{*} [And in France. In France the five extra days were called sans-cullottides.—M.]
[179] Sahagun, Hist. de Nueva-España, lib. 4, Apend.—According to Clavigero, the fairs were held on the days bearing the sign of the year. Stor. del Messico, tom. ii. p. 62.
[180] The people of Java, according to Sir Stamford Raffles, regulated their markets, also, by a week of five days. They had, besides, our week of seven (History of Java (London, 1830), vol. i. pp. 531, 532.) The latter division of time, of general use throughout the East, is the oldest monument existing of astronomical science. See La Place, Exposition du Système du Monde (Paris, 1808), lib. 5, chap. 1.
[181] Veytia, Historia antigua de Méjico (Méjico, 1806), tom. i. cap. 6, 7.—Gama, Descripcion, Parte 1, pp. 33, 34, et alibi.—Boturini, Idea, pp. 4, 44, et seq.—Cod. Tel.-Rem., ap. Antiq. of Mexico, vol. vi. p. 104.—Camargo, Hist. de Tlascala, MS.—Toribio, Hist. de los Indios, MS., Parte 1, cap. 5.
[182] Sahagun intimates doubts of this. “They celebrated another feast every four years in honor of the elements of fire, and it is probable and has been conjectured that it was on these occasions that they made their intercalation, counting six days of nemontemi,” as the unlucky complementary days were called. (Hist. de Nueva-España, lib. 4, Apend.) But this author, however good an authority for the superstitions, is an indifferent one for the science of the Mexicans.
[183] The Persians had a cycle of one hundred and twenty years, of three hundred and sixty-five days each, at the end of which they intercalated thirty days. (Humboldt, Vues des Cordillèras, p. 177.) This was the same as thirteen after the cycle of fifty-two years of the Mexicans, but was less accurate than their probable intercalation of twelve days and a half. It is obviously indifferent, as far as accuracy is concerned, which multiple of four is selected to form the cycle; though, the shorter the interval of intercalation, the less, of course, will be the temporary departure from the true time.
[184] This is the conclusion to which Gama arrives, after a very careful investigation of the subject. He supposes that the “bundles,” or cycles, of fifty-two years—by which, as we shall see, the Mexicans computed time—ended alternately at midnight and midday. (Descripcion, Parte 1, p. 52, et seq.) He finds some warrant for this in Acosta’s account (lib. 6, cap. 2), though contradicted by Torquemada (Monarch. Ind., lib. 5, cap. 33), and, as it appears, by Sahagun,—whose work, however, Gama never saw (Hist. de Nueva-España, lib. 7, cap. 9),—both of whom place the close of the year at midnight. Gama’s hypothesis derives confirmation from a circumstance I have not seen noticed. Besides the “bundle” of fifty-two years, the Mexicans had a larger cycle of one hundred and four years, called “an old age.” As this was not used in their reckonings, which were carried on by their “bundles,” it seems highly probable that it was designed to express the period which would bring round the commencement of the smaller cycles to the same hour, and in which the intercalary days, amounting to twenty-five, might be comprehended without a fraction.
[185] This length, as computed by Zach, at 365d. 5h. 48m. 48sec., is only 2m. 9sec. longer than the Mexican; which corresponds with the celebrated calculation of the astronomers of the Caliph Almamon, that fell short about two minutes of the true time. See La Place, Exposition, p. 350.
[186] “El corto exceso de 4hor. 38min. 40seg., que hay de mas de los 25 dias en el período de 104 años, no puede componer un dia entero, hasta que pasen mas de cinco de estos períodos máximos ó 538 años.” (Gama, Descripcion, Parte 1, p. 23.) Gama estimates the solar year at 365d. 5h. 48m. 50sec.
[187] The ancient Etruscans arranged their calendar in cycles of 110 solar years, and reckoned the year at 365d. 5h. 40m.; at least this seems probable, says Niebuhr. (History of Rome, Eng. trans. (Cambridge, 1828), vol. i. pp. 113, 238.) The early Romans had not wit enough to avail themselves of this accurate measurement, which came within nine minutes of the true time. The Julian reform, which assumed 365d. 5¼h. as the length of the year, erred as much, or rather more, on the other side. And when the Europeans, who adopted this calendar, landed in Mexico, their reckoning was nearly eleven days in advance of the exact time,—or, in other words, of the reckoning of the barbarous Aztecs;{*} a remarkable fact.—Gama’s researches led to the conclusion that the year of the new cycle began with the Aztecs on the ninth of January; a date considerably earlier than that usually assigned by the Mexican writers. (Descripcion, Parte 2, pp. 49-52.) By postponing the intercalation to the end of fifty-two years, the annual loss of six hours made every fourth year begin a day earlier. Thus, the cycle commencing on the ninth of January, the fifth year of it began on the eighth, the ninth year on the seventh, and so on; so that the last day of the series of fifty-two years fell on the twenty-sixth of December, when the intercalation of thirteen days rectified the chronology and carried the commencement of the new year to the ninth of January again. Torquemada, puzzled by the irregularity of the new-year’s day, asserts that the Mexicans were unacquainted with the annual excess of six hours, and therefore never intercalated! (Monarch. Ind., lib. 10, cap. 36.) The interpreter of the Vatican Codex has fallen into a series of blunders on the same subject, still more ludicrous. (Antiq. of Mexico, vol. vi. Pl. 16.) So soon had Aztec science fallen into oblivion after the Conquest!