We have now traced the idea of the Above and Below, Centre and Four Quarters in Ancient Peru. It remains to be noted that the capital itself, which was to be the image of the whole empire, was primarily divided into two halves and four quarters, and subdivided into 4×3=12 wards the names of which doubtlessly corresponded with that of their inhabitants. When the sacred centre of the capital is added to these it is clear that the City of Cuzco was subdivided into as many parts as there were directions in space, _i. e._ 13. It exemplified, therefore, an association of 2×10=20 categories of people classified according to ages, with thirteen directions in space, and a general subdivision of all classes into four parts. The Inca with the four Capacs and the Coya with the four Camayocs formed two groups of five each, which could well have been represented by a large central figure surrounded by four smaller ones of equal size. By coloring these with red, yellow, black and white, their assignment to the cardinal point could have been expressed. The central figure could be painted in four colors, for only the Inca and his lineage could wear many-colored garments, these being indicative that they represented the centre or union of the four quarters. Two important features of the system remain to be discussed: We have studied the minute and methodical classification of the entire population into distinct groups without touching upon the practical reasons why this was done. We have analyzed the great machinery of the Inca dominion as it lies broken and motionless. But endow the giant wheel with motion, introduce systematical rotation into its every part, regulate the occupations of the people by a fixed series of work-days and holidays. Send them forth to their work and collect the products of their labor at set intervals, _institute a calendar_, and you will have set the machinery of state in motion and realized how the classification of individuals according to rank, ages, and occupations was absolutely necessary in order to obtain a successful and harmonious result. It has already been shown that the institution of the calendar and establishment of twelve festival periods of thirty days each, in a year, succeeded the division of the people into groups and their assignment to fixed places of abode. “They commenced to count the year in the middle of May, a few days more or less, on the first day of the Moon ... in this month they held the festivals of the Sun” (Molina ed. Hakluyt, p. 16). I direct particular attention to the fact that it was the new May moon which controlled the beginning of the religious calendar, although the Incas observed the equinoxes and solstices and the cult of the Sun was under their special care. The twelve divisions of the year accord with the twelve wards of Cuzco surrounding the central enclosure which was always the place where the festivals were held and the people congregated.