142 BUEEAU OF AMERICAN ETHNOLOGY [bull. 57 



Applying this rule to the number 31,741, we have seen above that 

 its division by 365 gives 351 as the numerator of the fractional part of 

 its quotient. Assuming that the count is forward from the starting 

 point, it will be necessary, therefore, to count 351 forward in Table 

 XV from the position 8 Cumhu, the position of the day of the starting 

 point, 4 Ahau 8 Cumhu. 



A glance at the month of Cumhu in Table XV shows that after the 

 position 8 Cumhu there are 11 positions in that month; adding to 

 these the 5 in Uayeb, the last division of the year, there will be in all 

 16 more positions before the first of the next year. Subtracting 

 these from 351, the total number to be counted forward, there remains 

 the number 335 (351-16), which must be counted forward in Table 

 XV from the beginning of the year. Since each of the montlis has 

 20 positions, it is clear that 16 months will be used before the month 

 is reached in which will fall the 335th position from the beginning of 

 the year. In other words, 320 positions of our 335 will exactly use 

 up all the positions of the first 16 months, namely. Pop, XJo, Zip, 

 Zotz, Tzec, Xul, Yaxkin, Mol, Chen, Yax, Zac, Ceh, Mac, Kankin, 

 Muan, Pax, and will bring us to the begmning of the 17th month 

 (Kayab) with still 15 more positions to count forward. If the student 

 will refer to this month in Table XV he will see that 15 positions 

 counted forward in this month will reach the position 14 Kayab, 

 which is also the position reached by counting forward 31,741 posi- 

 tions from the starting position 8 Cumhu. 



Having determined values for all of the unknowns on page 138, we 

 can now say that if the number 31,741 be counted forward from the 

 date 4 Ahau 8 Cumhu, the date 12 Imix 14 Kayab will be reached. 

 To this latter date, i. e., the date reached by any count, the name "ter- 

 minal date" has been given. The rules indicating the processes by 

 means of which this terminal date is reached apply also to examples 

 where the count is hackward, not forward, from the starting point. 

 In such cases, as the rules say, the only difference is that the 

 numeratoi-s of the fractional parts of the quotients resulting from the 

 different divisions are to be counted backward from the starting 

 points, instead of forward as in the example above given. 



Before proceeding to apply the rules by means of which our fourth 

 step or process (see p. 138) may be carried out, a modification may 

 sometimes be introduced which will considerably decrease the size 

 of the number to be counted without affecting the values of the 

 several parts of its resulting terminkl date. 



We have seen on pages 51-60 that in Maya chronology there were 

 possible only 18,980 different dates — that is, combinations of the 260 

 days and the 365 positions of the year — and further, that any given 

 day of the 260 could return to any given position of the 365 only after 

 the lapse of 18,980 days, or 52 years. 



