days was in the hands of a professional priesthood and required much study to perform correctly. Since each “month” consisted of twenty days, and there were twenty day-signs, it is obvious that each month in a given year began with the same sign; but since the last month was followed by the five unlucky days, it follows that each year began with a day-sign five days later than the last. Also since 365 is divisible by 13 with 1 as remainder, it follows equally that each year began with a day-number one in advance of the last. Further, since there were twenty day-signs, and five (the least common multiple of 365 and 20) goes into twenty exactly four times, the year began with one of four signs only. Now the year was always distinguished by the sign of the day on which it began, and it is a peculiar fact that the commencement of the year never coincided with the commencement of the tonalamatl. The four signs which give the names to the years are the signs tecpatl, calli, tochtli and acatl, recurring in that order. Whether the day-number entering into the name of the year was that of the first day, as held by most authorities, or of the first day of the fifth month, as Seler tries to prove, need not be discussed here; the fact remains that the years were named successively, 1. tecpatl, 2. calli, 3. tochtli, and so on, until, after a period of fifty-two years (13 × 4), the same sign occurred again with the same number as the name-date of the year. This period of fifty-two years constituted the shorter cycle of the Mexicans, the longer cycle consisting of twice that number; but before proceeding further it will be necessary to say something about the months (see Appendix II). The first month was called Atlcaualco, and the first day according to Sahagun, who wrote about the middle of the sixteenth century, corresponded with the 2nd of February. This month marked the cessation of the rains,[3] and it was represented in calendars by a figure of the god Tlaloc, to whom, together with Chalchiuhtlicue, the religious festivals of the month were especially dedicated. Large numbers of children were sacrificed to the rain-god, chiefly on mountains, but also at a certain deep hole in the lagoon, and it was considered a good omen if the small victims wept on their way to the place of sacrifice, since their tears were supposed to portend a plentiful rain-supply. A gladiatorial sacrifice was also made to Xipe during this month.