In the first row of dates, we find that the third date on page 48 is 12 Chen. The number of days at the bottom of the page which need to be counted forward in order to reach the fourth date is 8. If the beginning day of the month were marked by the Mayas with 1, then the last day would be marked with 20, and by adding 8 days to 12 Chen, we should reach 20 Chen. But the date is not 20 Chen. The month is Yax,--the month immediately following Chen,--and the glyph which takes the place of the number has a form resembling two half-circles placed side by side. In other words, in this case 8 days from 12 Chen reach ? Yax, and as far as the first proposition is concerned, it is immaterial whether the form above given is called 0 or 20. Eight days have taken us out of the month Chen into the next month Yax, and to a day of that month which is not 1 Yax, but must be a day preceding 1 Yax, whether that is called 0 Yax or 20 Yax. Again, the first date of the first row of month dates on page 50 is 10 Kankin, and the number at the bottom of the page to be added in order to reach the second date is 90. Counting forward 90 days from 10 Kankin we should reach 20 Cumhu, if the beginning day of the month is 1 Cumhu. But the month is not Cumhu nor is it Pop, but it is undoubtedly the glyph for the five supplementary days, Uayeb. The glyph which takes the place of the number is the same as that which has just been found before Yax. This is additional evidence that the months began with 0 or 20 and not with 1. Again, on the first date of the second row of page 50 is 15 Cumhu, and the number of days to be added in order to reach the next date is 90, which appears at the bottom of the page. Counting forward this number of days from 15 Cumhu, we should reach 20 Zotz if the beginning day of the month were 1 Zotz. But the month is clearly Tzec, and the number is that which we have already found twice before as meaning 0 or 20. These cases would seem to show that after passing day 19 of any month, we reach the beginning day of the next month, and that this day is found with the glyph which means 0 or 20. Against this is the evidence of the last month date of the third row of page 49, which is clearly 9 Mac, and the number to be added at the bottom of the page is 236. This would take us to 20 Xul, if the beginning day of Xul is 1 Xul, but to 0 or 20 Yaxkin if the beginning day of Xul is 0 or 20. The first month date of the third row of page 50 is 0 or 20 Xul. This, I think, is clear, although the Xul glyph is not exactly like the other glyphs of this month. Here then are three cases which support Goodman's view and one against it. The weight of evidence is therefore in favor of his system so far.