Introduction

Celestial events have always played an important role in pre-historic societies, particularly in the magic/religious domain.
Once sedentism was established, it propitiated the observation of the solar and lunar rhythms, as depicted by the risings or settings of those celestial bodies in the horizon, an association with the seasons would be inevitable. The Sun rises further to the north as the heat builds up in the Summer, and swings further and further to the south as winter approaches. During midwinter the Sun rises on the limiting solsticial azimuth, and the Full Moon rises close to the northern solsticial line. As we leave midwinter the Sun swings and rises each day a little to the north of the previous day; conversely the Full Moon starts its south digression. Conditions improve as the extreme cold is left behind and the days are longer. However, the Full Moon is still rising north of the Sun. Perhaps when the cross-over occurs, close to the equinox, and the first Full Moon is observed to rise south of the Sun, this is a sign that the hardships are over, and that life is safer again. It is the onset of Spring, as Nature blossoms, new life appears in the bird nests, some animals come out of hibernation, etc . It is not inconceivable to think that the cross-over of the Full-Moon and the Sun is a sign of rebirth and resurrection, i.e. of the cosmic rule over everyday life, certainly a magic/religious sign to be incorporated in social rituals.
Georg and Vera Leisner (Leisner, 1948, 1949; Leisner and Leisner, 1956, 1959) started in the 1940's a systematic study of the funerary megalithic monuments of Central Alentejo, and from their data on dolmens in this region we can see that the corridors are preferentially oriented between E and ESE. However, the observed orientation dispersion is fairly large and many examples are found outside this range, in many cases even outside the solsticial directions. Generally, all over the country the corridors open to the eastern horizon, a fact which V. Gonçalves associated to the "first-light" just before sunrise (Gonçalves, 1992).
Extensive work was developed in the 1960's/70's, in Great Britain, on the analysis of the internal structure of megalithic sites and of their relation with the landscape (Thom, 1967, 1971, 1978). The controversy that followed (Freeman, 1976, 1979) seems to have ruled out the megalithic man as an advanced astronomer, but not his awareness of the sky, and the magic/religious understanding of the world around him, or even his use of the observation of the celestial bodies in the management of his social life. Indeed, recent data on the megalithic monuments of Central Alentejo and of Brittany in France, have reinforced the possibility of a culture aware of the cosmic order displayed by the most prominent celestial bodies, as reflected in the iconographic record, with many sites showing, for instance, figurative engravings of the crescent Moon and of the Sun. In fact, several menhirs (either isolated or part of enclosures) show engravings representing the Sun, and more frequently the Moon (Fig.s 1,2). Also, lines defined with the landscape and some internal alignments, seem to be related with the sky, in that they frequently coincide reasonably well with particular directions of astronomical significance (Alvim, 1996-1997; Alvim, 2003; da Silva, 2000; da Silva and Calado, 2003).
There are examples in which this relation with the sky is shown to be statistically significant, even in the absence of a supporting singular astral direction. As discussed by Thom, the direction in the horizon for which the rising Sun would take the same time to return (182/183 days), whether it would swing North through Midsummer, or South through Midwinter, defines the so called "megalithic equinox", i.e. a direction about halfway between the solstice sunrises. The Equinox is, then, what can be called a second order direction in that it requires a further insight into the dynamics of the observed motions of the cosmic bodies.

