On the morning of the 5th, Lord Cochrane looked in vain for the enemy. He had apparently been satisfied with the skirmish of the 4th, and had taken refuge in the harbour; so that His Lordship returned to the Moro de San Paulo, with only the satisfaction of having driven the enemy from the open sea. Meantime the Brazilian Imperial force that was posted behind the city, taking advantage of the absence of the fleet, and consequently of the two thousand seamen who served the artillery ashore, advanced from the sitio of Brotas, where their centre was quartered, towards the town. Madeira marched out to meet them, and an action took place entirely in favour of the Imperialists; and it is said that the King's fleet was recalled in consequence of this disaster. Lord Cochrane had no sooner returned to San Paulo than he made such provisions with regard to his squadron, as he judged most prudent for the public service. The vessel that has arrived here has brought down some of the ill-affected Portuguese. All, I believe, from the report of the officer who arrived in the prize, have been dismissed from the Pedro Primero. Lord Cochrane has taken the officers and English seamen of the Piranga and Nitherohy on board the Pedro, so that now he has one ship he may depend on: he has exchanged the eighteen-pound guns of the main-deck, for the twenty-four pounders of the Piranga, and has placed guns along his gang-ways; and we trust the next news we have from him, we shall learn something favourable to the cause of independence. As far as the government here could supply every thing to the squadron to insure its success, it was done in the most liberal manner; and the failures, where they occurred, were owing to the peculiar circumstances of the times and country, which admitted of no controul. That some things should have been imperfect was to be expected: that so much should have been done, and well done, excites admiration. But the Emperor appreciates the brave man who commands his fleet; and while that is the case, a difficulty as soon as felt will be obviated. _19th_.--My health grows worse and worse. The Creole sailed to-day. I have amused myself for two days with some English newspapers. If any thing can rouse me to health it surely ought to be news from England. Lord Althorp has, I see, made a spirited but ineffectual effort for the repeal of the foreign enlistment bill; a most interesting subject in this country: and I see with pleasure a virtual acknowledgment from the English ministers of the independence of Spanish America.