His son used the same name, and was a Colonel who died at the Battle of Waterloo. See James Inglis (Anderson) Hamilton
James Inglis Hamilton (?-1803) was a Major General in the British Army, and Laird of Murdostoun. He was a Scot, the third son of Alexander Hamilton of Cleland. In 1719 his father inherited the estate of Murdostoun from an uncle, Alexander Inglis, and as a condition of the will added Inglis to his last name.

Brigadier General Hamilton commanded the 21st Foot (Scots Fusiliers) in the American Revolutionary War. During the Battle of Freeman's Farm he commanded the Center Column of the three groups of advancing troops. He was part of the forces surrendered after the Battle of Saratoga. While a prisoner, he adopted a son, James Anderson, who was afterward known as James Inglis Hamilton.

Hamilton was a Major General in the west Indies campaigns of the 1790s, commanding the 15th Foot. He died at his estate in Scotland on July 27,1803 and his adopted son was his only heir.