solstitial points, to the cycles of sixty days, and 
the durations of the half lunations. 
We have already observed, that the Mexican 
year, like that of the Egyptians and Persians, 
was composed of three hundred and sixty days> 
to which were added five epagomena, termed 
furtive (muster aka) ^ or useless (nemontemij. 
If the Mexicans had been unacquainted with 
the excess of the duration of the revolution of 
the Sun over three hundred and sixty-five days, 
the beginning of their year, like that of the 
vague year of the Egyptians, would have passed, 
in about one thousand five hundred and eight 
years, through every season and every point of 
the ecliptic. Four centuries had elapsed after 
the reform of the Mexican calendar in 1091, be- 
fore the arrival of the Spaniards. The writers 
of that time affirm, that at this epocha the ca- 
lendar of the Europeans coincided within a few 
days with the Azteck calendar : and the accu- 
rate calculation of the eclipses of the Sun 
marked in the Mexican annals even render it 
probable, that the difference observed between 
the two calendars proceeded wholly from our 
own not having yet undergone the Gregorian 
reform. Let us now examine what was the 
mode of intercalation, by which the Mexicans 
avoided the errors of their chronology. 
The Mexican year being solar, and not lunar. 
