| A3 = | 9 × | 144,000 = | 1,296,000 |
| B3 = | 18 × | 7,200 = | 129,600 |
| A4 = | 5 × | 360 = | 1,800 |
| B4 = | 0 × | 20 = | 0 |
| A5 = | 0 × | 1 = | 0 |
| ———— | |||
| 1,427,400 | |||
Therefore 1,427,400 will be the number used in the following calculations.
The second step (see step 2, p. [135]) is to determine the starting point from which this number is counted. According to rule 2, page [136], if the number is an Initial Series the starting point, although never recorded, is practically always the date 4 Ahau 8 Cumhu. Exceptions to this rule are so very rare that they may be disregarded by the beginner, and it may be taken for granted, therefore, in the present case, that our number 1,427,400 is to be counted from the date 4 Ahau 8 Cumhu.
The third step (see step 3, p. £136) is to determine the direction of the count, whether forward or backward. In this connection it was stated that the general practice is to count forward, and that the student should always proceed upon this assumption. However, in the present case there is no room for uncertainty, since the direction of the count in an Initial Series is governed by an invariable rule. In Initial Series, according to the rule on page [137], the count is always forward, consequently 1,427,400 is to be counted forward from 4 Ahau 8 Cumhu.
The fourth step (see step 4, p. [138]) is to count the given number from its starting point; and the rules governing this process will be found on pages [139]-[143]. Since our given number (1,427,400) is greater than 18,980, or 1 Calendar Round, the preliminary rule on page [143] applies in the present case, and we may therefore subtract from 1,427,400 all the Calendar Rounds possible before proceeding to count it from the starting point. By referring to Table [XVI], it appears that 1,427,400 contains 75 complete Calendar Rounds, or 1,423,500; hence, the latter number may be subtracted
from 1,427,400 without affecting the value of the resulting terminal date: 1,427,400 - 1,423,500 = 3,900. In other words, in counting forward 3,900 from 4 Ahau 8 Cumhu, the same terminal date will be reached as though we had counted forward 1,427,400.[[118]]
In order to find the coefficient of the day of the terminal date, it is necessary, by rule 1, page [139], to divide the given number or its equivalent by 13; 3,900 ÷ 13 = 300. Now since there is no fractional part in the resulting quotient, the numerator of an assumed fractional part will be 0; counting forward 0 from the coefficient of the day of the starting point, 4 (that is, 4 Ahau 8 Cumhu), we reach 4 as the coefficient of the day of the terminal date.
In order to find the day sign of the terminal date, it is necessary, under rule 2, page [140], to divide the given number or its equivalent by 20; 3,900 ÷ 20 = 195. Since there is no fractional part in the resulting quotient, the numerator of an assumed fractional part will be 0; counting forward 0 in Table [I], from Ahau, the day sign of the starting point (4 Ahau 8 Cumhu), we reach Ahau as the day sign of the terminal date. In other words, in counting forward either 3,900 or 1,427,400 from 4 Ahau 8 Cumhu, the day reached will be 4 Ahau. It remains to show what position in the year this day 4 Ahau distant 1,427,400 from the date 4 Ahau 8 Cumhu, occupied.
In order to find the position in the year which the day of the terminal date occupied, it is necessary, under rule 3, page [141], to divide the given number or its equivalent by 365; 3,900 ÷ 365 = 10250⁄365. Since the numerator of the fractional part of the resulting quotient is 250, to reach the year position of the day of the terminal date desired it is necessary to count 250 forward from 8 Cumhu, the year position of the day of the starting point 4 Ahau 8 Cumhu. It appears from Table [XV], in which the 365 positions of the year are given, that after position 8 Cumhu there are only 16 positions in the year—11 more in Cumhu and 5 in Uayeb. These must be subtracted, therefore, from 250 in order to bring the count to the end of the year; 250 - 16 = 234, so 234 is the number of positions we must count forward in the new year. It is clear that the first 11 uinals in the year will use up exactly 220 of our 234 positions (11 × 20 = 220), and that 14 positions will be left, which must be counted in the next uinal, the 12th. But the 12th uinal of the year is Ceh (see Table [XV]); counting forward 14 positions in Ceh, we reach 13 Ceh, which is, therefore, the month glyph of our terminal date. In other words, counting 250 forward from 8 Cumhu, position 13 Ceh is reached. Assembling the above values, we find that by calculation we have determined the terminal date of the Initial Series in plate [6], A, to be 4 Ahau 13 Ceh.