[175] See some account of these mummeries in Acosta (lib. 5, cap. 30),--also Clavigero (Stor. del Messico, ubi supra). Stone models of masks are sometimes found among the Indian ruins, and engravings of them are both in Lord Kingsborough’s work and in the Antiquités Mexicaines. [176] 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. [177] Ibid., ubi supra.--This learned Mexican has given a very satisfactory treatise on the arithmetic of the Aztecs, in his second part. [178] Herodotus, Euterpe, sec. 4.{*} {*} [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.