The AGAMEMNON was again engaged with her yesterday's antagonist; but she had to fight on both sides the ship at the same time.

The CA IRA and the CENSEUR fought most gallantly: the first lost nearly 300 men, in addition to her former loss; the last, 350.

Both at length struck; and Lieutenant Andrews, of the AGAMEMNON, brother to the lady to whom Nelson had become attached in France, and, in Nelson's own words, "as gallant an officer as ever stepped a quarter-deck," hoisted English colours on board them both.

The rest of the enemy's ships' behaved very ill.

As soon as these vessels had struck, Nelson went to Admiral Hotham and proposed that the two prizes should be left with the ILLUSTRIOUS and COURAGEUX, which had been crippled in the action, and with four frigates, and that the rest of the fleet should pursue the enemy, and follow up the advantage to the utmost.