There can be no doubt, however, as stated above, that the cycles were numbered from 1 to 13, inclusive, and then began again with 1. This sequence strikingly recalls that of the numerical coefficients of the days, and in the parallel which this latter sequence affords, the writer believes, lies the true explanation of the misconception concerning the length of the great cycle in the inscriptions. TABLE XI. SEQUENCE OF TWENTY CONSECUTIVE DATES IN THE MONTH POP 1 Ik 0 Pop 2 Akbal 1 Pop 3 Kan 2 Pop 4 Chicchan 3 Pop 5 Cimi 4 Pop 6 Manik 5 Pop 7 Lamat 6 Pop 8 Muluc 7 Pop 9 Oc 8 Pop 10 Chuen 9 Pop 11 Eb 10 Pop 12 Ben 11 Pop 13 Ix 12 Pop 1 Men 13 Pop 2 Cib 14 Pop 3 Caban 15 Pop 4 Eznab 16 Pop 5 Cauac 17 Pop 6 Ahau 18 Pop 7 Imix 19 Pop The numerical coefficients of the days, as we have seen, were numbered from 1 to 13, inclusive, and then began again with 1. See {112} Table XI, in which the 20 days of the month Pop are enumerated. Now it is evident from this table that, although the coefficients of the days themselves do not rise above 13, the numbers showing the positions of these days in the month continue up through 19. In other words, two different sets of numerals were used in describing the Maya days: (1) The numerals 1 to 13, inclusive, the coefficients of the days, and an integral part of their names; and (2) The numerals 0 to 19, inclusive, showing the positions of these days in the divisions of the year--the uinals, and the xma kaba kin. It is clear from the foregoing, moreover, that the number of possible day coefficients (13) has nothing whatever to do in determining the number of days in the period next higher. That is, although the coefficients of the days are numbered from 1 to 13, inclusive, it does not necessarily follow that the next higher period (the uinal) contained only 13 days. Similarly, the writer believes that while the cycles were undoubtedly numbered--that is, named--from 1 to 13, inclusive, like the coefficients of the days, it took 20 of them to make a great cycle, just as it took 20 kins to make a uinal. The two cases appear to be parallel. Confusion seems to have arisen through mistaking the _name_ of the period for its _position_ in the period next higher--two entirely different things, as we have seen.