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The Astronomical Potential of

the Paps of Jura from a

Prehistoric Site on Islay, Scotland

 by Martin J. Powell


The island of Islay lies North-west of the Kintyre peninsula in Scotland.  It is the Southernmost island of a region known as the Inner Hebrides, and the third largest of the group, measuring 40 km N-S by 32 km E-W.  It is relatively low lying and fertile, its highest point being Beinn Bheigeir on the South-east of the island, which stands to a height of 491 metres above O. D.

Islay is not outstandingly rich in prehistoric remains.  Six chambered tombs survive from the Neolithic period, all of the Clyde type.  Two stone circles, eleven cairns and sixteen cists survive from the Bronze Age.  The density of such monuments per kilometre is small when compared to other Scottish counties.  Standing stones, however, are fairly numerous, there being about forty surviving examples.  Some of these occur in pairs, or alignments of three or four.  Unlike mainland Argyll and Jura, which are well known for their prehistoric monuments, and most notably those that are considered to have astronomical functions,1 Islay has not contributed a great deal towards the study of either prehistory or archaeoastronomy.

 Location maps of Islay and Loch Finlaggan (41 KB)Figure 1   Location maps of Islay and Loch Finlaggan (click for full-size image, 41 KB). The highest mountains of the region are shown, with heights in metres above O. D. The two Paps visible from Finlaggan, Beinn an Oir (785m) and Beinn a Chaolais (734m) are also shown. Heights of the highest mountains on Islay and western Jura are also indicated.

In 1994, an exploratory excavation revealed the presence of a previously unknown stone chamber on a small hill near a loch on the island (see location map Figure 1 (41 KB) and contour map Figure 2, 55 KB).  When viewed from the hill, a standing stone a short distance away seems to indicate a prominent mountain range to the North-east called the Paps of Jura.  A geophysical survey carried out during the excavations revealed the presence of possible ‘pit’ features near the stone, which also seem to have been aligned on the mountains.  The author decided to investigate the possibility that astronomy could help explain the positioning of the standing stone and the ‘pit’ features.  Could the hill have been used in prehistoric times as a kind of ‘platform’ from which to observe significant solar or lunar rising positions over the Paps?

The loch in its prehistoric setting, with contours in metres above O. D. (55 KB)Figure 2  The loch in its prehistoric setting, with contours in metres above O. D. (click for full-size image, 55 KB). Roads and buildings have been omitted for clarity (Based on the Ordnance Survey 1:50,000 scale map).

Assessment methods & Error ranges

Ordnance Survey maps were used to obtain details of heights, distances and horizon elevations.  The 1:50,000 scale series provided the necessary information for the Paps, whilst the 1:10,000 scale (the largest scale available) was used to obtain data for the immediate vicinity of the loch.2  A photograph taken from the hill near the loch was used to adjust the calculated profile of the Paps (Figure 3, 65 KB).  Since the data has been derived from maps, the values are evidently subject to error, mainly due to contour rounding and height estimation.  The calculations assume an observer’s eye height of 1.55m above ground level and a horizon free of vegetation cover.  Unless otherwise stated, the azimuths and horizon elevations quoted are considered accurate to ± 0º.1, with a consequent effect on indicated declinations of about the same magnitude. Declinations have been calculated taking the necessary allowances for refraction and, where applicable, lunar parallax.

The Paps of Jura seen from the top of Cnoc Seandda (65 KB)Figure 3  The Paps of Jura seen from the top of Cnoc Seandda (click for full-size image, 65 KB). The standing stone can be seen a short distance in front of the field wall below Beinn a Chaolais, the right-most Pap (Picture courtesy of The Finlaggan Trust).

Loch Finlaggan

Scotland is well known for its lochs (lakes), and many small examples occur on Islay.  The island’s second largest inland example is Loch Finlaggan, situated about 4 km South-west of Port Askaig, a small village on the island’s East coast.  Finlaggan is a secluded loch measuring about 2 km long by 0.5 km wide, elongated NE-SW.  The loch has had an important role in Scottish history, for it is here that the MacDonald family, elected Lords of the Isles, established a Gaelic kingdom effectively independent from English rule in the thirteenth century A.D.  Loch Finlaggan became the administrative centre of the Western Isles, where the Lords would hold council in a large hall situated on Eilean Mór, the largest of two islets at the Northern end of the loch.

