206 



supernumerary day forms at the end of each indie- 

 tion a small entire period, and a tlalpilli contains 

 three hundred and sixty-five of these periods : 

 that is, as many weeks of thirteen days, as the 

 year has civil days. A year of the ritual alma- 

 nack has twenty half lunations, or two hundred 

 and sixty days, and this same number of days 

 contains fifty-two half decades, or small periods 

 of five days ; the Mexicans then found, in the 

 concordance of these two reckonings of the 

 Moon and the Sun, their favourite numbers of 

 five, thirteen, twenty, and fifty-two. A cycle of 

 fifty-two years contained one thousand four hun- 

 dred and sixty small periods of thirteen days ; 

 and, if to these we add thirteen intercalary days, 

 we shall have one thousand four hundred and 

 sixty- one small periods ; a number which acci- 

 dentally coincides with that of the years consti- 

 tuting the Sothiac period. 



The cycle of nineteen solar years, which cor- 

 responds to two hundred and thirty-five luna- 

 tions, and which the Chinese knew more than 

 sixteen centuries before Meton *, finds its multi- 

 ple neither in the cycle of sixty years, which is 

 in use among the greater part of the nations of 

 eastern Asia^ and among the Muyscas of the 

 elevated plain of Bogota ; nor in the cycle of 

 fifty- two years, adopted by all the nations of the 



* La Place, Expos, torn. 2, f . 2G7. 



