In my Note on the Ancient Mexican Calendar System, communicated to the International Congress of Americanists at Stockholm, in 1894, I stated certain historical and astronomical facts which showed that the New Cycle, which began in 1507 with the year Acatl, had commenced on March 14th three days after the vernal equinox and that this delay had obviously been intentional, in order to wait for the new moon, which fell on March 13th at 11.40 A. M., and the planet Venus, “which was possibly visible both as morning and evening star between March 14th and 18th.” The above facts, which have remained unchallenged since their publication, afford an insight into the astronomical attainments of the sun-priests and moon and star-priests and show an evident desire to begin a new era at a favorable time, when there was a conjunction of the heavenly bodies. Thus the terms of office of the lords of the Above and Below were entered upon and the machinery of state set into motion, in unison with striking celestial phenomena. It is impossible not to realize how great must be the antiquity of a system which, evolving from the rudimentary, ceremonial division of a tribe into seven parts, as a consequence of its primitive observation of the Septentriones, developed into a great and complex government dominated and pervaded by the abstract conceptions of the seven-fold divisions of the Above, Below, Middle and Four Quarters. Deferring further comment I will proceed to demonstrate the practical value, for governmental purposes, of the classification of a community into twenty divisions with as many representative heads, their localizations at given points of the compass, and association with a calendar-sign and day, and will only refer to what I have already published in my Note on the Calendar, namely, how, by means of the combination of 13 numerals with the 20 signs, a unit of 260 days was obtained, and how each sign was combined but once with the same number, and a perfect system of rotation of periods, regulating office, labor, etc., was instituted. It is not possible for me to enlarge here upon the features and merits of the system which I do not hesitate to term one of the most admirable and perfect achievements of the human intellect. My present purpose is to lay stress upon the fact that, in Mexico, the major calendar-signs were borne as titles by the rulers of the four quarters who presided in rotation over a year—the name of this and of their title being always in correspondence. Nezahualcoyotl, the lord of Tezcoco, is recorded as possessing the title Ome Tochtli=2 Rabbit, and would obviously have presided over the calendar periods of that name. This inference is undoubtedly corroborated by Nuñez de la Vega’s following statement, quoted by Boturini:(44)