236 MAYAN Calendar systems [eth. ann. 22 



13 Ahan? Goodman says 4 Aliau. He bases this, doulitless, on the 

 fact that many of the initial series of the inscriptions liave as their 

 first day 4 Aliaii S Cumhu, wliich he assnmes, apparently correctly, is 

 the first day of a great cycle. It is apparent, following his method of 

 nnmbering, that if one gi'cat cycle begins with 4 Ahau, all the rest do. 

 As yet we have not introduced the year as a factor, but before this 

 is (lone attention is called to the result of following the vigesimal sys- 

 tem in counting the higher orders of units, or time periods, as Good- 

 man considers them. According to this system, which, as I have 

 stated, prevails in the Dresden codex, not only does it take 20 ahaus 

 to make 1 katun and 20 katuns to make 1 cycle, but also 20 cycles 

 to make 1 great cycle. The order in which the numbers of the initial 

 days of the ahaus, katuns, and cycles follow one another will be the 

 same in the one scheme as in the other and as already given. The 

 difference between the two theories appears in the numbers of the 

 initial days of the great cycles. Following the method of calculation 

 indicated, we multiply 4 by 20x20x20 (or 8,000) and divide by 13. 

 This gives a remainder of 7. The order of the numbers is therefore 

 13, (3, 12, 5, 11, -4, 10, 3, 9, 2, 8, 1, 7, 13, 6, 12, etc., and this is found 

 to be correct by the absolute test of writing out the numbers of the 

 first days of the cycles in proper order and taking every 20th one. 

 The initial dates of a sufficient number to cover all probable require- 

 ments are given here, 4 Ahau S Cumhu being adopted as the basis or 

 check point from which to count forward and backward. In this 

 calculation we must In'ing into the problem the year factor. 



Initial days of the i/rraf cycles, followiiiy ilie I'igesimal system 



1 3 Ahau 8 Muaii, year 4 Ben 



2 11 Ahau 13 Zotz , year 4 Laniat 



3 4 Ahati 3 Ceh, year 3 Ezanab 



4 10 Ahau 8 Poi), year 3 Ben 



5 3 Allan 18 Mol, year 3 Akbal 



6 9 Ahaii 8 Pax, year 1 Ben 



7 3 Ahau 13 Tzec, year 1 Lamat 



8 8 Ahau 3 Mac, year 13 Ezanab 



9 1 Ahau 8 Uo, year 1 3 Ben 



10 7 Ahau 18 Chen. year 13 Akbal 



11 13 Ahau 8 Kayab. year 1 1 Ben 



13 6 Ahau 13 Xul, year 11 Lamat 



13 13 Ahau 3 Kankin, year 10 Ezanab 



14 .5 Ahau 8 Zip, year 10 Ben 



1.5 .... 11 Ahau 18 Yas. j'ear 9 Akbal 



16 4^ Ahau S C'ldiihu, yea,r 8 Ben 



17 10 Ahau 1 3 Yaxkin, year 8 Lamat 



18 3 Ahau 3 Muan, year 7 Ezanab 



19 9 Ahau 8 Zotz, year 7 Ben 



30 3 Ahau 18 Zac , year 6 Akbal 



As no larger number of great cycles has been recorded than 14, in 

 one of the Copan inscriptions, G being the highest given in the Dres- 



