Not that the moving heavens were without computation: astronomy, though secondary, was indispensable.[56] The day, of course, is the creation of the journey of the sun; and the day, as a time-unit, plays in the Mexican count a part altogether commensurate in importance with that given to the sun in myth and ritual. The moon, though far less prominent in every respect, is still conspicuously figured. The morning star (far and wide a great deity of the American Indian nations) was second in significance only to the sun; indeed, one of the most extraordinary achievements of aboriginal American science was the identification of Phosphorus and Hesperus as the same star, and the computation of a Venus-period of five hundred and eighty-four days (the exact period being five hundred and eighty-three days and twenty-two hours). Comets and meteors were regarded as portents; the Milky Way was the skirt of Citlalicue, or was the white hair of Mixcoatl of the Zenith; and in the patterns of the stars were seen the figures that define the topography of the nocturnal heavens. Sahagun mentions three constellations, which he vaguely identifies with Gemini, Scorpio, and Ursa Minor; and in the chart of heavenly bodies, given with his Nahuatlan text, he figures two other stellar groups; while five is the number which Tezozomoc names as those for which the king elect must keep watch on the night of his vigil. Doubtless many other star-patterns were observed, but these five seem predominant. Stansbury Hagar, resolving what he regards as the Mexican Scorpio into Scorpio and Libra, would see in Sahagun's figures half of the zodiacal twelve; and in both Mexico and Peru he believes that he has identified a series of signs closely equivalent to that of the Old World zodiac. Another view (presented by Zelia Nuttall) conceives the Aztec constellations as forming a series of twenty, corresponding to the twenty day-signs employed in the calendar. A third interpretation, on the whole, accordant with the evidence, is that of Seler, who maintains that the five constellations named by Sahagun and Tezozomoc represent, instead of a zodiac, the four quarters and the zenith of the sky-world, and are, therefore, spatial rather than temporal guides. Seler identifies Mamalhuaztli, "the Fire-Sticks," with stars of the east, in or near Taurus. The Pleiades, rising in the same neighbourhood, he believes to have been the sign of the zenith; and at the beginning of a new cycle of fifty-two years the new fire was kindled when the Pleiades were in the zenith at midnight—the very hour, according to Tezozomoc, when the king rises to his vigil. Citlalachtli, "the Star Ball-Ground," is called "the North and its Wheel" by Tezozomoc, and must refer to the stars which revolve about the northern pole. Colotlixayac, "Scorpion-Face," marks the west; while Citlalxonecuilli—so named, Sahagun tells us, from its resemblance to S-shaped loaves of bread which were called xonecuilli—is clearly identified by Tezozomoc with the Southern Cross and adjacent stars. Thus it appears (granting Seler's interpretation) that the constellations served but to mark the pillars of this four-square world.

Essentially the Mexican calendar is an elaborate day-count. As with many other American peoples, the system of notation was vigesimal (probably developed from a quinary mode of counting), and the days were accordingly reckoned by twenties: twenty pictographs served as day-signs, endlessly repeated like the names of the days of the week. These twenty-day periods are commonly called "months" (following the usage of Spanish writers), though they have no relation to the moon and its phases; they are, however, like our months, used as measures of the primitive solar year of three hundred and sixty-five days, the Aztec year comprising eighteen months (or sets of twenties) plus five nemontemi, or "Empty Days," regarded as unlucky. According to Sahagun, six nemontemi were counted every fourth year; if this were true (it is widely doubted), the Mexicans would have had a calendar which was Julian in effect. Like our months, each of the eighteen twenties of the solar year had its own name and its characteristic religious festivals; during the nemontemi there were neither feasts nor undertakings. The beginning of the solar year is placed by Sahagun on the first day of the month Atlcaualco—corresponding, he says, to February 2—the period of the cessation of rains, and the time of rites in honour of Tlaloc and Chalchiuhtlicue. Some authorities, however, believe that the year really began with Toxcatl, corresponding to the earlier part of May, the period of the celebration of the great festival of Tezcatlipoca, when his personator was sacrificed and the next year's victim was chosen. The location of the nemontemi in the year is not certain.

