That's better known as 'Salmon Tails Up Water'. There was a third part to it when used for the Siege of Ennis. Another tune used in the same set was 'The Grand Old Dame Brittania' aka 'Leather Away the Wattle-O'.
The Siege of Ennis appears to be one of those dances that any group of Irish people can, and will, get up to perform. And they haven't been too fussy about the tunes when I've seen it done.