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 or just as many combinations as are equal to their product. Thus every year had its appropriate symbol, by which it was, at once, recognised. And this symbol, preceded by the proper number of "bundles," indicating the half centuries, showed the precise time which had elapsed since the national epoch of 1091.1 The ingenious contrivance of a periodical series, in place of the cumbrous system of hieroglyphical notation, is not peculiar to the Aztecs, and is to be found among various people on the Asiatic continent,—the same in principle, though varying materially in arrangement.2

The solar calendar, above described, might have answered all the purposes of the nation; but the priests chose to construct another for themselves. This was called a "lunar reckoning," though nowise accommodated to the revolutions of the moon.3 It was formed, also, of two periodical series; one of them consisting of thirteen numerical signs, or dots, the other of the twenty hieroglyphics of the days. But, as the product of these combinations would only be 260, and, as some confusion might arise from the repetition of the same terms for the remaining 105 days of the year, they invented a third series, consisting of nine additional hieroglyphics, which, alternating with the two preceding series, rendered it impossible that the three should coincide twice in the same year, or indeed in less than 2340 days; since 20x13x9=2340.4 Thirteen was a mystic number, of frequent use in their tables.5 Why they resorted to that of nine, on this occasion, is not so clear.6

This second calendar rouses a holy indignation in the early Spanish missionaries, and Father Sahagun loudly condemns it as "most unhallowed, since it is founded neither on natural reason nor on the influence of the planets, nor on the true course of the year; but is plainly the work of necromancy, and the fruit of a compact with the Devil!"7 One may doubt, whether the superstition of those who invented the scheme was greater than that of those who thus impugned it. At all events, we may, without having recourse to supernatural agency, find in the human heart a sufficient explanation of its origin; in that love of power, that has led the priesthood of many a faith to affect a mystery, the key to which was in their own keeping.

By means of this calendar the Aztec priests kept their own records, regulated the festivals and seasons of sacrifice, and made all their astrological calculations. The false science of astrology is natural