Archaeo Astronomy - Article in CURRENT ANTRHOPOLOGY

	The announcement of a possible first archaeoastronomical site (called Namoratunga II) in sub-Saharan Africa by Lynch and Robbins (1978) and its subsequent reappraisal by Soper (1982) have renewed interest in an East African calendrical system, the Borana calendar, first outlined in detail by Legesse (1973:180-88). I shall here reinterpret the calendar as Legesse describes it in the light of astronomical constraints. The Borana calendar is a lunar-stellar calendrical system, relying on astronomical observations of the moon in conjunction with seven particular stars (or star groups). At no time (except indirectly by way of lunar phase) does it rely upon solar observations. The Borana year is twelve lunar synodic months (each 29.5 days long), 354 days. While it will not correspond to the seasons, this may not be of primary importance for people this close to the equator. There are twenty-seven day names (no weeks), and since each month is either 29 or 30 days long, the first two (or three) day names are used twice in the same month starts on a new day name. The day names are listed in Table 1, the month names in Table 2. The first six months can be identified at the beginning of the month with a particular astronomical observation, whereas the last six months can be so identified only around the middle of the month. The first six months begin with the observation of the new-phase moon in conjunction with six positions in the sky marked by seven particular stars or star groups. Thus the phase of the moon is held constant while its position varies. The last six months are identified by a particular-phase moon seen in conjunction with the first star position. Thus, here, the lunar phase changes and the position is held constant. The seven stars or star groups in order are Triangulum (which I take to mean Beta Trianguli), Pleiades, Aldebarran, Belletrix, central Orion (around the sword), Saiph, and Sirius. They are given in Table 2 next to the months they define. The New Year starts with the observation of the new moon in conjunction with Beta Trianguli. (The term "new moon" here will be taken to be within two days of zero phase, although the Borana allow up to three "leap" days’ leeway, the astronomical observation determining the correct day to start on. This is indicated in the day nomenclature by the assignment of like prefixes to two or three day names before the approximate time an important astronomical observation is to take place.) Since the new moon can be seen only just before sunrise or just after sunset, twilight makes the observation of Beta Trianguli (a third-magnitude star) in conjunction with a new moon impossible with the naked eye.
	Assuming that such an observation, however, was possible, would the next new moon be in conjunction with the next star group. Pleiades? (Conjunction here is taken to mean "rising with" or "setting with," having the same right ascension. Legesse says (p. 182), "Let us assume that a new moon was sighted last night and that is appeared side by side with the star Sirius, which the Borana call Basa.") Since the sidereal period of the moon is 27.3 days long, it will arrive back at the Triangulum position more than two days before completing its synodic month. At the sidereal rate of 13.2° per day, the moon will be within 3° of Pleiades when it rises in the new phase again. However, by the time of the third month it rises, not with Aldebarran, the next star, but a little past Belletrix, the fourth star, which is supposed to start the fourth month. By the fourth month the new moon is rising past Sirius, the sixth start, and the calendar is clearly not working as described. It should be added that the right-ascension positions of the stars in the area from Beta Trianguli to Sirius change with time, at the rate of roughly 15° every thousand years. However, the stars stay in approximately the same configuration, and arguments based on their present right-ascension relationships will hold over the past several thousand years as well. What happens if we take the term "conjunction," or "side by side," as Legesse has it, to mean not "rising with" but "rising single-file," that is, at the same horizon position (in other words, having the same declination)? Examining the idea that it is not the proximity of the moon to the star that is important but its horizon rising (or setting) position with respect to that star’s horizon rising (or setting) position, we immediately find that the first necessary observation, the new moon rising at the horizon position of Beta Trianguli, is not currently possible. Beta Trianguli rises (at the equator) about 35° north of the east point (0° declination), while the moon (on the northernmost average) rises at 23.5° north of east, never rising farther north than 28.5° from the East Point. The earth’s rotation axis is known to precess over the centuries, and while this does not change the lunar orbital positions significantly, it does change the apparent position of the stars. We can calculate the positions of the seven Borana stars at a time when Beta Trianguli was well within the moon’s declination limits to see if the calendar would have worked then. In 300 BC, Beta Trianguli was rising at a declination of +23° north of east. The right-ascension positions at the time still do not allow a "rising with" interpretation of the calendrical system. We can begin by defining the start of the Borana year as the new moon rising at the rising position of 300 BC Beta Trianguli. (The date of 300 BC was strongly suggested by the preliminary dating of Namoratunga II, but it was chosen because +23°, Beta Trianguli’s declination at the time, is the northern average of the moon’s monthly motion. I will take the moon’s motion, for the example here, from the Nautical Almanacs for 1983 and 1984.) The next new moon rises at 14° north of east, which corresponds precisely to the 300 BC horizon rising position of Pleiades, the next Borana star. The next four new moons (starting the next four Borana months) rise at +9 degrees, +1 degree, –11 degrees, and –17 degrees declination. These positions correspond to the 300 BC horizon rising positions of the Borana stars Aldebarran. Belletrix, central Orion—Saiph (taken together), and Sirius, respectively (Table 3).
	The seventh month should be identifiable 14 or 15 days from its automatic start (about 29 days after the start of the sixth month) by a full moon rising at the Beta Trianguli position, and this is indeed the case. Each subsequent moon rises at this horizon position 27.3 days later (sidereal month) in a phase (synodic month) about two days less waxes (since it is on its way to the full phase again) each time. (Legesse has a waning moon, but this must mean waning with respect to each subsequent monthly observation, not with respect to the Phase State for that month.) On the thirteenth or first month, the moon is seen rising in the new phase again ("new" meaning within a couple of days of zero phase), and another year begins. Tracing the moon’s motion as it arrives at these positions in the sky (which are, however, no longer directly marked by the seven stars), we can derive the calendar (see Table 4). This outline is still general with respect to what is sometimes called the lunar excursion (regression of the line of nodes of the lunar orbit). The three "leap" days the Borana calendar allows for the starting of some of the months just before an important astronomical observation could account for this declination excursion of the moon (± ca. 5° from 23.5° declination on an 18.6-year basis), but this would certainly require confirmation in the field. The Borana calendrical system as described by Legesse is, therefore, a valid timekeeping system, subject to the astronomical constraints outlined here, and the pillars found in northwestern Kenya by Lynch and Robbins and preliminary dates at 300 BC could, as they suggest, represent a site used to derive that calendar. The calendar does not work in right-ascension sense, but it does work if taken as based on declination. It might have been invented around 300 BC, when the declinations of the seven stars corresponded to lunar motion as the calendar indicates, and the star names would therefore apply to the horizon positions as well. Because the horizon rising positions constitute the important observations (over half of which must be made at twilight), some sort of horizon-marking device would seem to be necessary. Since the calendar is still in use, and the horizon-making pillars can no longer be set up by aligning them with the horizon rising positions of these stars, it would seem that the Borana may be using ancient (or replicas of ancient) horizon markers and this possibility should be investigated. I look forward with great interest to a test of these hypotheses.