The Spring Moon

We have proposed (da Silva, 2004) an alternative interpretation for the "megalithic equinox", albeit one that is more distant from the East-West line known today, but one that would correspond to the megalithic man subjective perception of the cycle of seasons, and to the value he would have attributed to the establishment of Spring as the first sign that the hardship of winter was past behind.
In describing the cycle of seasons from an ancient astronomy point of view, one normally relies on the steady change of the Sun in the sky. It has not been generally stressed that the Full Moon also exhibits the same regularity although in opposition to the Sun, and this could be significant to an ancient observer in pre-literate societies.
The following takes over the proposed argument and describes a very simple observation that could have been realized in megalithic times, in which the azimuths of the rising Sun and of the rising Full Moon, after Midwinter, are getting closer until they cross-over, i.e. until the Full Moon is seen to rise South of the direction in which the Sun was observed to rise in the same day. We know that this occurs about the time of the Equinox, and this cross-over may be used to provide an alternative definition of the "megalithic equinox".
This observation requires an operational definition of the Full Moon rising day, and an operational definition of the cross-over day.
Of the various Moon cycles the "lunation" is the most conspicuous. From a pure observational point of view, in megalithic times, this cycle would start with the first appearance of a very thin crescent, soon after the Moon was absent from the sky (what we now call New Moon). For about 14 days the rise of the Moon is practically not observed as it occurs during daylight, and the Moon is perceived when it is already high in the sky. Close to the Full Moon, on a clear day, if we know approximately where to look, we can perceive the Moon rise in the eastern horizon, as the Sun sets in the western horizon. As a guideline, one day before the Full Moon the Moon is high on the sky (~15º) at the sunset, prompting a careful observation of the moonrise in the next day. Notwithstanding the first appearance of the thin crescent, the Full Moon rise is probably the most remarkable moment of this lunar cycle, and one to which observers in pre-literate societies would have paid particular attention.
Presently, the most obvious criterion to define the Full Moon day is to choose the moonrise closest to the astronomical Full Moon. This can be controlled by the observation, in previous days, of the altitude of the Moon in the eastern horizon as the Sun sets in the western horizon. In most cases this identification of the day of Full Moon has no ambiguity when the Moon is less than 6º above the horizon at sunset (equivalent to about half an hour since moonrise), but in certain cases the decision may be postponed to the next day, even if the Moon is to rise after the sunset by an amount which would be necessarily equivalent to less than half an hour. The onset of the night darkness makes it impossible to perceive the horizon after that, and relate the moonrise to the horizon profile.
Thus, the sunset is the reference mark against which the Full Moon day can be selected.

The observation of the cross-over requires that the sunrise azimuth is noted against a reference mark, normally in the horizon. Presently, one would generally expect the Sun and the Full Moon to rise very close to East at cross-over. If on Full Moon day the moonrise azimuth is greater than the sunrise azimuth in the same day then this is the first Full Moon rise past the Sun. However, if the cross-over has not occurred on the Full Moon day, the observer would have to wait for the next Full Moon. Also, the decision on the azimuth may be affected by an ambiguity as to the acceptance or not, of those rather less frequent occasions in which the difference in azimuths is less than, say, half a degree (i.e. the diameter of the solar or lunar discs). Any of these circumstances, either isolated or in conjunction, may result in the postponement of the cross-over to the next Full Moon, or the acceptance, as cross-over, of a not well defined situation. The Full Moon thus identified, in one way or the other, would be the first Full Moon past the Sun, and could appropriately be called "Spring-Full-Moon". These circumstances favor the occurrence of Spring-Full-Moon azimuths greater than 90º.

In order to understand the regularities involved in the observation of the Full-Moon-rise, the azimuth and time of the moonrise were computed over a period of 110 years, i.e. well over 5 lunar node regression cycles. These calculations (USNO) were performed for a period in the present (1940-2049) to take advantage of a precise knowledge of the Moon orbital parameters. We find this representative of what could have been observed in megalithic times since, according to present day astronomy, the essential lunar orbital parameters have not changed significantly in the last millennia.
As discussed (da Silva, 2004), the analysis of the referred computations shows that the Spring-Full-Moon rise is distributed in the azimuth interval [ 85º-110º ] with an average value greater than 90º . It also shows that this feature is already well established for any period of the order of the regression of the lunar nodes cycle, and that second order fluctuations are smoothed out over the period of 110 years, giving an average value of about 97º and a standard deviation of 5º for the azimuth of the Spring-Full-Moon rise.

