'[7 February 1776] Sailed on for the island Labuan on our way to Borneo, for provisions. Labuan is the island, to which the English retired from Balambangan: it lies opposite the mouth of the river of Borneo Proper....
[10 February 1776] Rowed a good deal: at midnight got up the river, and anchored abreast of the resident's house. I found here the Luconia Scow, Captain Rossin, belonging to the honourable Company. On the 11th [February 1776], at sun-rise, saluted the factory with five guns, and had the same number returned. At seven o'clock went ashore, and waited on the resident, Mr Jesse who by the kindness of his manner, made my short stay very agreeable...
[18 February 1776] At four, found the vessel made more water than usual: she had sprung a leak on the starboard side, three streaks from the keel... ran back to Borneo; and at eight in the morning came to, abreast of Mr Jesse's house....
On Tuesday the 27th [February 1776], I had got every thing ready for sea. In the afternoon, Mr Jesse and Captain Rossin came on board; also Mr. Kirton, Captain Rossin's chief officer, a very ingenious young gentleman, who had. sailed round the world with Captain Carteret, and had commanded several country ships. We then weighed, and ran down the river. At sunset, they left us, and I saluted them with three guns. I followed my friends to the town; at eleven, took leave of them and returned on board.'
'In the month of November, 1773, I was appointed (over the heads of others) to the post of sub-secretary, in the room of Mr. John Jesse, who proceeded on the unfortunate expedition to Balambangan, in the return from whence he died at Borneo'.This could imply that Jesse had expired as early as 1777 since no reference to any activities by him after that period have been found.