138 BUEEAU OF AMERICAX ETHNOLOGY [bull. 57 



dealing: with this kind of series that the student will iind the g:reatest 

 number of exceptions to the general rule. 



Having determined the direction of the count, whether it is forward 

 or backward, the next {fourth) step may be given. 



Fourth Step in Solving Maya Numbers 



To count the number from its starting point. 



We have come now to a step that involves the consideration of 

 actual arithmetical processes, which it is thought can be set forth 

 much more clearly by the use of specific examples than by the state- 

 ment of general rules. Hence, we will formulate our rules after the 

 processes which they govern have been fully explained. 



In counting any number, as 31,741, or 4.8.3.1 as it would be 

 expressed in Maya notation,^ from any date, as 4 Ahau 8 Cumhu, 

 there are four unl'Cnown elements which have to be determined before 

 we can write the date which the count reaches. These are : 



1. The day coefficient, which must be one of the numerals 1 to 13, 

 inclusive. 



2. The day name, which must be one of the twenty given in Table I. 



3. The position of the day in some division of the year, which must 

 be one of the numerals to 19, inclusive. 



4. Tlie name of the division of the year, which must be one of the 

 nineteen given in Table III. 



These four unknown elements all have to be determined from (1) 

 the starting date, and (2) the number which is to be counted from it. 



If the student will constantly bear in mind that all Ma^^a sequences, 

 whether the day coefficients, day signs, positions in the divisions of 

 the year, or what not, are absolutely continuous, repeating themselves 

 without any break or mterruption whatsoever, he will better under- 

 stand the calculations which follow. 



Itw^as explained in the text (see pp. 41-44) and also shown graph- 

 ically in the tonalamatl wheel (pi. 5) that after the day coefficients 

 had reached the number 13 they returned to 1, following each other 

 indefinitely in this order without interruption. It is clear, therefore, 

 that the highest multiple of 13 wliich the given number contains may 

 be subtracted from it without afl'ecting in any way the value of the 

 day coefficient of the date which the number ^^dll reach when counted 

 from the starting point. This is true, because no matter what the 

 day coefficient of the starting point may be, any multiple of 1 3 will 

 always bring the count back to the same day coefficient. 



1 For transcribing the Maya numerical notation into tiie characters of our ovra Arabic notation Maya 

 students have adopted the practice of writing the various terms from left to right in a descending series, 

 as the units of our decimal system are written. For example, 4 katims, 8 tuns, 3 uinals, and 1 kin are 

 written 4.8.3.1; and 9 cycles, 16 katuns, 1 tun, uinal, and kins are written 9.16.1.0.0. According to this 

 method, the highest term in each number is written on the left, the next lower on its right, the next lower 

 on the right of that, and so on down through the units of the first, or lowest, order. This notation is very 

 convenient for transcribing the Maya numbers and will be followed hereafter. 



