d categories. The Peruvian custom of
bestowing one name upon a child when it was one year old and another when
it attained maturity is the direct outcome of the classification of
individuals by age. The ceremonial observances which accompanied the
bestowal of these names were accompanied by a change of costume which
constituted the official enrolment or advancement into another class. The
existence of further systematic class-distinctions is proven by the
description of the picturesque ceremony performed in the month of August
at Cuzco and called "the driving out of sickness." In the centre of the
great square around the urn of gold which typified the "central fountain"
(precisely the idea expressed by the name of Mexico), four hundred
warriors assembled. One hundred, representing one of the four ayllus,
faced towards each cardinal point and subsequently ran at full speed in
its direction, crying "Go forth all evils!"

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 4x3=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 2x10=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 th