Although they're called the Cook Islands, Palmerston is the only one on which Captain Cook ever set foot himself. He discovered it on his second voyage in June, 1774, but it wasn't until Sunday, April 13, 1777, during his third Pacific voyage, that he went ashore. He and his crew took on board supplies of "scurvy grass, palm cabbages, birds, fish and cocoanuts etc" , but they didn't find any fresh water. He landed on a tiny coral atoll which (according to "A Gazeteer of Central Polynesia" published in 1857) was not more than three feet above sea level but had numerous trees and bushes on it and the remnants of a canoe.
Cook named the tiny and remote island after Lord Palmerston who was First Lord of the British Admiralty and father of a future British Prime Minister. The ancient name was supposedly Avarau, meaning 200 harbours.
Acccording to 19th century British missionary, the Rev William Wyatt Gill, the Bounty mutineers also touched on Palmerston but decided it was not quite what they were looking for.