Passage Tombs

Recently Hoskin and Calado [1998], surveyed the megalithic tombs in Central Alentejo and confirmed earlier observations that the tombs would generally face the eastern-south-eastern horizon. It must be stressed that their particular choice of the seven-stone-chambered tombs, and the uniform criterion used for the measurement of the azimuth, provided a very consistent set of tombs pointing to the use of the sky for the corridor orientation. The statistical analysis of the 91 azimuths for the seven-stone chambered tombs gives an average value of Ztombs = 99º, and a standard deviation of 10º .We find it significant that the above Spring Moon interval matches very well Hoskins and Calado corridor orientation data (Fig. 3), and that the average values coincide within less than a fraction of the standard deviation. In fact, more than three quarters of the tomb azimuths fall within the computed [85º -110º] Spring Moon interval.

Megalithic sites

Recent surveys in Central Alentejo by Calado and others (Calado, 2004; Gonçalves, 1983; Gomes, 1986; Oliveira, 2001) have shown a variety of megalithic architectural sites in addition to passage tombs. These range from isolated menhirs and groups of menhirs, to closed elliptical enclosures, and horseshoe enclosures.
Although one of the enclosures is clearly a horseshoe design (Vale d'El Rei), several others hint at this shape with different degrees of imprecision (Fig. 4). However, these enclosures generally feature a large menhir placed off-axis, near the apex., a feature that is well recognized in the case of Almendres, Portela de Mogos, Vale Maria do Meio and Tojal. These sites are normally sitting on top of a slope facing east. Also, the horseshoes are generally open to the eastern horizon.
Chronologically the menhirs and enclosures of Alentejo, as those of Algarve or Brittany (France) seem to be older than the Dolmens (Antas) and were most probably the first megalithic monuments of pre-historic Europe (CaladoD, 2000).

Vale d'El Rei
This very clear example of an horse-shoe enclosure was first reported by the Leisner couple (Leisner, G.; Leisner, V., 1959) at a time when the stones were still mostly upright, close to their original implantation on socks. The plan originally published by the Leisner's was rather inaccurate and was later more carefully redrawn (Fig. 5) by Zbyszewsky (Zbyszewsky et al., 1977). This plan suggests that the axis of symetry is pointing in a direction close to a lunar minimum standstill direction, thus associating this site with the Moon. Presently, all the stones have been removed by farming and are all lumped together some 20 meters to the North. However, recent excavation of the site (Calado, 2004) has been able to show the initial positions of the stone implantation socks. The plan drawn by Calado, using a "total station" system, differs slightly in orientation suggesting that the azimuth of the symmetry axis is not greater than 100°: actually, a careful survey confirms this orientation fixing the axis azimuth at about 98°, indicating that most probably the Zbysewsky data was affected by an imprecise value of the magnetic declination. A project underway, with the cooperation of the local municipality, will restore the menhirs to their original socks.

Vale Maria do Meio
Vale Maria do Meio is undecided between a closed elliptical layout (in this case most of the Northern arm is missing) and an open enclosure of the horseshoe type. The overall layout can be broken into two structures: the West top of the monument resembles a small horseshoe, and the South-East part seems to define a linear structure.

The monolith nr.25 (Calado, 2000b)(here designated by "A") seems to have a clear role in the monument as an observing position. The linear structure seen from "A" is a clear corridor in the direction of the lunar minor standstill. However, from "A" the Sun can be seen to set on monolith nr.10 in the equinox. The overall arrangement of the monoliths close to the equinoctial sunset, is very similar to that observed in the Almendres enclosure. However, a conspicuous feature common to both (V. M. do M and Almendres) is the presence of a very large monolith, larger (and taller) in each group. In both cases this monolith lies a few degrees to the North of the East-West direction. Looking in the opposite direction this line defines an azimuth close to 100° with "A". The similarity of the overall arrangement, however, is so apparent that they seem to have been built to the same model, and we could easily conjecture (judging from the size of development of each) that VMM was a precursor of Almendres, where the alignments were tested first, before the construction of this larger, and certainly more impressive monument.

