Combining the above values, we find that in counting forward 322,920 (or 260) from the starting point 13 Ik 0 Zip, the terminal date reached is 13 Ik 0 Pax.
In order to illustrate the method of procedure when the count is backward, let us assume an example of this kind. Suppose we count backward the number 9,663 from the starting point 3 Imix 4 Uayeb. Since this number is below 18,980, no Calendar Round can be deducted from it. Dividing the given number by 13, we have: 9,663 ÷ 13 =7434⁄13. Counting the numerator of the fractional part of this quotient, 4, backward from the day coefficient of the starting point, 3, we reach 12 as the day coefficient of the terminal date, that is, 2, 1, 13, 12 (rule 1, p. [139]). Dividing the given number by 20, we have: 9,663 ÷ 20 = 4833⁄20. Counting the numerator of the fractional part of this quotient, 3, backward from the day sign of the starting point, Imix, in Table [I], we reach Eznab as the day sign of the terminal date (Ahau, Cauac, Eznab); consequently the day reached in the count will be 12 Eznab. Dividing the given number by 365, we have
9,663 ÷ 365 = 26173⁄365. Counting backward the numerator of the fractional part of this quotient, 173, from the year position of the starting point, 4 Uayeb, the 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 backward 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 Cumhu, 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 0 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 count be forward or backward, the method is the same, the only difference being in the direction 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 points and terminal dates, without assigning either set of dates to their proper positions in Maya chronology; 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 distinct 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 Cumhu, 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 distinguished 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: "Counting forward 9 cycles, 0 katuns, 0 tuns, 0 uinals, and 0 kins
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."[[102]] Or again: