86 BUREAU OF AMEEICAN ETHNOLOGY [bull. 57 



sity for the use of even one Initial Series on every monument, in 

 order that one date might be fixed in the Long Count to which the 

 others (Secondary Series) coukl be referred. For all practical pur- 

 poses, as we have seen, Period-ending dating was as accurate as 

 Initial-series dating for fixing dates in the Long Count, and its sub- 

 stitution for Initial-series dating resulted in a further saving of 

 glyphs and a corresponding economy of space. Still later, probably 

 after the Maya had colonized Yucatan, the u kahlay katunob, which 

 was a direct application of Period-ending dating to the Long Count, 

 came into general use. At this time a rich history lay behind the 

 Maya people, and to have recorded all of its events by their corre- 

 sponding Initial Series would have been far too cumbersome a prac- 

 tice. The u kahlay katunob offered a convenient and facile method 

 by means of which long stretches of time could be recorded and events 

 approximately dated; that is, within 20 years. This, together with 

 the fact that the practice of setting up dated period-markers seems to 

 have languished in the north, thus eliminating the greatest medium 

 of all for the presentation of Initial Series, probably gave rise to the 

 change from the one method of recording time to the other. 



This concludes the discussion of the five methods by means of 

 which the Maya reckoned time and recorded dates: (1) Initial-series 

 dating; (2) Secondary-series dating; (3) Calendar-round dating; 

 (4) Period-ending dating; (5) Katun-ending dating, or the u kahlay 

 katunob. While apparently differing considerably from one another, 

 in reality all are expressions of the same fundamental idea, the com- 

 bination of the numbers 13 and 20 (that is, 260) wdth the solar year 

 conceived as containing 365 days, and all were recorded by the same 

 vigesimal system of numeration; that is: 



1. All used precisely the same dates, the 18,980 dates of the Cal- 

 endar Round; 



2. All may be reduced to the same fundamental unit, the day; and 



3. All used the same time counters, those shown in Table VIIT. 

 In conclusion, the student is strongly urged constantly to bear in 



mind two vital characteristics of Maya clironology: 



1. The absolute continuity of all sequences which had to do with 

 the counting of time: The 13 numerical coefficients of the day names, 

 the 20 day names, the 260 days of the tonalamatl, the 365 positions 

 of the haab, the 18,980 dates of the Calendar Round, and the kins, 

 uinals, tuns, katuns, and cycles of the vigesimal system of numera- 

 tion. When the conclusion of any one of these sequences had been 

 reached, the sequence began anew Arithout tlio interruption or omis- 

 sion of a single unit and continued repeating itself for all time. 



2. All Maya periods expressed not current time, but passed time, 

 as in the case of our hours, minutes, and seconds. 



On these two facts rests the whole Maya conception of time. 



