THOMAS] MYSTIC USE OF NUMBERS 955 
x 7=364), and that each of the four groups was assigned to a particu- 
lar cardinal point. Although it is true that the Tonalamatl, as given 
in some of the Mexican codices, seems to show, by the upper and lower 
border Jines, which contain 52 figures each, some indications of a 
year of 364 days, this does not account for the introduction of the 13; 
moreover, Dr Férstemann’s explanation introduces the factors 7 and 
91 (7X13), and 7 and 28 (47), which are not found in the time counts 
of the codices or inscriptions. However, it is possible that the 28 
(4x7) may be supposed to indicate the true lunar period, and the 4 
times 7 the four changes of the moon. Mr Cushing suggests another 
explanation based on his observations among the Zuni. In the cere- 
monies of this people the complete terrestrial sphere is symbolized 
by pointing or blowing smoke toward the four cardinal points, to the 
zenith and nadir, the individual making the seventh number. When 
the celestial sphere was symbolized only the six directions were added 
to the seven, no further reference to the individual being made. Thus 
13 typifies the whole universe. While this explanation seems plausi- 
ble, we lack the evidence that such a custom was 1n vogue among the 
people using the native calendar, nothing suggesting it being stated in 
the authorities or indicated in the codices, unless in the so-called title- 
pages of the Troano codex and Codex Cortesianus, which are sup- 
posed by most investigators to be parts of one plate or series. There 
we find the four cardinal point symbols taken in one direction fol- 
lowed by two symbols, which Seler believes indicate the zenith and 
nadir; these are followed by the cardinal point symbols taken in the 
opposite direction, and these by three other symbols, two of which 
appear to be the same as the supposed zenith and nadir symbols. 
Unfortunately the third, which makes the thirteenth, is too nearly 
obliterated to determine its form. The number symbols 1 to 13 
stand above these. 
Other suggestions as to the reason of the use of this number as a 
factor in the time system have been offered, but, like those mentioned, 
they are not entirely satisfactory. That 13 was considered important 
by most of the tribes is true, and that it was used by some otherwise 
than in time counts is true, but why is as yet an unsolved mystery, nor 
is there any satisfactory evidence that it was preceded by the twenty- 
day period, though this is probable. Clayvigero asserts that the Mexi- 
‘ans, in their computations of time, disregarded months and years, 
counting by thirteens, but he evidently means by this that 13 was used 
as the multiplier, and, like Goodman, evidently confounds the system of 
numeration with the time system. However, this will be discussed 
more fully in a subsequent paper relating to the native time system. 
