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 characters, and making them run thirteen times, as the preceding, until terminating a new sacred cycle. This concluded, they continued the falling behind with other five days, making use of the third group of characters; and, finally, at the closing of the fourth cycle of 104 solar years, theoretically have entered into the arrangement, as initial years, all of the twenty day characters of the month, permitting that the new period of 416 years should commence anew with Cipactli. The idea, for which there exist no conclusive proofs, has been very ingeniously suggested by Mrs. Nuttall. Each time that the long-drawn-out period arrived at its end, the calendars of the two stars actually adjusted themselves, at the time when they returned to concur in the same respective position in the firmament. The harmony and beauty of this arrangement are indeed marvelous.

The distribution of the day Signs in the planet's calendar results as follows:

The great cycle ended in Malinalli, to begin with Cipactli in the one and the other calendar. We shall see this confirmed in the edifice of Xochicalco, where Malinalli separates the allegorical representatives of 416 years; let us say for the moment that these groups of day symbols are those which are met within the four Serpents of page 12 of the Borgian Codex. Their true significance has eluded the archaeologists until now. Seler limits himself to see in the page mentioned the four parts of the tonalámatl. This would not explain satisfactorily why the monsters have thirteen divisions in the body; by our hypothesis, the thing is simple; they are the number of times which the five chronographic signs run in one huehuetiliztli. In total, 52 occasions: the number of the pentagons of the monolith.

At the same time, the number 151,840 (number of days in 416 solar years) has the notable property, not yet observed so far as we know, of being a multiple, with the difference of a single unit, of the