Page:The Conquest of Mexico Volume 1.djvu/108

 ancient Romans; a more simple arrangement, probably, than any existing among Europeans.1 Twenty was expressed by a separate hieroglyphic,—a flag. Larger sums were reckoned by twenties, and, in writing, by repeating the number of flags. The square of twenty, four hundred, had a separate sign, that of a plume, and so had the cube of twenty, or eight thousand, which was denoted by a purse, or sack. This was the whole arithmetical apparatus of the Mexicans, by the combination of which they were enabled to indicate any quantity. For greater expedition, they used to denote fractions of the larger sums by drawing only a part of the object. Thus, half or three-fourths of a plume, or of a purse, represented that proportion of their respective sums, and so on.2 With all this, the machinery will appear very awkward to us, who perform our operations with so much ease by means of the Arabic, or rather, Indian ciphers. It is not much more awkward, however, than the system pursued by the great mathematicians of antiquity, unacquainted with the brilliant invention which has given a new aspect to mathematical science, of determining the value, in a great measure, by the relative position of the figures.

In the measurement of time, the Aztecs adjusted their civil year by the solar. They divided it into eighteen months of twenty days each. Both months and days were expressed by peculiar hieroglyphics,—those of the former often intimating the season of the year, like the French months, at the period of the Revolution. Five complementary days, as in Egypt,3 were added, to make up the full number of three hundred and sixty-five. They belonged to no month, and were regarded as peculiarly unlucky. A month was divided into four weeks, of five days each, on the last of which was the public fair or market day.4 This arrangement, different from that of the nations of the Old Continent, whether of Europe or Asia,5 has the advantage of giving an equal number of days to each month, and of comprehending entire weeks, without a fraction, both in the months and in the year.

As the year is composed of nearly six hours more than three hundred and sixty-five days, there still remained an excess, which, like other nations who have framed a calendar, they provided for by intercalation; not, indeed, every fourth year, as the Europeans,6 but at longer intervals, like some of the Asiatics.7 They waited till the expiration of fifty-two vague years, when they interposed thirteen