134 BUEEAU OF AMERICAN ETHNOLOGY [btjll. 57 



We have seen in the foregoing pages (1 ) how the Maya wrote their 20 

 numerals, and (2) how these numerals were used to express the higher 

 numbers. The next question which concerns us is, How did they use 

 these numbers in their calculations; or in other words, how was their 

 arithmetic applied to their calendar ? It may be said at the very 

 outset in answer to this question, that in so far as known, numbers 

 appear to Jiave had hut one use throughout the Maya texts, namely, to 

 express the time elapsing between dates} In the codices and the inscrip- 

 tions alike all the numbers whose use is understood have been found 

 to deal exclusively with the counting of time. 



This highly speciahzed use of the numbers in Maya texts has 

 determined the first step to be taken in the process of deciphering 

 them. Since the primary unit of the calendar was the day, all numbers 

 should be reduced to terms of this unit, or in other words, to units of 

 the first order, or place. ^ Hence, we may accept the following as the 

 first step in ascertaining the meaning of any number: 



First Step in Solving Maya Num bers 



Reduce all the units of the higher orders to units of its first, or 

 lowest, order, and then add the resulting quantities together. 



The application of this rule to any Maya number, no matter of 

 how many terms, will always give the actual number of primary units 

 which it contains, and in this form it can be more conveniently utiHzed 

 in connection \\ath the calendar than if it were left as recorded, that is, 

 in terms of its higher orders. 



The reduction of units of the higher orders to units of the first order 

 has been explained on pages 105-133, but in order to provide the 

 student with tliis same information in a more condensed and accessible 

 form, it is presented in the following tables, of which Table XITI is 

 to be used for reducing numbers to their primary units in the inscrip- 

 tions, and Table XIV for the same purpose in the codices. 



1 This excludes, of course, the use of the numerals 1 to 13, inclusive, in the day names, and in the numer- 

 ation of the cycles; also the numerals to 19, inclusive, when used to denote the positions of the days in 

 the divisions of the year, and the position of any period in the division next higher. 



2 Various methods and tables have been devised to avoid the necessity of reducing t he higher terms of 

 Maya numbers to units of the first order. Of the former, that suggested by Mr. Bowditch (1910: pp. 302- 

 309) is probably the most serviceable. Of the tables Mr. Goodman's Arch.ric Annual Calendarand Archajic 

 Chronological Calendar (1S97) are by far the best. By using either of the above the necessity of reducing the 

 higher terms to units of the first order is obviated. On the other hand, the processes by means of which 

 this is achie\ed in each case are far more complicated and less easy of comprehension than those of the 

 method followed in this book, a method which from its simplicity might be termed perhaps the logical way, 

 since it reduces all quantities to a primary unit, which is the same as the i)rimary unit of the Maya cal- 

 endar. This method was first devised by Prof. Eifnst 1 orstemann, and has the advantage of being the most 

 readily understood by the beginner, sufficient reason for its use in this boolc. 



