On the 19th November the Eagle’s crew was increased to 420 men, and she was kept cruising throughout the winter, and on the 4th January 1757 she was caught in a heavy gale off the Isle of Wight, where she had most of her sails blown out of her.  On 25th May she sailed from Plymouth Sound in company with H.M.S.  Medway, and a day or two afterwards they fell in with and chased a French East Indiaman, the Duc d’Aquitaine, in rather heavy weather.  The Medway was leading, but when getting close, had to bring to in order to clear for action, as otherwise she would be unable to open her lee ports.  Pallisser, on the other hand, was all ready, and pressed on, bringing the chase to action.  After a hard set-to, lasting about three-quarters of an hour, the Frenchman struck, having lost 50 men killed and 30 wounded, whilst the Eagle lost 10 killed and 80 wounded; and the list of damages to the ship reported to the Admiralty shows that the action was sharp though short.  The Medway was only able to afford assistance by firing a few raking shots, and suffered no damage except having ten men wounded by an accidental explosion of gunpowder.  The masts and sails of the prize were so much damaged that she lost them all in the night; one of the masts in falling sank the Medway’s cutter.  It was found she had a complement of 493 men, and was armed with 50 guns.  She had landed her East Indian cargo at Lisbon, and then proceeded to cruise for fourteen days on the look-out for an English convoy sailing in charge of H.M.S.  Mermaid.  She had succeeded in picking up one prize, an English brig, which was ransomed for 200 pounds.  This was Cook’s first experience of an important naval action, and Pallisser was complimented by the Lords of the Admiralty for his gallant conduct.  The Duc d’Aquitaine was purchased for the Navy, and was entered under her own name as a third-rate, 64 gun ship, with a complement of 500 men.

The Eagle returned with her consort and her prize to Plymouth, and soon afterwards Cook’s connection with her came to an end.  According to Dr. Kippis, Mr. Walker had interested the Member for Scarborough, Mr. Osbaldiston, on the subject of Cook’s promotion, but the rule was that candidates for Lieutenancy must have been employed on board a king’s ship for a period of not less than six years, and an order had recently been issued that this regulation was to be strictly adhered to.  Captain Pallisser therefore wrote to Mr. Osbaldiston that Cook: 

“had been too short a time in the service for a commission, but that a Master’s warrant might be given him, by which he would be raised to a station that he was well qualified to discharge with ability and credit.”

The result of this correspondence is shown in the Eagle’s muster roll, for on 27th June James Cook attended his last muster, and on the 30th he was discharged.  The succeeding rolls registering “D. 30th June 1757.  Solebay prefmnt.”

The Mercury cook.