Some four hundred metres North-east of the islets, on land gently sloping downwards to the loch, is a small limestone hill known as Cnoc Seandda (NR 3911 6847).  The hill is almost circular in plan and dome-shaped in profile.  It is about 45 metres in diameter and stands to a height of 5 metres ± 0.5m.  Nearly two hundred metres North-east of the hill, at about 69 metres above O. D., is a solitary standing stone.  It is 2 metres in height, and measures 1.4 metres by 0.7 metres at its base (NR 3927 6856).  It is orientated in a NW-SE direction, and has a squat appearance, tapering to a blunt point.3  A map of the area immediately around the hill is shown in Figure 4 (40 KB).

Cnoc Seandda and the standing stone at Loch Finlaggan, in their local setting (40 KB)Figure 4  Cnoc Seandda and the standing stone at Loch Finlaggan, in their local setting (click for full-size image, 40 KB). Heights are given in metres above O. D. (Based on the 1:10,000 scale Ordnance Survey map).

Excavation findings

Excavations have taken place in and around the loch since 1989, when the Finlaggan Trust was set up to promote interest in the archaeology of the region.  Much of the excavation had revealed evidence of thirteenth century occupation, and it was eventually decided to extend the investigation to Cnoc Seandda in the hope that the inauguration stone used by the Lords may be found here.  The hill was thought to be in quite a prominent position, overlooking the loch, and so might have been the location where the Lords themselves were crowned.  The Trust enlisted the help of the Time Team, a group of three archaeologists and three researchers whose skills were combined for the production of a British television series on archaeology.4  In the three days allotted to the team for excavation, they unearthed flint cores and blades from the Mesolithic period and, on the final day of excavation, a setting of stones, possibly a chamber, set into the top of the hill.5  When the chamber was exposed, the bones of an animal, complete with joints, were found inside.  This had probably been ritually slaughtered and subsequently buried whole.  The date of construction of the chamber is not known but, like the standing stone, such structures are commonly associated with the Early Bronze Age, typically the period 2500 to 1500 B.C.  It is not presently known whether the chamber and standing stone are contemporary features.  A geophysical survey carried out in the vicinity of the standing stone also revealed the presence of a series of possible ‘pit’ features, perhaps an alignment.  Although their complete layout is not currently known, on first indications they appear to have been aligned with the Paps.

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Mountain foresights

The Paps of Jura are a mountain range on the island of Jura, only a short distance across the water from Islay.  They are so named because of their similarity to the female breasts when seen in profile.  Their dark, quartzite form are an obvious sight from along much of the Eastern seaboard of Islay, although their summits are frequently covered in mist.  Appropriately, only two of the four major Paps are visible from Finlaggan, and these both appear at very nearly the same elevation.  Viewed from the top of Cnoc Seandda, the Paps are partly obscured at their base by local land some 0.9 km distant.  Curiously, the local horizon appears to ‘fall away’ across the azimuthal range of the Paps, so revealing slightly more of them.  The resulting visual effect is dramatic (Figure 3).

No other mountains have as much impact as the Paps across the whole of the North-eastern quadrant visible from the site.  Aonach-bheinn (9.4 km), Glas Bheinn (11 km) and Dubh Bheinn (9.8 km), all on Jura, peak above the local horizon 12º, 17º and 26º South of the Paps respectively.  They extend 0º.3, 0º.3 and 0º.4 above the local horizon respectively.  By comparison, the two Paps extend 1º.2 and 1º.3 above the local horizon.  There are no significant mountain peaks protruding above the local horizon within an arc of 40º to the North of the Paps.

