The Codices contain numerous calculations intended to bring these various quantities into definite relations as aliquot parts of some arithmetical whole, which might be taken as a general unit. The scribes appear to have begun by establishing a period of 14,040 days. This equals 39 years of 360 days each, and also 54 years of 260 days each, together, of course, with the divisors of these numbers, 13, 18, 20, 65, etc. Then followed the determination of the period of 18,980 days, = 73 tonalamatl, = 52 solar years, so prominent in the calendar and ritual of the Nahuas.
This number, however, could not be adjusted to the cycle of the ahau katun, which was 24 years of 365 days each;[[28]] nor to the ceremonially prominent revolution of “the Great Star,” Venus, which coincides with the Earth’s revolutions in 2920 days, or eight solar years. To bring these into accord with the tonalamatl required a period of 104 solar years, or 37,960 days; and to adjust under one number the katuns, the ahau katuns, the revolutions of Venus, the solar year, and the tonalamatl, three times that number of days are required, that is, 113,880, = 312 years.
This period had still to be brought into relation to the old year of 360 days, and this requires the estimation of a term covering 1,366,560 days, or 3744 years; and this extended era we find expressed in the Dresden Codex, page 24, in the following simple notation, the interpretation of which into our system of calculation, according to the method above explained, I add to the right.
This long period allowed all their important time-measures to be dealt with as aliquot parts of one whole, and would seem to be sufficient for the purposes they had in view. The credit of establishing it from their ancient writings is exclusively due to Dr. Förstemann, whose demonstrations of it appear to be conclusive.[[29]]
 | 9 (unit = | 144,000) = | 1,296,000 |
 | 9 (unit = | 7,200) = | 64,800 |
 | 16 (unit = | 360) = | 5,760 |
 | 0 (unit = | 20) = | 0 |
 | 0 (unit = | 1) = | 0 |
| Total, | 1,366,560 |
This acute observer has, however, discovered some reasons to suppose that the native priests occasionally contemplated a much more extended era; some of their calculations seem to require an era which embraced 12,299,040 days, that is, 33,696 years![[30]]
No doubt each of these periods of time had its appropriate name in the technical language of the Maya astronomers, and also its corresponding sign or character in their writing. None of them has been recorded by the Spanish writers; but from the analogy of the Nahuatl script and language, and from certain indications in the Maya writings, we may surmise that some of these technical terms were from one of the radicals meaning “to tie, or fasten together,” and that the corresponding signs would either directly, that is, pictorially; or ikonomatically, that is, by similarity of sound, express this idea.
Proceeding on the first of these suppositions, Dr. Förstemann has suggested that the character, Fig. [4], No. 8, signifies the period of 52 years, the Nahuatl xiuhmolpilli, “the tying together of the years,” represented in the Aztec pictographs by a bundle of faggots tied with cords. The Maya figure is explained as the day-sign imix, representing the first day of the calendar, and, by a kind of synecdoche, the whole calendar, with a superfix.
7. Rules for Tracing the Tonalamatl, or Ritual Calendar.
That the computations of the tonalamatl underlie most of the numerals in the Codices is shown by the rules for reading them, formulated by Pousse with reference to the red and black numerical signs. These rules are as follows:—[[31]]