It was at daybreak that the _Mediator_ sighted five sail of the enemy, consisting of the _Ménagère_, thirty-six guns _en flûte_; the _Eugène_, thirty-six; and the _Dauphin Royal_, twenty-eight (French); in company with the _Alexander_, twenty-eight guns, and another brig, fourteen (American), formed in line of battle to receive the _Mediator_, which singly bore down upon them. The skilful seamanship and dashing gallantry of the English disconcerted the combinations of the enemy, and after several hours' fighting two of their vessels fell out of the line, and went away, badly crippled, to leeward. About an hour later the _Alexander_ was cut off, the _Mediator_ wearing between her and her consorts, and in ten minutes she struck. A chase then ensued after the larger vessels, and late in the evening the _Ménagère_, being raked within pistol shot, hailed for quarter. The rest of the squadron escaped, and the gallant _Mediator_, having taken possession of her two prizes, set sail with them for England, arriving in Cawsand Bay on the 17th of December. In the year following, Captain Luttrell, having been appointed to the _Ganges_, took with him Mr. Riou as second lieutenant. He served in this ship until the following summer, when he retired for a time on half-pay, devoting himself to study and continental travel until March, 1786, when we find him serving under Admiral Elliot as second lieutenant of the _Salisbury_. It was about this time that he submitted to the Admiralty a plan, doubtless suggested by his voyage with Captain Cook, "for the discovery and preservation of a passage through the continent of North America, and for the increase of commerce to this kingdom." The plan was very favourably received, but as war seemed imminent, no steps were then taken to carry it into effect.