The student will note the absence of all period glyphs from this Initial Series and will observe that the multiplicands of the cycle, katun, tun, uinal, and kin are fixed by the positions of each of the corresponding multipliers. By referring to Table [XIV] the values of the several positions in the second method of writing the numbers will be found, and using these with their corresponding coefficients in each case the Initial-series number here recorded may be reduced to units of the 1st order, as follows:

9 × 144,000 = 1,296,000
9 × 7,200 = 64,800
16 × 360 = 5,760
0 × 20 = 0
0 × 1 = 0
————
1,366,560

Deducting from this number all the Calendar Rounds possible, 72 (see Table [XVI]), it may be reduced to zero, since 72 Calendar Rounds contain exactly 1,366,560 units of the first order. See the preliminary rule on page [143].

Applying rules 1, 2, and 3 (pp. [139], [140], and [141]) to the remainder, that is, 0, the terminal date of the Initial Series will be found to be 4 Ahau 8 Cumhu, exactly the same as the starting point of Maya chronology. This must be true, since counting forward 0 from the date 4 Ahau 8 Cumhu, the date 4 Ahau 8 Cumhu will be reached. Instead of recording this date immediately below the last period of its Initial-series number, that is, the 0 kins, it was written below the number just to the left. The terminal date of the Initial Series we are discussing, therefore, is 4 Ahau 8 Cumhu, and it is recorded just to the left of its usual position in the lower left-hand corner of plate 31. The coefficient of the day sign, 4, is effaced but the remaining parts of the date are perfectly clear. Compare the day sign Ahau with the corresponding form in figure [17], c', d', and the month sign Cumhu with the corresponding form in figure [20], z-b'. The Initial Series here recorded is therefore 9.9.16.0.0 4 Ahau 8 Cumhu. Just to the right of this Initial Series is another, the number part of which the student will readily read as follows: 9.9.9.16.0. Treating this in the usual way, it may be reduced thus:

9 × 144,000 = 1,296,000
9 × 7,200 = 64,800
9 × 360 = 3,240
16 × 20 = 320
0 × 1 = 0
————
1,364,360

Deducting from this number all the Calendar Rounds possible, 71 (see Table [XVI]), it may be reduced to 16,780. Applying to this number rules 1, 2, and 3 (pp. [139], [140], and [141], respectively), its terminal date will be found to be 1 Ahau 18 Kayab; this date is recorded just to the left below the kin place of the preceding Initial

Series. Compare the day sign and month sign of this date with figures [17], c', d', and [20], x, y, respectively. This second Initial Series in plate [31] therefore reads 9.9.9.16.0 1 Ahau 18 Kayab. In connection with the first of these two Initial Series, 9.9.16.0.0 4 Ahau 8 Cumhu, there is recorded a Secondary Series. This consists of 6 tuns, 2 uinals, and 0 kins (6.2.0) and is recorded just to the left of the first Initial Series from which it is counted, that is, in the left-hand column.

It was explained on pages [136]-[137] that the almost universal direction of counting was forward, but that when the count was backward in the codices, this fact was indicated by a special sign or symbol, which gave to the number it modified the significance of "backward" or "minus." This sign is shown in figure [64], and, as explained on page [137], it usually is attached only to the lowest period. Returning once more to our text, in plate [31] we see this "backward" sign—a red circle surmounted by a knot—surrounding the 0 kins of this Secondary-series number 6.2.0, and we are to conclude, therefore, that this number is to be counted backward from some date.

Counting it backward from the date which stands nearest it in our text, 4 Ahau 8 Cumhu, the date reached will be 1 Ahau 18 Kayab. But since the date 4 Ahau 8 Cumhu is stated in the text to have corresponded with the Initial-series value 9.9.16.0.0, by deducting 6.2.0 from this number we may work out the Initial-series value for this date as follows: