Brill ton.] -^Oi^ [Oct. 6, 



§ 3. Mathematical Basis of the Calendar. 



The general outlines of this Calendar system are so well known 

 — or rather, I should say, are discussed in so many accessible 

 books — that I need not more than refer to them here. 



The basis is a so-called " month " of 20 daj'S. Each day is 

 designated by a name of some object, animate or inanimate ; and 

 besides its name, each day is numbered, but not from 1 to 20, 

 but only from 1 to 13, when the numbering begins again at the 

 unit. 



The result of this combination evidently is, that a day bear- 

 ing both the same name and the same number will not recur 

 until 13 of the " months " have elapsed. This gives a period or 

 cycle of 260 days, and this anomalous period is at the founda- 

 tion of the native Calendar. 



Why was it chosen ? Does it correspond to any series of re- 

 curring events in nature ? Is it astronomical ? Or was it purely 

 mythical and terrestrial ? 



The answers to these inquiries are not entirely satisfactory. 

 It is generally admitted that the number 20 was chosen because 

 the arithmetical system of these nations was vigesimal, and 

 grouping the days by twenties was a natural method with them ; 

 and it has usually been stated that the number 13 represents 

 one-half the number of daj'S during which the moon is visible 

 between its heliacal conjunctions, and that it owed its selection 

 to this observation.* 



An obvious difficulty in this theoiy is, that according to it the 

 Calendar ought not to take note of the days when the moon is 

 in conjunction, as otherwise after the very first month it will no 

 longer correspond with the sequence of natural events from 

 which it is assumed to be derived ; but as these days are counted, 

 it would appear, although the lunar relations of the calendar in 

 later da^-s cannot be denied, that it had some other origin. 



The month may have been counted from new moon to new 

 moon ; but the 26 days in which the moon was actually visible 

 alone have been included in a ritual or ceremonial lunar count, 

 13 of these being assigned to the waxing, 13 to the waning 

 moon. 



* See Orozco y Berra, Hisloria Antigua de Mexico, Tome ii, p. 12. Another theory which 

 he suggests is tliat the 13 may have had reference to the 13 lunar months which approxi- 

 mately make up a solar year. 



