The letter of the new government to His Imperial Majesty is dated the 12th of August, when every thing was finally settled. It begins by congratulating him on the happy state of things in general in Brazil. It then sets forth the wishes of the people of Maranham to have joined their brethren long since, but that these wishes had been thwarted by the Lisbon troops.--"But what was our joy and transport when unexpectedly we saw the ship Pedro Primeiro summoning our port!!! Oh, 26th of July, 1823! Thrice happy day! thou wilt be as conspicuous in the annals of our province, as the sentiments of gratitude and respect inspired by the virtues of the illustrious Admiral sent to our aid by the best and most amiable of Monarchs will be deeply engraven on our hearts and those of our posterity! Yes, august Sire! the wisdom, the prudence, and the gentle manners of Lord Cochrane, have contributed still more to the happy issue of our political difficulties, than even the fear of his forces, however respectable they might be. To anchor in our port; to proclaim independence; to administer the proper oaths of obedience to Your Imperial Majesty; to suspend hostilities throughout the province; to cause a new government to be elected; to bring the troops of the country into the town, and then only in sufficient numbers for the public order and tranquillity; to open communication between the interior and the capital; to provide it with necessaries; and to restore navigation and commerce to their pristine state: all this, SIRE, was the work of a few days. Grant, Heaven, that this noble Chief may end the glorious career of his political and military labours with the like felicity and success; and that Your Imperial Majesty being so well served, nothing more may be necessary to immortalise that admirable commander, not only in the annals of Brazil, but in those of the whole world!" And this, I think, is all of importance that I have learned with regard to the capture of Maranham to-day. It is true, the brig Maria, despatched by His Lordship on the 12th of August, only arrived to-day; so that much may be behind.