In Peru, there are many positive dates, yet I was the first to reduce them to chronological order. In Brazil and Guyana, but few dates are found. The Muyzcas had very early dates, yet few have been preserved; much obscured by personifications of dynasties, and Pietrahita begins their real annals only in 1490, or 45 years before the Spanish invasion. In the Antilles the dates are quite loose, and difficult to reduce even to a serial order. But in Central and Mexican America, we find many early dates with a regular chronology. Yet some are extravagant or contradictory. I shall endeavour to elucidate them, so as to reduce the whole to order. They must form the base of a regular American chronology, that ascends by dates to the flood and creation. In Yucatan the first regular date only reach to 940 after Christ. In North America, where the smallest number of dates existed; we have unexpectedly and quite lately, found that many ancient dates could be procured. Cusick has published those of the Ongwi traditions, and I have ascertained those of the Linapis. Both of which reach to the flood and creation, and afford series of available dates as early as 1600 years before our era; thus nearly as ample as those of the TOL-tecas, and as plain in some instances. Astronomy was cultivated by all the civilized nations of ancient America. They had cycles of 144, 104, 60, 52, 20, 15 and 13 solar years. Humboldt has well written on that subject; but much remains to be gleaned. The northern tribes reckon by generations as the Greeks, the Polynesians, &c., and by winters instead of years, moons instead of solar months. They had also a cycle of 60 years. In Central America, &c. the months were of 20 days, including 4 weeks of 5 days. But the Peruvians had months of 27 days, or 3 weeks of 9 days as the Etruscans. The Muyzcas small weeks of 3 days, &c. No where in ancient America, was found the sabatical week of days, based on the 7 planets and the 4 quarters of a lunation. This is remarkable, as evincing a remote antiquity, and separation before this week was adopted in Egypt, India, Syria, Celtica, &c. Until 120 years before Christ the TOL-tecas reckoned only 365 days in the solar year, as the primitive nations of Asia: then they added the hours to the year. This forms their astronomical era. The Muyzcas had a very complicated astronomy, and three kinds of years. The usual was of 20 moons, and the ecclesiastical of 37 moons. The horal division unknown in many parts of America, was of 4 hours in the day for the Muyzcas and Mexicans, elsewhere of 5, 10 and 20. The 24 hours and the Zodiac of 12 signs with 360 degrees were not known. The Mexican Zodiac had 13 signs and 104 degrees.