Notes
Page 64 (1).—Gama, Descripcion, Parte 2, Apend. 2. Gama, in comparing the language of Mexican notation with the decimal system of the Europeans, and the ingenious binary system of Leibnitz, confounds oral with written arithmetic.
Page 64 (2).—Gama, ubi supra. This learned Mexican has given a very satisfactory treatise on the arithmetic of the Aztec, in his second part.
Page 64 (3).—Herodotus, Euterpe, sec. 4.
Page 64 (4).—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.
Page 64 (5).—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), liv. 5, chap. 1.
Page 64 (6).—Sahagun intimates doubts of this. "Another festival was celebrated every four years in honour of the fire, and it is a reasonable conjecture that at this festival they introduced their correction by counting six nemonteni days." (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.
Page 64 (7).—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 de Cordillères, 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.
Page 65 (1).—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 I, 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.
Page 65 (2).—This length, as computed by Zach, at 365 d. 5 h. 48 m. 48 sec, is only 2 m. 39 sec. longer than the Mexican; which corresponds with the celebrated calculation of the astronomer of the Caliph Almamon, that fell short about two minutes of the true time. — See La Place, exposition, p. 350.
Page 65 (3).—"The small excess of 4 hours, 38 minutes, 40 seconds, over 25 days in each period of 104 years, would not amount to an entire day until the lapse of five of these periods, i.e. 538 years.”—(Gama, Descripcion, Parte i, p. 23.) Gama estimates the solar year at 365 d. 5 h. 48 m. 48 sec.
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