Portela de Mogos
We don't seem to have a reliable plan for the layout of this monument. However, the presence of a larger monolith in the middle of an open circular arrangement of smaller stones, is clearly a feature of the original layout. A group of stones seem to align generally in the East-West direction suggesting an equinoctial feature. Whether these stones still lie near their original positions or were removed in recent times to help define the boundaries of adjacent land plots of different owners is a matter to be scrutinized, and requires further investigation. It is not possible to assert whether this is a closed or an open megalithic arrangement but, if the outliers are anywhere near their original implantations, then again the large monolith is seen a few degrees to the North of the E-W western equinoctial sunset direction, when observed at sunset. What seems to be clear is that this site is well positioned to observe the near solstitial sunrise over Evoramonte, very close to the more astronomically rigorous line defined by the natural outcrop at the Godel settlement and by the menhirs at S. Sebastião da Giesteira. From these two sites the rising sun, in megalithic times, would have been seen to detach from the horizon exactly over the top of Évoramonte hill.

Almendres
This impressive eliptical enclosure has so many monoliths that it is possible to find any two that fit a particular purpose or orientation. Any interpretation will have to rely on special features or internal organization ranging from a study of spatial distribution of individual monoliths, the areas defined, the access "lanes" to the inner space, indeed a study of what in modern terms could be called architectural organization of space, to the volumetric distribution of the monoliths, the shape of the menhirs, and even the distribution of the engravings observed in some of them, and of their possible meaning. Indeed most of the large monoliths are assembled near the top of the hill close to the western apex of the general elliptical layout. And their general distribution resembles a simpler structure of two arms open to the rising equinoctial sun. It could have been that the initial layout was an horseshoe aligned on the East-West line, later completed in the lower half of the hill with smaller stones, serving other complementary purposes. Whatever conjectures can be made, there are two features that stand out in any simple observation, and that are not subject to interpretation. We refer to the two outstanding large monoliths. One standing on the eastern focus of the elliptical design which, as argued previously (da Silva, 2000) seems to be pointing to the rising sun on the megalithic equinox when observed from the western apex. The other corresponds to the feature that seems to be common to several enclosures, which is a large monolith, larger than their neighbors, close to the apex, slightly to the North relative to an east-west line, providing an arrangement (referred above earlier) that seems to be similar to VMM when observed at sunset near the equinox. Looking in the opposite direction, in the same way that the equinoctial sun seems to rise above the large monolith on the eastern focus when observed from the apex, this same monolith seems to be pointing to a point on the horizon, a few degrees south of East when observed from the other large monolith near the apex. Again this direction defines an azimuth close to 100°, which seems to be pointing to the average Spring Moon rise. Also a group of monoliths in the left arm seems to define a corridor in the same direction.

Landscape

Some megalithic sites, however, are so placed as to give apparent relevance to nearby landscape features, normally a well defined hill profile in the eastern horizon.
In Central Alentejo the hill of Évoramonte seems to define a summer solstice line for the rising Sun when observed from the sites at Mogos, Godel, or S. Sebastião da Giesteira, a fact that is well supported by carefull measurement of the sun rising azimuths.
However, for the observation of the equinoxes, two other outstanding hill profiles seem to be relevant.
One is the profile of Monsaraz as seen from the menhirs at Perdigões, Horta do Pomar, or from the cromelech at Monte da Ribeira. The range of the profile spans the interval 85º-110º in azimuth, providing good references for the observation of the rising Sun and of the rising Full Moon, close to the equinox, i.e. close to the crossover. A well defined notch in the profile appears to indicate a possible association with the particular, although rare, day in which the Sun and the Full Moon rise in the same point on the horizon. In fact, observing from Monte da Ribeira, where the original position of the cromelech is now uncertain, it is possible to find a nearby standing point from where the notch would be found to lie due East.
The other hill, recognized so far, is the profile of Montemor-o-Novo observed from the menhir located at the Courela das Casas Novas. From this site the profile also spans the same range of azimuths (85º-110º) relevant for the Spring Moon crossover observation.
We have recently verified that the profile of the hills at Valencia de Alcántara (Spain), when observed from the large menhir at Póvoa e Meada, also covers the same azimuth range, suggesting a third Spring Moon relevant landscape profile in the Alentejo region. This seems to be in good agreement with the general comments made by Lopez-Romero (2004) for the same landscape. Also, the line defined by Marvão when observed from the top of Sra. da Penha, Castelo de Vide, deserves similar consideration.
A different view of the landscape profile is the one observed in the case of the menhir nr.1 of Casbarra. Here, the distant eastern horizon is seen through a gap (Fig. 6) in the foreground landscape profile, that lies also approximately at the 100º azimuth.

