MOELEY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 63 



in which 18 units instead of 20 make 1 unit of the 3d place, or 

 order next higher (tuns) . The break in the regularity of the viges- 

 imal progression in the 3d place was due probably to the desire to 

 brmg the unit of this order (the tun) into agreement with the solar 

 year of 365 days, the number 360 being much closer to 365 than 400, 

 the third term of a constant vigesimal progression. We have seen on 

 page 45 that the 18 uinals of the haab were equivalent to 360 days 

 or kins, precisely the number contained in the third term of the 

 above table, the tun. The fact that the haab, or solar year, was 

 composed of 5 days more than the tun, thus causing a discrepancy 

 of 5 days as compared with the third place of the chronological sj^s- 

 teni, may have given to these 5 closing days of the haab — that is, the 

 xma kaba kin — the unlucky character they were reputed to possess. 



The periods were numbered from to 19, inclusive, 20 units of 

 any order (except the 2d) always appearing as 1 unit of the order 

 next higher. For example, a number involving the use of 20 kins 

 was written 1 uinal instead. 



We are now in possession of all the different factors which the 

 Maya utilized in recording their dates and in counting time : 



1. The names of their dates, of which there could be only 18,980 

 (the number of dates in the Calendar Round) . 



2. The date, or starting point, 4 Ahau 8 Cumhu, from which time 

 was reckoned. 



3. The counters, that is, the units, used in measuring the passage 

 of time. 



It remains to explain how these factors were combined to express 

 the various dates of Maya chronology. 



Initial Series 



The usual manner in which dates are written in both the codices and 

 the inscriptions is as follows: First, there is set down a number com- 

 posed of five periods, that is, a certain number of cycles, katuns, tuns, 

 uinals, and kuis, which generally aggregate between 1,300,000 and 

 1,500,000 days; and this number is followed by one of the 18,980 

 dates of the Calendar Round. As we shall see in the next chapter, 

 if this large number of days expressed as above be counted forward 

 from the fixed starting point of Maya chronology, 4 Ahau 8 Cumhu, 

 the date invariably ' reached will be found to be the date written 

 at the end of the long number. This method of dating has been 

 called the Initial Series, because when inscribed on a monument it 

 invariably stands at the head of the inscription. 



The student will better comprehend this Initial-series method of 

 dating if he will imagine the Calendar Round represented by a large 

 cogwheel A, figure 23, having 18,980 teeth, each one of which is 



1 There are only two knovvTi exceptions to this statement, namely, the Initial Series on the Temple of 

 the Cross at Palenque and that on the east side of Stela C at Quirigua, already noted. 



