An Introduction to the Study of the Maya Hieroglyphs

by Sylvanus Griswold Morley

1. The day coefficient, which must be one of the numerals 1 to 13, inclusive.

2. The day name, which must be one of the twenty given in Table [I].

3. The position of the day in some division of the year, which must be one of the numerals 0 to 19, inclusive.

4. The name of the division of the year, which must be one of the nineteen given in Table [III].

These four unknown elements all have to be determined from (1) the starting date, and (2) the number which is to be counted from it.

If the student will constantly bear in mind that all Maya sequences, whether the day coefficients, day signs, positions in the divisions of the year, or what not, are absolutely continuous, repeating themselves without any break or interruption whatsoever, he will better understand the calculations which follow.

It was explained in the text (see pp. [41]-[44]) and also shown graphically in the tonalamatl wheel (pl. [5]) that after the day coefficients had reached the number 13 they returned to 1, following each other indefinitely in this order without interruption. It is clear, therefore, that the highest multiple of 13 which the given number contains may be subtracted from it without affecting in any way the value of the day coefficient of the date which the number will reach when counted from the starting point. This is true, because no matter what the day coefficient of the starting point may be, any multiple of 13 will always bring the count back to the same day coefficient.

Taking up the number, 31,741, which we have chosen for our first example, let us deduct from it the highest multiple of 13 which it contains. This will be found by dividing the number by 13, and multiplying the whole-number part of the resulting quotient by 13: 31,741 ÷ 13 = 2,4418⁄13. Multiplying 2,441 by 13, we have 31,733, which is the highest multiple of 13 that 31,741 contains; consequently it may be deducted from 31,741 without affecting the value of the resulting day coefficient: 31,741 - 31,733 = 8. In the example under consideration, therefore, 8 is the number which, if counted from the day coefficient of the starting point, will give the day coefficient of the resulting date. In other words, after dividing by 13 the only part of the resulting quotient which is used in determining the new day coefficient is the numerator of the fractional part.[^[100]] Hence the following rule for determining the first unknown on page [138] (the day coefficient):

Rule 1. To find the new day coefficient divide the given number by 13, and count forward the numerator of the fractional part of the resulting quotient from the starting point if the count is forward, and backward if the count is backward, deducting 13 in either case from the resulting number if it should exceed 13.