The representations in these parallelograms, are believed to have originated in the Mexican fable of the SUNS, which will be hereafter noticed. The Aztecs believed that this luminary had died four times, and that the one which at present lights the earth, was the fifth, but which nevertheless was doomed to destruction like the preceding orbs. From the creation, the first age or sun, lasted 676 years, comprising 13 cycles, when the crops failed, men perished of famine and their bodies were consumed by the beasts of the field. This occurred in the year 1 Acatl, and on the day 4 Ocelotl, and the ruin lasted for thirteen years. The next age and sun endured 364 years or 7 cycles, and terminated in the year 1 Tecpatl on the day 4 Ehecatl, when hurricanes and rain desolated the globe and men were metamorphosed into monkeys. The third age continued for 312 years, or 6 cycles, when fire or earthquakes rent the earth and human beings were converted into owls in the year 1 Tecpatl, on the day 4 Quiahuitl;--while the fourth age or sun lasted but for a single cycle of 52 years, and the world was destroyed by a flood, which either drowned the people or changed them into fishes, in the year 1 Calli, on the day 4 Atl. The four epochs of destruction are precisely the days typified by the hieroglyphics in the four parallelograms A, B, C and D. It will be seen by adding the several periods together that the Aztecs counted 1469 years from the creation of the world to the flood; yet there is an incongruity in this imaginary antediluvian history. If the fourth age had lasted only 52 years, it would have terminated in the year 1 Tecpatl instead of 1 Calli. Bustamante, the publisher and annotator of Gama, states that some authorities contend for only three antecedent periods, and that the present age is expected to end by fire. But Mr. Gallatin alleges that the four ages and five suns have been generally adopted, and are sustained by the ancient Aztec paintings contained in the Codex Vaticanus, plates 7 to 10. Like most of the Mexican antiquities, this branch of the Chronology is admitted to be exceedingly obscure, for it is asserted in the Appendix to Mr. Gallatin's essay that the hieroglyphics annexed to these _paintings_, may be interpreted as giving to the four ages respectively the duration of either 682, 530, 576, and 582, or of 5206, 2010, 4404, and 4008 years.