Martin’s Second Stone

Finlaggan is poorly recorded in the literature.  The earliest reference to the standing stone is by Martin Martin who, following a visit around 1695, described the presence at Finlaggan of  two standing stones of equal height, located at the Eastern side of the loch.6  His description of the stones’ positioning in relation to the loch is puzzling, since a modern day researcher would normally consider the stone to be at the loch’s Northern end.  The second stone no longer exists.  Unfortunately Martin gave no indication of the position of the stones in relation to each other, so we can only speculate about its location.  There is a small possibility that Martin was referring to the now fallen stone at Kepolls at the South-west end of the loch (NR 3793 6663), which would have stood to a height of about 1.8 metres, but its isolated position at the opposite end of the loch makes this suggestion unlikely.7  The location of the Kepolls stone is shown on the map in Figure 2.

When seen from the summit of Cnoc Seandda, the existing standing stone is seen at an azimuth of 57º.7 ± 0º.9, nearly in line with a ‘V’-notch caused by the apparent intersection of the two Paps, Beinn an Oir and Beinn a Chaolais.  The error in the stone’s bearing is brought about because the centre of the hill can only be recovered to within  ± 3 metres, with a consequent azimuthal shift caused by parallax.  The effect of this uncertain centre point on the azimuth of the distant Paps, however, is negligible.

It is interesting to note that the orientation of the stone is perpendicular to the direction of the Paps, perhaps inferring that the stone’s broader face was intended to be viewed from the hill.  Furthermore, the shape of the upper section of the stone vaguely resembles the outline of one of the Paps.

First Astronomical Considerations

In considering the significance of the declinations indicated by the Paps it is as well to specify the values of the theoretical extremes of the Sun and Moon for the period under consideration.  As has already been mentioned, the date of construction of the row and standing stones are not known, but on the basis of currently accepted chronology, it would be reasonable to suggest that construction took place at some time between 2000 and 1500 B.C.  Even over this 500 year period, the slow precessional shift affecting the extreme declinations of the Sun and Moon amounts to only 0º.05.  For the present purposes it will therefore suffice to take a central date, say, 1750 B.C., for the site’s construction.  The Sun’s extreme declination at this date was ± 23º.9 (the obliquity of the ecliptic, symbol  E).  The inclination of the Moon’s orbit to the ecliptic (symbol  i) results in the lunar extremes of  ± 29º.04 at the Major standstill and ± 18º.75 at the Minor standstill.  The lunar extremes are subject to a variation of ± 0º.15, known as the minor perturbation (known as delta), which operates in phase with the eclipse year.

Figure 5 (27 KB) shows a profile of the Paps as they appear from the top of Cnoc Seandda.  The most likely focus of attention was the ‘V’-notch, labelled D on the profile. The azimuth of this point is 57º.1 and its elevation is 2º.4, which gives a declination of +19º.6.  This is not particularly significant, although it does lie within the range of the Sun’s declination.  The lunar declination is +20º.4, which is again rather insignificant, although it does lie within the declination range of the Moon at some point in the 18.6 year lunar node cycle.

The Paps of Jura, seen from the summit of Cnoc Seandda at Loch Finlaggan (27 KB)Figure 5  The Paps of Jura, seen from the summit of Cnoc Seandda at Loch Finlaggan (click for full-size image, 27 KB). Super-imposed on the profile are the centre disk rising paths of the Moon around the Minor standstill, assuming a date of 1750 B.C. Points A to E are selected foresights; the remaining points appear in Figure 4. The highlighted bands show the range of the full Moon’s computed midwinter declinations two years (right band) and three years (left band) before or after the Minor standstill. The midwinter full Moon is shown rising at  (a) ‘expected’ declination +21º.3, i.e. three years before/after the Minor standstill, and (b) ‘expected’ declination +20º.0, i.e. two years before/after the Minor standstill. The extant standing stone is also shown.

Since the smallest difference in declination between the indicated values at point D and the theoretical extremes are 4º.3 for the Sun and 1º.6 for the Moon, it would appear that the Paps could provide a foresight for the Moon when close to it's Minor standstill position.  Solar and lunar indications will now be considered in greater depth.

