My take on what was going through Jack's mind during that cabin scene. It's a little rambly, but I've tried to make it resemble a thought pattern. Reviews would be greatly appreciated.
Anyone walking into the cabin that moment might almost have failed to recognise Jack Aubrey. Sitting dejected and looking out to sea, his broad shoulders were slumped wearily and his normally ruddy cheeks were pale and drawn. Gone was his normal friendly joviality – instead his brows were knotted together with worry and fatigue.

He was facing the toughest decision of his life.

To turn his back on the Acheron would be like admitting defeat. He would be giving up on a ship that he had chased almost a quarter of the way around the globe. The Frog would win and 'Lucky Jack's' unending string of victories would come to an abrupt halt. He would have to swallow his pride, something that did not come easy to him. Not to mention would the ship would lose in prize money that would be awarded for capturing one of old Boney's Ships.

And Warley would have died for nothing, Jack thought bleakly. That was another thing which was fuelling his obsession to catch the Acheron. He wanted to prove himself to his men; to prove that there was no 'phantom-ship' which could match the Surprise. To prove that he had not over-stepped his orders for nothing. To prove that he was not a failure. That he had not let a man die for nothing.

Turning away from the sight of the smooth, rhythmic sea, Jack's gaze fell on the cello, resting so still and quiet in the corner: the cello which had so often been united in harmony with his own violin. A lump came to his throat and he slowly sat down.

Could he really bear to lose Stephen? Stephen, who had been the best and truest friend he could ever ask for. Stephen had been there for Jack through all the highs and lows of his career, always ready to offer advice; never wavering in his dependable loyalty. He put up with Jack's bad jokes and occasional tactlessness with very little complaint and risked his life for others without a second thought.

The surgeon's mate had said that it was too risky to remove the bullet at sea. Would Jack really be able to live with himself if Stephen died while he pursued that goddamned French ship? After all, what good was all the glory in the world if your best friend was not there to share it with you? What good was moving up the promotion ladder if you knew you had let your comrade die for you to get there?

Jack looked at the lonely cello again and his eyes filled with tears. There was no way that he could put Stephen's life at risk. Life without Stephen at his side seemed suddenly unthinkable. He would sacrifice his pride; his ambition. Stephen was worth it: he was his brother, his comrade and his very best friend.

Dashing his tears away, Jack got to his feet determinedly. He had not taken a single step before Pullings had appeared at the door, his face unusually grave.

"Sir?" he asked quietly, his eyes pleading that Jack had made the right decision.

"Set a course for the Galapagos, Tom," said Jack, a little hoarsely. "And get up as much speed as you can. Doctor Maturin must be treated as quickly as possible."

Pullings gave the smallest hint of a smile. He knew that his faith in Jack had not been for nothing. Captain Aubrey was truly a good captain, a good man and, most importantly, a good friend.

"Aye aye, sir," he nodded briefly. "At once." He sped out of the cabin again.

Left alone again, Jack heaved a heavy sigh, folding away the charts he had been consulting when planning to chase the Acheron. He resented letting the bloody Frog get away, but he did not regret the decision he had made.

Prizes and ships came and went. Stephen had always been there…and Jack intended to do everything in his power to ensure that he always would be.