150 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 



tJio only purls uctiuiUy rocorckHl jirc tho Iiiitial Sorios 9.12.2.0.16 



5 Cib 14 Yaxkin, and the Secondary Series 12.9.15 leadin*,^ to 9 Chuen 



9 Kankin; the Secondary Series 5 leadin<j; to 1 Cib 14 Kankin ; and 

 the Secondary Series 1.0.2.5 leatUnc? to 5 Imix 19 Zac. The Initial- 

 series values: 9.12.14.10.11; 9. 12.14. 10.10; and 9.13.14.13.1, belonj^- 

 ing to the three dates of the Secondary Series, respectively, do not 

 appear in the text at all (a fact indicated by the brackets), but 

 arc found only by calculation. Moreover, the student should note 

 that in a succession of interdependent series like the ones just given 

 the terminal date reached by one number, as 9 Chuen 9 Kankin, 

 becomes the starting point for the next number, 5. Again, the ter- 

 minal date reached by counting 5 from 9 Chuen 9 Kankin, that is, 

 1 Cib 14 Kankin, becomes the starting point from which the next 

 number, 1.0.2.5, is counted. In other words, these terms are only 

 relative, since the terminal date of one number will be tlie starting 

 point of the next. 



Let us assume for the next example that the number 3.2 is to be 

 counted forward from the Initial Series 9.12.3.14.0 6 Ahau 8 TJo. 

 Reducing 3 uinals and 2 kins to kins, we have 02 units of the first 

 order. Counting forward 62 from 5 Ahau 8 Uo, as incUcated by tlie 

 rules on pages 138-143, it is found that the terminal date will be 2 Ik 



10 Tzec. Since the Initial-series value of the starting point 6 Ahau 

 8 TJo is known, namely, 9.12.3.14.0, the Initial Series correspondmg 

 to the terminal date may be calculated from it as before: 



9.12.3.14.0 (Initial-scries value of the starting point) 5 Ahau 8 JJo 

 3.2 (distance from 5 Ahau 8 Uo forward to 2 Ik 10 Tzec) 

 [9.12.3.17.2] (Initial-series value of th;* terminal date) 2 Ik 10 Tzec 



The bracketed 9.12.3.17.2 in the Initial-series value corresponding 

 to the date 2 Ik 10 Tzec does not appear in the record but was reached 

 by calculation. The student may prove the accuracy of this result 

 by treating 9.12.3.17.2 2 Ik 10 Tzec as a new Initial Series, and 

 counting forward 9.12.3.17.2 from 4 Ahau 8 Cumhu (the starting 

 point of Maya chronology, unexpressed in Initial Series). If our 

 calculations are correct, the same date, 2 Ik 10 Tzec, will be reached, 

 as though we had counted only 3.2 forward from the Initial vSeries 

 9.12.3.14.0 5 Ahau 8 Uo. 



One more example presentmg a "backward count" will sullice to 

 illustrate this method. Let us count the number 14.13.4.17 bacJcward 

 from the Initial Series 9.14.13.4.17 12 Caban 6 Kayab. Reducing 

 14.13.4.17 to units of the 1st order, we have 105,577. Counting this 

 number backward from 12 Caban 6 Kayab, as indicated in the rules 

 on pages 138-143, we find that the terminal date will be 8 Ahau 13 Ceh. 

 Moreover, since the Initial-series value of the starting point 12 Caban 



6 Kayab is Icnown, namely, 9.14.13.4.17, the Initial-series value of 