From the fact that to the days of the year were assigned twenty endlessly repeating signs, and the further fact that the nemontemi were five in number (18 x 20 + 5 = 365), it follows that the first day of the year would always fall upon one of four signs; and these signs—Colli ("House"), Tochtli ("Rabbit"), Acatl ("Reed"), and Tecpatl ("Flint")—inevitably became emphasized in the imagination, not only with units of time, but also with the Quarters which divide the world.

But the designation of the days was not simply by the series of pictographic signs. An additional series was formed of the numbers one to thirteen, which, like the signs, were repeated over and over; so that each day had not only a sign, but also a number. Since only thirteen numerals were employed, it follows that if any given twenty days have the number one accompanying the sign of its first day, the sign of the first day of the ensuing twenty days will be accompanied by the number eight, the sign of the first day of the third twenty by two, and so on; not until the end of two hundred and sixty days (since thirteen is a prime number) will the same number recur with the initial sign. The representation of this period of thirteen by twenty days, in which the cycles of numerals and pictographs passed from an initial correspondence to its first recurrence, was called by the Aztec the Tonalamatl, or "Book of Good and Bad Days"—a set of signs employed for divination as the name implies. Since the Tonalamatl represents only two hundred and sixty days, it follows that the last one hundred and fifteen days of the year will have the same signs and numerals as the first one hundred and fifteen. For this reason De Jonghe and some others believe that a third set of day-signs was employed—the nine Lords of the Night, which (since two hundred and sixty is not evenly divisible by nine) would suffice to differentiate the days throughout the year. Seler, however maintains that he has disproved this theory; if so, there would still be the possibility of differentiating the days of the second Tonalamatl from those of the first by employing the sign of that one of the eighteen "months" in which the day fell.

PLATE XIV.

The Aztec "Calendar Stone," one of the two monuments (see Plate [V] for the other) found beneath the pavement of the plaza of the city of Mexico in 1790. The outer band of decoration is formed of two "Fire Snakes" (cf. Plates [VII] 3 and [XXI]), each with a human head in its mouth; between the tips of the serpents' tails is a glyph giving the date, 13 Acatl, of the historical Sun, that is, the beginning of the present Age of the World. A decorative band formed of the twenty day signs surrounds the central figure, which consists of a Sun-face, with the glyph 4 Olin; while in the four adjacent compartments are the names of the eras of the four earlier "Suns." Sun rays, with other figures, appear in the spaces between the inner and outer decorative bands. Below is given a key (after Joyce, Mexican Archaeology, page 74).

In addition to the Tonalamatl, there is another consequence of the double designation of the days. Each year, it has been noted, begins with one of four day-signs. But three hundred and sixty-five is indivisible, evenly, by thirteen; therefore, the day-signs and numerals for succeeding years must vary, the day-signs recurring in the same order every four years, and the numerals in the same order every thirteen years (since 365 = 13 x 28 + 1), while not until there has elapsed four times thirteen years will the same day-sign and the same numeral occur on the first day of the year. These divisions of the years into groups, determined by their signs and numbers, were of great significance to the Mexican peoples. The sign which began each group of thirteen years was regarded as dominant during that period, and as each of these signs was dedicated to one of the four Quarters, it is to be supposed that the powers of the ruling sign determined the fortunes of the period. The cycle was complete when, at the end of fifty-two years, the same sign and number recurred as the emblem of the year. Such an epoch was the occasion for prognostics and dread anticipations, and it was celebrated with a special feast at which all fires were extinguished and a new flame was kindled on the breast of a sacrificial victim. This festival was called "the Knot of the Years," and in Aztec pictography past periods were represented by bundles, each signifying such a cycle of fifty-two years.

It will be noted that the fifty-two year cycle is also the period for the recurring coincidence of the day-signs and numerals in the year and in the Tonalamatl (for, 365 factoring 73 x 5, and 260 factoring 52 x 5, it follows that 52 years will equal 73 Tonalamatls). It is, therefore, the more extraordinary that in the usual mode of figuring the Tonalamatl it is begun, not with one of the four signs which name the years and their cycles, but with another day-sign, Cipactli ("Crocodile"). The plausible explanation of this is that since the Crocodile was the monster from which Earth was formed by the creative gods, the divinatory period was inaugurated under his sign.