128 MEXICO AND CENTRAL AMERICA 
ing long stretches of time. It is also apparent that many 
of the sculptures represent conquests and it is extremely 
likely that portraits of actual rulers are to be seen in cer- 
tain carvings. It would be too much to expect events to 
happen regularly at the end of time periods and as a 
matter of fact we find at different cities repeated dates 
that do not occupy such positions. These repeated 
dates would seem to recall events of special importance 
to the city in question. 
The running co-ordination between the apparent order 
of the artistic styles and inscribed dates permits us to 
measure very accurately the rate of change which was 
rapid, indeed, at certain times. ‘The style of carving, on 
the other hand, enables us to put into definite 52 year 
periods many of the calendar round dates—if these are 
to be regarded as contemporaneous. ‘The result is that 
for the First Empire, as it has been called, there is an ex- 
ceedingly accurate chronology. A/ter the fall and aban- 
donment of the great southern cities dates are rare 
and we have to fall back upon remnants of history pre- 
served after the coming of the Spaniards. 
Books of Chilan Balam. The Books of Chilan 
Balam are digests of ancient chronicles preserved in the 
Mayan language but in Spanish script. The events are 
recorded as occurring in such and sucha katun. Now 
the katun of these chronicles is exactly the same length 
as the katun or fourth position in the ancient Initial Se- 
ries dates (20x 360 or 7200 days). All katuns are com- 
pleted on a day Ahau which may have any number from 
1 to 13. In the Kahlay katun ob or “‘record of the ka- 
tuns,’’ which gives the actual sequence of the terminal 
Ahaus, the numbers fall as follows: 18, 11, 9, 7, 5, 3, 1. 12, 
10, 8, 6, 4, 2, after which there is a repeat. The time 
covered by this wheel is 13 x 7200 or 93,600 days (almost 