Others

In this section we collect a diversity of not so clear situations that, lacking firm ingredients for a positive identification with any of the above items, share nevertheless with them some features that were found relevant when they occur together, but that may be only pure coincidence when observed in isolation.

Cuncos (Gomes, 1986) and Sideral (discovered by Pedro Alvim and Rafael Henriques) are enclosures that are not sufficiently defined to warrant any comments on the possible initial layout. Nevertheless these, like also the enclosure at Tojal, share common features with the previous monuments. They also have a monolith larger than the rest of the group, and are situated near the top of hills, facing East, except Sideral which faces near North.
The enclosure at Tojal seems to have had originally an horseshoe plan (Calado, 2003). The menhirs, most of which are not upright, seem to be lying close to their original positions, with the large menhir located in the upper half of the horseshoe.

It is also possible that pairs of megalithic monuments define lines whose azimuths may be close to 100º, and thus invoke some hidden relation with the Spring Moon. However it will be difficult to hold this argument when there is no direct intervisibility between the sites, as in the case of Almendres-Xerez which, in addition, are so very far apart (in the order of 50Km). The enclosure at Xerez, today removed due to the increase of the water level of the recent irrigation dam of Alqueva, is the most eastern specimen known, of the expansion of the megalithic enclosure phenomenon. Curiously, in this same line is located one of the most outstanding megalithic funerary monuments of Europe, the large Dolmen at Zambujeiro, as well as the larger pre-historic settlement up to now identified in Central Alentejo. We refer to the Perdigões settlement close to which lies the large menhir with the same name and a group of smaller menhirs.
Also the enclosures at Portela de Mogos and Vale Maria do Meio, although not intervisible nowadays define an azimuth close to 100º. This is the closest pair (1.5 Km) of enclosures in the whole region. Following this line we come to the Menhir nr.1 of Casbarra and the menhir of Mauriz.
Another pair of not intervisible enclosures with the same spatial alignment involves the Fontainhas and Vale d'El Rei enclosures. These are the only two identified in the area of Pavia, somewhat outside the axis Montemor-Évora-Reguengos where seem to lie the majority of the identified sites.
We must recognize that the absence of direct visibility would require an alternative strategy, certainly more complex, for the establishment of the referred orientations.

A brief reference should be made to the fact that the majority of isolated menhirs (or paired, as in the case of S. Sebastião da Giesteira) are implanted in the upper part of slopes facing East (Esbarrandadouro, Monte dos Almendres, Barrocal, Vale de Besteiros, Caeeira, Mauriz, Sideral, Vale dos Cardos) or, at least, in locations facing East (Outeiro, Belhoa, Perdigões, Gorginos, Vidigueiras).

Discussion

The remarkable agreement found between the orientation of the corridors of the passage tombs, and the Spring-Moon-rise, allows us to conjecture that the initial layout of the construction procedure of the tombs would have taken this direction into account, i.e. the direction of the Sun-Moon cross-over. Either the chamber back stone facing the corridor, would be set perpendicular to that direction in the beginning of construction, or that direction would be fixed, say, by a distant mark or set of marks, set at that time, defining and fixing, the layout of the corridor and chamber construction that would follow. This procedure is naturally amenable to the introduction of small orientation errors, however careful the builders may have been in following the initial plan, implying that the spread of orientations is greater than the spread of the Spring Moonrises. Also, the present day estimation of the azimuth of the corridors may be affected by the state of conservation of the tombs, possibly introducing a further increase in the spread of the observed values. Nevertheless, the average values are very similar, 97º in the case of the moonrise and 99º in the case of the corridors, which seems to indicate that the reference direction would be that of the fully detached Moon. These circumstances, at the same time that improve the compatibility of both sets of data, seem to increase the plausibility that the Spring Full Moon would have been used to guide the construction of the megalithic tombs, possibly associating the funerary process with a concept of new life, rebirth or resurrection.

