There were big demonstrations in Northern Ireland on Tuesday. Around 2,000 people, from both the South and the North of the divided island, converged on the fine old 18th-century manor house, rather misleadingly called a "castle," at Hillsborough in County Down. Ten miles away in Belfast city center, several hundred more took part in a prayer vigil outside the city hall. A casual observer might have thought that the old civil-rights movement of the late 1960s had come back to life, an impression that would have been fortified by the presence, at the first of those demonstrations, of an old...