K1 was used again by Cook for his third voyage (HMS "Resolution" 1776–80). In April 1779 off Kamchatka K1 stopped. A seaman with watchmaking experience cleaned it and started it again, but in June the balance spring broke and it could not be repaired. After its arrival in Britain in September 1780 it was returned to Kendall for repairs. K1 left England in May 1787 with the First Fleet voyaging to New South Wales in . K1 was transferred to HMAT "Supply" in the Indian Ocean, and arrived at Botany Bay on 18 January 1788. After some months ashore with Astronomer Lieutenant William Dawes, K1 was returned to HMS "Sirius" and travelled to Cape Town to collect supplies for the colony. After the wreck of "Sirius" at Norfolk Island in March 1790, K1 was put on board HMAT "Supply" which went to Batavia to collect more supplies, and eventually took K1 back to England via Cape Horn arriving in Plymouth in April 1792.