THOMAS] MYSTIC USE OF NUMBERS 953 
the month, ahau, year or katun, the so-called week not being recog- 
nized as a regular period in their systems, it entered into almost every 
time count and every time series in the codices and inscriptions. It 
was one of the factors on which the so-called ‘‘sacred year” of 260 
days and the cycle of fifty-two years were based. 
eing so important in the time systems, it would be expected to 
enter more or less into the activities of life; nevertheless it appears 
to have played a comparatively unimportant réle as a mystic or cere- 
monial number. It was the custom of several Mayan tribes to arrange 
their armies in thirteen divisions. It appears in the Votan myth among 
the Tzental, where ‘‘thirteen serpents” are referred to; and among 
the Cakchiquel the day numbered 13 was considered sacred. 
The number 20 is the base of the numeral system of the Mexican 
and Central American tribes, and it may perhaps also be correctly 
considered the base of their calendar system, although there are other 
necessary factors. Nevertheless 20 does not appear to have been 
used as a mystic number in rites and ceremonies, except so far as the 
calendar was made to serve divinatory purposes. Why twenty days 
were adopted as a time period and a division of the year has as yet 
received no entirely satisfactory explanation, though it is generally 
supposed that it was chosen because the arithmetical system of these 
tribes was vigesimal. That there is some connection between the two 
is quite likely, especially as this would seem to correspond with the 
probable order of the steps in the formation of the two systems. That 
the formation of the yigesimal system preceded that of the time sys- 
tem appears to be an absolute requisite, but the steps in the forma- 
tion of the latter can not be assumed with the certainty which we may 
have with regard to the former. 
That the custom of grouping the days by fives did not begin until 
26 had come into use is clear. Did the introduction of 13 as a factor 
precede or follow the adoption of 20% Dr Brinton states in his 
Native Calendar that he is persuaded that this period was posterior 
and secondary to the twenty-day period. Although this opinion may 
be, and probably is, correct, the evidence on which to base it is not so 
apparent as to leave no doubt. It seems probable, as Dr Brinton 
suggests, that the twenty-day period was derived from the vigesimal 
number system, but this does not explain the origin of the peculiarities 
of the unusual time system, which seems to have reference to no 
natural phenomena save the earth’s annual revolution. There are 
other peoples than those of Mexico and Central America who use 
the vigesimal system, but no others, so far as known, who adopt 
the twenty-day month or eighteen-month year. The moon’s reyo- 
lution is the factor on which the month in most of the world’s time 
systems is based, and the name for month in most, or at least several 

