Deducting from this number, as before, all the Calendar Rounds possible, 98 (see p. [203], footnote 3), and applying rules 1, 2, and 3 (pp. [139], [140], [141], respectively) to the remainder, remembering that in each operation the direction of the count is backward, not forward,—the starting point will be found to be 4 Ahau 8 Zotz. This is the first Initial Series yet encountered which has not proceeded from the date 4 Ahau 8 Cumhu, and until the new starting point here indicated can be substantiated it will be well to accept the correctness of this text only with a reservation. The most we can say at present is that if the number recorded in A3-A5, 13.0.0.0.0, be counted forward from 4 Ahau 8 Zotz as a starting point, the terminal date reached by calculation will agree with the terminal date as recorded in B5-A6, 4 Ahau 8 Cumhu.
Let us next examine the Initial Series on the tablet from the Temple of the Cross at Palenque, which is shown in figure [77], B.[[178]] The introducing glyph appears in A1-B2, and is followed by the Initial-series number in A3-B7. The period glyphs in B3, B4, B5, B6, and B7 are all expressed by their corresponding normal forms, which will be readily recognized. Passing over the cycle coefficient in A3 for the present, it is clear that the katun coefficient in A4 is 19. Note the dots around the mouth, characteristic of the head for 9 (fig. [52], g-l), and the fleshless lower jaw, the essential element of the head for 10 (fig. [52], m-r). The combination of the two gives the head in A4 the value of 19. The tun coefficient in A5 is equally clear as 13. Note the banded headdress, characteristic of the head for 3 (fig. [51], h, i), and the fleshless lower jaw of the 10 head, the combination of the two giving the head for 13 (fig. [52], w).[[179]] The head for 4 and the hand zero sign appear as the coefficient of the uinal and kin signs in A6 and A7, respectively. The number will read, therefore, ?.19.13.4.0. Let us examine the cycle coefficient in A3 again. The natural assumption, of course, is that it is 9. But the dots characteristic of the head for 9 are not to be found here. As this head has no fleshless lower jaw, it can not be 10 or any number above 13, and as there is no clasped hand associated with it, it can not signify 0, so we are limited to the numbers, 1, 2, 3, 4, 5,[[180]] 6, 7, 8, 11, 12, and 13, as the numeral here recorded. Comparing this form with these numerals in figures [51] and [52], it is evident that it can not be 1, 3, 4, 5, 6, 7, 8, or 13, and that it must therefore be 2, 11, or 12. Substituting these three values in turn, we have 2.19.13.4.0, 11.19.13.4.0, and 12.19.13.4.0 as the possible numbers recorded in A3-B7, and reducing these numbers to units of the first order and deducting the highest number of Calendar Rounds possible from each, and applying rules 1, 2, and 3 (pp. [139], [140], and [141], respectively) to their remainders, the terminal dates reached will be:
| 2.19.13.4.0 | 5 Ahau 3 Pax |
| 11.19.13.4.0 | 9 Ahau 8 Yax |
| 12.19.13.4.0 | 8 Ahau 13 Pop |
If this text is perfectly regular and our calculations are correct, one of these three terminal dates will be found recorded, and the value of the cycle coefficient in A3 can be determined.
The terminal date of this Initial Series is recorded in A8-B9 and the student will easily read it as 8 Ahau 18 Tzec. The only difference
between the day coefficient and the month coefficient is that the latter has a fleshless lower jaw, increasing its value by 10. Moreover, comparison of the month sign in B9 with g and h, figure [19], shows unmistakably that the month here recorded is Tzec. But the terminal date as recorded does not agree with any one of the three above terminal dates as reached by calculation and we are forced to accept one of the two conclusions which confronted us in the preceding text (fig. [77], A): Either the starting point of this Initial Series is not the date 4 Ahau 8 Cumhu, or there is some error in the original text.[[181]]
Assuming that the ancient scribes made no mistakes in this inscription, let us count backward from the recorded terminal date, 8 Ahau 18 Tzec, each of the three numbers 2.19.13.4.0, 11.19.13.4.0, and 12.19.13.4.0, one of which, we have seen, is recorded in A3-B7.
Reducing these numbers to units of the first order by means of Table [XIII], and deducting all the Calendar Rounds possible from each (see Table [XVI]), and, finally, applying rules 1, 2, and 3 (pp. [139], [140], and [141], respectively), to the remainders, the starting points will be found to be:
| 7 Ahau 3 Mol | for 02.19.13.4.0 |
| 3 Ahau 18 Mac | for 11.19.13.4.0 |
| 4 Ahau 8 Zotz | for 12.19.13.4.0 |