Sir: I have the honour to inform you, that on the morning of the 23d instant, at half past ten, when about to anchor off the north end of the island of Tristan d'Acunha, a sail was seen to the southward and eastward, steering to the westward, the wind fresh from the S. S. W. In a few minutes she had passed on to the westward, so that we could not see her for the land. I immediately made sail for the westward, and shortly after getting in sight of her again, perceived her to bear up before the wind. I hove to for him to come down to us. When she had approached near, I filled the main-topsail, and continued to yaw the ship, while she continued to come down, wearing occasionally to prevent her passing under our stern. At 1.40 P.M. being within nearly musket shot distance, she hauled her wind on the starboard tack, hoisted English colours and fired a gun. We immediately luffed to, hoisted our ensign and gave the enemy a broadside. The action being thus commenced, a quick and well directed fire was (p. 251) kept up from this ship, the enemy gradually driving near to us, when at 1.05 minutes he bore up apparently to run us on board. As soon as I perceived he would certainly fall on board, I called the boarders, so as to be ready to repel any attempt to board us. At the instant every officer and man repaired to the quarterdeck, where the two vessels were coming in contact, and eagerly pressed me to permit them to board the enemy; but this I would not permit, as it was evident, from the commencement of the action, that our fire was greatly superior both in quickness and effect. The enemy's bowsprit came in between our main and mizzen rigging, on our starboard side, affording him an opportunity to board us, if such was his design, but no attempt was made. There was a considerable swell on, and as the sea lifted us ahead, the enemy's boom carried away our mizzen shrouds, stern davits, and spanker boom, and he hung upon our larboard quarter. At this moment an officer, who was afterwards recognized to be Mr. M'Donald, the first lieutenant, and the then commanding officer, called out that they had surrendered. I directed the marines and musketry men to cease firing, and, while on the taffrail asking if they had surrendered, I received a wound in the neck. The enemy had just then got clear of us, and his fore-mast and bowsprit being both gone, and perceiving us wearing to give a fresh broadside, he again called out that he had surrendered. It was with difficulty I could restrain my crew from firing into him again, as he had certainly fired into us after having surrendered. From the firing of the first gun, to the last time the enemy cried out he had surrendered, was exactly 22 minutes by the watch.