102 BUREAU OF AMEEICAN ETHNOLOGY {bull. 57 



Period-ending dates. According to the Maya conception of time, 

 when a period had ended or closed it was at zero, or at least no new 

 period had commenced. Indeed, the normal form for zero in figure 

 47, the head^ variant for zero in figure 53, s-w, and the form for zero 

 shown in figure 54 are used interchangeably in the same inscription 

 to express the same idea— namely, that no periods thus modified are 

 involved in the calculations and that consequently the end of some 

 higher period is recorded; that is, no fractional parts of it are present. 

 That the hand in "ending signs" had exactly the same meaning 

 as the hand in the head variants for zero (fig. 53, s-w) receives striking 

 corroboration from the rather unusual sign for zero shown in figure 

 54, to which attention was called above. The essential elements of 



Fig. .5-1. A sign for 0, used also to express the idea "ending" or "end of" in 

 Period-ending dates. (See figs. 47 and 53 s-iv, for forms used intercliangeably 

 in the inscriptions to express the idea of or of completion.) 



this sign are ^ (1) the clasped hand, identical with the hand in the 

 head-variant forms for zero, and (2) the large element above it, con- 

 taming a curlmg infix. This latter element also occurs though below 

 the clasped hand, in the "ending signs" shown in figure 37, Z, m, n, 

 the first two of which accompany the closing date of Katun 14, and 

 the last the closing date of Cycle 13. The resemblance of these three 

 " ending signs" to the last three forms in figure 54 is so close that the 

 conclusion is well-nigh inevitable that they represented one and the 

 same idea. The writer is of the opmion that this meaning of the 

 hand (ending or completion) will be found to explain its use through- 

 out the inscriptions. 



In order to f annliarize the student with the head-variant numerals, 

 theu' several essential characteristics have been gathered together in 

 Table X, where they may be readily consulted. Examples covermg 

 their use with period, day, and month glyphs are given in figure 55 

 with the corresponding English translations below. 



Head-variant numerals do not occur as frequently as the bar and 

 dot forms, and they seem to have been developed at a nmch later 

 period. At least, the earliest Initial Series recorded with bar and dot 

 numerals antedates by nearly two hundred yeai-s the earhest Initial 

 Series the numbers of which are expressed by head variants. This 

 long priority in the use of the former would doubtless be considerably 

 diminished if it were possible to read the earliest Initial Series which 



I The subfixial element in the first three forms of fig. 54 does not seem to be essential, since it is wanting 

 in the last. 



