950 NUMERAL SYSTEMS [ETH. ANN.19 
there were thirteen divisions. The same Annals, alluding to the ori- 
gin of the people, speak of four men (leaders), four Tulans or tradi- 
tional homes, and four rulers. The great Mexican festivals occurred 
on the fourth, thirteenth, and fifty-second years. Four arrows were 
placed in the hand of their great deity, Huitzilopochtli. At the great 
feast symbolizing the death of this deity four of the chief priests ofti- 
ciated and four youths were chosen as attendants. 
The Guatemalans recognized four culture heroes; at Cholula, four 
disciples of Quetzalcoatl were charged with the government; in Tlax- 
calla, four princes formed the supreme council; and finally, according 
to Brasseur, almost all the villages or tribes of Mexico were divided 
into four clans or quarters. According to the Popol Vuh, in the 
descent to Xibalba (Inferno?) four roads were encountered; one of 
these was red, one black, one white, and one yellow. And Gucumatz, 
in his ascent to heaven and descent to Xibalba every seven days, under- 
went four changes in form, becoming first, a serpent; next, an eagle; 
next a tiger, and last, coagulated blood. 
This number and 5, together with the product of 4+ and 5, 20, form 
the base and scaffolding of the Mexican and Mayan numeral and time 
systems, though two other factors,13 and 18, were brought into the 
latter. y 
Although the number 5 does not appear to have entered so exten- 
sively into the mythology and ceremonials—that is to say, in so many 
different relations—as the 4, yet in some respects it was more promi- 
nent. For example, there is scarcely a page of the Troano, Dresden, 
or Cortesian codices without from one to four groups (usually columns) 
of five days, arranged in some regular order, which bear some rela- 
tion to the accompanying symbolic figures and numerals. Similar 
groups of five days frequently occur in the Mexican codices, where 
they also bear some relation to the accompanying symbolic figures. 
The day symbols in the Tonalamatl, as found in three of these codices, 
are arranged in 5 lines of 4 times 13 days each. 
The use of this number with a mystic or mythological significance 
appears to be shown on several plates of the Mexican codices, as for 
example, on plates 11 and 12 of the Borgian codex. On each of these 
plates are five scenes or groups of figures in five sections, placed as is 
shown in the diagram (figure 41). 
The fact that the chief symbolic figure in each is the Rain god, Tlaloc, 
and that the lower portion of each section apparently denotes earth and 
vegetation growing therefrom, renders it probable that there is some 
reference here to the seasons or the vicissitudes of cultivated plant 
life. Be this as it may, the reference to five is apparent, not only 
from the number and position of the sections, but also from the colors 
of the Tlalocs on plate 12, one of the outer four being red, another 
blue, another yellow, and another black, while that in the center is 
striped with red and white. 
