But since, in the years when Ik is the 1st name, Manik will be the 6th, Eb the 11th, and Caban the 16th, and in the years when Manik is the 1st, Eb will be the 6th, Caban the 11th, and Ik the 16th, and in the years when Eb is the 1st, Caban will be the 6th, Ik the 11th, and Manik the 16th, and in the years when Caban is the 1st, Ik will be the 6th, Manik the 11th, and Eb the 16th, it is clear that any one of this group which begins the year may occupy also three other positions in the divisions of the year, these positions being 5 days distant from each other. Consequently, it follows that Akbal, Lamat, Ben, and Eznab in Table V, the names which occupy the second positions in the divisions of the year, will fill the 7th, 12th, and 17th positions as well. Similarly Kan, Muluc, Ix, and Cauac will fill the 3d, 8th, 13th, and 18th positions, and so on. This enables us to formulate a third-- _Rule._ The 20 day-names are divided into five groups of four names each, any name in any group being five days distant from the name next preceding it in the same group, and furthermore, the names of any one group will occupy four different positions in the divisions of successive years, these positions being five days apart in each case. This is expressed in Table VI, in which these groups are shown as well as the positions in the divisions of the years which the names of each group may occupy. A comparison with Table V will demonstrate that this arrangement is inevitable. {55} TABLE VI. POSITIONS OF DAYS IN DIVISIONS OF MAYA YEAR --------------------------------------------------------------------+ | | { 1st, | 2d, | 3d, | 4th, | 5th, | | Positions held | { 6th, | 7th, | 8th, | 9th, | 10th, | | by days | { 11th, | 12th, | 13th, | 14th, | 15th, | | | { 16th | 17th | 18th | 19th | 20th | |----------------+----------+---------+---------+---------+---------+ | | { Ik | Akbal | Kan | Chicchan| Cimi | | Names of | { Manik | Lamat | Mulac | Oc | Chuen | | days in | { Eb | Ben | Ix | Men | Cib | | each group | { Caban | Eznab | Cauac | Ahau | Imix | --------------------------------------------------------------------+