Brinton.] -^^4: [Oct. 6, 



that is, the upper and the under worlds, the same number, 13, 

 results, as it is held that in each the suu stands for the individ- 

 ual, being in turn the day-sun and the night-sun, the light and 

 the dark sun, but ever the same, and therefore counts but once. 



The number 13 possesses certain properties and relations 

 •which appear to have recommended it widely for divinatory 

 purposes and games. The Mexican " cycle " was composed of 

 52 years arranged in 4 series of 13 each ; precisel}^ analogous to 

 a pack of our playing cards. These cards can be traced back to 

 primitive games plaj^ed for purposes of divination ; and no 

 doubt the numbers were selected and combined in both instances 

 from the same motives. 



The Nahuas certainly regarded the ritual year of 2C0 days as 

 equivalent to 9 lunations, as they divided it in some of the most 

 important of their Calendars — the celebrated " Tonalamatl," for 

 instance — into 9 equal divisions, ruled over by the so-called 9 

 " Lords of the Night ;" thus 29 X 9 = 261 ; though what they 

 did with the supernumerary day is not clear.* 



An ingenious theory of the mathematical development of this 

 Calendar has been offered by Mrs. Zelia Nnttall. It assumes 

 that at the close of each period of 20 X 13 = 260 days, 5 inter- 

 calary daj^s were inserted before the next 260-day period was 

 technically commenced. This naturally brought its commence- 

 ment on the next subsequent Dominical day, and also caused 

 the whole period, 265 days, to equal, very nearly', nine lunations. 

 If it can be shown that this intercalation actually took place, 

 Mrs. Nuttall's suggestion will have cleared up one of the most 

 obscure problems in American archaeology. 



It seems inherently probable that there was some such ver\^ 

 accurate hieratic plan of keeping the time count, as we are as- 

 sured by many writers that certain native festivals, etc., were 

 observed precisely on days of the year fixed by the European 

 Cakndar.f 



*0n the Tonalamatl see Dr. Seler's very thorough article in the Compte-Rcndu of the 

 Congress of Americanists for 1888, p. 527, seq. 



t Dr. Stoll has shown that the Cakchiquels must have subtracted^ days from the 260 in 

 order to keep tlieir reckoning as we know they did. {Ethnologie der Indianersldmme von 

 Guatemala, p. 66. Leiden, 188!).) His comparison of the methods of reckoning time 

 among the Nahuas, Mayas and the nations of Guatemala is highly suggestive. 



