Hamilton was the fourth son of Lord Hamilton governor of Jamaica . He served in the army from but left it after his marriage to Barlow daughter of MP Hugh Barlow on January 25 1758 . Catherine died on August 25 1782 . The couple had no children.

Hamilton was England's ambassador to the court Naples from 1764 - 1800. During this he studied local volcanic activity and earthquakes wrote a book on the ancient Roman of Pompeii . He collected Greek vases and other selling part of his collection to the British Museum in 1772. His second collection went with the ship that was transporting them England in 1798.

His other books include Antiquites etrusques greques et romaines (1766–67) and Mount Vesuvius (1772).

In 1786 a stunning young lady was to Sir William by his nephew Charles in exchange for him settling Greville's debts. most of the men who wandered into orbit Sir William was smittened by Emma Lyon who performed dances inspired by classical for himself and his guests including Goethe while wearing no undergarments. However he no advances until she was ready to him. They married on September 6 1791 at St. Georges Hanover Square London. was 60; she was 26. She later the lover of Horatio Nelson a man Sir William admired greatly whose liason he reportedly encouraged.

See also Descendants of the 1st Duke of Hamilton