Lawyer. Born in Hamilton (South Lanarkshire), the eldest son of the noted chemist Prof. William Cullen (1710-90). The family moved to Edinburgh, and Cullen was educated at the Old High School in the city and then read law at the University of Edinburgh. He was admitted to the Faculty of Advocates in 1764, served as their Librarian (1770-75), as a Senator of the College of Justice (1796-99), and as Lord of Justiciary (1799 - 1810). With his father and younger brother, he was a founding fellow of the Royal Society of Edinburgh in 1783.
