eighteen months, each of which comprises a full round of the day-signs, is complete in itself and suggests that this was the original "year." The number of the day-signs, viz. twenty, is obviously based upon the vigesimal system of counting current among these peoples, but the selection of the thirteen numerals which accompany them has not yet been satisfactorily explained. As remarked before, it is obvious that an agricultural population would soon observe that the seasons gradually became out of harmony with the year, and they must have cast about to find some check by which the discrepancy could be corrected. This check they found in the synodical revolutions of the planet Venus. We know that the Aztec and Maya both calculated the reappearance of this planet (as seen in the codex Borgia and analogous MSS., and the Dresden codex), and the glyph which has been identified as that of the morning star appears upon the early monuments. It is worth noting that the early Maya method of calculating time, by means of a long count of days rather than by years, rendered the discrepancy of comparatively small account. The lack of harmony between the year and true solar time would, it is true, affect the seasonal feasts, but these could be transferred from month to month as occasion demanded. As said before, I believe the greater proportion of the inscriptions embody calculations which had as their object the due allocation of the feasts to the proper seasons. I have already made the suggestion that the previous "suns" marking world periods may typify periodical rearrangements of the calendar to square with solar time, and it is to be noted that both in the Aztec and in the Quiché account the tribes await the rising of the sun while observing the morning star. The first rising of the sun, awaited with such impatience by Aztec, Quiché and Kakchiquel alike, means, I believe, the adoption of the solar calendar, or rather the fixing of a date to form a starting-point for
