5. Four stars and also four star-groups or planets which seem to have been associated with the cardinal points and are indicated by four discs exhibiting two concentric circles and four glyphs placed around them. Although at a disadvantage, not being able to substantiate my statement here, I shall mention that, amongst the above, the Pleiades and the planets Venus and Jupiter doubtlessly figure, the latter as two evening and two morning stars.
6. The human lords of the four regions who respectively governed the four divisions of the population, who were classified as the Fire, Air, Water and Earth people, the identical classification being applied in turn to each class and so on _ad infinitum_.
7. Rotation or a movement encircling the four quarters imagined as "quadruple motion." This was not confined to the Septentriones, for the ancient Mexican astronomers had recognized what they termed the "four movements of the Sun"--namely, its apparent rising in the east and progress to the north; and setting in the west and progress to the south. According to Leon y Gama, the first to describe the stone in 1832, the central "nahui ollin" portrayed the "four movements of the sun" and recorded the solstices and equinoxes. His opinion has since been shared by other writers, amongst whom I cite Señor Troncoso. According to Sir Norman Lockyer, moreover, the symbol does correctly and appropriately figure the annual course of the sun. It must be admitted that the invention of a figurative symbol which not only records the annual rotation of the circumpolar star-groups but also the annual apparent course of the sun is an achievement which has never been surpassed in primitive astronomy and merits admiration and recognition. The record of the periodical movements of the heavenly bodies, constitutes, at the same time naturally a register of the four seasons.
8. Simultaneously with the division of the year into four equal parts, the ollin (and pyramid) typified the division of the 20-day period into four quarters as well as the four 13 year periods which constituted the epoch of fifty-two years. As the Calendar periods will be discussed in my monograph on the subject, I shall only mention here a fact showing how completely the quadruplicate idea had influenced native speculation. The Mexicans believed that four great eras had passed since the creation of the world and designated these as the earth, air, fire and water eras. They believed that, although humanity had always escaped utter annihilation, the world had been almost completely destroyed by three of the elements in succession at the end of three of these eras. At the time of the Conquest, the Mexicans supposed themselves to be living in a fourth age which was doomed to perish by fire.