twenty days had passed of the preceding month, and that their count was regulated by the number of days which had passed. As far as the month dates are concerned, however, it is absolutely unimportant whether the beginning day is called 0 or 20. Goodman says that the Mayas had no need of a zero (following the Romans in this respect), since zero was of no use as a multiplier. This is hardly conclusive. It may be true, as Goodman says, that the Mayas in their month dates spoke of the twenty days which had passed in the preceding month; but it is equally true that they may have expressed this idea by attaching the number zero to the beginning day on the ground that no days of the current month had elapsed. Indeed the latter explanation is the more credible, since, if they had spoken of the twenty days of the preceding month as having elapsed, it would seem possible at least, and perhaps probable, that they would have used the name of the preceding month as well, and would have called the beginning day of Yaxkin, for instance, 20 Xul and not 20 Yaxkin. But this it seems they did not do, unless the instance on the Temple of the Cross and that of the Dresden Codex, already cited, would bear this construction. These instances, however, are contradicted by all the other cases and are themselves capable of a different interpretation. It would seem as if the Mayas probably called the beginning day of a month by the name of the current month, and that they attached the zero to it, meaning that no days of that month had elapsed. Moreover such a plan is very much easier for calculation and there is less liability to error; for it is natural to think of a day with the number 20 as following a day with the number 19 and as being the last day of a month containing 20 days, rather than the beginning day of a month. I do not place too much reliance on this, however, for it is hardly safe to argue back from what we at this time would consider the best thing to do, in order to find out what some other nation at some other time would have done.

The chief evidence in favor of giving the 0 or 20 glyph the meaning of 20 is, that this glyph is often drawn with a hand stretching across its lower part, especially when the main part of the glyph is a face. Now the face glyphs which represent the cycle of 144,000 days and the katun of 7,200 days are very similar, except that the cycle glyph has also a hand across its lower part, and the cycle is equal to 20 katuns; but this evidence is somewhat weak, since it is clear that even if the 0 or 20 glyph should be decided to mean 20, in all calculations it is to be treated as 0, as is proved by many of the inscriptions of Palenque, Piedras Negras, Copan, and elsewhere.

On the whole, therefore, I think the weight of evidence is in favor of the hypothesis that the Mayas called the beginning days of their month Day 0 and numbered the days of their month from 0 to 19.