Lieutenant-Colonel @ William Williams (alias Campbell) date of birth has been approximated to be circa 1720. (from "An Enlightened Duke; The Life of Archibald Campbell (1682-1761) Earl of Ilay, 3rd Duke of Argyll") pg. 80
Further evidence of his age " in 1739, when he was about nineteen, was given a life post as Deputy Auditor of the Exchequer of Scotland, a place worth 200 pds. a year. Ilay saw to his advancement in the Army where he rose in the end to a General's rank and to the Coloneley in the 3rd Foot Guards, later the Scots Guards. He died in 1786. (from "An Enlightened Duke; The Life of Archibald Campbell (1682-1761) Earl of Ilay, 3rd Duke of Argyll") pg. 80