MORLET] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 43 



Rule 2. The sequence of the numerical coefficients 1 to 13, inclusive, 

 repeats itself again and again without interruption, 1 following im- 

 mediately 13. 



Rule 3. The 13 numerical coefficients are attached to the 20 names, 

 so that after a start has been made by prefixing any one of the 13 

 numbers to any one of the 20 names, the number next in order is 

 given to the name next in order, and the sequence continues indefi- 

 nitely in this manner. 



It is a simple question of arithmetic to determine the number of 

 days which must elapse before a day bearing the same designation 

 as a previous one in the sequence can reappear. Since there are 

 13 numbers and 20 names, and since each of the 13 numbers must 

 be attached in turn to each one of the 20 names before a given number 

 can return to a given name, we must find the least common multiple 

 of 13 and 20. As these two numbers, contain no common factor, 

 their least common multiple is their product (260), which is the num- 

 ber sought. Therefore, any given day can not reappear in the se- 

 quence until after the 259 days immediately following it shall have 

 elapsed. Or, in other words, the 261st day will have the same 

 designation as the 1st, the 262d the same as the 2d, and so on. 



This is graphically shown in the wheel figured in plate 5, where the 

 sequence of the days, commencing with 1 Imix, which is indicated 

 by a star, is represented as extending around the rim of the wheel. 

 After the name of each day, its number in the sequence beginning \\dth 

 the starting point 1 Imix, is shown in parenthesis. Now, if the star 

 opposite the day 1 Imix be conceived to be stationary and the wheel 

 to revolve in a sinistral circuit, that is contra-clockwise, the days will 

 pass the star in the order which they occupy in the 260-day sequence. 

 It appears from this diagram also that the day 1 Imix can not recur 

 until after 260 days shaU have passed, and that it always follows the 

 day 13 Ahau. This must be true since Ahau is the name immediately 

 preceding Imix in the sequence of the day names and 13 is the number 

 immediately preceding 1. After the day 13 Ahau (the 260th from 

 the starting point) is reached, the day 1 Imix, the 261st, recurs and 

 the sequence, having entered into itself again, begins anew as before. 



This round of the 260 differently named days was called by the 

 Aztec the tonalamatl, or "book of days." The Maya name for this 

 period is unknown ^ and students have accepted the Aztec name for 

 it. The tonalamatl is frequently represented in the Maya codices, 

 there being more than 200 examples in the Codex Tro-Cortesiano 

 alone. It was a very useful period for the calculations of the priests 

 because of the different sets of factors into which it can be resolved, 



1 Professor Seler says the Maya of Guatemala called this period the kin katun, or "order of the days." 

 He fails to give his authority for this statement, however, and, as will appear later, these terms have 

 entirely different meanings. (See Bulletin 28, p. 14.) 



