"Bung Yer Eye", also known as "The Brisk Young Lad", "The Earl of Dunmore", "The High Cauld Cap", "The Jolly Old Man", "Lanigan's Ball", "Mary the Maid" and many other names.
It is Scottish and English with many occurences in America under various names.
The term 'bung your eye' means to 'shut your eye', taken from the bung used to stopper a hole in a cask,. 'Bung your eye' was also a euphemism for gin in the sense that an excess of gin will 'bung your eye' through blind drunkenness.
It was printed in Robert Ross's A Choice Collection of Scots Reels or Country Dances & Strathspeys (1780), Aird's Selection of Scotch, English, Irish and Foreign Airs, vol. 1 (1782), Gow's 1st Repository (1799), Sharps Country Dance Tunes (1909), Williamson's English, Welsh, Scottish and Irish Fiddle Tunes (1976), Bayard's Dance to the Fiddle (as Lanigan's Ball)(1981).
It also appears in Moon's Musick of the Fifes and Drums, vol. 3 Medleys in "Medley 3 Scottish Dances".