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Cincinnati Society of Natural History. 



Tochtli") in order to find accurately the number of years in their 

 histories, you must substract one unit from the number of "bind- 

 ings of years," and multiply the remainder by 52, and you will 

 have exactly the number of years elapsed from the first festival to 

 the last Xiuhmolpilli. 



The second thing is that, having commenced to count their first 

 cycle after twenty-six years had elapsed from their exodus from 

 Aztlan, which is their epoch, in order to find any particular year 

 referred to in their histories, or of any special events, to the prod- 

 uct of the cycles completed, reckoning from "ce Tochtli," you 

 add, besides the passed years of the following cycles, the twenty- 

 six which has elapsed since the exodus from Aztlan, and the sum 

 will be the number of years reckoned from their epoch. For ex 

 ample, in the year "ce Acatl, " the year in which the Spaniards 

 entered Mexico, which was the first of the second indiction after 

 the ninth ' 4 Xiuhmolpia, " you will ascertain those that have elapsed 

 since their epoch. If, to the product 416 of the 8 completed 

 cycles, you add the 13 years that have elapsed of the first follow- 

 ing indiction and the 26 years that have passed since the exodus 

 from Azatlan until the first Xiuhmolpia, there results 455 years 

 which have elapsed from the Mexican epoch to the arrival of the 

 Spaniards, which sum, substracted from 15 19 of our calendar, 

 gives for the exodus from Aztlan the year 1064 of the Christian 

 era, as has already been stated. 4 16+13 +26=45 5- l >5 1 9 — 455 

 = 1,064. 



9. Each one of the years of their civil period consisted of 365 

 days, a distinction from the solar tropical year of 365 days, 5 

 hours, 48 minutes and 50 seconds ; hence, this excess of almost 6 

 hours makes in each quadrennial the retrocession of one day in 

 the commencement of the year. 



At the end of 52 years the retrocession would amount to 13 

 days, which they knew perfectly well, and, in order to make the 

 correction, they added to the last year, not precisely that number, 

 but only 12*4 days, as is clearly proved in the history of their 

 chronology, and, consequently, 25 complete days at the end of 

 their grand cycle of 104 years, which correction appears to be the 

 most exact of any that has been invented in order to reduce the 