Solar Indications

The solar declinations indicated by eight selected points on the Paps are given in Table 1 (37 KB) and they are illustrated in Figure 5 and Figure 6 (19 KB).  The points selected are necessarily subjective, and have been chosen for their usefulness as potential foresights.  They give some idea of the range of declinations indicated across the Paps.

The declinations given in the table are not only for the centre disk indication, but also for the central declination referred to the upper and lower limbs.  The declination range at each point is therefore about 0º.5, i.e. a Sun diameter.  It is considered necessary to give the three values since it is not known which part of the Sun’s disk would have been observed.

Also shown in the table are the approximate Gregorian calendar dates at which the Sun attains the declinations at points A, D and H, which represent the central and extreme points of the Paps.  These give an idea of the usefulness of the mountain foresights as an aid to establishing a calendar.  Two sets of dates are given for each set of declinations since, with the exception of the solstices, the Sun attains all declinations in the range  ± E twice in the course of the year.  One value will be attained when the Sun is ascending the ecliptic and the other when it is descending.

Rising paths of the Moon and Sun behind Beinn a Chaolais, around 1750 BC (19 KB)Figure 6  The Southernmost Pap, Beinn a Chaolais, seen from the summit of Cnoc Seandda at Loch Finlaggan (click for full-size image, 19 KB). Points F to H are selected foresights, continued from Figure 5. The Moon’s centre disk rising paths are super-imposed on the profile, assuming a date of 1750 B.C. The highlighted band shows the range of the full Moon’s computed midwinter declinations one year before or after the Minor standstill. Rising positions marked are  (a) centre disk path of the Minor standstill declination +(E - i), and (b) upper limb of the Sun rising at the the mid-quarter declination +16º.7. The upper limb of the full Moon at the midwinter standstill declination +(E - i + delta) is shown a short distance below point F. The lower limb of the Moon rising one day before or after the midwinter full Moon is indicated by point G, with the Moon emerging behind the mountain.

The similarity of indicated declinations between points A, B and C and also between points D and E show how the gradient of the Northern slopes of both Paps approximate to the rising angle of a celestial body in this part of the horizon.8  This phenomenon may have helped to draw the attention of the prehistoric folk to the rising of the Sun or Moon over the Paps.

The Sun would attain the declinations at points A, D and H at intervals of between 6 and 12 days, depending upon which part of the disk would have been observed.  The dates approach the summer solstice to within 26 or 27 days.  The time interval from one edge of the Paps to the other is about 20 days.  It is interesting to note a declination of +16º.7 ± 0º.2 for the upper limb of the Sun at point H, where the local ground appears to intercept the Southern slope of Beinn a Chaolais (see line ‘b’ in Figure 6).  The calendar dates at this point approximate to those of the Celtic festivals of Beltane and Lughnasad, which occurred mid-way between the equinoxes and the summer solstice.  Although these festivals are known to date from the Iron Age, it is likely that their roots lie much further back in prehistory.

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Lunar Indications

The lunar declinations for the eight selected points are given in Table 2 (31 KB).  It can be seen from the data that the Minor standstill moonrise will be seen to occur behind the Southern slope of Beinn a Chaolais, although the declination +(E - i) is not actually indicated by any particular foresight.  The rising path of the Moon at this declination is shown by the dashed line marked ‘a’ in Figure 6.  Points F and G mark notable changes in gradient on the mountain’s Southern slope.  Point F is the more obvious of the two and nearly indicates the upper limb of the midwinter full Moon rising at the Minor standstill, when the declination is +(E - i + delta).  Point G could serve a minor role in providing a day’s notice of the event, when the Moon’s declination would fall short of the maximum value by about 0º.5.9  In Figure 6 the Moon is seen emerging from behind the mountain one day before the midwinter standstill full Moon, when the lower limb is indicated by point G.  This value would also occur one day  after the midwinter standstill full Moon.  It will be noted that the maximum northerly moonrise closest to the Minor standstill, whether having a positive, negative or null value of  delta, will only occur South of (i.e., below) point F.

