MOELEV] INTKODUCTION TO STUDY OF MAYA HIEEOGLYPHS 147 



9,663 ^ 365 = 26^-|-|. Counting backward the numerator of the frac- 

 tional part of tliis quotient, 173, from the year position of the starting 

 pomt, 4 Uayeb, tlie year position of the terminal date will be found to 

 be 11 Yax. Before position 4 Uayeb (see Table XV) there are 4 

 positions in that division of the year (3,2, 1,0). Counting these hack- 

 ward to the end of the month Cumhu (see Table XV), we have left 

 169 positions (173—4 = 169); this equals 8 uinals and 9 days extra. 

 Therefore, beginning with the end of Cumliu, we may count backward 

 8 whole uinals, namely: Cumhu, Kayab, Pax, Muan, Kankin, Mac, 

 Ceh, and Zac, which will bring us to the end of Yax (since we are 

 counting backward). As we have left still 9 days out of our original 

 173, these must be counted backward from position Zac, that is, 

 beginning with position 19 Yax: 19, 18, 17, 16, 15, 14, 13, 12, 11; so 

 11 Yax is the position in the year of the day of the terminal date. 

 Assembling the above values, we find that in counting the number 

 9,663 backward from the starting point, 2 Imix 4 Uayeb, the terminal 

 date is 12 Eznab 11 Yax. Whether the comit be forward or back- 

 ward, the method is the same, the only difference being in the direc- 

 tion of the counting. 



This concludes the discussion of the actual arithmetical processes 

 involved in counting forward or backward any given number from 

 any given date; however, before explaining the fifth and final step 

 in deciphering the Maya numbers, it is first necessary to show how 

 this method of counting was applied to the Long Count. 



The numbers used above in connection with dates merely express 

 the difference in time between starting pomts and terminal dates, 

 without assigning cither set of dates to their proper positions in Maya 

 cln-onology ; that is, in the Long Count. Consequently, since any Maya 

 date recurred at successive intervals of 52 years, by the time their 

 historic period had been reached, more than 3,000 years after the 

 starting point of their chronology, the Maya had upward of 70 dis- 

 tinct dates of exactly the same name to distinguish from one another. 



It was stated on page 61 that the 0, or starting point of Maya 

 chronology, was the date 4 Ahau 8 Cumliu, from which all subsequent 

 dates were reckoned; and further, on page 63, that by recording the 

 number of cycles, katuns, tuns, uinals, and kins which had elapsed 

 in each case between this date and any subsequent dates in the Long 

 Count, subsequent dates of the same name could be readily distin- 

 guished from one another and assigned at the same time to their 

 proper positions in Maya chronology. This method of fixing a date 

 in the Long Count has been designated Initial-series dating. 



The generally accepted method of writing Initial Series is as follows: 

 9.0.0.0.0. 8 Ahau 13 Ceh 

 The particular Initial-Series written here is to be interpreted thus: 

 "Comiting forward 9 cycles, katuns, tims, uinals, and kins 



