According to the sleeve notes for the "Chieftains, 3" album, the tune was composed in honour of the 4th Earl. There is a portrait of the, (I think,) 1st Earl, in Manchester City Art Gallery. In the notes accompanying the portrait it says he was called Burner Inchiquin because he and his troops sacked the town of Cashel and also that he had the "distinction" of serving both the Protestant and Catholic sides. It's a nice little tune, not difficult.