"Flow gently, sweet Afton, among thy green braes, Flow gently, I'll sing thee a song in thy praise. My Mary's asleep by thy murmuring stream." The singer praises the river, and bids it not to disturb Mary's sleep
Burns obviously had a tune for this, but the common melody was copyrighted in 1838 by Jonathan Edwards Spilman.
Available records do not seem to indicate whether Burns wrote this song before or after the death of his beloved Mary Campbell. - RBW