Mr Bateson had five offspring, not one.
THOMAS BATESON (1705-91) succeeded his father in the Lancashire estates, but disposing soon afterwards of those, he removed to Ulster, and settled at Orangefield House, County Down.
He wedded, in 1747, Margaret, daughter and co-heiress of of Mr White, of White Hall, County Antrim, and widow of William Hartley Esq, of Dublin; and had issue,
THOMAS, of whom we treat;Dying in 1791, Mr Bateson was succeeded by his eldest son,
RICHARD, who died unmarried in 1783;
WILLIAM, died unmarried;
JANE, who wedded, in 1782, John Dunne Esq, KC, in Ireland;
FRANCES, who married, in 1805, Hans Mark Hamill Esq, of County Down.
THOMAS BATESON (1752-1811), married Elizabeth, daughter of George Lloyd FRS, of Hulme Hall, Lancashire.