SIR:--I have the honor to inform you that we have this morning captured, after an action of forty-two minutes, his Britannic Majesty's brig Epervier, rating and mounting eighteen thirty-two pound cannonades, with one hundred and twenty-eight men, of whom eleven were killed and fifteen wounded, according to the best information we could obtain. Among the latter is her first lieutenant, who has lost an arm, and received a severe splinter wound in the hip. Not a man in the Peacock was killed, and only two wounded, neither dangerously. The fate of the Epervier would have been decided in much less time, but for the circumstance of our foreyard having been totally disabled by two round-shot in the starboard quarter, from her first broadside, which entirely deprived us of the use of our fore-topsails, and compelled us to keep the ship large throughout the remainder of the action. This, with a few topmast and topgallant backstays cut away, and a few shot through our sails, is the only injury the Peacock has sustained. Not a round-shot touched our hull, and our masts and spars are as sound as ever. When the enemy struck he had five feet of water in his hold; his maintopmast was over the side; his mainboom shot away; his foremast cut nearly away, and tottering; his forerigging and stays shot away; his bowsprit badly wounded, and forty-five shot-holes in his hull, twenty of which were within a foot of his water-line, above and below. By great exertions we got her in sailing order just as night came on. In fifteen minutes after the enemy struck, the Peacock was ready for another action, in every respect, except the foreyard, which was sent down, fished, and we had the foresail set again in forty-five minutes--such was the spirit and activity of our gallant crew. The Epervier had under convoy an English hermaphrodite brig, a Russian, and a Spanish ship, which all hauled their wind, and stood to the E. N. E. I had determined upon pursuing the former, but found that it would not be prudent to leave our prize in her then crippled state, and the more particularly so as we found she had on board one hundred and twenty thousand dollars in specie. Every officer, seaman, and marine did his duty, which is the highest compliment I can pay them. I am, &c., L. WARRINGTON.