William Douglas, 3rd Earl of Ruglen and 3rd Earl of March, later 4th Duke of Queensberry (1725-1810), was the heir general as the only son of the elder daughter (Lady Anne Hamilton, later 2nd Countess of Ruglen) of the eldest daughter (Lady Anne Kennedy, later Countess of Selkirk and Ruglen) of the 7th Earl.
As far as I can ascertain, on his death, the heirs general of the body of the 7th Earl became extinct. The line of such heirs would then pass through the younger daughter of the 6th Earl, as follows:
- Lady Catherine Kennedy, later Lady Cochrane (d. 1653)
- John Cochrane, Lord Cochrane, later 2nd Earl of Dundonald (d. 1690)
- William Cochrane, 3rd Earl of Dundonald (d. 1705)
- John Cochrane, 4th Earl of Dundonald (1687-1720)
- William Cochrane, 5th Earl of Dundonald (1708-1725)
- [Lady Anne Cochrane, later Duchess of Hamilton and Brandon (1707-1724)]
- James Hamilton, Marquess of Clydesdale, later 6th Duke of Hamilton and 3rd Duke of Brandon (1724-1758)
- James Hamilton, 7th Duke of Hamilton and 4th Duke of Brandon (1755-1769)
- Douglas Hamilton, 8th Duke of Hamilton and 5th Duke of Brandon (1756-1799)
- [Lady Elizabeth Hamilton, later Countess of Derby (1753-1797)]
- Edward Smith-Stanley, Lord Stanley, later 1st Baron Stanley and later still 13th Earl of Derby (1775-1851)
So if the future Duke of Queensberry had been successful in his claim, on his death the Earldom would have passed to the then Lord Stanley, who would have become 10th Earl of Cassilis. It would then have been inherited by his son, the Prime Minister, and would have passed along with the Earldom of Derby to the present day. It would currently be held by his descendant the 19th Earl of Derby and 16th Earl of Cassilis.