THOMAS] MAYA METHOD OF CALCULATION 283 



As the differeut kinds of symbols used by the Mayas to express 

 :iuinl)ers have been referred to, I asstime that the reader is familiar 

 with them. That direct multiplication and division would seem to be 

 impossible with their characters where both numbers included units 

 above the first order, or, at most, first and second orders, will be 

 admitted. The suggestion by Professor McGee (referred to in the 

 paper on numeral systems) that these operations might ha\'e been 

 performed by addition and subtraction seems to be the key to the prob- 

 lem, as I shall attempt to show. 



That the Mayas could add and sul)lract numbers expressed in the 

 ordinaiy numeral symbols (dots and short lines) is known from hun- 

 dreds of examples in the Dresden codex; and that for these characters 

 they could readily substitute equivalent symbols of other forms in 

 use is evident. Take, for illustration, part of a .series from plate 

 XXIV, Dresden codex (see plate LXXXii), which has been reversed, so 

 that it is to be taken from left to right instead of from right to left, as 

 in the original. The date below each column is written out, and 

 instead of the naught symbol a cipher (0) is inserted: 



(1) (2) (3) (4) (5) (6) 







9 Allan -i Ahau 12 Ahaii T Ahau 2 Ahau 10 Allan 



If we write these in Arabic figures, preserving the relative positions 

 and omitting the dates, as those given can be referred to, the series 

 will be as follows: 



112 2 



8 16 4 12 8 



3 4 (i 5 (8) 10 12 







Doubling the fir.st column (8-2-0) we get 10-4-0; adding again 

 8-2-0, we get 1-4-6-0; adding again 8-2-0, we get 1-12-8-0 (the 5 in 

 this column should be 8, as by adding 8-2-0 to it as thus corrected 

 we get 2-0-10-0, the 5th column, etc.). 



If we write the equivalent of each numlier in days, maintaining the 

 same relative positions, and give the sum of each column below (mak- 

 ing the correction noted), the result will be as follows: 



2.920 5,840 8.700 11,680 14,600 17,520 



