There is still another and somewhat probable supposition in regard to the object of this division of the days of the month into groups of five, which will obviate one objection to the explanation given in my former work, viz, the very large number of dates given in the Manuscript Troano on the supposition that there are four years to each numeral connected with, the day columns. It is possible that the days of one group indicate the year intended; that is, whether it is a Cauac, Kan, Muluc, or Ix year. For example, column No. 4 (Table IV), or some other, one of the four, may relate to Kan years; No. 1 to Muluc years; No. 2 to Ix years, and No. 3 to Cauac years. Assuming this to be correct, then the example heretofore given, where the days named are 1 Cib, 1 Ahau, 1 Kan, 1 Lamat, and 1 Eb, and the month the first (Pop), would indicate only the years 7 Muluc, 3 Muluc, 12 Muluc, 8 Muluc, and 11 Muluc. These would all come in Ahau No. VI, as before, but would indicate that the festival, or whatever they referred to, occurred but once every four years, in the first month of the year. Hence if the five days of a column (as of the Manuscript Troano) are all taken from one side of the quadrilateral of our scheme they will refer to years of one dominical sign only; if alternately from opposite sides, then to the years of two dominical signs, but if taken alternately from the four sides they would refer to the four classes of years. This will reduce the number of dates in the Manuscript Troano very considerably from the other supposition, but will not in any way change the position of the Ahaues in the Grand Cycle. As one further item of evidence in regard to this method of arranging the twenty days of the month in four groups or columns, I call attention to what is found on Plate 32 of the Dresden Codex. Here we find the four columns of five days each, corresponding precisely with the arrangement of the Maya days into four groups, as heretofore. I present here the arrangement as found on this plate: TABLE X. _a._ _b._ _c._ _d._ Manik. Cib. Chicchan. Ix. Chuen. Ahau. Muluc. Ezanab. Men. Kan. Been. Ik. Cauac. Lamat. Caban. Cimi. Akbal. Eb. Ymix. Oc. It will be seen by comparing this grouping with that in Table IV that column _a_ of this plate contains the same days as column 3 of the table; column _b_ the same as column 4; column _c_ the same as column 1, and column _d_ the same as column 2. But so far have found no entirely satisfactory explanation of the order given in many of these columns and in three of the sides of the quadrilateral of the Cortesian plate.