William DouglasBorn 1724
3rd Earl of March (1731-). 4th Duke of Queensberry (1786-). His grandfather was William Douglas (1655-1705), 1st Earl of March, a brother of James Douglas (1662-1711), 2nd Duke of Queensberry, the father of Charles Douglas, 3rd Duke of Queensberry.
William Douglas later on became known as Old Q.
According to the website of the National Portrait Gallery, Douglas was a "notorious gamler, rake and stud owner". (Link)
Life with Boswell:
Boswell visited him in London on December 6, 1762. They probably met a few times at Lord Eglinton's as well, during Boswell's stay in London 1762-63, at least on July 9, 1763.