with a Cauac year. On each, the divisions between the Ahaues are marked by solid, heavy, black lines; the usually counted twenty years of each are surrounded by a single dotted line, and the period covered by the four plates by a continuous waved line. The point at which the grand cycle begins is marked thus: :o:. If we examine Table XIV we see that 1 Cauac is the first year of a cycle, and 1 Muluc the first of the usually "counted years" of an Ahau, and that both are within the period covered by the four plates; each is surrounded by a ring in order to designate it. As a matter of course, each is the first year of an "Indication" or week of years; so are 1 Kan and 1 Ix in the same period, yet neither of these is thus distinguished.
If we turn now to Table XV, in which the cycle begins with a Kan year, we can see no reason why either the 1 Cauac or the 1 Muluc in the period embraced by the waved line should have any special mark of distinction.
It is proper to state here that unit numerals surrounded in a similar manner by a circle of dots, are to be found on other plates where it is difficult to apply the theory here advanced.
Another difficulty which arises, if we adopt Perez's theory, is that the last Ahau of a grand cycle does not close with the end of that period, but includes one or more years of the following, according to the place the division begins.
Taking all these facts into consideration, it appears that the calendar system followed by the author of the Troano Manuscript commenced the cycles and the Ahaues with a Cauac year. I think, therefore, the evidence that the Ahaues at least began with a Cauac year is too strong to leave any doubt on this point.
As bearing upon, and, as I believe, tending strongly to confirm this conclusion, I will introduce here some examples from the Manuscript. In the second division of Plates XXX and XXXI, commencing on the left half of the former and continuing through the latter, we observe a series of figures all similar to each other, except the one to the right on Plate XXX, which is the long-nosed god.
Over each figure, except one, there is a red numeral, but these differ
