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,[178] 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.[179] This arrangement, differing from that of the nations of the Old Continent, whether of Europe or Asia,[180] 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.[181] 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,[182] but at longer intervals, like some of the Asiatics.[183] They waited till the expiration of fifty-two vague years, when they interposed thirteen days, or rather twelve and a half, this being the number which had fallen in arrear. Had they inserted thirteen, it would have been too much, since the annual excess over three hundred and sixty-five is about eleven minutes less than six hours. But, as their calendar at the time of the Conquest was found to correspond with the European (making allowance for the subsequent Gregorian reform), they would seem to have adopted the shorter period of twelve days and a half,[184] which brought them, within an almost inappreciable fraction, to the exact length of the tropical year, as established by the most accurate observations.[185] Indeed, the intercalation of twenty-five days in every hundred and four years shows a nicer adjustment of civil to solar time than is presented by any European calendar; since more than five centuries must elapse before the loss of an entire day.[186] Such was the astonishing precision displayed by the Aztecs, or, perhaps, by their more polished Toltec predecessors, in these computations, so difficult as to have baffled, till a comparatively recent period, the most enlightened nations of Christendom![187]