In the southwestern corner of the cathedral, inlaid in the exterior wall, is the celebrated calendar stone of the ancient Mexicans. It is a huge mass of gray porphyry, having a circular face seven feet in diameter, on which the figures that represent the months are sculptured in relief. In the centre is a head, from the mouth of which water seems to flow--surrounded by two circles, a large and a small one--the latter divided into twenty parts, with hieroglyphics which designate the twenty months of eighteen days each, into which the Mexican year was divided. The remainder of the face is ornamented with figures in relief. The _Palace_, filling the eastern side of the _Plaza_, occupies a square of six hundred and sixty feet by six hundred, within which space are comprised the residence of the president, the offices of the different departments of the government, the senate chamber and that of the deputies, the mint, prison, botanic garden, and the barracks of a regiment of infantry. On this spot Cortes fixed his residence after the capture of the city; but he exchanged it subsequently for the site of Montezuma's palace, on which now stands the _Casa de Estado_, the family mansion of the conqueror. This classic ground is to the west of the cathedral, fronting it; and the space, believed to have embraced the residence of the Mexican kings, is a square of about six hundred feet. On the northern side of this square passes the street running west, _Calle de Tacuba_, by which Cortes retreated on the memorable _noche triste_ (unfortunate night) when he was driven from _Tenochtitlan_, or _Tenictitan_, as Cortes writes the name of the ancient city. The botanic garden occupies an inner _patio_, or court of the palace, and is altogether unworthy of the celebrity which it has obtained in foreign countries. It is confined and crowded. Collections of seeds sold by the superintendent at high prices, have, to the great chagrin of foreigners, been found invariably to comprise the most ordinary plants, when the most rare and valuable were promised to the purchasers. An additional garden has been laid out recently at _Chapoltepec_. There are two tall trees of the _Manitas_, in the botanic garden--all, with the exception of one at _Toluca_, that are said to be growing in the republic. The Professor of Botany, _Don Vicente Cervantes_, informed me that it is a common tree in Guatemala. The flower is exceedingly beautiful, of a bright scarlet color; its supposed resemblance to a hand, gives the name to the trees, _Arbol de las Manitas_--but it is far more like a bird's claws. * * * * *