In the solar or civil year, each sign had its day, but as the computation of years passed by, each sign in due rotation ruled during one year. It was only when each sign had had an equal rule that the cycle completed itself, and, in turn, became a part of a greater cycle of time. To realize the marvellous ingenuity with which the rotation of days and consequently the working of the entire machinery of state was carried on, it is necessary to have before one’s eyes, a series of reconstructive tables, such as I have prepared for my paper on the subject. For the present, however, I trust that some idea of the harmonious organization of the state may have been conveyed to the reader. One important feature remains for consideration. As already mentioned, one of the four annual midnight positions of the Bear star-groups, and presumably a “royal star,” pertained to each cardinal-point and consequently to each of the four divisions of people. To this statement, which can be supported by substantial evidence, I must add that each of the sixteen minor signs likewise designated constellations, of which there were thus four in each region of the heaven. The twenty familiar day-signs thus actually constituted also the native zodiac. As the region to which each constellation pertains is clearly designated by the cardinal-point signs, their identification is merely a matter of time. Since ten of the signs represent animals, and these were the clan totems, it is easy to realize how animal forms, composed of stars, came to be traced in the heavens. Deferring further discussion of the native zodiac I will but point out what an intimate relation was thus established and maintained between star-groups and human beings; and how the periodical rotation and stations of the celestial bodies actually guided or, at all events, coincided with the periods of human activity in various branches. I am not, as yet, prepared to formulate a final opinion on the meaning of the narrow band that surrounds the zodiacal belt, which is at the same time the list of years and days and of tribes and clans, but shall merely note that it exhibits four large and four lesser rays which designate the quarters and half-quarters of the whole. A few words concerning the symbolism of these rays should find place here. In Nahuatl the ray was named “tona-mitl,” literally “the shining arrow,” “shaft of light.” Ixtlilxochitl tells us that it was an ancient custom of his people on taking possession of new territory “to shoot with utmost force four arrows, in the directions of the four regions of the world.”(72) This interesting passage shows us that the rays, _i. e._ arrows of light, carved on the stone, conveyed the idea of possession of the four regions and four sub-regions by the central power.