until 1735, three years after he left the university to accept a position as schoolmaster at Kirkby Stephen in Westmorland.
He was a justice of the peace for the counties of Westmorland and Cumberland, and devoted himself to the study of law.
In 1762, after Burn had attained notoriety as a legal scholar, the University of Oxford awarded him an honorary LL.D.
The last-named work, published after the author's death by his son, was an update of William Blackstone's Commentaries on the Laws of England.
He collaborated with Joseph Nicolson to compile The History and Antiquities of the Counties of Westmorland and Cumberland, published in 1777.