Having noted the rising position of the Moon at the Minor standstill, the author considered it of interest to examine the wider potential of the Paps as indicators of the lunar cycle.  The most Northerly declination indicated by the Paps (point A) is +22º.3 ± 0º.2, whilst the central indication (point D) is, as noted above, +20º.4.  Both of these declinations are attained by the Moon at some point in its 18.6 year node cycle.

In order to assess the times at which the Moon attains these declinations, the author ran a computer program to generate the declination maxima of the full Moon closest to the winter solstice.10  The midwinter full Moon is the easiest time to determine the most Northerly Moonrise position, being perhaps the most dramatic phase, and occurring when the Sun is at the lowest point of the ecliptic.11  The years around the Minor standstill were extracted from the computed output, and the declination ranges were then determined for each year before and after the standstill.  The results of this study are given in Table 3 (15 KB).  Also shown are the values that are expected to occur.12  The range of computed midwinter full Moon declinations in the three year period either side of the Minor standstill are shown by the highlighted bands in Figure 5 and Figure 6.  Two points should be noted regarding these bands.  Firstly, any two successive midwinter full Moons will not occur on the same date, since twelve synodical months (lunar phase months) equal 354 days, which is 11 days short of a tropical year.  Secondly, the continuous movement of the lunar nodes causes the maximum Moonrise declination to change at varying rates per year between the Major and Minor standstills.  As a result of these two factors, the declinations observed for the midwinter full Moon between the standstills are seen to occur across a range of values rather than at a single ‘expected’ value.

The range of declinations plotted in Figure 5 and Figure 6 are seen to become successively narrower as they near the standstill declination.  The declination ranges  three years before or after the standstill occur predominantly over Beinn an Oir, the Northernmost Pap. Two years before or after the standstill, the band narrows and moonrises occur predominantly over Beinn a Chaolais, but not any further South than point F.  One year before or after the standstill, shown in Figure 6, the declination range is less than two Moon widths, and its average declination occurs at point F.  Hence when the Minor standstill was known to be approaching and the midwinter full Moon rose at or just above point F, the standstill could be expected to occur in the following midwinter.  As can be seen by the lower limit of the highlighted band in Figure 6, there will sometimes be no noticeable difference in declination between the midwinter standstill full Moon and the midwinter full Moons in the year immediately before or after the standstill.  On such occasions, unless corroborated by separate evidence, it is unlikely that the prehistoric folk would have been able to isolate in which of these two years the standstill occurred.


This paper set out to examine the possibility that the Paps, when viewed from the hill at Loch Finlaggan, could have been used as a foresight to observe the rising of the Sun or Moon.  This study has shown that this could have been the case, since both solar and lunar risings are seen to occur over the Paps.  The potential of these indications will now be considered.

With regard to the Sun, the Paps could have provided a simple indication of the approaching or receding solstice, or even the mid-quarter days of summer.  However, the potential for establishing a useful calendar by using an indicated period of just 20 days (a total of 40 days in the year) is very limited.

The Paps were less useful as a solar indicator as a lunar one.  The Paps could have proved useful in giving warning of the impending Minor standstill.  The rising of the full Moon at the winter solstice is perhaps the most visually dramatic moonrise of the whole year.  If its position was noted from one year to the next in relation to prominent mountain foresights, the time of the standstill could have been determined, probably to within a year.  Certain associations may have been established by such a continued series of observations.  For example, the midwinter full Moon three years before or after the standstill would be seen to rise predominantly over Beinn an Oir, and the Minor standstill Moon would only rise South of point F.  The Paps could thus be used to monitor seven of the nineteen years which comprise the Metonic cycle.  Most studies of the Moon in archaeoastronomy have concentrated on its theoretical extreme positions.  Little work has been done on the rising or setting positions between the extremes, although this perspective is now changing.13

Minor standstill indications are few in relation to the total number of suggested lunar lines in Argyll.  Of the 52 astronomical lines suggested by Thom, only 11 are Minor standstill indications and this is probably because of the relative difficulty in determining its position amongst so many other lunar risings and settings in this part of the sky.14  The Paps could have helped determine this position, since they were both prominent and visually isolated, and hence devoid of a multitude of surrounding mountain foresights which could otherwise confuse any series of observations.  The Paps would have focused attention on a narrow arc of the sky.

