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He was the son of Admiral of the Fleet Sir Thomas John Cochrane, son of Admiral the Honourable Sir Alexander Cochrane, sixth son of Thomas Cochrane, 8th Earl of Dundonald (see the Earl of Dundonald for earlier history of the Cochrane family).
Houx afterwards equipped a brig, which he named Revanche de la Superbe, and sent an invitation to Fitton to meet him at a place named; however, before the message arrived Fitton had been superseded as captain by the 17-year old Thomas John Cochrane, son of admiral Sir Alexander Cochrane, who was then commanding officer of the Leeward Islands station.