All the evidence taken gives a very strong presumption in favor of Goodman's theory that the month began with 0 or 20.
It is also interesting to notice that of the other dates given above where the calculation does not help us, three of these are 0 or 20 Pop (provided we have identified the number glyph correctly, which is certainly none of the known glyphs for any of the numbers 1 to 19). This date would not be significant if 20 Pop were the last day of the month, but it would be very significant if it were the beginning day of the month, that is the beginning day of the New Year. I think, therefore, that it is safe to assume as a good working hypothesis that the beginning days of the month were designated as 0 or 20, and the last day of the month as 19.
The second of our questions,--namely, whether this beginning day was called Day 0 or Day 20,--must now be taken up. Of course if we had decided that those cases which we have been considering represented the last days of the month, there would have been no question that the number glyphs which were not any of the numbers from 1 to 19 must be the number 20. It would have been very improbable that after having numbered the days of a month from 1 to 19 they would have called the last day 0. But it is not as certain that they might not have called the beginning day of a month 20, considering that 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.