Lord Carnwath was the son and heir of Sir John Dalzell, 2nd Baronet and Harriet Murray.
The Earldom has a special remainder to heirs male whatsoever bearing the name and Arms of Dalzell.
The senior heir male is merely required to have the surname and Arms of Dalzell, if not by birth, then by Deed poll and Royal Licence.
They had one son, Alexander Dalzell (2 February 1721 – 3 April 1787), who would have been Earl of Carnwath, but for the attainder.
[1] Lord Carnwath fought in the Battle of Preston on 14 November 1715, for the Jacobites, and was taken prisoner.