The K1 chronometer was such a great success that the Board of Longitude decided to outfit each of her Majesty’s ships with one. However the price of the K1 was prohibitively expensive at £400 - the cost of a whole ship at the time (such as the HMS Resolution) was £1800!
So Kendall proposed constructing a less expensive, less sophisticated version of the K1 chronometer, but based on the same principles. His proposal was accepted and he completed the K2 in early 1772.

The K2 was given to Captain John Phillips who took it on his expedition in search of the Northwest Passage and in 1787 William Bligh in command of HMS Bounty, took it on board his ship. The K2 attained fame because of the mutiny on the Bounty on its return journey from Tahiti. After a meandering odyssey of almost 70 years, during which it was handled by several captains, and exposed to extreme weather conditions and other vicissitudes, the K2 found its way back to England in 1840. It was given to the British Museum by Captain Herbert of HMS Calliope and the K2 now rests at the Royal Observatory of Greenwich, in London