It will be seen, on consulting the journals of the present time, that the Government of the United States lays strong claim to that portion of the kingdom of New Spain, east of the bay of St. Bernardo; it having been declared in congress, that Galveston Bay, where the insurgents have been attempting to form settlements, in order to annoy from thence, the coasts of San Luis Potosi and Vera Cruz, is within the limits of the United States. Should this assertion, which is founded on the treaty of 1783, be well grounded, the Spanish government will have no other barrier to oppose to any future aggression of that power, than the great river Bravo del Norte, which will bring the Americans within a very short distance of the capital, and will leave them some of the richest silver mines in the government of San Luis Potosi. We shall now give a description of the capital of New Spain, as in it the commerce, the wealth, and the power of the country, is, as it were, concentrated. METROPOLIS OF NEW SPAIN. MEXICO, the capital of the Spanish vice-royalty of New Spain, is situated in 19° 25ʹ 45ʺ north latitude, and 99° 5ʹ 5ʺ west longitude, in a beautiful valley near the banks of the lake Tezcuco. The houses are mostly founded on piles, on account of the marshy nature of the ground, and the town is intersected by numerous canals. The scite of the city is the same as that of the ancient Mexico, which is said to have been so denominated from the god of war of the Mexicans, whose appellation was Mexitli, as he had a temple erected there to his worship. A palace was erected by Cortez, opposite to the scite of the palace of Montezuma. This city is a very fine one, and it is asserted that, with the exception of some parts of Westminster, Petersburgh, Berlin and Philadelphia, there is no city of the same magnitude which bears any comparison with Mexico for its great regularity, the extent of the public buildings and places, the level, and the general architecture. The railings and gates of the houses are of iron, ornamented with bronze, and the roofs of the houses are flat, and formed into terraces. The great breadth and length of its streets is an object of admiration to strangers, but it is said they are nevertheless dirty. The streets are paved and lighted by large reflecting lamps, and generally run in straight lines, from west to east, and from north to south; the footpaths are guarded by little stone-pillars, and a covered sewer runs along the middle of the streets, as in France.