Son of John Hope (1704-1781), 2nd Earl of Hopetoun, and Anne Ogilvy (d. 1759). Brother of James Hope.
He died in Portsmouth on June 6, 1766 shortly after his return from a journey to the West Indies.1
Boswell met him at the court of Charles I at Brunswick on June 27, 1764. The young Lord was accompanied by his tutor, William Rouet.
Note 1: http://www.electricscotland.com/HISTORY/nation/hope.htm
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For most of his adult life Boswell was better known for his "Account of Corsica", which lead to the sobriquet Corsica Boswell, than for his friendship with Dr. Johnson.