I have fairly vague memories of the lats time there was a new century.  I suspect the title of this tune refers to the one before that.  The absence of my having been born adds to my amnesia regarding that event.  I hope I've at least remembered the tune.  I think it is in O'Neill's and on the "Contentment is Wealth" record of Sean Keane and Matt Molloy.  You could check those sources for a bit of reassurance.