NUMERATION AND SIGNS FOR NUMBERS. 



'-©s"-3j£5>£<33s3"^®-i 



The key to the inscriptions is a knowledge of the Maya numerals. What advance I 

 have made has been attained by purely mathematical processes, and it is solely by the 

 same means that the ultimate solution must be achieved. There can be no certainty 

 of the correctness of an interpretation, in most cases, until the character and value of 

 a glyph are mathematically demonstrable. This requirement would render the full 

 clearing up of the mystery a hopeless undertaking were it not that so great a proportion 

 of the characters are qualified by numerals or are numerals themselves that to arrive 

 at their significance is only a question of patient effort, and that a knowledge of them 

 will probably reveal the meaning of the few remaining glyphs that have no apparent 

 numeric values or affixes. Hence, the identification of the numerals and the discovery 

 of the methods of using them are the most important steps toward further advancement 

 in the study. 



The greatest difficulty in following Maya computations is the absence of signs 

 showing the particular process employed. It may be that addition, subtraction, multi- 

 plication, and division are all indicated in some way, either by signs or by the relative 

 positions of the factors ; but, if so, I have detected but two signs that by any 

 possibility imply the process to be used, and these occur so seldom and irregularly that 

 I do not feel entire confidence in their supposed significance. I shall speak of them 

 more fully in connection with the day series of numerals. Generally, however, the 

 numerals are set down so at random that it is a difficult exercise to ascertain what is to 

 be done with them — the more puzzling as the problem is frequently a complex one, 

 involving two or more distinct processes or the employment of the same one several 

 times over. There seem to have been no sure rules in Maya mathematics. While 

 they added, it was usually only till they arrived at some convenient number for multi- 

 plying ; while they multiplied, it was commonly by only a few favorite numbers ; and 

 while they divided and subtracted, it was only in such an occasional way as to render 

 these features of their mathematic system of very little account. They appear to have 

 made no use of fractions, but arrived at fractional results in intricate computations by 

 the employment of varied integers whose aggregate produced the same effect. 