There are other aspects to consider when assessing a site such as Finlaggan.  Recent studies have considered the role of the ‘earth mother’ when assessing the lunar indications.15  The appearance of the full Moon emerging from the Paps (from the breasts or belly of the earth mother) and ‘poising’ at the summit of the mountain (as, for example, at position ‘b’ in Figure 5) would perhaps be a highly spiritual experience for the onlookers.  Moonrises over the Northern slopes of either of the Paps would have been the most visually dramatic, even though they did not actually indicate the extreme positions.

It has been assumed throughout this study that Cnoc Seandda was used as a ‘platform’ from which to observe the celestial phenomena.  The presence of a chamber built into its summit suggests that the hill was considered sacred in some respect, perhaps over generations.  The hill may have become sacred as a result of the astronomical potential that it possessed, and because of both its form and location it effectively eliminated the need for prehistoric man to build his own tumulus in a carefully determined position.

When assessing the precision of the indicated declinations over the Paps it should be remembered that Cnoc Seandda is not an artificial structure, but a natural hill.  Consequently any significant astronomical positions seen from this location are purely the result of chance.  The question is whether prehistoric man recognised such chance alignments on celestial phenomena and used them to his advantage.  The presence of megalithic remains at such sites is evidence that he may have done so.  The suspected platform at Kintraw on mainland Argyll is an example.16  At Finlaggan, a more complete excavation would provide a clearer picture of the nature of this ritual landscape.  A more definitive assessment could then be made of the relationship between the hill, the stones, the ‘pit’ features and the distant Paps of Jura.


The author would like to thank Mrs Linda McArthur of the Finlaggan Trust for providing me with the excellent photograph of the Paps taken from Cnoc Seandda.  I am also grateful to Dr David Caldwell of the Society of Antiquaries of Scotland for supplying me with information on the preliminary excavations, and to John Gater of Geophysical Surveys of Bradford (now Sumo Survey Services) for substantiating the geophysical survey details.

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1.  For examples of such sites see A. Thom,  Megalithic Lunar Observatories (Oxford, 1971), 45-53 and 56-65.  The only Islay site to have been investigated astronomically by Thom is Ballinaby on the West coast, in A. Thom and A. S. Thom, Megalithic Remains in Britain and Brittany (Oxford, 1978), 169-70.

2.  Ordnance Survey maps 61 (1:50,000 scale) and NR 36 NE (1:10,000 scale).

3.  Royal Commission on Ancient and Historical Monuments of Scotland, Argyll, Volume 5 (1984), 68 (No. 97). A close-up photograph of the standing stone can be seen at Wikimedia Commons.

4.  A booklet was produced to accompany the television series, entitled  The Time Team Reports (Channel 4 Television, London, 1995), 5-11.  The excavation details that follow are largely based on the account in the booklet.  The specific episode on the Islay excavation (series 2, episode 1) can be seen on-demand at the Channel 4 Television website.

5.  Dr David Caldwell, leader of the excavations, later confirmed the feature to be a stone lined chamber measuring about 6 metres long by 1 metre wide.  It is somewhat curved in plan and is orientated roughly N-S (private communication, April 1995 and December 1996).  Close to the chamber was a denuded kerb-cairn 3 metres in diameter.  A brief article on the excavation appeared in the local Islay newspaper Ileach in late 1995, which included a plan of the chamber and the nearby cairn.

6.  M. Martin, A Description of the Western Islands of Scotland (London, 1716), 243.

7.  Royal Commission on Ancient and Historical Monuments of Scotland (ref. 3), 69 (No. 105).  Dr David Caldwell later identified two large recumbent boulders at location NR 3957 6854 (about 295 metres to the West of the extant standing stone) one of which he considers to be the stone to which Martin referred (private communication, December 1996).  The recumbent slabs are marked on the Ordnance Survey map Pathfinder 411 (1:25,000 scale) and on NR 36 NE as "Stones".

