Thus the Mayas seem to have had uncompounded names for the numerals from 1 to 11, 20, 400, and 8,000, and to have formed all numbers by the addition or multiplication of these. The manner in which the combinations were made seems clear up to the number 40. Thus we have 10 and 2, 10 and 3, etc., up to 19; 20 is hun-kal, 21 is hun-tu-kal, etc., indicating that tu, which I do not find in any dictionary, is simply 'and' or a sign of addition. The composition of lahu-ca-kal is clear only in the sense of ten from twice twenty; 40 is two twenties, 60 is three twenties, and so on regularly by twenties up to 400, for which a new word bak is introduced; after which the numbers proceed, twice 400, thrice 400, etc., to 8,000, pic, corresponding to the Nahua xiquipilli. But while the composition is intelligible so far as the multiples of 20 and 400 are concerned, it is far from clear in the case of the intermediate numbers. For instance, 40 is ca-kal, and forming 41, 42, etc., as 21 was formed from 20, we should have hun-tu-ca-kal, ca-tu-ca-kal, etc., instead of the names given, hun-tu-yox-kal, etc., or, interpreting this last name as the former were interpreted we should have 61 instead of 41. The same observation may be made respecting every number, not a multiple of 20, up to 400; that is, each number is less by 20 than the composition of its name would seem to indicate. If we gave to tu the meaning 'towards,' then hun-tu-yox-kal might be interpreted '1 (from 40) towards 60,' or 41; but in such a case the word for 21, hun-tu-kal, must be supposed to be a contraction of hun-tu-ca-kal, '1 (from 20) towards 40.' Other irregularities will be noticed by the reader in the numbers above 400. I have thought it best to call attention to what appears a strange inconsistency in this system of numeration, but which may present less difficulties to one better acquainted than I with the Maya language.[1098]
THE MAYA CALENDAR.
Authorities on the Maya calendar of Yucatan, the only one of which any details are known, are Bishop Landa and Don Juan Pio Perez. The latter was a modern writer who devoted much study to the subject, was perfectly familiar with the Maya language, and had in his possession or consulted elsewhere many ancient manuscripts. There are also a few scattered remarks on the subject in the works of other writers.[1099]
The Maya day was called kin, or 'sun'; malik ocok kin was the time just preceding sunrise; hatzcab was the time from sunrise to noon, which was called chunkin or 'middle of the day'; tzelep kin was the declining sun, or about three o'clock P. M.; oc na kin was sunset. The night was akab, and midnight was chumuc akab. Other hours were indicated by the position of the sun in the daytime, and by that of some star—the morning star, the Pleiades, and the Gemini as Landa says—during the night.
Days of the Maya Calendar.
The following table shows the names of the twenty days with the orthography of different writers, and the meaning of the names so far as known:
The hieroglyphics by which the names of the days were expressed are shown in the accompanying cut in their proper order of succession,—Kan, Chicchan, etc., to Akbal; but it is to be noted that although this order was invariable, yet the month might begin with any one of the four days Kan, Muluc, Ix, and Cauac.