THOMAS] INITIAL SERIES OF QUIRIGUA INSCRIPTIONS 207 



reach 12 Caban 5 Kayab, the required date, as with the preceding 

 series. Looking farther we find 6 Ahau 8 Ceh in the 2d cycle, 12th 

 katun, 6th ahau, giving the series 54-2-12-6-4-17, which also carries 

 us to the proper date (12 Caban 5 Kayab). The date 6 Ahau 8 Ceh 

 is also found in the 4th cycle, lOtli katun, 1.5th ahau, and other places 

 in the 54th great cycle, each of which gives the proper result. But 

 this is not all, as we also find 6 Ahau 8 Ceh in the 5.3d great cycle in 

 the 1st cycle, 7th katun, and 12th ahau, giving the series 5.3-1-7-12- 

 4-17, which, counted from 4 Ahau 8 Zotz, the fii'st day of the 53d 

 great cycle, brings us to 12 Caban 5 Kayab, the required date. Other 

 series whicli will give the proper result might be noted, but these will 

 suffice to show that the initial and terminal dates and the chuens and 

 days do not afford sufficient data by which to determine the series. 

 It is necessary, therefore, to know the numbers attached to one or 

 more of the other time periods of the series, and these must be ascer- 

 tained in every instance by inspection and by a previously obtained 

 knowledge of the value of one or more of the face numerals. 



Referring again to the initial series under consideration — 54-9-11— 

 1.3-4-17, 12 Caban 5 Kayab — and holding to our assumption that the 

 number of the chuens and days is correct, the date being satisfac- 

 torily determined, we proceed to learn what additional data are neces- 

 sary to determine the series. 



If inspection aud a knowledge of the face numbers prove the one 

 attached to the cycle in this instance to be 9, then the series as given 

 above is the only one that will agree with the data, and wo are thus 

 enabled to determine the value of the face numerals attached to the' 

 katun and ahau symbols; and should that giving the number of days 

 be imperfect or obliterated, it would still be possible to determine the 

 series, as the date with the other items mentioned (number of chuens 

 and cycles) is always sufficient to fix the other numbers in the series. 

 If the number attached to the chiiens be unknown, then the series 

 could not be determined with the other data mentioned. 



Suppose the number (9 in this case) attached to the cj'cle symbol 

 to be imperfect or unknown, but that attached to the katun (14 in 

 this instance) to be known, the series given above is the only one that 

 will agree with the data. If the numbers attached to the cycle and 

 katun be indeterminable, but that attached to the ahau symbol (13 in 

 this instance) be known, the series can still be determined, and will 

 be as given. It is apparent, therefore, that, with the initial and ter- 

 minal dates and chuens and days kiiowu, the number attached to one 

 of the other elements in the series is necessary in order to determine 

 the series. It is also demonstrable that with these data the series 

 can be at once determined by Goodman's tables, though this, as I 

 shall show, does not prove that his theory of the Mayan time sj'stem 

 or his method of numbering the cycles or great cycles is correct. 



