The rest of the tunes from Mitchell's 'Highland Fair' are also on Jack Campin's website. (You can click onto it from my homepage).

Burns song is in 'The Scots Musical Museum', #309, 1792. James Dick, 'The Songs of Robert Burns', p. 461, 1903, said:

A fragment of the old song is in Herd's Scots Songs, 1769, 314. Burns made a few alterations in the first stanza, the second being entirely his.

............. Wm. Stenhouse in 'Illustrations to SMM' pointed out the fragment given by Herd, and printed it, and said at that time (before 1821) he had a manuscipt copy of Burns' song in Burns' handwriting. Burns two verses fit the version of the tune in SMM once through (16 measures of 6/4 time).