A much more familiar shanty. Surely every boy's favourite? (especially when sung with the verse about the captain's daughter, eh?). Here's it done by those old masters the The Clancy Brothers with Tommy Makem (It's Tommy on the whistle I think):
Apparently it's origins lie in a traditional Scottish/Irish dance and march tune called "Oró Sé do Bheatha 'Bhaile." You can find the score on The Session, I'm sure.