OTHER NUMERAL SIGNS. 65 



our style of numeration. Thus, their twentieth was what we would call the first ; 

 their first, what we would call the second ; and so on, the numbers always being one 

 less than the order in which the periods actually occur. 



For a long while, misled by reputed authorities, I attributed the sense of naught, or 

 no count, to the signs for an initial period, which in some respects is certainly prefer- 

 able to designating it as the twentieth, the notation being rendered easier and more 

 readily comprehensible. For instance. 9 — — — X is a more intelligible notation 

 than 9 — 20 — 20 — 18x20, and it practically amounts to the same thing; for, in respect 

 to the initial period itself, the 20 is only an equivalent of 0, it pertaining, in reality, to 

 the preceding period and no additional count having accrued in the new reckoning : — 

 in other words, all numerals, when employed to express periods, are used in their 

 ordinal, not their cardinal, sense ; the foregoing notation reading : the 9th cycle, 

 20th katun, 20th ahau, 18th chuen and 20th day — not: 9 cycles, 20 katuns, 20 ahaus, 

 18 chuens and 20 days. 



But while this no-count method was easy and apparently gave true results, reflectiou 

 convinced me that, despite all the assumed authorities, there could be no naught in 

 the Maya numeral system, as there was no necessity for it. The cipher belongs 

 exclusively to the Arabic scheme, between which and the Maya there is no affinity. 

 So far as the Maya is analogous to any style familiar to us it is to the Roman, in which 

 there is no character for naught, as the cipher by itself would be useless for purposes 

 of notation and its employment in compounds out of keeping with the spirit of the 

 system. Having thus arrived at the conclusion that the signs qualifying initial periods 

 did not imply no count, it remained to establish what they did mean. From the 

 practice in similar instances, and the use made of some of these signs in other relations, 

 I became satisfied that the initial period in all cases Avas given the highest number 

 belonging to its particular class. It was manifest from several inscriptions in Palenque 

 and Quirigua, that the thirteen cycles constituting a great cycle were numerated 13, 1, 

 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. The reason for this — the numeral in all instances 

 being intended to denote the number of cycles fully elapsed — should be equally 

 applicable to all other classes of periods. Moreover, the sign marked u in the list of 

 20 signs, made use of to denote that a date falls on the first day of a month, is some- 

 times varied to the symbol marked t, which in other places unmistakably has the value 

 of 20. Then, in the lunation tables of the Dresden Codex the elliptical character, b, 

 which elsewhere designates initial periods, always occurs — except in the chuen line — 

 where the sum of the added factors is 20. Again, the sign most commonly employed 

 in the inscriptions to designate a beginning katun, ahau, or chuen — that marked a in 

 the same list, and which, by the way, I consider to be merely a conventionally 

 quadrated knot — occurs frequently where multiplied by other figures (the process 

 involving an ascription of the value of 20 to this) the product is 3,000, and in this 

 relation it becomes the characteristic feature of one of the 10-ahau symbols. This is 



BIOL. CENTR.-AMER., Archseol. 9 



