Note 194 — Chapter IV · MEXICAN HIEROGLYPHICS—MANUSCRIPTS—ARITHMETIC—CHRONOLOGY—ASTRONOMY

According to Gama (Descripcion, Parte 1, pp. 75, 76), because 369 can be divided by nine without a fraction; the nine “companions” not being attached to the five complementary days. But 4, a mystic number much used in their arithmetical combinations, would have answered the same purpose equally well. In regard to this, McCulloh observes, with much shrewdness, “It seems impossible that the Mexicans, so careful in constructing their cycle, should abruptly terminate it with 360 revolutions, whose natural period of termination is 2340.” And he supposes the nine “companions” were used in connection with the cycles of 260 days, in order to throw them into the larger ones, of 2340; eight of which, with a ninth of 260 days, he ascertains to be equal to the great solar period of 52 years. (Researches, pp. 207, 208.) This is very plausible. But in fact the combinations of the two first series, forming the cycle of 260 days, were always interrupted at the end of the year, since each new year began with the same hieroglyphic of the days. The third series of the “companions” was intermitted, as above stated, on the five unlucky days which closed the year, in order, if we may believe Boturini, that the first day of the solar year might have annexed to it the first of the nine “companions,” which signified “lord of the year” (Idea, p. 57); a result which might have been equally well secured, without any intermission at all, by taking 5, another favorite number, instead of 9, as the divisor. As it was, however, the cycle, as far as the third series was concerned, did terminate with 360 revolutions. The subject is a perplexing one, and I can hardly hope to have presented it in such a manner as to make it perfectly clear to the reader.