148 BUREAU OF AMERICAN ETHNOLOGY iBi ll. 57 



from 4 Ahau 8 Cumhu, the starting point of Maya chronology (always 

 unexpressed in Initial Series), the terminal date reached will be 8 

 Ahau 13 Ceh." ^ Or again: 



9.14.13.4.17. 12 Caban 5 Kayab 

 This Inital Series reads thus: "Counting forward 9 cycles, 14 katims, 

 13 tuns, 4 uinals, and 17 kins from 4 Ahau 8 Cumhu, the starting 

 point of Maya chronology (unexpressed), the terminal date reached 

 mil be 12 Caban 5 Kayab." 



The time wliich separates any date from 4 Ahau 8 Cumhu may 

 be called that date's Initial-series value. For example, in the first 

 of the above cases the number 9.0.0.0.0 is the Initial-series value of 

 the date 8 Ahau 13 Ceh, and in the second the number 9.14.13.4.17 

 is the Initial-series value of the date 12 Caban 5 Kayab. It is clear 

 from the foregoing that although the date 8 Ahau 13 Ceh, for example, 

 had recurred upward of 70 times since the beginning of their chro- 

 nology, the Maya were able to distinguish any particular 8 Ahau 13 Ceh 

 from all the others merely by recording its distance from the starting 

 point; in other words, giving thereto its particular Initial-series 

 value, as 9.0.0.0.0. in the present case. vSimilarly, any particular 12 

 Caban 5 Kayab, by the addition of its corresponding Initial-series 

 value, as 9.14.13.4.17 in the case above cited, was absolutely fixed 

 in the Long Count — that is, in a period of 374,400 years. 



Returning now to the question of how the counting of numbers was 

 appUed to the Long Count, it is evident that every date in Maya 

 chronology, starting joints as well as terminal dates, had its own 'par- 

 ticular Initial-series value, though in many cases these values are not 

 recorded. However, in most of the cases in which the Initial-series 

 values of dates are not recorded, they may be calculated by means 

 of their distances from other dates, whose Initial-series values are 

 known. This adding and subtracting of numbers to and from Initial 

 Series ^ constitutes the appUcation of the above-described arithmetical 

 processes to the Long Count. Several examples of this use are given 

 below. 



Let us assume for the first case that the number 2.5.6.1 is to be 

 counted forward from the Initial Series 9.0.0.0.0 8 Ahau 13 Ceh. By 

 multiplying the values of the katuns, tuns, uinals, and kins given in 

 Table XIII by their corresponding coefficients, m this case 2, 5, 6, 

 and 1, respectively, and adding the resulting products together, we 

 find that 2.5.6.1 reduces to 16,321 units of the first order. 



Counting this forward from 8 Ahau 13 Ceh as indicated by the rules 

 on pages 138-143, the terminal date 1 Imix 9 Yaxkin will be reached. 



1 The student may prove this for himself by reducing 9.0.0.0.0 to days (1,296,000), and counting forward 

 this niunber from the date 4 Ahau 8 Cumhu, as described in the rules on pages 138-143. The terminal 

 date reached will be 8 Ahau 13 Ceh, as given above. 



2 Numbers may also be added to or subtracted from Period-ending dates, since the positions of such dates 

 are also fixed in the Long Count, and consequently may be used as bases of reference for dates whose posi- 

 tions in the Long Coimt are not recorded, 



