The _gnomon_, discovered by me in December, last year, in the ruined city of Mayapan, would tend to prove that the learned men of Mayab were not only close observers of the march of the celestial bodies and good mathematicians; but that their attainments in astronomy were not inferior to those of their brethren of Chaldea. Effectively the construction of the gnomon shows that they had found the means of calculating the latitude of places, that they knew the distance of the solsticeal points from the equator; they had found that the greatest angle of declination of the sun, 23° 27´, occurred when that luminary reached the tropics where, during nearly three days, said angle of declination does not vary, for which reason they said that the _sun_ had arrived at his resting place. The Egyptians, it is said, in very remote ages, divided the year by lunations, as the Mayas, who divided their civil year into eighteen months, of twenty days, that they called U--moon--to which they added five supplementary days, that they considered unlucky. From an epoch so ancient that it is referred to the fabulous time of their history, the Egyptians adopted the solar year, dividing it into twelve months, of thirty days, to which they added, at the end of the last month, called _Mesoré_, five days, named _Epact_. By a most remarkable coincidence, the Egyptians, as the Mayas, considered these additive five days _unlucky_. Besides this solar year they had a sideral or sothic year, composed of 365 days and 6 hours, which corresponds exactly to the Mayas[TN-25] sacred year, that Landa tells us was also composed of 365 days and 6 hours; which they represented in the gnomon of Mayapan by the line that joins the centers of the stela that forms it. The Egyptians, in their computations, calculated by a system of _fives_ and _tens_; the Mayas by a system of _fives_ and _twenties_, to four hundred. Their sacred number appears to have been 13 from the remotest antiquity, but SEVEN seems to have been a _mystic number_ among them as among the Hindoos, Aryans, Chaldeans, Egyptians, and other nations. The Egyptians made use of a septenary system in the arrangement of the grand gallery in the center of the great pyramid. Each side of the wall is made of seven courses of finely polished stones, the one above overlapping that below, thus forming the triangular ceiling common to all the edifices in Yucatan. This gallery is said to be seven times the height of the other passages, and, as all the rooms in Uxmal, Chichen and other places in Mayab, it is seven-sided. Some authors pretend to assume that this well marked septenary system has reference to the _Pleiades_ or _Seven stars_. _Alcyone_, the central star of the group, being, it is said, on the same meridian as the pyramid, when it was constructed, and _Alpha_ of Draconis, the then pole star, at its lower culmination.