seler] 



THE MEXICAN CHRONOLOGY 

 Table II 



15 



\ 



We see that, if we presuppose a year of 305 days, only four of the 

 twenty day signs fall on initial da3"s — four signs which are five signs 

 distant from each other. 



And we see that if we accept the theory of a year of 305 days a 

 period of 52 years necessarily ensues. For since 365 — 5 X 73, and 73 

 is a prime number, it can only occur after 260-^5, or 5'2, years, that the 

 same number and the same sign of the tonalamatl will fall on the initial 

 day of the year. Now we know by the unanimous statements of his- 

 torians and documents that the Mexican nations designated their years 

 after the fashion shown by the above tables of initial days of the year, 

 and it is authoritatively stated of certain races that these names of the 

 years were taken from the names of their initial days. On the other 

 hand, we know that all the ancient nations of Mexico knew a period of 

 52 years and reckoned by it. We must therefore conclude that the 

 year of 365 days was indeed accepted in Mexico, as was stated above, 

 and therefore that the computation of time fell l)ehind the actual 

 length of the year l)y 6 hours, 9 minutes, and 1(> seconds in the inter- 

 calary year and by 5 hours, 4S minutes, and 48 seconds in the ordinary 

 year. 



This simple and clear, and, when we consider the degree of civilization 

 of the ancient Mexicans, by no means very remarkable fact, has up 

 to the present time been obstinately overlooked by the authors who have 

 written upon Mexican chronology. There are three circumstances 

 in particular which interfere with a correct conception of the state of 

 aiiairs— tirst, certain assumptions in respect to the last ti\e days of 

 the year; then, the assertions of historians in regard to interpolations 

 which are supposed to have taken place at certain regularly I'ecurring 

 periods; and, lastly, the variability of the beginning of the year among 

 various races and also, as it seems, at various times, which has hitherto 



