Capt. James Cook’s involvement with Capt. Constantine John Phipps is the subject of a web page in the website of the Captain Cook Society. That page focuses largely on the 1773 attempt by Phipps to reach the North Pole by ship.
They came closer than anyone on previous voyages, and Phipps became (it is said) the first European to write about the polar bear. The voyage is, of course, covered in a number of other sources, including Phipps’s own published account, as well as an unofficial journal which was published in 1774.