64 



OTHER NUMERAL SIGNS. 



Having given separately the only complete series I know, except the dot-and-bar one, 

 I shall present collectively some other numeral signs, of whose value I am tolerably 

 confident, merely arranging them under appropriate heads. I do not include the 

 dot-and-bar series — in which each dot represents one and each bar five — it being too 

 familiar to most of the parties into whose hands this work is likely to come to require 

 reproduction here ; yet there are two or three things concerning it of which the best 

 informed of them may not be apprised. In the first place, the curves, angles, and 

 crosses, which sometimes support a single dot or separate two dots, have no value, but 

 appear to have been introduced to avoid blank space or to render the glyph more 

 symmetrical. Next, there are three signs for 20 that go with this series — 



-the last of the three being drawn with a great variety of detail. 



The first of these signs is used almost exclusively to designate the beginning, or 20th, 

 day of a month, while the second is employed in ordinary computation. Their value, 

 in these respects, has been correctly stated by a number of persons ; but the same 

 authorities have declared the last of the three to be a sign for naught. They were led 

 into this mistake, undoubtedly, by its peculiar use and position. It is employed in 

 the codices solely to designate initial periods, and in that position it is the equivalent 

 of 20 in all cases except that of the chuen, where, like the other 20-signs, it denotes 

 but 18. I shall speak more fully of this exception later on. Finally, in some instances 

 the dots and dashes in themselves do not express the full notation, but are coupled 

 with other signs whose value must be added to theirs in order to complete it — as in 



o 



, which denote respectively 17 and 18. The 



these combinations, 



same perplexing practice was indulged in with the face signs and other forms of 

 numerals. 



In both the annual and chronological calendar, 20 takes precedence of the unit in 

 enumerating the days, ahaus, and katuus. This results from the Maya practice of not 

 counting any period until it had wholly passed, for which purpose a period was always 

 given a numeral designating the number of the preceding one, reckoned according to 



