28-4 MAYAN CALENDAR SYSTEMS [etii. ann. 22 



By adding 2,920 to tlio tii>t, we obtiiin the sum of tlie second columu; 

 and adding the same numl>er to the siim of the second, we obtain the 

 sum of the third, and so on. By counting forward 2,920 daj's from 

 9 Ahau, the date under the first column, we reach -t Aliau, the date 

 under the 2nd column, etc. 



These primarj' steps are, of course, well understood by readers who 

 have given any attention to the subject, but it is necessary to present 

 tlieni as leading up to the object in view in the discussion. 



It is evident that • • , or 2,920, is tlie factor or added number used 



in this series, but the ijrocess is carried on by addition. However, 

 before we proceed, it is necessary to call to mind certain facts in rela- 

 tion to the calendar. The first is that a daj^ of any given name 

 returns at every 20th day, whether we count backward or forward, 

 but not with the same number; the second, that any given day returns 

 witli the same daj^ number at every 200th day, whichever way we 

 count, but not in the same month nor on the same day of the month 

 beyond the first year. As each count reaches Ahau in this instance, 

 and 200 is not an even divisor of 2,920, the basal factor must be 20, 

 and the daj' numbers will be different, as we find them to be. Although 

 we may not be able alwaj-s to state whj' particular factors or counters 

 are selected, yet in this case it would seem that 2,920 was chosen 

 because this is exactly the number of days in eight years. As the 

 dates are therefore just eight years apart, they necessarily fall in years 

 having the same dominical day, and, consequently, on the same day of 

 the month. However, these specific features must be understood as 

 api)lical)le to this j)articular series, and not as of general application, 

 for we shall find series in which there is no reference to the year; but 

 these time periods have a bearing on the practical method used in 

 Maya calculations. 



Now, let us see theoretically how, starting with a given date, the 

 initial date of a high series maj' be reached. Nine cycles and the 

 lower fractional numbers, counting from 4 Ahau 8 Cumhu as the 

 initial date, form the most frequent series of the Copan and Quirigua 

 inscriptions. We will try to form such a series, selecting at random 3 

 Cliicchan 18 Yax, year 1 Lamat, as the terminal date, and -i Ahau 

 8 Cumhu as the initial date. As the former date must be tlie more 

 recent on this supposition, it follows that the count was backward 

 (though this is by no means necessary, as it could be forward as well) ; 

 so our count in this case will be backward. In order not to make the 

 series too long and tedious, we will select as our factor or sum to be 

 added — 



