The brick bridge to Tipperary.
This bridge, built in the 1640's, crosses the Little Brosna River within the Demesne.  Where the bridge crosses, the river is the boundary between Counties Offaly (in which the village of Birr and most of the Castle's Demesne lie) and Tipperary.  Since Offaly is in the province of Leinster and Tipperary is in Munster, the bridge also connects two of Ireland's four provinces to one another.
This view is from the Leinster (Offaly) side.