8.  The average slope of the Northern faces of the Paps measured relative to the horizontal are 29º for Beinn an Oir and 28º for Beinn a Chaolais.  By comparison, the rising angle of a celestial body in this part of the horizon is about 26º.  The time taken for the Sun or Moon to traverse the Northern slopes of Beinn an Oir and Beinn a Chaolais are about 8 minutes and 9 minutes respectively.

9.  Thom considers the drop in declination before or after the standstill to behave as a parabola in the form  y = kt2.  At the Minor standstill we put  k = 30, hence over one day (t = 1), the reduction is 30 minutes of arc, or 0º.5.  See A. Thom,  Megalithic Lunar Observatories (ref. 1), 23-4.

10.  The computer program was written using the formulae given in P. Duffett-Smith,  Practical Astronomy with your Calculator (Cambridge, 1981), 139-42.  In order to check on the accuracy of the output, the program was initially run using the present value of E = 23º.441 and the declinations were then checked against various almanac data.  As a result the declinations are considered to be accurate to ± 0º.1.  The program was then re-run using the obliquity of the ecliptic for 1750 B. C., i.e., with E = 23º.902.  In order to reduce possible rounding errors introduced by calculation over long periods of time, the midwinter declinations were run for an equal period either side of the epoch (1980.0), rather than on just one side of it.

11.  The actual declination extreme of the Moon at the Minor standstill is attained around the time of the equinoxes, when the declination is +(E - i - delta).  The Moon’s phase at this time must be either First or Last Quarter, and consequently it is less convenient to observe than the full phase.  See A. Thom and A. S. Thom,  Megalithic Remains in Britain and Brittany (ref. 1), 11.  There is no obvious foresight on the Paps which indicates this extreme position.

12.  Since the lunar node cycle is 18.61 years, then for any given midwinter full Moon, the declination maximum will be found to repeat very closely after 93 years, or five Metonic cycles.  The computed values given in the table have been deduced from observations taken over three 93 year periods.  The value of the Moon’s maximum declination varies in a sinusoidal manner.  The drop in declination below the maximum is given by  2i.sin2(3.142t/P), where i is the magnitude of the lunar inclination (5º.145),  t is the time elapsed since the standstill and  P is the period of the node cycle.  See A. Thom,  Megalithic Lunar Observatories (ref. 1), 23.  Since the values under consideration are for midwinter observation, the ‘expected’ values shown in the table have been increased by the magnitude of the minor perturbation delta = 0º.15.

13.  Recent work on the island of Mull, some 40 km North of Islay, suggests that stone rows were not only orientated towards the standstill positions, but also towards other points in the 18 year cycle.  See C. L. N. Ruggles, “The linear settings of Argyll and Mull”, Archaeoastronomy,   no. 9 (1985), S105-32.  The astronomical significance of prominent hill summits in Mull is examined extensively in C. L. N. Ruggles, “The North Mull Project (3): Prominent hill summits and their astronomical potential”, Archaeoastronomy, no. 17 (1992), S1-13.

14.  A. Thom,  Megalithic Lunar Observatories (ref. 1), 76, Tables 7.1 and 7.2.

15.  Some recent studies have examined the relationship of prehistoric monuments to their surrounding landscape features in considerable detail.  For example, see C. Tilley,  A Phenomenology of Landscape: Places, Paths and Monuments (Oxford, 1994).  The possible relationship of the extreme Moon with an ‘earth mother’ symbolism is examined in M. Curtis and R. Curtis, “Callanish: maximising the symbolic and dramatic potential of the landscape at the southern extreme Moon”, in C. L. N. Ruggles (ed.), Archaeoastronomy in the 1990s (Loughborough, 1993), 309-16.

16.  A. Thom,  Megalithic Lunar Observatories (ref. 1), 37-40.

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