In 1291 King Edward I of England was given the task of choosing the next king of Scotland from a field of 14 contenders. Robert Bruce and John Balliol were the only serious candidates and the others were just there to make up the numbers. One of the also-rans was a Patrick Galythly whose claim to fame was that his late father Henry Galythly or Galychtly was an illegitimate son of King William I, "William the Lion".
Galythly (etc.) is the surname which nowadays is spelt Gellatly or Gallitly, and if like me you have that name in your family-tree, I suppose with a bit of imagination you could claim to be a descendant of King William.
Harry