The Billy Paterson melody is apparently related to Humors of Bantry and the Appalachian tune, "Fire in the Mountain."

Here's a link:
http://memory.loc.gov/cgi-bin/ampage?collId=mussm&fileName=sm/sm1884/21500/21561/mussm21561.db&recNum=1&itemLink=D?mussm:2:./tem