Since this discussion is centered in megalithic times, no comments will be made on more recent uses of the first full Moon after the astronomical equinox.

However, the development of the concept of centrality associated to the crossover observation may have prompted, at a certain stage, the need for an accurate procedure to determine the middle point between the solstices. The association of a counting process to the observation of successive sunrises could have defined this middle point to lie at an azimuth corresponding to a distance of 91/92 days from each solstice. As referred by Thom (1967, 1971) this procedure could have been used in megalithic times, although the deliberate use of such alignments is not generally accepted (Ruggles, 1998). Earlier work [da Silva, 2000, 2003] however, seems to have indicated sufficient evidence for the possible Central Alentejo celebration of the Spring Equinox in megalithic times.
No evidence is found, however, to show that one method could have originated before the other. Both procedures may have coexisted, and may have been used together for the purpose of defining the Spring Moon. This could be the case, in particular, if the menhirs and megalithic enclosures are older than the seven-stone-chambered passage tombs, as suggested by recent work [Calado, 2004, Gomes, 1994] .A reanalysis of the computed data shows that this assumption provides essentially the same results for the azimuth average and interval as the common sense approach, and is less dispersing than the worst cases considered for the ambiguities.

The general seniority of the menhirs, and in particular of the Alentejo megalithic enclosures, relative to the more recent dolmens may be interpreted in terms of models developed before, in a non funerary context. May be the use of large stones and a construction process with recourse to the sky, are interesting illustrations of this transposition. We have good reasons to assign to the Neolithic (earlier-meso-final) a certain continuity in a process in which the innovations are articulated, without transposition, to the domain of the ritual funerary processes, of the concepts and evident ruptures with a cultural background whose origins go back probably to the Final Mesolithic(Cassen et al., 200; Cummings, 2002)
The geometry of the megalithic enclosures largely open to East seems to have been adopted in first place by the proto-megalithic tombs also with a horseshoe shape (Fig. 7), which may have evolved to those forms of differentiated corridor that characterize the dolmens (antas) of Alentejo (Rocha, 1999), and later to the tholoi. It should be noted that the shapes of a horseshoe, or of a semicircle, correspond to basic arrangements of the human habitat, which can be found in shelters since the Paleolithic, and even in the way a human group sits around a fire (Binford, 1991).
The much later occurrence in European pre-history, of circular enclosures without apparent doorways, as are most of the known Ireland an Great Britain examples (Darvill, 1997; Bradley, 1998; Burl,1999), must imply a conceptual development and new ritual practices built over a megalithic substrate of which the much older examples are identified in Brittany (Giot, 1988; Cassen et al., 2000; Le Roux, 2003) and in the south of Portugal (Central Alentejo and Algarve) (Calado, 2002; CaladoD, 2000).

Finally, it should be noted that the orientation of megalithic monuments with recourse to the Spring Moon, considering that it is a situation in which the solar observation is also present, implies a much different scenario than the one usually proposed for the evolution of the British and Irish pre-historic monuments. Here a transition is observed from solar to lunar orientations (Ruggles, 1999; Bradley, 2004). In fact, other orientations seem to occur also in the Central Alentejo monuments, either solar (equinox, solstices) or lunar (major and minor standstills)(da Silva, 2003). These monuments, whose complexity manifests itself in different scales (landscape, location, plan, monolith, engravings) are certainly not only of astronomical interest. In our opinion this is only one of many aspects of a new notion of ritual space together with a new attitude of symbolic representation in the magic/religious context.

Acknowledgments
We wish to thank Dr. Manuel Nuno Marques, former Director of the Observatório Astronómico de Lisboa, for advice on available ephemeris software.

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