I give here the first and last terms of a list of the beginning days of the Katuns 13 Ahau in a complete round of 18,720 years occurring after the beginning of the grand cycle called by Goodman Grand Cycle 54, which began with 4 Ahau 8 Cumhu. It is of little consequence what particular number is given to the grand cycle, as the whole series forms a continuous count, and I shall therefore follow Goodman, who gives the number 54 to the grand cycle glyphs common to Copan, Quirigua, etc. If 54.13.0.0.0.0. or the beginning of the grand cycle, called Grand Cycle 54 by Goodman, begins with 4 Ahau 8 Cumhu, a Katun 13 Ahau will appear two katuns after this or with the count of 54.13.2.0.0.0. 13 Ahau 8 Mol Year 10 Ix, and other Katuns 13 Ahau will follow at intervals of 13 katuns as here given: 54.13.15.0.0.0. 13 Ahau 8 Pax Year 6 Ix. 1. 8. " 3 Xul 3 Cauac. 2. 1. " 3 Kankin 12 " . . . . . . . . . . . 57.5.19.0.0.0. 13 Ahau 18 Ceh 11 Kan. 6.12 13 Uo 8 Muluc. 7. 5. 13 Yax 4 " 18. 13 Cumhu 13 " 57.8.11.0.0.0. 13 Ahau 8 Mol 10 Ix. But we are seeking a Katun 13 Ahau in which 14 tuns have elapsed and of which 6 tuns still remain unexpired. We must, therefore, add 14 tuns or 14 × 360 days = 5040 days to each of the dates given and we shall then have the following complete list of the beginning days of Tun 14 of Katun 13 Ahau for the term of 18,720 years: