62 BUEEAU OF AMEEICAN ETHNOLOGY (bull. 57 



2. That after this long period had elapsed all the dated monunients^ 

 had their origin in the comparativeh' short period of four centuries. 



Consequently, it is safe to conclude that no matter what the Maya 

 may have believed took place on this date 4 Ahau 8 Cumhu, in reality 

 when this day was present time they had not developed their dis- 

 tinctive civilization or even achieved a social organization. 



It is clear from the foregoing that in addition to the Calendar 

 Round, the Maya made use of a fixed starting point in describing 

 their dates. The next question is, Did they record the lapse of more 

 than 3,000 years simply by using so unwieldy a unit as the 52-year 

 period or its multiples? A numerical system based on 52 as its 

 primary unit immediately gives rise to exceedingly awkward num- 

 bers for its higher terms; that is, 52, 104, 156, 208, 260, 312, etc. 

 Indeed, the expression of really large numbers in terms of 52 involves 

 the use of comparatively large multipliers and hence of more or less 

 intricate multiplications, since the unit of progression is not decimal 

 or even a multiple thereof. The Maya were far too clever mathema- 

 ticians to have been satisfied with a numerical system which employed 

 units so inconvenient as 52 or its multiples, and which involved 

 processes so clumsy, and we may therefore dismiss the possibility of 

 its use without further consideration. 



In order to keep an accurate account of the large numbers used in 

 recording dates more than 3,000 years distant from the starting point, 

 a numerical system was necessary whose terms could be easily 

 handled, like the units, tens, hundreds, and thousands of our own 

 decimal system. ^^Tiether the desire to measure accurately the 

 passage of time actually gave rise to their numerical system, or vice 

 versa, is not known, but the fact remains that the several periods 

 of Maya chronology (except the tonalamatl, haab, and Calendar 

 Round, previously discussed) are the exact terms of a vigesimal sys- 

 tem of numeration, with but a single exception. (See Table VIII.) 



Table VIII. THE MAYA TIME-PERIODS 



20 2 cycles=l great cycle =2,880,000 days 



Table VIII shows the several periods of Maya chronology by means 

 of which the passage of time was measured. All are the exact terms 

 of a vigesimal system of numeration, except in the 2d place (uinals) , 



' This statement does not take account of the Tuxtla Statuette and the llolactun Initial Series, which 

 extend the range of the dated monuments to ten centuries. 



'^ For the discussion of the number of cycles in a great cycle, a question concerning which there are 

 two different opinions, see pp. 107 et seq. 



