92 



BUEEAU OP AMERICAN ETHNOLOGY 



[bull. 57 



(1) as we have seen in Table VIII, 20 units of any order (except the 

 2d, in which only 18 were required) were equal to 1 unit of the order 

 next higher, and consequently 20 could not be attached to any period 

 glyph, since this number of periods (with the above exception) was 



^^^ 



Fig. 45. Sign for 20 in the codices. 



always recorded as 1 period of the order next higher; and (2) although 

 there were 20 positions in each period except the uinal, as 20 kins in 

 each uinal, 20 tuns in each katun, 20 katuns in each cycle, these posi- 

 tions were numbered not from 1 to 20, but on the contrary from to 

 19, a system which eliminated the need for a character expressing 20. 



In spite of the foregoing 

 fact, however, the number 

 20 has been found in the 

 codices (see fig. 45) . A pe- 

 culiar condition there, how- 

 ever, accounts satisfactorily 

 for its presence. In the cod- 

 ices the sign for 20 occurs 

 only in connection with to- 

 nalamatls, which, as we 

 shall see later, were usually 

 portrayed in such a manner 

 that the numbers of which 

 they were composed could 

 not be presented from bot- 

 tom to top in the usual 

 way, but had to be WTitten horizontally from left to right. Tliis 

 destroyed the possibility of numeration by position,^ according to 

 the ^faya point of view, and consequently some sign was necessary 

 which should stand for 20 regardless of its position or relation to 

 others. The sign shown in figure 45 was used for this purpose. It 

 has not yet been found in the inscriptions, perhaps because, as was 

 pointed out in Chapter II, the inscriptions generally do not appear 

 to treat of tonalamatls. 



If the ^laya numerical system had no vital need for a character to 

 express the number 20, a sign to represent zero was absolutely indis- 



FiG. 46. Sign for in the codices. 



The Maya numbered by relative position from bottom to top, as will be presently e.xplained. 



