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The son of Sir Arthur Acheson, 5th Baronet, he succeeded to the baronetcy upon the death of his father, and was subsequently created Baron Gosford in 1776 and Viscount Gosford in 1785.
Arthur Acheson, 1st Earl of Gosford (1742/45–1807) the grandson of above; the title Earl of Gosford was created for him
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Sir Arthur Acheson, 5th Baronet (1688–1748), the son of Nicholas Acheson, 4th Baronet
Olivia Acheson (d. 12 February 1863), daughter of the 1st Earl of Gosford, on 8 October 1822 at London.