ceding and the first cycle of the following grand cycles. As I have assumed that the cycle (and hence the great cycle) commenced with the year 1 Cauac, it follows that, in carrying out the above supposition, the first Ahau of the series must also begin with this year. The divisions between the Ahaues are marked on the table by transverse solid black lines. The point at which the first great cycle ends and the next (which is given complete) begins is marked thus::o:. I next locate the foregoing groups of years so as, if possible, not to clash with each other, and also in such a manner that the period represented by a group shall fall within one of the Ahaues marked off on the table.
Each group is surrounded by a continuous dark line, so as to be easily distinguished from other periods marked on the same table; they are also numbered at the sides thus: (11), (9), (7), (5), (3), these numbers corresponding with the day numbers by which the different groups were obtained.
These groups, each consisting of twenty years, not only fall within the lines marking the Katunes, but come in regular succession, leaving four uncounted yeai's between each two periods—two belonging to one and two to that which follows. In other words, while the Katun or Ahau as a whole, according to the theory upon which I am now proceeding, always commenced with a Cauac year, the twenty "counted years" in the present example begin with a Muluc year. But, as appears from what has already been shown, this is not always true in regard to these periods, yet it is generally the case.
If we observe carefully the five figures in the first or uppermost division of the plates under consideration, we see that they correspond in character to those in the second division to which we have just alluded, and that the black numeral is also the same, (11). The only red numerals recognizable are the 13 over the long-nosed god on Plate XXX, the 8 facing the lefthand figure on Plate XXXI, and the 2 over the left-hand figure on Plate XXX. According to the arrangement of the numbers in the second division, those in this division would be 8, 6, 4, 2, 13, reading from left to right. If we assume these numbers to be correct, and the days to be Eb, Kan,
