948 NUMERAL SYSTEMS [ETH. ANN. 19 
determined, their application and use in the connections in which 
they are found has not been ascertained. 
It is apparent from the data presented that the Aztec or Mexican 

Fic. 40—Symbol for 19,600. Vatican codex 3738, plate 123. 
tribes by whom the codices were made were not so well advanced in 
mathematics and time count, or in the symbolic designation of num- 
bers, as the Mayan tribes. 
THE MYSTIC AND CEREMONIAL USE OF NUMBERS 
In taking up this branch of the subject we enter upon a field where 
the evidence must be drawn very largely from the early (chiefly Span- 
ish) authorities; their testimony is, however, corroborated to some 
extent by the codices and inscriptions. As there is no intention of 
entering at this time upon a general discussion of the subject of the 
mystic and ceremonial use of numbers among the Mexican and Central 
American tribes, but simply of presenting the data so far as they may 
seem to have relation to the subject treated in this paper, this part 
will be brief. 
As 2 is a number connected in some way with almost every action 
of life, and necessarily referred to in almost every ceremonial and 
mystie rite, it is difficult to determine where it is specially referred to 
because of its numeral value. I therefore omit it from considera- 
tion in this respect. Three is a number so seldom brought anto use 
in the customs of the natives of the regions mentioned that it may be 
passed over. 
Reference to the number + in myths and ceremonials as well as in 
other relations by savage tribes, as also by peoples of more advanced 
‘ture, is so general and so well known that it requires no proof 
here. This, as is well understood, arises to a large extent from the 
universal custom of considering the horizontal expanse with reference 
to four cardinal points, governed primarily by the rising and setting 
of the sun—east and west—the midway points on the cirele being the 
north and south. The number, even outside of any process of count- 
ing, would become apparent in any figure or structure in the form of - 
a square, the four sides and the four corners; and in the personal rela- 
tions, front and back, right and left, as is suggested by Professor 
