant members of the Royal Society including Alexander Dalrymple still believed a massive southern continent would eventually be found.