true solar time, and it is probable that the feasts appropriate to certain seasons were shifted from month to month when the discrepancy became noticeable. Perhaps then these calculations had reference to the ritual calendar in accordance with which the various festivals were held. It must be remembered that the Maya in their count of days reckoned only elapsed time, expressing only a full tale of days. Thus each date is in one sense one day behind the date as we express it. This sounds complicated, but the difficulty disappears if we regard their method from the same point of view as our own reading of the clock. Whereas we speak of the fifteenth of June while the day is yet incomplete, yet we refer to a point in the third hour after noon in terms of two o’clock, viz. 2.20, or 2.45. Thus for the first day of a month we find the symbol zero, and 0. zotz means that the month zip is concluded, but that the first day of zotz is not yet complete. So it is that the katuns (and other periods) are known by the name of the last day of the previous katun, 5. ahau, 3. ahau, and so on, and are not named after the day imix which is the first of the series of twenty day-signs, and is actually the first day of the time-periods from cycle to tun. The Maya method of dating enabled them to fix the position of a definite day without risk of confusion over long periods of time. If the day-sign with its attendant number, and the position in a definite month, is given, that day is fixed for a period of 52 years. If the number of the tun in which it occurs is also stated, it is fixed for a period of 936 years (i.e. 936 years must elapse before a day with a similar series of signs and numbers can recur). If the number of the katun is also expressed, the position is determined for 18,720 years; and if the number of the cycle as well, a period of 374,400 years. [Illustration: FIG. 56.--Date inscriptions. A. Normal numerals, reading 9. 15. 0. 0. 0.[6] 4. _ahau_, 13 _yax_. (Copan, altar S). B. Face-numerals, reading 9. 16. 10. 0. 0. 1. _ahau_, 3. _zip_. (Quirigua, stela F). (_After Maudslay_)]