[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.