Unlike the Mexican months, however, these were used in dating, and a given day was expressed with its month-sign, together with a numeral to show which day of the month it was. Thus 6. caban, 5. pop, means the day 6. caban, after 5 days of the month pop have passed. The numerals were not expressed on quite the same system as the Mexican. Dots were used for the numerals up to four, but a bar was used for five, two bars for ten, and so on, odd days over a multiple of five being expressed by the requisite number of dots. On the monuments, if the supernumerary dots were few, the space between or on either side of them was filled with small crescents, which are merely ornamental and must be carefully distinguished from the dots themselves. Occasionally in the more elaborate carvings the numbers from 0 to nineteen are expressed by faces. In the case of 0 the lower jaw is formed by a hand, and numbers over ten are expressed by the face assigned to the corresponding unit but with a fleshless jaw. Ten itself is the head of the death-god. Zero in the normal notation is expressed either by a hand or a figure shaped somewhat like a Maltese cross. The use of the zero is explained later. The Maya, like ourselves, were in the habit of expressing a high number by a succession of figures which combined to form a numeral, but they did not employ the decimal system. Their system, when applied to the computation of time, was on the whole, but not entirely, vigesimal, and was as follows. Twenty days, or kin, formed a uinal, and the uinal thus corresponded to one of their months; but the next higher unit, the tun, consisted of eighteen uinal, and contained 360 days, being thus equivalent to a year minus the five uayeb days. Twenty tun made a katun (7200 days), and twenty katun went to another period of which the name is not known, but which is usually called a cycle (144,000 days). There are indications that a higher unit still was recognized, the so-called “great cycle,” consisting of thirteen cycles (1,872,000 days). Each of these periods was expressed by an appropriate glyph, and these glyphs were in two styles, being either what is usually termed “normal” signs, or face-signs (Fig. [55]). The latter exhibit considerable variation, especially that of the great cycle; but the cycle bird-face is recognizable by the jaw-bone in the shape of a hand (recalling the face-paint of the Mexican gods into whose name the numeral five enters as a component part), the katun by a similar bird-face with a normal jaw, the tun by the normal glyph which it bears on its head, or its fleshless jaw, the uinal by its frog-like appearance and the curl at the corner of its mouth, and the kin by the glyph on the forehead or the filed teeth. In many of the more elaborate carvings the significance of the sign is shown more by its position in the series than by anything else. Now a great number of the stelæ bear inscriptions which start with a high number expressed in this manner (Fig. [56]); at the top is the great cycle glyph, which is an elaborate affair and really means little more than that a count of days is to follow, since there could hardly be any mistake regarding this period which represents over fifty-one centuries. Below, usually in two columns of glyphs, is a number of days, expressed in cycles, katuns, tuns, uinals and kins, and this is followed by a day-and-month date. In the transliteration of Mayan dates, the numerals alone are given as a rule; thus the date shown in Fig. [56, b], transliterated as 9. 16. 10. 0. 0. 1 ahau, 3 zip, means the day 1 ahau, after 3 days of the month zip have passed, being 9 cycles, 16 katuns, 10 tuns, 0 uinals, and 0 kins from the chronological starting-point of the present “Great Cycle.” Now the astonishing fact is this, that throughout the whole of the Maya country, i.e. the area over which ruins in the Maya style are scattered, including Chiapas, Guatemala, Yucatan and northern Honduras, if the long count of days (expressed in cycles, katuns, etc.) be reckoned back from the final day-and-month date, the same day is always reached, viz. 4. ahau,
8. cumhu. Thus all Maya reckoning dates from one definite day in the past, and this day must almost certainly be an artificial date in the sense that it must have been obtained by calculation at a far later time, since it is practically four thousand years from the earliest date which can in any sense be claimed as historical.[5] The starting date itself is found at Quirigua (on a stela which also bears a date in the ninth cycle), and here it is shown to be the concluding date of a cycle thirteen, which must be the last cycle of the preceding “grand cycle.” Many, if not most, of the inscriptions seem to be devoted to the calculation of dates; in the course of the glyphs, most as yet unreadable, one continually comes upon a “distance-number” expressed as above, and then the day-and-month sign to which this leads, reckoning from the date last given. In the longer inscriptions, notably that in the “temple of inscriptions” at Palenque, which contains over six hundred consecutive glyphs, these calculations extend over considerable periods of time. The great probability is that such calculations are not historical, but of a ritual nature. The Maya had no system of intercalary days by which the year of 365 days could be squared with true solar time, and it is probable that the feasts appropriate to certain seasons were shifted from month to month when the discrepancy became noticeable. Perhaps then these calculations had reference to the ritual calendar in accordance with which the various festivals were held. It must be remembered that the Maya in their count of days reckoned only elapsed time, expressing only a full tale of days. Thus each date is in one sense one day behind the date as we express it. This sounds complicated, but the difficulty disappears if we regard their method from the same point of view as our own reading of the clock. Whereas we speak of the fifteenth of June while the day is yet incomplete, yet we refer to a point in the third hour after noon in terms of two o’clock, viz. 2.20, or 2.45. Thus for the first day of a month we find the symbol zero, and 0. zotz means that the month zip is concluded, but that the first day of zotz is not yet complete. So it is that the katuns (and other periods) are known by the name of the last day of the previous katun, 5. ahau, 3. ahau, and so on, and are not named after the day imix which is the first of the series of twenty day-signs, and is actually the first day of the time-periods from cycle to tun. The Maya method of dating enabled them to fix the position of a definite day without risk of confusion over long periods of time. If the day-sign with its attendant number, and the position in a definite month, is given, that day is fixed for a period of 52 years. If the number of the tun in which it occurs is also stated, it is fixed for a period of 936 years (i.e. 936 years must elapse before a day with a similar series of signs and numbers can recur). If the number of the katun is also expressed, the position is determined for 18,720 years; and if the number of the cycle as well, a period of 374,400 years.

Fig. 56.—Date inscriptions.

A. Normal numerals, reading 9. 15. 0. 0. 0.[6]   4. ahau, 13 yax. (Copan, altar S).

B. Face-numerals, reading 9. 16. 10. 0. 0.   1. ahau, 3. zip. (Quirigua, stela F).

(After Maudslay)

Since the year contained 365 days, and the day-signs were 20 in number, it is obvious that the year began on one of four days. These days, later called “year-bearers,” were, at the time of the monuments and the writing of the Dresden codex, ben, eznab, akbal and lamat, which correspond to the days which began the Mexican year, acatl, tecpatl, calli and tochtli. However, the year-bearers as given by Landa, and also as they appear in the Troano-Cortesianus codex, are kan, muluc, ix and cauac. This means that in the interval the commencement of the year had shifted (5 × x) + 1 days, x being an unknown quantity. By this time too the long count in its most elaborate form seems to have been abandoned, and the katun became the highest unit, known by the name of its “initial” day, e.g. katun 6. ahau, or katun 4. ahau. It is this method of reckoning which is employed in the books of Chilan Balam. Most of the other races of Maya stock, as far as is known, possessed calendars which included a series of twenty day-signs (see Appendix I) combined with the numerals one to thirteen, but the count of the Kakchiquel was different, being purely vigesimal. The periods involved were one of 400 days (20 × 20), called huna, and a larger of 8000 days (20 huna), called may. The huna was known by its initial day ah (corresponding to ben and acatl) together with the number which might be attached to it, and the time count dated from the destruction of a rebellious sub-tribe, the Tukuchi, which occurred in a huna 11. ah.

Fig. 57.—Upper row, world-direction signs; lower row, colours.